an analysis of the madaras rotor power planta- alternate method for extracting large amounts of...
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AN ANALYSIS OF THE M A D A M ROTOR POWER PLANT- AN ALTERNATE METHOD FOR EXTRACTING LARGE AMOUNTS OF POWER FROM THE WtND
Volume 2. Technicid Report
BY Dale H. Whitford John E. Minardi fjlaine S. West Robert J. Dominic
lune 1978
Work Performed Under Contract No. EX-76-SU1-2554
University bf Dayton Research Institute I = I
' ' Dayton, Ohio
U.S. Department of Energy
''Solar Energy
DISCLAIMER
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DSE-2554-78/2(V01.2) Distribution Category UC-60
AN ANALYSIS OF THE MADARAS ROTOR POWER PLANT ---- AN ALTERNATE METHOD
FOR EXTRACTING LARGE AMOUNTS OF POWER FROM THE WIND
VOLUME 2 TECHNICAL MPORT
- ~ .. .
DISCLAIMER
Dale H. Whitford John E. Minardi Blaine S. West Robert J. Dominic '
warranly. express or implied. or e n v m any legll liabilitv or raponribilily for the aaurecv. mmpleleness. or urefulnes of any information. upparatus. pmduct. or era- dirlored. or rgrmntr lhal i ( l "re *auld not infringe o r i ~ l e l y owned righir Reference herein to any Specific mmmercial produo. process. or rervice by trade mme. trademrk. manufacturer. or orherwire. does mt net-rily mnrlixuic or imply irr endorrement. reammendation. or favorina by the United Staler Government or any agency thereof. The view and opinions of authors expreued herein do no! neeuarilv rtaicor reflect tho=of the Uniled Sieies Gwernment or any ageno thereof.
. -- - . .- - - .- . - - I
UNIVERSITY OF DAYTON RESEARCH INSTITUTE 300 College Park Avenue
Dayton, Ohio 45469
June 1978
PREPARED FOR
THE UNITED STATES ENERGY RESEARCH AND DEVELOPMENT
ADMINISTRATION DIVISION OF SOLAR ENERGY FEDERAL WIND ENERGY PROGRAM
ERDA CONTRACT NO. E (49-18) -2554
PROJECT SUMMARY
The purpose of the program was to analyze and up-date the
design of the Madaras Rotor Power Plant concept that had been
developed in the 1930's to determine the technical and economic
feasibility of this system to be competitive ~ 5 t h conventional
horizontal axis wind turbines. The,Madaras concept uses rotating
cylinders, vertically mounted on flat cars, to react with the .wind
like a sail and propel an endless train of connected cars around
a closed track at constant speed. Electricity is,generated by . . alternators on each car that are .'geared. to the wheels. Electriaali
power is transmitted from each car to the power house by a Lr-olley
system.
A four-task program consisting of a series of wind tunnel
tests,. an electro-mechanical analysis, a performance, analysis,
and a cost analysis was conducted. Wind tunnel testEs were conducted
to validate rotating cylinder data in the literature. and to obtain
non-existing data that relates aerodjliamic performaqce to rotating
cylinder (rotor) geometry. Supporting studies included' etructural
design, mechanical component design, and 'an.electri~at,.system
design to provide a realistic set of inputs to'a p.eurformance trade
study.which provided the basis for selecting a single rotor con- figuration and set of operating conditions which were considered
to represent a good', but not.necessarily an optimum,design.
Studies to determine. the minimum spacing between cars'governed
by inter-rotor aerodynamic interference also were conducted.
Drawings and, specifications o,f.the system were used to
estimate costs, and cost/p8lformance computer runs were
made to correlate plant cost, annual output, and energy cost as
a function of plant, size parameters. These cost studies
incorporated appropriate learning curves to account for reduction
in cost resulting from improved production techniques and increased
productivity.
Primary results of this study are:
a Madaras plants having circular track ,plan-forms probably
will not be economically attractive, but those having .racetrack
plan-forms appear to be of .interest.
a Madaras racetrack plants appear to be competitive with
a farm of MOD-1 horizontal axis machines of equal total power
generation capability (to within the overall accuracy'of estimation * . . .
for' both schemes) in cost per unit rated power and 'cost'per unit
of energy delivered. Cost comparisons were based upon estimates
made in this study and estimates made by ~ightower' and General
~lectric~ for the MOD-1 machine. A Lubs'tantial economicbenefit
favoring the Madaras scheme does not appear, althoug,h thhs possibility
may exist (under more "optimal" designs determined through more
detailed analysis.) . . .
- Madaras racetrack plants having rated capacities as high
as 228 MW and annual energy outputs of 975 x l o 6 kW-hr/year were studied, and analyses indicated that even large,r, more efficient
plants could be developed. Thus, Madaras plants can produce energy
in the quantities of interest to the electric, utility indushy.
a Madaras plants are more.complex, have higher electrical
and mechanical losses, and hence will require higher operation
and maintenance costs than horizontal axis machines. Further, a
racetrack plant configuration for Madaras plants limits them to
regions having generally unidirectional winds (including reciprocal
directions) in which large expanses of relatively flat land aFe available. (However, similarly-sized HA-P?TG plants require twice
the land area as Madaras plants.)
At this, stage of, the investigation, it is not .possible to . .
state conclusively -whether or not.the Madaras system will significantly
out-perform a similarly-sized horizontal axis wind turbine system.
The Madaras &stem seems to outperform horizontal axis systems in
the areas of structural durability., economy of scale, amount and
efficiency in use of land, and possibly energy cost. Therefore,
in view of this potential, it appears that an in-depth optimal
design study of the system is warranted.
TABLE OF
SECTION PAGE
I INTRODUCTION
1.1 Concept Description and Background 1.1.1. System Description' 1..1.2' History of the Madaras Project 1.1.3 Prior Research - Magnus Effect 1.1.4 Prior Research - Tracked Vehicle
Airfoil Concept ,
.i 1.2 University of Dayton Preliminary Studies
of Madaras System 1.2.1 Performance Analysis 1.2.2 Preliminary Economic Comparisons
1.3 Key. Features of the Madaras System
1.5 Unanswered Questions
I1 OBJECTIVES AND SCOPE
2.1 Objectives and Scope
2.2 Ground Rules
I11 WIND TUNNEL TESTS
3.1 Wind Tunnel Study Objectives
3.2 Wind Tunnel Test Plan 3.2.1 Test Matrix 3.2.2 Wind Tunnel ~escription 3.2.3 Test Model Development 3.2.4 Model Mounting in Wind Tunnel 3.2.5 Calibrations and Operational
Cheeks 3.2.6 Atmospherjc Boundary Layer
Simulation Study 3.2.7 Typical Cylindcr Tcct Procedure
3.3 Free Stream Test Results 3.3.1 Typical Set of Raw Free-Stream
Data 3.3.2 Selection. of Test Reynolds
Number 3.3.3 Basic Free Stream Data 3.3.4 Effect,of e/d Ratio Variation
on CL and CD 3.3.5 Effect of Aspect Ratio Variation
on CL and CD 3.3.6 Comparison of UDRI Aerodynamic
Data with Pertinent Existing Data 3.3.7 Power Required to Rotate Cylinder
TABLE OF CONTENTS (~ontiinued)
PAGE
3.4 Boundary Layer' Test Results
IV STRUCTURAL' .AND MECHANICAL DESIGN
4 .1. Ground Rules'
4.2 DesTgn Loads 4.2'. 1 Aerodynamic. Loading on .the
Cylinder 4.2.2 : Aerodynamic Loading on the Cap 4.2.3. System Accelerat'ion Loads 4.2.4 Snow'and Ice Accumulation 4.2.5 Car Weight, Wheel Loads, and
Restraining Loads 4.2.6 Fatigue
4.3 Structure 4.3.1 Rotor Cap 4.3.2 Rotor Cylinder 4.3.3 Rotor Bearings 4.3.4 Support Tower 4.3.5 Rotor Tower 4.3.6 Car Layout 4.3.7 Car Structure 4.3.8 Power Transfer Trolley 4.3.9 Inter-Car Coupling 4.3.10 ~ynamic Balancing of the Rotor
4.4 Design Modifications 4.4.1 Revised Rotor Configuration 4.4.2 Rotor Drive System 4.4.3 Rotor Bearings
4.5 Site Design 4 :5.1 Track and Roadbed Design 4.5.2 Plant Buildirlgs
4.6 Mass Summary.of Rotor Cars
V ELECTRICAL DESIGN
5.1 ' Design Guidelines
5.2 Design Conditions
5.3 Rotor Spin System 5.3.1 Concept Selection 5.3.2 Spin System Sizing 5.3.3 Spin System Controller
5.4 Generator System
TABLE OF CONTENTS ' (Continued-)
SECTION
5.5
PAGE
Power Plant 154 5.5.1 Primary System Controller 154 5':s. 2 Secondary On-Car Controller 155 5.5..3 Radio Telemetry System 156 5 - - 5 . 4 Wind Sensor Network 157 5.5..5 Monitoring Instruments and Actuators157 5.5.6 Operator's Control Station 158
.stem Network Circuitry and Components 159 6.1 System Network Elements 159 6.2 Car Trolleys and Trolley Feeder 159
Bus 5.6.3 Distribution r-ircr~it: to the 160
Trolley Feeder Loop 5 . 6, 4 Synr:h r . r l r ~ c i ~ l s Reae tors 161 5.6.5 Utility Feeder Circuits 162 5.6.6 Substation 162
PERFORMANCE ANALYSIS
6.1 .Mutual Interference Study 165
6.2 Parametric Trade Study 173 6.2.1 Rotor Geometry and Size 177 6.2.2 spin'~otor and Track Size 181: e.2.3 Track Speod and Gylinder RPM 1.82 6.2.4 Spin Motor Schedule 185 6.2.5 Rotor and Plant Configuration
Selection 190
Net Power and Anni.aal. Energy Out.put 196 6.3.1 Wind Duration curve 196 6.3.2 Determination of Net Plant
Power Output 197 6.3.3 Development of Power .Duration
Curves 201
VII ECONOMIC ANALYSIS 204
7 ..Z Cost Estimating Procedure 204
C V E ~ ~ e r ~ ~ ~ i ~ l d r ~ ~ e / ~ l l a l ~ s i ~ 209 7.2.1 Unit Cost of Circular-Track 209
Plant Configurations 7.2.2 Unit Cost of Racetrack Plant 213
Configuration 7.2.3 Energy Cost 218
7.2'.3.1 Racetrack Configurations 219 7.2.3.2 Energy Cost Comparisons, 222
Best Plant Combinations
TABLE OF CONTENTS (Concluded)
SECTION PAGE *'
7.3 Effect of Land Cost and Learning 229 Curves on Energy Cost 7.3.1 Land Cost Effect 229 7.3.2 Learning Curve Effect ". 231
'7.4 Effect of Nonoptimum.,Wind Direction 240
7.5 Compar.ison of Madaras Plants with 243 Horizontal Axis WTG Plants 7.5.1 Medicine Bow Plant Comparison 245 7.5.2 Comparison of Plants at Sites 258
Having Mean Wind Duration Curves of 8.1 m/s at 9-m Height
7..5.3 .Summary of Madaras versus HA-WTG 260 Plant Comparison
VIII CONCLUSIONS . .
APPENDIX A: VORTEX ANALYSIS
APPENDIX C: ROTOR STRUCTURAL WEIGHT AND INERTIA 395 . SCALING EQUATIONS
REFERENCES 399
L I S T OF ILLUSTRATIONS
VOLUME 2
PAGE FIGURE
1.1 A r t i s t ' s Concepti'on o f Madaras .Plant , Popular Science Monthly, January 193'2.
Madaras P a t e n t .Diagram 3
Rotor and Support Tower Used In!Madarasl Tes t s , 5 Burl ington, N e w Je r sey , 1932.
Comparison of Rota t ing Cylinder Data from 1 2 Various Wind T u n n o l ~ (Referent: 2Q) .
'h.
Performance Comparison of a ~ o t a t i n g Cylinder 12 with' # W i 1 . y (Reference 2 3 ) for; TransLat.i.on Machines.
Performance Comparison of a Madar.as System 1 4 Used on a S t r a i g h t . o r a C i r c u l a r Track.
Comparison o f Madaras and UDRI Performance Computations.
Externa l P i c t u r e of Univers i ty of Michigan Aerospace Department Wind Tunnel.
Boundary Layer P r o f i l e Pressure Rake Array.
Assembly D.rawing of 152 m Dianteter Cylinder .
S ide V i e w , 152 mm Cylinder i n Tunnel with Lower Streamlined F a i r i n g Only.
Front View, 152 mm Cylinder i n Tunnel with lo we^. Streamlined F a i r i n g and Mirror S t r u t .
152 mm Diameter Cylinder aqd Car Ready fo r Simulated Boundary Layer Tes t , e/d = 3 %nd .P la tes , AR = 6.
C a l i b r a t i o n Loading F ix tu re f o r Wind Tunnel .
Balance System. 'a
Method of Simulating Atmospheric Boundary 39 Layers for 152 IIUII Cylinder .
Tunnel Boundary Layer. P r o f i l e P r i o r t o Modif icat ion, .97 m Free Stream Veloci ty , 11 m / s Above Floor . Curve 3 i s C e n t e r l i n e P r o f i l e .
v i i i
LIST: OF ILLUS.TRAT.1ONS (.C.ont inued
Simulated Atmospheric Boundary Layer for 152 mm Cylinder Having AR = 3'and AR ='6.
Ekman-like Spiral Resultant Wind Relative to Different Sec'tions of the Rotor:Produced by Vector Aadition of Translatory Motion of Rotor Car and Wind Boundary Layer Near Earth's Surface.
CL and Cp versus U/V for AR = 6, e/d = 3, Lower Falring.only Plus Mirror Strut.
/
HP versus U/V for AR = 6, e/d = :3. Neither. Fairing Nor Strut has any Effect on Data.
Study to Determine Test Reyno1d:s ~'urnber CD versus R for Various Values of U/V.
2 Freestream CD versus CL for Va&.ious AR, Two End Caps, e/d = 2.
~reestream CL versus U/V for Various AR, Two End Caps, e/d '= 2.
Freestream C versus CD for AR of 3 and 6 and e/d 4 Ratios of 1. 5, -2, and 3, d = 152 mm.
Freestream CL and CD versus U/V, AR of 3 and 6, and e/d Ratios.of 1.25, 2, and 3, d = 152 mm.
Freestream CL and CD versus U/V, AR of 3 and 6, and e/d Ratios of 1.25, 2, and 3, d = 152 mm.
Comparison of UDRI ~xtrapolated Data with Klemin's Measured Data.
Comparison of Interpolated UDRI Data with Gottingen Data.
e
Cross Plot of CD versus AR for e/d = 2. Used to Extrapolate UDRI Data'for AR = 6 to AR = 8 Data for Comparison with- &lemin's Data.
Cross Plot of CL ver'sus AR for e/d = 2. Used to Interpolate UDRI ~ a ~ a for AR = 4 to AR = 4 . 7 for Comparison with the Gottingen Data.
PAGE
42
LIST OF 1LLUST'RAT.IONS (Continued)
FIGURE
3.23
PAGE
Power Required to Rotate 'Cylinder: versus U/V and 67 rpm for AR = 3 and' 6 and for e/d of 1.25, 2, and 3.' Both Power Required in Still Air as well as Power Required at V, = 13.7 m/s are Given for the 'AR = 3 'Configuration, d = ,152 mm.
Comparison of Measured Power Required to Spin the 'Full-S'ized Madaras Rotor with Predicted Power .Required Based on Equations (2) and (3) . ~ o w c r / T J n i t T,ength versus ukameter uf R o k o r Having 72 Two End Capsi c/d - 1.35, and RotatSnnal speed of 120 rpm.
CL and CD Data from Boundary Layer Tests for e/d 75 Ratios of 1.25, 2, and 3, and for Aspect Ratios of 3 and 6, d = 152 mm.
CL, CD Power versus U/V for Boundary Layer Tests 76 for e/d Ratios of 1.25 and 2; one and two end Caps; and Aspect Ratios of 3 and 6, d = 152 mm.
Comparison of Aerodynamic Coefficients for Config- 77 i.~,xa.l!.ions. Madaxas Considered to be Equivalent.
Wind Duration Curve Uprated for 8 m/s Speed at ' 80 9 m. Wove Ground .to 8.8 m/s at 16.8 m/d m Above Ground.
Wind Velocity Profile. 83
Operational Design Loads for 8.0 m/s (-18 mph) Mean 85 Design Wind Speed. Derived from Preliminary Spin Schedule of Figure 5.1, in whiah U/V was Varied at Each $ O Incremental Position Around Orbit, Such that FTAN. is Maximized at Each Increment.
Ratio U/V versus Track Locations for 8.8 m/s Rated 86 Wind Speed.
Pressure Distribution Around the Center of a Rotating ,87 Cylihder at Various Values of U/V (Taken from Reference 13) . Madaras Rotor Cap Peak Pressure versus Radius. 88
Rotor and Cap Construction. 94
FIGURE
LIST 'OF 1LLUS.TRAT.XONS (Continued)
PAGE
Rotor Cap Truss Joint. 95
Location of Circumferential Rings. 97
Cap Module Radial View. 98
Rotor Cylinder Internal Structure. 101
Typical 45' Segment of Circumferential Stiffener. 102
Assembly Sketch of Rotor and Support Tower. , 104
Tower Base Segmentation Plan. 108
Three-View Drawing of the Rotor Car. 109
Rotor Car End Truck Assembly. 111
Car Structural Plan. 113
Sectional Elevations of Car Structural Layout. 114
Miscellaneous Skin and Stiffener Section. 115
Power Transfer Arm. 117
Revised Rotor Car Configuration. 120
Plant Layout. 123
Typical Elevation of Madaras Plant, One Car on 124 Track.
Preliminary Estimate of Aerodynamically Optimum 131 Rotational Speed Schedule.
5.2 Simplified Spin Schedule Used to Estimate Spin 135 Motor Size.
5.3 Rotor Steady-State Viscous and Bearing Friction 135 r Load for Simplified Spin Schedule.
5.4 Inertial Power Load, Ideal Performance, ~o'.~osses, 1'36 Regenerative Braking, Simplified Spin Schedule.
5.5 Total Power Load, Including Viscous Losses During 137 Spindown, Regenerative Braking, Simplified..
LIST OF ILLUS.TR?iT.XONS (Continued)
FIGURE
5.6
PAGE
Total Power Load, Including viscous Losses' During 139 Spindown, Regenerative 'Braking, Aerodynamically Optimum Spin.
percent' ~fficienc~ versus Percent Rated Output 141 Power for a Shunt-Wound dc Motor; Normal Operation.
Percent Efficiency versus Percent' Rated Output 142 Power for a Shunt-Wound dc Motor.
Percent Efficiency and Percent No-Load Speed 142 versus Percent Rated Output Power.
Percent Efficiency versus percent No-Load Speed 143 Motor Losses for a Shunt-Wound dc Motor.
Modified Spin Schedule for Various Spin Motor 146 Sizes.
Plant Power Output versus Spin Motor Size, 3,000-ft 147 Diameter Track, 186 rpm for Various Wind Speed.
5.13 Optimum Motor Size and Maximum Power Output/Rotor 148 versus Track Diameter, 30 mph Wirld Speed.
5.14 Optimum Motor Size and Maximum Power Output/Rotor 149 versuc Track B~aiilefer, 2fl 111ph Wirid aped.
5.15 Electrical Sche'matic of Circuitry on Each Rotor 163 Car.
6.1 Gross Power Output versus X for Various Wind 168 Speeds, One Rnt.nr Spinning at 183 rpm, 915 m Diameter Track. Professor Larsen's Vortex ~nalysis Accounts only for Aerodynamic Drag and Interference Losses.
6 . 2 Gross Power Oi.lkput versus Vw for one Rotor Spinning 170 at 186 rpm, 1524-m Diameter Track, Constant Track Speed of 13.4 m/s.
6.3 Gross Power Output versus Number of Rotors for 171 Various Wind Speeds for a Constant Rotor Speed of 186 rpm and Constant Track Speed of 13.4 m/s.
6.4 Mutual Interference Loss Factor versus Wind Speed 172 f ~ r Various Numbers of Car.. Constant Rotor Speed and Track Speed of 186 rpm and 13.4 Bij's,'respectively.
LIST OF ILLUSTRATIONS (Continued)
FIGURE PAGE
6.5 N e t Power f o r One Rotor v e r s u s Cyl inder 178 D i a m e t e r a s . a Funct ion o f e/d R a t i o and Cyl inder rpm f o r Constant P r o j e c t e d A r e a , Wind Speed and Track 'Speed; e/d = 1.25 and 2.
6.6 N e t Power f o r One .Rotor v e r s u s Cyl inder 180 rpm f o r Cons tan t Aspect R a t i o of 8 b u t w i th ,
Va'r iable D i a m e t e r and Var i ab l e P r o j e c t e d A r e a .
6.7 N e t Power Output f o r One Rotor v e r s u s X and Cy l inde r rpm f o r Various Cy l inde r
183
R o t a t i o n a l Speeds, Aspect Ra t io = 6, e/d = ~ 2 .
6.8 N e t Power Output ' . . for One Rotor v e r s u s A 184 and Cyl inder R o t a t i o n a l Speed, AR = 8 , e/d = 2.
6.9 N e t Power Output f o r One Rotor , Sp in Motor 186 Power, and Motor rpm v e r s u s Rotor P o s i t i o n on Track as Af fec t ed by use o f Viscous Braking, Regenerat ive Braking, and a Three- S t e p Transmiss ion t o Vary t h e Spin Schedule.
6 -10 N e t Power Output f o r one Rotor f o r Var ious 188 Spin Motor Speeds v e r s u s Track P o s i t i o n a t Which ' E i t h e r Regeneratkve Braking or Viscous Braking w a s 1 n i t i a t e . d .
6.11 N e t Power Output from one Rotor v e r s u s Track 194 D i a m e t e r as a Funct ion o f Wind Speed. Per- formance f o r Both C i r c u l a r and Racetrack Conf igu ra t ions .
6.12 N e t Power Output from one Rotor . v e r s u s A. as 195 a Funct ion o f Wind Speed. Performance i s P resen ted f o r Both a. 1372-m 'Diameter . C i r - c u l a r Track and a ' Racetrack hav ing 1372-m D i a m e t e r Ends and 4878 m S t r a i g h t Sec t ions .
6.13 Modified Design Wind Durat ion Curve t o 198 Represent Wind ' ~ o n d ' i t o n s a t a .Rotor Mid- Height o f 25 m , (82 f t ) Above Mean T e r r a i n Level .
6.14 Typ ica l N e t Power 'versus ,Vw Curve . f o r Two 202 Racetrack-Configured P l a n t s .
6.15 Power Durat ion Curves f o r t h e Two' P l a n t s 202 Shown in F i g u r e '6.14 Based on the v=9.6 r i ~ / s Design Wind Durat ion Curve a t 25-m Height (F igu re 6.13) .
LIST OF ILLUSTRATIONS (Continued)
FIGURE
7.1 Generalized Geometric Plant Layout and Equations for Computing Plant Cost, Plant Output, and Installed Cost Rated Plant Power Capacity.
Plant Cost versus Number of Rotors for Madaras Plants having Circular Track Configurations. Rated Power in Megawatts Indicated fo r Each Plant, Plants Having 1372-m and 1524-m Diameter Tracks were Studied.
Unit Plant Cost versus Length of Straight 3cction of Raoetrack . Pl ilrrl.: ~ o n f igurgtion as a Function of Number, of Cars and Inter- Car Spacing. Track Speed : 8.9 m/s (20 mph) .
PAGE
208
Unit Plant Cost versus Length of Straight 216 Section of Racetrack Plant Configuration as a Function of Number of Cars and Inter- Car Spacing, Track Speed: 13.4 m/s (30 mph).
Unit Plant Cost versus Rated Power for Race- 217 track Configuration as a Function of Inter- Rotor Spacing, Length of Straight Section of Track, and Number of Rotors. DOE Design Wind Duration corve: V - 8.1 m/s @ 9 m.
Energy Cost versus Rated Power for Racetrack 220 Configuration as a Function of Inter-Rotor Spacing, Length of Straight Section of Track, and Number of Rotors. DOE ~esign Wind Duration Curve: . = 8.1 m/s @ 9 m.
opt i m i i m Rot.na: Solidity Factor versus Length of Straight Track Section. . .
Ecfect of Monoptinun Wind Qura.tion on Cost. 241 of Madaras ~aeetrack Plank 49-60.
Typical ~~clogiro windmill at a -Speed Ratio of h = 2.
Trailing Vortex Sheet ~rray of One Blade.
Nondimensionalized Ideal Bound Vortex Strength as a Function of Phase Angle ~round'the Orbit for X = 2.
LIST. 'OF 'XLL'$TRAT.IONS
PAGE FIGURE
A. 4 Nondimensional.ized Ideal Bound Vortex Rate.of Shedding as a Function of Phase 'Angle due to Change' in Resultant Velocity at A ' = 2.
Ideal Cyclogiro Blade Element Vector Diagram.
Induced Velocity'.at an Arbitrary' Point Associated with a Finite straight Line . . Segment of Circulation, . r .
Nondimensionalized Velocity ~istribution in anLOseen vortex and'potential Vortex.,
Primitive Vortex he or^ Rotor and Wake Array '
Model.
Flow Field .of a Giromill at Maximum Power.
Variation of the X-Component'of the Resultant Velocity as a Function of A for a.Three- Bladed Giromill.
Rotor and'Wake Structure Assumed for Primitive Vortex Theory for a.Typica1 Cyclogiro. . .
. .
~cceleration-Deceleration Ramp Angle.
Nondimensional: Modulation schedule for.' a , V, or U/V. . .
Ideal Blade Element Vector Diagram of. ~yclogiro.
Real Blade- Element vector ~ i a ~ r a m of Cy~~ogiro.
Ideal Wake Structure- for a Three-Bladed Cyclogiro at a = .2.0;1.0, and 0.5 when the ~ake'~1iminates from the Blade Pivot Point, Angle of Attack = OO. . ,
Ideal Wake Structure for a Three-Bladed Cyclogiro Rotor at X =, 2'.0, 1.0, and 0.5 ~hen'the Wake Eminates from the Blade Trailing Edge, and the Blade is.Modulated from a'constant Angle.of Attack = '12O.
Semirigid Wake Structure for a Three- Bladed Cyclogiro 1llustratin.g'Distributed' . ,and Concentrated Vorticity.
LIST OF ILLUSTRATIONS (Concluded)
FIGURE PAGE
A.19 Wake 'Structure 'Assumed for the 'Improved Primitive Vortex Theo'ry.
A.20 Gross Power' Output versus h for Various Windspeeds, One Rotor Spinning at 183 rpm, 915 m Diameter Track.
A. 21 Ideal and Real Flow Around a Circular Cylinder for Various Circulation from 0 to a Supercritical Value.
A.22 Avcrage Gross Power Output from a Madaras P1an.L of Fourteen Rotating Cylinders versus X for Various Wind Sp~?wls . Fourtesn'Rotating Cylinders, Aspect Ratio = 6, e/d = 2, Cylinder Area = 2000 ft2, Diameter = 18.20 ft, Track Radius 1500 ft, Cylinder Rotating at 183 rpm.
A.23 Average Gross Power Output from Madaras Plant versus X for Various Wind Speeds. Sixteen Rotating Cylinders, Aspect Ratio = 6, e/d = 2, Cylinder Area = 2000 ft2, Diameter = 18.25 ft, Track Radius = 1500 ft., Cylinder Rotating at 183 rpm.
A.24 Average Gross Power Output from Madaras Plant versus X for Various Wind Speeds, Eighteen Rotating Cylinders, Aspect Hat.io = '6, e/d = 2, Cylinder Area = 2000 ft2, Diameter = 18.25 ft, Track Radius = 1500 ft, Cylinder Rotating at 183 rpm.
x v i
LIST OF TABLES
Table
3.1
Page
23 Six-Inch (152 nun) Diameter Cylinder Free Stream Wind Tunnel Test Matrix
Six-Inch (152 mm) Diameter Cylinder Simulated Atomspheric Boundary Layer Wind Tunnel Tests
Free-Stream Data for Cylinder with Bottom Fairing Only
Free-Stream Data for Cylinder with Both Mirror Strut and Bottom Fairing
Free Stream CL Data
Free Stream CD Data
Variables Studied in Mutual Interference, Vortex Analysis
Trade Study Variables
Comparison of Candidate Rotor Configurations, 1372 m (4500 ft) Track Diameter, 450 kW Spin Motor
Summary of Unit Cost Data 207
Computation of Madaras Plant Annual Costs 210
Cost and Performance of 20-Rotor Madaras Plants Having Circular Track
Comparison of Plant performance and Cost - 224 Circular and Racetrack Configuration
Effect of Land Cost or^ Plant and Energy Cost 232
Effect of Learning Curve and Land Cost on Energy 238 Cost for Plants Sited Where = 8.1 m/s @ 9-mHETGHT
Effect. of Learning Curve and Land Cost onEnergy 239 Cost for Plants .Sited wher.e = 9.7 m/s at 9-m HEIGHT (Medicine Bow Sea Level Plants)
Installed cost Breakdown of Madaras Plant 44-25M 247 and 98,000 kW Bureau of Reclamation Plant Proposed for-Medicine Bow, Wyoming
x v i i
'LIST OF TABLES (Concluded)
Table
7.9 Annual Cost Breakdown of .Madaras Plant 44-25M and 98,000 kW 'bureau of ,Reclamation HA-WTG Plant Proposed for Medicine 'Bow,' Wyoming
7.10 Overall Comparison of Several Madaras and HA-WTG Plants at Two Wind Regions . .
7.11 Madaras Versus HA-WTG Land Usage . . Effectiveness
Page
251
x v i i i
- FOREWORD . . ' .
This f i n a l r e p o r t desc r ibes t h e s tudy conducted by t h e
Universi ty o f Dayton Resiearch I n s t i t u t e d u r i n g t h e pe r iod from
October 1976 t o Febiuary 1978 on Contract ~ ( 4 9 - 1 8 ) -2554, spon-
so red by th.e Wind Energy Conversion. Branch, Divis ion o f S o l a r . . .
Energy, United S ta tes ' Energy Research 'and ~eve lopment
Administrat ion. D r . Robert Thres'her was P r o j e c t Monitor. . .
The s tudy was under d i r e c t i o n o f M r . Dale H . Whitford,
who, with D r . John E . Minardi, conducted t h e pre l iminary per-
formance analyses', planned t h e wind tunnel t e s t s , and analyzed
t h e wind tunnel t e s t d a t a . M r . Levere F. S t a r n e r and
M r . Blaine S. West were respons ib le f o r t h e s t r u c t u r a l a n a l y s i s
s tudy, and M r . Robert J. Dominic conducted t h e e l e c t r i c a l
a n a l y s i s .
The authors wish t o express t h e i r apprec ia t ion f o r t h e
e x c e l l e n t con t r ibu t ion t o t h i s program made by t h e personnel
o f the Gas Dynamics Laboratory, Aerospace Engineering Depart-
ment, Universi ty o f Michigan. Overa l l guidance, a s s i s t a n c e i n
developing t h e t e s t p lan , development of t h e method f o r gen-
e r a t i n g t h e s imulated atmospheric boundary l a y e r , and coord ina t ing
a l l a spec t s of t h e Universi ty o f Michigan e f f o r t was provided
by Professor William W . Willmarth. Tes t superv i s ion and
schedul ing o f support f o r t h e t e s t s was provided by
M r . David R. Glass. Mr. Danile 0. Scharf was respons ib le f o r
d i r e c t i n g t e s t s and process ing t h e d a t a , and M r . Charles Hogan,
M r . Leo G r i f f i n , and M r . C le tus I o t t were respons ib le f o r
ins t rumenta t ion , model i n s t a l l a t i o n , and opera t ion o f t h e wind
tunne l .
W e a l s o want t o acknowledge o t h e r major oon t r ibu t ions :
t h e vor tex a n a l y s i s s tudy conducted by Pro fessor Harold Larsen
o f the A i r Force I n s t i t u t e o f Technology; t h e d e t a i l e d s t r u c t u r a l
and mechanical design l ayou t done by M r . Francis Shannon o f
Maier and Associates; t h e economic a n a l y s i s conducted by
M r . John L . McClellan; and t h e aerodynamic c o n s u l t a t i o n
provided by D r . Frank L . Wattendorf.
F i n a l l y , we are e s p e c i a l l y a p p r e c i a t i v e of t h e support
o f t h e D e t r o i t Edison Company and t h e a s s i s t a n c e given by
M r . Walker L. C i s l e r , former Chairman of t h e Board o f t h a t
Company; and t h e c o n s u l t a t i o n . provided by M r . Russel l F. Hardy,
former Chief Engineer o f t h e Madaras .Rotor Power P r o j e c t ; and
D r . E .E. Lapin o f t h e Aerospace 'Corporation.
SECTION I
INTRODUCTION
The Madaras Rotor Power Plant concept was originally
developed in the-period from January 1930 .to April 1934. This
concept, conceived by Julius-D. .Madaras, made use of the 1 Magnus effect on a rotating circular cylinder to generate
electrical power.
1.1 CONCEPT DESCRIPTION AND BACKGROUND
An artist's rendering .of the Madaras Rotor Power Plant,
obtained from the January 19.32 issue of Popular Science, is
presented in Figure 1.1, and a copy 03 Madaras' patent is
presented in Figure 1.2.
The-Madaras project ranks as one of the more signifi-
cant wind power generation projects conducted in the United
States .because : (a) it was uniquely different from other
wind generation projects; (b) a full-scale rotor was designed,
built, tested,. and proven successful; and (c) it showed the
promise of generating the large quantities-of electric power
(e.g., 100 megawatts e.lectric) in a single power plant. In
view of the unusual method of wind energy conversion of this system and its promise of generating large amounts of power at
energy cost below that of coal-fired plants in 1934, this study
was conducted to determine-if a modernized Madaras design
would be economically competitive with horizontal axis wind
energy conversion systems.
The original concept.of the.Madaras plant consisted of
a circular track, an endless train of rotor units mounted on streamlined flat cars, .a power collection and distribution system,
and a control and maintenance bui1ding;all located. on a 323,752m 2
(80-acre) site. Des.ign .capacity ,was 18 ;000 kW for a 13.4 m/s
rated wind speed and a 8.9 m/s constant track speed.l A brief
description of the' 'system proposed by Madaras is given as
follows.
Big Electric Plant Run by Wind1......., ...
¥=.U ..., 4//.ill-BEARI,46 AT TOP OF*-*.:
- ' "/4 OURALUM,N , ILWOR• 'llllll DRIVE 5.AFT >UPPORTSQI"//li 'ME •Gir 01 ROTOR
1 ,1. ] - i -»-
, _ *5 ROTA-rio WITH OUTER (4_%%'·2:'S $„ELL BY 09'VE SHAFT ... , r
-Ait.& ... ...» -1,3.STATIONARYSUPPORTING
I. TOWER
I » , : - mr/* 1.a 0*-MA.C--7" ///////*4 + Amforoa + Lis.S,„-6 ,•e-••0 -nit-*fliw . '1 =4 9, ROTOR ,/*070RS wAS AP'PLISO TO A -*••· _9,$36. 8, ANTO" ......TNE. e .174„ 5,4.. ,UCCE„/ U...r CROS,le i1,4& ATLAN-rIC gl 1026 i. I .A & ROTORS AuTODIATKALLY./ I .4,1 F REVERSE ROTATION
1 © . ; A TWICE EACH TRIP.I Ik AROUND TRACK,AT
POINTS WHERETRAVEL,5 PARALLEL TO WIND
.**07*48. A.P..t<k.10- 0/ DIRECTIONme mOToR RE GERMANINVENTOR. P.ETTNER,/E5IGNEDTHIS ROTOR WiNOMILL TOGENERATE ELECTRICITY 3 SPINTANG ROTOR OF
SAIL TO Pt,OPEL CARALUMINUM ACTS AS
PMOTOGRAPH OF A MADARAS ROTOR MODEL f 1 -
(N A WIND TUNNEL MA CURRENTS FROMLEFT ARE SPEE.DED AT TOP AND IMPEDED 0 .Wi POWER HOUSE &AT BOTTOM, As 5-0.1 ;STS 5.04 CAUSING CD il , TEAM PLANT f EAC H ROTO R 15 90 FTROTOm TO MOVE- TOWARD PARTIAL JL_ -11. ..669/ #.*/„.NTS MIGH AND 22 FT. INvACUUM ABOVE 3 L _----14**4'2'.·'1"4- ' 'OWSR FROM 'P DIAMETER
1 SOTOR ON OAYS P
p : *UZ 11/.Md-* * 3. 14
M# =· 'fph·' .TT --
-=„,lk 4 -'.4 4 .1. ·1 ttr
'-*...*, 'r. -Ii-'mi'-- Li ): .ijaf .... ,--.P ' '11 , til
9 ' '·.· •' ' 07/ria#'P . ", : ..9/ flf'r· +3 . : 11 7 t:6
1 .., ,# *m. ft. »*.tr / 01*XZ'AS: - 4 3 --S 11 4'..#4<-*/ %31 SIR,:6 6 -:- . :ZST:· 1...'- 4- '.f 1 li S DRIVE SHAFT
44 ·4#Ok- 11 $,4,14$,A#f.-SMALL THIRD RAIL
ri ELECTRIC COLLECTS CURRENT
/:.124,42'.1-Spt= 1 12 f.. 1 1 jojr,6,02. FROM AL-L ROTORCARS AND CONDUCTS
CIRCWLAR TRACK. ·t . ... ......=:F-=.......=: -I.========= . 11 TO POWER HOUSE
OF 56·PT OAOE ANO 5,000 #T -a- d.61...ir--r- - -12'026-**4%reNDIAMETER,15 RAISED ON EM- --.BANIMENT TO 6,VE CLEAR SWEEP TO WHWO '4Jlil€7 0TREAMLirl=ED
7>·'· CAR * - tAf /., . -6. ...r .-844. fq. - . · ,€.Rfil-IN
'
kNER*96* DRIVE · .-..
POWER FROM THE AIR - p.41 -OEAR ".. - .•
./.
7 . A.·, 4.- * - ,«'- "Io Acr1,;...K .h.,w. 1·, ilee...1 ht,w t.,41.:.. r.,w:, plant willb, „t,rialt·il hy air *mwN /1,1,11 Will *trive /hi: 111
.- EN MATBA - A. 0..d.,% .r...,n-1 a ....... ....k '0 pr.'p.1 1.,rean,- RODUCES PO/ERFEEDS POWER
I.„.,1,1../.,,„ .01 1„,i,!·.2.,1,•, f·•EI-'«,9, 44'12,1,7 WIEN CAR TRAVELS 4, f FROM GENaRATORAROUND TRACK i & TO THIND RAIL
7 X AM,jZIN(; 'nierry-go-rouncl ' ing of the first $100.000 exirriniental n.·1- Scti:xcE Ato>:TitLY. Electricity from dy-
1-1 "ower 1,1:int ti) harness the wincl incler. Now rising at West liurlingtc,n. 11.inins oil the rotor cars. moving at a fixect
for electrical energy is soon to be N. J.. this seven-story-high shaft of alu- sirecl under automatic control, will litbuilt. somewhere in the East, if final minum recalls the c)·linclers that l,rol,elle(l collectecl by a third rail :incl concluct,·,1
tests now under w·a>: prove successful. (;ermany's famous -rotor ship" of a few to a substation for clistribution to the hur-
Twentv si,inning cylincirrs will rumhle years ago. Like them, it c,i,t·rates on the rounding country. Since the rotors niust
around a track 3.000 feet in diameter in i,rincil,le of the so-called 'Alagnus effect' 1,(: spun artifici:lily, a sm,Ill electric mult,ran endless train. They will propel flatcars -that a cylincler st,un iii the wincl tends keri,s rach one turning, 1,ut it uses onlyand turn dynamos geared to the axles. to move al right angles to the breeze. a small 1)rol,ortion of the power generated.
Fantastic as the project sounds. promi- The inventor. Julius D. Madaras. a With a twenty-eight-mile wind blowinBL
nent engineers have indorsed it. and six of Hungarian engineer living in Detroit. Te- Iadaras estimates, the completect I,lantthe most imponant power compal¥les in rcaled the cletails of the proposed power woulcl supply enough electricity for a citythe United States have linancetl the build- +tation iii an interview with l'opt'LAR of 150,000 inhabitants.
JANUARY. 193237
Figure 1.1. Artist's Conception of Madaras Plant, PopularScience Monthly. January 1932.
2
Figure 1 . 2 . Madaras P a t e n t Diagram.
1.1.1 System Descr ip t ion
Track :' A two-ra i l , s t e e l t r a c k o f 11 m gage,
457.3 m i n diameter wa's used t o guide t h e t r a i n o f r o t o r c a r s .
A s p u r t r a c k pe rmi t t ed t h e r e m v a l and exchange o f r o t o r c a r
u n i t s f o r maintenance.
Cars: F l a t c a r s about 1 2 . 2 m long, w e r e mounted
on four,two-wheel t r u c k s . The a x l e s were mounted r a d i a l l y with
r e s p e c t t o t h e c e n t e r o f t h e t r a c k , and t h e i n n e r wheels were
s m a l l e r than the ' o u t e r wheels t o e l i n u n a t e whcel s l ippage . Side
fo rces w e r e r e a c t e d by i d l e r wheels which r o l l e d on the r a i l
s i d e s t o f u r t h e r reduce t r a c k f r i c t i o n . The c a r s w e r e streamlined
t o minimize drag, arrd they conta ined ba l l a s t . Lo prevent over-
t u r n i n g . Weight o f each c a r and r o t o r was about 6 3 , 5 0 3 kg. The
c a r s w e r e connected i n an end less t r a i n by s t e e l cab les wi th a
80.2 m cen te r - to -cen te r d i s t a n c e between the r o t o r s .
Rotors: Eighteen r o t o r s , 27.4 m high by 6 . 8 m 2 i n d iameter , having a p r o j e c t e d a r e a of about 185.9 m , were
1.1sed i n t h e b a s i c p l a n t . The genera l cons t ruc t ion of t h e r o t o r
and i t s suppor t tower i s shown i n Figure 1.3. Each r o t o r was
provided w i t h a m t o r f o r revolving it a t t h e proper speeds i n
e i t h e r d i r e c t i o n . Twice each revo lu t ion of t h e t r a c k (at t r a c k
p o s i t i o n s f90° r e l a t i v e t o t h e wind) each r o t o r was braked by
t h e motor a c t i n g a s a genera to r and then was r o t a t e d i n t h e
o p p o s i t e d i r e c t i o n i n o r d e r t h a t t h e cu~nponcnt o f t h e Magnus
f o r c e t angen t t o t h e t r a c k would continuously propel all v e h i c l e s
i n a given d i r e c t i o n . 111 this way, I ~ I C J S ~ of t.hc r o t a t i o n a l energy
d i s s i p a t e d dur ing b rak ing was assumed t o be conserved f o r use i n
s p i n n i n g up o t h e r cars on khe opposi te s i d e o f t h e c i r c u l a r t r a c k .
Change o f r o t a t i o n a l d i r e c t i o n was i n i t i a t e d automat ica l ly by a
weather-vane-activated c o n t r o l system m u n t e d on top of t h e r o t o r .
Ar lo ta t i r ly end p l a t e having a diameter of about
10 .1 m was mounted .on t o p of t h e c y l i n d e r t o improve t h e aerodynamic
performance (by - inc reas ing c i r c u l a t i o n ; and hence l i f t ; and by
reducing induced drag b y . i n c r e a s i n g t h e e f f e c t i v e a spec t r a t i o of
t h e c y l i n d e r ) .
Figure 1.3. Rotor and Support Tower Used in Madaras' Tests, Burlington, New Jersey, 1932.
Power Generation: One induction generator was
carried on each car, gear-connected to one of the axles, Generated
power was delivered to contact wires arranged concentricially with
the track, and through feeders to the switch mat. A synchronous
condenser in the control house maintained a high power factor.
Control and Maintenance Building: A small
building on an 80-acre plant site housed, in addition to the
synchronous condenser and a motor-generated set, the control
switch board, instruments, supplies, and accommodations for the
operators-
1.1.2 History of the Madaras Project
The Madaras RuLor Fowcr Corp~ratinn was incorporated under the laws of the state of Michigan in August 1928. By the
end of 1929, seven public utility companies agreed to finance
the development of the rotor plant. The utilities forming this
B.-. group were:
The Detroit Edison Coo- Detroit, Michigan
Middle West Utilities (20.- Chicago, Illinois
North American Light and Power Coo-Chicago, XllinoiS
Public Service Electric and Gas Co.-Newark, New Jersey
Standard Gas and Electric orp para ti on-Chicago, IlLinois United Gas Improvement Coo-Philidelphia, Pennsylvania
The United Light and Power Co.-Chicago, Illinois
A three-step program was planned: (1) conduct wind
ti~nnel experiments on the Magnus effect and perform plant perform-,
ance and cost analyses based upon test results; (21 CanstrucL a
full-sized rotor unit and test its performance; and (3) construct
and test a commercial-sized plant of noL leas than 6,009 kW capacity. 2
The wind tunnel experiments were conducted at
the New York University Guggenheim School of Aeronautics under
the direction of Professor Alexander Klemin. Additional studies
were conducted by Professor Klemin; Professor FelixPawlowski of
the University of Michigan, and Professor Theodore von Karman
reviewed and concurred with the aerodynamic and performance
analysis. Step 1 was completed on January 23, 1931 at a cost
of $10,136. 3
In May 1931, the design, fabrication, erection,
testing, and analysis of data from a full-sized rotor began. The
rotor was mounted on a stationary platform on the property of
the Public Service Electric and Gas Corporation in Bwlington,
New Jersey. Principal contributors to this work were Mr. Walker
L. Cisler, Public Service Electric & Gas Company (recently
retired as Chairman of the Board, Detroit Edison Co,) , Mr, RussellF. Hardy (Chief Engineer of the Madaras Rotor Power
Corporation), and Messrs. Hirshfeld and Madaras. Consulting
assistance in structural design was obtained from Professor John D.
Akerman, University of Minnesota, and Professor Stephen Timoshenko,
University of Michigan. Construction started in October 1931,
and was completed ten months later; but a ten-month delay occurred
as a result of difficulty in developing a satisfactory force-
measuring system. Tests were conducted from June to October,1933.
The cost of the second phase was $161,691. Thus total project
cost was $171,827. 4
Because of the severity of the depression and the
lack of venture capital, the project was abandoned before the
prototype plant could materiali~e.~ Thus, the economics and com-
plete operation of the Madaras concept was never fully evaluated.
Very little information and no technical reports
were published in the open literature on the project because of
the strong desire of Madaras to protect his patents and the
equally strong desire of the utility companies to make sure that
the system was completely proven and that only completely reliable
data be released publicly. They did not want informat-ion on
cost of power at the plant boundary to be interpreted as cost to
the consumer. Consequently, only carefully-controlled news
releases were disseminated. Thus, the scientific community had
nothing with which to evaluate the program until recently when \
the University of Dayton was .given the entire report file by the
Detroit Edison Company. I \
1.1.3 Prior Re.search-Magnus Ef feet 1 I
A significant amount of work has been done to I
study the Magnus effect. After the work of ~a~nus,' the first
quantitative data on rotating cylinders was obtained by Lafay 1 '
I from 1910-1912, r 7 As a result, Anton Flettner became interested;
in the possibilities of this device for propelling,ships, and
convinced Prandtl and others at GBttingen to conduct wind tunnel 1 tests on cylinders. his work resulted in one of the classic sets of data .on the subject. 8v9r10 Flettner was encouraged by \ '
the results and convinced the directors of the Friedrich Krupp 1 ..
A, G. Germania-Werf t to dutf it a boat with two vertically-mounted
cylinders. These cylinders were 15.6 m high by 2.8 m in diameter, and were outfittedwitn end caps having a diameter 1.4 times that
of the cylinder. Each cylinder was turned by its own 11 kW electric
motor at a speed of 120. rpm. lo Flettner had two successful ocean'
voyages, one in the 'North Sea 'and.one round trip ac.ross the Atlantic
to New York. The rotors performed.wel1, and even in four or five
days of dangerously stormy weather performed without malfunction'
or damage. Flettner.said after the tests, "The trials of the
Baden Baden have proved.that all expectations which were based on
the GbZtingen experiments have been entirely fulfilled," A second
ship, the Barbara, having three rotors also was built and
successfully demonstrated.
Probably.the most complete work on rotating
cylinders was done by Thorn at the University of Glasgow between
1925 and 1935, He in~e~tigated effects of Reynolds numbers, end
plates, surface roughness, end conditions, and other variables.
(Reference 11-16 inclusive .)
The first significant contribution in the United
States was that of ~eidl'l in 1924. Later, in 1930, Klemin was
retained by the Madaras Company to conduct tests for use in
predicting the performance of the Madaras power plant.
Klemin's work, described in Reference 2,
included'wind tunnel studies of 0.20 m diameter cylinders having
lengths of 0.89, 1.14, 1.40, and 1.65 m. Tests were conducted
without end plates and with end plates having diameters 0,38 and
0.45 m. . Peripheral-speed to wind-speed ratios from 0 to 6.6 at
Reynolds numbers up to 3 x lo5 were used in the tests. Klemin
concluded that the cylinder performance agreed well with that of
~Uttingen, Reid, and.Thom, .and.tha't the disturbance between
adjacent cylinders is negligible beyond six diameters. He con-
cluded that end plates were very beneficial and should be used
for the Madaras system.' Unfortunately, Klemin.'s data were not
published and we .have found only that for the.,1.65 m cylinder
having only the 0.45 m end plates.
In 1960, rotating cylinder studies at Reynolds 5 5 numbers between 1.3 x 10. and 6.1 x 10 with end plate-to-cylinder
diameter ratios of 2.0 were conducted by ~atthewsl~ and by
Griffiths in 1968 at the University of Wales. l9 Both of these
studies agree well with the early data. An excellent survey of
the old and recent data was reported by Swanson in 1960. 20
Figure 1.4 is a.reproduction of lift coefficient curves showing
all types of data with and without end plates. We have added.
Klemin's data, labeled 1, for comparison. Swanson's contribution
is probably the first truly infinite aspect ratio result that has
been generated. He noted that .the addikion of end discs will
yield maximum lift coefficients that are greater than those of a .
two-dimensional infinite aspect ratio cylinder. This result is
attributed to the super circulation caused by the.superposition
of the flow around a finite rotating cylinder with that of'a
rotating end disc.
Thom's work has been recently validated by
Dean R. Stuart in the laboratories of the University of Waterloo,
Ontario, Canada. 21
We infer from Swanson's and Stuart's modern
studies that the work of Klemin agrees with the modern data trends.
Since Swanson's findings indicate that Reynolds number effects on
lift and drag coefficients are negligible at cylinder rotational
surface speeds greater than the wind speed, above the critical
Reynolds number, and that it simulated very well the performance
of the full-scale cylinder (27.4 m high x 6.8 m diameter) which 6 operated at Reynolds numbers on the order of 6 x 10 .
1.1.4 Prior '~esearch- Tracked Vehicle Airfoil' Con'cept
compared a wing with a rotating cylinder
for powering a tracked vehicle. The conclusion was that the
winged vehicle will extract five times more power from the wind
than a cylinder. This, conclusfon .was based upon inappropriate
simplifying geometric and aerodynamic assumptions which permitted
him to solve his equations of motion in a simple closed form.
The basis. for our conclusion on Stalker's work
can be seen from the following equation derived from the power
output of a vehicle moving d0wn.a track:
where P is the output power, A is the projected area of the wing
or cylinder, VR is the resultant velocity, Vw the wind speed, Vt -
the track speed, p is the air density, and, of course, CL and CD
are the lift and drag coeff.icients respectively. The only
difference in per£~rmance,between .a wing and a cylinder having a siven area, A, for given values of Vw and Vt is the'lift
coeificient and the CD/Ci ratio. The CL term of a cylinder over-
powers that of a wing to such an extent (10:l ratio) that the
superior CD/CL ratio of a wing over that of a cylinder does not
compensate for this difference in CL at low values of track speed.
As the values of VL become large,. the first bracketed term over-
comes the cylinder's CLt advantage and Lhe wing generates more I
power than a cylinder. The.CD term could include the losses due
to rotating the cylinder as well as the other common losses
to both systems; so a.direct comparison of the lift-drag polars
for the lifting surface does not tell'the whole story. To further
substantiate this perf0rmanc.e comparison, our computer data is -
compared with that of a wing23 in Figure 1.5 for low track speeds.
A recent, excellent study by ~ a ~ i n * ~ also confirmed the superiority
of a cylinder over a wing at low track speeds.
We believe that this analysis clearly demonstrates
why a cylinder-powered vehicle is a low speed translator and that
while in its low speed regime, it should be superior to the
tracked wing vehicle. This low-speed, high-performance feature
is the key to the promising potential of the Madaras concept.
The University first became interested in the Madaras
system as a result of discussions with Mr; Russell F. Hardy, who
was'the Chief' Engineer responsible for the design, erection, and
testing of the full-sized rotor system. The potential of the. .
system .looked so attractive that the. University, of Dayton agreed
to finance. a study o f theconcept. . This study included: (a) a literature search 'and evaluation; (b) the writing of a computer
program for simulating the performance of both the Madaras system
and a tracked vehicle-airfoil system; (c) the running of some
parametric studies to check Madaras results; and (d) a study of
the data in:technical'reports obtained. from Mr. Walker Cisler .of
Detroit Edison. . Th6 reports include the final reports for the
Phase I wind tunnel-tests and performance 'analyses and the Phase I1
full-scale rotor test, as well as other supporting documents of
consultants. (These documents are listed as' References 2, 3, 4,
and 25 through '36 .)
We have also discussed the Madaras project with Mr. Walker L. Cisler, who was responsible for. the full-scale test support.
He and Mr. Hardy believed that the system was proven to.be techni-
cally feasible, and that..a modernization of the design ,and a
current economic analysisof its potential' should be conducted.
They both have served as advisors on the present program.
Coi-a(at-~++w. of Power 0utputdra.m-Rota.t,i ng cy'l-i-nde-r and \:fl~nd vach w f i l a -pro jected Area o f '186m2.
Straight Track
V t = Track Speed i V, 10.3 m/s I I
Rotating, Cylinder I (Univ. of Dayton Computations)' t I :
I I I
I C
I I I
I I
I / /
t a
/ / /
0 . I 0 z 0
(4.5; (LC!). (1y.4) (lY.9) Wind Speed. Vw+mph (m/s)
Figure 1 .5 . Performance COm- par,i,so,n nf a. Rotating Cylinder w i t h a Wing (Refer- ence 2 3 ) f o r 'l'rans- l a t i o n Machines.
F i g u r e 1.4 ' . Comparison o f ~ o t a t i n g - Cyl inde r Data from Various
Wind Tunnels (Reference 2 0 ) .
Ronux*.
Ide-1 Ilvid
End Plate. 3. syl-dl..
~ o d a t e . I. 7 a q l -d~a .
Rough Sanded Surlaso
SRM* SUHSC.
Unpubliohcd (Carno In.%)
Continuou. End Sectloxu
End Flates 1. 25 = -1-dia
S u t i o n . ~ End Plate* i. syi-Ji.; .(..m. .. -8". 5 )
Rdmllds Number
(5.3 to 8.nh1o3
(1.9 to 11.6).10~
5.2 = lo4
1.6x10'
(0.16 u a1u10'
(3 to 9).lo4
(3 to ~ W I O '
5.2 10'
(5.4 urd 18)rlo4
5.10'
l (0 .9 to 3. l t a 1 0 ~
1.9 to 6.1a103
Come Lnvo.tlg.tor
ra.udU
b Tbom
D Reid
d Gttingem
Tbom
1 c.=*.... I mrn h m o m
1 Cb'ningm
j Sch-niberg
k Swanmom
1 laomin . W t t h o r .
AIpeel h t l o
12.5.26
13.3
4.7
8
5.7
5. i 4.7
4.5
2
4.4 to 8.
5.7
1 .2 -1 Per fo:rmanc'e Analysis
Figure 1.6 contains power output curves we cal-
culated for various wind and track speeds for a circular track
and a straight track. We found that we had sufficient data to
follow and critique the Madaras computations, and our independent
computations using Madaras' dataagrees closely with Madaras'
results, as shown in Figure 1.7. As a result of our preliminary
studies, we were unable to find any statement or evidence that the
system had been proven either technically or economically unsound.
1.2.2 Preliminary Economic Comparisons
The foundation for our preliminary analysis of
the Madaras system was the cost and performance analysis conducted
by Madaras and the utilities in 1931 and our computer study. In
the 1931 study, the consulting firm of Stevens and wood3 was
retained to work with engineers from the public utility compan'ies,
and not under the direction of Madaras. A set of checks and
balances were established by utilities. to prevent the inventor
from being carried away by his enthusiasm. The estimators pre-
pared preliminary designs, obtained equipment quotes, and then
priced all manufactured parts. The utility companies reviewed
the costs, and reported that "the estimates are liberal andthat
the total would easily cover the plant cost. ,I 3
The Madaras performance analysis predicted the
gross rotor power generation performance based on Klemin's wind
tunnel tests at various wind speeds, and deducted track losses;
axle, bearing, and friction losses; electrical generator losses;
and losses due to the power required to. rotate and reverse the
rotors.
These data on net power generated were then used
by Madaras in conjunction with -three wind duration curves, of which
the most favorable curve was nearly identical to the V = 8.0 m/s
curve specified by NASA for the General Electric and Kaman studies.
Estimates also were made for annual.operating and maintenance
charges, which were developed and approved by the utility companies.
AV
ER
AG
E
PO
WE
R,
PA
W ( m
w)
P
- -
h,
UI
0
in
0
I I
I
AVE
RA
GE
NE
T PO
WER
OU
TPU
T PE
R C
YC
LE - M
EGA
WA
TTS
From this analysis it was predicted that a plant with a rated
output of 18,000 kW at a rated wind speed of about 13 m/s could
be constructed at a cost of $38.50/kWr and that electric power
cost at the busbar would be 1.22 mills/kWh. This was based upon
the wind duration curve which yielded a specific output of
4425 w. It should be noted that in 1934 this cost was considerably lower than that of coal-fired steam plants in the
Pittsburgh area, where the costs for the Duquesne Light Company
varied from 4 to 5 mill/kWh for newer plants to 6 to 7 mills/kWh
for the total system. In fact, coal costs in 1934 were from
1.25 to 1.5 mill/kWh. 29
By scaling this early Madaras cost data to the
1945 and 1975 time periods, we were able to compare the Madaras
system economic predictions with those of the Smith-Putnam 37
and General ~lectric- ama an^* horizontal axis wind turbine. These comparisons indicated that the Madaras system could provide
energy at lower cost than all of the above horizontal axis
machines, and hence the Madaras system was potentially attractive
from an economic standpoint.
1.3 POTENTIAL FEATURES OF THE MADARAS SYSTEM
a System shows potential for power production in large quantities at least in the range of 10-100 MW.
a Concept can capitalize on economy of scale; large systems are generally more economical than small systems.
a Simplicity and ruggedness of rotor structure will permit scaling up to large sizes with fewer structural problems than for long, flexible rotor blades
a Rotor has extremely high lift coefficients (10 times greater than an airfoil) .
a Rotor can generate high power output at low track speeds.
a Systemdoes not need expensive towers to elevate and structurally support both the conversion unit and the heavy transmission-generation equipment high above the ground.
Previous full-scale tests on the 27.4 m high by 6.8 m diameter rotor as well as wind tunnel tests have proven the technical feasibility of the concept.
e The cost of further development has been reduced because of the wealth of technical information that has been completed, the understanding of the system and its problems by the proposed ' staff ; subcontractors, and consultants, and the computer software that already .has been developed.
Historical cost estimates by independent consultants and the one included herein indicate the system is competitive with fossil-fueled systems.
1.4 MAJOR ISSUES
Potential issues that have caused some people to question
the Madaras system are:
The concern that the early wind tunnel data on the Magnus effect were not valid and that-performance estimations based on this data may be overstated.
e The opinion that the total of aerodynamic, mechanical, and electrical losses would be excessive.
The opinion that the Burlington tests did not provide the economic basis for successful competition with other forms of power generation.
e The f a o t that fo rn r s are ~ilour~ttd elouc to the gsoiinrl in the zone of friction retardation of the winds.
The fact that there has been little publi'shed technical data in the open literature concerning the early experiments and analysis arid Lhe absence of a hardware delll~n~trati~n of a total igadaras electric power generation system.
The concern that since the Flettner rotor ship was not considered an economio GUGCBSEY the Madaras system aleo would not be a success.
1.5 UNANSWERED QUESTIONS
We believe that w e answered most of the above issues
in our preliminary study. ow ever, four important questions remained that had not been answered to our satisfaction. These
questions were:
What is the fewest number of rotors required to extract as .nearly as possible the theoretical maximum amount of power per'unit area from the wind?
What aerodynamic performance can be expected from full- sized cylinders operating in the lower levels of the atmospheric boundary layers in terms of the various geometric and operational design variables which affect performance.
What are the design requirements for structural, electrical and mechanical.subsystems; and what per- formance of a Madaras.system can be expected when modern, commercially-available electrical and mechanical components' are used?
What is the capital cost and the cost of electric power generated by modernized Madaras plants of different sizes in vari0u.s climatic areas of the United States?
SECTION I1
OBJECTIVES AND SCOPE
2.1 OBJECTIVES AND SCOPE
The primary objective of this program was to demonstrate
the degree in which Madaras power plants having capacities in the
10 MW to 200 MW range are competitive with horizontal axis wind
turbines. This objective was achieved by addressing the four
unanswered questions stated in Paragraph 1.5,
These objectives and the major questio~is were addrc~sed
in a four-phase study. These phacos were:
8 An aerodynamic study which included wind tunnel testing to deternine the aerodynamio performanr:~ of a rotating cylinder as a function of geometry, free stream flow conditions, and boundary layer profile . An electromechanical study aimed at updating the structural, mechanical, and electrical.components to present-day technology and design criteria.
e A performance analysis involving the use of va~ious computer simulation codes to determine the performance of various sizes of Madaras plants for various geometries and wind conditions.
An economic analysis to determirle the eost of installation, and the cost of electric power.
2.2 GROUND RULES
The following ground rules, as stated at the bagi.nning
of the study, will further define the scope and nature of this
investigation.
e The project was a conceptual design study which analyzed the basic Madaras system with only those changes which could be incorporated simply with no major development efforts nor efforts to develop an optimized design,
Analysis techniques, design approaches, and equip- ment will reflect the current state-of-the-art.that is commercially available.
o Madaras s y s tern performance w i l l be compared- -w'ith t h e b e s t a v a i l a b l e s t u d i e s o f h o r i z o n t a l - a x i s wind t u r b i n e s w i thou t s t o r a g e .
Wind s i t i n . g , wind d u r a t i o n cu rves , and des ign l o a d and l i f e cr i ter ia w i l l b e i n accordance w i t h t h a t d a t a s p e c i f i e d f o r General E l e c t r i c s t u d i e s .
Costs w i l l be genera ted i n accordance w i t h accep ted ,.
p u b l i c u t i l i t y p r a c t i c e , and cos . ts w i l l be based on produc t ion l o t s of 1, . a n d 100 p l a n t s .
SECTION 111
WIND TUNNEL TESTS
The performance o f t h e Madaras r o t o r i s complicated by
t h e i n t e r a c t i o n o f t h e a tmospher ic boundary l a y e r w i t h t h e flow
f i e l d o f t h e s p i n n i n g r o t o r . The i n t e r a c t i o n r eg ion r e p r e s e n t s
a compl ica ted problem i n three-dimensional , nonuniform flow. The
s e p a r a t e d flow i n t e r a c t i o n i s g r e a t e r n e a r t h e ground a t t h e
b a s e o f t h e c y l i n d e r . The flow invo lves t h e i n t e r a c t i o n , s t r e t c h -
i n g , and d i f f u s i o n o f t h e v o r t i c i t y i n t h e a tmospher ic boundary
l a y e r and t h e v o r t i c i t y produced by t h e f low f i e l d o f t h e
s p i n n i n g r o t o r .
Although r e f e r e n c e s tu Lhe lna jor c o n t r i b u t i o n s t o r o t a t incj
c y l i n d e r performance l i t e r a t u r e were g iven i n Paragraph 1 .1 .3 , a
s tudy ' of t h e s e d a t a i n d i c a t e t h a t a complete set of d a t a w i th a s p e c t
r a t i o s and end p l a t e s i z e s measured i n modern f a c i l i t i e s d i d no t
e x i s t . F u r t h e r , a l l of t h e a v a i l a b l e d a t a were measured under
uniform, upstream f low c o n d i t i o n s f r e e from a boundary l a y e r ; hence
no in fo rma t ion on t h e e f f e c t s o f t h e e a r t h ' s boundary l a y e r p r o f i l e 24
on c y l i n d e r performance was a v a i l a b l e . Lapin was p a r t i c u l a r l y
concerned about bo th t h e q u a n t i t y and v a l i d i t y o f t h e d a t a ob ta ined
i n t h e 1920-1935 t i m e p e r i o d , and recommended t h a t new wind tunne l
tests be run . H e was p a r t i c u l a r l y concerned t h a t t h e v a l u e s of
CD i n t h e o l d e r d a t a seemed t o be t o o smal l .
S ince t h e t h r e e - d i m n s i o n a l f low f i e l d around a r o t a t i n g
c y l i n d e r imrnersed i n t h e lower l e v e l s o f t h e e a r t h ' s buur~dary
l a y e r i s s o complex t h a t i t cannot be efficiently d~ ld lyzed Ly
a n a l y t i c a l t e chn iques , and s i n c e no wind t u n n e l d a t a has been
developed f o r t h i s curicl i t iur~, i L was decided t o modcl t h e
boundary l a y e r f low f i e l d and perform measurements o f t h e per-
t i n e n t aerodynamic f o r c e s i n a wind t u n n e l t es t program designed
s p e c i f i c a l l y t o ana lyze t h e Madaras system. E x i s t i n g a n a l y t i c a l
t e c h n i q u e s such a s t h e v o r t e x a n a l y s i s t echnique developed by
P r o f e s s o r Larsen o f t h e A - r Force I n s t i t u t e of Technology
(described i n Reference 3 9 ) , w e r e t hen used t o s tudy t h e
mutual i n t e r f e r e n c e and minimum spac ing q u e s t i o n t h a t was
r a i s e d in . Paragraph 1 .5 . This a n a l y s i s w i l l be desc r ibed i n
s e c t i o n 6 .
3.1 W I N D TUNNEL STUDY 0BJECTI.VES
Th,e ob j ,ect ' ives o f . the aerodynamic s tudy were t o :
Obtain a complete set o f f ree-s t ream r o t a t i n g c y l i n d e r aerodynamic d a t a a s a func t ion o f ranges o f geomet r ica l parameters p e r t i n e n t t o t h e Madaras system.
Obtain a complete set o f aerodynamic geometric d a t a on r o t a t i n g c y l i n d e r s i n a s imu la t ed a tmospher ic boundary l a y e r p r o f i l e .
Obtain d a t a on power r e q u i r e d t o r o t a t e t h e c y l i n d e r under a l l flow and geometric c o n d i t i o n s .
Determine t h e v a l i d i t y o f e x i s t i n g r o t a t i n g c y l i n d e r d a t a , e s p e c i a l l y t h a t used by Madaras f o r h i s per- formance c a l c u l a t i o n s .
Determine by a n a l y t i c a l methods t h e r e l a t i o n s h i p between va r ious boundary l a y e r p r o f i l e s and aerodynamic c o e f f i c i e n t s .
I n a l l o f t h e above tests , flow c o n d i t i o n s were designed
t o r e p r e s e n t adequa te ly t hose o f a f b l l - s i z e Madaras r o t o r .
3.2 W I N D TUNNEL TEST PLAN
The wind t u n n e l program c o n s i s t e d o f t h r e e p a r t s :
o Developing methods f o r s i m u l a t i n g a tmospher ic boundary l a y e r s f o r two s i z e s o f c y l i n d e r s .
s Conducting e x p l o r a t o r y f ree-s t ream and boundary- l a y e r t e s t s on a 2-inch ( 5 1 mm) diameter c y l i n d e r hav ing a geometric a s p e c t r a t i o o f 4 and end p l a t e t o diameter r a t i o s (e /d) o f 1 , 2 , and 3.
Conducting e x t e n s i v e f ree-s t ream and boundary-layer tests on a s e r i e s o f 6-inch (152 mm) diameter c y l i n d e r s hav ing geometric a s p e c t r a t i o s o f 3, 4 , 5 , and 6 ; and end p l a t e t o d iameter r a t i o s (e /d) o f 1 .25, 2, and 3.
One o f t h e impor t an t f e a t u r e s o f t h i s t es t p l an w a s t h a t
e a c h test was conducted a t a c o n s t a n t wind speed (V) th roughout
t h e U/V range (U i s t h e p e r i p h e r a l speed o f t h e c y l i n d e r r e s u l t -
i n g from i t s r o t a t i o n ) . This is a unique f e a t u r e o f t h i s t e s t
p l a n . I n t h e p a s t , exper imenters have decreased V i n o r d e r t o
o b t a i n h i g h e r U/V va lues because o f motor speed and power
l i m i t a t i o n s . However, f o r t h i s program, motor s e l e c t i o n was _I
based upon i t s a b i l i t y t o p rov ide s u f f i c i e n t power and speed s o
t h a t maximum U/V va lues o f 6 o r more could be o b t a i n e d a t a l l
t e s t w i n d speeds .
The t e s t p l a n is described i r l the fo l lowing paragraphs.
The b a s i c wind tunne l t e s t m a t r i x f o r t h e 6-inch
(152 mm) c y l i n d e r is p r e s e n t e d i n Tables 3.1 and 3 . 2 which shows
a l l combinat ions o f t e s t , 'model, and flow c o n f i g u r a t i o n s t e s t e d .
A t o t a l o f 106 basic t e s t s were conducted, reduced, and ana lyzed ,
n o t . c o u n t i n g r e r u n s o r s p e c i a l tests. The r e s u l t i n g d a t a is
t h e most complete set o f r o t a t i n g c y l i n d e r d a t a a v a i l a b l e i n the
l i t e r a t u r e .
The 51-mm cy'l.i.nder tests were p r i m a r i l y exploratbt ly
i n v e s t i g a t i o n s t o d e f i n e t h e design and tes t requi rements , prob-
l e m areas, and t h e ranges o f v a r i a b l e s w e would want t o tes t i n
o u r more complete s ix - inch c y l i n d e r tes t s e r i e s . Thus, primary
emphasis was p l a c e d upon t h e s ix - inch c y l i n d e r tests, whereas
t h e two-inch c y l i n d e r d a t a w e r e used as a back up and a s arl
independent means f o r checking r e s u l t s and t r e n d s i n so^ Of
t h e s ix - inch c y l i n d e r d a t a .
3 . 2 . 2 Wind Tunnel Desc r ip t ion
The subson ic wind t u n n e l o f t h e Un ive r s i t y o f
Michigan 's Aerospace Engineer ing Department was used f o r t h i s
program. This t u n n e l is a c l o s e d c i r c u i t , s i n g l e r e t u r n t u n n e l
w i t h an e s s e n t i a l l y r e c t a n g u l a r t es t s e c t i o n 2 .1 m wide by 1 .5 m
h i g h by 7.6 m long . The c o r n e r s o f t h e tes t s e c t i o n are f i l l e t e d
TABLE 3 .1
SIX-INCH (152 mm) DIAMETER CYLINDER FREE STREAM WIND TUNNEL TEST MATRIX
TABLE 3.2
SIX-INCH (152 mm) DIAMETER CYLINDER SIMULATED ATMOSPHERIC BOUNDARY LAYER
WIND TUNNEL TESTS
Run Conditions
Run !Description Number
3 400-14A
. Test Conflguratlon
pspect 5 Ratio 6
Q, C Y ~ Helght cm - - - - 400-14C
400-ldD
e/d
None
\1/
2 2 1 1
3 2 1 1
2 2 1 1
2 2 1 1 - 2 2 2
2 1 1
2 2 2
2 1 1
2 1 1
2 1 1
3 1 1
Slodel Locatlon
None
AR
None
Approx. hef v 1 elgh?
30 38 46 5 3 I
Track
None
CY 1 Car
None
1 3 'same as 4 Above 5
b
3 Game as 4 Above 5
6
Tare Test Boundary Layer Tests
Tare Test Boundary Layer Tests
Tare Test Boundary Layer Tests . Tare Test Boundary Layer Tes LS
Tare Test game B/L as in Tests 541-XX
Boundary
ests
NO. End Plates
None
W \/ 1.25
4 6 .. 52 . .
30 38
! :: 3 30
3 1 30
ref. I vel. I R m/s ~U/V
\I
4
400-14E 1/2 Car in 400-l4P / Ftenz o f 406-14G I Rakes 4~0-14# , 600-14~ ' 1/2 car on 600-14B 1 1/2 of Track
13.7
2.0
606-14C 600-14D
531-00 531-14 531-14A 531-148
532-00 532-14 532-14A 532-146
533-00 533-14 533-14A 533-14B
541-00 541-14 541-14A 541 -LOP
542-00 542-141) 542-14C
542-14 542-14A
3.0 1 0 0 38 13.7 1.43 3 8
J 3 8 V L/ 3 0
1.25 4 38
46 -- .__ 3 8
2.0 38 0 0 5 6 13.7 1.43 5 6
46
\J/
3 8 T~ack. B Floor
543-00 j~yl. Elev.,
v 0
13.7 1
X X X X
X X X X
X X X X
X X X X-
X X X
X X X
X X X
X X X
X X x X X X
X X x
in Front Qf Rakes
Cyl. 6 Car on Balance Free From Track or Floor
r,/
Cyl Elevated Car on Floor
Cyl & Car ion Balance
3.0
\I 1.25
3.0
i
Ref. 543-14D 543-14C
ests 541-XX
543-14 313-14A 543-14B
551-14 551-1421 551-14B
552-14 552-14A 552-14B
553-14 553-14A 553-148
1.43 1
X X X
None
X X X
None
X X X
None
X X X
- m e None None None
X X
None
Nono None None
X X
None
X X
None
X X
None
X X
None
Car on Floor
Cyl. & Car UII bolanaa Free From
Track & Floor
d
- - - -
0 1.43
542-14B
4
.J 5
I
0 0
Free from
3 8 3 8 3 8 30
- - - - 6
- - - - 3 8 3 8 3 8 30
38
d 4 6
0 13.,7
V' 13.7
- \J
0 1.43
7 56 5 G 46
46 4 6 3 0
5 7 5 3 46
53 53 43
5 3 5 3 46
kt 1
1093
V V V
1
I
TABLE 3.2 (Concluded)
SIMULATED ATMOSPHERIC BOUNDARY LAYER WIND TUNNEL TESTS
.
I
Test Description
I s 561-14
I i 561-14A 1561-14B
i ! 562-14 1562-1411
I 1562-14B
1563-14 1 563-14A
. 1563-14B
. Cyl
Height
Run Conditions
Run Number
Approx. Ref.Ve1.
e/d IAR , Height
I 1 : i X
Test Ref Vel m/s
Confiquration
Model Location
38
4 38 38
38 38
R Max$ lom5 .U/V Track
CY 1 Car
61 6 1 53
1 13.7 i i
NO. End
Plates
61 61 5 3
6 1 6 1 53
1.43 / 6 i '
0.48 0.96 1.44 1.92 2.40 2.88 3.36 3.84 4.32 1.80
1.44 1.44
1.44 1.44
4.6 9.1
13.7 18.3 22.9 27.4 32.0 36.6 4 1 42.7
13.7 13.7
13.7 13.7
- - - - - - - ' - - - 6 6
6 6
Cylinder 1642-05 Cylinder X Static and Car X CD Versus R runs 642-20 Free from
\J \J
X 2 X 1
in i 642-25 Boundary 1642-30 Layer I 642-35 642-40
1642-45
!
d
\i/
X
1 X
d I i:
I None I 1 '
X X
\/
Floor ' X I X
2 2
2 2
i
X X x X
X X
X X
.. .
2 Spinning end plates
one end plate on top, one end plate in center of ,cylinder
2.0 3.0
2.0 3.0
642-50
642-14 643-14
662-14X 662-14X
V
4 4
6 6
38
53 5 3
0.2 m up each w a l l , t h u s reducing t h e c ross - sec t iona l a r e a t o 2 abou t 3.2 m . Severa l f i n e mesh sc reens i n t h e s e t t l i n g chamber
combined wi th t h e h igh con t rac t ion r a t i o (15 : l ) r e s u l t i n
unusual ly low turbulence i n t h e test s e c t i o n .
The tunne l i s capable o f continuous opera t ion a t
test s e c t i o n v e l o c i t i e s o f up t o 67 m/sec (150 mph) wi th a model 2 3 having an e f f e c t i v e blockage o f about 0.28 m ( 3 f t ) . Somewhat
h i g h e r v e l o c i t i e s a r e a t t a i n a b l e wi th l e s s blockage.
The f r o n t s i d e o f t h e tunne l has many windows
i n i t and a few windows age i n t h e t o p of t h e tunne l . The s i d e
windows e s p e c i a l l y provide r e l a t i v e l y good oppor tuni ty f o r
viewing o r photographing t h e model. Addi t ional windows can be
provided where s p e c i f i c a l l y needed.
The wind tunnel f a c i l i t i e s have i n s t r u r e n t a t i o n
systems f o r measurement and recording of a l l necessary q u a n t i t i e s .
The fo rce and moment d a t a a r e obta ined from t h e wind tunne l
pyramidal s t r a i n gage balance system. This balance i s mounted
below t h e tunne l test s e c t i o n wi th t h e s t i n g (7.6 mm i n diameter)
p a s s i n g through t h e tunne l f l o o r f o r a t tachment t o t h e model.
Force capac i ty i s 2670 N (600 l b ) l i f t , 980 N s i d e , and 980 N
drag. The s i d e and d raq force and a l l t h r e e components o f
momnt were used f o r t h i s tesl; s e r i e s . A hollow s t i n g i s used
t o f a c i l i t a t e t h e r o u t i n g o f f l e x i b l e tub ing from t h e model
p r e s s u r e t a p s t o t h e p ressu re measuring system. This balance
can support a m d e l o f gross weight over 136 kg. It provides
f8r t h e measurement of a l l t h r e e moments, each having an
accuracy of f 2 i n - l b (0.226 N-m) by means of va r ious combinations
o f s t r a i n gages. The s i x s t r a i n gage s i g n a l s , c o r r e s p o r ~ d i ~ ~ y t o
each o f t h e s i x components, a r e d i g i t i z e d and fed i n t o variable gain a m p l i f i e r s . The ou tpu t s a r e d isp layed by d i g i t a l panel
v o l t r e t e r s . The tunne l dynamic p ressu re and temperature a r e
a l s o d i sp layed on d i g i t a l panel meters. A l l t hese d isp layed
va lues can be recorded manually i f d e s i r e d , b u t a l l t h e meters a r e
equipped t o ou tpu t t o a Digi tec punched paper t ape recording
system. Thus, simultaneous readings o f a l l meters can be
recorded on paper tape whenever a record of test data i s desired. The paper tape can then be fed i n t o a computer t o provide a tabular p r in tou t o r graph of t he desired parameters. A p ic ture o f the wind tunnel, t h e balance system, and the data console is presented i n Figure 3.1. One of t he 152 mm models being t e s t e d can be seen through the window.
The boundary l a y e r p ro f i l e s were measured by f i v e pressure rakes nrounted behind the model a t various s t a t i o n s across the tunnel a s shown i n Figure 3.2. Velocity measurements
w e r e obtained a t nine heights above the tunnel f loo r a t each rake posit ion. Velocity data from a l l 45 readings w e r e recorded instantaneously on a scanner valve using a Sa t ra systems pressure transducer and then was punched i n t o paper tape, and reduced automatically on the computer.
Data obtained during each t e s t included tunnel speed, dynamic pressure, atmospheric conditions, cyl inder ro t a t iona l speed (by means of a photoelect r ic c e l l ) , and measurements of lift, drag, moments due t o l i f t and drag, and motor torque (yaw mment) from t h e s i x component balance.
3.2.3 T e s t Model Development
The general requirements f o r t he design of both the 51 nun and the 152 mm diameter test model designs were t h a t they must be: (1) adaptable t o the University of Michigan s i x component balance system; (2) capable of being ra i sed and supported a t various heights above the tunnel f l o o r fo r f r ee
stream tests and the e a r t h ' s boundary l aye r t e s t s ; (3) dynamically balanced over a speed range from 0 t o 20,000 rpm (0 t o 12,000
rpm f o r the e/d = 3 end p l a t e s ) ; ( 4 ) ab le t o be configured f o r end p l a t e t o cylinder diameter ratios of about 1, 2, and 3; and
(5) t h a t t h e cyl inders be driven by motors housed within them t o minimize model whipping which could occur from an externally- mounted motor. In addit ion, t h e 152 mm cylinder design was
required t o provide f o r aspect r a t i o var ia t ions of 3, 4 , 5, and 6; whereas the 51 mm cylinder design was f ixed a t an aspect r a t i o of 4.
Figure 5.1- r1xtrmal Picture of University of Michigan Aerospace Department Wind Tunnel.
Figure 3 . 2 . Boundary Layer P r o f i l e Pressure Rake Array.
An assembly drawing of the 152 mm diameter cylinder
is presented in Figure 3.3. This cylinder was configured in much
the same way as the 51 mm cylinder, but its size, the tremendous
centrifugal forces generated on it, and the requirement to change
sleeves in order to make aspect ratio changes required more care
in both design and manufacture in order to insure safety and
vibration-free operation. Both manual stress computations and
finite element computer analyses were used to confirm the
structural integrity of this large cylinder.
A Tech Development, Incorporated pneumatic motor
was used to drive the cylinder. This is a four-stage turbine
capable of delivering 37.3 kW at 15,000 rpm. Under lighter loads,
maximum speeds of 20,000 rpm were attained. This motor, which
weighed 4.5 kg and was 82.5 mm diameter by 16.5 mm long, was leased by the University of Dayton for the tests. The air
supply and exhaust was fed through the tunnel sting extension,
and the air hoses were routed so that no net force was exerted
on the balance system by the air impulse. Maximum compressed air
flow rate required was 0.45 kg/s (1 lb/sec) at 1.38 MPa (200
psi). Air supply was provided by the University of Michigan's
filtered, pressurized tank system which was capable of providing
air for one day of testing before repressurizing was required.
Four, 152 mm diameter sleeves were made having varying lengths from 457 mm to 914 mm. Thus, geometric aspect
ratias of 3 , 4, 5, and 5 were available for tests. Thessu ler1gC1.re
were selected to bracket the AR of 4 used for the original
Madaras cylinder design and to bridge between the AR = 8 cylinder
tested by Klemin for Madaras.
Three sets of end plates having diameters varying
from 29.5 mm to 456 mm provided end plate to diameter ratios of 1.25, 2, and 3. All rotatinq components were made of aluminum
and the support structures are made of steel. High-speed,
precision ball bearings were used at each end of the cylinder
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and these were oiled by an oiling device wnlcn automatically
pumped oil into each bearing every 20 seconds. The oil lines
were led inside the support sting beside the air hose.
The 152 mm cylinder was manufactured by Tech
Development, Incorporated in Dayton, the manufacturer of the J
air turbine motor used to drive the cylinders. Tolerances
and concentricity were carefully held; however, the larger size,
centrifugal forces, and the requirement to utilize one set of
end plates on each of the four cylinder sleeves necessitated
dynamically balancing all end-plate, cylinder combinations.
Care was taken in providing match marks to assure the cylinders
bere kepein the balanced configuration during reassembly.
After balancing, each cylinder sleeve with all
end plate combinations was instrumented and spun up in a test
cell to check operation under still air conditions. These
tests were completely successful, and the cylinders were then
released for wind tunnel testing.
Thc mod01 car was rectangular in plan form with
dimensions of 383 mm long, 295 mm wide, by 38 mm thick. All
sides were streamlined with approximately a 45' wedge angle
rounded at the top surface. As with the 51 mm cylinder, the car was capable of being mounted to the balance system, free
from the floor, so that the influence of car drag would be included
in the measured results.
3 - 2 . 4 Model Mounting i n Wind Tunnel
Since for the free stream tests, it was necessary
to elevate the aylinder about 30.5 mm above the tunnel floor with
a relatively large-diameter, rigid sting, it was necessary to
provide a streamlined housing around but free from the sting in
order to prevent drag loads on the sting from being transmitted
to the balance system. A typical photograph of the tower fair-
ing used for the 152 mm cylinder is shown in Figure 3.4
In view of the s i z e of t he housings i n r e l a t i o n t o the cylinders, it was thought t h a t t he test data would be affected by the presence of the housing. Therefore, a mirror
image streamlined s t r u t was designed t o extend from the c e i l i n g of the test sect ion down to , but no t touching the cylinder. Each streamlined housing and mirror s t r u t was carefu l ly al igned r e l a t i v e t o the tunnel cen te r l ine a s w e l l a s r e l a t i w t o each
other. Clearance between the streamlined members and the cyl inder was of the order of 3 m o r less. A pic ture showing t h i s test setup is presented i n Figure 3.5.
Tests w e r e run f o r each cyl inder and p l a t e com- bination with the lower housing only and with both the lower housing and the mirror s t r u t . Any differences i n the data noted was then used t o cor rec t the aerodynamic data f o r the e f f e c t of
the lower housing so t h a t free stream cyl inder data would r e s u l t .
A much simpler procedure was used f o r munt ing t h e cylinder and c a r f o r the a tm~spher i c boundary l aye r tests.
The c a r was constructed so it could be clamped t o the s t i n g extension o f the balance system a t t he po in t where the s t i n g extension entered the tunnel f loor . About 3 mm clearance between the c a r and the f loo r was provided t o prevent f r i c t i o n between the car and the tunnel f loor . The cyl inder a l s o was mounted on the s t i n g with minimal clearance between the c a r and the cylinder. Figure 3.6 depicts this mounting arrangement f o r t yp ica l
152 mm cylinders. Both top p l a t e only and top plus bottom end p l a t e configurations were used f o r these tests.
The preceding munt ing configurations w e r e those used f o r the primary data acquis i t ion e f f o r t , Additional tests not l i s t e d i n the test matrix, were used t o obta in back- ground data. Some of these tests included the use of one revolving and one s ta t ionary end p l a t e under f r ee stream con-
d i t i ons ; a t tach ing the c a r t o the f loo r bu t l e t t i n g it f l o a t
f r ee from the cylinder, mounti.ng the cyl inder on the f l o o r with- out the car ; mounting the c a r alone i n f ron t of the pressure rakes
Figure 3.4. Side V i e w , 152 mm Cylinder i n Tunnel With Lawer Streamlined Fairing Only.
Figure 3.5 . Front V i e w , 152 nun Cylinder i n Tunnel With Lower Streamlined Fairing and Mirror Strut .
Figure 3 . 6 . 152 m Diameter Cylinder and Car Ready for Simulated Boundary Layer TesL, eJd = 3 End Plates , AR = 6 .
a t var ious angles o f a t t a c k t o study the e f f e c t on the veloci ty
p r o f i l e of t he car; mounting an e levated t r ack model i n f ron t of
the rakes; and m u n t i n g t h e cy l inder and c a r on an e levated
t r a c k t o determine t h e a m u n t o f low a l t i t u d e veloci ty enhance-
m n t t h i s arrangement would make.
3.2.5 Ca l ib ra t ions and Operational Checks
Standard force ca l ib ra t i on techniques w e r e used t o c a l i b r a t e t h e balance systems. A cy l ind r i ca l extension w a s
mounted on the balance system s t i ng , and varyir~y s la Lic loads w e r e app l ied a t various heights and d i rec t ions by means of a
load ing f i x t u r e a s shown i n Figure 3.7. Outputs of each data
channel w e r e recorded on the automatic data acquis i t ion system,
and matrix ana lys i s techniques w e r e used t o co r r ec t f o r load
i n t e r a c t i o n s . The c a l i b r a t i o n data obtained w e r e found t o be
l i n e a r and repeatable over t h e e n t i r e range of i n t e r e s t .
A f t e r a l l c a l i b ra t i ons w e r e completed and a l l
computerized da t a processing and p l o t t i n g rout ines w e r e checked, an o v e r a l l opera t ional check was conducted. With one of t he
152 mm cy l inders mounted on the balance system, loads of t h e
o r d e r o f 222 N and 155 N w e r e appl ied individual ly a t the top, cen t e r , and bottom o f t h e cyl inder i n bath the l i f t and drag
d i r ec t ions . The balance response t o each load w a s recorded on
the da ta acquis i t ion system, punched i n t o paper tape , and then t h e tape was computer reduced and p lo t ted . The r e s u l t s indicated
accuracy o f about 1 percent and &ikoasLraked t h a t t he e n t i r c system was opera t ing s a t i s f a c t o r i l y .
No further checks w e r e done f o r the 51 mm cy l inder , bu t the test procedure for t h e 152 rruu cy l inder w a s approached caut iously , one s t e p a t a t i m e because of t he
p o t e n t i a l s a f e t y hazard associa ted with s t ruc tu re f a i l u r e of
t h i s cyl inder .
Af t e r the 152 mm cy l inder was mounted on the
balance system, t h e cy l inder was spun throughout i ts range with
no tunnel a i r blowing t o make sure t h a t t he cyl inder d id not
Figure 3.7. Calibration LoadFng Fixture for Wind Tunnel Balance System.
e x c i t e any resonances i n the balance system, which was less r i g i d than the f loo r of the test cel l i n which the cyl inder had been run-up previously. These tests showed t h a t cylinder operation over the range from 0 t o 19,000 rpm w a s e n t i r e l y sa t i s fac tory . During this run, data were recorded and processed t o assure ourselves t h a t no undesirable t a r e loads resu l ted from the incoming and exhausting a i r used i n driving t h e turbine. No problems w e r e observed.
F ina l ly , a cyl inder having an aspect r a t i o of 4
and end p l a t e t o cyl inder diameter r a t i o of 2 (e/d = 2 ) was given a preliminary test over its e n t i r e ro t a t ing speed range a t f r ee
5 stream Fteynolds numbers varying from 0 .5 x 10' t o 2.9 x 10 . Results indicated t h a t a test lbynolds nurtlber of 1.45 x 10 5
would provide data t h a t could be extrapolated r e l i ab ly t o fu l l - s i z e cyl inders . This is comparable t o a tunnel speed of 45 f t / sec (13.7 m/s) .
3.2.6 Atmspheric Boundary Layer Simulation Study
During the period when the mdels w e r e being developed, University of Michigan personnel developed the methods t o be used f o r generating an a r t i f i c a l l y thickened boundary l a y e r beginning a t the t w n e l which simulated the e a r t h ' s atmos-
pher ic boundary layer .
The p r o f i l e se lected, obtained from Reference 40, w a s t h a t t yp ica l o f wind blowing over f l a t , grassy p la ins i n which wind speed var ies a t h '*18. ~ l t h o u g h t h i s p r o f i l e i s s l i g h t l y d i f f e r e n t from the h p r o f i l e l i s t e d i n our design c r i t e r i a , w e bel ieve it simulates r e a l conditions c losely , $ad
hence is s a t i s f a c t o r y for this study.
The methods used f o r boundary l aye r simulation were s i m i l a r t o those used by Professor W i l l m a r t h a t the
University of Michigan f o r s tud ies of wind loads on buildings.
A photograph of the e x p e r i ~ n t a l se tup f o r the 152 xWn cylinders is presented i n Figure 3.8. Boundary layers of up t o 0 .6 m
t h i ck were obtained by t h i s method f o r the wind tunnel speeds planned fo r the t e s t s .
Figure 3 . 8 . lkthod of Simulating A t m o s p h e r i c B o u n d a r y Layers for 1 5 2 mm C y l i n d e r .
As can be seen in Figure 3.8, beginning at the point where the entrance cone enters the test section, three
rectangular strips having a 127 nun high by 12.7 mm wide cross- section were spaced on 457 mm centers across the tunnel floor.
From there on, twelve, 12.7 nmn diameter rods followed by six, 19 m quarter round mldings spanned the tunnel floor at 0.3 m
intervals.
In order to assure a uniform boundary layer pro-
file across the entire tunnel width, auxiliary fans directed
toward the tunnel walls were placed in the entrance cone of the tunnel. Excellent results were achieved. Tests were con-
ducted and data were reduced in a form that would permit the
test director to specify a value of Voo which would provide the
desired profile and the desired reference wind velocity at a
given reference height above the floor. The reference height
selected was that at the midpoint of the cylinder when munted
on a car.
Typical results are plotted in Figuree 3.9 and
3.10a. Figure 3.9 depicts the standard tunnel boundary layer
which demonstrates that our free-stream tests for both the 51 nun and 152 mm cylinder were conducted in a uniform vleocity field.
In all free-!Stream tests Lhe bottom of the cylinder vaa elevated
12-inches (305 nrm) above the tunnel floor. The reader should
note that although the 51 mm cylinder and the 152 mm cylinders having aspect ratios of 3 and 4 were completely immersed in the
variable boundary layer, the longer aspect ratio cylinders (5 and
6) were partially in free stream flow. This test condition was
beyond the control of the University of Michigan because a 0.6 m
thick boundary layer was the maximum that could be generated.
One of the primary reasons for conducting the
boundary layer test.series was to help validate the air load
model used in our Madaras system performance simulation computer
program. The following paragraphs describe this air load model.
0.0 0.2 0.4 0.6 0.8 1 .O 1.2 VELOCITY RATIO
Figure 3.9. Tunnel Boundary Layer Profile Prior to Modification, 11 m/s Free Stream Velocity, .97 ilt Above Floor. Curve 3 is Centerline Profile.
0.0 0.2 0 . 4 0.6 0.8 1.0 1.2 VELOCITY RATIO
AR = 6
0 . 0 0 .2 0.4 0.6 0 . 8 1.0 1.2 VELOCITY RATIO
Figure 3.10a. Simulated Atmospheric Boundary Layer for 152 mm Cylinder Having AR = 3 and AR = 6.
RESULTANT GROUND LEVEL LOCAL WIND RELATIVE TO ROTOR RELATIVE T O TRACK
" T R A C ~ -TANGENT TO TRACK
L x
Figure 3.10b. Ekman-like Spiral Resultant Wind Relative to Different Sections of the Rotor Produced by Vector Addition of Translatory Motion of Rotor Car and Wind Boundary Layer Near Earth's Surface.
Two airload distributions are imposed on a rotor
which is moving alona a track at a speed, Vt: (1) a uniform
airload versus rotor height caused by rotor car motion along the
track; and (2) a nonuniform atmospheric boundary layer airflow
distribution versus rotor height caused by the wind blowing
over the surface of the earth at an angle @ relative to the
track. The combination of these two flows yields a resultant
velocity envelope along the height of the rotor that somewhat
resembles an Ekman spiral* as shown in Figure 3.10b. Since
this combination of air flows cannot be obtained in a conventional
wind tunnel, it became necessary to develop an empirical model
to predict the spira.1-like airload distribution on the rotor.
Our computational procedure first included the
determination of the magnitude and direction of the resultant
local wind velocity vector VR versus rotor height as a function
of: (1) the free-stream wind vslocity, V relative to the W track at any given track location; (2) the wind boundary layer
distribution; and (3) the constant track speed of the rotor
car, Vt.
Then, for a given rotor size (aspect ratio,
rotor diameter, end plate size, and number of end plates) and
the appropriate value of U/VR~ (ratio of rotor surface speed
to resultant wind speed at height h) we computed the spiral-
like airload vector distxihi~t.ions of lift and drag as s
function of height. These distributions were integrated relative
to rotor height to obtain the total lift and total drag forces,
and then the centroids and lines of action of the total lift
and total drag forces relative to the line of tangency to the
track were computed.
* Ekman - Theory first applied to slow currents at ocean
floor - large scale plus coriohis effect "~ber die Beinflussung von Windbahnen durch Gegirge" - Bietr. Phys. ~tmosphare 19: 272-274; 1932.
The final step was to resolve the total lift
ant total drag vectors to determine the net normal and tangential
force components relative to the track caused by the two airload
distributions. These normal and tangential values were then
used in our Madaras performance simulation computer program to
compute rotor loads and power output.
The aerodynamic data obtained from our boundary
layer tests were used as an independent means for validating
our ability to reliably compute the total lift force, the
total drag force, and the centroid of these forces caused by
the nonuniform boundary airload distribution alone.
Using actual measured boundary layer velocity
profiles for a given cylinder size (such as that in Figure 3.10a
for a cylinder having an aspect ratio = 6) and using CL and
CD versus U/V data from freestream wind tunnel tests, we
computed resultant values of CL, CD, and centroid locations
of these forces using the approach described above for the
condition of a stationary rotor car (i.e., Vt = 0). Direct
comparisions were made of the computed CL, C ~ f and centroid
data with respective data measured under comparable conditions
during the simulated boundary layer flow tests. This
comparison indicated that errors in the computed force and
centroid data were less than 3 percent. Therefore, the model
described above' was considered to be satisfactvry for use in
our performance computations.
3.2.7 Typical Cylinder Test Procedure
A brief description of a typical free stream
test is given to assist the reader in understanding the test
conditions and the resulting data. Nearly the same procedure
was used for the boundary layer tests.
A f t e r t h e c y l i n d e r was mounted i n t h e tunnel
and a l l f a s t e n e r s were checked, t h e ins t rumenta t ion a m p l i f i e r s
w e r e ad jus ted t o t h e i r p r e t e s t p o s i t i o n s . Instrumentat ion
c i r c u i t s were normally l e f t energized a t a l l times, even over-
n i g h t , s o t h a t a l l systems would be thoroughly warmed up and
s t a b i l i z e d p r i o r t o t h e t e s t .
Barometric pressure readings were taken from
a p rec i s ion mercury barometer, and p r e t e s t zero readings w e r e
then recorded on punched paper t ape . A t e s t l o g was kept
throughout t h e t e s t by t h e t e s t d i r e c t o r . Two o t h e r opera to r s
were required: one t o opera te t h e tunnel and one t o r e g u l a t e
t h e a i r flow which drove t h e c y l i n d e r tu rb ine .
Next, tunnel a i r was a c c e l e r a t e d t o the d e s i r e d
speed, s t a b i l i z e d , and da ta readings from a l l channels were.
recorded on paper t ape . This t e s t p o i n t represented t h e zero rpm
fo rce measurement on t h e cy l inder . The ins t rumenta t ion system
" f reezes" a l l readings a t t h e i n s t a n t a "Read" but ton is pressed
i n o rde r t o provide choronological ly co inc iden t readings from
s e v e r a l measurements, which were then punched i n t o t h e paper tape .
D i g i t a l readouts on panel v o l t meters were a l s o a v a i l a b l e t o
v i s u a l l y m n i t o r each measurement a t any t i m e .
From t h i s p o i n t on, t h e c y l i n d e r motor a i r was
tiimed on, and c y l i n d e r speed was c a r e f u l l y r egu la ted and
s t a b i l i z e d near a speed corresponding t o U/V = 0.5. (The
vel.ncity, U, i s t h c circumferei~Lfd1 speed ( 2 r r n ) and tr is t h e
f r e e s t ream tunnel speed.) When the rps counter i n d i c a t e d speed
had s t a b i l i z e d , t h e "Read" but ton was pressed, and da ta were
recorded a s before.
The c y l i n d e r speed was success ive ly inc reased
i n U/V increments o f 0.5 up t o a t l e a s t U/V = 5 o r poss ib ly
h igher i f it appeared from t h e panel readings t h a t c y l i n d e r s t a l l
had n o t occurred. During t h i s e n t i r e procedure, t h e tunnel
o p e r a t o r c a r e f u l l y r egu la ted h i s p r o p e l l e r speed t o maintain
cons tan t q, a s read from a manometer. Thus, each da ta set was
o b t a i n e d a t near ly c o n s t a n t q over t h e e n t i r e U/V range. Care-
f u l a t t e n t i o n had t o be pa id t o tunnel q, because t h e 152 mrn
c y l i n d e r s caused cons iderable turbulence, e s p e c i a l l y when t h e e/d
= 1.25 end p l a t e was used. A s end p l a t e s i z e increased , the
t u r b u l e n c e over t h e t o p o f t h e c y l i n d e r decreased, and tunnel
f a n b lade s t a l l was n o t as much of a problem.
Upon recording da ta a t t h e maximum r p m , t h e
c y l i n d e r was p e r m i t t e d t o dece le ra te t o zero rpm, and a complete
d a t a set a t zero rpm and a t t e s t wind speed was taken. The
t u n n e l was then s h u t down, and when q dropped t o zero, a post-
test zero was recorded.
Configurat ion changes such a s adding o r
removing t h e mi r ro r s t r u t o r changing t h e end p l a t e s were made,
and then t h e procedure was repeated. L
A f t e r a l l runs a t a given aspec t r a t i o and a l l
end p l a t e s i z e s were completed, t h e da ta were computed, p l o t t e d ,
and analyzed. I f a l l appeared s a t i s f a c t o r y , approval was given
t o change t o t h e n e x t a s p e c t r a t i o .
3 . 3 FREE STREAM TEST RESULTS
I n U r i s and t h c fol lowing pab-agraphs, w e wili prceserit
t h e more important r e s u l t s o f t h e wind tunnel tests.
The primary conclusions drawn from t h e s e tests were:
A 1 1. test models operdlad s a t i o f a c t o r i l y .
i T ~ G genera l arrangement and test procedure w a s s a t i s f a c t o r y , and t h e method for genera t ing the s imula ted atmospheric boundary l a y e r was s a t i s f ac to ry .
e T e s t r e s u l t s were s a t i s f a c t o r y , and CL and Cu ourves c o r r e l a t e d we l l wi th those i n t h e l i t e r a t u r e .
The d a t a a r e s a t i s f a c t o r y f o r computing fo rces on f u l l - s i z e d cy l inder s .
Since t h e 152 mm data s e t was t h e r rms t r e l i a b l e and
ex tens ive , . only t h i s d a t a w i l l be presented.
3.3.1 T v ~ i c a l S e t o f Raw Free-Stream Data
The i n i t i a l ou tpu t of t h e s e tests from t h e com-
p u t e r cons i s t ed of a number o f d a t a t a b u l a t i o n s and Cazcomp p l o t s
o f t h e da ta . During da ta processing, t h e da ta were read i n t o t h e
computer by means o f punched paper t a p e , and t h e r e s u l t s were
s t u d i e d by t h e o p e r a t o r using a CRT d i sp lay . A t t h i s s t a g e
a d d i t i o n a l i d e n t i f y i n g inpu t s were en te red , and da ta e d i t i n g was
done. The approved e d i t e d da ta was then s t o r e d , f i n a l computations
were made, and output was t a b u l a t e d and p l o t t e d . .The f i n a l r e s u l t s
were a l s o s t o r e d on d i s c .
A s e t o f f i n a l raw d a t a ou tpu t inc ludes :
F ina l Data Tabulation
p l o t , o f CL versus U/V
P l o t o f CD versus U/V
P l o t o f H P versus U/V
A t y p i c a l s e t of t h e s e d a t a f o r t h e free-s tream
t e s t 363-14 and 363-14A a r e presented i n Tables 3.3 and 3.4 and i n
Figures 3.11 and 3.12. Orlly one r o t a t i o n a l .horsepower p l o t i s
presented (Run 36 3-14) because t h e r e was no d i f f e r e n c e between it
and 363-14A. These and a l l o t h e r t e s t s a r e l i s t e d i n Tables 3.1 and 3.2.
From t h e da ta presented , t h e reader can s e e
t h a t t h e expected l a r g e CL values have been v e r i f i e d , and a t y p i c a l
d rag bucket i s a l s o ev iden t . The d a t a t r e n d s seem smooth and
o rde r ly .
The raw da ta w e r e c o r r e c t e d f o r t h e s t r u t e f f e c t
t o o b t a i n t h e n e t f r e e s t ream d a t a by adding o r s u b t r a c t i n g
t h e d i f fe rence between o r d i n a t e s o f two comparable curves a t a
given U/V, a s appropr ia t e . Thus, f o r t h e CL curve a t U/V = 5 ,
s i n c e t h e a d d i t i o n o f t h e sccond (mir ror ) s t r u t (363-14A)
caused an apparent inc rease i n CL d a t a from t h a t when only t h e
lower f a i r i n g was used (363-14) , t h e d i f f e r e n c e between t h e two
curves a t U/V = 5 was s u b t r a c t e d from t h e value o f 363-14 t o
o b t a i n the cor rec ted f ree stream curve.
TABLE 3 . 3
FREE-STREAM DATA FOR CYLINDER WITH BOTTOM F A I R I N G ONLY
RUN 36314 PM 1?/3? I?: 7?: 7? 4TM PRESSURE 74.80 CM HG
CYLINDER HEIGHT 36. 000 IN CENTER LINE HEIGHT 30. 500 IN DIfiMETER 6. 000 IN VELOCITY 43. 000 FT/SEC
E/'D 3. 000 REYCIOLDS FlClMBEE 14% t h 1
U/V CL CD CHL CMD Y ( tlL) J'D Y ( MD) /D CIP REV/GEC
U/V LIFT LB DRAG LB ML IN-LB Mb IN-LB TEIVlV F DENSITY P3 VEL
TABLE .3 .4
FREE STREAM DATA FOR CYLINDER WITH
BOTH MIRROR STRUT AND BOTTOM FAIRING
RUN 36314A FM 1?/3? I?: 7?: 7? ATM PRESSURE 74.80 CM HG
CYLINDER HEIGHT 36. 000 IN CENTER LINE HEIGHT 30. 500 IN DIAMETER 6. 000 IN VELDCITY 45. 000 FT/SEC
E/D 3. 000 REYNOLDS NUMBER 145161.
U/V CL CD CML CMD Y(RL)/D Y(MD)/D HP REV/GEC
U/V LIFT LB DRAG LB ML IN-LB MD IN-LB TEMP F DENSITY FS VEL
91 - t - =D + Lower Fairing Odly
4 8 Lower Fairing P l u s I ' + @ + . Mirror Strut
I e
Figure 3.11. CL and CD versus U/V for
AE = 6 , e/d = 3, Lower Fairing only and Lower Fairing Plus Mirror Strut .
Ficnre 3.12. HP versus U/V for AR = 6, e/d = 3. Neither Fairing Nor Strut Has any Ef fec t
v on Data.
A s i m i l a r t echnique was used t o c o r r e c t t h e CD
curve, b u t t h e p roces s was r eve r sed : t h e d i f f e r e n c e was added
t o t h e 363-14 CD curve .
No c o r r e c t i o n s f o r t h e horsepower curve w e r e
r equ i r ed . Note t h a t it took about 5.2 hp t o d r i v e t h i s c y l i n d e r
a t 8,640 rpm (184 r p s ) . Our method f o r deve lop ing e q u a t i o n s f o r
s c a l i n g t h e s e power d a t a t o a r o t o r o f any geometry and s i z e is
p re sen ted i n Paragraph 3.3.7.
S e l e c t i o n o f T e s t Reynolds Number
swanson20 determined t h a t free stream Reynolds number, R , was. n o t t h e governing .parameter f o r f low s i m i l a r i t y f o r
a r o t a t i n g c y l i n d e r a s it is f o r an a i r f o i l . H i s exper iments
on an i n f i n i t e a s p e c t r a t i o c y l i n d e r i nc luded a c q u i s i t i o n o f
d a t a a t va lues o f R r ang ing from 0.36 x l o 5 t o 5 x l o 5 and
f o r U/V va lues from 0 t o 17. H e determined t h a t beyond U/V
v a l u e s , o f about 1 .0 , t h e r e appeared t o be v i r t u a l l y no d i f f e r -
ence i n t h e CL ve r sus U/V and CD ve r sus U/V d a t a a s a func t ion
o f R. A s t h e U/V , i nc reases beyond 1, t h e r o t a t i n g c y l i n d e r
i s g radua l ly immersed i n an a i r f l o w that is s i g n i f i c a n t l y
h i g h e r i n speed than t h a t i r l t h e f r e e s t ream, and hence it i s
t h i s l o c a l flow reg ion t h a t governs flow s e p a r a t i o n and
t r a n s i t i o n .
I n view o f Swanson's expe r i ence , w e a n t i c i p a t e d
t h a t it would n o t be necessary t o conduct o u r exper iments a t a
f ree-s t ream Reynolds number a t o r beyond t h e c r i t i c a l Reynolds
number o f a s t a t i o n e r y c y l i n d e r i n an a i r s t r e a m (o f t h e o r d e r o f 5 3.5 x 10 ) . Tests a t t h i s speed would havc pushed the speed
and power requi rements , and t h e wind t u n n e l ba l ance system beyond
p r a c t i c a l limits. Thus, w e conducted a s imple series o f tests t o
check Swanson's o b s e r v a t i o n s and t o determine t h e va lue o f f r e e
s t r e a m R beyond which C D v e r s u s U/V d a t a would be r e l a t i v e l y
u n a f f e c t e d by f u r t h e r i n c r e a s e s i n R.
The r e s u l t s o f t h i s s tudy are p l o t t e d i n F igure
3.13. Data from b o t h t h e 51 mm diameter and 152 mm diameter
c y l i n d e r s w e r e used where a v a i l a b l e . W e a l s o ove r l ayed CL and
C D d a t a from a d j a c e n t d a t a s e t s t o check e f f e c t s o f changes i n
R. FrQm t h i s s t u d y w e determined t h a t adequa te test r e s u l t s
would be o b t a i n e d a t R = 1.45 x l o 5 , which was e q u i v a l e n t t6 i~
t i - l n n e l speed o f abou t 13.7 m / s . Thus, t h e e n t i r e tes t program -
5 w a s run a t a Reynolds number of about 1 . 4 5 x PO . ~ u r t k e r , to
p r e s e r v e t h i s d e s i r e d running c o n d i t i o n , care w a s e x e r c i s e d t o
ruri a l l t e s t s a t c o n s t a n t dynamic p r e s s u r e .
T h e r e t o r e , since Reynolds number ef fect.s have
been p r o p e r l y cons ide red , w e w i l l be a b l e t o scale t h e wind
t u n n e l d a t a d i r e c t l y t o f u l l - s i z e d c o n f i g u r a t i o n s o v e r t h e
e n t i r e t e s t ranges o f U/V, e /d , and AR.
3 . 3 . 3 B a s i c Free Stream. Data -- The complete set ul f r e e s t r cam aerodynamic d a t a
i s summarized i n Table 3.5 and Table 3 . 6 . This d a t a i s unique
i n t h a t it i s t h e most complete in format ion on r o t a t i n g c y l i n d e r
aerodynamic performance i n terms o f geometr ic v a r i a t i o n s t h a t
e x i s t s i n t h e l i t e r a t u r e tuday . 'I'he s d d i t i o i i of t .he boundary
l a y e r da t a ( d e s c r i b e d i n Paragraph 3 . 4 ) makes t h e data even
more c x t e n s i v e . 2
A t y p i c a l CD versus C p l o t a119 i t s accompany- L i n g CL ve r sus u/V p l o t a r e p r e s e n t e d i n F i g u r e s 3.14 and 3.15,
r e s p e c t i v e l y , f o r end caps hav ing d iameters t w i c e t h a t o f
t h e c y l i n d e r d i ame te r (e /d = 2 ) . The ~iumbered p o i n t s o n the
cu rve r e p r e s e n t t h e cor responding u/V va lues o f t h o s e p o i n t s .
F i g u r e 3.13. Study t o Determine T e s t Reynolds Number CD v e r s u s R for v a r i o u s Values of U/V.
TAELE 3 . 5
FREE STFXAM C, DATA
TABLE 3 . 6
FPXE STREAM C, DATA
: F i g u r e 3.14. F r e e s t r e a m CD v e r s u s cL2 f o r Var ious AR, Two
End Caps, e /d = 2 .
F i g u r e 3.15. F r ee s t r eam CL v e r s u s U/V f o r Var ious AR, Two End Caps, e/d = 2 .
A l l d a t a s e e m t o f i t smooth curves wi th minimal s c a t t e r except
f o r t h e AR = 5 curve a t U/V values o f 4 and 5. Since these most
i n a c c u r a t e p o i n t s a r e e i t h e r w i t h i n f 6 pe rcen t o f t h e co r res -
ponding CD va lue o r wi th in +3 pe rcen t of t h e corresponding CL
va lue , we b e l i e v e t h a t t h e d a t a s e t i s w e l l w i th in acceptable
accuracy l i m i t s . Fur ther , t h e f a i r e d d a t a t r e n d s were checked
i n o t h e r c r o s s p l o t s a s a funct ion of AR and e/d r a t i o , and
t h e s e t r e n d s w e r e found t o be c o n s i s t e n t wi th in t h e complete
d a t a set. It i s be l i eved t h a t t h e l a r g e r e r r o r s meritioned above
were t h e r e s u l t o f i ~ l c o ~ s i s t e n t behavior dur ing the o n s e t of
s t a l l and t h e beginning o f t h e super -c i rcu la t ion phenomena.
E r r o r band's due t o t h e ins t rumenta t ion were no l a r g e x than i1-
percen t . The uniformity o f the p l o t t e d r a w d a t a t r e n d s i n
Figures 3.11 and 3.12 a l s o i s i n d i c a t i v e t h a t t h e d a t a a r e
r e l i a b l e . 1
In view of t h e s a t i s f a c t o r y t r ends i n t h e data
s e t as a whole, w e be l i eve t h e da ta can be used conf iden t ly i n
performance s imula t ions o f f u l l - s i z e d Madaras systems. Other
d a t a c r o s s p l o t s w i l l be p resen ted i n paragraphs which follow.
3 -3.4 E f f e c t of e /d Rat io Var ia t ion on CL and CD .
Typical p l o t s o f CL versus CD, CL versus U/V,
and CD versus U/V f o r a l l va lues o f e/d r a t i o a r e presented
i n Figures 3.16 and 3.17. Data f o r a spec t r a t i o s 3 and 6
w e r e s e l e c t e d t o show the effect of e/d r a t i o f o r t h e bj-miting
va lues o f t h e a s p e c t r a t i o range s tud ied .
One of t h e f i r s t observa t ions one makes a f t e r
s tudy ing Figures 3.16 and 3.17 is tha , t CL m x d r a l ~ L i c a l l y
i n c r e a s e s a s e /d r a t i o i n c r e a s e s , and t h a t t h e i n c r e a s e i n CL
max caused by changing e/d r a t i o from 1.25 t o 2.0 i s much more
s i g n i f i c a n t than f o r changing e/d r a t i o f r o m 2 .0 t o 3.0 .
Fur the r as a s p e c t r a t i o i n c r e a s e s , t h e i n c r e a s e i n CL max
caused by e /d changes from 2.0 t o 3.0 becomes l e s s s i g n i f i c a n t .
Figure 3.16. Freestream CL versus C f o r AR of 3 and 6 and e/d Ratios of 1.25, 2, and 3, d = 158 mm.
U / V U / V
7
6
5
CD
1
3
2
I
0 0 I 2 3 4 5 6 0 I 2 3 4 5 6
u/v U / V
F i g u r e 3.17. F r e e s t r e a m CL and CD v e r s u s U/V, AR of 3 and 6', and e/d R a t i o s o'f 1 .25 , 2, and 3, d = 152 mm.
Thus it would appear t h a t an optimum des ign p o i n t may occur
n e a r e /d = 2 i n view o f t h e t r a d e o f f between t h e small CL max
ve r sus t h e l a r g e i n c r e a s e i n power r e q u i r e d t o s p i n t h e c y l i n d e r
when end p l a t e r a t i o i s i n c r e a s e d from 2 t o 3. (Power d a t a w i l l
be p re sen ted l a te r . )
For t h e CD cu rves , t h e e f f e c t o f a s p e c t r a t i o
o r induced d r a g i s apparen t , and one can see a s m a l l r e d u c t i o n
i n CD w i t h i n c r e a s e d e / d up u n t i l s t a l l occu r s . Beyond s t a l l ,
bo th l i f t and d r a g o f t h e e /d = 1.25 cu rves i s e s s e n t i a l l y unchanged.
Although CD f o r t h e e /d = 1.25 curves looks s m a l l a t U/V va lues
beyond s t a l l , t h e L/D r a t i o i s small and so i s power o u t p u t . I t
shou ld be no ted t h a t t h e maximum CD va lue f o r an e/d r a t i o o f 3
i s less than t h a t f o r an e /d r a t i o o f 2 f o r a l l a s p e c t r a t i o s ,
b u t t h a t t h e incrementa l change i n CD i s about t h e same f o r each
a s p e c t r a t i o s t u d i e d . This d i f f e r e n c e i n CD a l s o g i v e s weight
t o o u r p rev ious o b s e r v a t i o n t h a t t h e r e may n o t be enough improve-
ment i n aerodynamic performance t o j u s t i f y end p l a t e r a t i o s much
g r e a t e r t h a n 2.
3.3.5 E f f e c t o f Aspect Ra t io V a r i a t i o n on CL and Cn
F igu re 3.18 p r e s e n t s f o r e /d r a t i o s o f 1.25 , 2 ,
and 3 , a se t o f cu rves r e p r e s e n t i n g t h e v a r i a t i o n o f CL ve r sus
U/V and CD ve r sus U/V f o r each o f t h e a s p e c t r a t i o s t e s t e d .
The l i f t curve s l o p e s a r e c o n s i s t e n t , and t h e
pronounced d r a g bucke t s observed . i n e x i s t i n g r o t a t i n g c y l i n d e r
d a t a are p r e s e n t i n o u r d a t a .
There i s a d e f i n i t e i n c r e a s e i n CL max w i t h AR
i n c r e a s e f o r a given va lue o f e /d . However, i t i s i n t e r e s t i n g
t o no te t h a t t h e e f f e c t o f a s p e c t r a t i o on CL max dec reases a s
e /d i n c r e a s e s u n t i l t l e r e i s very l i t t l e e f f e c t on CL max
caused by a s p e c t r a t i o f o r e/d = 3.0. These curves a g a i n show
t h a t CL max i s a f f e c t e d more s t r o n g l y by e /d r a t i o t han by
a s p e c t r a t i o .
On t h e o t h e r hand, a s would be expec ted , a s p e c t
r a t i o i n c r e a s e s i n t h e .range t e s t e d caused marked r e d u c t i o n s i n
59
Figure 3.18. Freestream CL and CD versus U/V, AR of 3 to 6, and e/d Ratios of 1.25, 2, and 3 ; d = 152 - 0
C a s a r e s u l t o f dec reas ing induced d rag . L a t e r , w e w i l l show D
t h a t t h e i n c r e a s e d power r e q u i r e d t o r o t a t e t h e c y l i n d e r w i t h
i n c r e a s e d a s p e c t r a t i o i s n o t a p p r e c i a b l e , s o t h a t a good aero-
dynamic des ign p o i n t shou ld f a v o r use o f a h i g h e r a s p e c t r a t i o .
The improved wind speed nea r t h e t o p o f t a l l e r c y l i n d e r s a l s o
f avo r s a h igh a s p e c t r a t i o ; however, t h e r e s u l t i n g i n c r e a s e i n
c a r weight t o compensate f o r t h e r e s u l t i n g i n c r e a s e i n over-
t u r n i n g moment may l i m i t t h e magnitude o f t h e a s p e c t r a t i o .
I t i s an i n t e r e s t i n g h i s t o r i c a l no t e t h a t t h e
o r i g i n a l Madaras design proposed by P r o f e s s o r Klemin o f N e w
York U n i v e r s i t y was f o r a c y l i n d e r 125 f e e t h igh by 16 f e e t
d iameter ( A R = 7.8) However, P r o f e s s o r Pawlowski o f t h e
U n i v e r s i t y o f Michigan convinced Madaras t o reduce t h e c y l i n d e r
p r o p o r t i o n s t o 27.4 m high by 6.8 m i n d iameter i n o r d e r t o
reduce bending moments and o v e r t u r n i n g moments. 2
S ince w e showed (Paragraph 1 .16, Equation 1) t h a t
t h e Madaras system is in f luenced l a r g e l y by CL and n o t s o much
by CD/CL because t h e system i s a low speed t a n s l a t o r , des ign p o i n t s
f a v o r i n g t h e h i g h e r l i f t c o e f f i c i e n t s a t t h e expense o f h i g h e r
d r a g c o e f f i c i e n t s cou ld r e s u l t i n a more, ' favorable o v e r a l l sys tem
des ign . This i s t h e type o f compromise P r o f e s s o r Pawlowski
probably made i n 1931. S ince aerodynamic performance o f t h e
c y l i n d e r w i t h AR = 3 i s s o much below t h a t o f t h e o t h e r
c y l i n d e r s , an a s p e c t r a t i o o f 3 probably w i l l n o t be compe t i t i ve .
However, a o y l i n d c r hav ing an aspecL rc l t iu i n t h e 4 t o 6 range
w i t h an e /d r a t i o o f 2 appeared t o be a t t r a c t i v e .
3.3.6 Comparison of U D R I Aerodynamic Data w i t h P e r t i n e n t E x i s t i n g Data
W e b e l i e v e t h a t t h e wind tunne l d a t a gene ra t ed
by Klemin f o r Madaras and t h a t gene ra t ed by Betz , e t a l ,
( W t t i n g e n ) f o r t h e F l e t t n e r r o t o r s h i p a r e t h e most p e r t i n e n t
s e t s o f e x i s t i n g d a t a w i t h which t o compare o u r d a t a . Unfor-
t u n a t e l y , o n l y one o f Klemin's cu rves has been found, and it i s
f o r AR = 8 .1 w i t h e/d r a t i o o f 2.25. The Gat t ingen d a t a were f o r
t h r e e c o n f i g u r a t i o n s a l l of AR = 4 . 7 with e/d r a t i o s of 1 . O , 1 .7,
and 2.0.
A s a means o f providing checks of t h e da ta
r e p o r t e d he re in , we s e l e c t e d Klemin's da ta and t h e Gbttingen
d a t a having t h e e/d r a t i o of 2 f o r comparison. These comparisons
are p resen ted i n F igures 3.19 and 3.20.
The comparison with Klemin's da ta i s i n t h e form
o f l i f t - d r a g p o l a r s of Klemin's da ta and UDRI da ta e x t r a p o l a t e d
t o a s p e c t r a t i o of 8 f o r e /d = 2 . For s i m p l i c i t y , ou r extrapo-
l a t e d method accounted only f o r the decreases i n induced drag
caused by aspec t r a t i o . No account was made for t h e increased
CL which would r e s u l t from t h e e/d inc rease from 2 t o 2.25 and
due t o t h e a s p e c t r a t i o inc rease from 6 t o 8 . Nor was CD
decreased due t o t h e d i f f e r e n c e i n e/d r a t i o . Thus, we b e l i e v e
o u r e x t r a p o l a t i o n i s conservat ive .
Our e x t r a p o l a t i o n was accomplished by two
independent methods. F i r s t , a c r o s s p l o t was made o f t h e CD
d a t a versus AR f o r var ious va lues o f U/V f o r a l l e/d = 2 . This
i s shown i n Figure 3.21. From t h i s p l o t , appropr ia t e t r e n d s o f
CD v a r i a t i o n ve r sus AR a t var ious U/V l e v e l s were e s t a b l i s h e d .
Seconriiy, t h e decrease In induced dray cdused
by changing a s p e c t r a t i o from 6 t o 8 was computed by t h e w e l l
known induced drag equat ion:
I n this computation, t h e CL value used f o r each value o f U/V
from 0 t o 6 was t h a t obta ined from Run 362 (AR = 6, e/d = 2 ) . A f t e r computing t h e values o f C D ( a s p e c t r a t i o s
o f 8) f o r U/V va lues from 0 t o 6 by Equation 2, t h e computed
d a t a were p l o t t e d on the crvss p l o t , Figure 3.21. Then t h e da ta
t r e n d s and t h e computed da ta were c r o s s checked. A s can be seen,
t h e t r e n d s and t h e computed d a t a agreee r a t h e r we l l . The com-
puted d a t a then w e r e used t o p l o t t h e e x t r a p o l a t e d l i f t - d r a g
p o l a r on Figure 3.19.
Figure 3.19. Comparision o f UDRI Ext rapola ted Data wi th Klemin's Measured Data.
Figure 3.20. Comparison o f I n t e r p o l a t e d UDRI Data with Gattingen Data.
0 I I 1 I I I 1 I I I I I 2 3 4 5 6 7 .8
A s p e c t R a t i o
Figure 3 . 2 1 . C r o s s P l o t of CD versus AR for e/d = 2 . U s e d t o E x t r a p o l a t e ITDRI D a t a .for AR = 6 to AR = 8 D a t a for C o m p a r i s o n w i t h K l . e m i n ' s D a t a . . ,-
The r e s u 1 . t ~ i n Figure 3.19 a r e q u i t e encouraging.
Klemin's da ta shows lower drag than t h e UDRI d a t a i n the region
below U/V = 2.5. This r e s u l t i s v a l i d because Klemin ran h i s
tests a t varying Reynolds numbers i n o r d e r t o o b t a i n t h e d e s i r e d
U/V values because o f motor speed l i m i t a t i o n s . H i s lower U/V
ranges s t a r t e d a t R = 3.1 x l o 5 compared t o our t e s t Reynolds 4 number o f 1.45 x 10 . Thus a t zero o r low r o t a t i o n a l speeds,
h i s CD da ta should be lower than ours . On t h e o t h e r hand, our
conservat ive ly e x t r a p o l a t e d d a t a has h igher L/D r a t i o s than
Klemin's above U/V values of 2.5.
A second comparison o f our da ta was made wi th
t h e Gd'ttingen r o t a t i n g c y l i n d e r da ta der ived from t e s t s o f a
c y l i n d e r having an aspec t r a t i o o f 4.7 and an e/d r a t i o o f '2.0.
This comparison i s ' shown o n ' F i g u r e 3.20. UDRI d a t a were i n t e r -
pola ted from t h e c r o s s p l o t s shown i n Figures 3.21 and 3.22
t o ob ta in t h e curve which would be comparable t o t h e W t t i n g e n
d a t a . Thus, c o r r e c t i o n of both U D R I ' s CL and CD da ta were made,
and t h e r e f o r e a d i r e c t comparison was poss ib le .
The i n t e r p o l a t i o n procedure was s t r a igh t fo rward .
Figure 3.21, was used t o i n t e r p o l a t e values o f C versus U/V a t D AR = 4.7, and CL versus U/V d a t a a t AR = 4.7 was obta ined i n
a s i m i l a r manner from Figure 3.22.
We be l i eve t h e da ta c o r r e l a t e very w e l l , and
as i n t h e Klemin comparison, o u r d a t a appears t o have lower CD
values and h igher CL values than Gs t t ingen ' s , e s p e c i a l l y a t
h igher U/V values. The f a c t t h a t o u r d a t a were obta ined a t a
Reynolds number which was t h r e e t i m e s h igher than t h a t of t h e
Gd'ttingen t e s t s may account f o r t h e lower drag below U/V = 1.5.
3.3.7 Power Required t o Rotate Cylinder
P l o t s o f horsepower r equ i red t o r o t a t e c y l i n d e r s
having AR o f 3 and 5 a r e presented i n Figure 3.23. Both graphs
p r e s e n t power requi red a t t h e test wind speed (13.7 m / s ) versus
U/V, In a d d i t i o n , t h e AR = 3 graph p resen t s curves f o r power
r equ i red t o r o t a t e t h e cy l inder s i n s t i l l a i r ( r e f e r t o t h e rpm
Anpect R a t i o
F igure 3.22. Cross P l o t o f CL versus. AR f o r e/d = 2. Used . t o I n t e r p o l a t e UDRI Data f o r AR = 4 t o AR = 4.7 f o r Comparison w i t h t h e Gb'ttingen Data. (The apparent cu rva tu re shown by experimental p o i n t s f o r CL = CL(AR) f o r U/V > 3.0 could e x i s t , o r it could r e p r e s e n t d a t a scatter. More s tudy is requi red t o s o l v e t h i s anomaly. )
Figure 3.23. Power Required t o Rotate Cyl inder versus U/V and rpm f o r AR=3 and 6 and f o r e /d o f 1.25, 2 , and 3 . Both Power Required i n S t i l l A i r as W e l l as Power Required a t Vw = 13.7 m / s are Given f o r t h e AR = 3 Conf igura t ion , d = 152 mm.
sca le) . Note t h . a t more power is r e q u i r e d i n s t i l l a i r than i s
r e q u i r e d i n the' 'wind f o r a given va lue o f r p m . Th i s r e s u l t i s ' 17 c o n s i s t e n t with ' ' d a t a from Reid.
An impor t an t t r e n d t o n o t i c e i n t h e d a t a i s t h e
marked amount o f power r e q u i r e d t o r o t a t e a c y l i n d e r w i t h an
e /d = 3 end p l a t e r a t i o v e r s u s a c y l i n d e r w i t h an e /d = 2 end
p l a t e r a t i o .
Based on o u r c a l c u l a t i o n s , t h e power r e q u i r e d
t o t u r n a c y l i n d e r wi thout end p l a t e s a.L a speed of 10,000 rpm
varies from 224 W f o r a 152 mm c y l i n d e r hav ing an a s p e c t r a t i o
o f 3 t o o n l y 447 W f o r t h e sane d iameter c y l i n d e r hav ing an aspect r a . k i u of G '
The c a l c u l a t e d v a r i a t i o n o f power r e q u i r e d wi th
end p l a t e s i z e i s a n o t h e r m a t t e r , a s i s shown i n F igu re 3.4.
For o u r exper iment , t h e c a l c u l a t e d power f o r two d i s c (end
p l a t e s ) w i t h o u t a c y l i n d e r r e v o l v i n g a t 10,000 r p m i s as fol lows:
So, it can be seen t h a t it i s d e f i n i t e l y t h e e r ~ d p l a t e s and not
t h e c y l i n d e r t h a t absorb most o f t h e power.
Th i s comparison s u b s t a n t i a t e s o u r e a r l i e r conten-
t i o n , t h a t t h e d e s i g n e r pays a l a r g e p e n a l t y i n power absorbed i n
t u r n i n g t h e c y l i n d e r for a small ga in i n performance when one
selects an e /d o f 3.0 i n s t e a d o f an e /d of 2.0 f o r end p l a t e
s i z e .
Our computer program which s i m u l a t e s Madaras power
p l a n t performance r e q u i r e s i n p u t d a t a t o account f o r t h e v i scous
and b e a r i n g l o s s e s caused by r o t a t i n g t h e c y l i n d e r . Th i s i n p u t
must be capab le o f accoun t ing f o r f u l l - s i z e d c y l i n d e r power
l o s s e s f o r any geometry d e s i r e d . Although t h e power-required
d a t a p r e v i o u s l y d e s c r i b e d a r e adequate f o r model-sized c y l i n d e r s ,
w e needed t o develop a r e l i a b l e method f o r s i m u l a t i n g performance
o f f u l l - s i z e d c y l i n d e r s . Our method made use o f a set o f
emper ica l e q u a t i o n s developed by Theodorsen and ~ e ~ i e r ~ l and
t o independent ly check t h e p r e d i c t i o n c a p a b i l i t y o f t h e s e
e q u a t i o n s by o u r wind t u n n e l r e s u l t s and t h e f u l l - s i z e d c y l i n d e r
r e s u l t s o b t a i n e d by Madaras i n t h e 1930 I s .
Theodorsen and Regier conducted a series o f
a n a l y t i c a l s t u d i e s and tests t o determine t h e t o rque r e q u i r e d
t o revolve d i s c s , c y l i n d e r s , and s t r e a m l i n e d rods a t c o n s t a n t
speed. The purpose o f t h i s work w a s t o o b t a i n d a t a a t speed
regimes h i g h e r t han those s t u d i e d e a r l i e r by Von Karman, P r a n d t l ,
Ackeret , and Taylor . Theodorsen and Regie r ' s d a t a v e r i f i e d t h e
e a r l i e r work and a l s o prov ided in format ion a p p l i c a b l e t o Mach
numbers up t o 1 .7 and Reynolds numbers up t o 7,000,000. S ince
t h e s e tests extended t h e e a r l i e r r e s u l t s up t o and beyond t h e
range. o f Reynolds number o f i n t e r e s t t o t h e Madaras . s t u d y , w e
f e l t t h a t t h e r e s u l t i n g e q u a t i o n s shou ld be v a l i d and u s e f u l f o r
o u r computer s i m u l a t i o n .
These e q u a t i o n s f o r computing power r e q u i r e d t o
overcome v i scous l o s s e s a r e :
e For one end p l a t e ( d i s c ) i n t u r b u l e n t flow:
1 Power r e q u i r e d = CM z pa5 w 3 ( 3
where
For one c y l i n d e r i n t u r b u l e n t flow:
4 3 Power - r equ i r ed = CD r p r w 9.
where
In these equations, CM is the disc moment
coefficient, p is the air density, .a is the disc radius, w is the
angular velocity, CD is.the cylinder drag coefficient, R is
Reynolds number based on free stream velocity and cylinder (or
disc) radius, r is cylinder radius, R is the cylinder length,
and M is the coefficient of viscosity.
By appropriately combining these equations, an
empirical relationship for a cylinder of any diameter and length
and having either 0, 1, or 2 end plates was generated.
These equations were used to compute power
required to turn each of our 152 mm diameter rotor models, and
the computed results were compared with the wind tunnel test
data. Comparisons for all cylinder AR and e/d combinations
were made using both 1 and 2 end plates mounted on a rotor car
in a simulated atmospheric boundary layer. The comparison
showed good agreement between measured and computed values, with
a 3 a error of less than about 10 percent for all U/V values and
for all of the 24 configurations studied.
One final check was made to validate the use of
the preceding equations to predict power required to rotate
full-sixed rotors. The equations were used to compute power
requjred to turn the fill-sized Madaras rotor (27.4 m high by
6.8 m diameter) and to coinpute power'required for the rotors to
rotate on three of Flettner's rotor ships. The Madaras data,
obtained from Reference 4, is plotted with'our cumputed data in
Figure 3.24. The Flettner data were ubtained from several
sources, principally from Reference PO, Lhe accsunto by Flettner
of his work.
Power required data from all of these large
cylinders (including one of the large configurations analyzed
for this present study) were scaled to a rotor configuration
having 2 end caps with an e/d ratio of 1.35 and a 120 rpm motor
speed. These scaled results were plotted in terms of power/
unit length of rotor versus rotor diameter and are presented
in Figure 3.25.
RPM
Figure 3 .24. Comparison of Measured Power Required t o Spin the Full-Sized Madaras Rotor with Predicted Power Required Based on Equations ( 2 ) and ( 3 ) .
HEIGHT HEIGHT ROTOR FT (m) FT (m)
0 MADARAS 90.0 (27.4) 22.2 (6.8) + BADENBADEN 51. 1 (15.6) 9 . 1 (2.8) 8 BARBARA 58.4 (17.8) 13.1 (4.0) @ SMALL YACHT 19.0 (5.8) 3.6 ( 1 . 1 ) 0 PRELIM UDRl DESIGN 109.5 (33.4) 18.2 (5.5)
ALL ADJUSTED TO : e/d = 1-35 2 END PLATES 120 RPM
CYLINDER DIAMETER- FT (m)
Figure 3.25. Power/Unit Length versus .Diameter of Rotor Having Two End Caps, e/d = 1 .35 , and Rotation'al Speed of 1 2 0 rpm.
The Madaras d a t a were measured a f t e r t h e end
cap was blown o f f by high winds, s o t h e computation i n Figure
3.24 was made f o r t h e condi t ion of AR = 4.05 and e/d = 1.0.
One can s e e i n Figure 3 .24 t h a t t h e computed
r e s u l t s p r e d i c t lower power requirements than those measured.
W e b e l i e v e t h i s d i f f e r e n c e is p r imar i ly due t o t h e b e a r i n g
f r i c t i o n and d r ive gear l o s s e s of t h e l a r g e Madaras cy l inder .
These l o s s e s were n e g l i g i b l e f o r o u r 152 mm diameter t e s t models
which used ABEC-7 minia ture p rec i s ion b a l l bear ings and no d r i v e
gearing. Since b e a r i n g manufacturers have assured us t h a t
f r i c t i o n i n l a r g e diameter bearings w i l l be much g r e a t e r
( r e l a t i v e l y ) than our small bear ings , we assumed t h a t t h e bear ings
w e would use on our p resen t study would have f r i c t i o n of t h e
magnitude requi red t o s h i f t our computed curve upward u n t i l it
coinc ides with t h e Madaras curve. Thus, our computed power
requi red curve would co inc ide with t h e o r i g i n a l Madaras r e s u l t s .
We b e l i e v e t h i s adjustment w i l l y i e l d conservat ive
performance p r e d i c t i o n s i n t h e l i g h t o f t h e advancements i n bea r ing
manufacturing t h a t have been made s i n c e 1933.' This increment of
b e a r i n g power r equ i red versus rpm obta ined from Figure 3.24
was added t o each c y l i n d e r we analyzed dur ing our performance
computations.
The 'comparison of powers requi red t o r o t a t e t h e
va r ious F l e t t n e r and Madaras r o t o r s , shown i n Figure 3.25 f i t s
very w e l l t o an o r d e r l y p a t t e r n t h a t approximates' a func t ion which v a r i e s a s t h e f o u r t h power of the' diameter' , a s theory p r e d i c t s .
Therefore, we be l i eve t h a t the' 'use o f t h e previous power-required
equat ions wi th a p p r o p r i a t e a d d i t i v e ' f a c t o r s f o r mechanical and
e l e c t r i c a l l o s s e s i s a r e l i a b l e 'method f o r p r e d i c t i n g r o t a t i o n a l
power requirements f o r a l a r g e Madaras-type ro tor of any geometry.
3.4 BOUNDARY LAYER TEST RESULTS
The boundary l a y e r t e s t s conducted were those having
500 s e r i e s numbers i n t h e test matr ix i n Table 3.2 which
follows Paragraph 3.2.1. The 'pr'imary purpose of this tes't .series
was to obtain aerodynamic data for che'cking our. empirical model
which 'describes the 'combined air flow that .strikes.the cylinder
(see Paragraph '3.2.6) . The' 'tes'ts also enabled us to determine
whether or not one 'of the'MadarasV bas.ic assumptions were correct:
i.e., Madaras assumed that his wind tunnel aerodynamic coefficients
could be used without modifications to predict the performance
of rotor plant, even though the'conditions were not the same in
both cases. A comparison of comparable conditions is shown below.
Item - Air Flow
W %n'd Tu'n'n'e 1 ---
Roto'r' 'i'n' Potuer P l'an t
Constant V with Variable (boundary layer) Vw rotor heigk with rotor height
e/d Ratio 2 1.3
No. Rotating End Plates
1 on Top
Gap Between Rotor N/A Free stre'am Assumed none and Ground Plane,.' Actuallv 10 ft
This set of tests also provided insight into the effect of the trade-
off between aerodynamic coefficient magnitude and power required to
spin the cylinder in a boundary layer flow as a function of number
of rotating end plates.
These boundary layer tests were run at s free stream
Reynolds number of 1.45 x lo5, the same as that used for the free
stream tests.
Typical boundary layer data are presented in Figures 3.26
through 3.28, inclusive. Also, a typical data tabulation showing
forces, coefficients, and points of application of each force as
a function of U/V is shown in Table 3.6.
As with the free stream data, the data trends and accuarcy
are satisfactory. Also, the data verified our prediction of the
lift and drag force and their centroids obtained from our model
which combines the boundary layer wind distribution with the
uniform velocity caused by rotor car speed down the track.
ROTOR ON CAR 2 END PLATES BOTH ROTATI N G
ROTOR ON CAR I END PLAT AT TOP ROTATING
Figure 3 . 2 6 . C and CD Data from Boundary Layer Tes t s f o r efd Rat ios of 1 . 2 5 , 2 , and 3 , and f o r Aspect Rat ios of 3 and 6 .
F i g u r e 3.27. CL. CD, Power v e r s u s U/V f o r Bounda,ry Layer T e s t s f o r e/d Ra t io s o f 1 .25 and 2; one and two end Caps; and Aspect R a t i o s of 3 and 6 , d = 152 mm.
- AR= 6, e/d = 2 , 2 Moving end plates, free stream --- A R = 3, e/d = 2 , I Moving end plate at top, plus car, boundary layer
U/V Figure 3.28. Comparison of Aerodynamic Coefficients for
Configurations Madaras Considered to be Equivalent.
Figure 3.28 as well as 'Figures 3.'26 and 3..27 indicate that
he could use directly his Madaras' assumption wind tunnel data for
his plant performance 'computation was in error, and hence his
performance computat5ons ba'sed on these assumptions were over-
stated. The end plates function as air pumps which not only reduce
induced drag in the classical end plate sense; but also they aid
in developing additional circulation. Thus, at a g,iven value of
U/V, generally in the range of U/V > 2 ) a rotor with a larger end
plate will have a higher life coefficient. This effect is more
pronounced at the smaller aspect ratios than at larger ones. See
Figures 3.17 and 3.26 which demonstrate ,this observation.
Most of the conclusions drawn from the free stream data
apply to the boundary layer data; however, as expected, the
maximum lift coefficient in the boundary layer flow is lower
than that in free stream flow for similar geometrical configurations.
Some of the more important observations are:
The use of two end plates instead of one provides significantly higher lift coefficients at the expense of higher drag coefficients and higher motor power to spin the cylinder.
The small increase in CL resulting from the use of end plates having an e/d ratio greater than 2 is not justified in view of the power consumed.
Aspect ratio has very little effect on power consumption but increasing aspect ratio markedly improves lift/ drag ratio and C max at e/d ratios of about 2 (see Figure 3.27f. It appears that the optimum geometry in the range tested will be at an aspect ratio of 6 and at an e/d ratio of 3 or leas,
SECTION I V
STRUCTURAL AND MECHANICAL DESIGN
The o b j e c t i v e s o f t h i s s t ruc tu ra l -mechan ica l des ign
s tudy w e r e t o :
Def ine l o a d s t h e s t r u c t u r e must w i th s t and .
Develop a r e a l i s t i c des ign based on t h e o r i g i n a l Madaras c o n f i g u r a t i o n which w i l l f u l f i l l a l l des ign c r i t e r i a s p e c i f i e d i n Paragraph 2.3, and w i t h s t a n d a l l l oads de f ined h e r e i n .
Spec i f v s t r u c t u r a l c o n f i g u r a t i o n , f a b r i c a t i o n t echn iques , and purchased components.
The des ign r e s u l t i n g from t h i s s tudy is b e i n g developed
as a means f o r d e f i n i n g system f e a s i b i l i t y , and as such i s n o t
t h e l e v e l o f des ign which one would develop f o r p l a n t f a b r i c a t i o n .
Hence, t h e development o f an optimum des ign c o n f i g u r a t i o n and,
d e t a i l e d s p e c i f i c a t i o n s was beyond t h e scope o f t h i s s t u d y .
4 . 1 GROUND RULES
The o b j e c t i v e o f t h i s p o r t i o n o f t h e s tudy was t o d e f i n e
t h e s t r u c t u r e and t h e methods o f f a b r i c a t i o n . The s t u d y was
governed by t h e ground r u l e s l i s t e d below. The dimensions o f
t h e r o t o r were s i m i l a r t o t h e r o t o r t e s t e d i n 1934; however, t h e s e
dimensions do n o t n e c e s s a r i l y r e p r e s e n t t h e optimum r o t o r a s p e c t
r a t i o .
1. Rotor
Rotor Height = 27.4 m (90 f t )
Rotor Diameter = 6.8 m (22.2 f t )
Cap Height = 0.91 m ( 3 f t )
Cap Diameter = 10.2 m (33 .3 f t )
2. Design Wind and Opera t ing Condi t ions
o Wind d u r a t i o n curve hav ing a mean wind of 8 .1 m/s a t an a l t i t u d e o f 9 meters above t h e t e r r a i n . This curve w i l l be up-ra ted by t h e 0.167 power law t o
provide a des ign d u r a t i o n curve having a mean wind speed of 8.8 m / s a t r o t o r mid-height (16.8 m above t e r r a i n ) , a s shown i n
Figure 4 . 1 .
S t r u c t u r e must wi ths tand s teady winds of 53.6 m/s wi th r o t o r i n t h e nonoperat ional s t a t e .
S t r u c t u r e must wi ths tand wind gus t s o f 26,.8 m/s whi le o p e r a t i n g a t r a t e d wind speed.
The assumption i s made t h a t t h e r o t a t i o n a l v e l o c i t y o f t h e r o t o r w i l l be decreased f o r winds exceeding t h e man r a t e d wind v e l o c i t y such t h a t t h e power o u t p u t f o r t h e mean r a t e d condi t ions is maintained ( i .e . , t h e aerodynamic loading a t any s teady wind o p e r a t i n g condi t ion w i l l n o t exceed t h e aerodynamic loading f o r t h e mean design operatiwn c o n d i t i o n ) .
System land speed w i l l be nominally cons tan t a t 8 .9 i~t,/s (20 mph) .
a The r o t a t i o n a l v e l o c i t y of t h e r o t o r s w i l l be v a r i e d a s a funct ion o f t r a c k p o s i t i o n and wind v e l o c i t v t o o ~ t i m i z e Dower outwut.
For the r a t e d wind speed and nominal c a r speed de f ined above, t h e maximum . r o t a t i o n a l v e l o c i t y of t h e r o t o r is approximately 185 rpm.
3 . L i f e and Envi,ronmental Cri ter ia
Design l i f e o f t h e c a r exc luding t h e r o t a t i n g c y l i n d e r and bearings i s 50 years .
Design l i f e o f t h e r o t a t i n g c y l i n d e r i s 30 yea r s .
Design l i f e of t h e bear ings i s 30 yea r s .
Design l i f e uf the track,' road bed, and. r e s t r a i n i n g system i s 50 yea r s .
The s e r v i c e l i f e loading spectrum s h a l l be &filled on a b a s i s o f design wind cond i t ions and wind dura t ion curves.
U l t i m a t e and y i e l d f a c t o r s o f s a f e t y w i l l be a p p l i e d t o a l l design loads . These f a c t o r s w i l l be c o n s i s t e n t wi th app l i cab le design code requirements .
a The system must wi ths tand h a i l up t o 1-inch i n diameter , ope ra te i n a temperature range o f -51°C (-60°F) t o 4g°C (120°F), and opera te i n snow, r a i n , l i g h t n i h g , i c i n g , s a l t vapor, windblown sand, and d u s t .
HOURS IN YEAR
F i g u r e 4 . 1 . Wind Dura t ion Curve Uprated from 8 m / s Speed a t 9 m Above Ground t o 8.8 m/s a t 16.8 m Above Ground.
4. Sytem C r i t e r i a
.Track conf igura t ion - c i r c u l a r o r r ace t rack .
a Power o u t p u t compatible wi th requirements o f e x i s t i n g pub l i c u t i l i t y networks.
a F a i l s a f e automatic p l a n t opera t ion .
a No power s t o r a g e c a p a b i l i t y .
a One complete s p a r e r o t o r c a r p e r p l a n t .
a Met-hod f o r removing a c a r from t h e t r a c k f o r maintenance and r e p a i r s .
4 . 2 DESIGN LOADS
The inposed f o r c e s a c t i n g on t h e system have beell
c a t e g o r i z e d a s fol lows :
a Aerodynamic fo rces r e s u l t i n g from t h e Magnus e f f e c t .
a Body f o r c e s r e s u l t i n g from t h e r o t a t i o n o f t h e c y l i n d e r and t r a n s v e r s e motion o f t h e c a r .
a S t r u c t u r e dead weight.
a Loads due t o snow and i c e accumulation.
III a design effort: d i r e c t e d toward act.1.1a1 pliir~L cons t ruc t ion , '
cons ide rab le a t t e n t i o n w i l l have t o be given t o t h e dynamic response
o f t h e system. However, such an a n a l y s i s i s considered beyond
the scope of t h i s f e a s i b i l i t y s tudy.
4 . 2 . 1 Aerodynafnia Loading on the^. Cyl i n d e r .-
The v a r i a t i o n i n wind v e l o c i t y wi th alt.it1l.de is
i l l u s t r a t e d i n Figure 4.2 f o r t h e r a t e d wind speed a t t h e r o t o r
midheight of 8.8 m/s ( 1 9 . 7 mph) . The s t r u c t u r e a l s o must wi ths tand gus t s t o 26.8
m / s (60 mph) whi le o p e r a t i n g a t r a t e d cond i t ions . For t h e worst-
case cond i t ions , the d i r e c t i o n of the gus t v e c t o r w a s assumed t o
d i f f e r by 180' from t h e d i r e c t i o n o f t h e r o t o r c a r vec to r a s t h e
c a r t r a v e l e d a long t h e t r a c k . Thus, t h e r e s u l t i n g maximum r e l a t i v e
wind speed f o r an o p e r a t i n g r o t o r c a r would be 35.6 m/s ( 8 . 8 m/s
Figure '4.2. Wind Velocity Profile.
wind + 26.8 m/s gust) the normal and tangential forces are listed below. These loads could occur at any track location, depending
upon wind direction variation, as shown in Figure 4.3.
= 583,930 N (131,280 lb) Fresultant
These forces are also dependent on the linear velocity of the
cylinder surface (U) as shown in Figure 4.4, which is a simplifica-
tion of the spin schedule shown in Figure 5.1. The nonoperational
wind condition (53.6 m/s) results in a drag load of 114,180 N.
This load is significantly less than the operational gust condition.
Figure 4.5 shows the effect of cylinder rotation on the cylinder
pressure coefficients. This data illustrates the relative in-
significance of the nonoperational condition for the static
analysis of the system. Figure 4.5 is based on data taken from
Reference 13. These comets on the insignificance of the non-
operational condition apply only to the static analysis of the
system. Any analysis relating to the dynamic response of the
system should reconsider Ll ie nsnopcrstional ccrndi.tion.
on the Cap
The peak positive and negative pressures on the
underside of the cap have been defined as a function of radial
location for both the mean design wind condition and the operational
gust condition. The nonoperational gust condition is judged ,Lo
be less severe than the operational gust condition and will not
be considered further as a static load condftion.
These pressure distributions are shown in
Figure 4.6. The peak positive and peak negative pressures aeeur at circumferential locations which are diametrically opposed.
The peak pressures have been assumed to act on all 0r.a portion
of the cap in such a manner as to create a must critical load
condition with regard to the structural members in the cap and
the attachment of the cap to the cylinder.
+ - DEG
Figure 4.3. Operational Design Loads for 8.0 m/s (18 mph) Mean Design Wind Speed. Derived from preliminary Spin Schedule of. Figure 5.1, in which U / V was Varied at Each 5 O Incremental Position Around Orhit, Such that Ftan is Maximized.at Each Incremgnt.
U =LINEAR VELOCITYOF THE CYLINDER SURFACE
5.00- V = VELOCITY OF THE RELATIVE WINO VECTOR
I
U - v
CO cn
I
1 .oo ,-
r
Figure 4,.4. Batic U/V versus Track Locations f - ~ r 8 . 8 m/s Rated Wind Speed.
u = Resu l t an t Wind Vector
v = Linea r Ve loc i ty of t h e Cyl inder Su r face
p = Mass Densi ty o f A i r
P = Pressu re
F igure 4 .5 . P re s su re D i s t r i b u t i o n Around t h e Center o f a Ro ta t ing Cyl inder a t Various Values of U/V (.Taken from Reference 13) .
Figure
20- (9.6) -
, .
GUST 60 MPH WIND
11.0 12.0 13.0 14.0 15.0 16.0 (3.4 (3.7) (4.0) (4.3) (4.6) (4.9)
RADIUS - FT. ( m )
STEADY WIND DESIGN 20 MPH ( 8.9 n5/3)
- 2 0 - ( 9.6) -
11.0 12.0 13.0 14.0 (3.4)
15.0 (3.7)
16.0 (4.0). (4.3) (4.6) (4.9)
RADIUS - FT. ( m
4.6. 'Madaras Rotor Cap Peak Pressure versus Xadius.
4.2.3 System Accelerat ion Loads
The system acce le ra t ion loads a r e those loads
a s soc ia ted wi th t h e r o t a t i o n a l m t i o n of t h e cy l inder and t h e
t r ansverse motion o f t h e c a r a long t h e t r a c k .
The normal a c c e l e r a t i o n a s s o c i a t e d with t h e
r o t a t i o n o f t h e c y l i n d e r is equa l t o t h e product of t h e r ad ius
and t h e square o f t h e r o t a t i o n a l v e l o c i t y . A t a r o t a t i o n a l
v e l o c i t y o f 186 rpm, t h e normal a c c e l e r a t i o n a t t h e su r face o f
the c y l i n d e r i s 130.8 g, and a t t h e o u t e r r ad ius of t h e r o t o r
cap, 196.2 g. The maximum r a t e o f r o t o r spin-up, f o r design
purposes, i s def ined by a cons tan t a c c e l e r a t i o n from 0 rprn t o
186 rpm over a 15-degree a r c o f t h e c a r t r a c k assuming t h e c a r
i s t r a v e l i n g a t a r a t e of 8.9 m/s . This spin-up r e s u l t s i n a
t a n g e n t i a l a c c e l e r a t i o n of 0.97 g. The normal o r r a d i a l acce lera-
t i o n a s s o c i a t e d .with t h e motion of t h e c a r around a 457.3 m
(1500 f t ) diameter c i r c u l a r t r a c k i s 0.036 g. The t a n g e n t i a l
a c c e l e r a t i o n s a s s o c i a t e d wi th changes i n c a r v e l o c i t y a r e
n e g l i g i b l e and w i l l n o t be considered a s a design load.
4,.2.4 Snow and Ice Accumulation
The l i k e l i h o o d of l o c a t i n g t h e Madaras Power
P l a n t i n a temperate zone i s r a t h e r c e r t a i n ; t h u s , loading due
t o snow and i c e accumulation i s a concern. Snow accumulation
dur ing opera t ion . w i l l probably n o t be s i g n i f i c a n t f o r t h e
fol lowing reasons.
The cap is l o c a t e d i n a r e l a t i v e l y windswept environment while i n opera t ion .
The r a d i a l a c c e l e r a t i o n due t o r o t o r r o t a t i o n is q u i t e high. A t 186 rpm, t h e r a d i a l a c c e l e r a t i o n of t h e o u t e r ex t remi ty o f t h e r o t o r cap (R = 5 . 1 m) , the i ~ o r ~ n a l a c c e l e r a t i o n i s 196.2 g. Thus, t h e r a d i a l a c c e l e r a t i o n should prevent snow accumulation except i n the extreme c e n t e r o f t h e r o t o r cap.
The o u t e r por t ion of the r o t o r cap w i l l be s loped l i k e a roof a t an angle of 20 t o 30 degrees, which w i l l a i d i n the prevent ion o f snow accumulation.
I n t h e c a s e of severe storms dur ing which t h e
power p l a n t might be s h u t down, a s i g n i f i c a n t snow accumulation
could occur . A s t h e system i s r e s t a r t e d , t h e po in t a t which t h e
motion of t h e r o t o r would remove most of t h e snow is somewhat hard
t o d e f i n e because of t h e tendancy of snow t o adhere t enac ious ly t o
a . s t r u c t u r e . A t t h e same t i m e , ope ra t ion f o r moderate l eng ths of
time wi th s i g n i f i c a n t l y unbalanced loads on t h e t h r u s t bear ings
cou ld have a ve ry d e t r i m e n t a l e f f e c t on bear ing l i f e . Snow loads 2
could reach 2.39 k ~ / m ~ (50 p s f ) t o 3.83 kN/m (80 p s f ) i n some
r e g i o n s of t h e United S t a t e s ( a s def ined i n Reference 4 2 ) . I n
l i g h t of t h e d e t r i m e n t a l e f f e c t high snow loads can have on
b e a r i n g l i f e , the fo l lowing p o s i t i o n s have been taken regarding
snow accumulation.
0 The system wj..I..l. be designed t o accommodate a moderate snow load o f 0.4 8 klJ/m2. his amount o f snow accumulation would permit r e s t a r t s a f t e r seve re snow storms without provis ions f o r snow removal i n most a r e a s of t h e United S t a t e s where t h i s type o f power p l a n t is l i k e l y t o be s i t u a t e d .
I n those a r e a s where snow accumulation could exceed 0.48 k ~ / m ~ dur ing a severe storm, p rov i s ions f o r snow removal p r i o r t o restart must be provided.
A comment w i l l be made he re regarding snow accumulation i n the
nonopexa.tiona1 s t a t e . The snow load c a p a b i l i t y o f t h e r o t o r cap
whi le s t a t i o n a r y w i l l be s i g n i f i a a n t l y greater than 0 . 4 8 k ~ / m ~
s i n c e t h e s t r u c t u r a l members i n t h e r o t o r cap w i l l be s i z e d
p r i m a r i l y by t h e body fo rces a s s o c i a t e d wi th t h e normal a c c e l e ~ a t i o n
r e s u l t i n g from r o t o r r o t a t i o n . Limi ta t ion o f snow loads i n t h e
o p e r a t i o n a l s t a t e i s requ i red t o provide a more d e s i r a b l e bear ing
l i f e ; however, s i g n i f i c a n t l y g r e a t e r snow accumulations w i l l be
pe rmi t t ed i n t h e nonopera t ional s t a t e .
I c e aeeumulat ioi~ on the cap and c y l i n d e r m u s t be
considered. The l i k e l i h o o d o f cap i c e accumulation exceeding 2 0.48 kN/m i s r a t h e r remote; however, a r a t h e r small depth o f
ice accumulation can induce s i g n i f i c a n t loads i n t o t h e s t r u c t u r a l
e lements of t h e c y l i n d e r and cap when considering t h e r a d i a l
a c c e l e r a t i o n a s s o c i a t e d wi th r o t o r r o t a t i o n . Also, some concern
exis ts r e l a t i v e t o t h e dynamic unb.alance which would r e s u l t i f
t h e cap o r c y l i n d e r would shed a por t ion of t h e accumulated i c e .
The p o s s i b i l i t y of r o t o r unbalance would have t o be considered i n
a dynamic a n a l y s i s .
4.2.5 Car Weight, Wheel Loads, and Res t ra in ing Loads
The aerodynamic loading on t h e c y l i n d e r r e s u l t s
i n a s i g n i - f i c a n t over turn ing moment about t h e base of t h e c a r .
When t h e over tu rn ing momnt exceeds t h e r e s t o r i n g moment o f t h e
c a r , s t a b i l i t y w i l l be maintained. This over tu rn ing s t a b i l i t y
can be p r o v i d e d ' e i t h e r by v e r t i c a l r e s t r a i n t and/or by t h e weight
o f t h e r o t o r c a r .
The design r e s t r a i n i n g loads, wheel loads , and
c a r weight a r e governed by one o r more of four design requirements.
a . Operation a t t h e design wind condi t ion (8.3 m/s wi th t h e c a r t r a v e l i n g a t a t r a c k speed of 8.9 m / s ) .
b. Operation a t t h e gus t condi t ion which i n t h i s worst cond i t ion a n a l y s i s was assumed t o be equ iva len t t o a r e s u l t a n t cons tant wind speed of 35.8 m / s along t h e t r a c k w i t h t h e r o t o r t u r n i n g a t 186 rpm. ( L i f t load normal t o wind causes t h e g r e a t e s t over turn ing load . )
c . Nonoperation of t h e p l a n t while s a t i s f a c t o r i l y with- s t a n d i n g winds having speeds of. 53.6 m / s .
d. Provis ion o f wheel t r a c t i o n under t h e most severe wind loads which w i l l provide s u f f i c i e n t torque t o d r ive a 1 MW generator geared t o t h e wheels.
Our s t u d i e s i n d i c a t e d t h a t condi t ion d ( t h e
t r a c t i o n requi red t o t u r n t h e genera tor ) governs t h e design c a r
weight and wheel loads ; t h a t t h i s design weight w i l l be s u f f i c i e n t
t o ove'rcome a l l over turn ing cond i t ions ; and t h a t no v e r t i c a l res -
t r a i n t w i l l be required. Since t h e c a r wheels w i l l have i n s u f f i c i e n t
c a p a b i l i t y t o r e a c t , the r a d i a l aerodynamic fo rce (wheels wi thout
f langes w i l l be used) f r o n t and r e a r l a t e r a l r e s t r a i n t s i n the
form of i d l e r wheels a c t i n g on t h e s i d e s o f t h e r a i l s w i l l be
requi red .
Assuming an e i g h t wheel conf igura t ion (1 p a i r o f
wheels a t each corne r o f t h e c a r ) , and assuming t h a t each p a i r of
wheels w i l l d r ive a 250 kW generator , a gross c a r mass of 327,950kg
(723,000 l b ) i s r e q u i r e d t o develop t h e necessary t r a c t i v e force .
(Th i s is based on a c o e f f i c i e n t o f f r i c t i o n o f 0.07 a t t r i b u t e d
t o a s t e e l wheel r o l l i n g on a s t e e l t r a c k . ) For t h i s c a r ,
maximum wheel loads w i l l be 556,000 N (,125,000 l b ) , and maximum
h o r i z o n t a l r e s t r a i n i n g fo rces w i l l be 580,900 N (130,600 l b ) . This h o r i z o n t a l r e s t r a i n t w i l l be d iv ided between four r eac t ion
p o i n t s , two l o c a t e d a t t h e f r o n t and two a t t h e r e a r of t h e c a r .
4 . 2 . 6 Fa t igue I
The Madaras Power P l a n t must opera te with a high
degree o f r e l i a b i l i t y . On t h e o t h e r hand, var ious s t r u c t u r a l
members w i l l underqo an enormus number o f stress cyc les i n me' l i f e o f . t h e system. Consider t h e r o t o r . Assuming t h e average
r o t a t i o n a l v e l o c i t y o f t h e r o t o r i s 90 rpm, t h e load cyble
a s s o c i a t e d wi th one r o t o r r evo lu t ion w i l l be app l i ed 5.6 x 10 8
t imes i n a 30 y e a r l i f e , based on a 40 pe rcen t p l a n t f a c t o r .
Of course , t h e s e load cyc les w i l l be app l i ed a t var ious load
l e v e l s . The loads a s s o c i a t e d wi th r o t o r spin-up w i l l be app l i ed
twice p e r t r a c k revo lu t ion . Assuming cons tan t opera t ion a t
8.9 m/s, the number o f cyc les f o r t h e 30 yea r l i f e o f t h e r o t o r 6 is 2 .3 x 1 0 . The corresponding number o f c y c l e s f o r t h e 50 yea r
6 l i f e o f t h e c a r i s 3.9 x 10 . E x i s t i n g design codes such a s t h e " S t e e l Con-
s t r u c t i o n Manual" publ ished by t h e American I n s t i t u t e o f S t e e l
Construct ion a r e n o t based on s t r u c t u r e s which experience such-ta
h igh number o f l o a d a p p l i c a t i o n s . These e x i s t i n g codes can be
used i n a f e a s i b i l i t y s tudy o f t h i s type; however, t o i n s u r e
a high degree o f r e l i a b i l i t y i n t h e case of a f i n a l design, a more s o p h i s t i c a t e d approach i s recommended. A cumulative f a t i g u e
damage ( d u r a b i l i t y ) o r a crack propagation s tudy should be conducted
based on t h e s e r v i c e l i f e loading spectrum. S t a t i s t i c a l methods
should be app l i ed t o determine a requi red mean l i f e t o i n s u r e
adequate r e l i a b i l i t y wi th in t h e s e r v i c e l i f e of t h e s t r u c t u r a l
components.
4 . 3 . STRUCTURE
I n i t i a l c o s t s f o r c o n s t r u c t i o n and assembly a r e expec t ed
t o r e p r e s e n t a s i g n i f i c a n t p o r t i o n o f t h e c o s t s f o r t h e Madaras
Power P l a n t . These c o s t s might very w e l l have t h e s t r o n g e s t
i n f l u e n c e on t h e f e a s i b i l i t y o f such a system. The r o t o r c a r s
a r e l a r g e enough t h a t complete assembly i n a f a c t o r y i s n o t
real is t ic . On t h e o t h e r hand, f i e l d f a b r i c a t i o n and assembly
o f t h e e n t i r e car would r e s u l t i n a much more c o s t l y s t r u c t u r e .
Thig c o s t p i c t u r e s u g g e s t s t h e use o f a modular c o n s t r u c t i o n
approach whereby segments o f t h e s t r u c t u r e would be f a b r i c a t e d
i n t h e f a c t o r y and o n l y f i n a l assembly would be r e q u i r e d a t t h e
p l a n t s i t e . This concept does n o t e l i m i n a t e t h e n e c e s s i t y f o r
a f i e l d shop; however, it does minimize t h e assembly e f f o r t
r e q u i r e d a t t h e c o n s t r u c t i o n s i t e . The modules shou ld be made
as l a r g e as p o s s i b l e wh i l e keeping s h i p p i n g c o s t s a t a r ea sonab le
l e v e l .
General d e t a i l s r e l a t i n g t o t h e r o t o r cap are
i l l u s t r a t e d i n F igu re 4 .7 . The primary l o a d c a r r y i n g members are
8 t r u s s s t r u c t u r e s which are p o s i t i o n e d r a d i a l l y on 4 5 degree
c e n t e r s . The t r u s s e s are a t t a c h e d t o a s t i f f c y l i n d r i c a l s h e l l
a t t h e c e n t e r o f t h e r o t o r cap . The outs i .de d i a m t e r o f t h e
c y l ' i n d r i c a l s h e l l is 0 .9 m. Both t h e upper and lower chords o f
t h e - . t r u s s are a t t a c h e d t o a v e r t i c a l r o t o r t r u s s a t t h e ro tor -cap
in t e r f ace . . . T h i s is t h e on ly connec t ion which a t t a c h e s t h e r o t o r
cap t o t h e r o t o r s t r u c t u r e .
The upper and lower chords o f t h e cap t r u s s w i l l
c o n s i s t o f a "T" s e c t i o n . The d i agona l and v e r t i c a l members w i l l
be a t t a c h e d t o t h e s t e m o f t h e "T" s e c t i o n s u s ing welded connec t ions .
A t y p i c a l eanncc t i an i s i l l u s , t r a .ked i n Figure 4 . 8 . The v e r , t i c a l
and d i agona l members c o n s i s t o f s t r u c t u r a l t ub ing . The j o i n t s
w i l l be d e t a i l e d such t h a t t h e c e n t e r l i n e s o f t h e v e r t i c a l and
d iagona l mexrbers i n t e r s e c t a t t h e c e n t r o i d o f t h e t r u s s chord
which w i l l minimize bending moments i n the t r u c ~ members.
SECTION "D" SClN SECTION " E "
E E C E h
:j
HOLLOW TUBING TYPIC& CAP rma i
Figure 4.7. Rotor and Cap Construction. -*
Figure 4 . 8 . R o t o r Cap Truss J o i n t .
A s shown i n Figure 4.7, t h e modular cons t ruc t ion
o f t h e r o t o r cap w i l l c o n s i s t o f 8 s e c t i o n s , each s e c t i o n con-
s i s t i n g o f a 45-degree segment. A s t r u c t u r a l angle w i l l be
l o c a t e d a t t h e boundary o f each module on both t h e upper and
lower s u r f a c e s . The f lange o f t h e angle w i l l be turned outward
s o t h a t it mates wi th t h e corresponding angle o f t h e ad jacen t
module t o form a "TI' s e c t i o n . Adjacent modules w i l l be connected
w i t h b o l t s through t h e "T" s e c t i o n s t e m and/or by a welded
connect ion . Addi t iona l members which have s t r u c t u r a l s i g n i f i c a n c e
are shown i n F igures 4 . 9 and 4 -10. Figure 4 . 9 i l l u s t r a t e s t h e
l o c a t i o n o f c i r c u m f e r e n t i a l members. A r i n g w i l l be l o c a t e d a t
each j o i n t on the upper and lower chord of t h e t r u s s . Members
K, E, E, and (Figure 4.10) w i l l form a t r u s s network i n 'the
c i r c u m f e r e n t i a l d i r e c t i o n which w i l l provide a load pa th t o t h e
r a d i a l t r u s s . Members and CD w i l l be s t r u c t u r a l tubing .
Members EF and ?% w i l l be s t r u c t u r a l angles . A segment of t h e
heavy c y l i n d r i c a l s h e l l w i l l be a t t a c h e d t o each module a t t h e
i n n e r r ad ius . This concept i s i l l u s t r a t e d i n V i e w B on Figure 4.7.
The m a t e r i a l a l terna. t i .ves considered i n t h i s
f e a s i b i l i t y s tudy a r e s t e e l and aluminum. Som advantages and
disadvantaqes o f each are l i s t e d below.
1. S t e e l is more e a s i l y welded.
2 .. Aluminum weighs less which is advantageous from t h e viewpoint o f b e a r i n g loads and r o t o r spin-up e f f i c i e n c y .
3 * Radial body forces associated with r o t o r r o t a t i o n are s i g n i f i c a n t l y less f o r aluminum (approximately 1 / 3 of t h e va.bl~e f o r s t e e l ) .
4. Some grades o f s t e e l would requ i re pel'iodic maintenance t o provide co r ros ion p r o t e c t i o n .
5. S t e e l c o s t s l e s s than aluminum.
Aluminum m a t e r i a l c o s t s a re . approximately f i v e t imes t h e c o s t o f
ASTM A-36 steel and about f o u r times t h e c o s t o f a cor ros ion
r e s i s t a n t steel such as ASTM A-242. Thus, from a m a t e r i a l c o s t
s t a n d p o i n t , steel i s much more d e s i r a b l e . However, the candidate
Figure 4.9. Location of Circumferential Rings.
N O T T O SCALE CAP SKIN NOT SHOWN
Figure 4 ..lo. Cap Mod.ule Radial View.
s t r u c t u r a l grade s t e e l s and aluminurns have r e l a t i v e l y comparable
s t r e n g t h s y e t t h e d e n s i t y o f s teel is approximztely 2.85 t imes
t h e d e n s i t y o f aluminum.
Body f o r c e s r e s u l t i n g from c y l i n d e r r o t a t i o n
r e p r e s e n t by f a r t h e most s i g n i f i c a n t source of s t r u c t u r a l load ing .
S ince one p r i m design goal i s t o prov ide a h i g h l y r e l i a b l e
s t r u c t u r e , an aluminum s t r u c t u r e can be des igned w i t h lower
nominal stresses as compared t o a s teel s t r u c t u r e and, as a r e s u l t ,
w i l l be less s u s c e p t i v e t o f a t i g u e problems. I n a d d i t i o n , t h e
lower weight aluminum s t r u c t u r e w i l l reduce t h e a x i a l l o a d on
t h e upper b e a r i n g and t h e power requirements f o r r o t o r spin-up.
I n i t i a l c o s t o f aluminum should be o f f s e t somewhat by reduced
maintenance and r e p a i r c o s t s . I n l i g h t o f t h e s e des ign cons idera -
t i o n s and t h e lower maintenance c o s t o f aluminum, t h e material
s e l e c t e d f o r t h e cap was 2024-T4 Alc l ad aluminum a l l o y .
4.3.2 Rotor Cyl inder
D e t a i l s r e l a t i n g t o t h e r o t o r c o n s t r u c t i o n a l s o
a r e shown on F igure 4.7. The r o t o r w i l l have 8 l o n g i t u d i n a l
t r u s s s t i f f e n e r s which ex t end t h e e n t i r e l e n g t h o f t h e c y l i n d e r .
These l o n g i t u d i n a l members w i l l be l o c a t e d on 45-degree c e n t e r s .
The c y l i n d e r w i l l a l s o have 9 c i r c u m f e r e n t i a l s t i f f e n e r s . The
lower 25.6 meter p o r t i o n o f t h e c y l i n d e r w i l l con ta in 8 s t i f f e n e r s
l o c a t e d on 3.66 meter c e n t e r s . The remaining s t i f f e n e r w i l l be
l o c a t e d a t t h e t o p o f t h e c y l i n d e r w i t h a 1 .83 meter spac ing between
t h e s t i f f e n e r and t h e c y l i n d e r ' s t o p end ,
Both t h e l o n g i t u d i n a l and c i r c u m f e r e n t i a l s t i f f e n e r s
w i l l b e t r u s s s t r u c t u r e s . The chords o f t h e t r u s s e s w i l l b e
e i t h e r t u b i n g o r a n g l e s . U t i l i z i n g a 'IT" s e c t i o n f o r t h e t r u s s
chord has t h r e e d i s t i n c t advantages : t h e o u t e r f l a n g e p rov ides
a means f o r a t t a c h i n g t h e s k i n ; t h e i n n e r f l ange prov ides a
means for a t t a c h i n g i n t e r n a l ' s t r u c t u r a l members which t r a n s m i t
l o a d s t o t h e b e a r i n g s ; and t h e s t e m of each "T" s e c t i o n prov ides
a means f o r a t t a c h i n g t h e r a d i a l and d iagona l members. The
r a d i a l and d iagona l members w i l l c o n s i s t o f s t r u c t u r a l t u b i n g
when p o s s i b l e ; however, the modular f a b r i c a t i o n w i l l p r o h i b i t t h e
use o f s t r u c t u r a l t u b i n g i n some i n s t a n c e s .
The modular f a b r i c a t i o n c o n s i s t s o f f a b r i c a t i n g
s e m i - c y l i n d r i c a l segments 3 . 6 6 meters i n h e i g h t w i t h t h e except ion
o f t h e t o p c y l i n d r i c a l s e c t i o n which w i l l b e 1.83 meters ( 6 - f t )
i n h e i g h t . F i e l d assembly c o n s i s t s o f mat ing two semi -cy l ind r i ca l
s e c t i o n s t o form a c y l i n d r i c a l s e c t i o n . Each 180 degree segment
w i l l have v e r t i c a l t r u s s s t r u c t u r e s l o c a t e d a t t h e 45, 90, and
135 degree l o c a t i o n s . These t r u s s l o c a t i o n s a r e i l l u s t r a t e d
s c h e m a t i c a l l y i n F igu re 4 . 1 1 . The t r u s s e s a r e e n l a r g e d i n t he
f i g u r e r e l a t i v e t o t h e c y l i n d e r d iameter t o show g r e a t e r d e t a i l .
The a n g l e s a t 0 and 180 degrees w i l l mate w i t h t he an~gles o f t h e
a d j a c e n t s e m i - c y l i n d r i c a l nlodule t o form a t r u s s chord at t h e
j u n c t u r e . The r a d i a l and d i agona l members a t t h e 45, 9 0 , and
135 degree l o c a t i o n s w i l l be t ub ing ; hu~ever, ang le s a w r q u i x e d
a t t h e 0 and 180 degree l o c a t i o n s . The "T" s e c t i o n of t h e
c i r c u m f e r e n t i a l s t i f f e n e r w i l l be formed hy mat ing t h e a n g l e s of
a d j a c e n t c y l i n d r i c a l s e c t i o n s . The r a d i a l and d iagona l members
of t h e c y l i n d r i c a l s t i f f e n e r s w i l l be a n g l e s throughout . Some
d e t a i l s o f t h e c i r c u m f e r e n t i a l s t i f f e n e r s a r e i l l u s t r a t e d i n
F igu re 4 . 7 . An a d d i t i o n a l f l ange cou ld be sandwiched between
a n g l e s of a d j a c e n t modules where a d d i t i o n a l s t r u c t u r a l c a p a b i l i t y
i s r e q u i r e d . The s e m i - c i r c u l a r p o r t i o n of a c i r c u m f e r e n t i a l
s t i f f e n e r c o u l d be a s senb led from subassembl.ies uf 45 o r 90 degree
segments. A t y p i c a l 45 degree segment i s i l l u s t r a t e d i n Figure 4.12.
The s k i n of t h e c y l i n d e r w i l l be c i r c u m f e r e n t i a l l y
c o r r u q a t e d because t h i s c o n f i g u r a t i o n p rov ides e f f i c i e n t circum-
f e r e n t i a l s t i f f e n i n g and because it is a c o s t / e f f c c t i v e produc t ion
t echn ique . Where l o n g i t u d i n a l seams a re reyuircd, t h o over lap
w i l l be s u f f i c i e n t s o t h a t t h e c o r r u g a t i o n c o n t i n u e s t o a c t as a
hoop. I n a d d i t i o n , c o r r u g a t i u n o v e r l a p i n the l o n g i t u d i n a l
d i r e c t i o n may be r e q u i r e d a t t h e j unc tu re of a d j a c e n t c y l i n d r i c a l
s e c t i o n s . The c o r r u g a t i o n could be e i t h e r welded o r r i v e t e d t o
t h e s t i f f e~iers.
. OVERLAP O 0
Figure 4.11. Rotor Cylinder Internal Structure.
Figure 4-12. Typical 45 ' Segment of Circumferential Stiffener.
Practical fabrication tolerances could result
in some rotor ovalization, and the aerodynamic loading also
could cause rotor ovalization. If ovalization becomes a problem,
a spoke assembly could be incorporated inside the rotor to maintain
the required circular aross-section. However, it was decided to
control ovalization by stiffening the circumferential truss members,
since this approach seems less labor intensive and therefore
should reduce cost.
As for the rotor cap, 2024-T4 Alclad aluminum
alloy was selected for the rotor because the source of structural
loading to the rotor cylinder is the body force resulting from
cylinder rotation.
Rotor Bearings
Rotor bearings need to be very large, and hence
represent a significant cost to the Madaras Power Plant. Thus,
it was necessary to select this component carefully. The Madaras
test and both Flektner ship rotors used two ball bearings.
The bearing locations and internal cylinder
structure are illustrated in Figure 4.13. The upper &nd the lower
bearings are located at elevations of 21.9 m and 7.3 m above the
base of the cylinder, respectively. An early decision was made
to transmit all of the rotor weight to the tower through the
upper bearing. If the weight were transmitted through the lower
bearing, the structural weight and the aerodynamic suction loads
on the under side of the cap would combine and subject the
longitudinal stiffeners to combined compressive and bending loads.
However, if the upper bearing supports the rotor weight, a
significant portion of the longitudinal stiffener will be sub-
jected to combined tensile and bending loads, and improved elastic
stability and reduced weight is the result. The axial location
of fhe bearings was governed primarily by the need to minimize
the radial loading, but also to provide a suitable load path
for transmitting loads from the cylinder to the bearing.
Preliminary Assembly Sketch of Rotor and Support Tower.
Two factors limited the size range of the lower
bearing. The lower limit on the bearing diameter is governed by
the bending stresses in the tower due to the aerodynamic loading
on the cylinder. The upper limit on the lower bearing diameter
is dependent on the diameter of the cylinder. Thus, in order to
maintain a reasonable thickness of the cylindrical tower shell,
the minimum inside diameter should be about 3 m. The maximum
practical outside diameter should be about 4.6 m, a diameter which
is dependent upon the cylinder diameter and the size of the cir-
cumferential truss structure.
The upper bearing shares the same upper limit
on the outside bearing diameter; however, the tower stresses
due to aerodynamic loading are significantly less at the upper
location. Thus, the inside diameter of the upper bearing could
be less than 3 m,.
The specified bearing life at both locations is
30 years. However, with regard to fatigue damage, this life can
not be met with a spherical roller bearing. Only two bearing
types are acceptable for this use: a cylindrical roller bearing
or a double row tapered roller bearing. Basedon cost estimates,
the cylindrical roller bearing is found to be the most economical
choice for the lower bearing location. At the upper location,
the more flexible inner diameter size permits the use of a double
row tapered roller bearing which can be selected from stock sizes
currently in production. This selection results in d significant
cost saving. A B-10 life of at least 20 years is believed to be
easily attainable. Whether or not a B-10 life of 30 years is
attainable is somewhat less certain. Manufacturers indicated
bearing life may be governed more by environmental factors than
by fatigue.
Very little information is available on3 m
diameter bearings rotating at an angular speed of 186 rpm. Most
bearings of this size are used in heavy construction equipment
(cranes, etc.) which rotate at a relatively low speed. Vibration
and other dynamic problems could exist at the high rotational
speeds. However, data on successful use of smaller diameter
bearings at higher speeds, and hence higher linear speeds than
those of the Madaras application are encouraging. Nevertheless,
bearing selection has been designated as an area needing further
study prior to constructing a plant. Full scale bearing tests
may be necessary.
As an indication of the state of the art of .
large bearing manufacturing and design, the design torque equations
of two major manufacturers did not contain the same variables
(in fact, one equation did not contain a speed ,term). Also, one rnanufa~~~~rer said actual bearing torque could vary by a
factor of five from his equations, and the variability of torquc between.bearings of a given type was large.
4.3.4 Support Tower
The rotor is suppor.ted on a nonrotating tower
which is attached to the deck of the car. The tower must support
axial loading, transverse Loading, and a torsional moment. The
axial loading is a result of rotor structure dcad weight, snow and
ice accumulation on the cap, and the sumnation of the aerodynamic
forces on the upper and lower Surfaces of the rotor cap. RQtdr
spin-up will induce a torsional moment in the tower, and aerodynamic
loading on the cylinder surface is the source of transverse loading.
The transverse loading was found to be the most significant in sizing the to we^ cross-section.
4.3.5 Rotor Tower
The rotor and bearings are supported by a
nonrotating tower which is attached Lo the dcuk of the car. The
tower must support axial loading, transverse loading, and a
torsional moment. The axial loading is a result of rotor structure dead weight, snow and ice accumulation on the cap, and
the net aerodynamic forces on both sides of the rotor cap. Rotor
spin-up will induce a torsional moment in the tower, and
aerodynamic loading on the cylinder surface is the source of
transverse loading. The transverse loading is most significant
in sizing the tower cross-section.
A two-piece tower is envisioned. The tower would
consist of a welded cylindrical monocoque structure supported
at the base by a truncated conical section. Since weight was of
less concern for this nonrotating structure, it was decided to
construct the tower from ASTM A-242 steel. Although ASTM A-242
steel costs about 25 percent more than ASTM A-36 steel, the A-242
alloy was considered the better choice since its corrosion
resistance would reduce life cycle cost. The total tower height
will be about 23 m, with the cylindrical section being 3m in
diameter by 17 m high. The truncated conical section will be
about 6 m in height and 4.6 m in diameter at the base. The
thickness of the cylinder and cone will be in the range af
9.5mm to 12.7 mm. Additional stiffness may be required in the
region of the bearings to prevent ovalization and undue stresses
on the inner bearing races.
The cylindrical section of the tower can be
completely fabricated in a factory and shipped to the site in
one piece. However, the truncated conical section would be.
shipped to the construction site in three pieces. An illustration
of the fabrication' breakdown of the tower base is shown in Figure
4.14.
.I Field assembly of the tower would consist of weldinq the conical ~cgments to form the truncated cone followed
by welding the conical portion to the cylindrical portion. The
tower could be either welded or bolted to the car deck. A sketch
of the tower is shown in Figure 4.13.
4.3.6 Car-Layout
External views of the car are shown in Figure 4.15.
With the streamlined contour of each edge overhanging the wheels,
tne overall dimensions of the car are:
Figure 4.14. Tower Base Segmentation Plan.
Figure 4.15. Three-View Drawing of Rotor Car.
Length: 19.2 m (63 f t )
Width: 17.4 m (57 f t )
Height: 2.3 m (9.5 f t )
Deck Height Above Track: 3.8 m (12.5 f t )
The suspension system cons i s t s of four , 2-wheel
t rucks located a t each corner of t he car. The longi tudinal
spacing of t h e t ruck cen te r l i ne is l l m and the two 1.2 rn diameter
wheels i n each t ruck a r e spaced 1.8 m apar t . The wheels, which
have a 279 mm wide t r ead , a r e forged from AISC 1045 steel hardened
t o a depth of 25 mm t o Rockwell C-46. The l a t e r a l spacing of
the t rucks is 11 meters, which w i l l permit the use of a lf-meter
t r a c k gage (36 f t ) as was used by Madaras. Each t ruck is f r e e t o
p i v o t about i t s v e r t i c a l cen t ro ida l a x i s t o f a c i l i t a t e negot ia t ing
curved p a r t s of t h e t rack .
The wheels i n each t ruck a r e coupled together
by a chain d r i v e system, and from the re through a f l e x i b l e coupliny
t o a 9.3:l speed increaser , through a second f l e x i b l e coupling,
and f i n a l l y t o a 250 kW, 4160 V, induction generator having a r a t e d speed of 1150 rpm a t a n 8 . 9 m / s t r a c k speed. Some of the
o t h e r d e t a i l s of t h e end truck assembly a r e shown i n Figure 4.16.
The inal ined wheel housing on the forward and
read s i d e s of t h e f r o n t and rear t rucks sexves two functions: it
provides a means f o r scraping foreign ob jec t s off t h e track ( l i k e
t h e cow catcher on a steam locomotive) and it serves a s a mount f o r
four i d l e r wheels, two on each s ide of t he r a i l f o r each truck.
There a r e s ix teen of these 127 mm-diameter, i d l e r wheels (four
i d l e r s on each of four wheel housings), hence e i g h t of these i d l e r s
a r e always ava i l ab l e t o r e a c t t h e r a d i a l aerodynamic load f o r a l l wind d i r e c t i o n s r e l a t i v e t o t h e power p l an t t rack. More ana lys i s
on t h e s i z ing and support of these wheels is needed.
Each wheel is supported by i ts own 203 mm-
diameter ax le and two pi l low blocks, so t h a t wheels on t h e ins ide
and outs ide r a i l can tu rn independently.
Figure 4-16. R o t o r C a r End Truck Assembly.
4.3.7 Car Structure
The structural plan of the car is illustrated
in Figure 4.17. This layout is based upon the use of a series of
deep, built-up, longitudinal and lateral box beams positioned in
such a way to provide the required bending stiffness. Closed
section box beams made from welded steel plates were selected
because the closed section yields considerable torsional stiffness
compared to an open section and because use of a closed section
eliminates the need for inter-beam bracing, Two beam sizes
were selected. The side beams, those to which the tower is
fastened, and other longitudinal interior members are made from
0.9 m deep by 0.4 m wide steel plate (Section C-C). The forward
and rear members, which transmit the radial bending moments to
the wheels, will be even larger: 1.22 m deep by 0.41 m wide
(Section D-D). All of these beams will be fabricated from 19 mm thick steel plate welded alonq all edges. Sectional elevatinn~
of this structural member layout are presented in Figure 4.18.
The streamlined fairing of the car extends at
a 45O angle downward from the main frame on all four sides. This
fairing is stiffened by eight closed tube sections on each side
that are 305 mm deep, 76 nun wide, and 6 nun thick. The fairing
is reinforced at each corner by 12.7 mm x 12.7 mm by 6.3 mm
thick diagonal tubes. The bottom perimeter of the fairing is
stiffened by a 152 mm-diameter, Schedule 46 steel pipe. The top
deck and fairing framework is completed with a network of longi-
tudinal and lateral stringers made of rectangular tubes varying
in depth from 152 mm to 25 mm. The frame is covered by a stressed
.--:-skin - .* covering of the tape deck and fairing by panels fabricated L . I
b'7---from 3 m-thick Corten steel, which will pruvide a corrosion- - , ,&<
resistant weather surface. The use of Corten steel for the tower " ..
and car was recommended by U.S. Steel for this project. Figure
4.19 contains some of these miscellaneous skin and stiffener sections.
The bottom floor of the car provides the final
structural detail. The floor, not shown on the drawings, will be
flush with the bottom of the streamlined housing, and will provide
P L A N
Figure 4 . 1 7 . Car Structural Plan.
Norr : I . CLCVATIOY~O* IS CN S Q l J W - l l M U C U ONLY
W IS AT 8-C OF ROTOR 1 m P OF LOWlll POTATIS40 CCC.
LRkr~l~6 b3.s?, 2100 -7
Flgcre 4.15. Sections1 Elevations of Car Structural Layout.
or nonrLco (ILl.HD U P X W 'WILLIAMS CATLO # LOCI W A 5 a R -. eu TYP INCLINE PANCL (ROTATLD 45.1 I2 n r o ' e / ~ u r ~ %A= - s-. 1 ~ 0 -
-I'P I
Figure 4.19. Miscellaneous Skin and Stiffener Section.
{TIP.) FRONT 6 REAR PANL CONNLCTIOU To' IT- 3"* .~~-TVDE acAlr - a'= '%I*
, I I I I
Z C U C . ON TOP W Y LTYP.1
an enclosed compartment about 2.9 m high in areas that are not
obstructed by main beams, etc. The floor will be stiffened by
tubes, as was the top deck, and appropriate cut-outs for trucks,
etc. will be provided.
The compartment thus formed will have three
major functions. First, it will provide environmental protection
for the expensive motors, generator, gearing, and other electrical
and electronic control and instrumentation equipment. It also
will provide safe working space which can be occupied by main-
tenance personnel even while the car is in motion. Russell F.
Hardy, Madarasl Chief Engineer, indicated noise inside the rotor
was not objectionable. Finally, the floor will provide additional
structural rigidity as well as a means for supporting a pre-cast
concrete slab if ballast is required.
The mechanical drive system for the rotor
(partly shown in Figure 4.15) will be described in paragraph 4.4.2.
The electrical and electronic components mounted in the car will
be described in Section 5.
4.3.8 Power Transfer Trolley
The electrical power output from each car will
be transferred to an overhead trolley rail by one, spring-loaded,
trolley arm attached to each car as shown in Figure 4.20. The
trolley arm, located on the side of the car facing the inside of
the track, provides support for three collector brackets and
shoes, one for each electrical phase. Each of these shoes,
which have two contactors, ride on collector rails and the
contactor rails are fastened to expanded steel joists which are
0.4 m deep. The joists are supported by municipal-type, metal
lighting poles spacinq 12.2 m apart (see Figure 4.20). An
electrical description of the trolley rails is presented in
Paragraph 5.6 .2 .
4 - 3 . 9 Inter-Car Coupling
The cars will be coupled together into an8 x
endless train by steel cables attached by a pin-and-clevis
arrangement at the mid-point of the front and rear of each car.
.. --5 -- \
\ \
.\ \ \ \ \
I
---I
- -- - -- - - ela -0.
-- 7-- I= --A IWDIA. ANCKIR~
+I"V" t CAR I
IU-0-
6 I
MAlER h ASSOCIATES, INC. m U M O W . OHD
4 OIO IU*RIUC*.,,".~ "0 nn* I -m*Oi I - I HADARAS POWER P L L U T
W IOP.tlO* 'I ELECT. CSLLCCTOR, .I -IL I T I P L-SVI'TIONC
* --- q.1 . . -.. . ,,..zm.*, 4. 2 7
Figure 4.20 . Power Transfer Arm.
The cable is attached, as shown in Figure 4.18, to the main,
1.22 m deep lateral beam with cable loads fed into the 0.91 m deep
longitudinal beams by a closed tube having a rectangular cross
section of 203 mm by 305 nun and a wall thickness of 10 mm. The
point of cable attachment is 3 m above the top of the track. This
is ample height to allow for the 1.22 m catenary deflection expected
in the cable. Each inter-car connection cable will consist of two wire ropes, each having a diameter of 70 mm. The length of the
cable will be determined by the minimum spacing between Cars, which is discussed in Section 6, Performance Analysis. Cables will be
tensioned after train assembly to improve rigidity of the train system.
4.3.10 Dynamic Balancing of the Rotor
The rotor will be balanced dynamically after it
is assembled in the on-site assembly building, which is described
later in Paragraph 4.5.4. The procedure used will be essentially
the same as that used by Madaras. 5
Assembly of the structure will be checked at all
stages to insure that required circular concentricity of the tower
and rotor is maintained. This maintenance of concentricity will
be particularly important at the bearing locations to improve
bearing life.
Dynamic balancing then will be accomplished by
slowly rotating the rotor by its motors measuring the degree of
imbalance, and then distributing lead weights along the length
of the rotor in the longerons and frames as required. This
process will be repeated until the rotor is operating smoothly
above the rated speed. The Madaras rotor was so well balanced
that, at a speed of 160 rpm, oscillations on a machinist's dial
indicator applied to the measuring apparatus were barely noticeable. 5
4.4 DESIGN MODIFICATIONS
~uring the course of the program, results from our various
studies and information received at the ERDA Third Wind Energy
Workshop indicated that it would be advisable to change some of
the original design criteria presented in Paragraph 4.1. These
changes and the basis for these changes are as follows:
1. Rotor Configuration: changed from Madaras configuration to Aspect Ratio 6, e/d Ratio = 2, two end caps, area unchanged. A rotor having the following size:
Height: 33.4 m (109.5 ft) Cylinder Diameter: 5.6 m (18.25 ft)
a End Cap Diameter: 11.1 m (36.5 ft)
Basis: Results of wind tunnel tests and performance analyses indicatedgross output would improve significantly.
2. Rated Wind Speed: Change from 8.18 m/s to 13.4 m/sec
Basis: Madaras selected this rated speed figure and we wanted to correlate with his computations. Also, our performance analyses indicated this level would be attractive.
3. Gust Criteria: changed from 26.8 m/s to 15.6 m/sec. This is the incremental gust over and above rated operating conditions.
Basis: This condition designed the structure and car weight. Inasmuch as GE in their MOD 1 design reduced their gust speed to 15.6 m/s, we also changed to have a more equitable basis for comparing the Madaras and the GE systems.
4. Track Configuration: changed from circular to racetrack.
Basis: Computer studies indicated improved performance for winds that fluctuated no more than + 45O from the design direction. Since there is no penalty for reciprocal wind direction changes, we noted that a racetrack configuration could be used in many parts of the country quite effectively. Also, the larger amount of track will permit use of more cars and will enable plant capacity to be increased at an improved economy of scale.
The effects of these criteria changes were evaluated, and
the results of these evaluations are presented in the following
paragraphs.
4.4.1 Revised Rotor Configuration
The revised rotor mounted on its rotor car is
shown in Figure 4.21. Other than the geometric aspect ratio and
e/d ratio of the rotor, the most important change is the addition
I - 1 - Figure 4.21. Revised Rotor Car configuration.
of the lower end cap. Note that the lower end cap is inverted
in order to permit a continual, orderly flow of air over the
streamlined fairing of the car into the rotor cylinder. This same
configuration was used by Flettner on all of his rotor ships. The
lower cap was made 37% thinner than the top cap in order to smooth
air inflow even more. Notice also that the tower diameter was
decreased from 3.04 m to 1.82 m in order to reduce rotor inertia,
bearing size, bearing outer race speed, bearing lubrication problems,
bearing inertia, and cost.
No changes were made to the design of the rotor
car or described in Paragraphs 4.3.5 and 4.3.6.
After reanalyzing the loads for the new conditions,
it was concluded that the load changes would have no effect on
the governing design structural concept. The required modifications
were made to provide realistic data for costing and appropriate
inputs to our simulation program. The car weight previously
computed was sufficient to prevent overturning and to provide
traction for power generation; hence, no change in car weight was
made.
4.4.2 Rotor Drive System
After studying the initial rotor-spin-motor, drive
system, the decision was made to relocate the motor from the position
near the upper bearing, which was about 32 m above ground to the
position shown in Figures 4.15 and 4.21 on the floor of the rotor
car. This position was selected to facilitate motor and drive unit
changes and to simplify routine maintenance and servicing of these
components. Although this second approach will require the addition
of a long drive shaft, which will increase first costs, it was
believed that the life cycle cost will be reduced by incorporating
this change. Drive methods which eliminate the shaft should be
considered further, however.
The drive system consists of a 450 kW, 1150 rpm,
500 vdc motor coupled to a right-angle speed reducer having a
2.25/1 gear ratio. The speed reducer is then conncctcd to a
29 m long by 203 mm diameter, vertical, drive shaft, which is
composed' of 5 sect ions , each 5.8 m long. The dr ive sha f t is supported along its length by s i x bearings. Flexible couplings
w i l l be used t o join a l l d r ive sha f t and motor-gearbox connections.
The top end of the dr ive s h a f t is connected t o a 254 mm thick,
hardened-steel, pinion,spur gear having a 0.6 m p i tch diameter.
,Through a mating i n t e r n a l spur gear, which has a 1.66 m pi tch
diameter and which is fastened t o the ro to r s t ruc ture , torque
from t h e dr ive s h a f t a t a fur ther speed reduction of 2.77/1 i s t ransfer red t o dr ive the rotor . Thus, through the bottom and top
speed reducers, an overa l l motor speed reduction of 6.22/1 is
achieved.
4 . 4 . 3 R o t o r ncar inq~
I n view of the decrease i n support tower diameter
and the increase i n ro to r height over the or ig ina l design, bearing
changes were made. The new bearing loca t i sns , shown on Figure 4 .21
a r e 13.9 m and 32 m above ground. A s before, the upper bearing,
a 2.6 m OD r o l l e r bearing, reac ts a l l of the ro to r weight and
p a r t of the r a d i a l load; whereas a 3.4 m diameter lower bearing
r e a c t s only r a d i a l loads. The ra ted capaci t ies of these bearings
is w e l l above the load requirements of the governing design c r i t e r i a .
4.5 SITE DESIGN
The layout plan for our version of a Madayas Rotor Pmer
Plant u t i l i z i n g a race track r a i l configuration is presented i n
Figure 4.22. For the purpose of t h i s drawing, a t rack having a 229 m (750 f t ) end radius and a 612 m straight-away was selected.
The top of each t rack r a i l is 1.2 m above mean ground level . The
ac tua l s i z e of t h e track recommended w i l l be described i n Section
V I , since the t rack radius a f f e c t s spin motor perrormnce s ign i f i -
cant ly . An elevat ion drawing of the p lan t with one ro to r ca r on
the t rack is shown i n Figure 4.23.
2 The t o t a l a rea of 0.65 k m (160 acres) is required f o r the
configuration shown. The p lan t consis ts of the 11 m (36-ft)
gauge track with a spur t rack t h a t can be used t o t r ans fe r a rotor
c a r from t h e ac t ive t rack area t o the maintenance building and
vice versa.
I!! ? ! In
F i g u r e 4.22. Plant Layout.
~ W I ~ % O Q - 9
Figure 4.23. T y p i c a l E l e v a t i o n of lladaras P l a n t , One C a r on T r a c k .
Surrounding t h e ou t s ide o f t h e t r a c k i s a 7.6 m wide,
r e in fo rced concre te road which w i l l enable s e r v i c e veh ic les t o
gain access t o any r o t o r c a r i n the t r a i n . A 4.6 m c learance
space is provided between t h e i n s i d e edge of t h e road and t h e
o u t e r r a i l o f t h e t r a c k .
The power c o l l e c t i o n t r o l l e y , presented a s Figure 4.20
and a l s o shown i n Figure 4.23, is loca ted 5.5 m inboard o f t h e
i n s i d e t r a c k , supported by metal, municipal-type l i g h t poles t h a t
a r e 6.5 m high and form a complete loop i n s i d e o f and p a r a l l e l t o
t h e t r a c k loop. This power c o l l e c t i o n system i s descr ibed i n
Paragraphs 5.6.2 and'.5.6.3.
The a r e a i n s i d e t h e t r ack i s a v a i l a b l e f o r any use t h a t
does n o t d i s t u r b t h e a i r f low. Obviously,' s i n c e t h e top of t h e
r o t o r c a r deck ( t h e bottom o f t h e r o t o r ) i s 5 m above ground,
t h e use o f t h e i n t e r n a l a r e a f o r any farm crop o r graz ing would
n o t i n t e r f e r e wi th p l a n t opera t ion . The formation of a l ake o r
wa te r r e s e r v o i r i n t h i s a rea a l s o could be a t t r a c t i v e . However,
most uses o f t h i s l and would r e q u i r e a tunne l under t h e t r a c k
f o r access . E f f e c t i v e use o f t h i s i n t e r n a l a r e a , o r t h e s i t i n g
o f a p l a n t a t a l o c a t i o n where t h e land i s n o t use fu l w i l l improve
p l a n t economics.
4 -5.1 Track and Roadbed Design
Figure 4.22 i l l u s t r a t e s some d e t a i l s o f t h e
t r a c k and roadbed s t r u c t u r e . A wel l-constructed road bed i s an
important f a c t o r in f luenc ing t h e l i f e of t h e t r a c k . Rai l road
research personnel whom w e contac ted recommended' s t r o n g l y t h a t
every precaut ion ' should be taken t o provide a sound t r a c k foundation
i n o rde r t o minimize r e p a i r and replacement c o s t s .
The c a r wheels run on f l a t s t e e l r a i l s made of
p l a t e s having a width of 51 cm and a th ickness of 10 cm. Each
s t e e l p l a t e w i l l rest on a sepa ra te , continuous, s t e e l -
re inforced , concre te pavement t h a t i s 2.. 4 m wide by 35.5 cm t h i c k .
In o r d e r t o a s su re t h a t l e v e l t r a c k s u r f a c e i s achieved, t h e t r a c k
w i l l be shimmed b y , a 5 cm-thick l a y e r o f grout having s t r e n g t h o f
68-MPa(10,OOO p s i ) . The s t e e l r a i l w i l l then be b o l t e d t o t h e
concre te road bed by two countersunk b o l t s , 3.1 cm i n d i a m t e r
by 43 cm long every 1.2 m o f t r a c k length .
The suppor t ing pavement w i l l be s t e e l ' . :reinforced
concre te . S ince replacerrent o f a l l o r p a r t o f t h e pavement would
be a very c o s t l y opera t ion i n terms of ma te r i a l , l a b o r , and l o s t
revenue, a f a c t o r o f s a f e t y o f f i v e i s recommended.
The b a l l a s t l a y e r which suppor ts t h e concrete
pavement c o n s i s t s o f a mixture of coarse aggregate and f i n e s t h a t
m u s t be proper ly balanced. An i n s u f f i c i e n t propor t ion of f i n e s
cou ld r e s u l t i n excess ive abras ion of t h e aggregate wi th repeated
Load a p p l i c a t i o n s , whereas t h e aggregate tends t o f l o a t i n t h e
f i n e s i n a case o f excess ive f i n e s . This l a t t e r s i t u a t i o n could
r e s u l t i n poor compaction of t h e b a l l a s t l a y e r .
I n a d d i t i o n t o a proper mixture o f aggregate and
f i n e s , a s o i l s t a b i l i z a t i o n admixture should be mixed with t h e
f i n e s t o i n s u r e a maximum degree o f compaction, t o r e t a r d c a p i l l a r y
a c t i o n , and t o avoid p o t e n t i a l problems' with f r o s t . The s t a b i l i z e d
b a l l a s t should have an u l t ima te bea r ing capac i ty o f 958 KPa
(20,000 l b / f t 2 ) . Assuming a p o i n t load on t h e t r a c k and a shea r
l a g angle o f 45 degrees, t h e bea r ing p ressu re on the b a l l a s t would 2 Le 197 IZPB (4125 lb/fC ) , T h u ~ , f o r a factor of s a f e t y o f 5 .(I,
2 t h e al lowable p r e s s u r e would be 1 9 1 KPa ( 4 0 0 0 l b / f t ) . The
b a l l a s t l a y e r f o r each r a i l i s about 6 .3 m wide by 2 . 1 m deep
wi th a 1 i n 2 s l o p e f o r drainage. The bottom of t h e b a l l a s t rests
on a s o i l foundation excavated 0.9 m below grade.
The foundation bed should be well-compacted,
g r a n u l a r m a t e r i a l . A s i n t h e case o f t h e b a l l a s t l a y e r , a f a c t o r
o f s a f e t y o f 5.0 i s d e s i r a b l e . I f t h e p l a n t s i t e i s l o c a t e d i n
a r eg ion o f c l a y and/or s i l t y s o i l s , an adequate por t ion of t h i s
m a t e r i a l should be excavated and replaced wi th a s u i t a b l e granular
m a t e r i a l . The s u s c e p t i b i l i t y o f c l a y t o c a p i l l a r y a c t i o n when
exposed t o m i s t u r e can r e s u l t i n a l o s s of bea r ing capac i ty ,
cxcess ive h y d r o s t a t i c p ressu re , and volume changes a l l of which
could be very de t r imen ta l t o t h e l i f e of t h e t r a c k and t o t h e
opera t ion o f t h e f a c i l i t y . The compacted g ranu la r m a t e r i a l should 2 have an u l t ima te bea r ing capac i ty o f 4 7 9 ~ ~ a (10,000 l b / f t ) .
Two, 30 cm porous d r a i n t i l e s w i l l be used t o d r a i n wa te r from
each t r a c k r a i l foundation.
4.5.2 P l a n t Bui ld inas
Two types of bu i ld ings a r e requi red: an assembly-
maintenance b u i l d i n g and a c o n t r o l bu i ld ing .
The assembly-maintenance b u i l d i n g w i l l be b u i l t
dur ing t h e e a r l y s t a g e s o f p l a n t cons t ruc t ion i n o r d e r t o provide
t h e necessary f a c i l i t i e s t o assemble t h e r o t o r and r o t o r c a r s
from t h e fac to ry - fabr i ca ted segments t h a t a r e shipped t o t h e s i t e .
The plan form of t h i s b u i l d i n g w i l l be about 30 m wide by 50 m
long.
The assembly b u i l d i n g w i l l have two roof he igh t s .
The f i r s t 25 m of b u i l d i n g l eng th w i l l have a c l e a r c e i l i n g he igh t
of about 4 2 m t o permit t h e complete assembly o f a r o t o r on a c a r
i n s i d e t h e bu i ld ing . The second h a l f o f t h e b u i l d i n g w i l l have a
c e i l i n g h e i g h t o f about 9 m i n o r d e r t o provide room f o r assembling
p a r t s of a c a r a lone. Thus, t h e r e is room f o r a two-car assembly
l i n e i n s i d e t h e bu i ld ing . While one c a r i s be ing assembled,the
r o t o r can be assembled and mounted on t h e second c a r . The c a r s
w i l l be assembled on an extens ion o f t h e spur t r a c k i n s i d e t h e
b u i l d i n g t o permit easy t r a n s f e r o f completed r o t o r c a r s t o t h e
o v a l t r ack . An overhead, 30-ton br idge crane and two 15-ton
j i b c ranes a s w e l l a s welding and o t h e r f a b r i c a t i o n equipment w i l l
compl imnt t h e bui ld ing . Off ice space, t o o l rooms, and supply
rooms a l s o w i l l be provided.
Af te r cons t ruc t ion o f t h e p l a n t i s completed,
t h i s b u i l d i n g w i l l then se rve a s a r e p a i r f a c i l i t y and w i l l house
one complete s p a r e r o t o r c a r .
The c o n t r o l b u i l d i n g w i l l be 15 m long by 9 m
wide by 4 m high. This b u i l d i n g w i l l be b u i l t a g a i n s t t h e edge
o f t h e assembly b u i l d i n g n e a r e s t t h e t r a c k . This b u i l d i n g w i l l
house t h e o p e r a t o r ' s c o n t r o l s t a t i o n , t h e ' c e n t r a l proces 'sor, and
t h e t e l emet ry system. An e x t e r n a l s u b s t a t i o n w i l l con ta in t h e
equipment r equ i red t o i n t e r f a c e the' 'power'from t h e Madaras p l a n t
w i t h t h e u t i l i t y system power g r i d . See S e c t i o n V f o r a d e s c r i p t i o n of t h e s e c o n t r o l and i n t e r f a c e components.
P rov i s ions have been made i n t h e c o s t a n a l y s i s
f o r a prime mover t o push t h e c a r s around t h e p l a n t a r e a dur ing
car assembly, t r a i n assembly, and maintenance.
4.6 MASS SUMMARY O F ROTOR CAR
The fol lowinq t a b l e p r e s e n t s a summary of t h e mass of t h e
major components o f each r o t o r c a r .
COMPONENT
Car, Motor, Speed Reducer
End Trucks, Speed Reducers, Generators , ( 4 each)
Tower
~ b t o j t Cylf nder Rotor End Caps ( 2 each)
Miscellaneous E l e c t r i c a l Components
B a l l a s t (Concrete on Car Floor)
TOTAL MASS
Mass kg
232,700
32,700
37,200
8,600
4,500
1,400
10,900
328,000
l b
513,000
72,000
82,000
18,900
10,000
3,000
24,100
723,000
SECTION V
ELECTRICAL DESIGN
The o b j e c t i v e s o f t h i s s tudy were t o de f ine e l e c t r i c a l
requirements, de f ine and spec i fy e l e c t r i c a l components, and
determine e l e c t r i c a l l o s s e s . The e l e c t r i c a l design inc ludes
cons idera t ion o f t h e fol lowing components :
a . Rotor sp in system
b. Generator system
c . Control and instrunatntat ion system
d. E l e c t r i c c i r c u i t r y t o i n t e r f a c e these t h r e e systems
wi th each o t h e r and t o d e l i v e r output power t o t h e ou t s ide power
g r i d .
5 .1 DESIGN GUIDELINES
Guidelines given were t o design a system of maximum
e f f i c i e n c y and minimum c o s t . Considerat ions under c o s t would
include both i n i t i a l c a p i t a l investment and maintenance c o s t .
Whenever poss ib le , s tandard marketplace components were t o be
u t i l i z e d .
5.2 D E S I G N CONDITIONS
The fol lowing design c r i t e r i a had a major e f f e c t on t h e
designs :
a . C i r c u l a r t r a c k of 1500 f t (approximately 457m)
diameter ( l a t e r increased t o 3000 f t o r g r e a t e r ) . b . Eighteen equa l ly spaced c a r s l inked on t h e t r a c k .
c . Track speed o f 8.9 4 s .
d. Rated gross genera tor output o f 1 MW p e r c a r 2 e. Rotor r o t a t i o n a l i n e r t i a o f 61,820 Kg-m -
f . Maximum r o t o r r o t a t i o n a l speed l i m i t o f 186 rpm
g. Speed c o n t r o l of r o t o r r equ i red throughout t h e c a r ' s
t r a v e r s e o f t h e c i r c u l a r t r ack .
h. Reversal o f the r o t o r ' s d i r e c t i o n of r o t a t i o n a t two
d iamet r i ca l ly oppos i te po in t s on the t r a c k .
i. Wind direction and velocity measurements required at
various points along the track.
j. Rotor viscous friction and rotor bearing loss load
in accordance with equations in Paragraph 3.5.
k. Preliminary motor rpm schedule shotm in Figure 5.1
obtained by varying speed at each 5O increment of track position
(9) such that power extracted is maximum at each track position.
1. Compatibility of power generated with utility company
power grid.
5.3 ROTOR SPIN SYSTEM
5.3.1 Concept Selection
The rotor spin system has some very serious con-
straints imposed on it by the design conditions. The most
serious constraints are the requirements: (1) for continuously
variable speed control; (2) for a direction reversal approximately
every 80 seconds for the given track size and track speed; and (3)
the high rotational inertia of the rotor. These constraints limit
the system to direet current motor nr to a constant speed motor driving through a continuously variable speed transmission and
revessihg gear s y s b c m . Thc latter prohah1.y wvuld have to include a brake system to stop the rotor motion for reversal. The trans- mission andebrake system was discarded because of cost, inefficiency,
and maintenance considerations for a system of adequate size.
A direct c u ~ ~ e n t rnokor drive has advantages in
that regenerative braking is available to recover part of the
inertial energy of the rotor during spindown and because motor
hardware and controller hardware are commercial catalog items.
However, the 80 second period for spinap, spindown,and direction
reversal (based on track speed of 8.9 m/s and track diameter
of 457 m) requires the motor to operate in its most inefficient
mode of operation: a constant start-stop duty cycle which causes
very high niotor int&nal heat load and high power losses.
Several alternatives were considered to replace or supplement an
electric motor drive.
8 (DEGREES).
Figure 5.1. Preliminary Estimate of Aerodynamically Optimum Rotational Speed Schedule.
Two a l t e r n a t . i v e s t o an e l e c t r i c d r i v e were
cons idered: an a i rmotor and a hydraul ic motor d r i v e . Each
would be b e s t implemented by having a l a r g e e l e c t r i c motor d r i v i n g "
a compressor. The a i r s t o r a g e t anks requi red f o r t h e a i r volume
needed t o s p i n up the' r o t o r would be l a r g e and expensive. I n
a d d i t i o n , t h e c o s t of t h e l a r g e airmotor and compressor, a valving
system t o r e v e r s e r o t a t i o n a l d i r e c t i o n , and t h e c o s t of increased .
i n e f f i c i e n c y of an a i r system over an e l e c t r i c a l system lead t o t h e
c o ~ c l u s i o n t h a t an a i r system would be i n f e r i o r t o an e l e c t r i c .
system. The same reasoning holds t r u e f o r a hydraul ic motor s p i n
system. I n a d d i t i o n , a hydraul ic system might r e q u i r e heat ing-
for s t a r t - u p on co ld win te r days and cool ing on warm o r ho t days.
F u r t h e r , no hydrau l i c motors a s l a r g e a s t h e s i z e requi red are
a v a i l a b l e a s s tandard i tems, and a developmental program would .be
needed t o o b t a i n them. Thus, c o s t and t e c h n i c a l u n c e r t a i n t i e s
,.,.,~eemed t o r u l e t h e s e a l t e r n a t i v e s o u t a s s o l u t i o n s a t t h i s t i m e . . .. . .%
Flywheel systems were considered a s a load l e v e l i n g
means t o improve t h e e f f i c i e n c y o f t h e e l e c t r i c a l s p i n motor system.
A flywheel much l a r g e r than any previous ly cons t ruc ted would be
r e q u i r e d f o r t h e expected spinup load. The i n e r t i a of t h e Madaras
system r o t o r is very high, b u t a flywheel would be opera ted a t a
much h igher r o t a t i o n a l v e l o c i t y . Modern flywheels have been
designed f o r such uses a s load l e v e l i n g and d e c e l e r a t i o n load
recovery on commuter t r a i n s and buses, and on h e l i c o p t e r mounted
high-capaci ty l i f t i n g cranes . Most sue11 devices have used an
e l e c t r i c motor-generator t o t r a n s f e r energy i n t o and o u t o f t h e
i n e r t i a wheel. R e l i a b i l i t y o f t h e s e devices is very much i n
q u e s t i o n with a few hundred hours aL b e s t be ing quoted as t h e
mean t i m e between f a i l u r e s . Energy recovery e f f i c i e n u y is not
very h igh , 30 t o 40 pe rcen t , because of t h e same problem t h a t
plagues an e l e c t r i c motor s p i n system; i .e . , low e f f i c i e n c y o f
e l e c t r i c motors o r genera tors a L speeds vcry much below o r above
t h e i r design speeds. The development c o s t , purchase p r i c e , and
maintenance problems and c o s t s of f lywheels s e e m d s u f f i c i e n t I
reason t o r u l e them o u t o f cons ide ra t ion dur ing t h i s conceptual
des ign s tudy.
Consequently t h e dec i s ion was made t o s e l e c t t h e
system u t i l i z i n g a d i r e c t c u r r e n t s p i n motor d r i v i n g t h e r o t o r
s h a f t through a gear t r a i n . The use o f regenera t ive braking f o r
energy recovery during t h e r o t o r spindown segment of t h e s p i n
cycle was a l s o considered f o r t h i s system. This i s by f a r t h e
s imples t and lowest c o s t system t o implement i n t h e r equ i red
power range.
, 5.3.2 Spin System S i z i n g
The s p i n system motor s i z e i s s e n s i t i v e t o t h e angular a c c l e r a t i o n demanded and t h e motor speed a t which t h i s
a c c e l e r a t i o n occurs . Although our c a l c u l a t i o n s ind ica ted t h e
r o t o r ' s s t eady-s ta t e maximum load was 350 kW a t 186 rpm, t h e load a c t u a l l y v a r i e s from 0 kW a t 0 rpm t o t h e upper 350 kW l i m i t . How- eve r , t h e r o t o r provides a cons tan t s t eady-s ta t e motor load a t any
cons tant r o t a t i o n a l speed. Thus, a s a minimum, t h e s p i n system must be
a b l e t o d e l i v e r a 350 kW load t o t h e r o t o r s t r u c t u r e . This load,
w i l l be app l i ed t o t h e r o t o r through a gearbox o r an e q u i v a l e n t
gear ing system; and a gearing l o s s must be ass igned t o t h i s
funct ion. I f a four pe rcen t gear ing l o s s i s es t imated , i n
accordance wi th o t h e r wind t u r b i n e design programs, 39 the l i m i t
s t eady-s ta t e load becomes 365 kW a t t h e motor s h a f t .
The a c c e l e r a t i o n load requirement on t h e s p i n
d r i v e system is caused by t h e r o t o r i n e r t i a , . t he r o t a t i o n a l speed
schedule, .and t h e maximum r o t a t i o n a l v e l o c i t y . A t a t r ack speed
o f 9 d s e c a time i n t e r v a l of 40 seconds i s requi red t o t r ans -
verse 90 degrees o f a 457-meter-diameter, c i r c u l a r t r a c k .
Figure 5.1 shows .a r o t o r a c c e l e r a t i n g t o approximately 186 rpm
i n t h i s t i m e period.. For a cons tan t a c c e l e r a t i o n schedule, the 2
r o t a t i o n a l a c c e l e r a t i o n would be 0.472 rad/sec ; and t h e i n p u t
power r equ i red t o a c c e l e r a t e t h e r o t o r t o 186 rprn would be 568
kW. Adding t h e four percent gear ing l o s s , a motor which d e l i v e r s
592 kW t o t h e motor s h a f t i s requi red . Thus, f o r t h e given design
condi t ions (schedule i n Figure 5.1) , t h e motor must be s i z e d t o
overcome n o t only t h i s 592 kW a c c e l e r a t i o n load , b u t a l s o it must
provide .Wle s t eady-s ta t e viscous and bea r ing load of 365 kW a t
186 rpm. Consequently, under t h e s e cond i t ions , a 958 kW
m t o r i s requ i red t o a c c e l e r a t e and maintain r o t a t i o n of each
c y l i n d e r according t o t h e schedule i n Figure 5.1.
The t i n r e h i s t o r y o f t h e s p i n motor load can be
deduced from t h e c h a r a c t e r i s t i c s o f t h e two previously-descr ibed
r o t o r loads. The f i r s t load ( s t eady-s ta t e viscous and bea r ing
load) i n c r e a s e s a s a cubic funct ion o f rprn and r o t o r bea r ing load
i n c r e a s e s l i n e a r l y wi th rpm. For o u r purposes he re , t h e t e s t
d a t a curve developed by Madaras (Figure 3 .24) f o r a r o t a t i n g b u t
n o t t r a n s l a t i n g c y l i n d e r , a s modified by o u r own wind tunne l test
data w i l I be used (see Paragra'ph 3.3.7) . Thc seoond load
( a c c e l e r a t i o n load) inc reases a s a q u a d r a t i c f u ~ l c t i o n o f rpm
dur ing spinup and spindown.
I n o r d e r t o s impl i fy t h i s d iscuss ion of t h e r o t o r ' s
r o t a t i o n a l schedule , we w i l l modify t h e Figure '5.1 r o t a t i o n a l
schedule i n t h e form o f a l i n e a r l y i n c r e a s i n g o r decreas ing rpm
( c o n s t a n t a c c e l e r a t i o n and dece le ra t ion) f o r each quadrant o f
t r a c k , a s shown .in Figure 5.2. It should be' recognized t h a t t h i s
s i m p l i f i e d s p i n r o t a t i o n a l schedule w i l l generate considerably
less power from t h e c y l i n d e r than t h e optimum r o t a t i o n a l schedule
p resen ted i n Figure 5.1; hence t h e l i n e a r i z e d ayGtem would not. be
used i n an o p e r a t i n g system.
The s t e a d y - s t a t e load requirement f o r a 180'
t r a v e r s e o f t h e t r a c k wi th t h e s i m p l i f i e d s p i n schedule would
approximate t h a t shown i n Figure 5.3. The a c c e l e r a t i o n load arid
i d e a l i n e r t i a l energy recovery would approximate t h a t shown i n
Figure 5 . 4 , and would i d e a l l y r e s u l t i n no n e t energy expended '
dur ing each revo lu t ion of t h e t r a c k . Thus, f o r t h i s s i m p l i f i e d
s p i n schedule t h e t o t a l motqr s h a f t load would be t h a t shown i n Figure 5.5, (summation o f Figure 5 .3 and Figure 5.4) which
accounts f o r t h e viscous energy l o s s e s dur ing spindown.
Unfortunately, t o maintain t h i s r o t a t i o n a l s p i n
schedule , a very l a r g e and c o s t l y sp in system motor must be used,
and t h e r e a r e very s e r i o u s a d d i t i o n a l s p i n system m t o r i n e f f i c i e n c :
l o s s e s . These w i l l be considered l a t e r i n t h i s s e c t i o n .
SCHEDULE - 18MPH WIND CIRCULAR TRACK
s a 120. c
90 120 150 180 210 2 4 0 2 7 0
F i g u r e 5.2. S i m p l i f i e d S p i n Scheduled Used t o ~ s t i m a t e . Sp in Motor S i z e .
F i g u r e 5.3. Rotor S t eady -S t a t e Viscous and Bear ing F r i c t i o n Load f o r S i m p l i f i e d Sp in Schedule .
5 0 0 -
400
300
a I
2 0 0
100
. ,
STEADY STATE POWER LOAD FOR SIMPLIFIED SPIN SCHEDULE
--- ..
ROTOR VISCOUS FRICTION AND DEARING FRICTION POWER LOSSES
o / I I I 1 I
90 120 150 180 210 2 4 0 2 70 8 DEGREES
8 DEGREES
Figure 5 .4 . I n e r t i a l Power Load, I d e a l Performance, N o Losses, Regenerat ive Braking, S impl i f i ed Spin Schedule.
8 DEGREES
Figure 5.5. T o t a l Power Load, Inc luding .Viscous Losses During Spindown, Regenerat ive Braking, S impl i f i ed . -
I t can be seen from Figure 5.5 t h a t no more than
42 pe rcen t o f t h e t o t a l s p i n motor s h a f t i n p u t power can be
recovered by regenera t ive braking dur ing spindown f o r t h e
s i m p l i f i e d s p i n schedule, assuming no motor i n e f f i c i e n c y l o s s e s
d u r i n g spinup and spindown.
For t h e aerodynamically-optimized s p i n schedule
(F igure 5.1) t h e r e s u l t i s less encouraging a s shown i n Figure 5.6.
This f i g u r e shows recovery o f only 20 percent of t h e spinup
energy dur ing regenera t ive braking because of t h e h igher l o s s e s
(compared t o those o f t h e Figure 5.2 s i m p l i f i e d schedu le ) .
These added l o s s e s a r e caused by t h e h igher v i scous - f r i c t ion-
power, load-schedule dur ing t h e major por t ion of t h e spindown
pe r iod . Thus, t h e viscous-friction-power load consumes mosc of t h e i n e r t i a l energy i n p u t t o t h e r o t o r , even without cons ider ing
motor e l e c t r i c a l l o s s e s dur ing both t h e spinup and spindown
p o r t i o n s of t h e schedule.
The a n a l y s i s above shows that use of a 457 m
diameter t r a c k r e q u i r e s a l a r g e , expensive, s p i n motor which con-
sums an unacceptable amount o f power. Fur ther , we f i n d t h a t very
l i t t l e spinup power i s recoverable , e s p e c i a l l y f o r t h e aero-
dynmically optimum s p i n schedule (F igure 5.1) . Therefore, it
appears t h a t w e must minimize both t h e i n e r t i a l load and viscous
l o a d r e q u i r e m n t s . Unfor t~mat-e ly , given a r o t o r s i z e and rpm schedule,
w e have l i t t l e c o n t r o l ove r t h e s t eady-s ta t e load o t h e r than by
reducing s t r u c t u r a l i n e r t i a . However, w e cannot reduce c y l i n d e r
i n e r t i a apprec iably because o f s t r e n g t h requirements. Therefore,
t h e only means f o r reducing a c c e l e r a t i o n l o s s e s a r e by i n c r e a s i n g
t h e t r a c k diameter and by changing t h e spinup schedule. W e
eva lua ted t h e in f luence o f t h e s e concepts i n a computerized s tudy
o f t h e Madaras system opera t ion ; b u t before we d i scuss t h e s e
r e s u l t s , it is appropr ia t e t o d i scuss t h e e f f i c i e n c y losses i n
t h e s p i n motor.
8 ' DEGREES
Figure 5.6. Total Power Load, Including Viscous Losses During Spindown, Regenerative Braking, Aerodynamically Optimum Spin.
Figure 5 .7 is an e f f i c i e n c y versus power ou tpu t
curve f o r a shunt-wound .dc motor , the type o f s p i n . system motor
t h a t must be used i n o r d e r t o rec'over energy 'by regenera t ive braking.
This curve i s f o r a motor running n,ear r a t s d speed. .However,
f o r the speed schedule o f a m t o r which would be used i n t h e
Madaras s p i n system, t h e e f f i c i e n c y versus power ou tpu t curve
would be t h a t shown i n Figure 5.8. I f w e p l o t t h e corresponding
speed versus power o u t p u t da ta w i t h , t h a t o f Figure 5.8, Figure
5 .9 is obta ined . Then, i f e f f i c i e n c y versus speed a t *given power
l e v e l s a r e c r o s s - p l o t t e d from Figure 5.9 t h e e f f i c i e n c y f o r a
complete Madaras speed schedule appears 9s i n Figure 5.10. The
speed-ef f ic iency range f o r normal usage o f l a r g e motors a l s o i s
shown i n Figure 5.10. Large motors are r a t e d for t h i s usage a t
no more than two starts p e r hour; whereas, t h e Madaras s p i n motor
would have t o s t a r t 45 times p e r hour (based 'on a 457-m diameter,
c i r c u l a r t r a c k , and a 8.9 m / s t r a c k speed) . Thus, t h e Madaras
s p i n motor is used i n a very severe and unfavorable mode from a
m t o r design and e f f i c i e n c y s t andpo in t and would r e q u i r e coding.
The magnitude o f t h e power l o s s e s f o r a regenera t ive
s p i n schedule a r e a l s o s t a t e d on ~ i g u r e 5.10. For t h i s
schedule, 100 pe rcen t power is immediately supp l i ed t o t h e motor -
and speed b u i l d s up a s shown i n t h e curve. Speed i n c r e a s e s a s
motor power overcomes i n e r t i a and viscous loads . Unfortunately,
h igh motor l o s s e s i n t h e form o f h e a t a l s o a r e r e a l i z e d . Con-
sequen t ly , about 56 pe rcen t o f t h e e l e c t r i c a l energy i n p u t t o t h e
motor w i l l be l o s t through h e a t i n g o f t h e m u t u ~ , arid an a d d i t i o n a l
f o u r pe rcen t o f t h e s h a f t ou tpu t w i l l be l o s t because o f r o t o r
qear inq . Thus a s shown i n Figure 5.10, regenera t ive braking during
spindown of t h e r o t o r can recover only 40 pe rcen t o f t h e i n e r t i a l
energy i n the s p i n n i n g r o t o r less t h e power consumed by t h e
g radua l ly dec reas ing s t eady-s ta t e viscous load during spindown.
S ince only 40 p e r c e n t o f t h e powek i n p u t t o t h e motor remains
a f t e r spinup, and s i n c e t h i s red:hihs i n e r t i a l energy is 4 . l 0 1
regenera ted a t only 40 pe rced t &ff ic ie l icy , only 0.40 x 0.40 o r
16 p e r c e n t o f t h e e l d c t r i c i l eiii?rw i n i t i a l l y inpu t t o t h e motor
% RATED POWER OUTPUT
F i g u r e 5 .7 . Pe r cen t E f f i c i e n c y v e r s u s Pe rcen t Rated Output Power f o r a Shunt-Wound d c Motor, Normal Opera t ion .
'10 RATED OUTPUT POWER
Figure 5.8. Pe rcen t E f f i c i e n c y v e r s u s Pe rcen t Rated Output Power f o r a Shunt- Wound .dc ' ~ o t o r .
0 100 200 300 '10 RATED OUTPUT POWER
Figure 5.9. Pe rcen t E f f i c i e n c y and Pe rcen t No-Load Speed v e r s u s Pe rcen t Rated Output .
Power.
RANGE, NORMAL MOTOR USAGE--/+ I
RANGE SHOWN FIGURE 5.7 - w 100
56% HEATING LOSS PLUS 4% SPEED REDUCER LOSS
W - LL L W
40% SHAFT INPUT POWER USED
2 0 40 60 80 100
% NO LOAD SPEED
F i g u r e 5.10. P e r c e n t E f f i c i e n c y v e r s u s P e r c e n t No-Load Speed Motor Losses f o r a Shunt-Wound dc Motor.
d u r i n g spinup can be saved by regenera t ion , and then t h i s amount
must be decreased by t h e s t eady-s ta t e spindown energy demand.
With only 20 p e r c e n t o f t h e spinup energy a v a i l a b l e f o r regenera t ive
b r a k i n g because o f viscous l o s s e s dur ing spindown, a s was
shown i n Figure 5.6, then only 20 pe rcen t of 16 pe rcen t , o r 3 . 2
p e r c e n t o f t h e t o t a l spinup energy could be recovered dur ing spin-
down. Therefore, it is obvious t h a t t h e Figure 5.1 s p i n schedule
w i t h r egenera t ive b rak ing i s n o t p r a c t i c a l f o r a 457-m-diameter
t r a c k (which governs t h e spinup, spindown a c c e l e r a t i o n time
p e r i o d ) , o r f o r t h e r o t o r geometry s tud ied . Thus, a s e r i e s of
computer runs were made t o determine a better design.
The Madaras system computer program e v a l u a t e s the
power ou tpu t from a sp inning c y l i n d e r a t 5O increments around
a c i r c u l a r t r a c k f o r any r o t o r conf igura t ion and weight , t r a c k
d iameter , wind speed, and t r a c k speed. Power and aerodynamic fo rces
a r e computed a t each p o i n t , and then power i s accumulated and
averaged t o give t h e average power output l e v e l p e r c i r c u i t
o f t h e t r a c k . This program a l s o con ta ins rou t ines t o eva lua te
t h e s p i n motor power requirements and t o a s s e s s l o s s e s f o r o t h e r
m c h a n i c a l and e l e c t r i c a l components o f t h e system. Losses o t h e r
than those o f t h e s p i n motor system amount t o 2 7 pe rcen t of t h e
c y l i n d e r o u t p u t power. These l o s s e s inc lude:
15 p e r c e n t genera to r l o s s e s
4 pe rcen t genera to r gearing l o s s e s
1 p e r c e n t wheei bea r ing l o s s e s
. 5 p e r c e n t synchronous condenser l o s s e s
2 percen t t r o l l e y , c o n t r o l , and o t h e r miscellaneous l o s s e s .
I n addi Lion, l o s s e s due t o mutual in ter fe . rence ,
aerodynamic drag , and r a i l f r i c t i o n a r e incorpora ted i n the
aerodynamic comput5ations and a r e a d d i t i v e t o t h e s p i n motor
l o s s e s and t h e above miscellaneous l o s s e s .
The folLowing design condi t ions were s t u d i e d i n
o u r s p i n motor computer a n a l y s i s .
Track speed: 8.9 m/s
Wind speed: 8.9 and 13.4 m/s
e Track d iameter : 457, 915, 1372, 1830 m
Spin motor s i z e : 450, 675, 900, 1200 kW
Motor e f f i c i e n c y - speed curve a s i n F igure 5.10
f ib tor s p i n schedule
Cons tan t s p i n motor power a t r a t e d l i m i t ' a p p l i e d d u r i n g sp inup and spindown
Maximum r o t o r speed o f 186 rpm a t power l e v e l r e q u i r e d t o mainta in c o n s t a n t r o t o r speed
Regenerat ive b r a k i n g beg inn ing a t t h e p o i n t where 8 = 240°.
9 See F igu re 5 .11 f o r power and speed schedu le s used f o r va r ious motor s i z e s . This i s n o t an optimum schedule , b u t it i s s a t i s f a c t o r y f o r motor s i z i n g s t u d i e s . The motor i s s i z e d f o r t h e i n i t i a l a c c e l e r a t i o n a t 8 = 90'.
These computer runs y i e l d e d d a t a which w e r e
p l o t t e d i n t h e form shown i n F igure 5.12. The optimum s p i n motor
s i z e and t h e maximum power o u t p u t f o r each s e t o f c o n d i t i o n s
was then s e l e c t e d from Figure 5.12 and t h e s e optimum p o i n t s w e r e
p l o t t e d ve r sus t r a c k d iameter ' f o r t h e 13.4 m/s (30 mph) and 8.9
m/s (20 mph) wind speeds a s shown i n F igu res 5.13 and 5.14
r e s p e c t i v e l y . F igures 5.13 and 5.14 show t h a t t h e o r i g i n a l
Madaras des ign f o r a 457-m-diamter t r a c k would e i t h e r consume
power o r a t b e s t y i e l d n e g l i g i b l e n e t power.
The on ly design c o n d i t i o n t h a t can be changed
w i t h o u t d i r e c t l y reduc ing t h e power o u t p u t f o r a c y l i n d e r i s
t r a c k d iameter . Tha t i s , t r a c k speed o r r o t a t i o n a l speed
r educ t ions reduce o u t p u t power d i r e c t l y , and r e d u c t i o n o f r o t a t i o n a l
i n e r t i a r e q u i r e s r e d u c t i o n o f r o t a t i o n a l speed because o f s t r e n g t h
requirements . I n c r e a s i n g t r a c k d i ame te r , however, reduces
c y l i n d e r a c c e l e r a t i o n requirements d i r e c t l y w i t h no e f f e c t on
c y l i n d e r aerodynamic o p e r a t i o n . Track d iameter i n c r e a s e s impact
u n i t p l a n t power c o s t o n l y s l i g h t l y i f number o f c a r s i n c r e a s e s
w i t h t r a c k . s i z e , provided t h a t t h e p r o p e r c a r s p a c i n g i s mainta ined;
i .e., car c o s t p e r u n i t o f t r a c k remains t h e same and p l a n t c o s t
p e r u n i t o f power i s i n c r e a s e d on ly s l i g h t l y because o f t h e co 's t
90- SPINUP * 8'VARlABLE WITH MOTOR AND 240-270 TRACK SIZE SPIN-
8 DEGREES DOWN
F i g u r e 5.11. Modif ied S p i n Schedule f o r Var ious S p i n Motor S i z e s .
,
1000
800
3 Y I 600
ILI W 3
4 0 0 H W I- V) $, 2 0 0 .
Ei - a m O
900 KW MOTOR
675 KW MOTOR ------------
450 KW MOTOR . . . . . . . . . . . . . . . . . . *
- 2 0 0
- 4 0 0
8 ' V A R I A B L E WITH MOTOR AND TRACK S lZE AS I S SPINDOWN POWER L E V E L AND PROFILE
400. I I - TRACK DIAMETER = 3 0 0 0 F T (915m)
RPM = 186
300 Vw =30MPH-
I
SPIN MOTOR SIZE - KW
Vw=20MPH ( 8.9 m/s)
Figure 5 . 1 2 . Plant Power Output versus Spin l . ~o tor S i z e , 3 , 0 0 0 - f t Diameter Track# 186 rpm for Various Wind Speeds.
TRACK DIAMETER - FEET (m)
, . 1400-
1200
1000-
800
3 Y
600- cr W 3 0
400-
Figure 5.13. Optimum Ilotor S i z e and Plaximum Por~rer Output/ Rotor ve r sus Track Diameter, 30 mph Wind Speed.
Lcyl = l lO FT (33.5m)
Dcyl = 18 F T (5.5 m) Icyl = 45,592 SLUG- FT* (6305 m-Kg-sec2)
Wmax= 186 RPM
Vw = 30 MPH (13.4 m /s)
- I ROTOR
F OPTIMIJM MOTOR SIZE -
MAXIMUM NET POWER OUTPUT
1830 I
( 2 4 4 0 ) 1 I I
1400-
1200-
1000-
8 0 0
3 Y
2 600- [r
s g ,400-
TRACK DIAMETER - FEET (m)
Lcyl = I lOFT(33.5m)
Dcyl = 18 FT(5.5m) Icyl = 45,592 SLUG- FT* (6305 m-~g-sec2)
Wmax= 186 RPM
Vw = 2 0 MPH (8.9 m/s)
I ROTOR
OPTIMUM MOTOR SIZE
-
Figure 5.14. Optimum Motor Size and Maximum Power Output/Rotor versus Track Siameter, 20 mph Wind Speed.
o f t h e g r e a t e r a r e a o f unused l and i n t h e c e n t e r o f t h e t r a c k .
However, s p i n motor s i z e , c o s t , and power assessment a g a i n s t
the power ou tpu t o f t h e c y l i n d e r a r e g r e a t l y reduced because
a c c e l e r a t i o n ,power requirements becom a decreas ing propor t ion
o f t h e s p i n motor power . load. a s t r a c k s i z e inc reases .
Figure 5 ..I3 shows t h a t f o r t h e given opera t ing
c o n d i t i o n s , optimum s p i n motor s i z e appears t o be approaching an
asymptote of 425 k i l o w a t t s a t very l a r g e t r a c k diameter , say 3 km,
o r 10,000-feet , and maximum ou tpu t power is approaching an asymptote
o f about 350 k i l o w a t t s . This means t h e g r e a t e s t power t h a t can
be ob ta ined from a c i r c u l a r track f o r a 13.4 m/s wind and t h e
given r o t o r conf igura t ion , speed l i m i t , and s t r u c t u r a l S t rength
i s 350 k i l o w a t t s p e r c a r . S i m i l a r l y , Figure. 5.14 shows an <
asymptote approaching 400 k i l o w a t t s f o r t h e optimum s p i n motor
s i z e and an asymptote approaching zero n e t output power from t h e
n e g a t i v e power l e v e l f o r a 8.9 m / s wind. That i s t o say , f o r a
wind speed o f 8.9 m / s , no n e t power can be produced by t h e r o t o r
des ign on any c i r c u l a r t r a c k s i z e . I t is expected t h a t performance
improvement could be ob ta ined on l a r g e diameter t r a c k s by a l lowing
t h e r o t o r t o c o a s t down i n rpm. on t h e upwind s e c t i o n of t h e t r a c k
and thereby conserving a p o r t i o n o f t h e s t eady-s ta t e power requi re-
ment. Then, a small amount o f dynamic braking, i n s t e a d o f regenera-
. t i v e braking , would be app l i ed j u s t p r i o r t o s p i n d i r e c t i o n
r e v e r s a l s i n c e m o s t o f t h e angular momentum would have been
d i s s i p a t e d dur ing t h e coastdown.
Fiqure 5.13 shows t h e t r a c k diameter should be
g r e a t e r than. 1220 m (4000 f t ) f o r reasonable opera t ion o f t h e
given system i n a 13.4 m/s wind; and a t r a c k diameter o f 1830 m
(6,000 f t ) i s requ i red t o o b t a i n maximum power ou tpu t wi th a
450 kW (600 hp) motor. Figure 5.14 shows a t r a c k diameter o f
915 m (3000 ' f t ) shou1.d be t h e minimum diameter considered f o r a
8.9 m/s wind, and t h a t t h i s i s nea r ly t h e minimum diameter f o r '
which optjmum opera t ion can be obta ined wi th a 450 kW s p i n motor.
Larger diameter t r a c k s w i l l give s l i g h t l y b e t t e r performance
w i t h t h a t same & t o r .
~ h u s , w e concluded t h a t a 450 kW ,. :500. v o l t dc
sp in motor would be used f o r o u r f i n a l ana lyses , and t h a t t h e
minimum t r a c k d i a n e t e r should be 13.72 m. S tudies of. t h e s p i n schedule a r e presented i n Sec'tion' VI.
This s tudy a l s o confirrtled i n i t i a l f ind ings t h a t
regenera t ive braking was of n e g l i g i b l e value t o t h e Madaras
system. W e confirmed t h a t regenera t ive braking under any of t h e
speed schedules s t u d i e d would recover less than 5% o f t h e energy
inpu t t o the s p i n motor. Fur the r , r egenera t ive braking i s not
necessary t o dece le ra te t h e c y l i n d e r , because viscous fo rces are
s o l a r g e t h a t power a c t u a l l y must be suppl ied t o maintain t h e
d e s i r e d sp in schedule dur ing spin-down. F i n a l l y , a c o s t pena l ty
is r e a l i z e d through use of regenera t ive braking. This penal ty
r e s u l t s from t h e need f o r more expensive motor c o n t r o l s ( a dc-ac
conver ter ) , l a r g e r c i r c u i t b reakers , and l a r g e r t r o l l e y bus b a r s .. .
t o d i s t r i b u t e t h e regenerate.d e l e c t r i c i t y t o t h e system. Thus,
we decided t o use c o n t r o l l e d motor spin-down followed by
resistor-activated.dynamic . . braking a t very low speeds t o b r i n g
t h e c y l i n d e r t o a complete s t o p .
Spin System C o n t r o l l e r
A commercial dc motor c o n t r o l l e r was s e l e c t e d t o
control t h e r o t o r s p i n motor. Units s e l e c t e d w i l l provide both
speed and dynamic braking c o n t r o l on each c a r . The c o n t r o l
system c o n s i s t s of a three-phase t ransformer feeding a s e t o f
S i l i c o n Contro l led R e c t i f i e r s (SCR's) . The S C R ' s can be f i r e d
by c o n t r o l c i r c u i t s over any por t ion of t h e i r conductive h a l f o f
t h e inpu t a l t e r n a t i n g c u r r e n t cyc le t o c o n t r o l t h e motor armature
power. Dynamic braking w i l l be r e s i s t o r c o n t r o l l e d , and d i r e c t i o n
r e v e r s a l w i l l be achieved by reve r s ing t h e p o l a r i t y o f power l eads
t o t he armature,
Speed c o n t r o l w i l l be achieved by ba lancing t h e
inpu t power l e v e l t o the armature a g a i n s t t h e demand of t h e
c o n t r o l funct ion s i g n a l . A motor vol tage , c u r r e n t , power, , o r
speed p r a f i l e t ime h i s t o r y can be used a s a motor c o n t r o l
f u n c t i o n , o r an e x t e r n a l c o n t r o l s i g n a l can be furn ished t o t h e
c o n t r o l l e r . S ince t h e c o n t r o l funct ion can n o t o b t a i n more power
from t h e t r a n s f o r m e r - r e c t i f i e r power supply than it is capable
o f d e l i v e r i n g , t h e c o n t r o l u n i t s must be s i z e d g r e a t e r than t h e
maximum demand f o r motor te rminal inpu t power. Therefore, we
s e l e c t e d c o n t r o l u n i t s s i z e d f o r a 450 kW, 500 v o l t motor.
One c o n t r o l l e r w i l l be mounted on each r o t o r c a r .
Modern c o n t r o l l e r s r e p r e s e n t a s i g n i f i c a n t advance i n motor use
technology. Thei r l o s s e s a r e s i g n i f i c a n t l y less than t h e l o s s e s
i n c u r r e d by t h e former methods of r e s i s t o r , vol tage c o n t r o l ,
a u t o t r a n s f o r m e r - r e c t i f i e r vol tage c o n t r o l , o r motor-generator
v o l t a g e c o n t r o l . They a r e more f l e x i b l e , respond m r e quickly
t o c o n t r o l i n p u t s , and c o s t no more than many of t h e o l d e r c o n t r o l
methods.
I n a d d i t i o n t o the c o n t r o l l e r system, a magnetic
d isconnect and over load . c i r c u i t breaker o r fus ing would be
r e q u i r e d f o r t h e s p i n motor. These elements would normally be
p laced on t h e power l i n e s i d e of t h e c o n t r o l l e r i n p u t t ransformer.
5 . 4 GENERBTOR SYSTEM
The genera to r system was s i z e d a t 1 MW r a t e d output by
t h e e l e c t r i c a l system design requirements. The fol lowing
paragraphs d i s c u s s t h e genera tor o p e r a t i n g condi t ions and the
approach t o genera to r s e l e c t i o n .
The genera to r s e l e c t i o n was l i m i t e d t o t h r e e b a s i c types
o f genera tors : synchronous genera tors o f t h e type used by mst
u t i l i t y companies; induct ion genera tors a s planned f o r use by
Madaras; o r d i r e c t c u r r e n t genera tors . The f i r s t two types a r e
60 Hz a l t e r n a t i n g c u r r e n t machines. The t h i r d would requ i re
some type o f i n v e r t e r system t o convert i ts ou tpu t t o power g r i d
frequency wi th a concurrent c o s t and e f f i c i e n c y pena l ty .
Synchronous genera tors could be opera ted a t 90 t o 95
pe rcen t e f f i c i e n c y , b u t with considerable pena l ty i n o p e r a t i o n a l
problems and c o s t . The o p e r a t i o n a l problems would c o n s i s t o f
a l i g n i n g and maintaining a l l t h e genera tors p r e c i s e l y i n phase
with t h e ou tpu t power g r i d frequency.. Since c u r r e n t p lans a r e
t o i n s t a l l four 250 kW genera tors on each c a r , t h e i n i t i a l
alignment of t h e t o t a l system would be a l a r g e problem. Speed
c o n t r o l of t h e system, speed changes between c a r s due t o
s t r e t c h i n g and c o n t r a c t i o n of in te rconnec t ing l inkages , and
speed changes on a c a r due t o wheel s l ippage would a l l cause
c i r c u l a t i n g c u r r e n t power l o s s e s . Because of t h e s e problems,
synchronous genera tors were e l imina ted from cons ide ra t ion f o r
t h i s s tudy. '
Induct ion genera tors a r e no t i n wide usage a t t h e
p r e s e n t t ime, however a number o f smal l e r wind t u r b i n e s a r e
using them. The genera tor c o n s i s t s o f an induct ion motor
connected t o a power g r i d with t h e s h a f t be ing dr iven above
synchronous speed by an e x t e r n a l m c h a n i c a l power source. The
generator/motor then feeds power i n t o t h e g r i d a t synchronous
frequencyf' and a t a l e a d i n g power f a c t o r . An induct ion genera tor
would a c t a s a governor on . the Madaras system. A s more power
becomes available from t h e r o t o r s , t h e c a r s would speed up
s l i g h t l y , produce more power from t h e genera to r s , and hence load
down t h e i n p u t s h a f t t o l i m i t t h e speed inc rease . I t i s b e l i e v e d
t h e genera tors woi11d nperate, a t 80 t o 85 pe rcen t e f f i c i e n c y a t
a power f a c t o r o f 0.8 t o 0.9 leading . The power f a c t o r would
be co r rec ted by a synchronous r e a c t o r system a t t h e c o n t r o l
house d i s t r i b u t i o n s t a t i o n . Induct ion genera tors would be
purchased a s 250 kW induct ion motors, f o u r t o a c a r , and 72 f o r
an 18-car p l a n t . A s wind decreases from t h e r a t e d va lue ,
i n d i v i d u a l genera tors could be dropped o f f t h e l i n e t o enable
t h e remaining connected u n i t s t o opera te a t peak e f f i c i e n c y .
Magnetic con tac to r s and fuses o r c i r c u i t b reakers would be
requ i red f o r each genera tor , four s e t s t o a c a r . No c o n t r o l s
would be requ i red except t h e magnetic con tac to r f o r each
genera tor . Each 250 kW genera tor would provide 4160V, 60 Hz,
3% power.
5.5 POWER PLANT
The c o n t r o l system c o n s i s t s o f t h e fol lowing components :
A minicomputer-based primary c o n t r o l l e r i n the c o n t r o l house.
o A microcomputer-based c o n t r o l l e r on each c a r .
0 A two-wayradio te lemetry system t o l i n k a l l t he c a r u n i t s t o t h e primary c o n t r o l l e r .
o A wind s e n s o r network d i spe r sed around t h e t r a c k and h a r d wired underground t o t h e primary c o n t r o l l e r .
e Monitoring ins t ruments and c o n t r o l a c t u a t o r c i r c u i t s on each c a r and on system network components.
.
An o p e r a t o r s s t a t i o n i n the c o n t r o l house c o n s i s t i n g of m n i t o r i n g instruments and manual over- r ides of t h e primary c o n t r o l l e r .
These components a r e d iscussed i n the s e c t i o n s which
fol low.
5.5.1 Primary System C o n t r o l l e r
The primary c o n t r o l l e r ' would be based on a mini-
computer of t h e PDP 11 family, probably one of t h e medium c a p a b i l i t y
s i z e s . The computer would be programed f o r complete a u t o s a t i c
c o n t r o l of t h e e n t i r e 'system inc luding r o t o r speed c o n t r o l and
a c t u a t i o n of c o n t r o l disconnec' ts on t h e c a r s ; t h e in terconnect ing
power network w i t h i n t h e s y s t e m ; and t h e i n t e r f a c e wi th t h e e x t e r n a l
power g r i d . Rotor speed c o n t r o l sof tware would be f l e x i b l e t o
permi t simple modif ica t ion t o o b t a i n optimum r o t o r performance
c h a r a c t e r i s t i c s based on c a r p o s i t i o n and wind speed and d i r e c t i o n
around t h e ' t r ack . However, it i s be l ieved t h a t an 'improved vers ion
of F igure 5.11 spin-up p r o f i l e would be used dur ing t h e major
p o r t i o n of spin-up t o minimize s p i n motor s i z e . Wind d a t a from a
network of wind sensors d i spe r sed around t h e t r a c k would be routed
i n t o t h e computer through a dedica ted mul t ip lexe r , a s would d a t a
from t h e in te rconnec t ing power network sensors . Data from and t o
t h e moving c a r s would be communicated through a c e n t r a l r a d i o
t e l emet ry s t a t i o n which would have i t s own mul t ip lexe r i n t e r f a c e .
The c o n t r o l funct ion would inc lude system
s a f e t y monitoring and c o n t r o l a s w e l l a s performance monitoring
and c o n t r o l . Parameters such a s vo l t ages , c u r r e n t s , phase ang les ,
bea r ing and motor temperatures, no i se and v i b r a t i o n l e v e l s ,
disconnect s t a t u s , and poss ib ly o t h e r s would be monitored.
Appropriate s t e p s , such a s d isconnect ing equipment, dropping
load by l i m i t i n g r o t o r rpm, o r s h u t t i n g down the system would be
performed a s s p e c i f i e d i n t h e c o n t r o l program by e i t h e r s a f e t y
o r o p e r a t i o n a l a lgori thms. Control ou tpu t s i g n a l s would be
t r a n s m i t t e d by te lemetry t o t h e c a r s and by hard w i r e t o t h e
remainder o f t h e system. An o p e r a t o r would have c o n t r o l over-
r i d e s t o s h u t down t h e system i n segments and i n i t s e n t i r e t y
f o r s a f e t y reasons a s i n d i c a t e d by h i s own s e t o f m n i t o r i n g
i n s t r m n t s . The primary c o n t r o l l e r would be backed up by a
s p a r e system o r an a l t e r n a t e o p e r a t i n g mode, otherwise t h e t o t a l
system would be nonfunct ional when a c o n t r o l l e r f a i l u r e occurred.
5.5.2 Secondary on-Car C o n t r o l l e r
Each c a r would have a microcomputer-based,
on-board c o n t r o l l e r t o t r ansmi t da ta s i g n a l s from t h e c a r t o
t h e c e n t r a l c o n t r o l l e r and t o rece ive c o n t r o l s i g n a l s and a c t on
them. Multiplexed two-way rad io te lemetry would provide t h e
communication l i n k . Primary d a t a from t h e c a r , such a s l o c a t i o n ,
r o t o r r p m , motor and genera tor and l i n e vol tages and c u r r e n t s
would be d i g i ' t i z e d and t r ansmi t t ed a t d i s c r e t e i n t e r v a l s . .Safety
func t ions such a s temperature and v i b r a t i o n l e v e l s .might be examined
by t h e l o c a l processor and only maximum- va lues o r s e l e c t e d samples
would be s e n t o u t . . S u f f i c i e n t capac i ty c o u l d , b e provided i n
the processor t o c o n t r o l r o t o r rpm on t h e c a r based on wind d a t a
f o r t h e c a r l o c a t i o n , a s received from t h e c e n t r a l c o n t r o l l e r .
The d i v i s i o n o f funct ions between the two c o n t r o l l e r s would depend
on t h e i r r e l a t i v e c a p a c i t i e s and t h e capac i ty o f t h e te lemetry
l i n k . Complete d e f i n i t i o n o f t h e s e systems i s n o t p o s s i b l e
wi thout a comprehensive~study which i s much beyond t h e scope
o f t h e p r e s e n t program.
The c o n t r o l l e r w i l . 1 have t o inc lude c o n t r o l
o u t p u t i n t e r f a c e s and c o n t r o l a c t u a t o r d r ive c i r c u i t s t o opera te
t h e s p i n motor speed c o n t r o l system and t h e o p e r a t i o n a l and
s a f e t y d isconnects . Disconnects w i l l be provided f o r t h e sp in
motor c o n t r o l l e r and f o r each o f t h e four genera tors a s a
minimum. Manually opera ted c i r c u i t . b reakers w i l l a l s o be
provided f o r each 'of t h e s e funct ions and f o r t h e c a r primary
l i n e s . C o n t r o l l e r c i r c u i t s would be organized on a modular
b a s i s s o . that c i r c u i t boards o r . equipment components could be
r e a d i l y r ep laced from a s tock of spa res . The onboard c o n t r o l l e r
program would be r e s i d e n t i n a ROM o r EPROM memory board i n
the processor which could be replaced o r reprogrammed.
5.5.3 Radio T e l e m t r y System
The r a d i o te lemetry system would c o n s i s t of a
c e n t r a l r e c e i v e r - t r a n s m i t t e r s t a t i o n loca ted a t t h e c e n t e r of
t h e t r a c k and hardwired t o t h e c e n t r a l processor . A rece iver - ,
t r a n s m i t t e r would be m u n t e d on each c a r and connected t o t h e
onboard c o n t r o l l e r . I t has n o t been determined y e t i f a. s i n g l e
o r mul t ip le c a r r i e r r a d i o beam would be requi red . In e i t h e r case ,
t h e s i g n a l from t h e c e n t r a l s t a t i o n would be t r a n s m i t t e d on a
f u l l - t i e b a s i s , wi th coded d i g i t a l command t r ansmi t t ed v i r t u a l l y
s imultaneously t o a l l . c a r s . The t r ansmi t t ed beam would
i n c l u d e a synchroniz ing code t o a c t i v a t e t h e t r a n s m i t t e r s on the
va r ious c a r s s e r v i c e d by . t h e c a r r i e r on a s e q u e n t i a l b a s i s . The
s i g n a l rece ived back would then be a continuous s i g n a l from a
s . e r i e s of a d j a c e n t c a r s . The c e n t r a l antennas could be
c o n t r o l l e d to . r o t a t e i n synchronism wi th t h e e a r s , i f necessary,
I t is expected t h a t seven o r e i g h t - b i t d i g i t a l
d a t a s i g n a l s would give s u f f i c i e n t r e s o l u t i o n of t r a n s m i t t e d
ana log da ta . Some d a t a might be t r a n s m i t t e d i n fewer b i t s , f o r
i n s t a n c e , d isconnect o r switch c l o s u r e s could be t r a n s m i t t e d
i n a s i n g l e b i t . Data t r a n s m i t t a l r a t e requirements a r e n o t
expec ted , t o be hi'gh ' a t t he ' planned c a r speed of 8 .9 m / s .
Telemetry system o v e r a l l requirements cannot be f i n a l i z e d u n t i l
t r a c k s i z e and c o n f i g u r a t i o n and c a r spac ing are e s t a b l i s h e d .
Commercial equipment is r e a d i l y a v a i l a b l e f o r most components
o f t h e system, b u t t h e m u l t i p l e x i n g scheme might r e q u i r e develop-
ment depending on t h e f i n a l s i z e o f t h e system. A s p a r e c e n t r a l
u n i t shou ld be provided.
Wind Sensor Network
The wind s e n s o r network would c o n s i s t o f an
a r r a y o f s t a n d a r d vane and cup in s t rumen t s mounted on p o l e s
around t h e i n s i d e and o u t s i d e pe r iphe ry o f t h e t r a c k l i n e , b u t
o u t s i d e t h e immediate f i e l d o f i n f l u e n c e o f t h e r o t a t i n g c y l i n d e r s .
A s p a c i n g between 152 m and 3 0 4 m, depending on p l a n t s i z e ,
shou ld prov ide adequate coverage o f t h e wind p a t t e r n impinging
on t h e upwind s i d e s o f t h e t r a c k . The d i r e c t i o n and v e l o c i t y
s e n s o r s would be ha rd wi red t o a m u l t i p l e x e r i n p u t s t a t i o n o f t h e
c e n t r a l c o n t r o l l e r . The s e n s o r d a t a would be processed t o d e f i n e
t h e changing wind flow f i e l d , and t h e i n d i v i d u a l r o t o r speeds
would be c o n t r o l l e d acco rd ing ly t o produce optimum power o u t p u t
from each car. The wind s e n s o r network would prov ide t h e primary
d a t a f o r . s t a r t u p and shutdown o f t h e system and . f o r c o n t r o l l i n g
it dur ing i t s o p e r a t i o n . C o m r i c a l s e n s o r s adequate f o r use
i n t h e network a r e a v a i l a b l e .
5.5.5 . Monitoring Ins t ruments and Ac tua to r s
Moni tor ing in s t rumen t s and a c t u a t o r s needed f o r
t h e system axe r e a d i l y a v a i l a b l e as commercial items. The
complement o f a c t u a t o r s would c o n s i s t on ly o f magnetic c o n t a c t o r s . A t l e a s t no o t h e r t ype has been i d e n t i f i e d as a requirement t o
d a t e . Monitoring in s t rumen t s would i n c l u d e vo l tme te r s , ammeters,
phase ang le o r power f a c t o r meters , v i b r a t i o n and n o i s e s e n s o r s ,
thermocouples - o r t h e r m i s t o r s , microswitches , and p o s s i b l y smoke
d e t e c t o r s .
The use o f t h e s e s e n s o r s i s s t r a i g h t f o r w a r d . a n d '
r e q u i r e s very l i t t l e exp lana t ion . Microswitches would b e used
t o measure wheel ro t - a t i ona l v e l o c i t y , t r a c k speed, t r a c k p o s i t i o n ,
a c t u a t o r c l o s u r e s , r o t o r rpm; and occupancy o f a c a r . Processing
o f microswitch codes o r c losure r a t e s would be performed by t h e
onboard.computer t o develop requ i red s i g n a l s o r c o n t r o l funct ions .
P h o t o c e l l c i r c u i t s might be used more cheaply and r e l i a b l y f o r
some o f t h e s e even t de tec t ion opera t ions .
I t is expected t h a t t h e system o r onboard com-
p u t e r s would have no d i f f i c u l t y .hand l ing t h e s i g n a l s from any o f
t h e r equ i red sensors if s u i t a b l e s i g n a l cond i t ion ing i s provided.
Many o f t h e ins t ruments can be purchased with accessory ' d i g i t a l l y
coded ou tpu t s . ~ l g o r i t h m s can be r e a d i l y provided f o r t h e pro-
c e s s o r opera t ions r equ i red t o analyze . t h e d a t a s i g n a l s and t o
txansmi t a s e l e c t e d subse t and a c r i t i c a l subse t t o t h e c e n t r a l
processor . A s e l e c t e d set o f d a t a a l s o would be provided t o
onboard d i g i t a l d i s p l a y instruments f o r use i n maintenance and
r e p a i r ope ra t ions . A c o n t r o l l e r i n t e r r o g a t i o n s e t with d i sp lay
could be provided t o access a l l t h e da ta i n the c o n t r o l l e r a t
n o t t o o g r e a t a c o s t . These op t ions would be def ined i n the
f i n a l d e t a i l e d design o f t h e o p e r a t i o n a l system.
An o p e r a t o r ' s con t ro l s t a t i o n con sol.^! wni?Ld he
provided i n the system c o n t r o l house. This s t a t i n n would have
ins t ruments d i s p l a y i n g a l l t h e system o p e r a t i o n a l parameters ,
i n c l u d i n g monitors o f t h e c e n t r a l processor and te lemetry system.
Also, any d a t a i d e n t i f i e d by t h e c e n t r a l c o n t r o l l e r as quest ion-
able o r c r i t i c a l fromthe c a r s , the system network, o r t h e wind
s e n s o r network would be displayed wi th i d e n t i f i c a t i o n data on
a s e t o f warning d i g i t a l readout d i sp lays . A computer c o n t r o l
console with cH1l' d i s p l a y and hardcopy c a p a b i l i t y would be fur-
n i shed t o i n t e r f a c e wi th ' the c e n t r a l c o n t r o l l e r and t o ob ta in
d e t a i l e d information on: t h e opera t ion of t h e system. A running
a n a l y s i s of t h e e n t i r e system opera t ion could be provided on t h e
hardcopy u n i t a s t h e major p a r t 'of t h e bookkeeping opera t ion .
In a d d i t i o n t o the d i sp lays descr ibed above, . t h e
o p e r a t o r ' s s t a t i o n would conta in switches t o over-r ide t h e con-
t r o l l e r t o s h u t down any c a r o r t h e e n t i r e system. Switches
would be a v a i l a b l e a l s o t o replace t h e c o n t r o l l e r and c e n t r a l
te lemetry systems with spa re u n i t s .
5.6 SYSTEM NETWORK CIRCUITRY AND COMPONENTS
The system network c i r c u i t r y and components a r e t h e e l e c t r i c a l
components requi red t o i n t e r f ace t h e e l e c t r i c a l u n i t s descr ibed
i n t h e previous s e c t i o n s of t h i s s e c t i o n wi th each o t h e r and wi th
t h e output commercial e l e c t r i c a l power l i n e g r i d .
5.6.1 System Network Elements
The system network elements inc lude t h e fol lowing:
a . Car t r o l l e y s and t r o l l e y feeder bus
b. D i s t r i b u t i o n c i r c u i t t o t h e t r o l l e y feeder bus
c . Synchronous r e a c t o r s f o r power f a c t o r c o r r e c t i o n
d. U t i l i t y f eeder c i r c u i t s
e . Subs ta t ion
The system network components l i s t e d i n items a , b , c , above would
a l l be 4160V, 60 Hz, 3% equipment. Transformers t o i n t e r f a c e t h e
4160V system network t o t h e commercial power g r i d and t o produce
480V, 3% and 120V, 1% u t i l i t y c i r c u i t s fox t h e l i g h t i n g and
e q u i p m n t c i r c u i t s o f i t em d would be included i n t h e s u b s t a t i o n
l i s t e d under i t em e above.
5.6.2 Car Tro l l eys and Tro l l ey Feeder Bus
The c a r t r o l l e y s would c o n s i s t o f three s l i d i n g
shoe trolleys opera t ing on. a 4160V, 3% t r o l l e y bus. The c a r
ground would c o n s i s t o f ground brushes and t h e c a r wheels running
on the grounded s t e e l t r a c k . Each o f t h e c a r t r o l l e y s would r e q u i r e
a c u r r e n t capaci ty o f 70 amperes minimum f o r incoming c u r r e n t t o
energize t h e r o t o r s p i n motors dur ing system s t a r t u p . This f i g u r e
assumes c u r r e n t l i m i t i n g i n t h e s p i n motor c o n t r o l l e r t o l i m i t
motor c u r r e n t t o 1000 amperes RMS, and no use o f t h e induct ion
g e n e r a t o r s a s motors . t o a s s i s t i n s t a r t u p . The l i m i t i n g design
cond i t ion , however, would occur ,with t h e genera tors a t f u l l out-
p u t dur ing a h igh wind cond i t ion wi th t h e s p i n motor coas t ing .
The t r o l l e y c u r r e n t then would be 140 amperes o u t o f t h e c a r .
W e have decided t o use a 500 ampere t r o l l e y arm manufactured by
Insul -8 , Inc. because o f t h e high vol tage c a p a b i l i t y o f t h e i r
t r o l l e y feeder bus. This w i l l provide long-l ived t r o l l e y shoes
a s w e l l a s cons ide rab le capac i ty f o r regenera t ive braking, i f
d e s i r e d .
A 4160V, 3 g r 500 ampere t r o l l e y bus system manu-
f a c t u r e d by Insul-8, Inc . would be supported .. - from po les around
t h e i n s i d e pe r iphery o f t h e t r a c k system. This 3% bus would
form a complete loop i n s i d e and p a r a l l e l t o t h e t r a c k loop. The
t r o l l e y shoes w i l l be supported from t h e c a r by a r t i c u l a t e d
suppor t ing arm devices a l s o manufactured by Insul-8, Inc . A
s k e t c h o f t h e t r o l l e y a r m i s shown i n Figure 4.20.
5.6.3 D i s t r i b u t i o n C i r c u i t t o t h e Trol ley Feeder Loop
A d i s t r i b u t i o n c i r c u i t is requ i red t o connect t h e
t r o l l e y feeder bus loop t o t h e syst.em 4160V, 3% t ransformer
c i r c u i t . W i t h a maximum c a r ou tpu t c u r r e n t capac i ty o f 140 amperes
and a 500 ampere t r o l l e y loop, t h e d i s t r i b u t i o n c i r c u i t w i l l
have t o b e connected t o t h e t r o l l e y loop conductor bus b a r s
w i t h i n a d i s t a n c e o f t h r e e and one-half c a r spacings. A t h r e e
car spac ing f o r in ter -connect ions would provide a capac i ty f o r
1.2 MW ou tpu t per car, which should be more than adequate.
The d i s t r i b u t i o n c i r c u i t connectors around t h e
t r o l l e y feed loop could be supported from t h e poles t h a t support
t h e t r o l l e y feed bus b a r s . Support ing them from t h e oppos i t e
s i d e o f t h e po les would t end t o balance t h e s i d e over turn ing
moment load on t h e p o l e s . The d i s t r i b u t i o n c i r c u i t would be
f e d i n t o t h e loop a t a p o i n t on t h e loop across t h e t r a c k from
t h e 4160V s u b s t a t i o n . The feed would b e s t b e p laced underground
t o c ross t h e t r a c k . I t would then branch r i g h t and l e f t around
t h e loop, each s i d e ca r ry ing h a l f o f t h e system ou tpu t c u r r e n t
o r s t a r t u p c u r r e n t . The conductors could be tapered down from
t h e branch p o i n t t o t h e opposi te p o i n t on the loop a t a r a t e
of 500 ampere decrease i n conductor c u r r e n t capac i ty a s each
in te rconnec t ion p o i n t t o t h e t r o l l e y loop i s passed. The main
feeder would have t o c a r r y both branch c u r r e n t s and should be
r a t e d a t 170 amperes p e r phase f o r each c a r on the system. The
branch conductors and t h e 4160V t ransformer and i t s switchgear can
a l l be s i z e d from the f i n a l capac i ty o f t h e 'feeder c i r c u i t . The
feeder c i r c u i t should be p ro tec ted wi th a c i r c u i t breaker . Also,.
a magnetic con tac to r should be provided t o t u r n the e n t i r e t r o l l e y
system on and o f f .
5 . 6 . 4 Synchronous Reactors
The requirements f o r synchronous r e a c t o r s s e e m s
t o be a dubious propos i t ion . I f t h e Madaras power became a
s i g n i f i c a n t p o r t i o n of t h e g r i d power, c o r r e c t i o n would be
necessary t o balance t h e l i n e more c l o s e l y t o t h e normal power
load. I n t h i s c a s e it would be b e t t e r t o f u r n i s h t h i s c o r r e c t i o n
i n o rde r t o preempt r e s i s t a n c e t o t h e use of u t i l i t y company
l i n e s .
Synchronous r e a c t o r s provide t h e c a p a b i l i t y t o
produce l a r g e va lues of r e a c t i v e loading f o r a s m a l l expendi ture
i n power l o s s e s . Fur the r , t h e r e a c t i v e load i s e a s i l y c o n t r o l l a b l e
by c o n t r o l l i n g t h e f i e l d of what i s genera l ly an i n - l i n e , s e l f - e x c i t e d , r e a c t o r f i e l d DC genera tor . I f r e a c t o r s a r e provided
they can be s i zed from t h e capac i ty of t h e system and t h e f a c t
t h a t t h e induct ion genera to r s would normally be operated a t 0.8
t o 0.85 leading power f a c t o r . A t 0.8 P.F. it would r e q u i r e a
synchronous r e a c t o r capac i ty of 45 pe rcen t of t h e system r a t e d
power ou tpu t capac i ty t o c o r r e c t t h e system output t o 1.0 P.F.
The r e a c t o r s would opera te a t about 98 percent e f f i c i e n c y ,
producing about 1 .5 pe rcen t e f f i c i e n c y pena l ty a g a i n s t t h e system
r a t e d output . They would be s e a l e d , hydrogen f i l l e d u n i t s . An
e x c i t e r f i e l d c o n t r o l po t should be provided on t h e o p e r a t o r ' s
console and a disconnect magnetic contractor operable by the
operator or by the automatic controller also should be provided.
An overload circuit breaker sho'uld be 'installed in the 3fl reactor
lines.
5.6.5 Utilitv Feed'er 'Circuits
Feeder circuits to operate lights and equipment
shoulh be provided for the control house and repair areas of
the system. These circuits must provide power for lighting,
heating, air-conditioning, controls and for power tools and
other utility equipment. The' circuits must provide 480V-3% and
120V-1% power. If a sizable crane is needed for the repair area,
a h i y h e r voltage cixcuit might be provided for that purpose.
These utility circuits could all be powered as branch circuits
from transformers loaded on the secondary of the system 4160V-3fl
transformer in parallel with the trolley feeder distribution
circuit. Each transformer would require a primary circuit
breaker. Secondary circuits would be protected in distribution
panels located in the control house and repair area.
In addition to the building utility circuits
lightinq, control, and utility equipment powcr would be required
on the operating cars of the system. A lighting transformer
and distribution panel would be provided on each car. This would
be the last major component of the car electrical equipment. An
electrical schematic of the car cirnilitry is shown in Figure 5.15.
The system substation will provide the interface
between the system and the high voltaqe commercial power grid
lines. The direct interface components would be a high voltage
circuit breaker protecting the input to the primary of a step
down transformer which would provide 4160V-3% power for the
operation of the Madaras system. The transformer would be
wye-configured with a grounded centertap. The rail system and
all stationary equipment should be tied to that grounding system
and a heavy earth ground should be provided.
Telemetry Antenna 4 each I nduct ion Gen.
Main & Branch Breakers, Circui ts, etc, 120 Vac, 10 - 10 each - 20 Amp Ci rcu i ts
Lighting Transformer 81 Breaker 24001120 Vac 20 KVA, 10
Figure
4160V, 30 , 250 KVA
4160V, 30 , 150 Amp
4160V, 30, 75 Amp
416015OOV, 30 WYI
Ground Brushes To Tracks Tracks Must Be Grounded To Power System Grid Ground
5.15. E l e c t r i c a l S c h e m a t i c of C i r c u i t r y on Each Rotor C a r .
The secondary of the 4160V transformer would be
fed to the trolley feeder distribution circuit through a circuit
breaker and magnetic contactor sized for the maximum capacity
of the generator system. The synchronous reactors would be
attached to the transformer secondary with their own circuit
breakers and magnetic contactors. Likewise, the utility
circuit transformer would be fed at that point through its own
primary circuit breaker or fusing. If a high voltage crane
circuit were required, it would also emanate from the subst .a t ion ,
Control circuits for the magnetic cnnt.antnrs and fo r the
synchronous reactor field exciter would have to be fed to the
substation.
The substation should be located outside the
track and adjacent to the control house. This will simplify
and shorten all the feeder circuits.
SECTION VI
PERFORMANCE ANALYSIS
The objectives of this analysis were to:
Predict the performance of the Madaras system as a function of geometry, major operating parameters, and losses inherent in the system.
Conduct trade studies to determine candidate plant configurations and sizes for use as inputs to the economic analysis.
Compute rated power output and annual energy output for various plant configurations using the best system selected.
As was stated before, the determination of an optimum
design for a Madaras system is beyond the time and budgetary . - . .. .
scope of this program. However, it is believed that the results .
of trade studies conducted in this section of the report will
isolate the important design parameters and will provide a
sufficient1.y efficient design to permit an objective evaluation
of the Madaras Power Plant concept.
Three basic studies were included in this performance
analysis:
a A vortex analysis conducted to determine the mutual interference between rotor cars and hence define the effect of rotor car spacing on gross plant output.
A trade study of the geometric and operational variables of a Madaras plant and their combined effects on aerodynamic, electrical, and mechanical losses and on net plant output.
The determination of net power outputversus wind' speed and annual energy production for various plant sizes.
6.1 MUTUAL INTERFERENCE STUDY
The mutual interference study made use of the vortex analysis technique developed by Professor H.C. Larsen of the Air Force
Institute of Technology for the Giromill vertical axiswknd turbine
currently under study by the McDonnell Aircraft Company. Since
the Giromill and the Madaras system are essentially comparable in
system concept, and since McDonnell's wind tunnel tests have
recently verified the analytical technique, the proven analysis
was modified for use on this study.
A detailed description of Professor Larsen's analysis as
it was developed for the Giromill and as it was modified and
used for this Madaras program is given in Appendix A. Thus, the
balance of this section will be used to present the results of using
the vortex analysis to determine gross power output of Madaras
plants. By gross power output we mean that the predicted power data
obtained from Professor Larsen's computer program accounts only
for the losses attributed to the aerodynamic drag of the rotor
(but not the rotor car) and the losses attributed to the induced
airflow caused by the interaction of the wind and the vortices
shed by each cylinder as it travels around the track.
All other types of losses associated with plant performance
are addressed.in the trade studies of Paragraph 6.2, and the com-
putation of net power output which accounts for the combination
of all types of losses is presented in Paragraph 6.3.
A list of the variables and ranges of the variables studied
to determine inutual interferenceeffects is presented in Table 6.1.
TABLE 6.1 .
VARIABLES STUDIED IN MUTUAL INTERFERENCE, VORTEX ANALYSIS
- -
Traak nmga OaliSiLy Rar~ye R a ~ ~ y t ! kiorbr A R / d Diamotor No. Cylinders a " t l v w vw Speed
m m n nd/D m / s -- .rpm ---
6 2 5.6 915 1 0.006 0.1-2.5 8.9-13.4 183 6 2 5.6 9 15 6-18 0.037-0.110 0.1-1.5 8.9-13.4 183 6 2 5.6 1220 6- 16 0.028-0.073 0.1-1.5 8.9-13.4 183 b 2 5.6 1524 8-14 0.029-0.051 0.0-1.5 8.9-13.4 1113 6 2 5.6 1829 16-18 0.049-0.055 0.8-1.5 8.9-13.4 183 6 2 5.6 2392 16 0.038-0.041 0.1-1.5 8.9-13.4 183 8 2 4.9 1372 1-20 0.004-0.071 0.5-1.5 7.8-13.4 186 8 2 4.9 1524 1-20 0.003-U.Ub4 0.3-1.5 4.5-13.4 186
Since t h e p r o h i b i t i v e number of ove r 161,000 computer runs
would be r e q u i r e d t o s tudy a l l combinations of a l l v a r i a b l e s i n
t h e range of i n t e r e s t , w e conducted a number o f p re l imina ry r u n s
of boundary cases t o determine t h e s e n s i t i v i t y of t h e v a r i o u s
v a r i a b l e s . his work, conducted by P r o f e s s o r Larsen, i s desc r ibed
i n Appendix A. W e a l s o used t h e r e s u l t s of o u r t r a d e s tudy r u n s
as i n p u t t o t h e s e l e c t i o n of t h e v a r i a b l e s l i s t e d i n Table 6.1.
A t y p i c a l p l o t of t h e complete performance map o f a s i n g l e
r o t o r s p i n n i n g a t a c o n s t a n t speed o f 183 rpm i s p r e s e n t e d i n
F igu re 6.1. T h i s p l o t shows t h e optimum va lue of X (Vt/Vw)
f o r each wind speed. One can see t h a t optimum va lue of X i n c r e a s e s
as Vw dec reases ; however, a t l e a s t f o r t h i s case, o p e r a t i o n a t a
c o n s t a n t t r a c k speed of about 10.6 m / s (35 mph), would permi t
o p e r a t i o n n e a r optimum A f o r a l l wind speeds .
W e want t o emphasize t h a t t h e r e s u l t s from t h e Appendix A
a n a l y s i s (F igu res 6.1, 6.2, and 6.3) account only f o r t h e r o t o r
d rag l o s s e s and t h e i n t e r f e r e n c e l o s s e s caused by t h e i n f l u e n c e
on t h e wind by t h e v o r t i c e s shed by t h e v a r i o u s r o t o r s i n a .
Madaras p l a n t . . T h u s , t h e ou tpu t from t h e v o r t e x a n a l y s i s has
been d e f i n e d as . t h e g r o s s ,output .
By d e f i n i n g t h e l o c a t i o n and n a t u r e of t h e peak va lue
o f h on t h e set o f runs i n F igure 6.1., it w a s no t necessary t o run
com9lete performance naps f o r a l l cond i t i ons . Some examples o f t h e
o t h e r d a t a from t h e f i r s t set of runs i s p re sen ted i n Appendix A.
From t h e s e s t u d i e s a s w e l l as o u r s t u d i e s conducted on
t h e va r ious l o s s mechanisms (Paragraph 6 . 2 ) , w e concluded t h a t a
1372-m (4500 f t ) t r a c k d iameter w a s n e a r l y optimum, and t h a t
probably no more t h a n 20' r o t o r s should be .used on a 1372-m t r a c k .
Th i s d e n s i t y i s e q u i v a l e n t t o an i n t e r - c a r spac ing of 215 m.
W e a l s o l e a r n e d t h a t t h e power o u t p u t / r o t o r car w a s e s s e n t i a l l y
c o n s t a n t when from one t o e i g h t r o t o r s are used on a 1372-m t r a c k ;
and t h a t t h e power p e r r o t o r d rops as t h e number of c a r s i n c r e a s e s
beyond e i g h t . Thus, o u r l a t e r s t u d i e s w e r e concen t r a t ed on t r a c k
d iameters of 1372 m and 1524 m and wi th i n t e r - c a r spac ing va ry ing
f r o m ' t h a t a s s o c i a t e d w i t h e i g h t t o twenty c a r s on a given t r a c k
A R = 6
z Rotor Diameter = 5.6m
Rotor Height =33.4m - I- Rotor Speed = 183RPM 3 0 Track Diameter =915m
0
U) U)
X = v, /v,
F i s u r e 6 . 1 . G r ~ s s 2ower O u t p ~ t ve r sus X fox Various Wine m e e d s , One Rotor Spinning a t 183 rpm, 915 m Diamecer Trzck . P r o f e s s o r La r sen ' s Vortex Anzilysis Accounts Only f o r Aerodynamic Drag and I n t e r f e r e n c e Losses.
diameter. For each track diameter',. the'performance of a 1-rotor
plant was first computedto provide a basis for defining a maximum
output condition.
our subsequent runs indicated that there was virtually
no difference in performance between plants utilizing 1372-m and
1524-m diameter tracks. Therefore, since the larger diameter
track would increase plant cost without performance benefits, the
smaller diameter track was selected for all subsequent studies.
Typical results of our later computations are shown
in Figures 6.2, 6.3, and 6.4. Figure 6.2 presents the gross
power generated'by one car, and data from it is used in developing
the mutual interference loss factor in Figure 6.4.
Gross power generated by plants utilizing from 8 to
20 cars, inclusive, on a 1524-m diameter circular track is
presented in Figure 6.3. The effect of mutual interference on
cut-in speed is quite pronounced as the number of cars increases.
Note that cut-in wind speed for 1 car (Figure 6.2) is about 3.3 m/s;
whereas for 10 cars and 18cars, cut in wind speed is about4.4 m/s
(10 mph) and 7.8 m/s (17.5 mph), respectively. Thus, as one would
expect, as the number of.cars increases (while track diameter and track speed are held constant) the cut-in wind speed increases
and the mutual interference loss increases.
The effect of increasing the number of cars, N, on power
loss is demonstrated more dramatically in Figure 6.4, where . .
mutual interference loss factor fn for a given wind speed is
defined by
where P is the gross power generated by an N-car p.lant at wind n Vw and track speed Vt (from Figure 6.3), and
P is the gross power generated by a 1-car plant at the same 1 wind speed Vw (From Figure 6.2) and track speed Vt.
Separate set' of f, loss factors were computed for each value of
Vt, hence f was considered to be a function of both Vw and Vt. n
F i q u r e 6 . 2 . Gross ?or?er Outpu t Versus Vn f o r one Rotor S p i n n i n g a t 1 8 6 r p n , 1 5 2 4 - n Diameter T r a c k , Constant Track Speed o f 1 3 . 4 m/s.
Figure 6.3. Gross Power Output versus FJumber of ' Rotors f o r Various Wind' .Speeds. f o r a Constant Rotor Speed,of 186 rpm and Constant Track Speed of 13.4 m/s.
171
Figur Speed Speed
,pect ive
1 .o
0.9 r I
1 1
1 I
/ I I I I I I I A R = 8 I e/d = 2 I I
Rotor Diameter = 4 . 9 m Rotor Height =39.2 m -
I Rotor Speed =186RPM I Track Speed .=13.4 m/s I I
Track Diameter =1372m to 1524m
I I I I - I I I
I 101
I
N = 8
#I
(L 0 r- 0 . 5 0
2 V) V) 0 0.4
W 0 z
0 . 3 W LL (L W C
z 0.2.
-1 a
-
3 I- 2 5 0.1 I C
Y.
O
I I 1
I l 4 16 1 2 0
121 I 181
5-- 10 2 0 2 5 30 l5 VW-MPH
I I I I I I I 1 1 1 I I 2 4 6 8 10 12 14
V,- m/s
e 6.4. Mutual In te r fe rence Loss Factor versus Wind f o r Various Numbers of Cars. Constant Rotor and Track Speed of 1 8 6 r p m and 13.4 m / s , r e s
1 7 2
The cut-in speed in Figure 6.4 for each value of N is
the V value at which each curve terminates near the x-axis. W
At wind speeds lower than these terminal points, the power
rapidly becomes negative.
The loss in power for an 8-car plant isnegligible
until Vw decreases below 5.6 m/s (12.5 mph), and 75 percent of the
power per car of a 1-car train will be available at wind speeds
of about 3.6 m/s (8 mph). However, a 20-car plant does not operate
as efficiently. At a wind speed of 13.4 m/s (30 mph) each of
the 20 cars will produce only 90 percent of the power of a one-
car train; and at the cut-in speed of 8.0 m/s (18 mph) only 5.5
percent of the power from a 1-car plant would be generated by
each car of the 20-car plant.
Interference loss factors like those shown in Figure 6.4
will be used in the computations described. in Paragraph 6.3 to
develop the power duration curves and to determine net rated
power output of a power plant. Values of fn for the 1372 m
(4500 ft) track diameter are presented in Figure 6.4.
6.2 PARAMETRIC TRADE STUDY
The computer program used in Section v to determine the spin motor power requirements was used for this trade study.
This program simulates the performance of a 1-rotor plant taking
into account all losses except for the mutual interference losses.
Thus, by combining the results from the vortex interference analysis
with those from this trade study analysis, net Madaras plant output
accounting for all losses was obtained.
The program was written in very general format to permit
flexibility in conducting parametric studies of both cylinder- .
driven and wing-driven cars as well as provisions for analyzing
both circular and race track configurations.
The program is designed for automatic, interactive com-
putations of average power output. Input to the program includes:
a Cylinder and end cap geometry in terms of AR, e/d, cylinder diameter, and cylinder projected area.
a Aerodynamic lift, drag, and center of pressure data corresponding to the geometry as a function of U/VR where U is the surface speed of the cylinder and VR is the resultant wind derived from the wind speed and track speed at all points around the track orbit.
a Frontal area of car and height of the car above ground.
a Track gage and diameter.
a Design rpm of the cylinder.
a Spin schedule - rotor rpm can be varied or held constant.
a Spin.motor, size.
a Spin motor speed-efficiency characteristic curves.
a Track speed.
a Wind speed.
Internal to the program are special routines which compute:
i Rotor weight, and moment of inertia corresponding to inputs.
Total vehicle wcight.
a Wind speed distribution with height representing the wind boundary layer flow.
Mean resultant aerodynamic velocity vector obtained by cnmhiniag the unilurxi~ hluw along thc length of the cylinder caused by rotor motion down the track with the nonuniform boundary layer distribution.
Gross power and loads on the rotor at any point on the t r ~ c k .
a All losses except for mutual interference losses at any point on the track.
a Net pbwer (excluding interference effects) at any point on the track.
0 Spin history of the rotor.
0 Average net power per cycle for a circular track.
Average net power per cycle for race tracks having sides varying in length from 610 m to 18,300 m with wind direction varying at 7 different angles between O0 to 90° relative to the straight track section. Thus, power for racetracks having all combinations of 40 lengths of straight tracks and 7 wind directions (280 racetrack length-wind combinations) is computed on each computer run.
Losses accounted for in the program are:
Cylinder aerodynamic drag loss.
w Rotor car aerodynamic drag loss.
o Vertical and lateral friction losses of the rotor car main wheels and idler wheels rolling on the track.
e Wheel bearing losses.
o Gearing losses associated with the step-up gear box required to drive the generators by the wheels.
Generator losses.
a Power conditioning, conversion, and transmission losses described in Section 5.
0 Rotor spin motor efficiency vs. speed (Fig. 5.10) during acceleration, steady state, and deceleration . operational modes.
Motor power required to overcome the inertia of the rotor during rotor spin-up.
Motor power required to overcome viscous drag bearing, and rotor drive system losses at all times during plant operation.
A summary of the computer runs made during this trade
study is presented in Table 6.2, which indicates the general
types of analyses that were conducted:
Cylinder geometry
o Spin motor size
Track speed and cylinder rpm
e Spin motor schedule
Plant configuration selection.
TABLE 6.2
TRADE STUDY VARIABLES
Note : For each o f t h a above r u n s , n e t power was ccmputed f o r a c i r c u l a r t r a c k a s well a s f o r a r a c e t r a c k hav ing s t r a i g h t s e c t i o n s v a r y i n g from 610 m t o 18,300 m and wind d i r e c t i o n r e l a t i v e t o t h e s t r a i g h t s e c t i o n s v a r y i n g from 90' t o 180°.
Study Category
C y l i n d e r Geometry
Spim Motor
S i z e
Track Speed and C y l i n d e r
Sp in Motor S c h e ~ u l e
P l a n t Conf igu ra t ion
S a l e c t l o n
Tr sck Rotor Range Range Range Range Sp in Trans- AR e/d d A Dia. Speed Vt /Vw vw Viscous Regen. Motor m i s s i o n
Braking Braking S i z e m mL m rpm m / s d e g r e e s d e g r e e s kW
4 1,256.8186 1372 186 1.5 13.4 - 240 450 none 5 7,3 6.1
6 1 5.5 ( 8 v 4.9 v 8 1.25 6.1 297 8 5.5 241 8 4.9 186 8 4.3 146
v v v 240 450-1200 none
6 609 6 6
1829 6 1.25 5.5 1 6 1372 120-186 0.7-2.3 6.7-13.4 - 240 450 none 6 2 5 - 5 1 150-200 - 8 1-25 4.9 1 I - 8 z 4 . 9 v v - I v 6 1-25 5.5 186 1372 150-200 0.3-2.7 6.7-13.4 none
I 220- 450 260
none 6 2 5.5
V
8 1.25 4.9 8 2 4.9 6 1.255.5 6 2 5.5 8 1.25 4.9 8 2 4.9 8 2 4.9 'J L V \/ V 2 50 none V 3-s t ep 8 2 0.5-2.8 5.6-13.8 250 none 450 none 8 2 4.9 186 i524 186 0.5-2.8 5.6-13.a 250 none 450 none
I v 220-260 I Te V
The results of these computer studies are presented in
the paragraphs which follow.
6.2.1 Rotor Geometrv and Size
Three studies were conducted. The first study
analyzed rotor power output as a function of 15 combinations of
aspect ratio (3,4,5,6, and 8), and end plate size ratio (e/d values
of 1.25, 2, and 3). All cylinders had an area of 186 m2, and
track and wind speed were held constant at 8.9 m/s and 13.4 m/s,
respectively. The results of this study indicated that the large
end plate required more power than was available to turn it by a
450 kW motor, and hence the consideration of an e/d ratio of 3
was dropped from .the study. We also learned that an aspect ratio
from 6 to 8 was of greatest interest and that e/d ratios of 1.25
and 2 should be considered further. See Appendix C for rotor
size and operational condition sealing used in all paramet'kic
studies.
The second study considered the variation of
diameter and cylinder rpm while holding area constant. The
results of this study are presented in Figure 6.5, which shows
power output versus cylinder diameter for rotors having e/d
ratios of 1.25 and 2.
The decreasing of diameter has three effects.
First, as diameter decreases with area being held constant, AR and
hence aerodynamic efficiency increases. This effect improved
power output, especially. for AR = 8, e/d = 2. The second
effect in decreasing diameter is to reduce rotor weight and
moment of inertia which improves net power output. The third
effect causes power loss: as diameter decreases so does cylinder
surface speed, U, and hence CL decreases with the resulting decrease
of U/V. This last effect is.beginning to show itself for the
e/d = 1.25 data, whereas the larger end plate (e/d = 2) is
improving aerodynamic efficiency sufficiently well to overcome
the effect of decreased U/V. Apparently, an AR > 8 would yield
better performance, however since the AR = 8 data were
extrapolated, we decided to stop this study at that point.
2 End Caps e/d = 1.25 Area = Constant
= 2 0 0 0 f t 2 (186m2) V = 30 MPH (13.4 m/s) .
V + = 2 0 MPH (8 .9m/s ) 0 - 186 RPM x - 150 RPM
Track Diameter = 4 5 0 0 f t ( 1 3 7 2 m )
DIAMETER .. .
I I I I J I 2 I G E 0 2 4 2 fl
CYLINDER DIAMETER - F t
2 End Caps e /d = 2
4 0 0 ~ Area = Constant AR = 8
Y = 2 0 0 0 f t 2 ( 1 8 6 m 2 ) V, = 3 0 MPH (13.4 m/s ) V, = 2 0 M P H ( 8 . 9 m / s )
2 0 0 - 0 -.I86 RPM \ x I 5 0 RPM m . W 1 0 0 - Track Diameter = 4500 f t 3 (1372 m )
4
-2001 1 I I I
12 16 2 0 24 2 8 I
CYLINDER DIAMETER - F t
Figure 6.5. Net Power for One Rotor versus Cylinder Diameter as a Function of e/d Ratio and Cylinder rpm for Constant Projected Area, Wind Speed and Track Speed; e/d = 1.25 and 2.
The decrease i n performance a s diameter exceeds 18 f t
(5.5 m) i s severe,and l o s s e s exceed ou tpu t a s AR approaches 5.
This l o s s i s caused by increased c y l i n d e r weight and i n e r t i a
r e s u l t i n g from diameter inc rease a s w e l l a s l o s s of aerodynamic
e f f i c i e n c y . Thus, c y l i n d e r s having aspec t r a t i o s l e s s than 6
were e l imina ted from f u r t h e r cons ide ra t ion .
The e f f e c t o f varying c y l i n d e r rprn was no t a s marked,
although t h e reduced U f o r AR = 8 (smal1,diameter c y l i n d e r )
r e s u l t e d i n l o s s of power output whereas a small i n c r e a s e i n
power occurred a t AR = 6 a s rprn was decreased. This l a t t e r
obse rva t ion was caused by reduced c y l i n d e r weight and i n e r ' t i a ,
because rprn in f luences t h e s e v a r i a b l e s markedly. Although t h e
l a r g e r diameter c y l i n d e r causes U t o inc rease , t h e decreased
rprn decreases U by t h e same percentage. Thus, t h e improved
performance a t AR = 6 i s t h e r e s u l t of decreased weight caused
by lower s t r u c t u r a l s t r e s s e s i n a c y l i n d e r designed t o opera te
a t 150 rprn versus 186 rpm.
. S i n c e an a s p e c t r a t i o of e i g h t looked promising, t h e
t h i r d s tudy analyzed t h e e f f e c t . o f varying cy l inder diameter and
cy l inder p ro jec ted a r e a while holding cons tan t a spec t r a t i o .
Since t h e end p l a t e absorbs a l a r g e amount of motor power and
i n c r e a s e s i n e r t i a s i g n i f i c a n t l y , w e s e l e c t e d an e/d r a t i o of
1.25 th ink ing t h a t t h e improved aerodynamic e f f i c i e n c y of AR=8
would o f f s e t some of t h e l o s s caused by t h e small end p l a t e .
This compromise combined wi th t h e improved weight and i n e r t i a of
t h e smal ler end p l a t e seemed a t t r a c t i v e .
The r e s u l t s of t h i s s tudy a r e presented i n Figure 6 .6 .
A l l of t h e e f f e c t s of changing diameter and speed mentioned
previous ly a r e exemplif ied. I n a d d i t i o n , one can observe t h a t
t h e power output i n c r e a s e s with increased diameter (and a r e a )
a t t h e lower r o t a t i o n a l speeds (150 rprn). However, a s rpm
inc reases , t h e e f f e c t of increased c y l i n d e r weight, i n e r t i a
aerodynamic d rag , and v iscous .drag t h a t occurs as diameter
i n c r e a s e s r e s u l t s i n h igher s p i n - m o t o r loads , and t h e r e s u l t
i s reduced power output .
Vt = 2 0 mph (8.9 m/s) SPIN MOTOR POWER = 4 5 0 kW TRACK DIAMETER = 4500ft ( 1372m)
= 14 (4 .3m) -
I10 120 140 160 180 200
CYLINDER RPM
Figure 6.6. Net Power for One Rotor versus Cylinder rpm for Constant Aspect Ratio of 8 but with Variable Diameter' and Variable 'Projected Area.
This effect is significant for the 20-ft (6.1 m)
diameter cylinder; however, the 16-ft (4.9 m) and 18-ft (5.5 m)
diameter cylinders have reached peak performance at about 186 rpm.
It appears that peak performance of the largest cylinder will be
at rotational speeds below 140 rpm.
The loss in area resulting from reducing cylinder
diameter below 16 ft (4.9 m) is so significant that no further
consideration was g.iven to a cylinder this small. Thus, the 16 ft,
18 ft, and 20 ft cylinders having AR=8 and e/d =1.25 were
retained for further study.
6.2.2 Spin Motor and Track Size
The computer trade study conducted to determine
spin motor size is described thoroughly in Paragraph 5.3.2,
and the graphical results of these studies are presented in
Figures 5.12, 5.13, and 5.14. The Figure 5.13 plot of motor
size and net power output vs track diameter is particularly
significant. If track diameter is too small, the motor power
requirements become excessive in order to accelerate'the rotor '
rapidly enough to effectively generate power before it is time to
decelerate the rotor. As track diameter increases, more time
is available for rotor spin-up (assuming a given track speed)
and hence motor power requirements decrease.
At a track diameter of 1372 m, a near optimum
motor size is shown to be about 450kW for plant operation at the
13.4 m/s (30 mph) rated plant capacity. ~lthough further reductions
in motor size could be achieved by increasing track diameter to
1830 m , it was thought that the increased cost track would
offset motor cost savings, and that the minor improvement in
plant output would be insufficient to offset this added cost.
Therefore, i,t was decided to restrict further
studies to track diameter in the 4500 ft (1372 m) to 5000 ft
(1524 m) range and to use a 450kW motor in all further studies.
6.2.3 Track Speed and Cylinder R P M
A summary of our results from studying combined
track speed and cylinder RPM effects for a 4500 it (1372 m) tfack
diameter and a 450kW spin motor are presented in Figures 6.7 and
6.8.
The improvement in performance of the rotor having
an aspect ratio of 8 over that having an aspect ratio of 6 is
significant. Also, the indication that a 150 rpm rotational
speed produces significantly more power than a 186 rpm speed for
the aspect ratio 6 cylinderfagain shows the importance of the
diameter-speed relationship'discussed previously. The improved
low wind speed performance of the aspect ratio 8 cy.lj.nc-3er is particularly important because this power output improvement
will increase significantly the annual energy yield of the plant.
As in Figure 6.1, the data shows that peak power
occurs at approximately the same track speed (25 mph) for both
of the wind speeds studied,even though the peak occurs at a
different value of A. This feature is quite advantageous in
that it is necessary to operate the plant at a given track speed
for all wind speeds. Although peak power occurs at different rpm
values as wind speed decreases from its rated value of 13.4 m/s,
our control system is designed to sense wind speed and adjust
rotational speed to its optimum value.
.It also should be noted that when we indicate
a particular run was made at n rpm, we also infer that the I
structure was designed to withstand a rotational speed of n rpm.
Thus, once this design variable is fixed, it cannot be increased.
Therefore., one cannot.operate a rotor at design rpm at one wind
speed and then operate the rotor above the designrpm at another
wind speed. Of course, one can always operate below the design
rpm, if desired. In fact, decreasing rpm is the means used for
"feathering" the rotor during wind conditions greater than the
13.4 m/s rated speed.
n- CYLINDER RPM:
3..
Figure 6 . 7 . N e t Power Output f o r 0ne"Rotor versus h and Cylinder rpm for Various Cylinder Rotational Speeds, Aspect Ratio = ,6, e / d = 2 .
h ~ = 6 e / d = 2 DIAMETER = 18ft (5.5m/s)
0 . 4 TRACK DIAMETER = 4 5 0 0 f t t I ROTOR ( 1 372 m) I- 3 a I-
2 0 . 2 - a W 3 0 a- . . I- 0 . W z
-0 .2
20 mph ( 8.9m/s)
0.3 0.5 0.7 0.9 I . I 1.3 1.5
Figure 6.8. N e t 'Power Output for One 'Rotor. versus. A and Cylinder Rotational Speed, 'AR =' 8 , e/d = 2 .
I
3 0.6
t
0.6-
3 2
1
5 0.4 n I- 3 0 a g 0.2 W n
b Z
0
I- 3
I ROTOR
0 n I- 8 .2 , W Z
( 8.9 m/s)
0 I 0.5 0.7 0.9 1 . 1 1.3 1.5 1.7
I AR=8 e/d = 2 DIAMETER = 16ft (4.9 m ) TRACK DIAMETER =4500ft (1372m)
1 20 140 160 180 200 n -CYLINDER RPM
\ A = 0.83
. - . Vw 20rnph(0.3 m / ~ )
- X = 1.25
This study shows a clear superiority of an
aspect ratio 8 configuration over that of aspect ratio 6, not
only because of the improved power output at rated wind speed,
but also because of vastly improved performances at low wind
speed even when operating at the design rpm (186) which.provides
maximum power at rated wind speed (13.4 m/s) .. It also was evident that maximum power at both wind speeds will be achieved
while the plant is operating at a track speed of about 25 mph
(11.2 m/s).
6.2..4 Spin Motor Schedule
The characterization of the spin motor schedule,
the motor's performance requirements, and losses were discussed
in Paragraph 5.3. Since spin motor losses are so significant,
a brief trade study was conducted to determine ways in which the
spin schedule could be varied in order to improve performance.
The study was restricted to the use of an electric motor.although
other sources of power (hydraulic, air motors, and flywheels)
were considered in a cursory manner. Within these ground rules,
then, we studied the use of different forms of braking to. improve
the deceleration portion of the cycle,and we simulated the use of
a three-step transmission (gear box and clutch) in our computer
program,to improve the acceleration portion of the cycle. The results 0% our studies of the mid-portion of the cycle were presented
earlier in Paragraphs 6.2.,1, 6.2.2, and 6.2.3.
A typical performance plot in terms of motor power
required, motor rpm, and instantaneous net power output as a
function of rotor position on a circular track is presented in
Figure 6.9. The cycle shown, in this figure represents only one-
half of an entire cycle, however the remaining half is similar to the portion of.the cyEk shown in Figure 6.9.
Our initial cycle incorporated regenerative
braking beginning at: 235'. (shown by the solid l.ines). Then., we
modified the cycle by turning off the motor at various points
between 215' and 265' and then Petting viscous friction decelerate
V,,, = l3A.mh AR = $
n = 1 8 RPM TRACK DIAMETER = 1372 m
INSTANEOUS POWER GENERATED
MOTOR POWER REQUIRED
INITIAL CYCLE WITH REGENERATIVE BRAKING : 380 kW ------ CYSLE WITH BEST VISCOUS BRAKING
*****-- EFFECT OF USING 3 - STEP TRANSMISSION AND IMPROVED VISCOUS BRAKING
I I 1 I t I I I I I I 90 100 1 2 0 140 160 180 200 2 2 0 240 2 6 0 2 7 0
ROTOR POSITION ON TRACK - 6 DEGREES
Figure E.9. Elet Power Output f o r One Rotor, Spin Motor Power, and Motor rpm versus Rotor p o s i t i o n on Track a s Affect2d by use o f Iriscous Braking, Regenerative Braking, and a Three-Step Tran~.mission +-#D Very the Spin Schedule.
the cylinder naturally (shown by the dashed lines). Similar studies
were conducted for regenerative braking. Note that both of these
studies affect only the deceleration portion of the cycle. The
results of using the transmission during the spin-up portion of
the cycle are depicted by the dotted lines.
The results of the braking studies are shown in
Figure 6.10. As we noted before, at the 8.9 m/s wind speed, more
power can be obtained at the 170 rpm rotational speed; and a
significant improvement in spin cycle performance is obtained by
the proper application of either viscous or regenerative braking.
Viscous braking at the 245 degree point appears to be the better
solution not only because of its 6-kW edge in power output, but
also because of the added cost of the heavier trolley components,
increased complexity in circuit design, and wear on the motor
which would result in use of regenerative braking. The poor
performance that occurs when regenerative braking is initiated
earlier than its optimum time is attributed to its ability to
stop the rotation too quickly (shown in Figure 6.9). By applying I
regenerative braking at 235O, the rotor is stopped by the time it
reaches 250°, and from there on the non-spinning rotor presents
itself as a large drag producer which must be driven by the train.
This situation was improved considerably by initiating regenerative
braking at 260'.
As can be seen in Figure 6.9, the net extra
eilergy regenerated is w r y sma31. (the small triangular section
in the negative region on the power curve). as was predicted in Section 5, since viscous'drag and motor losses consume much of
the power regenerated. The increase in average power per orbit
.of the track of only 2 kW (0.5%) was gained from the regenerative
cycle shown, and an average increase per orbit of only 11 kW (3%)
was developed for the best regenera.ti;ve cycle. This best case
adds only 1 percent to the total energy (kW-hr) generated in
this best cycle.
TRACK POSITION AT START OF BRAKING - 8
0.5
3. 2
1
2 0.4
F i g u r e 6 .10 . N e t Power Output f o r One Rotor f o r Var ious Sp in l lo tor Speeds v e r s u s Track P o s i t i o n a t ?!hi& Regene ra t ive Braking o r Viscous Bralcing v ~ a o I n i t i a t e d .
REGENERATIVE A R = 8 BRAKING e/d =2
----- VlSCOUS BRAKING DIAMETER = 16 f t (4 .9 m ) 0 DENOTES PEAK TRACK DIAMETER =4500 ft (1372m) -
VALUE Vw NOTED
Vt = 25mph ( I 1.2m/s) I ROTOR
I 1 436.2 kW 430.5 kW
w I
. --.
a 0- 0
t- 325kW 318kW )Vw=30mph 3 ( 13.4m/s 0 E 4
0.3 I
0 a F W Z
0.2 - Vw=20mph - ( 8.9 m/s)
0. I
0 .
210 220 230 248 250 260 270
Therefore, it was decided to utilize viscous 0
braking at 245 for all future runs.
The use of .a transmission in conjunction with
optimum viscous braking resulted in an increase of average power
generated of about 16 percent. This is a significant improvement in
performance, and the reason for a transmission's effectiveness
is shown in Figure 6.9. The primary benefit derived from use of
a transmission is to reduce the start-up load on the motor.
This load reduction permits the rotor to accelerate more rapidly
and thereby increases cylinder surface speed, U. The resulting
increase in U/V ratio over the go0-160' portion of the orbit
produces increased lift and consequently produces increased power
as shown in Figure 6.9. In addition, since a rotor equipped with
a transmission reached operating RPM (186 rpm in this case)
earlier (140' instead of 160') there is a small reduction in
power consumed by the motor (See the motor power curve in Figure
6.91.
Unfortunately, time was not available to study
the effects of various types of transmissions or performance as
well as to evaluate the life cycle cost and maintenance problems
associated with transmission use. All that can be said at this
time is that transmissions can have a significant effect on
performance, as shown in Figure 6.9 , and that further study of liransm~ss.ion.s is in order.
One interesting result of our study of trans-
missions was that transmissions are justified only. for Madaras
plants having a circular track configuration. For racetrack-type
plants, the power generated on the straight section is so much
greater than that on the circular ends, that the improved
performance on the ends is hardly discernable in the overall output.
6.2.5 Rotor and Plant Configuration Selection
A total of six rotor configurations, selected as
candidates for the final analysis, are itemized in the upper
section of Table 6.3. These were the rotor-operating-condition
combinations which appeared to be the most competitive of all
that were studied.
The figure of merit upon which initial screening
was based was the rotor mass per kW generated at rated wind speed,
listed in the las't column of Table 6.3. This figure of merit
was selected as a cost/performance indicator because of the close '
relationship that. exl.st.s between aoct and weigh,t 01 send-rr~onoeaque st.rncture like the rotor.
Of the six rotors listed, Configurations 1, 2, and
4 were considered to be the most attractive. Of the three,
Configuration 2 had clearly the better performance figure of
merit for a circular track (18.3 kg/kW vs. 22.2 kg/kW for
Configuration 4). .However, Configuration 2 is a very large rotor
having a height of 4 8 . 8 m (160 ft), a diameter of 6.1 m 2 (20 ft), and a projected axea of 298 m . Since this cylinder
was about 60 percent larger than that for which loads and stress
analyses had been conducted, and since time was not available to
conduct another iteration nf our design and concepts, Lhe
decision was made to eliminate Configuration 2 from further
consideration on this study. Should the Madaras system look
attractive, an investigat.ion of larger rotor of this size certainly
would be recommended.
This f i r s k screening left Configurations 1 and 4.
Both are the same size as the rotors analyzed; however Configuration
1 has an end cap ratio of 2, whereas configuration 4 has an end
cap ratio of 1.25. These two Configurations were re-run using
viscous braking instead of regenerative braking (used for the
initial comparisons) and the results are listed in the middle
section of Table 6.3. Notice that this second comparison considered
TABLE 6.3
COMPARISON OF CANDIDATE ROTOR CONFIGURATIONS 1372 m (4500ft) TRACK DIAMETER, 450 KW SPIN MOTOR
I Screened Configurations - Viscous Braking
Configuration Number
1 2 3 4 5 6
AR eid d h Area vw Vt n P Mass I ks/kW
m m m m/s m/s rpm kw ks- 2 2 ka-m . Circle
With ~egenerative Braking
8 2 4.9 38.1 186 13.4 11.2 186 380 8773 41,663 23.1 8 1.25 6.1 48.8 298 13.4 8.9 150 526 9646 60,350 18.3 8 1.25 5.5 43.9 2-41 13.4 8.9 186 400 10284 52,G50 25.7 8 1.25 4.9 38.1 186 13.4 15.6 186 324 7189 28,556 22.2 6 1,25 5.5 33.5 184 13.4 11.2 186 222 8162 40,761 27.8 6 2 5.5 33.5 184 13.4 11.2 150 280 7164 43,787 25.6
0
*Optimum Viscous Braking is initiated at the 245 point in the orbit.
I *
Selected Configurations, Optimum Viscous Braking
1 8 2 4.9 38.1 186 13.4 11.2 186 436 8773 41,663 20.1 8.9 11.2 170 '216 40.6
both the 13.4 m/s rated speed performance as well as performance
at the wind speed of 8.9 m/s.
This second comparison showed that Configuration 4
had a 15 percent lower value of kg/kW at the rated wind speed than
Configuration 1; although Configuration 1 provided about 6 percent
more power at the rated condition of 13.4 m/s. Configuration 1 was
clearly superior at the 8.9 m/s speed with a kg/kW value that was
about 60 percent smaller than that of Configuration 4. This
means that a Configuration 1 rotor would generate more power .
at low wind speeds, and since the lower wind speeds occur more
often during the period of a year, Configuration 1 probably *
would provide considerably mnre kw-hr of anexqy per ycar than
would Configuration .4. Finally, our computer studies indicated that. Configuration 1 would generate more power than Configuration
4 at rated wind speed if used in a racetrack plant layout. Thus,
in view of its superior low-wind-speed performance and the high
probability that a racetrack layout would prove to be the more
cost effective, we selected Configuration 1 for the final analysis.
Slight improvements in Configuration 1 performance were obtained
by optimizing the viscous braking routine, as shown in Figure 6.10.
The results of this optimization are shown in the lower part of
Table 6.3.
Having selected the rotor configuration, we next
directed our attention to the selection of the most appropriate
track configuration and size. Figure 6.11 presents a performance
plot of the power output from one rotor car of the size previously , .
2 selected (AR=8, e/d=2, d=4.9mt Area = 186 m ) vs track diameter
for various wind speeds. Performance on both circular tracks
and racetracks having a 4878-m (16,000 ft) straight sides is
presented. For illustration, these data were plotted for operation
at a design rotor speed of 186 rpm for all wind speeds at a Vt/Vw
ratio ( A ) that will optimize performance for the racetrack.
This selection was made because it is very likkly that a racetrack
configuration will be the more feasible. Should a circular-track-
plant appear attractive, the optimum track speed data are
available, so this selection is not irreversible.
Figure 6.11 demonstrates clearly the trend that
we have noted in our previous analyses of this data: the most
attractive track size is in the 1372 m (4500 ft) to 1524 m (5000 ft)
diameter range. Further, one can see that there is very little
difference in performance in selecting either of the two track
sizes. The 1372-m size is slightly favored for a racetrack con-
figuration, and a 1524-m circular track will provide a small
increase in output over that having a 1372-m diameter. Our cost
analysis will govern the final selection; however, at this time it
appears that a 1372-m diameter racetrack will prove to be the
most cost-effective.
It is also important tonoteagain here that
mutual interference effects described in Paragraph 6.1 become
more pronounced as track diameter decreases, and from these
studies we determine that interference losses would become
excessive if track diameter were decreased below 1219 m (4000 ft).
Figure 6.12 presents an overall performance map
of the selected rotor operating on a 1372-m (4500 ft) diameter
circular track and on a racetrack having 1372-m diameter ends and
4878-m (16,000 ft) straight sections. Figure 6.12 depicts two
principal advantages of the racetrack over the circular track:
(1) power output at a given Vw is nearly 2.5 times greater; and
( 2 ) power can be generated at lower wind speeds. Of course, the
racetrack has two principal disadvantages: (1) for optimum
operation, the wind direction should remain constant; and (2) it
requires much more land.
The 4878-m straight length has been selected
arbitrarily at this point. Our computer program currently
provides power vs straight section length in 150-m increments
from 610.m to 18,300 m, and it can be modified easily to provide
any length desired. In our cost analysis we will study the
effect of varying straight section length on plant efficiency and
energy costi
. - - .
TRACK DIAMETER - ft Figure 6.11. Net Power Output from One Rotor versus Track
Diameter as a Function of Wind Speed. Performance for Both 'Cylinder and Racetrack Configurations.
Figure 6.12. Net Power Output from One Rotor versus A as a Function of Wind Speed. Performanze is Presented for Both a 1372-m Diameter Circular Track and a Racetrack having 1372-n~ Diameter Ends and 4858 m Straight Sections.
1 .z
1.0
3 0.8 2 b 3 a k
0.6 .
a
o a I- 0.4 W z
0.2
0
-0.2. 0 2.8 3.2 3.6
X = v t /v,
.
,
1
/ /
/
(13.4 m/s) V,= 30 mphY7
A R = 8
/ /r-\,!w= 30 rnp! (13.4 r n / ~ ) ~ ' ~ =
d - 0
(I 1.2) 25 -.- -- / \, 12.5 (5.6)
0
/----
0.4 0.8 1.2 1.6 2 .O 2.4
/
/ /
/ /
/ /
f
/
8 I
/ /
0 0
- - ',IS (6.7)
DIAMETER = 16 f t (4.9 m) TRACK DIAMETER = 4500 f t (1372 m ) -
\ \ 86 RPM \ 25 ( 11.2) ROTOR I
0
/ - - I
/ /
CIRCULAR TRACK --- - RACETRACK WITH 16,000 f t SIDES
\ 20 (8.0) \ (4878 m)
6.3 NET POWER AND ANNUAL ENERGY OUTPUT
The results and discussion pertaining to plant performance
that have been presented prior to this section of the report
have considered the mutual interference effects for plants com-
posed of N rotor cars and the net power output from one rotor
car after considering all losses except for mutual interference
losses.
The purpose of this portion of the report is to: :
Develop wind duration curves appropriate for the mid-height of the rotor selected for this study.
Describe the methods used to determine the net output power of an N-ruLur-~ar p l a ~ i t as a function of wind speed.
Demonstrate how power duration curves were developed from wind duration curves.
The results of this study will then be used in the
economic analysis in Gection VII.
6.3.1 Wind Duration Curve -..,.,A\\-..,. .w-.~,",.. -,- ..... ... ,..- ......,.-.,..
The rotor selected for this final analysis has
the following . geometric . characteristics:
A R = 8 Diameter = 16 ft (4.9 m) Cylinder Length = 125 ft (38.1 m) e/d ratio = 2 End Cap Diameter = 32 ft (9.8 m)
Figure 4.23 indioatoc that thc top of thc track
rail is 4 ft (1.2 m) above mean terrain level, and the distance
from the top sf the rail to the bottom of the cy.l.j.nder, shown in
Figure 4.15, is 15.5. ft (4.7 m). Here, we define the bottom of
the cylinder as the lower point of intersection between the
cylindrical surface and the inclined, inside surface of the end
cap. Thus, according to Figure 4.15, the bottom of the cylinder
is 3 ft (0.9 m) above the top surface of the rotor car.
Using the above dimensions, the height above
ground of the mid-point of the rotor is:
The design wind duration curve is that used by
~ r u l l e ~ ~ in his Giromill study. This curve, which has a mean - wind speed, V = 18 mph (8.1 m/s) at a height 29.5 ft (9.0 m)
above ground, was specified by ERDA for use in the design of the
MOD-1 WTG. This design curve was specified for only a 9-meter
height,.whereas the center of the proposed Madaras rotor
design is 25 meters above ground. Thus, the wind duration curve
corresponding to the 25-meter height was ratioed from the basic
design.curve using the conventional method:
Where wind speeds V2 andVl are functions of t hours, and the sub-
scripts 1 and 2 refer, respectively, to the original 9-meter design
curve and the modified 25 m design curve. The modified design curve,
having a = 9.6 m/s at 25 m, also is presented in Figure 6.13.
The third wind duration curve presented in Figure 6.13 is that corresponding to average wind conditions
at a 25-meter height at Medicine BOW, Wyoming. These data
were obtained from the paper by Hightower and Watts contained in
the Proceedings of the Third Wind Energy Workshop. 43 The
Medicine Bow data are presented because that location would be
an ideal candidate site for a Madaras plant.
6.3.2 Determination of Net Plant Power Output
The net power output as.a function of wind speed
was computed for about 100 differently-sized Madaras plantc
using the data developed in Paragraphs 6.1 and 6.2 in the following
equation :
CUMMULkTlVE HOURS 2 GIVEN WIND SPEED OCCURS
Figure 6.13. Modified Cesign Wind Duration Curve to Represent Wind Conditions at a Rotor Mid-Height of 25 n (82 ft) Above Mean Terrain Level.
where P is the net plant output for wind speed V, v p1 is the net power output for one car not corrected for
mutual interference effects,
fn is the mutual interference correction factor for p , which varies with the spacing between cars and wit6 wind speed, and track speed, and
N is the tota-l number of cars in a Madaras plant.
Values of pl were obtained as a function of Vw and Vt for all
combinations of the following conditions:
Rotor configuration described at beginning of Paragraph 6.3.1
Track diameter = 1372 m (diameter of circle and of racetrack ends)
Rotor speed = 186 rpm
e Track speed = 8.9 and 13.4 m/s
Wind speeds varying from 3 m/s to 13.4 m/s
e Circular track as well as racetracks having straight sections varying from 610 m to 18,300 m.
The appropriate mutual interference factors were obtained from
Figure 6.4 for the above rotor and operating conditions, and for
rotor spacings varying from 215 meters to 540 m. Since specific
mutual interference factors correspond to a particular combination
of Vw, Vt, and b (rotor spacing), our computation of net power
as a function of wind speed does not assume that power varies as 3 a function of Vw , as is usually assumed for most WTG computations.
This assumption does not hold for the Madaras
system (and probably does not hold strictly for some other wind
turbine systems) because the mutual interference and other system 3 losses cause a power variation different from a'V ratio varia-
W tion. Figure 6.14 is indicative of the variation of net power
output vs wind speed for two, large, racetrack-configured
Madaras plants. Both of these plants are of the same physical
size and haveae same number of cars. The only difference in
capacity is caused by differences in track speed. Notice that
a lower cut-in speed and a lower rated capacity is realized
as a result of reducing track speed. Thus, Plant la would be
more effective than Plant 1 in a region having a wind duration
curve with a lower mean wind speed. Both plants are designed to
operate up to a cut-out speed of 29.1 m/s (65 mph). Constant
power output in the region from 13.4 m/s to 29.1 m/s is maintained
by means of reducing rotor rpm to "spill the wind". This '.
practice i s comparable to varying blade angle on horizontal
axis WTG.
In computing the data for the net plant power
o u t p i ~ t vs wind speed curve, the assumption was made that the
mutual interference factor fn for a given wind speed, track speed,
and inter-rotor spacing would be the same for both a circular
track and a racetrack having the same end diameters. Actually,
the fn factors were derived from Professor Larsen's vortex
analysis for a circular track. No attempt was made to revise
the vortex analysis to consider a racetrack because both the time required to revise the programs and computer run times
woula be prohibitive.
After studying the interference problem, we
believe that our assumption probably will yield smaller power
values than one would compute from a more rigorous analysis, and
hence, the end results of the study should be conservative.
The vortex analysis for the circular track includes effects of
the interaction of the vortices shed from each car in the train
on every other car in the train. Thus, all combinations of the vortices shed from N uara are cunsidered. However, when a
racetrack pattern is adopted, mutual interference should be
reduced'because the rotors on the average are more widely
separated than those in a circular pattern. The rotors on one
semi-circular end are much farther from the rotors on the other
semi-circular end than they would be if the track were circular.
Also, all of the rotors on the straight sections are at the maximum
upwind-downwind distance that rotor cars would'reach in a circular
pattern. Since for large plants, many more of the cars would
be on the straight sections than on the curved sections, it is
reasonable to expect interference would be, at most, equal to
that for a circular track and probably would be less. Finally, in
comparing the 1372-m separation distance proposed for this Madaras
study with the separation proposed for the 3.9 MW MOD-2 WTG,
which has a 107 m diameter blade, the Madaras separation is
greater. A separation distance of 10 diameters in a triangular
(HEX)" arrangement was proposed for "parks" of these large
machines in the Lockheed study. 44
On the other hand, the upwind-downwind spacing
between rotors on the straight track sections of the proposed
Madaras plant would be 36 rotor heights, and the minimum lateral
spacing would be 44 rotor cylinder diameters (or 22 end cap
diameters). Therefore, we believe the rotors on the straight
track sections are realistically spaced and that our method
for computing mutual interference for the present analysis of a
racetrack-configured Madaras plant will not cause an overstatement
of the results.
Development of Power Duration Curves and Energy Output
Power duration curves like those presented in
Figure 6.15 were developed in the usual manner by cross-plotting
the data from Figures 6.13 and 6.14, and the annual amount of
energy generated was obtained by integrating each curve. The
characteristics of the two plants shown are the same as those
described for Figure 6.14, the power-versus wind speed curves.
In addition, we found that Plant 1 will generate 343 million kW-hr
of energy annually: about 6.7 percent more energy than that of Plant la, whereas the load factor for Plant la is about 56 percent
compared to 49 percent for Plant 1. Since both plants would cost
PLANT @
@
ROTOR WIND SPEED - mph (m/s)
3 r 6 0 - t
I- 2 I- 240-
u s 8 I- W
20-
z
0
Figure 6.14. Ty~ical Net Power versus Vw Curve for Two Racetrack- Configured Plants,
PLANT l 80. --
PLANT la 3
60- l
I- 3 II I- s 40- LL
g a 1 YEAR 8 7 6 0 HR
c 2 0 - W z
0. 0 2 0 0 0 4000 6000
I 8 0 0 0 10000
HOURS I N ONE YEAR
10 2 0 30 40 50 60 7 0 (4.5 (0.01 (13.4) (17.9) (22.4) (2b.U) (31.3)
PLANT @ / - - - - - - ----------
0 V,, = 29.1 m/s
Fi5;urc 6.15. Power Duration Curves far the Two Plants Shown in Figure 6.14 Based on the = 9.6 m/s Design Wind Duration Curveat 25-m Height (Figure 6.13).
1372m DIAMETER BOTH PLANTS 6034m STRAIGHT 1 76 ROTORS
/ @ 80 MW RATED, Vt = 13.4 m/s /
I @ 66 MW RATED, Vt = 8.9 m/s
/ I
+-vCl I = 6.5 m/s
I l - ~ ~ ~ = 8.b m/o I I I I
the same (the only difference being that Plant 1 is.operated at
a 13.4 m/s track speed compared to an 8.9 m/s track speed for
Plant la), it appears that Plant 1 would provide the lowest energy
cost. These are only two of the .97 plant configurations studied.
Our comparison of the power output and annual energy production
of all plants analyzed is presented in Section VII, which follows.
SECTION VII
ECONOMIC ANALYSIS
A specific geometric configuration and operating con-
dition for a single rotor and our method for combining these
rotors into complete power plants were discussed in Section VI.
The purpose of this section of the report is to present the
methods used to compute the cost of a Madaras plant as a function
of plant size variables, to present the results of the cost trade
studies that were computed to investigate the effects of land
cost and learning curves on plant efficiency, and to compare
the plant configuration that appears to be the most efficient
Madards p l a n t with convcntional hurizontal axis wind turbine plants. Finally, a discussion of the feasibility of the Madaras concept
will be presented.
7.1 COST ESTIMATING PROCEDURE
Our basic approach to cost estimating was to develop unit
costs for the variable items which affected plant s i z b and energy
capacity; to combine these items so that a resonable estimate
of Madaras plant costs will be obtained; and to present the costs in a form that wvuld facilitate comparison with conventional
Rorizontal Axis Wind Turbine Generator (HA-WTG) plant.
The basic approach to cost estimating was to develop
unit costs for a Madaras plant and then to xatio the unit. costs
by appropriate size factors to obtain costs of various s i z e s of
Madaras plants. The following criteria were used to develop the
unit cost data:
Wind duration curve specified by ERDA for the large HA-WTG (Figure 6.13) up-rated to the appropriate height for the Madaras Rotor.
Rotor having an aspect ratio of 8, an e/d. ratio of 2, a 4.9-m diameter by 39.2-m height, a design midheight of 25 m, a rotor rotation speed of 186 rpm, a 450-kW spin motor incorporating viscous breaking at the 245' point on the orbit.
Overall structural and electrical design details as specified in Section IV and V.
Detailed plant and mechanical design layout as specified in the drawings included as Figures 4.15 to 4.23, inclusive.
Initial plant size as shown in Figures 4.22 and 4.23 having a race-track 'pattern, 457 m diameter ends, 610 m straight sec'tions, and 28 rotor cars.
Basic cost estimating work was done by M.L. McClellan and
Company, a professional engirieering firm which specializes in
estimating cost of large plants, building construction, and
machinery fabrication. In addition to using the bases for cost
estimating outlined above, quotations were obtained from vendors
for off-the-shelf items, manufacturers quotations were obtained
for fabricated items, and supplemental estimates were developed
based on standardized construction costs and pertinent standardized
material-weight-fabrication cost data.
In developing his cost data, McClellan used the following
major estimating assumptions:
Basis of cost was 1978 prices.
No architectural or engineering costs included.
C. No transmission line costs beyond boundary.
No railroad siding available--- all freight deliverable by available roads to the plant.
e Plant roadway construction included.
Site reasonably level and not heavily wooded.
One extra rotor car included as a spare.
e Cost for two viaducts under track to permit access to insure area in center is readily accessible for agriculture .'
a .- Cost of constructing a permanent fabrication-assembly- maintenance building and a plant control building included.
e No learning curve utilized.
Time of construction estimated to be 36 months.
The detailed cost estimate developed for this program I
is presented in Appendix B. This. information is summarized in
Table 7.1 by four major cost categories in the unit cost modular
form used for the cost-performance trade studies which will be
described in Paragraph 7.2. The cost of purchasing,land is not
included in Table 7.1 in order to permit comparison of Madaras
results with HA-WTG studies which. do not 'include land. This
approach also will permit the flexibility of adding any land cost
deemed appropriate by the reader. We' believe land cost must be
included when considerinq wind turhin~ "farms" or qparks" , and hence we will address this subject in,Paragraph 7.3.
The generalized plant layout and the equations used to
relate plant geometry, performance; and cost are .presented in
Figure 7.1. The generalized cost equation:
utilizes the equations of Figure 7.1 and the an constants developed
and listed in Table 7.1. Other inputs required for this computation
were the pl(S,Vw,Vt) values of power/car excluding interference
losses and the fn(b, Vw, Vt) interference loss factor data. These
data wele obtained from the compuker runs described in Paragraph
6.2 and 6.1, respectively. Of course, these pl and fn values
depend on other variables, but since we have fixed rotor geometry,
rotor rpm, and track diameter, the number of varjahles affecting the values of pi and fn is reduced.
The final cost computation, not indicated in Figure 7.1
is that of determining the average cost of erlergy delivered by a
given plant. Thls computation W a s done in the usual manner by
integrating the power duration curve for a given plant (Figure
6.15) to obtain the kW-hr/yr obtained.from a plant; computing annua
costs of plant operation; and then aomputing the cost per kW-hr.
Annual costs for the basic 28-car plant depicted in
Figures 4.22 and 4.23 were divided into categories of annual fixed
charges and operating and maintenance costs. These costs, which '
TABLE 7 . 1
SUMMARY OF UNIT COST DATA (1
I. COST/ROTOR CAR U n i t C o s t
e R o t o r C a r D i r e c t C o s t , ,28 cars $ 1 8 , 8 5 0 , 4 2 0 (2) . I n d i r e c t M e c h a n i c a l C o s t a t 22.7% . 4 , 2 7 6 , 4 0 0
a C o n s t r u c t i o n F i n a n c i n g a t 1 1 . 7 % of Direct C o s t s 2 , 2 0 5 , 5 0 0
T o t a l C o s t $ 2 5 , 3 3 2 , 3 2 0
11. COST SITE PREPARATION e B a s e d o n N e t Land A r e a of 70 A c r e s
( N e t A c e r a g e e x c l u d e s l a n d e n c l o s e d by . race t r a c k . )
T o t a l S i t e P r e p a r a t i o n Direct C o s t $ 2 1 9 , 5 0 0
I n d i r e c t C o n s t r u c t i o n C o s t a t 1 9 .l% 4 1 , 8 1 0
e C o n s t r u c t i o n F i n a n c i n g a t 1 1 . 7 % of D i r e c t . C o s t s 2 5 , 6 8 0
T o t a l C o s t $ 2 8 6 , 9 9 6 C o s t / N e t A c r e : a2= $ 4 , 1 0 0
111. COST UTILITIES, TRACK, TMLLEYS 8 T o t a l T r a c k L e n g t h = 8 , 7 1 2 f t
T b t a l Direct C o s t $ 1 0 , 6 4 9 , 5 3 0 I n d i r e c t C o n s t r u c t i o n a t 1 9 . 1 % 2 , 0 2 8 , 6 3 0
e C o n s t r u c t i o n F i n a n c i n g a t 1 1 . 7 % of D i r e c t C o s t 1 , 2 4 6 , 0 0 0
T o t a l C o s t $ 1 3 , 9 2 4 , 1 6 0 C o s t / f t of T r a c k : a3= $ 1 , 6 0 0
IV. FIXED COSTS Direct C o s t B u i l d i n g s and V i a d u c t $ 2 , 3 7 4 , 9 0 0
o I n d i r e c t C o n s t r u c t i o n a t 1 9 . 1 % 4 5 2 , 4 0 0 e D i r e c t C o s t Power and C o n t r o l
S y s t e m p l u s 1 S p a r e R o t o r C a r 1 , 0 9 0 , 2 8 0 a I n d i r e c t M e c h a n i c a l a t 22.7% 2 4 7 , 3 4 0
S u b t o t a l D i r e c t C o s t $ 3 , 4 6 5 , 1 8 0 C o n s t r u c t i o n F i n a n c i n g a t 1 1 . 7 %
of Direct C o s t 4 0 5 , 4 2 0 T o t a l F i x e d C o s t a4= $ 4 , 5 7 0 , 3 4 0
GRAND TOTAL PLANT COST $ 4 4 , 1 1 3 , 8 1 0
(1) From A p p e n d i x B
, ( 2 ) I n d i r e c t cost p e r c e n t a g e v a l u e s of 22.7 a n d 1 9 . 1 are r o u n d e d v a l u e s ; n u m e r i c a l cost v a l u e s are e x a c t a n d are i n a g r e e m e n t w i t h A p p e n d i x B.
6 . S = ~ b , m K i s number o f c a r s on s t r a i g h t t r a c k
7 . Nc = Number o f cars on c i r c u l a r p a r t o f t r a c k .
8. b = D S i n - 360 , i n t e r - c a r s p a c i n g based on c h o r d a l ZbJ,
d i s t a n c e on c i rc le , m . 9 . N = Nc + 2K
10. Cost = a N + a An + a T + a d , D o l l a r s 1 2 3
11. PR = PINf : P1 i s power f o r 1 r o t o r = pl ( s , V&, v t ) f n i s i n t e r f e r e n c e l o s s f a c t o r = f n ( b , V,, V t )
Cos t - 12. Cost/kW .= - - I n s t a l l e d ~ o s t / R a t e d Power Capac i ty P~
Figure 7.1. Generalized Geometric Plant Layout and Equations for Computing Plant Cost, Plant Output, and Installed Cost Rated Plant Power Capacity.
are itemized in Table 7.2, were estimated to be.about 46.5 percent
for operation and maintenance. costs. Thus, in the cost trade
studies to be presented.in .Paragraph 7.2, the cost of energy
generated by a Madaras plant will be based upon an.annua1 cost of
16.5 percent of the original plant cost.
Having selected the rotor size, track diameter, and
certain operating conditions, .the remaining.variables and their
ranges which were considered in the plant cost performance
analysis were:
a Track configuration: circle or racetrack
e Track speed: 8'.9 m/s (20 mph)' 11.2 m/s (25 mph) , and 13.4 m/s (30 mph)
a Number of cars: 8 to 190
,a Inter-Car, Spacing: 44 to 108 rotor diameters [4.9 m (16 ft) diameter]
a Length of straight track section: 0-18,300 m.
A total of 97 different plants representing 97 combina-
tions of the above variables were selected as a representa-
tive sample of the many possible plant combinations for our first
analysis. This set of plants consisted of three basic groupings:
a 22 plants having circular tracks
28 plants having racetracks with rotor-cars traveling at 8.9 m/s track speeds
e 47 plants having racetracks with rotor-cars traveljng at 13.4 m/s track speeds.
All plants were designed in terms of a 13.4 m/s (30 mph) rated
wind speed and the up-rated ERDA 7 = =.8.1 m/s (18 mph) wind
duration curve shown in Figure 6.13.
7.2.1 Unit Cost of Circular Track-Plant Configurations -
These initial computations indicated that,circular
track plant configurations are noncompetitive with horizontal axis
wind turbines. The circular-track-plant study. util.ized a track
speed of 11.2 m/s because earlier computations indicated optimum
power occurred at this speed.. Results of this.study are,presented
TABLE 7.2
COMPUTATION OF MADARAS PLANT ANNUAL COSTS (Based upon 28-Car Plant)
I. ANNUAL CHARGES
Mortgage payments : $44,123 ,'370', 30 years $4,171,700 at 8.75% per annum
a Depreciation: $44,123,370,at 30 years 1,470,800
a . Real Estate Taxes 455,500 e Income Taxes ' . 300,000
Annual charges = 14.5% Plant Cost $6,398,000
11. OPERATING AND MAINTENANCE COSTS e Wages
m Seoretary $13,000 Station Manager 50.000 Outside Labor 50,000
e Electricians (2) 50,000 a Millwrights (2) 50,000 s Labor Insurance and Taxes 30,000
$243,000
e Utilities-Heat and Light o Control Building 3,000 Q Assembly Building 9,000 --
$ 12,000
a Expendable Parts a Bearings(616)" 60 at $3500= $21,000 e Wheels (224) 8 at 3000= 24,000 o Reducers (140) 4 at 1509= 60,000 a Lube Oil Pumps (56) 2 at
1500 = 3,000 e Couplings (392) 16 at 450 = 7,200 o DC Brushes (56) 56 at 600 = 33,600 a Contactors (504) 504 at 80 = 40,320 e Trolley Shoes (84) 84 at
300 = 25,200 Collector Rails (13,180)
1200 at 40= 48,000 '$262,320
o ~iscellaneous, 115,000 o Insurance 250,000
Annual O&M Cost = 2% of Plant Cost $882 320 (Total Annual Cost = 16.5% Plant. Cost 5 7 , 2 8 U , 3 2 0
*Number in (xxx) is total number of items in a 28-car Plant.
+Kcte that in addition to these parts, 1 complete spare rctor car is included in the Plant cost of $44,123,370.
Figure 7.2. In addition to analyzing the standard 1372-m (4500. ft)
diameter track, a 1524-m.(5000 ft) diameter track was analyzed to
determine if a .larger track.diameter would improve performance.
However, although the Larger' diameter track improved rated plant
output slightly, it still appears that use 0f.a circular track
will not be economical. Thus, it can be seen -from Figure 7.2 that
the plant having the lowest unit cost is, one having 20 rotors on
'either a.1372-m or a 1524-m diameter track. The specific data
pertaining.to these two least expensive plants studied is pre-
sented .in Table 7 :3.
TABLE 7 . 3
COST AND PERFORMANCE OF A 20-ROTOR MADARAS PLANT HAVING CIRCULAR TRACKS (Land Cost ,not Included)
v& Vt Track Diameter Rated Cost' Unit Cost
m/s m/s m power ( M W ) lo6$ $/kW
From Figure 7.2 one can see that.as the number of cars increases,
the diameter has decreasing effect on unit cost and that the
increased rated power output advantage of the larger plant is
modified by its increasing cost.. After including the cost of land;
the larger plant would undoubtedly be less attractive than the
smaller plant.
0ne.can see in Figure 7.2 that our.study did not
identify the minimum cost circular plant; however, the 20-car
plant was rapidly approaching the minimum, which.probably occurs
at about 22,rotors', and minimum.cost is probably.not less than
$5600/kW. Limitations in time did not permit running higher than ,20-car configurations with,the vortex analysis computer
program.
This result is quite different from that predicted
by Madaras. F0r.a similar number of.cars having the same area (but
Figure 7.2. Plant Cost versus Number of Rotors for Madaras Plants having Circular Track Configurations. Rated Power in Megawatts Indicted for Each Plant. Plants Having 1372-m and 1524-m Diameter Tracks were Studied.
- I I I 1
o TRACK DIAMETER = 1524m(5000f t ) - TRACK DIAMETER= 1372m (4500f t ) LAND COST NOT INCLUDED
,I I I
w A R = 8 e/d = 2 d = 4 . 9 m ( 16ft) Vw = 13.4 m/s ( 30mph) Vt = 11;2 m/s ( 25mph) ROTOR SPEED=186RPM
8
/"' 5
/ \ . . 8' .- / >
5 / 4 '
I I
G 3 z V) ~r 8 4 A
00 - rc) ?I 0 6.
7 7 b.
8 10 12 14 16 18 2 0 NUMBER OF ROTORS
b 0 0
I-
5 6 J a
k z 3 5
-
-
I I
/
%9'
I
\ 0
4.
I
poorer .aerodynamic efficiency) he predicted plant output of over
20 MW at 13.4 m/s wind speeds, and he specified only a 457-m
diameter track for this.plant, The primary differences between
the results of our analysis and those of Madaras are:
Madaras did not realize the magnitude. of spin-motor 'power losses caused by .motor inefficiency, rotor inertia, and vis.cous friction. He predicted he needed only a 37 kW motor to :turn his 27.4 m high by 7.8-m diameter rotor ..compared to the 450 kW motor we have specified for our rotor.
Madaras did not account for mutual interference between cylinders.
The motor loss is severe, and is the only one of the two losses
that can be reduced. by engineering; thus, if a more' efficient means
for rotating the 'cylinder could be developed, a circular track
could again be attract.ive.. At the rated wind speed level, mutual
interference losses onthe 1372-m track were of-,the order of.10
percent, but motor losses' of'over 50 percent would. be expected.
Conversely, at Sower..wind speed levels, the mutual: interference
loss exceeds motor .losses, It.wil1 be shown laterthat the plant
energy output.was not sufficient to overcome the high-first-cost
of the Madaras, circular plant, and hence the cost'of energy also
would be expected to.be excessive.
ina ally, since the unit.cost of the circular Madaras plant is more than a factor,of three greater.than the
predicted cost of the MOD-l'WTG1s, the Madaras circular plant
concept was eliminated from -fur.ther consideration-. The elimina-
tion of this circular concept~is.unfortunate in that the plant
design cannot take advantage of.the inherent wind direction
independence of the circular plant.
7.2.2 Unit Cost of Racetrack Plant Configuration
.Our original performance computations indicated
that best.performance (withdut regard for interference losses)
for a racetrack plant would be obtained at a track speed of
13.4 -m/s.. However., after. studying the mutual interference data,
we determined that cut-in speeds for a given rotor spacing
decreased and wind plant cost increased as track speed decreased.
Therefore, plants utilizing two track speeds were studied in
order to determine whether or not the lower cut-in speeds would
enable a plant to increase its annual energy yield.
Results of our unit cost analyses of 56 of the
racetrack plant concepts are presented in Figures 7.3 and 7.4,
which represent, respectively, plants oper.ating at track speeds
of 8.9 m/s (20 mph) and 13.4 m/sec (30 mph). Each of these curves
shows the relationship between the number of rotors, inter-
rotor spacing, and the length of the straight section. of the.track.
Identical plant configurations were analyzed at both track speeds.
Thus, a comparison of the effect of track speed can be made by comparing a given set of coordinates in Figure 7.3 with its
counterpart set in Figure 7.4.
The data trends were as expected, with unit plant
cost decreasing as N (number of rotors) and S (length of straight
section) 'increase.and as b (inter-rotor spacing) decreases. Thus,
from a unit'plant cost standpoint, it is better to provide a very
long racetrack and maximize the number of cars on the track. Also,
by comparing Figures '7.3 and 7.4, it is'evident. that unit plant
cost increases as track speed decreases from 13.4 m/s to 8.9 m/s.
The ef,fect of variables S, b; and N on cost and
rated ,plant power is shown 'in' Figure. 7 . 5 . . As expected, rated power
increases markedly as N and .S increase., and one can' see that the
effectiveness of each rotor decreases as b increases. Additional
improvement in piant performance.can be achieved by decreasing b
and increasing N and S; however, reasonably good design .seems to
have been achieved for plants having rotor spacing of 44d and
at combinations of S > 3000'm and N > 76. Of the three variables,
the least benefit in increasing rated power would be achieved by
decreasing b, and the most benefit would occur from adding track
and rotors at the maximum density studied. Since the cost of
1 rotor is equivalent to 173 m (565 fk). of' track, a break-even
trade point would seem to occur when b = 173 m or 35 rotor
diameters (35d). This distance is equivalent to the spacing of
b~ INTER-ROTOR SPACING IN I AR = 8 ROTOR DIAMETERS 1 c / d = Z I .
WIND PERPENDICPJLAR TO STRAIGHT SECTION
I ROTOR DIAMETER, d = 4 .9m
6' LAND COST NOT INCLUDED ROTOR SPEED = 186 RPM TRACK END DIAMETER = 1372m Vw = RATED SPEED = 13.4 m/s V+ = 8.9 m/s RACETRACK P L A N T
h: P UI
!I - --b=49d Z 3 &6- ---b=44d
2 -
-
I 1 I I I I 1 I 1
4 6 8 10 12 14 16 18 20
. - Figure 7 . 3 . Uni t P l a n t Cost ve r sus Length of S t r a i g h t Sec t ion of Racetrack P l a n t
Ccnf igu ra t ion a s a Funct ion of Number of Cars and Inter-Car Spacing. Track Speed: 8 .9 m / s ( 2 0 mph) .
F i g u r e 7.4. U n i t Plank Cos t v e r s - ~ s Length o f S t r a i g h t S e c t i o n o f Race t rack P l a n t Conf igu ra t i o r as a Funczion of Number o f Cars and In t e r -Ca r Spacing, Track Speed: 1 3 . 4 m!s ( 3 0 mph).
6
3 x RACETRACK PLANT
h) I-' m
---
F - -
-
1 I 1 I I I I I 1 I . 4 6 8 II 0 12 14 16 18 20
LENGTH OF STRAIGHT SECTION - lo3 FT
b=lNTER - ROTOR SPACING I N ROTOR DIAMETERS
- WIND PERPENDICULAR TO STRIGHT SECTION LAND COST NOT INCLUDED
-
A R = ~ I e/d = 2 ROTOR DIAMETER, d = 4 . 9 m ROTOR SPEED = 186 RPM TRACK END DIAMETER = 1372 m - Vw = RATED SPEED = 13.4 m/s V+ = 13.4 m/s
I I I I I I I AR= 8 N' NUMBER OF ROTORS
I e/d = 2 S = LENGTH OF STRAIGHT ROTOR Dl AM ETER, d = 4.9m TRACK SECTION ROTOR SPEED = 186 RPM b = INTER-ROTOR SPACING TRACK END DIAMETER=1372m IN ROTOR DIAMETERS RATED WIND SPEED = 13.4 m/s WIND PERPENDICULAR TO S
LAND COST NOT INCLUDED NO LEARNING CURVE USED
2 0 40 60 80 100 120 140 160 180 2 0 0 220 240 260 RATED POWER - MW
F i g u r e 7.5. U n i t P l a n t C o s t v e r s u s Rated Power f o r Race t rack C o n f i g u r a t i o n a s a unction o f I n t e r - R o t o r Spac ing , Length of S t r a i g h t S e c t i o n o f Track , and Number o f i3otors. DOE Design Wind D u r a t i o n Curve: V = 8 . 1 m / s @ 9 m.
25 rotors around a 1372-m diametcr track. If more rotors can be
added toa given amount of track without incurring excessive
interference losses, a more economical design should be achieved.
However, it appears that a 25-d spacing would be counter productive.
As noted in Figures 7.3, 7.4, and 7.5, all cal-
culations up to this point have been based upon the assumption
that the wind is perpendicular to the track. We will address the
effect of .nonoptimum wind direction on plant performance later'
in this section of the report.
After str~lying the vsr io i~s p1 a n t s r e p r e s e n t . e d i n
Figures 7.3, 7.4, and 7.5, it appeared that those operating at a
track speed of 13.4 m/s (Figure 7.4) were superior to those
operating at the 8.9 m/s speed. Thus, only the best of the
8.9 m/s plants (N = 76, S = 20,000, b = 44d, Unit Cost =
$2389/kW) was retained for the energy cost study.
All of the 13.4 m/s racetrack plants covering
the range of operating conditions included in Figure 7.5 and the
best plant using a circular track configuration were retained for
the energy cost analysis.
7.2.3 Energy Cast
The energy cost. was compi.ited f ram a 1 1 pl ant.
configurations studied utilizing the usual equation:
Cost/kW-hr = Plant Cost x Annual Cost Annual Energy Output
where the annual cost was 16.5 percent of plant cost (developed
in Table '1.2) and the annual energy output in kw-hr/year was
obtained by integrating the power duration curve for each plant,
typical of those shown in Figure 6.15.
Four sets of energy cost data were computed;
one set for each of the following conditions:
1. Circular track plant, track diameter of 1372rn, track speed of 8.9 m/s and up-rated V = 8.1 m/s at 9m wind duration curve.
2. Racetrack plant, track diameter of 13.72' m, track speed of 8 -9' m/s and up-rated 7 = 8.1' m/s, duration curve.
3. Racetrack plant, track diameter of 1372 m, track speed of 13.4 m/s, and ~p-~ated' =' 8.1' m/s wind duration curve.
4. Racetrack plant, track diameter of 1372'm, track speed of 13:4 m/s and up-rated V = 9.7 m/s wind duration curve '(Medicine 'Bow, Wyoming).
7.2.3.1 Racetrack Configurations
The results of the third set of these com-
putations are presented in Figure 7.6. These energy cost data
correspond'to the 'same 47 plants used to compute the plant cost/
kW data presented in Figure '7.5. Although the characteristics
of the curves in Figures' 7.5 and 7.6 are similar, there are two
major differences in the cost/kW-hr data in Figure 7.6: (1) a
definite minimum cost point as a function of straight track dis-
tance, S, was realized; and (2) the effect of inter-rotor spacing
is much more pronounced in Figure 7.6. Actually, both of.these
differences are influenced by inter-car spacing, b.
In Figure 7.6, one can see a major drop
in energy cost for a given value of-rated power as - b decreases from 108 rotor diameters (108 d, where .d =' 4.9 m) to b = 87d.
From that point on, the effect of decreasing b - is less pronounced. However, between b = 8.7d-and b = 44d, a minimum energy cost is
realized. Thus, for a plant. defined by a given value of rated
plant power, the cost of energy . - is slightly higher for an inter-
rotor spacing of 44d than the minimum energy cost which occurs
at a larger value of rotor spacing. This trend can be seen in
Figure 7.6 by following the b-values at a constant rated power
level of 110 MW (i.e. energy cost decreases as .b progresses from
108d to 87d, to 73d, and to 63d. From that point on, energy cost
increases as b decreases to its minimum value of 44d.
This cost/performance trend is caused by:
(1) an increase in mutual interference and losses and hence a
decrease in annual energy yield of a plant having a 448 rotor spacing compared to a plant having a 63d.spacing1 and (2)
Figure 7 . 6 . Energy Cost v e r s u s Rated Power f o r Racetrack lConfiguration a s a Funct ion of In te r -Rotor Spacing, Length of S t r a i g h t S e c t i o n - of Track, and Number of 3 o t o r s . DOE Design Wind Dura t ion Curve: V = 8 . 1 m / s @ 9 m.
an increase in plant cost (and hence increased operating cost) of
a 446 plant over that of a 63d planthaving thg same value of rated
power. Thus, since the annual energy of a 63d plant is greater . .
.. . than that of a 44d plant, and since the annual cost of operating
a 63d plant is less, the energy cost of the 63d plant was smaller
than that of the' 44d plant. Note also that the optimum value
of - b at which'the'trend reversal occurs decreases as PR increases.
The other interesting result of this
study is that for all plant sizes studied, the minimum cost of
energy for a given value of S is obtained for those plants having
inter-rotor spacing of 49d. We did not plot the b=49d curve in
order to improve reading clarity in this region where the b-curves
are compressed due to the previously-mentioned trend reversal.
Thus, a rotor spacing of 49d will provide the minimum cost of
energy for a given value of St a mean wind speed of 8.1 m/s, ,and
no consideration of learning curves.
Another minimum energy cost condition also
was found: i.e., the optimum rotor spacing of the number of rotors,
N, is fixed. This trend can be seen by following the trends of
the N = 50, 75, 100, and 150 curves plotted in Figure 7.6. The
energy cost of a plant having 75 rotors, for example, decreases
rapidly as rotor spacing decreases, a minimum value is reached at
some value of b, and then the energy cost increases as rotor spacing
is further compacted. This effect is, of course, caused by rotor
interference. Unlike the locus of energy cost minima for various
values of St the optimum rotor spacing varies with number of cars. Thus, for plants limited to 50, 75, 100, and 150 rotors, the inter-
rotor spacing which will provide minimum energy cost would be 73d,
63d, 55d, and 49d, respectively. Of course, since varying the
number of cars also increases St and since power output increases
as S increases, (Pmax occurs at S = a) it would appear that
minimum energy cost will be achieved, by increasing S to the
maximum length practicable and then providing the number of rotors
required to achieve the optimum inter-rotor spacing for the
s e l e c t e d t r a c k l eng th . This approach sugges ts t h e d e f i n i t i o n of
an optimum s o l i d i t y f a c t o r , one o f t h e o b j e c t i v e s of t h i s s tudy;
i , e . , t h e d e f i n i t i o n o f . t h e minimum number of r o t o r s t h a t can
produce t h e lowest e n e r g y . c o s t i n a given l eng th of land per-
pendicular t o t h e wind. For a r a c e t r a c k p l a n t , t h e l eng th
perpendicular t o t h e wind i s S + D, where D i s t h e end diameter .
Thus, t h e propor t ion of t h i s l eng th occupied 'by N r o t o r s having
d iameter , d is:
where a i s t h e s o l i d i t y f a c t o r . Since t h e optimum value o f S f ~ r N r o t o r s can be approximated from Figure 7.6, t h e optimum values
of a and t h e a s s o c i a t e d va lues of N and S have been t abu la ted
and p l o t t e d i n F igure 7.7. This f i g u r e shows t h e marked
economic advantage of l a r g e r p l a n t s and i n d i c a t e s t h a t small
dec reases i n energy c o s t may be obtained by i n c r e a s i n g s o l i d i t y
f o r p l a n t s h a v i n g v a l u e s of S < 18,300 m (60,000 f t ) . Since
Figure 7.6 a l s o i n d i c a t e s t h a t our computations have n o t been
extended s u f f i c i e n t l y f a r t o o b t a i n an abso lu te minimum, it may
be adv i sab le t o i n v e s t i g a t e l a r g e r p l a n t conf igura t ions . Of
course t h e cost of land i s n o t included i.n +.he compvtations a t
t h i s p o i n t , so t h e e f f e c t o f land c o s t on p l a n t s i z e could a l t e r
t h e s i z e - e f f i c i e n c y r e l a t i o n s h i p . This land f a c t o r w i l l be
evalua ted i n Paragraph 7.3,
7.2.3.2 Energy Cost Comparisons, B e s t P l a n t Co~ibina t ions
The four d i f f e r e n t s e t s . o f p l a n t design
cond i t ions analyzed i n t h i s program w e r e i temized i n Paragraph
7 .2 .3 . These cond i t ions provided t h e oppor tuni ty of comparing
t h e energy c o s t of c i r c u l a r versus r a c e t r a c k p l a n t s , t h e e f f e c t
of t r a c k speed on energy c o s t f o r r a c e t r a c k p l a n t s , and t h e
e f f e c t of wind dura t ion curves on energy c o s t (v = 8.1 m / s v s
v = 9.7 m / s a t ~ e d i c i n e Bow, Wyoming) . The p l a n t s having t h e
lowest energy c o s t and o t h e r s which i n d i c a t e t h e e f f e c t of t h e
v a r i a b l e s on p l a n t economy are presented i n Table 7.4.
Figure 7 . 7 . Optimum Rotor So l id i ty Factor versus Length of Straight rack sec t ion .
0.044 - .- AR =8 e/d = 2
0.040 - 2
Rotor Diameter, d = 16 f t. (4.9m)
a Rotor Speed = 186 RPM
o Track End Diameter, D = 4 5 0 0 f t (1372in) t- o Rated Wind Speed = 3 0 mph (13.4 m/s)
0.036 - Track Speed = 3 0 mph ( 13.4 m/s)
> Wind Duration Curve V = 8.1 m/s @) 9m I- -
h) 0 N - W
V) c = N d
a S+D - 0 t-
- t o 0.024 -
0.020 = I I I I I 10 20 30 40 5 0 6 0
(3.0) (6.1 1 (9.1) (12.2) (1 5.2) (18.3) LENGTH OF STRAIGHT TRACK SECTION, S - k f t (km )
TABLE 7 . 4
COMPARISON OF PLANT PERFORMANCE AND COST - CIRCULAR AICD R?CETP!CK CONFIGURATIONS
MSIC RACETRACK PLANT - = 8 . 1 m/S
BASES OF COST
(1 ) Cost o f Land Not Included ( 2 ) Cost o f F i r s t Item --- N o Learning Curves ( 3 ) Annual Charge o f 16.5% ( 4 ) Medicine Bow, Wyoming Wind Duration Curve with Sea Level Density t o show only e f f e c t of
Wind Duration Cui-ve Duraticn,
The s u p e r i o r i t y o f t h e r ace t rack over
t h e c i r a u l a r - t r a c k p l a n t i s s t r i k i n g . The c i r c u l a r p l a n t s e l e c t e d
was t h a t found t o have t h e h i g h e s t performance i n Figure 7.2..
Although our s t u d i e s ind ica ted t h a t a s l i g h l y lower cost/kW could
be obtained by using more closely-spaced r o t o r s , and Figure 6.11
i n d i c a t e s t h a t a small amount of a d d i t i o n a l power might be
obtained from a l a r g e r diameter c i r c l e , w e b e l i e v e t h a t P l a n t
8a, t h e most e f f i c i e n t c i r c u l a r p l a n t s tud ied , . t y p i f i e s
t h e b e s t performance one might expect from a c i r c u l a r p l a n t .
Since c o s t of energy from t h i s p l a n t i s g r o s s l y noncompetitive
with that.. from h o r i z o n t a l a x i s wind machines and about twice a s
expensive a s t h e c o s t of energy from t h e most i n e f f i c i e n t Madar'as
r ace t rack p l a n t (see Figure 7.6) , w e again concluded t h a t t h i s . I
p l a n t type was n o t worthy of f u r t h e r cons ide ra t ion .
The e f f e c t o f t r a c k speed on p l a n t
economics can be determined by comparing P l a n t s 1 and l a . This
i s a comparison of t h e e f f e c t of t r a c k speed, Vt, on t h e opera t ing
c h a r a c t e r i s t i c s of one p l a n t . The only d i f f e r e n c e i n P l a n t s 1
and l a i s t h e t r a c k speed. The e f f e c t of t r a c k speed on cost/kW
was presented i n Figures 7.3 and 7.4, and t h e r e it was concluded
t h a t t h e decreased t r a c k speed decreased t h e performance of a l l ,
p l a n t s i z e s s t u d i e d , ! a n d hence increased t h e cost/kW'of each "low
speed" p lqn t . However, s i n c e t h e power dura t ion curves of t h e
"high speed" and "low speed" .p lan t s ( e .g., P l a n t s 1 and l a ) were
. s i g n i f i c a n t l y d i f f e r e n t i n both ' the low and h igh wind speed
regions ( see Figure 6 .15) , w e continued our s tudy t o determine i f
t h e lower t r a c k speed and t h e r e s u l t i n g lower cut - in wind speed
of P lan t l a would produce more energy annual ly than P l a n t 1.
Table 7.4 i n d i c a t e s t h e reverse. is t r u e , and t h a t P l a n t 1 n o t
only has a h igher power r a t i n g , b u t it a l s o w i l l produce energy
a t lower c o s t . Therefore, s i n c e P l a n t l a was t h e b e s t "low-speed"
p l a n t s tud ied , it was concluded. t h a t , f o r t h e design wind
d u r a t i o n curve used f o r t h i s s tudy, t h e 13.4 m / s (30 mph) t r a c k
speed would provide lower c o s t energy f o r any p l a n t conf igura t ion .
However, f o r lower mean-speed wind dura t ion curves, a lower t r a c k
speed may be advisable .
One interesting possibility should be
investigated in any future analyses of the Madaras system: con-
sider the use of a variable gear ratio drive from the rotor-car
wheels to the generators in order to permit operaking at two
or more track speeds. Refer to Figure 6.15. Here, one can see
the cross-over of the power duration curves of Plants 1 and la
at a wind speed of about '9.8 m/s (22 mph) . If a. variable-speed
drive were utilized, one could shift into the high gear ratio
and operate at Vt = 8.9 m/s (20 mph) when winds were in the
range between. 6.5 m/s (14.5 mph) and 9.8 m/s . Then, as the .9.8 m/s speed was approached, the gear.,ratio would be reduced and
track speed increased to 13.4 m/s (30 mph) . In this way, the
?lant cou'ld benefit from "the better of two worlds" and add the
area between the two curves below 9.'8 m/s to its annual energy
output. If the added energy offsets the' added cost of the
variable speed drive, the cost trade would be attractive.
The racetrack plants having the lowest
energy cost of.those studied are listed in the third grouping
of plants. As can be seen, ,each of Plants 49-10 through 49-60
represents the optimum cohfigur~tion for a given value of S
obtained from Figure '7.6. As noted Lrefore, each .optimum plant
utilized rotor spacing of 49 diameters. In addition, this grouping includes the largest of all 47 plants studked: Plant 44-60 which
has a rated capacity of over 227 MW and will produce 975 million
kW-hr/yr at an energy cost o f 6.6.7C/kW-hr (...OQ2C/k.W-hk higher than
Plant 49-60). The data in Table 7.4 .indicates that plants having
values of S < 3112 m (10,000 ft) probably will not be cost
effective even when mass-produced components are used. Also, a
significant drop in energy cost occurs up to Plant 49-30, and
from there on the performance improvement is slower. There is
not much..difference in energy cost for Plants 49-50, 49-60, and
44-601. The economy of sca1e.effec.t is quite evident from the
ever-decreasing unit cost ($'/k~) of the installed plant.
It also is particularly interesting to
ncte that Plants 49-60 and 44-60 are quite competitive with the
c o s t and energy c o s t of a sing1.e MOD-1 wind t u r b i n e 'not wired i n t o
,a p l a n t . ~hi ' s ' compar ison w i l ' l be made l a t e r a f t e r appropr ia t e
a p p l i c a t i o n of s i m i l a r ground ' ru les and condi t ions .
The l a s t group of p l a n t s l i s t e d i n Table 7.4
were operated i n a region having a mean wind speed of 9.7 m/s and sea
l e v e l dens i ty . Since t h i s wind dura t ion curve i s l i k e t h a t a t
Medicine Bow, Wyoming, one could th ink of t h e s e a s Medicine Bow Sea
Level (MBSL) p lan t s . These a r e presented t o show t h e e f f e c t on
p l a n t performance 'of varying only the"wind dura t ion curve. The e f f e c t
of a i r d e n s i t y a t Med.icine 'Bow, Wyoming, on performance w i l l be shown
in 'pa ragraph 7.5. A l l 47 b a s i c p l a n t s were run f o r t h i s condi t ion .
The f i r s t observa t ion of importance is
t h a t f o r t h e h igher wind dura t ion curve, optimum performance
. f o r a given va lue o f S was obtained from p l a n t s having i n t e r -
r o t o r spacing of 44d ins tead of 49d. This can be seen by .4
comparing P l a n t 49-60M wi th P lan t 44-60M. The marked inc rease
. in annual y i e l d by. P l a n t 44-60M more than o f f s e t s t h e added c o s t
of added r o t o r c a r s and t h e decreased e f f i c i e n c y of reducing
i n t e r - r o t o r spacing. Since c o s t and r a t e d power was t h e same f o r
t h e Medicine Bow p l a n t s and t h e b a s i c p l a n t s , t h e i n s t a l l e d u n i t
p l a n t cos ts , remained unchanged. The e f f e c t of t h e h igher wind
dura t ion curve i s a l s o seen i n t h e i n c r e a s e of about 20 percent
i n p l a n t f a c t o r f o r t h e MBSL p l a n t s and i n t h e 15.6 pe rcen t
reduct ion i n energy c o s t of P lan t 49.-60M over P l a n t 49-60.
The p a r t i c u l a r MBEL p l a n t s l i s t e d i n
Table 7.4 were s e l e c t e d t o i l l u s t r a t e some.of t h e design t r a d e s
a v a i l a b l e with t h e increased wind dura t ion curve. We a l ready
have.mentioned t h e a b i l i t y t o decrease r o t o r spacing t o o b t a i n
optimum energy c o s t . Another i n t e r e s t i n g comparison i s P l a n t '
44-45M wi th 49-60. Here a r e two p l a n t s of d i f f e r e n t r a t e d
capac i ty having t h e same i n s t a l l e d cost/kw. Y e t , t h e MBSL plant,
though 22 pe rcen t smaller i n r a t e d capac i ty , w i l l produce energy
a t a c o s t t h a t i s 1 4 percent lower than t h a t f rom. the l a r g e r p l a n t . J
A s i m i l a r r e s u l t i s obtained when comparing P l a n t 44-20M wi th
P l a n t 49-60. Here a r e two p l a n t s having approximately equal energy . .
costs, and yet this same performance by the 'MBSL Plant can be
achieved with a straight track section of only 6034 m (20,000 ft)
compared to a length of 18,198 m (60,000 ft) for Plant 49-60. Thus
for MBSL winds, only about one-half the land and only 43 percent
of the plant cost are required to produce energy at about the sane
cost as that in the' lower wind region. Of course, the basic plant's
rated capacity is almost three times as large as the Medicine Bow
plant.
From plant comparis~ns in Table 7.4, we conclude that the mos-t efficient basis pl.a.nt i .s Plant. 49-fin,
which has a rated capacity of 2110 MW, an installed unit cost of . .
$1781/kW, an annual energy yield of 931 million kW-hr, and an
energy cost of 6.65C/kW-hr. The largest basic plant is Plant
44-60, which has 227.77 MW rated capacity, an installed 'unit
cost of $1732/kW, an annual yield of 975 million kF7-hr, and an
energy cost of 6.67C/kW-hr. These two plants along with their.
MBSL counterparts were considered the best Madaras plants of those
analyzed. However, all plants listed in Table 7.4 will be considerel
i'n the analyses that follow in order to assure that the effects of land cost, learning curves, and off-axis wind conditions will not
alter the basic Madaras plant economic trends that have already
been noted.
We have no doubt, that given sufficient
space and high wind conditions, even larger Madaras plants than
Plant 44-60 could be built. Further, we again want to emphasize
that the plantdesigns in Table 7.4 do not represent an overall
optimized system design, but instead represent good conceptual
designs. Hence, given the opportunity to conduct a more
extensive design analysis, we belive basic system efficiency
could be improved over that stated in Table 7.4.
7; 3 EFFECT OF LAND COST AND LEARNING CURVES ON ENERGY COST
All computationsofpower and energy cost made previously
have included the cost of site preparation, grading, and general
earthwork. However, the cost of purchasing or leasing the land
has not been included. In addition, cost estimates have not
taken into account the cost reduction resulting from mass
production: a factor that must.be considered before the Madaras
system can be compared with modern horizontal axis WTG's.
This section of the report will address both of these
cost factors.
7.3.1 Land.Cost Effect
Three approaches to land acquisition and management
were considered:
Long term land lease.
Purchase of all land required both inside and outside the racetrack in conjunction with leasing the inside track area for agricultural use.
Purchase of only a right-of-way to a tract of land; i.e., the An defined in Figure 7.1 as that area outside the track plus land Occupied by the track and trolleys. The land inside the track then would remain the property of the original land owner to use for agriculture or other noninterferring use. Two viaducts, one at each end, would be built of sufficient size to permit access to the inner area.
After consulting with personnel at the Dayton Power & Light Company,
as wellas a local realtor, it was recommended that the third
approach be taken.: purchase outright only the net area. The
Dayton Power & Light Company.has.used this approach successfully
many times. This concept is .the same as that prepared by Lockheed
for their Wind Energy Mission ~nal~sis,~' which suggested that
large wind turbines be spaced 10 to 15 diameters apart in a hexagonal
pattem.:thatonly 15 acres around each wind turbine would be pur-
chased, and that the rest of the land would be retained by the
original owner and used for agriculture. Thus, large "parks"
P- of wind turbines would be developed, and only 6.4 percent of the
44 land required for such 'a "park" would have to be 'purchased.
(This study did not include the .land required'.for access roads.)
Since the area inside the racetrack is completely
open, free of obstructions, and can be very large'.'.(,6.500 acres for
the largest plant); a large-scale farmer would consider farming
this tract of land as an .attractive business venture.
Consequently, for Madaras plants, one would
purchase only that are designated An in Table 7 . 4 for each of
the plants being considered. .This amounts to the purchase of
from 745 to 748 acres for the two largest plants being considered
for this study. This land would..provide ample area for the , .
erection of the buildings, . a.power . . - . . . - substation, - a fenced-in, clear
' perimeter area, as well as space for the circumferential service
road, the track, the power distribution system,. and the wind
velocity sensing system.
Our land cost analysis was designed to bracket a
wide range of agricultural.land costs that might be prevalent
in areas which would be suitable for Madaras plants: i.e., a large
open expanse of land with essentially unidirectional winds.
Generally the Great Plains and certain Texas Gulf Coastal areas
are typical of the sites one might select. It is questionable
whether attractive land quality, wind strength and duration, and
wind direction combinations would be found in the North East,
the Midwest, or most of the Cornbelt States where land prices are
at premium levels. Thus, we selected the following four unit
land price levels which we believe will encompass the geographical
areas of interest to Madaras plants. These unit land costs were:
$500/acre; $1000/acre; $1500/acre; and $3000/acre. These costs
were input to our cost analysis program, and the total energy costs
were computed again using an annual cost rate of 16.5 percent of
plant cost (including land) to obtain energy costs.
These computations were made for al.1 47 racetrack
plants, both for the basic' and Medicine Bow wind duration curves.
No changes in trends noted in Table 7 . 4 were observed, and again ,-
the plants which were best for the basic analysis were also the
best where land costs were included,
The effect of land costs on these best plants
is shown in Table 7.5. For the planned land purchase approach
these data indicate that land cost has an insignificant effect
on plant cost and energy cost for large Madaras plants. Both
the plant cost ($/kW) and the energy cost (Q/kW-hr) had a maximum
increase of about 0.6 percent. This cost increase was essentially
the same for all of .the plants. in Table 7.5. For the smallest
Madaras plants studied (one with 20 rotors and a 3050 m straight
track section) the maximum increase due to land cost was about
1.1 percent. Therefore, it appears that land cost will have little
effect on Madaras plant performance even at $3000/acre land costs,
However, when learning curves are applied to the cost analysis,
land costs become more prominent.
7.3.2 Learnina Curve Effect
In preparing the cost estimate for the basic plant,
no provision for learning curves or mass production were included.
Since each of the large plants we are contemplating requires
laying about 268,000 ft (81,800 m) of nonconventional track rails
and the building of 170-190 rotor cars, it is readily apparent
that a learning-curve-type of cost reduction will be realized'in I .
building even one plant. This cost reduction will be even greater
if ~riure than one plant is built in a given prodiiction lot.
Learning curves are based on the concept that
each time production is doubled, the average cost of 2n production
items is a specified fraction of the average cost,of n items. Thus,
the ratio of the average cost of 2n items to the average cost of
n items defines the learning curve, Thus, for an 85 percent learning
curve, the average cost of two would be 85 percent of the first
item cost, and the average cost of the four items would be .85 2
percent of the average cost of two items [i .e . , ( .85) times
the cost of the first item] ;' etc. Thus :
TABLE. '7 .5
EFFECT OF LAND.COST ON PLANT AND ENERGY COST
* P l a n t D e s i g n a t i o n I n d i c a t e s S i z e
4 9 = R o t o r S p a c i n g = 49d = 784 f t (239 m) 60 = S t r a i g h t T r a c k L e n g t h = 60 ,000 f t ( 1 8 , 3 0 0 m) N o L e t t e r F o l l o w i n g = B a s i c Wind ~ u r a t i o n C u r v e M = M e d i c i n e Bow Wind D u r a t i o n C u r v e ( M B s L ) , S e a ~ e v e l ~ e n s i t y d = 1 6 ft ( 4 . 9 rn)
+ % Increase for $ 3 0 0 0 / a c r e l a n d o v e r n o l a n d cost
49-60M'*
1 7 0
7 4 5
.2.P.O.. 5 9
1103 .35
44-60
19.0
748
' 2.27.77
975 .43
44-60M*
1.9 0
748
227.. 77
1170 .17
11
P l . a n t N o .
Number R o t o r s
An Ac r.e s.
R MW
E n e r g y Our;pu t
1 0 kW-hr/yr
4.9-6.0
170
7.4 5
.2.1.0 ..5.9
931 .25
where
LC is the learning curve ratio (e.g., 0.85)
Kn is the average cost of n units of the cost of constructing only one item
Cn is the cost of the nth item of the. cost of constructing only one item
These equations were obtained from Hightower, who used them for
his HA-WTG plant design in Reference 45.
Thus, in order to use the learning cost reduction
concept, it was first necessary to define learning curves for . :
various parts of the plant and then to define the corresponding
production units to which the curves apply.
Our initial cost equation (.Equation (9) Paragraph
7.1) contains four terms: (1) cost .of rotor cars, (2) cost of
general site preparation, (3) cost of track, utilities, and roads,
and (4) the cost of the assembly and maintenance building, the ,,, control building, the power switching and conditioning equipment,
and the .control equipment. The fourth term also included the
spare rotor, which will be handled differently in the new equation
that will be developed.
After analyzing the site preparation and mis-
cellaneous components, items (3) and (4), we concluded that this
technology would be conventional and that skilled earth moving
and construction personnel would already be high on the learning
curve. Therefore, for our analysis, we assumed that components
(3) and (4) (less the spare rotor) would not benefit from learning
or mass production, and hence no learning curves were applied to
these cost components,
On t h e o t h e r hand, w e b e l i e v e t h a t it i s d e f i n i t e l y
a p p r o p r i a t e t o a p p l y l e a r n i n g cu rves t o t h e r o t o r cars and t h e
t r a c k l a y i n g . D i f f e r e n t approaches w e r e t aken t o develop a p p r o p r i a t e
l e a r n i n g cu rves f o r each of t h e s e components.
The manufacture and assembly o f t h e r o t o r cars
i s q u i t e s i m i l a r t o t h e manufacture o f l a r g e t r a n s p o r t a i r c r a f t .
The rotor is a semi-monocoque s t r u c t u r e des igned f o r h igh s t r e n g t h -
we igh t r a t i o and f a b r i c a t e d from aluminum and o t h e r l i gh t -we igh t
p a r t s . Although t h e r o t o r suppor t tower c a r and wheels are ve ry
mass ive , a l l u s e materials and manufactur ing techniques l i k e t h o s e
used for aircraft. I n a d d i t i o n , each m t o r and ear i s equipped
w i t h e l e c t r o n i c c o n t r o l s , e lectr ical equipment, gea r ing , and
b e a r i n g s , j u s t a s a n a i r c r a f t . Thus, s i n c e t h e manufac ture of
r o t o r cars does n o t have a manufactur ing c o s t expe r i ence base o f .
i t s own, w e e l e c t e d t o u t i l i z e an 85 p e r c e n t l e a r n i n g cu rve f o r
t h e r o t o r c a r , based on l e a r n i n g cu rve expe r i ence o f a i r c r a f t .
The s e l e c t i o n o f a l e a r n i n g curve f o r t h e t r a c k
l a y i n g was n o t as s t r a i g h t f o r w a r d . F i r s t , as can b e seen i n
Tab le 7.1, w e have inc luded a number o f o t h e r i t e m s i n t h e t r a c k
c a t e g o r y : i .e . , t r a c k , t r o l l e y s , d r a i n s , and o t h e r u t i l i t i e s ,
power c o l l e c t i o n and d i s t r i b u t i o n , and t h e service road. These
were combined w i t h t h e t r a c k because t h e y r a n p a r a l l e l t o t h e
t r a c k , and hence i n c r e a s e d i n s i z e and c o s t i n d i r e c t p r o p o r t i o n
t o t h e l e n g t h o f t h e t r a c k . These t y p e s of work r e p r e s e n t a
mixed group o f t e c h n o l o g i e s , some o f which a r e w e l l developed,
and some ( l i k e t h e t r a c k road bed and t r o l 1 e y s ) a r e h i g h l y non-
conven t iona l . Thus it w a s assumed t h a t a 90 p e r c e n t l e a r n i n g
c u r v e would b e a r e a s o n a b l e a v e r a g e l e a r n i n g curve f o r t h e t r a c k ,
e t a l .
The n e x t s t e p was t o develop an a p p r o p r i a t e u n i t
of p roduc t ion f o r t h e t r a c k system. One c o u l d ~ c o n s i d e r a u n i t o f
p roduc t ion t o be t h e l a y i n g o f one 6-m (20 f t ) l e n g t h o f r a i l ,
o r t h e b u i l d i n g o f a 305-m (1000 f t ) segment o f roadways.
However, ano the r method se rved t o b e more convenient : t h a t i s
to develop a track, roadbed, etc., unit equal to that length of
track associated with'each'rotor car. Thus, since there are N
rotors in a given plant with a track perimeter, T, there is one
length of track and roadbed, t, equal to T/N that is added each
time one rotor car is added to increase the size of a plant. Thus,
for an N-rotor plant, there are N track units, each having a
length t. This unit length, t, is not constant for all plants but
increases as inter-rotor spacing increases. Thus, an N-rotor plant
having rotor spacing of 49d will have a larger value of t than that
of an N-rotor plant having rotor spacing of 44d. In each case,
however, the number of production units would be the same as the
number of rotors. (Since all of our cost calculations were
carried out for the 49d and 44d spacing, the effect on the cost of
the track resulting from the different size t is less than 2 percent.)
Equation (9) , our basic cost equation, had to '-
be modified slightly to accommodate the learning curve terms as
well as to provide a better basis for comparing Madaras plants
with horizontal axis WTG plants. Our initial equation scaled the
number of rotors, the amount of site preparation, and the length
of track directly as these items varied from one plant size to
another. The fourth item, which was held constant, included the
cost of bluidings, power conditioning and switching equipment, . system control equipment, and one complete, spare rotor car.
Although for the original study it was recognized that the power
conditioning and switching equipment would increase with plant size, the cost of these items was found to be small relative to
the complete plant cost. However, for the learning curve study,
it was decided that a better cost estimate would be obtained
if the power conditioning and switching equipment were scaled
with plant size and if the cost of the spare rotor [which is the
(N+l)th rotor car purchased for a given plant] were developed
as a part of the learning curve experience of the total rotor
purchase. Thus, two new terms were added to Equation (9) such
that :
P l a n t Cost = al (N+1) KN+l
I n Equat ion ( 1 2 ) , t h e c o n s t a n t s a l , a2 , and a3were assumed t o be
t h e i d e n t i c a l u n i t c o s t rates de f ined i n Table '7..1, and:
Cost o f Power F a c t o r and Switching Equipment f o r 28 MW P l a n t 28 MW
P~ = Rated power o f t h e s c a l e d p l a n t i n MW
. a = Cost o f b u i l d i n g s , v i a d u c t s , c o n t r o l sys tems , which is 6 assumed c o n s t a n t f o r all p l a n t s i z e s s t u d i e d = $3,497,610.
F u r t h e r , i n d e f i n i n g t e r m s of Equation ( 1 2 ) :
N i s t h e number of r o t o r s i n one p l a n t
t i s the l e n g t h of each t raclr u n i t . i n one p l a n t = T / N
T = t o t a l t r a c k pe r ime te r l e n g t h
KN i s t h e average c o s t of N r o t o r u n i t s expressed a s
a f r a c t i o n o f t h e c o s t o f t h e f i r s t u n i t and i s a
f u n c t i o n of a g iven l e a r n i n g curve (85 p e r c e n t i n
t h i s c a s e ) . KT i s t h e average c o s t of R t r a c k u n i t s expressed
as f r a c t i o n of t h e c o s t of t h e f i r s t u n i t and i s
a f u n c t i o n o f a given l e a r n i n g curve (90 p e r c e n t
1.n thj s c a s e ) . Equation ( 1 2 ) was used t o compute p l a n t m s c s
and energy c o s t s f o r 1 4 p l a n t s thought t o b e of t h e most i n t e r e s t
f o r t h i s s t u d y . P l a n t s cons ide red i n t h i s s tudy inc luded a l l
o f t h o s e i n Table 7 .5 , some of t h o s e i n Table 7.4, and
o t h e r s t h a t would be of i n t e r e s t i n comparing t h e e f f e c t o f r o t o r
spacing and i n comparing.performance of Madaras p lants . with
HA-WTG p l a n t s . Thes'e computations were made f o r t h e fol lowing
condi t ions :
e' .Number of P lants : 1, 2 , 3, 10, 100, 500
Learning Curves: ,85% f o r r o t o r s , 90% f o r t r a c k u n i t s .
Annual Cost: 16.'5% P l a n t Cost
Land Cost/Acre: 0, $500, $.1000,$1500, and .$3000/acre.
By adding t h e ' land c o s t t o t h e a u n i t c o s t
cons tan t , w e were ab.l:e t o .inc.lude t h e land purchase c o s t , as
described previous ly :in Paragraph 7.3.1.
The ' r e s u l t s of t h e l e a r n i n g curve computation
f o r a l l . , of t h e s e . p l a n t s a r e 'pres'ented. i n Tables. 7<.6 and Table 7 -7 ,
f o r p l a n t s s i t e d - a t . mean wind speeds of 8.1 m / s and 9.7 m / s ,
r e s p e c t i v e l y ,
A s was expected, t h e l e a r n i n g curve reduced
p l a n t and energy cos t s ' d ramat ica l . ly . I n a d d i t i o n , . t h e l e a r n i n g
curve e f f e c t caused a s h i f t i n t h e optimum,plant conf igura t ion
from 49-60 t o 44-60. A s can be seen, t h i s t r e n d was .p resen t f o r
a l l of t h e ,p lan t . s i z e s s tud ied , and i s n o t j u s t a p e c u l i a r i t y of
t h e l a r g e s t p l a n t . This s h i f t : i n opt imal conf igura t ion occurs
because t h e p l a n t s having khe smal ler r o t o r spacing r e q u i r e more
r o t o r s f a n d hence a r e a b l e t o c a p i t a l i z e more on t h e l e a r n i n g curve
c o s t reduct ion. This same t r end i s a l s o noted f o r t h e Medicine
Bow P l s n t ~ i n Table 7.7.
The r e s u l t s . from P l a n t 8a , t h e b e s t c i r c u l a r
p l a n t , s t i l l ind ica ted t h a t c i r c u l a r p l a n t s were n o t . c o s t
e f f e c t i v e , even f o r 500. .p lan t .product'ion l o t s s i t e d a t MBSL
regions ( t h e most favorable c o n d i t i o n ) . The lowest energy
c o s t ob ta inab le was 5.17 C/kW-hr, and minimum i n s t a l l e d p l a n t
c o s t w a s $1539/kW, which ' is completely beyond t h e area ul
economic i n t e r e s t . The low a.nnual energy ou tpu t , t h e high
e l e c t r i c a l l o s s e s , and small p l a n t s i z e combine t o cause poor
performance of c i r c u l a r p l a n t s .
EFFECT. OF LEARN.ING CURVE AND LAND COST' 'ON ENERGY COST FOR PLANTS 'SITED WHERE = ,8.1 m / s AT 9-m HEIGHT
(1) Net area purchased.
(2) Number of Track Units = Number of Rotor Units. Number shown corresponds to number of plants.
(3) Installed cost per plant. Does not include land cost.
(4) Based on 16.5% of Plant Cost = Annual Cost.
Cost
S/kW
923
632
444
755 5 1 5 .
359
722
492
342
873
776
725
596
417
713
6 34
592
485
3 37
681
' 605
565
4 6 3 921
3575
2519
1858
1539
NO. (': Rotor
Units
82
820
8200
146
1460
14600
170 .
1700
17000
91
182
273
910
9100
162
314
486
1620
16200
190
380
570
l?OO 19000 .
20
200
2000
10000
NO. Plants
'-
1
10
100
1
10
100
1
10
100
1
2
3
10
100
1
2
3
10
160.
1
2
3
10
100
1
10
,100
500
A,'~)
Acres
437
661
745
437
,660
748
213
Rotors - 85% LC; Track -90% LC .
~nnual . Output
106kw-hr
407
788
9 31
424
820
9 7'5
33
P,
Mh'
92.4
178.3
210.6
99.2
191.4
227.8
78.5
3000
3.50
2.41
1.71
2.85
1.96
1.37
2.73
1.88
1.32
3.42
3.05
2.85
2.35
1.66
2.79
1.48
2.32
1.90
1-'34
2.66
2.37
2.22
1.82
1.27
14.46
10.28
7.67
6.41
plant NO.
- 49-25
49-50
49-60
44-25
44-50
44-60
8a
1500
'3.48
2.39 ,
1.69
2.84
1.94
1.36
2.71
1.86
1 3 0
.3.39
3..02
2.82
2.33
' 1.63
2.77
2.46
2.30
1.89
1.32
2.64
2.35
2.20
.1.80,
1 2
14.30
10.01
7.5l
6.25
C Laid
0
3.45
2.37
1.66
2.82
1.92
1.34
2.69
1.84
1.28
3.37
3.00
2.80
2.30
1.61
2..75
2.44
2.28
1.87
1.30
2.62
2.33
2.18
1.78 1.24
14.13
9.95
7.35
6.09
kW-hr (4) Cost,
500
3.46
2.37
1.67
. . 2.82
1.93
'1.35
2.70
1.84
1.28
3.38
3.00
2.81
2.31
1.62
2.76
2.45
2.29
1.88
1.30
2.63
2.34 .
2.18
1.79
1.24
14.19
10.00
7.40
6.14
$/acre
1000
3.47
2.38
1.68
2.83
1.94
1.35
.2.71.
1.85
1.29
3.39
3.01
2.82
2.32.
1.63
2.76
2.46
2.29
1.88
1.31
2.64
2.34
2.19
, 1.80
1.29
14.24
'10.01
7.45
6.19
TABLE .7 ..7
EFFECT OF LEARNING CURVE AND LAND COST ON ENERGY COST FOR PLANTS SITED WHERE = 9.7 m/s AT 9-m HEIGHT
(MEDICINE BOW SEA LEVEL PLANTS)
(1) Net area purchased.
( 2 ) Number of Track Units = Number of Rotor Units. Number corresponds to number of plants.
(3) Installed cost per plant. Does not include land cost.
(4) Based on 16.58 of Plant Cust = AIIIIU&~ Cust.
(5) Does not include engineering design cost or contingencies; 3 year construction period.
Plant No. - 49-25M
49-50M
49-60M
I 44-25M
44-50M
44-60M
8 aM
-Unit Cost
$/kW
923
632
444
755
515
359
722
492
342
873
776
725
596
417
713
634
592
485
337
681
605
565
463
321
3575
2519
1858
1539
PR
MW
92.4
178.3
210.6
99.2
191.4
227.8
78.5
A
Rotors -85% LC; Track -90% LC
An
Acres
437
661
745
4 37
660
748
213
Annual Output
106kw-hr
483
934
1103
509
985
1170
3 8
0
2.91
2.00
1.40
2.38
1.62
1.13
2.27
1.55
1.08
2.81 2.50
2.33
1.92
1.34
2.29
2.03
1.89
1.56
1.08
2.19
1.94
1.81
1.49
1.03
12.06
8.50
6.27
5.19
No. (2) Plants
- 1
10
100
1
10
100
1
10
100
1
2
3
10
100
1
2
3
10
100
1
2
3
10
100
1
10
100
500
(4) (5)
$/Acre
1000
2.93
2.01
1.42
2.39
1.63
1.14
2.28
1.56
1.09
2.82
2.51
2.35
1.93
1.36
2.30
2.04
1.91
1.57
1.09
0
1.95
1.83
1.50
1.04
12.15
8.59
6.36
5.28
C/kW-hr
Land Cost,
500
2.92
2.00
1.41
2.38
1.63
1.14
2.28
1.56
1.08
2.81
2.50
2.34
1.92
1.35
2.29
2.04
1.90
1.56
1.08
2.1
1.95
1.82
1.49
1.04
12.11
8.54
6.31
5.24
No. (3' Rotors
Units
82
820
8200
146
1460
14600
170
1700
17000
91
182
273
910
9100
162
324
486
1620
16200
190 380
570
1900
19000
20
200
2000
10000
1500
2.94
2.02
1.42
2.39
1.64
1.15
2.29
1.57
1.09
2.83
2.52
2.35
1.94
1.36
2.30
2.05
1.91
1.57
1.10
2.20
1.96
1.83
1.50
1-05
12.20
8.63
6.41
5.33
3000
2.96
2.04
1.45
2.41
1.66
1.16
2.31
1.58
1.11
2.85
2.54
2.38
1.96
1.38
2.32
2.07
1.93
1.59
1.11
2.22
1.97
1.85
1.52
1.06
12.33
8.77
6.54
5.47
The 100.-plant data. are interesting, but whether
or not the 85 percent learning curve.'cost reduction could con-
tinue for as many as 17,OO.O to 19,000 units needs to be determined. In Reference 44, Lockheed estimated that.their minimum cost would
be reached at 10,.000 units. Theref0re;unti.l further analysis
can be conducted, the validity of the 100-plant cost figures
certainly should be considered with caution. We .do believe that
the cost. reduction shown for 1.0 plant lots is reasonable, and the
energy cost-of 1.78 to 1.82 C/kW-hr for ten of the 44-60 type
Madaras plants is certainly in the economic.range of interest.
The cost range of from 1.49 C/kW-hr to 1.52C/kW-hr for ten 44-60M
(MBSL) 2s even more attractive.
7.4 EFFECT OF NONOPTIMUM WIND DIRECTION
The most versatile form of a Madaras plant is one having
a circular track pattern because its performance is independent
of wind directions. However, we demdnstrated above that for
several reasons, this plant type is completely beyond economic
consideration,' even if 500 plant units were to be built. We
also indicated in Table 7.7.that large racetrack-type plants
appear to be economical~y attractive. Unfortunately, racetrack
plants have one important weakness: they must be located at
a site that has .essentially unidirectional wind (including the '---.
reciprocal direction) to perform at full potential.
To illustrate the sensitivity of a racetrack Madaras plant to nonoptimum wind direction., the following example is
given. To simplify the illustrations it was assumed that X
percent of the time during the year, the wind. will be blowing
at. a given nonoptimum angle .&f3 'measured from a perpendicular
to the straight track (Figure 7.8). For the remainder of the
year [(1-X) of a year's time]', the wind will be blowing normal
to the straiylit track, i . e . , at an angle p = O . Then, the total
amount of energy generated during the year, ET, would be:
PLANT 49 -60 ' .
S = 6 0 , 0 0 0 f t ( 1 8 , 3 0 0 m )
0 2 0 .40 60 .80 100 X = ,O/o NON OPT1 MUM WIND ANGLE PER YEAR
('BALANCE ASSUMED OPTIMUM ANGLE Figure 7 .8 . Effect of Nonoptimum Wind Duration on Cost of.
Madaras Racetrack Plant 49-60.
where X(E Bzo:. is the total energy generated during X percent
of' the year when the wind vector is .not normal
to the track at an angle 'Af3
(1-X) (El f3=oo is the total energy generated during the balance
of the year when =OO; i.e,, the wind vector is
normal to the track.
Then, since average annual energy cost is inversely proportional
to the total annual energy output,.energy costs then increase by a
factor, F, caused by partial off-optimum wind direction during a
year relative to energy cost.for wind direction during an entire
year is:
where. (El B=O is the annual energy output when B=OO for an entire year.
lltypical trends for this simplified case arc pre~ented
for B= 0°, f15", f30°, and f45O for Plant 49-60 in Figure 7.8. The extreme at X = 0 represents optimum plant operation, and
hence the cost increase factor would be 1.0 and the other
extreme at X = 10U'percent represents the condition in which
the wind would blow all year at an angle where Bf 0'.
The sensitivity to large deviatons o f the wind from the
optimum is quite evident from Figure 7.8. Sniall angular deviations
of the wind vector are probably acceptable, as are large deviations
for a small portion of a year (e.q., 20 percent of the year at
f3 = f45O would increase cost of energy by only 14 percent).
However, large deviations of B from the optimum can affect energy cost substantially. In fact, although not shown in Figure 7.8,
f o r p l a n t s having s t r a i g h t t r a c k s e c t i o n s a s l o n g a s P l a n t 49-60
(18,30,0 m) , i f , B beeomes' as l a r g e a s k60 O., and a s t h e time t h a t
t h i s wind direct ion. . i s main ta ined .approaches one 'year, t h e p l a n t
energy output w i l l <approach z e r o a n d t h e c o s t w i l l , o f course,
approach ' i n f i n i t y .
Another f a c t o r , n o t shown i n Figure 7,.8 is of i n t e r e s t :
a s t h e s t r a i g h t t r ack . ' l eng th , S , , decreases t h e p l a n t becomes less
s e n s i t i v e t o B ( t h e arigle B i n c r e a s e s f o r a g i v e n value o f F and
X ) . A s a n % example, i f S i s decreased from 18,300 m t o 6100 m, t h e value of B f o r F = ,1.55, X = 100 would be l a r g e r t h a n +30°.
Thus,. i f a racetrack. 'Madaras p l a n t i s considered ' for a l o c a t i o n
a t which small v a r i a t i o n s i n w i n d d i r e c t i o n occur , an optimum
p l a n t . s i z e would be .'sma.l.ler than t h a t o f Plant 49-60, and t h e
energy c o s t .would .be . 'higher.
The example p l o t t e d i n F igure 7.8 i s an example of t h e
average annual energy cos t . i nc rease f a c t o r u t i l i z i n g only two
wind d i r e c t i o n s . The energy c o s t f a c t o r o r t h e t o t a l energy f o r
a n a c t u a l s i t e 'can be 'obtained by a double i n t e g r a t i o n over wind
d i r e c t i o n and speed. Because o f t h e s e n s i t i v i t y o f t h i s type
of p l a n t t o both wind d i r e c t i o n and speed, it w i l l be necessary
f o r one t o c o n d u c t - a s i t e . w i n d s u r v e y us ing . ins t ruments which
:provide d e t a i l e d annual w i n d d i r e c t o n d a t a a t . t h e s i te i n incre-
ments much.'more 'prec'ise than those obta ined from usual weather
s t a t i o n s . V a l u e g o f B i n increments of t5O would be appropr ia t e .
Fortunate1y;there 'are a number.of e s s e n t i a l l y uni-
d i r ec t iona l wind s i t e s ' - in t h e United ' s t a t e s t h a t . a r e s u i t a b l e
f o r a . Madaras r ace t rack 'p lant . The caution. we want t o o f f e r h e r e
Is t h a t one must sekec t ,and survey t h e s i te with 'care t o a s su re
t h a t t h e ' p l a n t . - i s opt.imally o r i e n t e d and s i z e d ,
7.5 COMPARISON OF MADARAS PLANTS W I T H HORIZONTAL AXIS WIND TURBINE GENERATOR (HA-WTG) PLANTS
The purgfose o f t h i s por t ion of t h e r e p o r t is t o compare
t h e c o s t and perfo'mance ' c h a r a c t e r i s t i c s o f t h e Madaras concept
and conventional HA-WTG plants in .order to determine whether.or
not the Madaras concept shows promise 'of producing energy at
lower cost than that 'from HA-WTG plants..
Since 'our-Madaras cost estimates ,include 'provisions for
interconnecting the' output of a number of rotors.into. a complete
plant as well as provisions for roads, utilities, buildings and
other plant facilities, it is not meaningful to compare Madaras
plant performance with that of a .single HA-WTG, or with a
number of isolated HA-WTG1s required to provide'an amount of
power equal to that o f a .Madaras plant.
Mr. S , T - Hj.ght.ow~r and .A.W. Watts 09 the E U ~ P A U of Reclamation, U.S. Department of the Interior, Denver, Colorado,
have developed a design for a 49-unit array of MOD-1 HA-WTG1s to be installed next to s hydroelectric facility in Medicine
Bow, Wyoming. 4 5 We selected this plant for comparison with the
Madaras plant for several reasons:
A complete plant design has been conducted, which included all components of a complete wind-powered .electrical power plant.
Up-rated, MOD-1 WTG1s proposed for the plant, have had the benefit of considerable design and production study, and henee are representative of soon-to-be available large HA-WTG1s.
Medicine.Bowls geographic and unidirectional wind characteristics are ideal for Madaras plants.
Our comparison of Madaras and HA-WTG plants is divided
into two parts: (1) Medicine Bow siting (B = 9.7 m/s at 9 m
height, an air density.ratio of 0.81 corresponding to the 7000 ft
(2134 m) height of the 'Medicine Bow plant site above sea level),
and Federal financing; and (2) siting at a location having mean
wind speeds of 8.1.m/s.at 9 m height, sea level air density,
and private financing. Since the cost info,rmation for the
Medicine Bow HA-WTG plant is readily available, it will be used
as a basis for comparison for both conditions studied.
The primary ground rules for the comparison are as
follows :
Cost estimates represent cost at the plant boundary. No substation or transmission line costs .are included.
Costs based on 1978 dollars.
Five-year construction period, with construction interest at 7 percent.
Thirty-year plant life.
Land cost at Medicine Bow is $200/acre~~ and at other sites, land cost was assumed to be $3000/acre.
Only that land required for the operation of the plant. will be purchased. Thus, for Madaras plants the net land area,An (Reference Figure 7.1) would be purchased, and for the HA- WTG plant a -457-m diameter circle of land would be purchased, This size was recommended by Hightower in a telephone conversation.
Capital fixed charge rate equal to 8.41 percent (excluding O&M) in accordance with Federal financing procedures46 for.!:.., Medicine Bow plants. Fixed charges of 15 percent will be used for plants privately financed in accordance with a personal communication with the Economic Planning section of the Detroit rEdison Company.
Construction and-0 and M costs in accordance with methods deemed most appropriate for each system.
Identical learning curve equations are used for both systems.
.. . 7.5.1 Medicine Bow P.lant Comparison
The WTG array planned for the Bureau's HA-WTG site
consists 01 Lkiee 'parallel', ataggesed rows having- 16, '17, and 16 turbines in each 'row, respectively. The turbines .are spaced in
an equilateral triangular array, with'the sides of the triangle
being.15 rotor diameters long (920 m), as recommended'by the
General Electric Company.
Each row of turbines is spaced about 795 m apart.
Thus, the overall plant layout is about 14,700 m long (North-South
perpendicular to the prevailing West wind) and about 1590 m wide.
A total of 49, up-rated, 2 MW, MOD-1 HA-WTG's are proposed. A
plant capacity of 98,000 kW and an annual output of 409.6 kW-hr
per year are predicted for this plant. Hightower and Watts also
contemplated a second (and even a . t h i r d ) p l a n t of t h e same s i z e t o
be i n s t a l l e d later should t h e need arise. .We bave ' se lec ted 'two - HA-WTG p l a n t s . f o r t h i s s tudy. One 'having 49 HA-WTG1s and one
having 98 HA-WTG1s. The Madaras p l a n t s most nea r ly comparab.le t o
t h e s e convent ional p . lants are i temized below.
-Madaras P l a n t HA-WTG P l a n t
44-25M 49 WTG 99,180 kW Rated 98,000 kW Rated
44-50M 191,430 kW Rated
98 WTG 196,000 kW Rated.
I n a d d i t i o n t h e performance'of t h e l a r g e s t . . Madaras . . p l a n t . s t u d i e d
(4.4-60~): w i l l be i temized f o r r e fe rence .purposes.
.The Madaras c o s t e s t ima tes developed i n Paragraph
7.3.2 were 're-combined i n . o r d e r t o . ' f a c i l i t a t e - a s nea r ly a s
p o s s i b l e t h e l ine-by-l ine comparison with t h e Bureau of R e c l a m a -
t i o n p l a n t s . F u r t h e r , t h e s e e s t ima tes were ad jus ted t o meet t h e
s tudy g round . ru les ' and t h e c r i t e r i a s p e c i f i e d by Hightower. The
methods used . f o r both 'p lant types .are presented i n Table 7.8
where t h e c o s t breakdown f o r Madaras Plant-48-25M and t h e 49-
r o t o r Bureau o f Reclamation p l a n t are compared-. The csit.eria f o r computing ..the var ious l i n e i tems. f o r ' t h e HA-WTG p l a ~ r t a r e
. l i s t e d . where .'known. The .bases f o r t h e Madaras c o s t . e s t i m a t e s . a r e
i n accordance w2th ' t he information presented in .Pa ragraph 7.1,
7,2, and 7 .3 a s w & l as t h e d e t a i l e d c o s t breakdown presented
i n Appendix B.
A l l c o s t s f o r t h e HA-WTG p l a n t s w e r e obtained
from Reference 4.5. and from f u r t h e r c l a r i f i c a t i o n provided by
Hightower. S ince h i s . e s t i n a t e s w e r e made ' i n 1977, a l l HA-WTG
c o s t s w e r e increased by 7.5 percent t o r e f l e c t . . t h e i n f l a t i o n
dur ing t h e l a s t year . .Th i s i n f l a t i o n r a t e w a s recommended
by t h e D e t r o i t Edison Company.
TABLE 7.8
INSTALLED COST BREAKDOhx OF MADARAS PLANT 44-'25M AND 98,000 kW BUREAU OF RECLAMATION
(1) Based on cost of $1410.94/ kW for the first production unit.
(2) Overall Madaras plant dimensions are 9213 m long by 1468 m wide: BofR plant dimensions are 14,700 m long by 1590 m wide.
: PLANT PROPOSED FOR MEDICINE BOW, WYOMING BUREAU OF RECLAMATION -T (98.000 kWl
I n
49 ea %TG = 55.~2'~)
N/A
6.85
15% WTG = 8.33 15% E1ec.Conn.a 1.02
9.35
Not Broken Out Included Above
15% WTG = 8.33 30% Elect .Conn= 30% (6.85+1.02)==
10.70
1988 acres 0.40 (2)
0.16
14.42
$97.40 - 98,000 kW
$994/kW
ITEM
1. ROTORS: 91 ea (85% Learning Curve)
2. TRACK: 91 ea, 707 ft long units. (90% learning curve)
*
3. ELECTRICAL CONYECTION Trolleys, P3wer Collection
. Power Conditioning, Switchin< Control Systems
e' Instrumentation TOTAL'
4.. SITE FACILITIES AND CONTINGENCIES
a. Facilities Utilities and Roads
e Buildings and Viaducts e Site Preparation
TOTAL b. Contingencies
1 Spare Rotor Car General Contingencies TOTAL 110% of all Costs Above1
5. DESIGN, MANAG3MENT , ENGINEERING, OVERHEAD (22.7% Mechanical, 19..1% Construction, 2.5% Direct Costs for Design)
6. LAND COST
7. ALLOWANCE FOF. FUNrXS USED FOR LAND DURING C:ONSTKUCTION (AFUDC) (7% Compounded over 5 years)
8. CONSTRUCTION INTEREST (1/2 E Items 1,2,3,4,5) x 7% x 5 years)
9. TOTAL PLANT COST
10. RATED CAPACITY
1.1 . INSTALLED CCST
MADARAS 44-251 -.(99,180 kW) . 106 Dollars (1978)
21.27 '
26.48
6.63 0.44 0.29 0.25
7.61
6.24 2.37 1.38 -
9.99
0.18 6.55 - 6.73
14 -87
4 3 7 Acres 0 -09
0.03
14.67
$101.74
99,180 kW
$1026/k~
The costs associated with the Madaras plant in
Table 7.8 were 'c'omputed in accordance with 'th@ 'data. in Table 7.1
and .aquation 12. However, ,since 'Hightower's cost breakdown e.lements
were different from those in Table 7.1, ,some of the 'Madaras cost
elements had to be subdivided in order to be directly comparable
with Hightower's cost elements. Although Table '7.8 is fairly
self-explanatory, some,'additional comments are in order. These will
be presented in an item by item basis.
'I'tem 1 - This item represents the direct cost of 91 rotors. From Table '7.1 the direct cost of 28 rotors is $18,850,420,
and the direct cost per rotor is $673,229. Thus, t.he cost of 91
rotors Lased on an 85 percent learning curve is: 91 x 673,229 x 6 0.34727 = $21.27 x 10 , w t ~ r r e KN = 0 . 3 4 7 2 7 . The 22.7 peracnt
indirect costs were included in Item 5 in Table 7.8, and construction
interest was computed in accordance with methods used by Hightower.
Items 2' and 3 - he Madaras plant cost breakdown combined costs of track, roads, utilities, and instrumentation into
one cost element because these were all associated with track
length. However, for the HA-WTG plant, track was not necessary,
and Hightower presented electrical connection and roads and utilities
in separate cost elements.
Thus, the cost for utilities, track, and trolleys
for the Madaras system from Table 7.1 and Equation 12 would normally
,be:
However, since only direct costs are to be compared
at this point, a3 from Table 7-1 was redefined ac:
Thus, since the number of track units equals the number. of
rotor cars (91), and since t equals 707 ft and Kt for a 90 percent
learning curve equals 0.50376 for 91 units, the cost. of utilities, 6 track, and trolleys would be (a3)d NtKt = $39.6 x 10 .
In order to develop cost elements comparable to
those of Hightower, this cost of .utilities,. track,' ,and trolleys
was broken down further as .follows.:
PLANT' 4 4 -2'5M
Element '% of To't'al ' 10 6 Dolla'rs
a. Track 66.87 26.48
b. Trolleys and Power Collec'tion 16.74 6.63
c. Instrumentation 0.63 0.25
d. Utilities and Roads '15.76 6'. 24
TOTAL 100..00 $39.60 x
The percentage of each element in the above table
was computed from the direct cost breakdown data in Appendix B,
Section B.1, item D. Then, these 'percentages. were used to compute
the dollar value of each 'of the above elements for each plant size.
The above example is .for Plant 44-25M. In Table 7.8, Element a is' - entered in Item 2, Elements' b and c are included in Item,3, and - - Element d is iccluded under Item 4. -
The remaining elements of Item 3 in Table 7.6
were obtained in the following manner.
Power conditioning and switching cost - this was computed as shown in Equation 12 except that is used instead of a5 in order to obtain only the direct cost per MW of power conditioning and switching equipment. The value (a ) was obtained from Appendix B, Section B.1, Item F. ~hzs! - 529f000 + 96f000 = $4464,~ - 28 14W
Since PR = 99.18 MW for Plant 44-25Mf then the cost of this conditioning and switching equipment would be $0.44 x lo6 as shown in Table 7.8. As before, the indirect cost and construction interest costs are included in items 5 and 8, respectively.
Control Systems- This direct cost is of computer control equipment, a line 'item in Appendix B, Section B.1, Item F and is equal .to $0.29 x 106 as shown' in Table 7,6.
'Item .4 - Site facilities .and contingencies were included as one item in the 'Bureau of Rec'lamati-on study. These
were estimated as a fixed percentage of WTG cost and electrical
connection cost. The ?4adaras estimate for site facilites comes
directly from our basic cost estimating procedure, and as a
contingency, one complete, spare rotor car had been planned at
the outset. In addition; we added a general contingency value of
approximately 10 percent.of all direct costs excluding land. Thus,
a total contingency of $6.73 million has been provided for Madaras
plants in the interest of realism and asnservathsm, Thus, a total
amount of $16.72 million has been proposed for' site facilities
and contingencies of the Madaras plant, which we believe is a
reasonable and conservative number to use in comparing the two
plant types. One should recognize that the Madaras plant, while
more complex., encompasses a smaller land area than the Bureau of
Reclamation plant. Thus, the cost of electrical connection of WTG
.units dispersed in three 14,700-m-long rows would probably exceed
similar costs of the Madaras system.
Item-5 - Management, field engineering and overhead was provided for in our basic cost estimate. However, since
Hightower indicated his study included plant design layout, an
amount of about 2.5 percent of direct construction and mechanical
costs was added to our estimate to cover this expense in accordance
with recomendatiollsfrom our cost estimating consultant.
Item - ---- 6 - Land cost based on Medicine Bow estimates by Hightower were used for'both plants. ~ h e estimate of 1988 acres
for the WTG was derived from Hightower's recommendation stated
in the ground rules. Thus, only that .land indicated in Iteni 5
would be purchased; the balance would be used for agriculture.
A pri,mary advantage of the 'Madaras system in this case 'is that the
unused area (..the "infield" of a racetrack) would provide the owner
with a 2904-acre, unobstructed area.of land (about 87 percent of
the original amount) which could.be efficiently farmed. By way of
contrast, not only does the HA-WTG plant require more land, but
only 66 percent of the involved area would be .available from a
"park "44 of distributed HA-WTG's, and this land would be broken
and criss-crossed by roads.
.Item 7 - Allowance for Funds Used During Construction (AFUDC) - this item was computed in accordance with Hightower '.s .analysis : The land would be. purchased outright,
and thus the -funds would ' be .unavailable to earn int&rest during.
the five-year construction. period. ~hus, a.compound interest
charge at 7 percent per year was charged. The Det.roit Edison
Company agreed .that this .rate. was reasonable.
Item 8 - Construction Interest - this item also was computed in accordance with Hightower's approach. It was
assumed that during.construction funds would be committed
gradually, and that the effect would be simple interest. at 7
percent on half the total plant cost (excluding land, which was
covered in Item .7) over the five year construction period.
The remainder of Table 7.8 is self explanatory.
.The cost of the two plants is nearly .the. same, with the Madaras
plant cost being about 4.4. percent higher, and the cost/k~. being
about 3.2 percent higher-.:. One also will note that low cost land
at $200/acre has negligible impact on plant cost. . .
The method. used for computing annual costs for .
each type of plant based on. Federal financing -rates is shown in
Table 7.9. This procedure'proposed by Hightower and Watts for
the Medicine Bow area, is fh accordance with 'eaonomic analyses 4 6 used in ~overnment.: hydroe.lec':tric ' projects.
The annual charges were divided into three areas:
(1) capital recovery on land investment; (2) annual fixed charges;
and (3) operation and maintenance costs. '
The capital recovery on land investment is simply
a levelized annual charge based on 7 percent .c.ompound.:..interest
over'a 30 year plant'life. .This chaxge is based not only on the
land cost but 'also on .the charge for loss .in' interest on'the money
tied up in land pi~rchir,se during construction (AFUDC - Item 7, Table '7 -8) .
251
TABLE 7.9'
. . ANNUAL COST BREAKDCWN:OF MADARAS PLANT 44-25M AND 98,000 kW BUREAU OF RECLAMATION
HA-WG PLANT PROPOSED FOR MEDICINE BOW, WYOMING
*Medicirae Bow Wind Dura t ion Curve and A i r Dens i ty R a t i o o f 0.81, S tandard Atmosphere.
BUREAU OF RECLAMATION HA-WTG PLANT
(98,000 kW) l o 6 D o l l a r s 1978
Same C r i t e r i a
0.05
Same C r i t e r i a
8.14
O&M BASE WTG Cos t @ Cos t o f 100 th Uni t Based on 85% Learn ing Curve 36.00 E l e c t r i c a l Connect i o n s 6.85 Land Cos t 0.40 S i t e F a c i l i t i e s
15%x36 -00 (WTG) 5.40 1 5 % ~ 6.85 (E lec . Conn . ) 1 .03
TOTAL BASE 49.68 2% o f 06M Base 0 -99
9.18 -
6 409 -6 x 10 kW-hr/yr
0 -48
22 -4 Milis/kW-hr
ITEM
1. CAPITAL RECOVERY ON LAND ZNVESFMEm 7 PERCENT COMPOUND INTIREST, IEVEL PAYMENT OVEP. 30 YEARS
2. ANNUAL FIXEI: CHARGES, FEDERAL FINANCING.
3 . OPERATION AND MAINTENAECE
4 . TOTAL ANNUAL COST
5. PERFORMANCE .9ND ENERGY COST
Annual Energy Yie ld
P l a n t F a c t o r
a Energy C o s t
MADXRAS PLANT 44-25M (99,180 kW)
10' D o l l a r s (1978)
CR = 0.0806 (0.087+0.035)= 0 .01 ( I n c l u d e s l a n d c o s t + AFUDC cost i n c u r r e d d u r i n g 5-year con- s t r u c t i o n p e r i o d ) .
I n t e r e s t Rats 7 .00% Deprec ia t ion (S ink ing Fund) 1 -06%
0.35% I n t e r i m Replacement 8.41%
8.41% ( P l a n t Cos t Less Land Cost) 8.55
OhCI BASE D i r e c t Cos t s ( I t e m s 1, 2,3 ,4a , Table 7.8) 65.35 Cont ingenc ies 6.73 Engineer ing and Overhead 14.07
e. Land Cos t 0.09
TOTAL BASE 87.04
2% o f 06M Base 1 .74
10.30
6 412.0 x 10 kW-hr/yr
0.47
25 .Dmills/kW-hr -
The annual f ixed charge and i t s components i s
descr ibed f u l l y i n Table 7.9, and it is app l i ed t o t o t a l p l a n t
c o s t l e s s land.
The b a s i s used by Hightower and Watts f o r com-
pu t ing O&M i s shown i n Table 7.9. They assumed t h a t O&M c o s t s
would be based on a l l 49 WTG's having a u n i t . c o s t equal t o t h e
100th i t e m us ing an 85 percent l e a r n i n g curve. They a l s o in-
cluded land c o s t , e l e c t r i c a l connections, and s i te f a c i l i t i e s
( a l s o reduced from Table 7.8 values due t o t h e reduct ion i n WTG
c o s t ) . Thei r e s t ima te t h a t O&M c o s t s should be 2 percent of WTG
c o s t s was .obtained from General E l e c t r i c , and f o r conservatism,
O&M c o s t s should a l s o inc lude 2 percent of t h e o t h e r i t e m s . l i s t e d ,
Our previous e s t ima tes ind ica ted t h a t t h i , s approach
t o developing t h e b a s e f o r O&M would n o t be meaningful f o r t h e
Madaras system. Ins tead , we assumed t h a t al .1 d i r e c t , i n d i r e c t , .
a n d . l a n d c o s t s ( l e s s i n t e r e s t ) were appropr ia t e f o r an O&M base l
Fur ther , t o account f o r unforeseen c o s t s , t h e $6.73 m i l l i o n
contingency amount was included i n t h e ' b a s e . We a l s o used a 2
percent f a c t o r f o r O&M r e l a t i v e t o . t h i s base , i n accordance wi th
our b a s i c c o s t s tudy r e s u l t s . We b e l i e v e t h i s approach is proper ,
and c e r t a i n l y c o r r e c t . r e l a t i v e t o t h e HA-WTG, which should n o t
r e q u i r e a s l a r g e an annual expenditure f o r O&M a s t h e Madaras
s y s tem..
The 'computation of t h e performance and energy c o s t
completes Table 7.9, Here, . the a c t u a l a i r d e n s i t y r a t i o of 0.81,
corresponding t o . a n a l t i t u d e of 7000 f t (2134 m) above sea l e v e l ,
was used t o compute t h e annual ou tpu t and p l a n t f a c t o r of both
types of p l a n t s . Thus, t h e performance r e s u l t s i n Table 7.9
r ep resen t t h e combined e f f e c t s of t h e Medicine Bow wind dura t ion
curve .and a i r d e n s i t y r a t i o , whereas r e s u l t s i n Table 7.7 r e f l e c t
t h e e f f e c t of t h e Medicine Bow wind dura t ion curve alone. Since
t h e annual c o s t of Nadaras P l a n t 44-25M a r e about 1 2 percent
h igher and the annual y i e l d is only s l i g h t l y h igher (0.6 percent )
than those of t h e HA-WTG p l a n t , t h e 25.0 mill/kW-hr energy c o s t
p r e d i c t e d f o r P l a n t 44-25M i s about 1 2 percent h igher than t h a t
o f t h e HA-WTG plant . : I n v i e w o f t h i s small d i f f e r e n c e i n energy
cos t d i f f e r e n c e and t h e 'uncer ta in t ies ' . i nvo lved ' in p r e d i c t i n g t h e
c o s t and performance 'of both ' the Madaras .and t h e HA-WTG systems
w e b l i e v e t h a t : th=s 'e r e s u l t s do not ' neces ' sar i ly i n d i c a t e
s u p e r i o r i t y .of one system over t h e o t h e r .
The d a t a f o r t h e comparison of t h e t h r e e ~ a d a ' r a s
and two HA-WTG p l a n t s previous ly m e n t i 0 n e d . i ~ presented i n
Table 7.10. Data p e r t a i n i n g t o p l a n t geometry, performance,
and i n s t a l l e d cost , annual c o s t , and gnergy a o g t are presented.
The t a b l e i s . d i v i d e d i n t o t h r e e p a r t s : (1) p l a n t I D numbers 1 t o
3 which p e r t a i n t o Medicine Bow p l a n t s ; ( 2 ) p l a n t I D numbers 4
t o 6 which p e r t a i n t o t h e same p l a n t s designed for Medinine BOW
b u t s i t u a t e d a t sites where = 8.1 m / s ; and ( 3 ) p l a n t I D numbers
7 and 7a which are t h e same a s P l a n t s 5 and 5a b u t do no t inc lude
l a n d c o s t i n , t h e i r c o s t a n a l y s i s . The f i r s t p a r t of Table 7.10
w i l l be d i scussed here . The o t h e r p a r t s w i l l be d iscussed i n
Paragraph 7.5.2.
I n Table 7.10 a l l p l a n t s having only a numerical
I D number a r e Madaras ,p lants , and those with t h e l e t t e r - a s u f f i x
a r e HA-WTG p l a n t s . P l a n t s t o be comapred d i r e c t l y have t h e
same numerical pa r t of t h e I D number. Thus, P l a n t 1 and 1 a
are t o be c3mpared, etc.
The 'methods u s e d . t o compute t h e c o s t and energy
c o s t o f a l l of t h e s e p l a n t s w e r e ' i d e n t i c a l t o those descr ibed
i n Tables 7.8 and 7;9. We a l ready have compared P l a n t s 1 and l a
( t h o s e h r v i ~ i y PR = 98 Ni) and iioted t h a t t h e Madaras p l a n t energy
c o s t was numexically about 1 2 ' p e r c e n t hi:gher than those of t h e
HA-WTG p l a n t having 49 wind t u r b i n e s a t Medicine Bow, Wyoming.
P l a n t s 2 and 2a a r e twice t h e s i z e a s P l a n t s 1 and
l a , with. t h e r a t e d capac i ty o f P l a n t 2a be ing about 2 percent
l a r g e r than P l a n t 2. Because 'of. economy of scale, both p l a n t s
provided energy a t reduced c o s t over P l a n t s 1 and l a ; however,
t h e Madaras P l a n t 2 energy c o s t of 20.5 mills/kW-hr i s only 4
pe rcen t h i g h e r ' t h a n HA-WTG P l a n t 2a. Thus, as t h e s i z e of t h e
TABLE 7.10
OVERALL COMPARISON OF. SEVERAL MADARAS AND HA-WTG PLANTS A T TWO WIND REGIONS
PLANT GEOMETRY PERPORMANCE PLANT TRACK NVneER ROTO (71 ID PLANT PLANT PLANT PLANT NET AREA PERI- ROTORS/ WFG $1 I @ RATED ANNUAL PLANT "R NO. DESIGNATION LENGTH WIDTH AREA PURCHASED METER WTG SPACING 9 m CAPACITY OUTPUT PAClVR @ 9 m
m I m l Acre I Acre m I - I m W s I n~ )10bkw-hr - I m/s . .
1 Wl'G spaced in three rows, Scaggered, equllatrral triangular array at 15 rotor diameter (d = 61 ml (2)' Continqencies in HA-WG plant inched in site and facilities figure. (31 Includes allowance for funds used during construction, due to outright purchase of land. (41 The suffix letter. 1 refers to Medicine Bow plants? all others for wind duration curve = 8.1 Ms. (51 Continqencies for HA-WTG plants are included in the electrical connection cost. (61 Pixed charges for Medicine Bow plants based on Federal financing at fixed charge of 8.41 percent. A11
others, fixed charge = 15 percent. (7). Based on air density ratio of 0.81-7000 ft(2134ml above msl.
"a
ii - w . c m a
O d
I> 2
@
@
44-50 191.43 No Land Cost
HA-WTG 196.0MW NO Land Cost
16,863
14,700
1468
3975
61i5
'14,457
660
3976
34,910
N/A
162
98
215
920
8.1
8.1
191.43
196.0
819.5
725.2
0.49
0.42
13.4
li.2
p l a n t doubled, , t h e energy c o s t advantage of t h e HA-WTG p l a n t
dropped from 1 2 pe rcen t t o 4 percent . One a l s o can see t h a t a s
t h e Madaras p l a n t s i z e i n c r e a s e s f u r t h e r t o 227.77 MW ( P l a n t I D 3 ) ,
t h e energy c o s t d e c r e a s e s t o 19.6 mills/kW-hr. Since no l i m i t a t i o n
i , n Madaras plant' s i z e 'has been found, f u r t h e r reduct ion i n energy
c o s t seems p o s s i b l e . i
Thus it appears from t h i s comparison t h a t
Madaras p l a n t s show promise o f producing energy a t a c o s t nea r ly
equa l t o and poss ib ly lower than comparable HA-WTG p l a n t s .
The reasons for t h e promise of better economy
of t h e M a d a r a s . p l a n t s . a r e t h e i r non l inea r improvement o f annual
energy y i e l d wi th s i z e , t h e i r b e t t e r a b i l i t y t o b e n e f i t from
cost reduc t ion through..mass .production, and t h e i r requirement
f o r less l a n d f o r a given r a t e d . p l a n t capac i ty .
Madaras p l a n t s having race t rack p l a n t l ayou t s
i n c r e a s e i n performance and economy non l inea r ly a s t h e length
o f t h e s t r a i g h t s e c t i o n inc reases . This t r e n d i s shown i n
F igure 7.5. A s t h e l eng th 'of t h e s t r a i g h t t r a c k i n c r e a s e s ,
t h e l o s s e s a t . the c i r c u l a r ends.become a smaller. and smal ler p a r t
o f t h e average power .per r o t o r pe r o rb i t ; and p l a n t power inc reases
n o n l i n e a r l y as shown i n . the fol lowing equat ion:
where
N i s t h e 'number o f r o t o r s
p1 i s t h e n e t power ou tpu t o f a s i n g l e r o t o r a t a given wind and t r a c k speed,
C l.s the mutual interfsr-encsr faclor-. n
The t e r m pl i n c r e a s e s t o a maximum a s t h e length of s t r a i g h t
t r a c k approache$ i n f i n i t y . I f c a r spacing is kept cons tan t ,
t h e n f n does n o t change, and P is then a funct ion of N and
P1' Thus, as t h e , s t r a i g h t t r a c k l eng th inc reases a t i n t e r v a l s .
which 'permi t t h e a d d i t i o n o f c a r s w i t h o u t a f f e c t i n g f n , no t
only w i l l t h e power inc rease bec'ause of t h e i n c r e a s e i n N, b u t
a l s o t h e power p e r c a r , P1, w i l l increase. ' These two i n c r e a s e s
then w i l l combi'ne.to inc rease n o t only r a t e d power, b u t a l s o
annual energy output . Comparison o f P l a n t s 1 and 2. demonstrates
t h i s e f f e c t w e l l . Although t h e s t r a i g h t t r a c k l e n g t h ' o f P l a n t 2
is twice t h a t of. p l a n t 1, t h e t r a c k perimeter . and number of c a r s
of P l a n t 2 a re . 78 percent g r e a t e r than those of P l a n t 1; however,
r a t e d capac i ty and annual energy ou tpu t of P l a n t 2 a r e 93 percent
g r e a t e r than t h e i r counte.rpar ts i n , P l a n t 1. Obviously, t h i s
e f f e c t decreases as t r a c k inc reases . On t h e o t h e r hand, HA-WTG
p l a n t ou tpu t i s s t r i c t l y l i n e a r wi th number of r o t o r s (provided
they a r e n o t spaced t o o c l o s e l y t o g e t h e r ) , and t h e HA-WTG p l a n t
capac i ty and e n e r g y o u t p u t cannot b e n e f i t irom economy of s c a l e
from t h e performance s t andpo in t as can t h e Madaras p l a n t .
One o f . t h e major reasons f o r . t h e ' c o s t improve-
ment o f t h e Madaras p l a n t s over t h a t of t h e HA-WTG p l a n t s was
t h e c o s t decrease ' res 'u l t ing from a p p l i c a t i o n of l e a r n i n g curves.
Although f o r t h e s e c o s t s t u d i e s , only one p l a n t o f each type
was planned, t h e '1arges't.number' of Madaras r o t o r s ( 9 1 i n P l a n t
1 compared t o 49 W T G 1 s .iri Plan t l a ) enabled t h e l e a r n i n g curve
t o work more toward . t h e b e n e f i t of t h e Madaras p l a n t . W e b e l i e v e
t h a t t h i s l e a r n i n g curve ' cos t improvement i s v a l i d f o r t h e
number of u n i t s p r o p o s e d . f o r . t h i s s tudy, and probably could
improve much more i f a major assembly l i n e could be e s t a b l i s h e d
t o b u i l d r o t o r c a r s f 0 r . a number of p lan t s . However-,. t h e e x t e n t
t o which such improvement could cont inue w i l l . r e q u i r e f u r t h e r
s tudy a s w e l l a s t h e l o c a t i o n of a s u f f i c i e n t number o f
acceptable sites. f o r b u i l d i n g a number o f Madaras p l a n t s . However,
i f many more HA-WTG p l a n t s than Madaras p l a n t s a r e ordered,
a r e v e r s a l of t h e . t rend . could occur.
The f i n a l economic advantage of a Madaras p l a n t
over an HA-WTG plant. i s t h a t a Madaras p l a n t uses less land pe r
MW o f r a t e d p l a n t capac i ty , and t h e Madaras p l a n t land use is
more e f f i c i e n t and conducive t o c o e x i s t i n g opera t ions wi th
a g r i c u l t u r e (.and even indus t ry and/or.co-rce). This f e a t u r e
was mentioned before ; however, us ing d a t a from Table 7.10 t h e
comparative va lues of acre/MW a r e shown i n Table 7.11.
TABLE 7.11
MADARAS VERSUS HA-WTG LAND USAGE EFFECTIVENESS
Thus, not only does this data indicate the Madaras plant
is less land intensive, the-data show again how economy of scale
improves .for Madaras plants but not for HA-WTG plants. Table
.7:-11. shows another interesting compari.son of land. uee effective-
ness. Note that ~ia.nh '3. can proauce 2.32 times the power
of Plant la on .only 37.6 percent of the land purchased for
Plant la. However, at Medicine Bow,, where .the,land is very
inexpensive, the land cost is only about 0.6 percent of Plant la
cost, and hence has neqliqible effect on enerqy cost at Medicine
Bow.
7.5.2 Comparison of Plants at Sites Having-Me.9-n Wind Duration Curves of 8.1 m/s at 9-m Height
,
RATED MW
99 -18
98 .OO
191.43
196 -00
227.77
PLANT ID
1
la
2
2a
3
The basic ground rules for this program required
the use of a wind duration curve having = 8.1 m/s at a 9-m height
' to predict Madaras plant performance. Thi-s.was.done in section 6
and.7, and here we want to compare , , Madaras and HA-WTG pl'ants at
these sites. In addition, since the Medicine Bow study was
based on use of Federal ,financing and inexpensive. land, it was
decided to determine 'the 'effect of using 15 percent annual fixed
charges as rec0mmended.b~ the.Detroit Edison Company and price the land at $3000 per acre.. Finally, .sea level air density was used.
. .
With these. changes, it was believed that results
would apply to a wider. ..range of' sites. The results of.this study
are.'presented in the second part of Table 7.10 (I.D Numbers 4 to 6).
NET ACRE/MW
4.41
20.29
3.45
20.29
3.28
.LAND PURCHASED NET .ACRES
437
1988
660
3976
748
all cost analysis procedures were the same as before; however,
only the different.values based on the new criteria are presented
in Table 7.10. Note that it.was assumed O&M costs wouldbe the
same as at Medicine 'Bow, and that the '15'percent fixed charge
was charged. against the total plant cost.Further, annual output
for the WTG's was obtained direct1.y from the General Electric
paper on the 2000 kW MOD-1 WTG presented at the Third Wind Energy 43 Workshop,
In Reference 43, ~enerdl Electric predicted
annual.energy output from the MOD-1 HA-WTG would be 7.4 x 10 6
kW-hr/year for, each unit, assuming 90 percentWTG availability. 6 Thus ,: annual .output for' a .49 ' ,unit plant 'would be 362..6 x 10' kW-hr .
The larger percentage. difference between annual
energy. output. of Plants.' 4 over -4a (16.9 percent). compared to that
of Plant 1 over..Plant la (0.6 percent).. is mos.tly due to the 90
percent availability (I0 percent derating),,specified by ~enerai
Electric for their MOD-1 in the = .8.l m/s region. Hightower
and Watts assumed 100 percent availab.ility in their Medicine
Bow study, and 100.percent.availability for the Madaras system
was assumed at both 'the .Medicine Bow and the = 8.1 m/s
regions. In both regions, we used the annual outputs without
modification. that were predicted for the MOD-1 by Hightower and
Watts. and by.Genera1 .Electric. Thus, ..t.he source of the remaining
6 percent difference in the MOD-1 energy.yi.eld.prediction between
.Medicine.Bow and the other region is unknown'. . Possibly the
fact that the General Electric study reflected a more recent
analysis .explains. the difference. Apparently,.General Electric
believed it was.realistic to'assume a 90 percent availability
for the MOD-1, However, .because- one completely-assembled,
operational..spare rotor car-,and .ample financial provisions for
spare parts 'and ,preventative.'maintenance - have:been provided for
each ,Madaras plant, we believe.'it :is .realistic. to assume 100
percent availability for the 'Madaras plants..
,It.is interesting to note that the air density
e f f e c t on annual output was suc.h:that.the annual energy output
i n the 8.1 m/s region was greater than that at Medicine Bow where
Although t h e increased c o s t s used f o r t h e V = 8.1
m / s region inc reased t h e energy c o s t of each p l a n t , t h e comparative
r e s u l t s w e r e r eve r sed from those a t Medicine Bow. Madaras P lan t 4
energy c o s t was p red ic ted t o be about 1 4 percent l e s s than energy
c o s t of P l a n t 4a and Madaras P l a n t 5 energy c o s t was predic ted t o
be 2 2 percen t less than energy from HA-WTG P l a n t 5a. The c o s t
o f l and had a marked e f f e c t on HA-WTG p l a n t c o s t ( 9 percent
o f p l a n t c o s t f o r P l a n t 5a) whereas t h e land c o s t f o r P l a n t 5
w a s on ly 1.7 pe rcen t o f t o t a l p l a n t c o s t , Although t h e i n s t a l l e d
cost/kW of P l a n t 1 w a s s l i q h t l y h igher than t h a t of P lan t l a
a t Medicine Bow, t h e Madaras P l a n t 4 had a lower i n s t a l l e d c o s t / -
kW t han P l a n t 4a -a r e v e r s a l of t r e n d brought about by land
c o s t . Thus, t h e more e f f e c t i v e use of land by Madaras p l a n t s
helped t o improve t h e i r economic p o s i t i o n r e l a t i v e t o HA-WTG
p l a n t s .
S ince t h e a c t u a l p r i c e one would have t o ' pay f o r
l a n d f o r a wind-powered e l e c t r i c p l a n t i s specu la t ive , we conducted
one more comparison t o determine t h e s e n s i t i v i t y of energy c o s t
from t h e s e two p l a n t types t o land c o s t i n a V = 8 .1 m / s
r eg ion . The r e s u l t s of t h i s s tudy a r e presented i n t h e
bottom s e c t i o n o f Table 7.10: P l a n t s 7 and 7a. Here, we
assumed no land c o s t , a $3000 per a c r e decrease . These two p l a n t s
are comparable t o P l a n t s 5 and 5a, r e s p e c t i v e l y . One can s e e
t h a t t h e 40.8 m i l l p e r KW-hr energy c o s t of P l a n t 5a is 22.2
p e r c e n t h igher than' t h e enerqy c o s t f o r P l n a t 5 . By e l imina t ing
l a n d c o s t , t h i s spread was reduced t o 13.7 pe rcen t . Thus, land
c o s t i s a more important f a c t o r i n energy c o s t of an HA-WTG p l a n t
t h a n i n a Madaras p l a n t . S ince Madaras p l a n t s u t i l i z e land more
e f f i c i e n t l y , t h e i r compet i t ive pos i ton r e l a t i v e t o HA-WTG p l a n t s
w i l l improve as . land .cos ts a r e included i n t h e .ana lys is .
7.5.3 Summary of Madara's versus HA-W'YG P l a n t Compa.rison
The s tudy previous ly descr ibed was conducted on
an e q u i t a b l e b a s i s f o r both p l a n t s f o r two wind regimes, t h r e e
lcrnd c o s t l e v e l s , and two methods of f inancing , Federa l - and p r i v a t e .
We have sought e x p e r t p ro fess iona l a s s i s t a n c e i n
developing our b a s i c c o s t e s t ima te , and w e be l i eve we have been
conservat ive y e t r e a l i s t i c i n developing t h e c o s t f o r t h e Madaras
p l a n t s . Fur the r , we be l i eve t h a t our c o s t s and cont ingencies are
comparable t o o r more conservat ive compared t o those developed
by o t h e r s f o r HA-WTG p l a n t s . F i n a l l y , we have had s e v e r a l
communications with Hightower, and have been assured t h a t we
were i n t e r p r e t i n g h i s r e s u l t s c o r r e c t l y and equ i t ab ly .
For t h i s s tudy we have used our b e s t e s t ima tes
on f inancing and land c o s t s , based upon advice received from
our consu l t an t s and adv i so r s . We r e a l i z e t h a t h igher f i x e d
charge r a t e s and f inancing schemes a r e proposed by o t h e r
i n v e s t i g a t o r s . Yet, we have app l i ed t h e f inanc ing formulas
i d e n t i c a l l y t o both systems, and a s tudy of t h e d a t a i n d i c a t e
t h a t s i n c e t h e p l a n t c o s t s of t h e two system types a r e s i m i l a r ,
n e i t h e r one w i l l be p a r t i c u l a r l y favored by t h e f inanc ing scheme
s e l e c t e d , even i f h i s h e r f ixed charges a r e assessed .
Thus, we conclude t h a t t h e s tudy was adequate
t o compare t h e c o s t e f f e c t i v e n e s s of one p l a n t a g a i n s t t h e o t h e r ,
which was t h e s t u d y ' s main purpose. On t h e o t h e r hand, w e
b e l i e v e t h a t t h e values of energy c o s t contained i n Table 7.10
should be looked upon a s r e p r e s e n t a t i v e and comparative c o s t s
more than a s abso lu te va lues u n t i l a more d e t a i l e d s tudy i s
conducted.
The r e s u l t s of t h i s s tudy i n d i c a t e t h a t t h e
Madaras system could b e . a n a t t r a c t i v e a l t e r n a t i v e , from an energy
c o s t s t andpo in t , t o hor i zon ta l a x i s wind tu rb ines . We were
p a r t i c u l a r l y encouraged by t h e favorable way i n which our non-
optimized Madaras design seems t o have compared wi th t h e MOD-1
WTG, which has had t h e b e n e f i t of s e v e r a l i n t e n s i v e design and
manufacturing s t u d i e s . Nevertheless , we be l i eve it i s premature
t o s t a t e d e f i n i t e l y t h a t t h e Madaras system i s more o r less
c o s t e f f e c t i v e than HA-WTG systems -a much more d e t a i l e d
system design and manufacturing a n a l y s i s i s requi red before such
a s ta tement could be made with confidence.
SECTION VIII
CONCLUS.IONS
This conceptua.1 design study of the Madaras Rotor.Power
Plant included an analysis of all major components of the Madaras
system, has addressed each of the four unanswered questions
itemized in Paragraph 1.5, and has fulfilled the basic study
objective delineated in Paragraph 2.1. As a result of this analysis,
it is believed that a reasonably efficient conceptual design; which
is consistent from criteria and loads to cost, has been.developed.
It also is believed that the analyses have.provided a satisfactory
critique of Madaras' early work, and. has discussed all major
problem areas as well as all primary advantages of ,the system.
The more significant conclusions drawn from this study are itemized
below.
1. The Madaras Rotor Power Plant concept using a race-
track plant configuration appears at least to be economically
competitive with horizontal axis wind. turbine generators, and
the concept shows promise of out-performing horizontal axis
systems from a number of standpoints: structural durability,
economy of scale, energy yield, effkc'ient use. of land, and energy
cost. The results of'this study indicate that,' although at'this
stage of analysis, the concept does not appear to-offer a substantial
economic improvement in wind energy conversion technology, Madaras
racetrack-plant energy cost varied from 12 percent higher to 22
percent lower than the energy cost of .MOD-1 plants. It is believed
that these results are conservative since we believe our methods
of analyses have overstated electrical spin-up losses and mutual
interference losses for racetrack plants. This potential Madaras
cost advantage, although attractive, is diminished by the-Madaras
system's .limited.application arising from a possible scarcity of
large, flat, land areas having sufficiently unidirectional wind
velocities. Although more e'ff ici-ent HA-WTG systems (MOD-2) are
being developed, it is believed that more efficient Madaras
systems can be developed given the opportunity to conduct the
design and development studies comparable to those that have been
conducted for horizontal axis machinery. It is ,believed that
the 125-ft high (38-m) Madaras rotor offers a superior structural
alternative to the 200-ft to 300-ft (61 m to 91 m) diameter,
flexible, wind-turbine blades when subjected to wind, gust, and
tower loads. Thus, the Madaras system should be analyzed further
in order to determine more accurately how well it fulfills the
promise indicated in this present study.
2. Capital costs of installed Madaras plants are about
the same as those of horizontal axis wind turbine plants. Neither
the Madaras plant nor the horizontal axis wind turbine plant
seemed to gain an advantage over the other i~ terms of energy cost
as fixed annual charge rate was varied.
3. Madaras plants having rated capacities varying from
7.9 MW to over 227 MW with annual energy output varying from 6 6 32 x 10 kW-hx to 975 x 10 kW-hr are feasible. No limitations
were noted that would restrict maximum plant capacity to 227 MW.
In fact, improved efficiency is highly probable as plant size
increases. Thus, Madaras plants are capable of providing plant
capacities of interest to electric utility companies.
4. The.most efficient Madaras plant studied is described
as follows:
Rotor and Car Geometry
6 Aspect Ratio = 8 e Rotor Diameter = 16 ft (4.9 m)
Cylinder Length = 12.5 ft (38.1 m) End Cap Diameter = 32 ft (9.8 m)
e e/d. Ratio = 2 Rotor Car Weight = 723,000 lb (328,600 kg) Rotor Mid-Height = 82 ft (25 m) above ground
Plant Geometry - - -- - .. - -
Racetrack, two rails, 36 ft (11 m) Track end diameter = 4500 ft (1372 m) Track straight section = 60,000 ft (18,300 m)
Area Encompassed = 7209 acres Net Area Purchased = 748 acres (Balance of racetrack infield used for agriculture.) Number of Rotor Cars = 190
6 Spacing between Rotors = 705 ft (215 m)
Operational Conditions
Track Speed = 30 mph (13.4 m/s) Rated Wind Speed = 30 mph (13.4 m/s) Cut-Out Windspeed = 65 mph (29 m/s) Rotor Rotational Speed = 186 rpm Viscous Braking
Electrical Eaui~ment
Spin Motor, 450 kW, 500 Volt dc Generator = 1 MW'per car, Induction Generator, 4160 V, 60 Hz, 30
Performance
Rated Capacity = 227.8 MW 6 Annual Energy Yield = 947.7 x 10 kW-hr @ 7 = 9.7 m/s @ 9 m height and an elevation of 2130 975.4 x lo6 kW-hr @ = 8.1 m/s t! 9 m height at sea l~veP,
Cost
a 7 = 9.7 m/s, 8.41% Federal Financing, Land Cost @ $200/acre
Plant Cost = $183.5 x 10 6
Unit Cost = $806/kW Total Annual Cost = $18.08 x 10 6 Energy Cost = 31.4 mills/kW-hr
- a V = 8.1 m/s, 15% Private Financing, Land Cost
@ $3000/acre Plant Cost = $186.4 x 10
6
Unit CosL = $818/kW Total Atl~lual Cost = $31.08 x 10
6
Energy Cost = 31.4 mills/kW-hr
5. Madaras plants having circular track configurations
were not sufficiently efficient to compete with horizontal axis
wind machines. Circular track plants are limited primarily by the
large electrical losses of the spin motor during spin-up and
spin-down. These large electrical spin-up and spin-down losses
constitute a major performance penalty for aircular-atrack Madaras plants, and the study of these losses deserves considerably more
attention than was possible to allot in the study reported herein.
Thus, it appears that useful Madaras plants could be restricted
to racetrack configurations unless means for substantially reducing
electrical spin-motor losses are found. Possible methods for
reducing spin-motor losses' include:
Development of optimized spin-sch.edules
Improved motor efficiency during spin-up
e Reduction in rotor weight, radius of gyration, and end plate size Improved rotor bearings
Reduced rotor design rpm
Use of transmissions during spin-up
Development of a method for conserving inertial energy.
6. The potential problem areas and disadvantages,of
the Madaras system relative to horizontal wind turbine plants
are:
6 The Madaras system is more complex, has higher losses, and will require higher operation and maintenance costs than a horizontal axis wind turbine system.
e Unless electrical and aerodynamic design improvements are.made, the use of a racetrack 'plant configuration is necessary for optimum Madaras plant performance. Thus, Madaras plants will be limited to regions having nearly unidirectional winds or-to those regions in ,,
which off-axis winds have an angular variation of less than + 4 S 0 and which occur only a small portion of a total-year.
7. The advantages of a Madaras Plant over a comparably-
sized horizontal.axis wind turbine plant are:
A rotating cylinder rotor structure is simpler and can be built to have greater structural strength, durability, and reliability compared to large, flexible rotor blades exposed to a wind and gust environment.
Madaras plants show higher sensitivity to economy of scale.
a Madaras plants make more efficient use of land and use less land than HA-WTG plants.
8. Although the losses of a Madaras plant are significantly
larger than those of a horizontal axis wind tur.bine plant; the
large area swept by the rotors overcomes the total losses to such
an extent that the Madaras system appcars to compete with
horizontal axis wind machine plants on a cost per annual energy
output bases.
9. Power required to rotate the rotor is markedly influenced
by the end plate diameter rather than by cylinder le~lyth. There-
fore, a significant reduction in electrical spin-up power
requirements, and hence a. reduction of electrical -losses may be
achieved by one or more of the following cylinder and end plate
design approaches:
Rotating cylinder with a fixed end plate
Large diameter, non-rotating end plate in which a smaller-diameter, .flush-mounted, rotating end plate is housed.
Rotating cylinder with nonpowered, .free wheeling end plates
Fixed cylinder and end plates with boundary layer blowing and suction on the cylinder and/or end plates.
Wii~d Lunnel tests would have to be conducted t.n determina whether
or not any of these approaches will provide an improved cost-
performance ratio.
10. A complete set of free stream and boundary layer
rotating cylinder data in terms of rotor geometry and operating
conditions.was obtained. Data included lift, drag, moments
caused by lift and drag, and rotor power required as a function of
wind speed and rotor rpm. These data are the most extensive and
complete set 'of infoxmation.on rotating cylinder performance versus
geometry and wind speed profile available in the literature. The
data set appears consistent within its own parametric boundaries
and also is in agreement with recent and early data obtained in
the mid-to-late 1920's which was used by Madaras.
11, The wind tunnel aerodynamia data obtained during this
program are capable of being used directly to predict full-sized
cylinder performance i.n a free stream flow whi..ch creat.es a uniform
wind velocity distribution along the height of the cylinder. This
direct utilization is possible because free stream Reynnlds
number not govern scaling of model data to full-scale results
when the rotor rotational surface speed to resultant wind speed
ratio (U/V) is greater than 1.0. For predicting rotor performance
in the atmospheric boundary layer, the wind tunnel data must be
comhined with a model which develops the resultant velocity
profile along the height of the cylinder. The required model yield=
a resultant spiral velocity distribution versus cylinder height
after the vector combination of: (1) the uniform height-wise
velcity distribution caused by rotor movement along the track;
and (2) the nonuniform velocity distribution versus cylinder height
bf the wind in'the atmospheric boundary layer region. The
boundary layer data obtained in the wind tunnel provided an
independent means for validating this model.
12. Standard off-the-shelf .electrical, mechanical, and
structural components as well as materials and fabrication
techniques seem to fulfill requirements for. building the Madaras
system proposed herein. Other than the electrical spin motor
loss problem previously mentioned, the only.o,ther equipment area
that should receive attention is the life of the main rotor
bearings. The bearing manufacturers were not able to predict with
any reliability the life of the large bearings elected for the
rotor, and it was questionable if 30-year bearing life could be4
achieved.
13. The track roadbed design quality is of utmost importance
to minimize maintenance costs. A track system including proper
consideration of subsoil stabilization, good ballast, steel
reinforced concrete pavement, and good steel track is required.
These studies indicate that such a system can be designed for ,
the loads and life required by the design criteria. Also,
consideration should be given to the cost effectiveness of terrain
modification along the roadbed in order to increase the wind
velocity distribution along the lower portions of the rotor.
14. Other structural techniques should be investigated
to take advantage of modern designs and fabrication concepts
in order to decrease the cost and weight of the 'rotor. Filament
optimization techniques are obvious approaches.
15. The Madarae.system performance was found be be .lower
than that predicted by Julius Madaras and his consul.tants,
particularly in the areas of net power generated per rotor, power
generated per unit area of land, and annual energy output. This
lower performance is attributed to the following incorrect
assumptions made by Madaras, et al.:
Although the problem was addressed, Madaras erroneously
assumed that mutual interference effects were negligible for rotor
spacing as close as 5 diameters on a circular track diameter
of 1500 ft (457 m). Thus, for a 457-m diameter track, Madaras
predicted a rated plant capacity of about 47 MW. On the present
study, minimum rotor spacing was found to be 44 rotor diameters,
and the optimum track diameter was found to be 1372 m'. Thus, for
a circular plant this size, we predicted the maximum rated plant
capacity would be only 7.8 MW.
Madaras also grossly under-estimated the electrical
losses required to spin up the rotor, and incorrectly assumed he
could recover nearly all of the kinetic energy of the spinning
rotor during regenerative braking. He also under estimated the
size of the motor required to accelerate the rotor in accordance
with his selected spin schedule and track speed that would yield
optimum power output at each point along the track.
Madaras assumed incorrectly that the CL and CD values
for a rotating cylinder having an aspect ratio of 8, two large
rotating end plates, and immersed in uniform free-stream flow
were identical to the CL and CD values of a rotating cylinder
having an aspect ratio of 4, one smaller rotating end plate, one
stationary end'plate, and immersed in nonuniform atmospheric boundary
layer flow,
1 , A t t h i s s t . a g e nf t.he investigation, it is not
possible to state conclusively whether or not the Madaras system
will significantly out-perform a similarly-sized.horizonta1 axis
wind turbine system. However, the results of the present study,
which are thaught to be conservative, are sufficiently encouraging
to warrant further investigation. Areas requiring further study
include : \
Definition of mutual interference for racetrack plants and for circular track plants having track end diameters greater than 8000 ft (2439 m)
Development of optimal spin schedules which include modulating rotor speed at all points along.the track such that the propulsive force is optimized'at all times
Further consideration of different types of electrical equipment, transmissions, and braking techniques
Analyses of different end plate designs which promise to reduce viscous friction and inertia loads, and hence reduce spin power., without a proportionate decrease' in aerodynamic performance
Reuction of rotor weight and inertia by optimized design and use of new materials and construction techniques that are cost effective. Included in this analysis should be the consideration of larger rotors and filament.winding techniques
In-depth studies of power collection distribution as 'well as system control
A thorough study.of manufacturing techniques to deve'lop the most cost-effective methods for producing. Madaras plants, and the determination of detailed c0st.s of mass-produced units
A. life cycle cost study to include system reliability as well as maintenance, operation, and depreciation costs of the system
APPENDIX A
CYCLOGXRO VORTEX APPLIED TO THE MADARAS SYSTEM TO' DETERMINE MUTUAL INTERFERENCE LOSSES BETWEEN ROTORS
Prafessor Harold C. Larsen A i r Force I n s t i t u t e of Technology
Wright-Patterson A i r Force B a s e , O h i o
APPENDIX A
TABLE OF CONTENTS
Section
A- 1 HISTORICAL DEVELOPMENT OF THE CYCLOGIRO
A . l . l I n t roduc t ion t o t h e C y c l o g i r o A. 2 . 2 T e c h n i c a l B a c k g r o u n d
IDEAL BLADE ELEMENT THEORY OF THE CYCLOGIRO
PRIMITIVE VORTEX THEORY OF THE CYCLOGIRO
A. 3.1 V o r t e x Propert ies A.3 .2 K u t t a - J o u k o w s k y Law
IMPROVED .PRIMITIVE VORTEX THEORY OF THE CYCLOGIRO
BLADE MODULATION SCHEDULE
IDEAL BLADE VECTOR DIAGRAM
REAL BLADE VECTOR DIAGRAM
CIRCULATION AT THE BLADE AS A FUNCTION OF PHASE ANBLE
SEMIRIGID WAKE STRUCTURE
WAKE. MODEL FOR IMPROVED PRIMITIVE THEORY
APPLICATION TO THE MADARAS ROTOR PLANT
P a g e
LIST OF SYMBOLS
CFX
CF Z
CFQ
CQ
CFR
CP
Aspect r a t i o b2/s,. a lso area
Force coe,ff i c i sn t , general CF = F/ ( l /2pv2 S)
Drag coeff icient C~
= ~ / ( 1 / 2 p v ~ S)
L i f t coefficient 2 CL = L / ( 1 / 2 p V S )
Pitching moment coefficient 2 C, = M/(1/2pV S)
Resultant force coefficient 2 CR = R / ( 1 / 2 p V S )
Rotor X force coefficient CFX = FX/ (1/2pv2 bD)
Rotor Z force coefficient CFZ = F Z / ( ~ / ~ P V ~ bD) I
Rotor torque force coefficient CFQ = FQ/ ( 1/2pv2 bD)
Rotor torque coefficeint CQ = ~ / ( 1 / 2 p ~ ~ b d ~ )
Rotor radia l force coefficient CFR = F R / ( ~ / ~ ~ v ~ bD)
Rotor power coefficient CP = p/(1/2pv3b~)
Rotor th rus t coefficient
Rotor diameter D = 2 R
Drag, component of aerodynamic force para l le l t o re la t ive velocity
Force, general
Rotor X force. Time average value of sum of x component of force on the bl..ade.
Rotor radia l force. Instantaneous value of force on blade i n radia l direction.
Rotor torque force, Time average value of sum of tangential component of force on blade along the o rb i t or path of rotation.
Rotor Z force. Time average value of sum of z . component 'of forces on the ~ l a d e s .
,Moment of i ne r t i a about pivot axis of blade.
LIST OF SYMBOLS (Continued)
Advance r a t i o J = V/nd
Left component of aerodynamic f o r perpendicular t o r e l a t i v e v e l o c i t y
L i f t t o drag r a t i o
P i t ch ing moment. Aerodynamic moment about t h e y a x i s
Number of b lades i n t h e r o t o r
N u m b e r of r o t o r r a d i i equal t o length of va lue used i n . c a l c u l a t i o n .
Power
Torque
Rotor. r ad ius . Distance from a x i s of r o t a t i o n to . p i v o t i n b lape o r c e n t e r of r o t a t i n g cyl inder .
Resul tant aerodynamic force .
A r e & . Planform a r e a of b lade , o r b lade element o r p ro jec ted area of r o t a t i n g cy l inder , o r genera l a rea .
Thrust.
Rotat ing c y l i n d e r p e r i p h i a l v e l o c i t y a t s u r f a c e = w r and a l s o t h e induced v e l o c i t y along t h e x-axis of t h e r o t o r ,
Freestream v e l o c i t y , o r t r a c k speed f o r Madaras r o t o r ,
P e r i p h i a l v e l o c i t y of b lade on t h e o r b i t . 'VP = 27rnR =QR.
Resultant. ve loc i ty . Vector sum of a l l v e l o c i t y components.
X component of t h e res 'u l tan t . ve loc i ty .
Z component ,of t h e r e s 'u l t an t v e l o c i t y .
Wind speed o r induced ve loc i ty .
X component of t h e induced v e l o c i t y
Z component of t h e induced v e l o c i t y
LIST OF SYMBOLS (Continued)
x coord ina te a x i s i d e n t i f i e d , o r x coordina te
y c o o r d i n a t e a x i s i d e n t i f i e r , o r y coordina te
z denote a x i s i d e n t i f i e r , , o r z coordina te
Slope of t h e l e f t c o e f f i c i e n t versus angle of a t t a c k curve.
Span of the blade o r r o t r , cpan i n gcncral .
Chord of t h e blade o r b lade element
D i a m e t e r of p r o p e l l e r o r windmill
Normal d i s t a n c e from vor tex segment t o genera l p o i n t
rpm, r p s , o r r evo lu t ions p e r u n i t t ime
Radius
Radius
Arc. l e n g t h
x component of v e l o c i t y l o c a l p e r t u r b a t i o n o r induced component.
y component of v e l o c i t y l o c a l per turba t i .on o r induced component.
z cu~nyu~ le~ l t uf v e l o c i t y l o c a l percurbacian or induced component.
x aoord ina te
y coord ina te
z coord ina te CL SV
C i r c u l a t i o n r = 2b f r e e and bound vor tex s t r e n g t h .
Accelera t ion-decelera t ion ramp angle to.. r eve r se angle of a t t a c k .
LIST O F SYMBOLS (Continued)
Phase angle of blade on o r b i t measured from t h e x a x i s , o r t h e angle between t h e plane of r ,o t a t ion and r e s u l t a n t v e l o c i t y a t p r o p e l l e r d isk .
Blade rocking angle - angle between chord l i n e o f b lade and X-axis:
Resul tant v e l o c i t y o r i e n t a t i o n angle measured from t h e x-axis on t h e angle between t h e p lane of r o t a t i o n and r e s u l t a n t v e l o c i t y f a r from t h e d i s k
Angular v e l o c i t y , radians/sec
Angle of a t t a c k - angle between re fe rence l i n e i n a i r f o i l t o r e s u l t a n t v e l o c i t y .
Angle of a t t a c k f o r zero l i f t . Angle measured from re fe rence l i n e t o r e s u l t a n t v e l o c i t y when l i f t is zero.
E c c e n t r i c i t y angle - angle of diameter jo in ing f l i p po in t s measured . from t h e axis, o r b lade angle ' of measurement measured from plane of r o t a t i o n .
Rat io of s p e c i f i c h e a t s o r y = tan-' (D/L) .
5 = w/V nondimensional v e l o c i t y r a t i o .
rl = v/V nondimensional v e l o c i t y r a t i o o r e f f i c i e n c y of p r o p e l l e r o r windmill'
Tip speed rat io ,X = 21~nr /v = Rr/V.
Kinematic v e l o c i t y of f l u i d
5 = u/V nondimensional induced v e l o c i t y r a t i o
Mass dens i ty of t h e f l u i d
s o l i d i t y = CRS/A = - ITd
Veloci ty o r i e n t a t i o n a x i s measured from x-axis o r p lane of r o t a t i o n .
Phase angle f o r r o t o r , o r r e s u l t a n t v e l o c i t y a t d i sk o r i e n t e d angle.
Angular ve loc i ty .
LIST OF SYMBOLS (Concluded)
Subscripts
crit C r i t i c a l
may Maximum
min Minimum
1 , 2 , 3 , 4 . . S p e c i f i c po in t var iable designator
m po in t f o r maximum
pot . p o t e n t i a l value
yseen Baeeii vortex voluc
r , R r e s u l t a n t
t track
w wind
SECTION A . 1
HISTORICAL DEVELOPMENT OF THE CYCLOG,ZRO
Hor izonta l a x i s wind t u r b i n e s a r e inhe ren t devices t h a t
must be operated a t high t i p speed t o wind speed. r a t i o s t o o b t a i n
good e f f i c i e n c y . However, though t h e t i p s may opera te a t high
e f f i c i e n c i e s , t h e i n n e r two-thirds por t ion of each b lade o p e r a t e s
a t low e f f i c i e n c y . Since t h i s reg ion comprises four-ninth of t h e
t o t a l d i sk a r e a , t h e - i n t e g r a t e d d i sk e f f i c i e n c y i s only 30- t o 4 0
percent . This low i n t e g r a t e d e f f i c i e n c y r e l a t i v e t o t h e l i m i t i n g
Betz e f f i c i e n c y of 59 percent has prompted e f f o r t s t o f i n d
a l t e r n a t e h igher-ef f ic iency means of e x t r a c t i n g energy from t h e
wind. I f t h e e n t i r e blade could be made t o opera te a t t h e same
e f f i c i e n c y , t h e i n t e g r a t e d e f f i c i e n c y could approach.. t h e Betz
l i m i t . The cyclogi ro , a v e r t i c a l - a x i s wind t u r b i n e i s one con-
f i g u r a t i o n which shows promise of achieving t h i s objec t ive , .
A. 1.1 Int . roduct ian 'to the Cyblogxro
A typkcal four-blade modern cyclog2ro i s ' i l l u s t r a t e d
i n Figure A . l . The cyclogkro c o n s i s t s of a group of c o n t r o l l a b l e
pivoted b lades with t h e p ivo t a x i s p a r a l l e l t o t h e a x i s of r o t a t i o n
about which t h e b lades r o t a t e on support ing arms, wi th t h e a x i s
of r o t a t i o n perpendicular t o t h e f rees t ream v e l o c i t y , V. The
blades a r e assumed t o r o t a t e a t a cons tant angular v e l o c i t y
R = 2~x1, s o t h a t p e r i p h e r a l o r . o r b i t ve l 'oc i ty .of t h e b lade i s QR.
The res 'u l t an t v e l o c i t y , VR, whi'ch d r i v e s t h e blades i s t h e v e c t o r
sum of V and RR o r
I t i s noted that VR i s t h e same magnitude a l l a long t h e b lade i n
c o n t r a s t t o a p r o p e l l e r b lade where VR v a r i e s from r o o t t o t i p .
This vec to r sum is shown i n Figure A . l f o r t h e b lade p o s i t i o n s
shown. VR v a r i e s i n magnitude and d i r e c t i o n , a s can be seen.
The i n d i v i d u a l b lades a r e c o n t r o l l e d (.or modulated a s it i s
Figure A . l . Typical Cyclogiro Windmill at a Speed Ratio of b = 2.
c a l l e d ) t o be placed a t an angle of a t t a c k r e l a t i v e t o VR.
Depending upon whether t h e angle of a t t a c k is p o s i t i v e o r negat ive
and i t s . loca t ion on t h e o r b i t r e l a t i v e t o VR, t h e cycloqjiro can
be made t o genera te a p o s i t i v e o r negat ive t h r u s t and a p o s t i v e
o r negat ive s i d e force. Both can be zero. A negat ive t h r u s t
corresponds t o a windmill type of opera t ion , and t h e b lades i n
Figue A . l have been so -o r i en ted . Associated wi th VR a n d . t h e
angle of a t t a c k , a , i s a blade l i f t f o r c e which i s
2 L = CL 3 SVR .
The l i f t f o r c e a s s o c i a t e d with each b lade has been shown a s t h e
heavy arrow perpendicular t o t h e l o c a l r e s u l t a n t v e l o c i t y , VR.
The l i f t fo rce has been shown propor t iona l t o V R ~ and i s approxi-
mately c o r r e c t i n magnitude. .There i s a l s o a d rag f o r c e , but
s i n c e t h i s i s from one-twentieth t o o n e - f i f t i e t h t h e magnitude
of t h e l i f t . , it i s t o o smal l t o be shown on t h i s s c a l e . The
v a r i a b l e magn.itude and d i r e c t i o n of t h e l i f t fo rce i n d i c a t e s t h a t
cyc log i ro flow i s very unsteady. I f t h e r a d i u s is l a r g e and t h e
rpm i s low, the ' : f low may be considered quasi-s teady. To produce
u s e f u l l i f t , and t h r u s t , .or t o a c t a s a windmill , t h e angle of
a t t a c k must be reversed a t two p o i n t s .on t h e o r b i t , u sua l ly a t
oppos i te ends of a diameter. By changing t h e angle of a t t a c k
r e v e r s a l p o i n t , t h e ' r e s u l t a n t r o t o r fo rce developed can be v a r i e d
cont inuously t n generake a pnre ' p o s i t i v e thrust and a s m a l l s i d e
force, ' a pure s i d e fo rce and no t h r u s t , 0 r . a pure negat ive t h r u s t
and. small s i d e for.ce. The angle a t wh5ch t h e angle of a t t a c k
reversal occurs i s c a l l e d t h e e c ' c e n t r i c i t y angle , B , and t h e
r e v e r s a l p o i n t i s c a l l e d t h e b lade f l i p poin t . For b lades having
an L/D equal t o o r g r e a t e r than 20 and t h e l i f t c o e f f i c i e n t of
t h e b lade i s i n t h e l i n e a r range, t h e t h r u s t and s i d e . force a r e
a l s o l i n e a r with angle of a t t a c k .
The l o c a l l i f t and drag fo rce a t each po in t on t h e
o r b i t can be resolved i n t o t h r u s t and s i d e fo rce components, and
i n t o r a d i a l and t a n g e n t i a l o r torque fo rce components. I f a
u s e f u l t h r u s t is produced, t h e torque i s p o s i t i v e which r e q u i r e s
power t o t u r n t h e r o t o r . This is t h e . . p r o p e l l e r s . t a t e . I f t h e
pure l i f t s ta te e x i s t s , power must s t i l l be p u t i n t o t h e r o t o r .
I n t h e windmill s ta te t h e to rque i s negat ive and power i s e x t r a c t e d
from t h e airs t ream.
The modulated cyclog,$ro i s s e l f s t a r t i n g and s e l f l imi t ing .
The r i g i d b lade c y c l o g i r o cannot s t a r t by i t s e l f , but once beyond
a c e r t a i n rpm o r t i p speed r a t i o , it runs w e l l and i s s e l f l i m i t i n g .
The ~ a r r i e u s r o t o r is a r i g i d b lade cyc log i ro of s p e c i a l b lade
shape. The c y c l o g i r o b lades does n o t have t o be s t r a i g h t o r
c o n s t a n t cord. Even d e l t a ( A ) shaped r o t o r s have been proposed.
It a l s o i s n o t necessaxy t o use b lades f o r a c y c l o g i r ~ .
Rota t ing c y l i n d e r s , which can produce l i f t , and jet f l a p augmented
l i f t can be used. The Madaras r o t o r which uses r o t a t i n g cyc l inder s
i s a type of c y c l o g i r o and can be t r e a t e d by t h e theory developed
f o r a blade.
A. 1 . 2 Technica l Back,ground
The cyclogi'ro may be t h e o l d e s t windmill known. The
a n c i e n t ~ e r s i a n panemone was i n p r i n c i p l e a cyc log i ro opera ted by
d r a g fo rces i n s t e a d o f by l i f t fo rces . To improve i t s performance
it w a s placed on a tower which sh ie lded t h e advancing b lades and
he lped d i v e r t f low t o t h e r e t r e a t i n g blades. I t was a c t u a l l y a
v a r i a t i o n of t h e undershop water wheel mounted v e r t i c a l l y , and
it w a s used t o pump water . .
The f i r s t recorded cyclogi ro was a p a t e n t by Congreve 47
i n 1828. his p a t e n t w a s f o r a man-powered, man-carrying a i r c r a f t
c a l l e d t h e aer ia l c a r r i a g e . Since t h a t t ime, many i n d i v i d u a l s
i n many c o u n t r i e s around t h e world have con t r ibu ted t o t h e theory
and experimental development. 48 I n t e r e s t i n t h e concept have
occurred i n i n t e r v a l s of from 20 t o 40 y e a r s s i n c e Congreve's
p a t e n t . The primary concept has been i n a i r c r a f t propulsion and
l i f t , bu t is has been s u c c e s s f u l l y app l i ed t o s h i p propulsion
and a s a wind wheel t o power a sawmill. Madaras proposed t o use
t h e concept us ing r o t a t i n g c y l i n d e r s t o d r i v e a t r a i n of c a r t s
around a c i r c u l a r t r a c k t o genera te l a r g e amounts of power from
t h e wind. A pro to type r o t a t i n g c y l i n d e r was b u i l t and t e s t e d
i n t h e wind i n a s t a t i o n a r y s i te i n 1933, a s was descr ibed i n
Sect ion 1 of t h i s r e p o r t .
I n v e s t i g a t o r s i n France, Germany, Sweden, and Japan
s tud ied cyclogLro a p p l i c a t i o n s t o a i r c r a f t and s h i p propulsion . .,
and cons t ruc ted machines which w e r e t e s t e d . Only t h e Voight-
schneider4' system and t h e F l e t t n e r r o t o r systems were a c t u a l l y
used f o r s h i p propulsion, and they w e r e q u i t e successfu l .
One of t h e outs tanding c o n t r i b u t o r s i n t h e United
S t a t e s i n both theory and experimentat ion was D r . ~ i r s t e n ~ ' of
t h e Universi ty of Washington who was an a c t i v e r e sea rcher from.
1922 t o 1950. H e showed t h a t t h e pa th of t h e b lade moving about
a . c i r c l e and t r a n s l a t i n g a t a uniform v e l o c i t y r e l a t i v e t o s t i l l
a i r was a p r o l a t e cyc lo id , a c y c l o i d , ' o r a c u r t a t e cyc lo id . .
dependent upon t h e r a t i o of t h e p e r i p h e r a l v e l o c i t y of t h e b lade
about i t s a x i s of r o t a t i o n t o . t h e uniform t r a n s l a t i o n v e l o c i t y .
This r a t i o i s known'as t h e t i p speed r a t i o , A . Thus, A = ,VP/W =
2.rrnR/Wt where VP is t h e p e r i p h i a l speed., W i s . t h e t r a n s l a t i o n a l
speed, R is t h e r ad ius from t h e a x i s of r o t a t i o n t o t h e p i v o t i n
t h e b lade , aiid n i s t h e number of r evo lu t ions pe r u n i t t i m e .
The f a c t t h a t t h e path of t h e blade r e l a t i v e t o a f ixed a x i s system
i s a cyc lo id has given t h e device t h e name of c y c l o g ~ r o .
Kirs ten c o r r e c t l y formulated t h e " i d e a l b lade theory"
de tezn~iiied Llie i d e a l b lade modulation schedule (.eontinuouo
o r i e n t a t i o n of t h e b l a d e ) , devised ways t o produce it, and showed
t h e necess i ty of angle of a t t a c k r e v e r s a l . He showed how l i f t
and t h r u s t would be c o n t r o l l e d by varying t h e p o s i t i o n of angle
of a t t a c k reve r sa l . H e then t e s t e d a device t o v a l i d a t e t h e
theory and combined t h e i d e a l theory with t h e momentum theory
t o improve i t s c a p a b i l i t y . The N A C A ~ ~ t e g t e d t h e cyc log j ro and
concluded it was a f e a s i b l e method of producing l i f t and propulsion,
t h a t i t c o u l d be u s e f u l f o r v e r t i c a l takeoff and landing a i r c r a f t , t h a t high 'propulsive e f f i c i e n c y could be. achieved, and t h a t it
w a s compet i t ive wi th p r o p e l l e r s . However, it e x h i b i t e d severe
v i b r a t i o n , and t h e l ack of an adequate theory l i m i t e d i ts use-
f u l n e s s and hampered development a t t h a t t i m e .
During World W a r I1 t h e cyc log i ro again was proposed
as a means of p ropu l s ion and l i f t . Ki rs ten was a c t i v e i n t h e
5 2 f 5 3 Af te r two development of t h e a i r c r a f t des ignated t h e XP-77. . .
y e a r s of development and t e s t i n g of t h e propulsion system, t h e
p r o j e c t w a s abandoned because t h e mechanical v i b r a t i o n and s t r u c t u r a l
problems were cons idered $nsurmountable a t t h e t i m e .
. M r . R.V. .Bru l l e , . while a t t e n d i n g t h e A i r . Force I n s t i t u t e
of.Technology i n 1954, l ea rned of t h e cyclogi ro . H e developed
and p a t e n t e d a cyclog:$ro pump. La te r as an engineer wi th t h e
~ c ~ o q n e l l - D o u g l A s Company, he conceived t h e i d e a of us ing fly-by-
w i r e t echniques t o c o n t r o l t h e blade.modulat ion of t h e cyc log i ro
and determined t h i s scheme would s o l v e t h e v i b r a t i o n problems
asso 'c ia ted wi th mechanical b lade moddlation. H e designed a c o n t r o l
system t o accomplish t h e t a s k and then designed a small cyc logi ro
a i r c r a f t ,
B r u l l e knew t h a t t o develop an adequate b lade modula-
t i o n c o n t r o l system f o r fly-by-wire it would be necessary t o have
acCurate d a t a on t h e inf low and sidewash v e l o c i t y a t every po in t
on the5 o r b i t f o r a l l condi t ions . Late i n 1971 he appealed t o
P r o f e s s o r H.C. Larsen f o r a s s i s t a n c e t o so lve t h e problem. Since
t h e A i r Force was i n t e r e s t e d i n p o s s i b l e a p p l i c a t i o n s t o a i r c r a f t ,
permission was g ran ted-and resea rch support was provided,
Larsen r e a l i z e d t h a t t h e e x i s t i n g t h e o r i e s were
merely an a p p l i c a t i o n of wing theory (more proper ly a i r f o i l
t h e o r y ) , m d . t h a t they d i d n o t a t t empt t o ~ o l v e t h e fundamental
problem as -Prandt l had done f o r three-dimensional wing theory
and Goldstein had done f o r p r o p e l l e r theory. I n t h e s e t h e o r i e s ,
t h e wing and propel ler b lade a r e replaced by a bound vor tex
d i s t r i b u t i o n with, an assumed r i g i d t r a i l i n g . vor t ex shee t . P rand t l
and ~ e t z ~ ~ assumed t h e t r a i l i n g vor tex shee t was f l a t and
e s t a b l i s h e d i n t e g r a l s f o r t h e l i f t and drag of t h e wing. H e t h e n
solved t h e problem t o minimize t h e drag. H e w a s . success fu l i n
f ind ing a c losed s o l u t i o n f o r t h e e l l i p t i c a l load d i s t r i b u t i o n ,
which enabled him t o w r i t e equat ions f o r t h e l i f t and drag
c o e f f i c i e n t s of t h e wing. A l l o t h e r load d i s t r i b u t i o n s r e q u i r e
numerical a n a l y s i s , but t h e r e s u l t s were shown by Glauert t o be
reducib le t o a f a c t o r t i m e s t h e e l l i p t i c a l load d i s t r i b u t i o n
r e s u l t s . P r a n d t l ' s theory requ i red s i x yea r s t o develop, was
h ighly success fu l i n c o r r e l a t i n g t h e drag of wings, and in t roduced
t h e concept of a spec t r a t i o . It was considered one of t h e tr iumps
of t h e o r e t i c a l hydrodynamics.
P r a n d t l , Betz, and o t h e r s attempted t o extend t h e wing
theory t o p r o p e l l e r s . The t r a i l i n g vor tex shee t w a s assumed t o be
a r i g i d h e l i c a l vor t ex shee t . I n t e g r a l s were e s t a b l i s h e d t o try
t o so lve t h e b lade c i r c u l a t i o n d i s t r i b u t i o n , but t h e i n t e g r a l s
w e r e i n t r a c t i b e l . P r a n d t l succeeded i n f ind ing an approximate
s o l u t i o n which was used i n design. The r e s u l t s were i n good
agreement with 'measurements f o r l i g h t l y loaded p r o p e l l e r s , and
improvements over t h e simple b lade element. theory were achieved.
However, it was r e a l i z e d t h a t t h e s o l u t i o n was not exac t .
I n 1928, Sidney ~ o 1 d s t e i . n ~ ~ publ ished h i s theory of
p rope l l e r s . Like P r a n d t l , he assumed a blade c i r c u l a t i o n d i s -
t r i b u t i o n s a n d a t r a i l i n g vor tex shee t . TO ob ta in a s o l u t i o n it
was necessary t o assume a l ight ly- loaded p r o p e l l e r . There w a s no
s l i p s t r e a m con t rac t ion and t h e t r a i l i n g shee t became a r i g i d
h e l i c a l shee t . Goldstein obta ined a s o l u t i o n with t h e a i d of a
p o t e n t i a l func t ion which s a t i s f i e d t h e equat ions of motion when
a p o t e n t i a l d i f f e r e n c e e x i s t e d a c r o s s t h e vor tex shee t . Goldstein
obtained a s o l u t i o n f o r t h e p o t e n t i a l funct ion f o r any number of
b lades , and showed t h a t it was a Lome11 funct ion , a complex form
of t h e Besse l funct ion . Unfortunately, only even number of b lades
could be computed a t t h a t time. Goldstein r e l a t e d t h e p o t e n t i a l
t o t h e c i r c u l a t i o n d i s t r i b u t i o n func t ion , and u l t ima te ly t h e
l o c a l l i f t c o e f f i c i e n t and s o l i d i t y wfiich enabled t h e l o c a l b lade
chord and t w i s t d i s t r i b u t i o n t o be determined f o r t h e design
condi t ion . H e t h e n evolved a design procedure and i n d i c a t e d how
t o compute o f f design performance.
he odor sen'^ extended t h e Goldstein theory t o heavi ly-
loaded p r o p e l l e r s and con t rac t ion e f f e c t s . H e used an e l e c t r i c a l
analogue t o e v a l u a t e t h e i n t e g r a l s and introduced s o l u t i o n s f o r
coun te r r o t a t i n g p r o p e l l e r s . H e developed design c h a r t s which
have been a p p l i e d t o t h e development of improved s u c c e s s f u l
p r o p e l l e r s . This i s considered another triumph f o r t h e o r e t i c a l
a n a l y s i s .
Both Prand t l and Goldstein assumed r i g i d wakes which
do n o t occur. I t i s r e l a t i v e l y easy t o show t h a t a f r e e wake
d i s t o r t s . The wing wake r o l l s - u p i n t o t w o c o n c e n t r a t e d v o r t i c e s
l o c a t e d a t t h e c e n t e r of v o r t i c i t y on each semiwing t o form
e s s e n t i a l l y t h e famous horseshoe vor tex which Prandt ly developed
and assumed was v a l i d f o r a uniformly loaded wing. Roll-up is
q u i t e pronounced wi th in one semispan of t h e wing. Glauert
i n v e s t i g a t e d t h i s problem. Westwater solved t h e ro l l -up problem
wi th numerical i n t e g r a t i o n . The p r o p e l l e r wake a l s o d i s t o r t s ,
and i s thought t o form a s e r i e s of t o r o i d a l r i n g s f a r downstream
of t h e p r o p e l l e r . Vortex wakes are u l t ima te ly damped nlit hy the
a c t i o n o t v i s c o s i t y and tu rbu lence , y e t they pe r s i s ' t f o r s u p r i s i n g l y
long t imes. Near t h e wing and p r o p e l l e r b lade t h e vor tex s h e e t i s almost i d e n t i c a l t o t h e p o t e n t i a l s o l u t i o n , while f a r from the
winq o r p rope l l ex , t he wake i s h igh ly d i s t -o r t ed and does not
resemble t h e p o t e n t i a l so lu t ion . This p resen t s a dilemna. In
t h e cyc log i ro wake, s t r o n g concent ra ted v o r t i c e s e x i s t a t t h e b lade
f l i p po in t s and dominate t h e flow. They cause d i s t o r t i o n and s h e e t
;3-1-up t o proceed almost immediately. How t o a t t a c k t h i s , problem
N a s a d i f f i c u l t dec i s ion , a s t h e a n a l y s i s used would depend upon
'he b a s i c assumptions made.
Larsen then decided t o s t a r t with f i r s t fundamentals
. a n d t o at tempt t o .find a p o t e n t i a l . so lu t ion . Figure A.2 repre-
s e n t s t h e r i g i d t r a i l i n g vor tex shee t shed from t h e t r a i l i n g edge
of a s i n g l e cyclogi ro opera t ing a t a t i p speed r a t i o of X = 2.
This s h e e t is a p r o l a t e cyc lo ida l s u r f a c e , and t h e v o r t i c i t y i n
t h e s h e e t v a r i e s both ac ross t h e span (due t o three-dimensional
loading) and cont inuously along t h e shee t due t o t h e d r y i n g
r e s u l t a n t v e l o c i t y a t t h e blade. The p a r a l l e l s t r a i g h t l i n e s
d iagonal ly o r i e n t e d i n Figure A.2 r ep resen t t h e continuously shed
spanwise v o r t i c i t y due t o t h e changing ,veloci ty . , The heavy
diagonal l i n e s r ep resen t i n t e n s e concentrated v o r t i c i t y due t o
a n . assumed ins tantaneous r e v e r s a l i n angle of a t t a c k . The
streamwise prolat? c y c l o i d a l l i n e s r e p r e s e n t spanwise v a r i a t i o n
i n me v o r t i c i t y shed i n a .streamwise d i r e c t i o n assoc ia ted wi th t h e
var i+le . ' loading ac ross t h e span. I n t h e c e n t e r t h e v o r t i c i t y , : i s nea r ik cons tan t i n t h e spanwise .d i rec t ion , but as t h e t i p i s
approached t h e spanwise v o r t i c i t y changes r a p i d l y due t o shedding,
and t h e streamw4se l i n e s a r e c l o s e r together . There i s a s t r o n g
streamwise .vor tex a t each t i p due t o t h e very r a p i d change of
s p a n w i s e . v o r t i c i t y near t h e t i p requi red t o s a t i s f y t h e t i p
preslsure condi t ions. This s h e e t i s modeled a f t e r P r a n d t l ' s th ree -
dimensional wing theory. 57 The problem is t o f i n d a p o t e n t i a l ,
funct ion which s a t i s f i e s t h e boundary condi t ions and .which gi.ves
t h e c o r r e c t l i f t and drag of t h e system.
A r i g i d c y c l o i d a l wake was assumed s i n c e i t s shape
could be computed. I f a p r o l a t e c y c l o i d a l wake occurred, t h e wake
i n t e r s e c t e d i t s e l f f o r a s i n g l e b lade , while m u l t i p l e blades had
mul t ip le i n t e r s e c t i o n s . Each i n t e r s e c t i o n was a s i n g u l a r p o i n t ,
and t h e p o t e n t i a l would be mult ivalued with m u l t i p l e connected
regions. In add i t ion , t h e p o t e n t i a l would be t i m e dependent. I f
t h e wake was a c u r a t e cyc lo id , a s i n g l e b lade would be s i n g l e
valued, but mul t ip le b lades would have mul t ip le connected regions
and s i n g u l a r p o i n t s a t each i n t e r s e c t i o n . A l l s o l u t i o n s would
be time dependent. The prospect of f ind ing a p o t e n t i a l s o l u t i o n
was remote. It it could be found, it would have t o be extended
piecewise from region t o region which would p resen t enormous
cornpu ta t iu~~ pr'oblems. 285
F'icure A-2. T r a i l i n g Vortex Shee t Array of One Blade.
A second approach was t o start wi th t h e Helmholtz
vor tex laws58 and t o w r i t e i n t e g r a l s a s P r a n d t l had done i n wing
theory. I n t h i s approach, t h e r o t o r would be s t a r t e d impulsively
and t h e wake allowed t o develop i n a step-by-step manner.
D i f f e r e n t i o - i n t e g r a l equat ions would r e s u l t which could be so lved
by f i n i t e d i f f e r e n c e techniques. The complete problem requ i red
a spanwise d i s t r i b u t i o n of v o r t i c i t y t o be used. An e l l i p t i c a l
loading o r a Schrenk approximation would be used, but the re :was
no j u s t i f i c a t i o n f o r e i t h e r assumption. The problem was formulated,
but when a computer program was w r i t t e n , t h e computing t ime was
found t o be .excess ive and not f e a s i b l e . To s impl i fy the .problem
a uniform loading was assumed. Even t h i s s i m p l i f i c a t i o n requ i red
excess ive computing time. Because of t h e need f o r a usable theory
i n a s . shor t a t ime a s poss ib le , an acceptable approximation w a s
needed.
An examination of t h e s t r e n g t h of t h e v o r t i c i t y shed
i n t h e wake a s t h e blade moved around t h e circle was made us ing
i d e a l b lade ' theory . A t t h e b lade f l i p p o i n t s , t h e v o r t i c i t y shed
is twice t h e l o c a l value, and i s given by
(which is represented i n normalized form i n Figure A.3) and t h e
r a t i o of t h e l o c a l v o r t i c i t y shed t o t h e v o r t i c i t y shed a t b lade
f l i p becomes i n magnitude:
where A is t h e l o c a l phase angle and B i s t h e phase angle a t
blade f l i p , o r e c c e n t r i c i t y angle. For t h e i d e a l windmill, 'lr B=kn/2 f o r t h e f l i p po in t s . Choosing B= - t o ob ta in t h e
maximum, t h i s reduces t o t h e fol lowing f o r cons tan t CL, which i s
p l o t t e d i n Figure A. 4 : 2 87
F i g u r e A . 3 . Ncn6imensional ized I E e z l Eound Vor tex S t r e n g t h as a F u n c t i o n o f Phase Angle Around t h e O r b i t f o r X = 2 .
Figure A.4. Nondimensionalized Ideal Bound Vortex Rate 0 5 Shedding as a Function of Phase Angle due to Change in Resultant Velocity at X = 2.
1 dl: -A Cos$ I I'r max 2 (l+~) 4 1 + - 2 ~ ~ i n $ I
This shed vorticity is small compared to the concentrated vorticity
and is referred toas the distributed vorticity. It may be shown
that the distributed vorticity has a maximum for X < 1, when Sin $
= A, and for A > 1 when Sin $= 1/A, The corresponding value of
the maximums are X < 1,
These occur in the lower half of the circle near the lower con-
centrated vortex. It is symmetrical with respect to the Z axis. 'lT The distributed vorticity is zero at $= - - 2 and gradually
increases in magnitude to the maximum in the lower half of the
circle, and then decreases in magnitude until it is zero at $ = ~/2. A plot of the magnitude of k h e distributed vorticity
shows that there is more in the lower half of wake than in the
upper half. Depending on B , the distributed vorticity is usually
of the same sign as the lower concentrated vorticity. When f3 = T . l'r
C-
2 u~ , the sum of the lower concentrated vorticity and the distributed vorticity is equal in magnitude and opposite in sign
to the upper concentrated vorticity. This satisfies the irro-
tationality condition for the undisturbed flow in two dimensions. For other values of p , there are some regions where the distributed
vorticity has the same sign as the upper concentrated vorticity,
and the magnitude of the sums of opposite sign vorticity is again
equal so that irrotationality is again satisfied.
1 -A I 2 m and A > 1,
The motion of t h e two.unequa1 v o r t i c e s i n two
dimensions i n a f l u i d a t r e s t is i n c i r c u l a r pa ths about a common
c e n t e r whose l o c a t i o n depends upon t h e magnitude and s i g n of
v o r t i c i t y . I f they are equal i n magnitude and oppos i te r o t a t i o n ,
t h e . v o r t e x p a i r w i l l t r a n s l a t e a t uniform v e l o c i t y along s t r a i g h t
p a r a l l e l l i n e s . It can be shown t h a t i f t h e r e i s a f i n i t e number
of d i s c r e t e v o r t i c e s i n an undisturbed f l u i d a t rest, then each vor tex w i l l t end t o r o t a t e i n a c i r c u l a r pa th about t h e c e n t r o i d
of v o r t i c i t y and t h i s can be used t o deduce how a cycloidal-shaped
wake w i l l d i s t o r t .
I f t h e t o t a l v o r t i c i t y i s divided i n t o two p a r t s
which have a sum of equal magnitude t a k i n g i n t o account t h e alge-
b r a i c s i g n , t h e upper h a l f w i l l have v o r t i c i t y of both s i g n s
whkle t h e lower h a l f w i l l have v o r t i c i t y of t h e same s ign . Then,
c a l c u l a t e t h e c e n t r o i d of v o r t i c i t y of each h a l f , and it w i l l be
found t o l i e very c l o s e t o concentrated v o r t i c i t y of each h a l f .
The r e s u l t i n g motion w i l l t end t o be i n c i r c u l a r pa ths around ,
each cen t ro id . The motion w i l l n o t be c i r c u l a r , s i n c e each h a l f
w i l l t end t o i n f l u e n c e t h e motion of t h e o t h e r h a l f . A s a r e s u l t ,
t h e v o r t i c i t y tends t o ro l l -up around t h e c e n t r o i d of each h a l f ,
t o form two equal' and oppos i te v o r t i c i e s concent ra ted a t t h e
cen t ro id , bu t joined by s p i r a l i n g t h r e a d s of v o r t i c i t y which
decrease i n s t r e n g t h as t h e v o r t i c i e s rol l -up. This p a i r w i l l
then tend t o . t r a n s l a t e back toward t h e r o t o r which shed them,
bu t t h e ' f reestream t r a n s l a t e s them downstream. The n e t r e s u l t
is t h e rol led-up p a i r does no t t r a n s l a t e downstream a t t h e w,ind
speed, but a t a somewhat l e s s e r speed.
The r o t o r i s i n t h r e e dimensions, s o t h i s p a i r w i l l
be joined a t t h e t i p t o form an essentially rec tangu la r ring
which w i l l t end t o d i s t o r t t o a t o r o i d a l shape f a r downstream.
Because of s t r e n g t h of t h e concentrated v o r t i c i t y , ro l l -up begins
soon a f t e r t h e c.oncentrated vor tex i s shed, usua l ly wi th in one
diameter of t h e rotor. .
Larsen deduced t h i s s t r u c t u r e , l a t e r v e r i f i e d by
d e t a i l e d c a l c u l a t i o n s , and formulated h i s "Pr imi t ive Vortex Theory
of t h e Cyclogiro" on t h i s model of t h e wake. I t was r e a l i z e d
t h a t t h i s w a s n o t an exact model, bu t represented an approximation
t o t h e a c t u a l s t r u c t u r e of t h e wake.
McDonnell-Douglas, under t h e d i r e c t i o n of B r u l l e ,
used t h i s theory t o analyze t h e performance of t h e ' c y c l o g i r o which
used t h e wake model and t h e bound v o r t i c i e s t o compute t h e
i n d i v i d u a 1 , v e l o c i t y a t each blade. A wind tunne l model was b u i l t
and t e s t e d , and t h e r e s u l t s were i n e x c e l l e n t agreement with t h e
theory . 59
The following s e c t i o n s desc r ibe t h e b a s i c t h e o r i e s
behind t h e development of t h e P r imi t ive and t h e Improved Pr imi t ive
Vortex theory of t h e Cyclogiro, a s w e l l a s t h e a p p l i c a t i o n of t h i s
theory t o r o t a t i n g c y l i n d e r s i n o r d e r t o s tudy the.Madaras system.
SECTION A-2
FDEAL BLADE ELEMENT THEORY OF THE CYCLOGIRO
The ideal blade element theory of the cyclogiro assumes
that a lifting surface is rotating at constant angular velocity,
.52, in a c-ircular path about an axis of rotation in a constant
uniform parallel flow of magnitude, W, as illustrated in
Figure A. ,5 , 'It is assumed that aerodynamic coefficients obtained
in a uniform parallel flow are applicable to the rotating
lifting surface. Since these coefficients are functions of the
angle of attack of the lifting surface relative to the resultant.
velocity -at the blade'element, it is necessary to establish the
resultant velocity and angle of attack at the blade element.
The resultant velocity is the vector sum of the relative wind, W,
and the rotational velocity, V = QR, of the blade element or
the periphial velocity, V . ;;..
It is convenient to use the axis system shown in Figure ~ . 5
with the origin at the axis of rotation at the mid span location
of the blade, x pointing into the relative wind, W, z , downward,
and y out the right side of the rotor. A blade is located
instantaneously at the angle JI from the x axis. The angle $ is
referred to as the phase angle or the blade orbit angle, and the
circle on which the blade moves is referred to as the orbit. The X and Z components of the resultant relative velocity to the
blade are:
VX = V Sin I/J - W, and vz = -v Cos JI.
The resultant velocity, VR, is then:
V R = 4 ~ x 1 ~ + ( V Z I ~ = J ( v Sin JI- w I 2 + (-vcos $) 2
= J v 2 + w2 - 2 mi sin g = w /I + i2 - 2 sin o:,
where X = V/W the tip .speed ratio.
Figu re A . 5 . Ideal Blade Vector D i a g r a m .
The direction of the resuLtant velocity from the x axis is the
angle, 0, or,
-1 -1 0 = tan (Vz/VX) = tan (-V Cos $/ (V Sin $ - w)) .
The resultant velocity is the aerodynamic velocity
which produces the lift and drag forces on the blade. The lift
force is at right angles to the resultant velo.city, and the drag
force is parallel to and in the direction of the resultant
velocity. The direction of the lift force depends upon the angle
of attack, a, of the blade relative to the resultant velocity.
A positive angle of attack is measured counterclockwise from
the chord line of the blade to the resultant velocity.. This
corresponds to the lift leading the drag by 90' for positive a,
and lagging by 90' for negative a. The lift and drag forces
acting on the blade are illustrated in Figure A . 5 for a positive
angle of attack.
Determination of the performance of the rotor requires the
establishment of the dependence of the lift force generated by
the rotor or Z force normal to the relative wind, the thrust
force generated by the rotor, or x force parallel to the relative
wind , and the torque force normal to the radius ~ . f the blades or t force along the orbit as functions of the primary variables.
Since power is the product of force times velocity, the power
absorbed or generated by the rotor is the torque force times the
peiiphe,,ral velocity ., The instantaneous contribution of a blade
to each of these forces can be computed from the geometry in
Figure A - 5 . They are:
'IT FX = L Cos (@ + -) + D Cos ib = - L Sin @ + D Cos 0, 2
W FZ = L Sin (4 + -) + D Sin 4 = L Cos@+ D Sin@, 2
= L Sin ($ - 0) + DCos ( $ - $1,
71 FQ = L Sin ( $ - @ - T ) + D Sin ($ - $ 1
= - L Cos (9 - $I) .+ D Sin ($- @ ) .
Since 4 is a function of $ , these forces are all functions of $. Also, since L = C~ B v R ~ , 2 and D = CD V R ~ , and
d VR = W th + h2 - 2h Sin$ , and CL = ,- 'I, (a - aLo) , and CD = C (C 1 ,
da D L
these forceg are functions of $, w, h, and a or CL. Also,
S i n 4 = VZ/VR,= - A C0s $/ 4 1 + h2- 2hSin 111 , and Cos 4 = VX/VR =
(A sin $ -I)// 1 + h2 - 2h Sin$, it is possible after substitutionof these definitions and simplification of the results
to obtain explicit expression for the instantaneous values of
these forces. They are:
2 2 FX = W . CL . [A Cos $ + (CD/CL) (A Sin $-I)] Jl+A -2'1 Sin $ , 2
2 Fz = W , CL . [A Sin +-1 - (CD/cL) h Cos rV 1 )/ 1+X2-2X Sin J, ,
FQ = & w2. 2 2 C~ . [Cos $ + (cD/CL) ( h - Sin $)I d l + h - 2hSin $ .
For constant CL, CD, and A ' the instantnnanllr values of
these forces are functions $. Since d$= Qdt, the time average
value of these forces can be obtained by integrating around the
orbit, and from the mean value theorum of the integral calculus.
In the ideal theory no blade interference is assumed so that the
mean value is directly proportional to the number of blades, NB.
The time average values become:
2 where f (A,$) = 1 + A - 2ASina ,
Even with cons tan t s CL, CD, and A , t h e s e i n t e g r a l s cannot be
evalua ted i n d o s e d form due t o t h e presence of t h e r a d i c a l ,
and.numerica1 methods must be used. The i n t e g r a l of COS$ t imes fkhe
r ,adical ' can be evalua ted i n c losed form,, whi le t h e i n t e g r a l of s i n $
t i m e s t h e r a d i c a l cannot be evalua ted i n c losed form and must be
evalua ted numerical .1~. Inspect ion shows t h a t c e r t a i n t e r m s can
be evalua ted i n c losed form. Also, t h e mean. va lue theorum f o r t h e
i n t e g r a l of t h e product of two func t ions can be .used t o o b t a i n
approximate r e l a t i o n s which can i n d i c a t e t r ends . I f CL i s a ,
cons tan t , CD i s a cons tan t , and t h e mean value would be d i r e c t l y
p ropor t iona l t o CL. Thus, t o o b t a i n high l i f t and t h r u s t , h i g h '
l i f t c o e f f i c i e n t s should be used, and t h i s a l s o means high power
is r equ i red t o t u r n t h e rotor, or hi911 puwer would be e x t r a c t e d
by t h e r o t o r . F i n a l l y , t h e term NB PS w2 m u l t i p l i e s each i n t e g r a l .
Since a fo rce d iv ided by .-Z . 2 ps S g ives an aerodynamic
c o e f f i c i e n t which i s independent of s i .ze o r a c t u a l wind speed, i n
c o e f f i c i e n t form t h e s e i n t e g r a l s imply t h a t c o e f f i c i e n t s can be
obtained which depend only on CL, CD, and A . s i z e and wind speed
can be removed as long a s geometr ical s i m u l a r i t y i s maintained.
Thus, r o t o r s can be s c a l e d i n s i z e from one computation.
Because of the difficulty in evaluating the integrals, and
since- most investigators .assumed that air foils.would be used
for blades so that (CD/CL) << 1.0, the integrals we're simplified
by ignoring the drag contribution to the . integrals. . Numerical
evaluation was still re~uired in most cases. However, with this
simplification, and a can be evaluated in closed form, and lead to an understanding of the behavior of the rotor performance
and the necessity of lift coefficient reversal to obtain useful
thrust and torque. These integrals will be evaluated, and then
the mean value theorem will be utilized to show the effect of
the' drag term. This is particulary important for the Madaras rotor
which uses spinning cylinders which can generate very large values
of CL, but CL/CD is of the order of 3 to 5,which makes the drag
term important in each integral.
Neglecting the drag term and expressing the inte-g-ral in
coefficient form, the integral for the thrust coefficient behavior
becomes :
2IT
C F X = FX 2 w 2
1 + X - 2 Sin $ Cos +dl1 NB
2IT = - C~ 11. + x ~ - z x Sin $ 1 3/2 / 3 ZiY
0
assumed constant. Thus, if the lift coefficient is constant around
the orbit no thrust is developed . If it is assumed that the lift,
coefficient is reversed in sign at Jl = B and $ =n+ B so that CL >O
if IT + f3 < $ < ZIT+ £3, the .expression for CFX becomes with
I - cLI = IcL( and constant
7r+B CFX = - A J.1 + h2 - 2x sih $ cos q dq
+ LyB+ X X + A ~ - 2 ~ sin g 0 WW]
- {I + n2 -. 2~ Sin 6 1 3/2J
It is seen that if B > 0 .a positive thrust is developed, while'..if
< 0 a negative thrust is. developed. Thus, if the sign on CL is
re'versed at some angle B'thrust can be developed, and the control
of thrust is through the angle B . To reverse the lift coefficient,
the angle of attack must be made negative for B 5 $ < .rr + B, and the angle .of attack must be made positive for (IT + €3) 5 .$ < (27r +$.I . TO obtain a constant lcL 1, the blade must be maintained at a con-- stant angle relative to $ - Since + = tan-' (VZ/VX) = tan -1
(-V Cos$/ (V Sin $- W ) ) , the orientation of the blade must be
continuously varied as the blade traverses the orbit. At $ = 8
and JI = 7r .t 8 , the angle of attack must be reversed. This con-
tinual variation of blade orientation is referred to as blade
modulation, and the reversal of blade.angle of attack is
referred to as blade flip. Kirsten showed that the ideal blade
modulation could be achieved by the so called "swingir:~ $.l,i,ding block mechanism.." He devised mechanical means to accomp1ish:this.
In a similar manner, it can be shown that the torque force
coefficient can be found to be
- If B >O, CFQ > O f and power must 'be supplied to the rotor, -
while if B < 0, C F Q > 0, and power is extracted by the rotor. Thus - -
if B > 0 CFX:.> O., CFQ > 0, and the device is a propulsive device, - - while ifB< 0 CFX <O, C F Q < 0, and the device is a windmill which
extracts power from the airstream. -
Since V. FQ-is a power, the power coefficient becomes
C P = P = 121 {l + h2+2h sinf31~/~- {I + h2-2h Sin B} 3n [ 3/21 NP 9 w3 - -
= h CFQ = CFX
This ideal analysis provides some insight into. the perform- -.
ance of the rotor. The integral for CFZ which is the lift force
or side force of the rotor cannot be evaluated in closed form, but - if B 0, CFZ <'0, and if B < 0, CFZ ? 0. This is found from
numerical computation. It may also be shown that CFZ is a IT maximum in magnitude for f3 = kT . Thus, a lifting rotor could
take off vertically at f3= 0, and by making f3 > 0, could produce
'both lift and thrust with power input. The cyclogiro would then
behave much like a helicopter. It can be shown that in the
event of power failure, the rotor will autorotate, and a safe
landing is possible. Wind tunnel tests have verified this analysis.
The integrals for the aerodynamic coefficients can be
evaluated with the aid of the second mean value theorem of the
integral calculus. Because of blade modulation and mathematical
restriction on the mean value theorurn, piecewise integration is
required. The resulting expressions indicate the 'trends of the
coefficients,but are not convenient for application as numerical
integration is still required. The theorem states'
b b
a J f(x) g (XI dx = f (6i) g (x) dr where f (6i) a
b - . -
(bla) f (x) dx. Where f (x) and g (x) are integrable,
a
and g(x) is always positive or always negative on the interval
(b-a) . Now:
0 L
whe're .'f , ( .A, $,I = 1 + A 2 - 2 Sinqand
C~ g ($1 = [XCos $ + (-) (XSin $-I) 1 , with blade modulation CL< 0
C~
if f3 - < $ 5 (IT+ @),and CL > O if ( + + a ) $ $ < (21i+B). It is necessary - -
to consider four intervals, B 5 $ ( IT, IT 5 $ L(IT+~), (IT+@ - < $ - <ZIT, and 27r J, - < ( 27r + 6). f ($) on each interval is evaluated by
numerical integration to give f ,f ($2) , f ($ j ) and f (q4) . The
algebraic sign of CL is used on each interval. The expression for -
CFX becomes with lcLl being constant and CD being positive and constant
2r - CFX = 2IT [f (q1)JIT- g($)d$ + f($3)s g(@)d$ + f ($4)
B ;I :
IT+B a. ,
2r+B
g . ($ ) d$] . . Substituking for g ($) , carrying out the
indicated integration, substituting limits, and simplifying, the - expression for CFX becomes
- lcLl CFX = - IT [f ($1) { XsinB
1 + f ( q 3 j {A Sin I3 -. , &I [n-8 +i(l+ COSB)~ 1
Inspection reveals that the drag term reduces the thrust - 620. When$= 0 , f ($2) = f ($4) = 0, and CFX becomes
This shows that drag causes a negative thrust at B= 0. n -
When .B = 2 f ( $ 1 =f (Y4) and f (q2) = f (g3) , and CFX becomes
Again, the drag term reduces the thrust from What it would
be at the ideal maximum thrust condition. Since f(ql) and f ($2) - increase with A, it is seen that CFX increases with A and CL and
is positive for B > 0. It is negative for B< 0 which can be determined from a similar computation.
- The expression for CFZ is found similarly and is
Note that at the same value of B, f (JI1), f (lU2), f(l13), and f(q4)
are the same for all the coefficients. This simplifies evaluation
of the coefficients. C ...
When B= 0, CFZ = If (JI1) (-2h+n)+f ( $ 3 ) (-2h-IT) 1 <O 2n
Note that the drag term does not affect CFZ at B= 0.
n When 8 = - 2 '
It may be inferred from this'that the drag term does not
affect the lift of the rotor.
The torque force coefficient, and hence -the power coefficient
is found similarly for B > 0 as:
- C CFQ = GI If ($lj {sin8 + I f l ( A (T-B) - (1 + CosB) 1 )
+ f($2) {SinB + 1 1 [AB- (1 + CosB ) 1)
The drag always makes a positive contribution to the torque
force, and hence increases the power required or reduces the power
extracted by a windmill. -
When: B= 0, CFQ = 2 .rr
IT - C When f3= I, CFQ = lL1 [f ($2) + 1(q2) 1 (2 + An ) 2lT C~
lT - m e n B= - C~ 2 , cFQ = lCL1 2n + fit2)] (-2 +Anjq/).
This analysis shows that when drag is present that the drag
contribution causes a negative increment in the thrust, a positive
increment in the torque, and hence power, and has no effect on the lT lift at B = 0 or rq , but may havean effect on the lift at other
values of B. If ICD/CLlis large and cannot be neglected, the
performance of the rotor is seriously degraded. 303
The fact that thrust and lift are generated by the rotor
shows that the ideal theory is incorrect. The momentum theorem
of fluid mechanics requires that if a force is generated on a
body immersed in a fluid that the fluid passing around the body
be given an increment of velocity in the opposite direction of
the force generated. The flow field 'is distsibuked. in all directions
out to infinity, and the assumption of a uniform parallel flow
through the rotor is not valid. The disturbances created by the
body are not uniform or constant, but vary throughout the flow.
The momentum theory of propellers assumed a thin actuator
disc and assumed a wake to exist behind the disc. The stream tube which passed through the disc was assumed to contract in the
direction of the flow. It was found that one-half of the final
velocity increment in the wake occurred prior to the flow
reaching the disc, and one-half after passing through the disc.
Similarly in Prandtl's wing theory, one-half the induced velocity
occurred prior to the wing and one-half after the flow passed the
wing. This led researchers in cyclogiro theory to make a similar
assumption about the flow through a cyclogiro. If the force on a
body is known, the final velocity increment in the wake can be
computed easily from the momentum theorem. Because of the linearity
of the equations, it is possib1.e to use components of the force.
The first correction to the ideal theory used these concepts.
FX and were computed from the ideal theory with no correction.
These forces were then used to compute the X and Z components of the final velocity increment in the wake. It was assumed that o'ne-half
the final velocity increment in the wake occurred at the rotor.
It was further assumed that the velocity increment at the rotor was
uniform and constant throughout the rotor. If WX is the X component
of velocity at the rotor and WZ the Z component of velocity at the
rotor, then the resultant velocity components at the rotor become
VX = V Sin 9- W + WX, and VZ = -V Cos$ + WZ so that
2 2 2 V R ~ = w +V +WX +wz2 -~v(w-WX) Sin $-2 (W wx + v WZ) ~osq.
.Let A= V/W, g = WX/W, .$= WZ/W. Then,
2 : V R ~ = W [ (1- 0 + X2 + <2 - 2 { (1- 5) Sin$ + g~os$l] and
= tan -1 - 'XCos $+ < - (1-'6) + Sin$ VZ and CosJl = - and Sin$ = - VR VX as VR
before. Following the same procedures as before, one finds:
CFX = 2r[~L (hCos$- <Sin$) - CD ( (1-6) Cos$ - <Sin$) 1
41-o2 + h2 + G* - zx [(I-5) Sin @ + COS$ 1
- CFQ = 'J ICL( (1-S) Cos $- <Sin$ ) + CD (A- (1-5) Sin $+ <Cos ) 1
2a 0
2lT - CFR = -. [ [cL(1- (1- 5) Sin $+ <Cos$) - ~ ~ ( ( l - ~ ) cos $- sing) I 2lT
These integrals are considerably more complex than in the
ideal theory, and none can be evaluated in closed form. The mean
values theorem can be used as before, but the results are somewhat
-3re complicated and will not be shown. Basically, the rotor per- -3rmance has the same character as before, but the performance is
degraded. Thrust is less, lift is less, and llower required is
greater. The reason is that the lift and drag forces are rotated
from the ideal orientation in a direction which produces those
effects.
An iterative procedure was used to find the aerodynamic
coefficients as defined by these integrals. For a given A, 8 , CL, - and CD, FX and W werecomputed from the ideal theory. WX and WZ
were then computed from the momentum theorem, and Sand n deter- mined. The aerodynamic coefficients were then computed from the
integrals with Sand TI corrections. Since = W~XNB and - 2 2 FZ = CFZ W. NB;. F X and FZ wero t h e n computed. R nedond
value o f WX and WZ were computed, and new values of'6and n computed. The procedure was repeated until WX and WZ were computed
to an acceptable accuracy. It required five to sixiteratidns
to achieve 1 percent accuracy. This procedure was accomplished
by manual calculations and was extremely laborious. Eight to
16 points were used on the orbit tp reduce the ampunt of effort
required'.. Th.e results. we.re in good agreement wi.th 'test .results
both. qualitatively and quantktatively, but over estimated the
performance actually achieved.
It wao rccogniccd that thcrc wcrc ocriouo dcficicncica in
this attempt to compute the performance. The assumption of con-
stant uniform values of WX and WZ around the orbit was not a valid
assumption. Because of the finite roto,r radius WX and.WZ would be different at all points on the orbit. The flow is curvelinear
and the use of CL and CD obtained in uniform parallel was
questionable. The flow was clearly nonsteady and tended to be
oscillatory through the rotor. In addition, mutual interference
and interferen'ce 'of .the. wake 'was .negle.cted. The rotor .is actually
three' dimensional, and these..'theories- assumed .that a l l of the blade
experienced the same. .velocity. This assumed two d'imensional flow, or
strip theory. Finally, the effect of any blade support structure
had been neglected. Kirsten assumed cantilever blades from
the side of a fuselage.
In spite of all these deficiencies, the results were
encouraging enough that the cyclogiro was seriously considered
f o r a f i g h t e r a i r c r a f t design i n World War 11, b u t mechanical
v i b r a t i o n and s t r u c t u r a l problems te rmina ted t h e e f f o r t a f t e r
two yea r s .
SECTION A-3
PRIMITIVE VORTEX THEORY OF THE CYCLOGIRO
Larsen reviewed t h e e x i s t i n g theory of t h e cyclogi ro , and
concluded t h a t it would be necessary t o use vor tex theory t o
s imula te t h e b lades a s P r a n d t l had done i n wing theory and
Golds te in had done i n p r o p e l l e r theory. This would permit com-
p u t a t i o n of t h e induced v e l o c i t i e s a t a l l p o i n t s on t h e o r b i t .
The problem was exceedingly complicated. Kirs ten had shown that
t h e path of t h e b lade r e l a t i v e t o t h e air was a prolate cyclo id ,
cyc lo id , o r c u r a t e cyc lo id dependent upon t h e va lue of A . Tn
a d d i t i o n , s i n c e a number of b lades would be used, t h e cyclo ids
i n t e r s e c t e d . This c r e a t e d s i n g u l a r i t y and mult ivalued funct ions .
P r a n d t l had asstuned t h a t t h e vor tex s h e e t shed from t h e wing
was p lane and r i g i d i n v i o l a t i o n of t h e Helmholtz vor t ex laws.
This was j u s t i f i e d on t h e argument t h a t t h e induced v e l o c i t i e s
w e r e smal l , and i n o r d e r t o l i n e a r i z e t h e equat ions it was
necessary. Analysis shows thlat t h e cen t ro id . of v o r t i c i t y
remains f i x e d , bu t t h e vor tex s h e e t is uns tab le and ro l l s -up
t o form two concent ra ted t r a i l i n g v o r t i c e s loca ted a t t h e spanwise
c e n t r o i d of v o r t i c i t y . Flow v i s u a l i z a t i o n techniques c l e a r l y
demonstrate t h i s phenomena i n wind tunne l t e s t s .
Golds te in assumed t h a t t h e vor tex s h e e t shed from t h e
b lades of a p r o p e l l e r was r i g i d , t r a n s l a t e d a t uniform v e l o c i t y ,
and being l i g h t l y loaded d i d no t c o n t r a c t . Bas ica l ly , h i s
assumptiolls a r e v a l i d f a r downstream from t h e p r o p e l l e r . The
v o r t e x s h e e t t r a i l i n g from a p r o p e l l e r i s no t s t a b l e , and w i l l
r o l l - u p s i m i l a r t o t h a t t r a i l i n g behind a wing. Because of t h e
t h r e e dimensional n a t u r e of t h e problem, t h e f i n a l conf igura t ion
i s n o t known. The r i g i d s h e e t would be a h e l i x . I f t h e s h e e t
rol led-up t o t h e cen t ro id of v o r t i c i t y , it would form a con-
c e n t r a t e d h e l i c a l vor t ex , one f o r each blade, How t h e s e m u l t i p l e
h e l i c a l v o r t i c e s would i n t e r a c t i s unknown, but t h e r e is some
experimental evidence t h a t t h e wake u l t i m a t e l y formed i s a s e r i e s
of equa l ly spaced t o r o i d a l vor t ex r i n g s joined by h e l i c a l
v o r t i c i e s of vanishing s t r e n g t h a s t ime progresses . This s t r u c t u r e
occurs f a r from t h e p r o p e l l e r and i s t h e r e s u l t of t h e c u r v e l i n e a r
a x i s of t h e vor tex , v i s c o s i t y , turbulence , and compress ib i l i ty .
Unfortunately, t h e equat ions cannot be solved because they a r e
nonl inear , but s o l u t i o n s obtained from s teady s t a t e l i n e a r
equat ions suggest t h a t a l l t h e s e e f f e c t s a r e p resen t and a f f e c t
t h e f i n a l s t r u c t u r e .
The s t r u c t u r e of vortex'wake f o r a cyc log i ro i s complicated
because i t i s nonsteady, nonr ig id , c u r v e l i n e a r , nonuniform, and
has regions of h ighly concentrated v o r t i c i t y a t t h e l i f t c o e f f i c i e n t
r e v e r s a l o r b lade f l i p poin ts . I f t h e wake s t r u c t u r e i s known,
t h e induced v e l o c i t i e s can be computed from t h e geometry and t h e
Biot-Savart law. I f t h e s t r u c t u r e i s unknown, t h e Helmholtz
vor tex laws, t h e equat ions of motion, and t h e Biot-Savart law can
be used t o compute t h e s t r u c t u r e and t h e induced v e l o c i t i e s a s
funct ions of time. Hopeully, a s t eady-s ta t e s o l u t i o n would
r e s u l t a f t e r t h e t r a n s i e n t s had d ied out . It is necessary t o
review vor tex p r o p e r t i e s i n o rde r t o understand t h e problem.
Associated with each increment of length of a vor t ex
f i lament t h e r e i s an induced v e l o c i t y a t every po in t i n t h e f i e l d .
The induced v e l o c i t y and t h e vor tex f i lament co-exis t . One does
not c r e a t e t h e o the r . The induced v e l o c i t y i s computed from t h e
B i o t - ~ a v a r t law a L a paink r , as
where r is t h e r a d i u s vec to r from t h e element of v o r t i c i t y , d s i s
t h e incremental vec to r length of t h e element ,of v o r t i c i t y and r i s t h e s t r e n g t h o f , t h e element of v o r t i c i t y . rn s c a l a r f o r m
which g i v e s only t h e magnitude and no t d i r e c t i o n . B is t h e
ang le between t h e element of v o r t i c i t y and t h e r ad ius vec to r , r. T h i s equa t ion . shows t h a t t h e induced v e l o c i t y f i e l d a s soc ia ted
wi th t h e element of v o r t i c i t y I'ds is concen t r i c c i r c l e s about 'IT t h e a x i s d s , t h e maximum v e l o c i t y occurs when B = - 2 and decreases
t o 0 a t B = 0. This means t h a t i f t h e vor tex i s c u r v e l i n e a r ,
t h e v o r t e x w i l l induce v e l o c i t i e s on i t s e l f a t any p o i n t where
B f 0.
Helmholtz sys temat ica l ly s t u d i e d v o r t i c e s and developed
theorems which desc r ibe t h e i r p r o p e r t i e s . They are:
1. The s t r e n g t h o f a vor t ex f i lament is cons tant along
i t s length .
2. A vor t ex f i lament cannot end i n a f l u i d , it must
extend t o t h e boundaries of t h e f lu id o r form a c losed path.
3. I n t h e absence of r o t a t i o n a l e x t e r n a l f o r c e s , a f l u i d
t h a t is i n i t i a l l y i r r o t a t i o n a l remains i r r o t a t i o n a l .
A c o r o l l a r y fol lows from Stokes theorem. I n t h e absence
of r o t a t i o n a l e x t e r n a l f o r c e s , i f t h e c i r c u l a t i o n around a path
enc los ing a d e f i n i t e group of p a r t i c l e s is i n i t i a l l y zero, it
w i l l remain zero.
Th i s also means t h a t i n t h e absence of r o t a t i o n a l e x t e r n a l
f o r c e s v o r t i c i t y remains a t t a c h e d t o t h e same p a r t i c l e s .
V o r t i c i e s have t h e a d d i t i o n a l proper ty t h a t i n t h e
absence of any t s a n s l a t o r y f o r c e they move wi th t h e looal velacity i n t h e flow.
I f t h e v o r t e x f i lament i s an i n f i n i t e l y lonq s t r a i g h t
l i n e , t h e flow i s two-dimensional, and t h e induced v e l n n i t y a t
any r a d i u s , r , i n a p lane normal t o t h e vor tex f i lament i s f o r
an imcompressible flow
The flow is concen t r i c c i r c l e s about t h e vor tex f i lament .
1s r * O , w+O, s o t h a t a t t h e f i lament t h e v e l o c i t y approaches
i n f i n i t y . It can be shown t h a t t h e flow i s i r r o t a t i o n a l every-
where except a t t h e f i lament . To cons t ruc t t h e vor tex s h e e t
t r a i l i n g behind a wing, it was necessary f o r P rand t l t o compute
t h e induced v e l o c i t y ' a t a po in t a s soc ia ted with an a r b i t r a r y
s t r a i g h t 1 i n e . f i n i t e length vor tex f i lament segment. This i s
obtained by i n t e g r a t i n g t h e Biot-Savart law over t h e length of
t h e segment. The r e s u l t is:
where w i s t h e induced v e l o c i t y a t t h e p o i n t , p , .h i s t h e normal P
d i s t a n c e from p t o t h e vor tex f i l ament , and a and 6 a,re t h e angles
between t h e l i n e of t h e vor tex f i l ament , and l i n e s jo in ing t h e
po in t p t o t h e efr t remit ies of t h e f i l w n t . This i s i l l u s t r a t e d
i n Figure A . 6 . A f i n i t e length segment v i o l a t e s t h e Helmholtz
vor tex theorems, hub can be used t o r ep resen t t h e bound vor tex
i n a wing, o r t o c o n s t r u c t a polygonal a r c t o approximate cutve-
l i n e a r flow with. .a f i n i t e number of segments. Of p a r t i c u l a r
i n t e r e s t i s the. problem of determining t h e v e l o c i t y a t t h e end of
a semi- inf in i te s t r a i g h t l i n e segment of a vor t ex f i l ament f & r
which a= 90° and B= 0. The r e s u l t is :
which. i s one-half t h e value fortwo-dimensiona.1 flow.
This r e s u l t was used by P r a n d t l i n computing t h e downwash
a t a wing due t o t h e t r a i l i n g p lane r i g i d vor tex s h e e t by
i n t e g r a t i n g ac ross t h e span.
The i n f i n i t e v e l o c i t y a t t h e f i lament impl ies t h a t f o r
incompressible flow and cons tant t o t a l energy t h a t a t a c e r t a i n
r ad ius t h e p ressu re would be zero, and f o r smal ler r a d i i t h e
p ressu re would be negat ive o r t h e f l u i d would have t o accept a
- A 6 - length of vortex segment
h = normal distance
P= arbitrary point Wp= induced velocity r = circulation
Figure A.6. Induced Velockty a t .an Arbitrary Point Associated . with .a F i n i t e Straight Line Segment o f . C i r c u l a t i o n , I
312
tension. This is impossible in a real fluid. The potential
vortex cannot actually simulate a real vortex, but is an excellent
approximation for the radius being large enough that the flow may
be considered incompressible.
0seen60 found a solution for the two-dimensional incom-
pressible 'viscous vortex in 1903. The solution is
r . 2 w =(--) [l-e -r /4ut p 2.rrr I
The velocity at a point P, w is seen to be a function of P'
r and t. At a given t, the velocity has a maximum at a radius rm,
when
That is, r = 1.120906423 It may also be shown that at a.
given t Wmax (rm)./wmax pot (rm) = 0.715331863. This is; the
maximum velocity in the Oseen vortex is 0.715331863 the velocity
at the same radius, circulation, and time as a potential vortex
at the radius for maximum velocity in an Oseen vortex. It may
also be shown that when r = 4.798525912 rm = RVO that wpot/wOseen
= 1 x 10-O. Thus, for r = 4.7985259128 rm, the velocity in the
Oseen vortex may be considered to be the same as that in the .
potential vortex. All the effects of viscosity may be considered
confined within the radius RVO. Outside that radius the flow
may be considered to be nonviscous. Figure A.7 is a nondimensional
plot of the velocity in an Oseen vortex and, for comparison, the
potential vortex. It is seen that near the axis of the vortex
the velocity increases nearly linearly with radius,,but the curve
is concave downward with gradually increasing' curvature. A maximum
velocity is reached at r/rm = 1.0. The curve continues to curve
downward and asymp,otically approaches an equilateral hyperbola.
At r = 4.798525912 fm, the curve may then be considered to be an
equilateral hyperbola. 313
RVOa RADIUS AT WHICH VlSCOSlf Y MAY BE NEGLECTED
0 0.4 0.8 1.2 1.6 20 2.4 2.8 t2 3.6 4.0 4.4 4.8 5; r 4rm
F i g u r e 2i.7. Ncnc ineas izmal ized V e l o c i t y Dis t r i ! ? .u t ion i n an Oneen Vor tex and P o t e n t i a l Vcr tex .
The Oseen vo r t ex ' i s an e x c e l l e n t approximation t o a r e a l
vor tex . I n s i d e of RVO t h e flow i s v i scous and r o t a t i o n a l . Out-
s i d e of RVO, t h e f low may be cons ide red p o t e n t i a l and t h e v e l o c i t y
computed from t h e p o t e n t i a l vo r t ex . V i s c o s i t y l i m i t s t h e maximum
v e l o c i t y . Evidence from developed to rnados i n d i c a t e t h a t t h e
maximum v e l o c i t y i n to rnados may r each t h e o r d e r of 400 mph. It
may be shown t h a t t h e maximum v e l o c i t y f o r a g iven c i r c u l a t i o n ,
r , dec reases as and t h e r a d i u s a t which t h e maximum v e l o c i t y
occurs i n c r e a s e s as c. I f r i s c o n s t a n t l i t h e Oseen v o r t e x
g r a d u a l l y decays a s t h e e f f e c t s of v i s c o s d t y propogate f a r t h e r
o u t i n t o t h e f l u i d a s RVO a l s o i n c r e a s e s as C a l c u l a t i o n s
show t h a t i f on ly v i s c o s i t y i s a c t i n g , Oseen v o r t i c e s are per-'
s i s t e n t . I t r e q u i r e s a s much as 4 8 hours f o r t h e maximum v e l o c i t y
t o decay t o 10 p e r c e n t of t h a t which occu r s s h o r t l y a f t e r t h e
v o r t e x i s s t a r t e d .
I n n a t u r e , real v o r t i c i e s are d i s s i p a t e d much more r a p i d l y .
This i s b e l i e v e d t o be due t o t u rbu lence which i s much more
powerful t han v i s c o s i t y i n d i s s i p a t i n g t h e vor tex . P r a n d t l ' s
mixing l e n g t h theo ry of t u r b u l e n c e and d a t a from t u r b u l e n t mixing
s o l u t i o n i n wakes and jets can be used t o estimate t h e e f f e c t of
t u rbu lence . When tu rbu lence i s used i n p l a c e of v i s c o s i t y
i n t h e Oseen s o l u t i o n , the ' t i m e f o r t h e maximum v e l o c i t y decay t o
10 p e r c e n t of t h a t which occurs s h o r t l y a f t e r s t a r t i n g i s from two
t o ' four hours . Measurements of t h e p e r s i s t e n c e of t r a i l i n g v o r t i c e s
l e f t by l a r g e a i r c r a f t i n f l i g h t v e r i f i e s t h a t p e r s i s t e n c e i s o f
t h e o r d e r of two t o f o u r hours . Thus, even w i t h t u r b u l e n c e t h e
v o r t i c i e s w i l l p e r s i s t f o r long p e r i o d s o f t i m e , and ex tend f a r
downstream from t h e i r p o i n t of o r i g i n . The Oseen s o l u t i o n i s
very u s e f u l . . .
The maximum v e l o c i t y which occu r s i n t o rnados raises t h e
q u a s t i o n o f t ,he i n f l u e n c e of c o m p r e s s i b i l i t y on v o r t e x s t r u c t u r e .
A t 400 mph, t h e e f f e c t s of c o m p r e s s i b i l i t y are beginn ing t o become
impor tan t . G. *. ~ a ~ l o r ~ l ob t a ined t h e s o l u t i o n f o r t h e non-
v i scous compress ible vo r t ex i n 1930. The r e s u l t i s :
and
s o t h a t
whcrc v i s t h e v r l u c i t y cor responding t o r o r p , Vmax i s t h e velo-
c i t y t h a t gas would ach ieve when exhaust.ing i n t o a vaauumi r i s
t h e c i r c u l a t i o n , and r is. t h e r a d i u s cor responding t o V and 1'
V when p= 0. For r < r , a p e r f e c t vacuum would e x i s t , r = max 5' t h e maximum v e l o c i t y would e x i s t , and p = p= 0. A t some c r i t i c a l * r a d i u s , r , t h e s o n i c v e l o c i t y i s reached. For r < r <r the ' flow
* 1 ' * i s s u p e r s o n i c , and f o r r > r t h e f low i s subsonic . When r >> r
t h e f low may be cons idered incompress ib le , and t h e incompress ib le
p o t e n t i a l s o l u t i o n may be used t o compute t h e v e l o c i t y i n t h e flow.
T a y l o r ' s compres s ib l e v o r t e x cannot e x i s t i n n a t u r e because of
t h e e f f e c t s o f v i s c o s i t y and t u r b u l e n c e , b u t t h e s o l u t i o n shows
t h a t t h e e f f e c t s of c o m p r e s s i b i l i t y may be cons ide red .tu be
conf ined t o a r e g i o n nea r t h e a x i s , and a t d i s t a n c e s far from
t h e a x i s t h a t t h e p o t e n t i a l s o l u t i o n may be used t o compute t h e
v e l o c i t y . I f (p/p,) = 0 . 9 9 , r/rl = 15 .78759774 .
The snl .u t i .nn for a v isaous , compress ible vortex has not been found, b u t i t s c h a r a c t e r may be i n f e r r e d from t h e 0seen
s o l u t i o n and t h e Tay lo r s o l u t i o n . V i s c o s i t y would n o t permit the
c r e a t i o n o f a vacuum a t t h e core and t h e v e l o c i t y d i s t r i b u t i o n
would resemble t h e Oseen s o l u t i o n . I f t h e s o n i c v e l o c i t y were
reached i n t h e f low, it would probably occur a t t h e ,maximum v e l o c i t y ; o t h e r w i s e , t h e r e wou1.d be subson ic c o r e , a supe r son ic
a n n u l a r r e g i o n , and a subson ic o u t e r reg ion . P r e s s u r e d i s -
t u rbance cou ld propogate a x i a l l y and r ad i a l l . y .on ly . l n t h e
subsonic regions , and t h e s e pressure d is turbances would c r e a t e
shock waves which would destroy t h e supersonic region. This may ' I
be t h e phenomena known a s "vortex bus t ing ." The s t a b l e con-
f i g u r a t i o n would be subsonic flow everywhere with t h e e f f e c t s
of v i s c o s i t y , turbulence , and compress ib i l i ty confined t o a
region near t h e a x i s of t h e vortex. Outside t h i s reg ion , t h e
p o t e n t i a l s o l u t i o n would be used t o compute t h e induced v e l o c i t y
.associa ted with t h e c i r c u l a t i o n . The vor tex would decay with .
t ime, grow i n s i z e , but p e r s i s t f o r r e l a t i v e l y long per iods of
time.
The d i s t r i b u t e d and concentrated v o r t i c i t y shed a t blade
f l i p po in t s i s d i s t r i b u t e d across t h e r o t o r from t h e upstream
s i d e t o t h e downstream s i d e . The blades i n t r a v e r s i n g t h e down-
s t ream s i d e of t h e r o t o r p e r i o d i c a l l y pass through t h e d i s t r i b u t e d
v o r t i c i t y and i n t e r a c t with t h e concentrated v o r t i c i t y . I f a
vor tex f i lament occurred, i n f i n i t e v e l o c i t i e s would occur as t h e
blade passed through t h e wake o r i n t e r a c t e d with t h e concentrated
v o r t i c i t y . This would cxeate both phys ica l and computing problems.
The bound vor tex i n t h e blade must follow t h e o r b i t a l o r c i r c u l a r
p a t h , while t h e v o r t i c e s i n t h e wake a r e f r e e t o move. The i n t e r -
ac t ion between t h e bound vor tex and any f r e e vor tex i s such t h a t
t h e f r e e vor tex would t end t o r o t a t e about t h e bound vor tex i n
a c i r c u l a r path r e l a t i v e t o t h e bound vortex. The f r e e vor tex
never comes i n con tac t with t h e bound vor tex , but may pass q u i t e
c l o s e t o t h e bound vortex. The f r e e concentrated v o r t i c e s can be
twice a s s t rong o r s t r o n g e r than t h e bound vortex. It can t h u s
induce very high v e l o c i t i e s on t h e bound vor tex which a f f e c t s t h e
magnitude and d i r e c t i o n of t h e r e s u l t a n t fo rce on t h e b lade , This
can cause l a r g e l o c a l v a r i a t i o n s i n t h e l o c a l fo rces a s we l l as
t h e i n t e g r a t e d r o t o r c h a r a c t e r i s t i c s .
The Oseen vor tex and t h e Taylor vor tex a r e u s e f u l i n
a s sess ing t h i s problem. A r e a l vor tex i s a combination of both.
Compressible e f f e c t s can and do e x i s t i n r e a l v o r t i c e s , but would
be confined t o a region near t h e ax i s . The Oseen vor tex shows t h a t
v i s c o s i t y , a l s o turbulence , l i m i t s compress ib i l i ty e f f e c t s and
p r e v e n t s t h e format ion o f a vacuum as a c o r e ; t h a t v i s cous
e f f e c t s are conf ined t o a f i n i t e a r e a n e a r t h e a x i s ; and t h a t
t h e maximum v e l o c i t y i s l i m i t e d . The Oseen v o r t e x a l s o shows
t h a t t h e v o r t e x grows i n a r e a w i t h t i m e , dec reases i n v e l o c i t y
w i t h t i m e , and i s p e r s i s t e n t .
The Oseen and Taylor v o r t i c e s can be used t o e s t i m a t e the
p h y s i c a l d imensions and v e l o c i t i e s i n t h e v i c i n i t y of t h e f r e e
c o n c e n t r a t e d v o r t i c e s i n t h e wake of a c y c l o g i r o dev ice . The
bound v o r t e x h a s a c i r c u a t i o n of
and t h e c o n c e n t r a t e d v o r t i c i t y h a s a va lue of t w i c e t h a t amount,
and t h e f r e e v o r t i c i t y has a c i r c u l a t i o n o f
IT The va lue of V a t t h e i n s t a n t t h e v o r t i c i t y i s shed when f3= fT
v=w ( X * l ) . To c o n s i d e r t h e wors t c a s e , t h e Madaras r o t o r can
ach ieve CL = 1 2 , S/b = 5.55 m and W = 11 m / s . The induced veloc: r i n a p o t e n t i a l v o r t e x i s w = - r ,ass=-
2rr 21~w '
F i r s t , compute t h e r a d i u s , r , f o r t h e Taylor v o r t e x a t
s t a n d a r d a tmospher ic c o n d i t i o n s , o f Tu = 518.6OR. The maximum
v e l o c i t y a i r can ach ieve when exhaus t ing i n t o a vacuum i s Vmax - -
To, w i t h Cp = 557 joules/Kg-OR. Then Vmax = 760m/s . I n
t h e Taylor v o r t e x , r occurs when p /po = 0, s o t h a t r = 'c . anr
But To = 12 x 5.56 x 11 = 733 rn2/sec s o t h a t rl = O.1Sm. max
Thus, i f t h e s e c o n d i t i o n s would e v e r be ach ieved , t h e r e would be
an a b s o l u t e vacuum co re approximately 0.15m i n r a d i u s . The
r a d i u s , r a t which p /po = 0.99, t h a t i s where c o m p r e s s i b i l i t y c cou ld be n e g l e c t e d rc = 15.79 rl = 2.4m. The v e l o c i t y a t t h i s
r a d i u s i s 4 8 m / s . S i m i l a r c a l c u l a t i o n s i n d i c a t e t h e p o t e n t i a l
v e l o c i t y a t . t h i s r a d i u s i s e s s e n t i a l l y i d e n t i c a l i n magnitude.
Thus, f o r t h i s very powerful vor tex , compressible e f f e c t s can be
ignored a t r a d i i g r e a t e r than 2 . 4 m from t h e c e n t e r of t h e vortex.
The region of inf luence of v i s c o s i t y f o r t h e Oseen vor tex
w i l l now be computed. I n t h e Oseen vor tex t h e maximum veloci ty
reached i s only 0.715 t imes t h e v e l o c i t y i n a p o t e n t i a l vor tex
of t h e same s t r e n g t h a t t h e same r a d i u s , rm. Thus, w = 0.715
w pot. Thus, i f we assume w Oseen = 152 m / s , then
This i s about 23 percent of t h e r a d i u s a t which compressible
e f f e c t s can be ignored. However, t h e r a d i u s a t , w h i c h viscous
e f f e c t s can be s a f e l y ignored is RVO = 4.80 rm = 2.6 m, which is
approximately t h e r a d i u s of t h e r o t a t i n g c y l i n d e r used f o r the.
Madaras r o t o r . The v e l o c i t y a t t h a t r a d i u s would be 44.5.m/s.
Fur ther , a t a d i s t a n c e of 91.5 m from t h i s vor t ex , t h e v e l o c i t y
induced by It would be 1.28 m/s .
The f r e e concentrated v o r t i c i e s are no t smal l , cause winds
having t o r n a d i c v e l o c i t y , and a r e p e r s i s t e n t . The v e l o c i t y f i e l d s
a s soc ia ted with t h e s e v o r t i c i e s extend over a cons iderable r a d i u s
before t h e induced v e l o c i t i e s a r e s m a l l . The p e r s i s t e n t wake
could present a hazard f a r downstream. There i s one f a c t o r which
probably w i l l a l l e v i a t e t h i s problem, and t h a t i s t i m e . Tay lo r ' s
s o l u t i o n does no t involve t ime, but assumes t h e vor tex e x i s t s i n
a compressible f l u i d , and desc r ibes r e l a t i o n s i n such a vortex.
The Oseen s o l u t i o n does involve t i m e ; it assumes a p o t e n t i a l
vo r t ex and t h a t t h e a s s o c i a t e d flow e x i s t s . p r i o r t o t i m e t = 0 ;
and desc r ibes how v o r t i c i t y is a l t e r e d by v i s c o s i t y as a func t ion
of time. Nei ther s o l u t i o n desc r ibes how t h e flow i s a c t u a l l y
i n i t i a t e d o r formed. That s o l u t i o n has never been found as it
r e q u i r e s t h e s o l u t i o n f o r an unsteady compressible v iscous flow.
One can only specu la te on t h e sequence of events . A f t e r
a vor tex i s shed from t h e su r face of a body, a s t a g n a t i o n p o i n t i s
e s t a b l i s h e d a t a p o i n t on t h e body determined by t h e combined flow
around t h e body and t h e r ecen t ly shed ad jacen t free vortex. The
f l u i d c a r r y i n g v o r t i c i t y g e n e r a t e d i n t h e boundary l a y e r tends t o
accumulate a t t h i s newly-formed s t agna t ion p o i n t , and it forms a
v o r t e x which i s he ld a t t h a t p o s i t i o n by t h e e x t e r n a l pressure i n
t h e flow s i n c e t h e i n t e r i o r of t h e vor tex has low pressure. A s
more f l u i d i s accumulated it c r e a t e s a bump on t h e body, and
p r e s s u r e s i g n a l s propogated a t t h e speed of sound a l t e r t h e t o t a l
f low p a t t e r n and e s t a b l i s h t h e induced v e l o c i t y f i e l d a s soc ia ted
wi th t h e vor tex . F l u i d accumulates and t h e c e n t e r of t h e vor tex
g radua l ly moves away from t h e body, and t h e vor tex begins t o
t r a n s l a t e t o t h e u l t i m a t e sepa ra t ion poin t . A t a c r i t i c a l s i z e
it s e p a r a t e s , and t h e core i s a compressible-viscaus Oseen vortex.
It may cont inue t c accumulate f l u i d and v o r t i c i t y from t h e boundary
l a y e r while i n t h e v i c i n i t y of t h e separa t ion po in t u n t i l it i s f i n a l l y pushed away by p ressu res . The core i s probably very
i n t e n s e , and t h e s o n i c v e l o c i t y may be reached i n t h e vortex.
Viscos i ty i s powerful enough due t o t h e l a r g e v e l o c i t y g rad ien t s
t o dominate .compressible e f f e c t s , and t h e f r e e vor tex decays s i m i l a r
t o an Oseen vortex.
P r a n d t l s t u d i e d t h e problem.using photographic techniques
which shows t h e process j u s t descr ibed. A c o l l e c t i o n of h i s photo-
graphs a r e shown i n Reference 6 2 . The s t a r t i n g process i s shown
i n t h e Reference i n Figures 2 4 t o 33 on pages 288 t o 292 . The
complete set of photographs from pages 279 t o 306 give a c l e a r
d e s c r i p t i o n of t h e vor tex flow assoc ia ted with separa t ion of flow
from bodies and t h e genera t ion of l i f t .
The eva lua t ion made f o r RVO shows t h a t t h i s r a d i u s can be
f a i r l y l a r g e , and t h a t ou t s ide t h a t r ad ius p o t e n t i a l flow can be
used s a f e l y without v iscous o r compressible e f f e c t s being important
enough t o cons ider . I f t h e wake i s ~ o n s i d e r e d ' r i ~ i d , RVO i s t h e
c l o s e s t approach a body can make t o a vor tex f o r t h e wake and
p o t e n t i a l flow used. I f t h e d i s t a n c e i s rm 5 d< - RVO, t h e Oseen
v o r t e x should be used, and compress ib i l i ty can s t i l l be neglected.
I f a body approaches rm, it i s s a f e t o assume t h a t it can ge t no
c l o s e r . This i s based upon t h e phys ica l f a c t t h a t i n t h e presence
~f bodies , v o r t i c e s move i n t h e flow a t t h e l o c a l v e l o c i t y , t h a t they
never a c t u a l l y touch a body, and a c t u a l l y move around it. This
f a c t and t h e Oseen vor t ex model was used t o compute t h e induced
' v e l o c i t y on t h e bound vor t ex when i n c l o s e p r ix imi ty t o a f r e e
vo r t ex i n t h e wake. I n t h i s manner s i n g u l a r p o i n t s w e r e awarded.
A. 3.2 Kutta'- Jouk'owsky Law.
~ u t t a ~ ~ and ~ o u k o w s k y ~ ~ showed independently t h a t i n two
dimensional flow. t h a t i f a c i r c u l a t i o n e x i s t e d about a body i n
a uniform flow t h a t t h e r e was a f o r c e a t r i g h t angles t o t h e
r e l a t i v e v e l o c i t y a s soc ia t ed wi th t h e c i r c u l a t i o n . . That is :
The magnitude of t h e f o r c e i s a s c a l a r a t r i g h t angles t o V and
r and i s F = pVr .
~ o u k o w s k ~ ~ ~ had developed a i r f o i l shapes by t ransforming
a c i r c l e ' i n t o an a i r f o i l , but found t h a t t h e r e was no l i f t o r
drag. When a c i r c u l a t i o n (corresponding t o a vo r t ex a t t h e c e n t e r
of t h e circle) was added, a l i f t was generated, b u t no d rag e x i s t e d .
This law has been extended t o t h r e e dimensions.
Assume a wing has uniform load ing of span b . Then
f o r a wing hsed a s a 1dXti-gg- element of a cyc logi ro .
It i s seen t h a t t h e magnitude o f t h e c i r c u l a t i o n depends
upon C o r a and V. Thus, a ch'ange i n a o r V w i l l change t h e L c i r c u l a t i o n . Now,
on t h e o r b i t of t h e c y c l o g i r o , s o t h a t i f CL i s h e l d c o n s t a n t
around t h e o r b i t , t h e c i r c u l a t i o n i s c o n t i n u a l l y changing. To
s a t i s f y t h e Helmholtz v o r t e x laws, spanwise v o r t i c i t y must be
c o n t i n u a l l y shed and pass downstream a t t h e l o c a l v e l o c i t y i n
t h e flow. Also, t o s a t i s f y t h e Helmholtz v o r t e x l a w s , t h i s shed
v o r t e x cannot end i n t h e f l u i d b u t must form a c l o s e d p a t h , and
must be jo ined t o t h e bound v o r t e x l o c a t e d i n t h e wing. Also,
a t t h e b l a d e f l i p p o i n t s , where t h e angle of a t t a c k i s r eve r sed ,
a s t r o n g c o n c e n t r a t e d v o r t e x would be shed. This shed v o r t e x
h a s a magnitude e q u a l t o t w i c e t h a t of t h e bound v o r t e x j u s t
p r i o r t o t h e t i m e of Shedding, and it has an oppos i t e r o t a t i o n .
I n between t h e f l i p p o i n t s , t h e r a t e of shedding i s s m a l l com-
pa red t o t h e shedding a t t h e f l i p p o i n t . T h e , v o r t e x shedding
w i l l be r e f e r r e d t o as t h e d i s t r i b u t e d v o r t i c i t y , and t h e shedding
a t t h e f l i p p o i n t s as t h e concen t r a t ed v o r t i c i t y . The r a t i o of
t h e concen t r a t ed v o r t i c i t y a t t h e f l i p p o i n t s i s
I t i s s e e n t h a t i f B f O , t h e magnitude of t h e doncent ra ted
v o r t i c i t y shed i s unequal and t h e d i f f e r e n c e becomes p rog res s ive l : Tr l a r q e r a s B approaches
kZ . Since each element o f v o r t i c i t y
w i l l be i nduc ing v e l o c i t y on every o t h e r e lement of v o r t i c i t y ,
t h e d i s t r i b u t e d and concen t r a t ed v o r t i c i t y w i l l move a long
w i t h t h e l o c a l v e l o c i t y which i s t h e v e c t o r sum o f t h e f r e e
stream v e l o c i t y and t h e t o t a l induced v e l o c i t y a t p o i n t .
T h i s causes t h e v o r t e x s h e e t t o d i s t o r t i n a spanwise and stream-
w i s e d i r e c t i o n . I t i s p o s s i b l e t o w r i t e d i f f e r e n t i o - i n t e g r a l
e q u a t i o n s which are t ime dependent t o d e s c r i b e t h i s motion, b u t
a c l o s e d s o l u t i o n i s not p o s s i b l e . An approximate s o l u t i o n can
be genera ted u s i n g f i n i t e e lement t echn iques , b u t t h e c o s t i n
computing t ime i s p r o h i b i t i v e , e s p e c i a l l y when spanwise l oad ing
i s cons idered . The t i m e i n c r e a s e s a s n2 + n, where n = number
o f b l a d e s x number o f spanwise s t a t i o n s x number o f p o i n t s i n
t h e wake. For example, a th ree-b laded r o t o r u s ing uniform
load ing , and 120 p o i n t s i n t h e wake p e r b l ade r e q u i r e d 6,000
seconds of CDC 6600 computer t i m e t o g e n e r a t e a wake s o l u t i o n .
This s o l u t i o n used p o i n t s 15' a p a r t on t h e o r b i t , and was n o t
cons idered a c c u r a t e enough t o compute t h e performance. I f lo
increment on t h e o r b i t had been used, 240 t i m e s t h e amount of
computing t i m e would have been r e q u i r e d .
This s o l u t i o n r evea l ed cons ide rab le q u a l i t a t i v e in format ion
on t h e s t r u c t u r e o f t h e wake. For t h e f i r s t t u r n nea r t h e r o t o r
t h e wake of each b l ade was n e a r l y c y c l o d i a l downstream t o t h e
p o s i t i o n o f t h e f i r s t lower concen t r a t ed v o r t e x a t which p o i n t
r o l l - u p o f t h e c l o s e l y spaced p o i n t s w a s beg inn ing t o become
appa ren t . The upper p a r t o f t h e wake had p o i n t s more widely spaced
and d i s t o r t i o n due t o ro l l -up w a s no t a s g r e a t . A f t e r t h e f i r s t
t u r n , d i s t o r t i o n from t h e c y c l o i d a l shape becomes p r o g r e s s i v e l y
g r e a t e r a s t h e wake tended t o r o l l - u p around t h e concen t r a t ed
v o r t i c i t y w i t h t h e d i s t r i b u t e d v o r t i c i t y t end ing t o form s t r a i g h t
l i n e s wi th widening spac ing between p o i n t s as t h e r o l l - u p
progressed . A f t e r two t u r n s t h e wake w a s n e a r l y concen t r a t ed
about t h e l o c a t i o n of t h e concen t r a t ed v o r t e x p o i n t s w i t h c~
n e a r l y uniform spac ing between t h e ro l l ed -up concen t r a t ed
v o r t i c i e s . The wake w a s forming h i g h l y concen t r a t ed v o r t i c e s
which occur red i n p a i r s c l o s e r spaced w i t h a s l i g h t l y l a r g e r d i s -
t a n c e between p a i r s i n t h e s t r e a n w i s e d i r e c t i o n . The wake became
wider a s it progressed downstream and t h e mean v e l o c i t y i n t h e
wake decreased . This s a t i s f i e d c o n t i n u i t y .
The behavior o f t h e wake i n t h e spanwise d i r e c t i o n w a s
p a r t i c u l a r l y i n t e r e s t i n g . I f t h e wake had been r i g i d , t h e t i p
j o i n i n g v o r t i c i e s would i n t e r s e c t . This d i d n o t happen i n t h e
f r e e wake. A s t h e wake approached t h e p o i n t o f i n t e r s e c t i o n , t h e
wake from t h e prev ious b l ade ( o r i f it formed a loop a s a t t h e
lower p a r t o f t h e wake f o r t h e p r o l a t e c y c l o i d ) moved inward
spanwise, and t h e most r ecen t ly formed wake moved outward span-
w i s e . T h i s occurred a t each wake i n t e r s e c t i o n . The wake widened
i n t h e spanwise d i r e c t i o n as it progressed downstream.
The wake t ends t o ro l l -up i n t h e spanwise d i r e c t i o n around
t h e po in t s of concent ra ted v o r t i c i t y , and t h e t i p - j o i n i n g v o r t i c e s
t end t o r o l l - u p along s t r a i g h t l i n e s jo in ing t h e spanwise con-
c e n t r a t e d v o r t i c i e s . This tends t o form a s e r i e s of gradual ly
i n c r e a s i n g r i n g s of v o r t i c i t y a s t h e wake progresses downstream
at. a vel..ocity which i s l e s s than t h e f rees t ream ve loc i ty . Near
t h e r o t o r t h e wake of each blade i s pseudo cyc lo ida l i n shape,
whi le f a r from t h e r o t o r t h e wake i s a series of e s s e n t i a l l y
oqual ly spaced r i n g s .
. . . . ... Larsen deduced t h e f a r f i e l d s t r u c t u r e of t h e wake from
cons idera tons of vor tex motions and t h e dominance of t h e con-
c e n t r a t e d v o r t i c i t y shed a t blade f l i p . He developed what he
c a l l e d t h e "Pr imi t ive Vortex Theory of t h e Cyclogiro" from t h i s
model of t h e wake, which he assumed t o he a s e r i e s of r i g i d r i n g s
of equal s i z e and s t r e n g t h which t r a n s l a t e d downstream a s t h e
r o t o r r o t a t e d a t a uniform v e l o c i t y computed from an a p p l i c a t i o n
of t h e momenteum theorem.
Figure A . 0 i s a slcetch of t h e r o t o r and wa.k,e model used i n t h e pr imat ive theory , and shows t h e r ec tangu la r r i n g s used t o
s imula te t h e wake. These a r e e s s e n t i a l l y t h e concentrated v o r t i c e s
shed a t angle of a t t a c k r e v e r s a l . The segments p a r a l l e l t o t h e
a x i s of t h e r o t o r a r e t h e v o r t i c i e s shed, and ' the segments a t r i g h t angles t o t h e s e a t e i t h e r end a r e r e f e r r e d t o a s t h e t i p
jo in ing v o r t i c i e s . The bound v o r t i c i e s f o r t h i s four-bladed
r o t o r a r e t h e spanwise l i n e r between t h e c i r c l e s . The bound
v o r t i c i e s were c losed with t i p jo in ing v o r t i c i e s along r a d i a l
l i n e s . No d i s t r i b u t e d v o r t i c e s were considered.
Figure A . 9 i s a flow f i e l d example computed with t h e
pr imative theory . The o r b i t of t h e r o t o r i s t h e c i r c l e a t t h e
c e n t e r of t h e axes. Figure A.9 i s a c ross s e c t i o n through t h e
p lane of symmetry a t t h e cen te r of t h e r o t o r . The concentrated
F i g u r e A. 8. Primitive Vortex Theory Rotor and Wake ~ r r a y Model.
1
i
R = 50 FT.(15.2m) B= 130 FT. (39.6m) SB=600SQ.FT.(55.8 m2) 4 BLhDES ALPHA= 12' BETA= -80° V.22 FT./SEC.(6.7m/s) RPM= 10. 125 KW
Tigure 24.9. Plow Field o.E a Giromill at Maximum Power.
v o r t i c i t y i s t h e a r r a y of c i r c u l a r a r c arrows which form t h e .
wake s i m i l a r t o a von Kaiman v o r t e x s t r u t . F ive v e l o c i t y pro-
f i l e s were computed one r o t o r r a d i u s a p a r t . These p r o f i l e s beg in
one r o t o r d iameter upstream, and extend t o one d iameter down-
s t ream of t h e r o t o r . The magnitude of t h e f r e e s t ream v e l o c i t y
i s t h e d i s t a n c e between t h e two v e r t i c a l p a r a l l e l l i n e s a t each
p r o f i l e . The induced v e l o c i t y due t o t h e wake i s t h e h o r i z o n t a l
d i s t a n c e between t h e l e f t v e r t i c a l l i n e a t each p r o f i l e . a n d t h e
heavy l i n e of t h e p r o f i l e . The Z component of induced v e l o c i t y can
be i n f e r r e d from t h e s l o p e of each of t h e r e s u l t a n t v e l o c i t y
v e c t o r s shown a t each p r o f i l e .
A t S t a t i o n A t h e wake dec reases t h e x component of v e l o c i t y
only a few pe rcen t . This e f f e c t i s f e l t f a r t o t h e s i d e of . .
t h e r o t o r . A t approximately t h r e e r a d i i t o e i t h e r s i d e t h e x
component of v e l o c i t y i s equa l t o f rees t ream. A t f u r t h e r l a t e r a l
d i s t a n c e s , i t i s g r e a t e r than f r e e s t r e a m as demanded by c o n t i n u i t y .
S t a t i o n B i s j u s t a t t h e f r o n t of t h e r o t o r . The v e l o c i t y
d e f e c t i s s t i l l sma l l , b u t a t approximately two r a d i i l a t e r a l l y
t h e v e l o c i t y becomes g r e a t e r t h a n f rees t ream. S l i g h t d ivergence of
t h e f low i s apparen t .
S t a t i o n C i s on t h e r o t o r ' s a x i s of r o t a t i o n . Here t h e
v e l o c i t y d e f e c t i s q u i t e l a r g e a t t h e c e n t e r of t h e r o t o r . A t t h e
in tersect ion of S t a t i o n C and t h e r o t o r o r b i t , t h e v e l o c i t y i s
almost f r ee s t r eam i n magnitude, bu t t h e v e l o c i t y v e c t o r has been
r o t a t e d s o t h a t t h e ang le of a t t a c k of t h e a i r f o i l h a s been
s e r i o u s l y . a l t e r e d . I n t h e r o t o r t h e f low i s d i v e r g e n t s o t h a t
p a r t of t h e f low pas ses o u t s i d e t h e wake between a d j a c e n t v o r t i c e s
t o s a t i s f y c o n t i n u i t y . Outs ide t h e wake, t h e v e l o c i t y is. con-
s i d e r a b l y g r e a t e r t han f r e e s t r e a m . ' This e f f e c t ex tends t o
i n f i n i t y b u t d i e s o u t a sympto t i ca l ly .
A t S t a t i o n D, t h e r e a r of t h e r o t o r , t h e v e l o c i t y d e f e c t
i s l a r g e , and flow divergence i s q u i t e pronounced. High l o c a l
d i s t o r t i o n nea r v o r t i c e s i n t h e wake i s apparen t . The v e l o c i t y
d e f e c t i s n e a r l y cons t an t a l l a c r o s s t h e wake. . .. -,
A t S t a t i o n E , two r a d i i from t h e c e n t e r of t h e r o t o r ,
t h e v e l o c i t y d e f e c t i s s t i l l i n c r e a s i n g , b u t d i s t o r t i o n o f t h e
p r o f i l e n e a r t h e concen t r a t ed v o r t i c i t y i n t h e wake i s occur r ing .
T h i s i s due t o t h e sidewash a s s o c i a t e d wi th t h e s i d e f o r c e on
t h e r o t o r .
C a l c u l a t i o n s show t h a t t h e f i n a l v e l o c i t y i n t h e wake is
n e a r l y reached i n one-diameter downstream from t h e c e n t e r o f t h e
r o t o r . This f i , g u r e i l l u s t r a t e s t h a t t h e v e l o c i t y d e f e c t i s
changing c o n t i n u a l l y through t h e r o t o r and t h a t s e r i o u s changes i n
the angle of a t t a c k occur. Thus, t h e assumption of uniform and
c o n s t a n t v e l o c i t y defect throilgh the r o t o r i s n o t j u s t i f i c d .
The flow i n F igu re A.9 i s f o r one i n s t a n t of t i m e . A s t h e
wakes con t inue t o ' p a s s downstream, c o n d i t i o n s are changing con-
t i n u o u s l y a t each p o i n t i n t h e flow. The theo ry t r a n s l a t e s t h e
wake, and computes t h e i n s t an t aneous v e l o c i t y and ang le of a t t a c k
a t each b lade . When t h e f o r c e s are i n t e g r a t e d around t h e o r b i t ,
. a t i m e average v a l u e i s obta ined .
F igu re A.10 p r e s e n t s r e s u l t s of u s ing t h e P r i m i t i v e Theory
t o p r e d i c t t h e X a x i s of a th ree-b laded q i r o m i l l as a f u n c t i o n of
t i p speed r a t i o , X . his r o t o r had a span-to-diameter r a t i o of
1 . 5 , and t h e chord t o r a d i u s r a t i o of CR = 0.1. The d a t a was
computed f o r a l i f t c o e f f i c i e n t of CL = 1.5 which i s nea r t h e
maximum ach ievab le a t Reynolds numbers which would occur i n
l a r g e r o t o r s . T h e d a t a has been nondimensionalized s o t h a t
s i z e and a c t u a l wind speed are no t impor tan t . The d a t a would apply
t o g e o m e t r i c a l l y s i m i l a r r o t o r s a t a1.1 wind speeds. S ince X =
2rnR/W, a~ W i n c r e a s e s , n musk increase p r o p o r t i o n a l l y it A i s
t o be c o n s t a n t .
The c o o r d i n a t e axes are chosen wi th t h e o r i g i n a t t h e
a x i s of rota t i011 a t t h e midspan s t a t i o n , t h e X-axis i s i n t h e
d i r e c t i o n of t h e wind f a r i n f r o n t of t h e r o t o r , t h e Y-axis is
a long t h e a x i s o f r o t a t i o n , and t h e z-axis Is t o t h e s i d e .
The f l i p p o i n t i s assumed t o be a t B = 7~/2 o r a long t h e Z-axis.
The theo ry and model used f o r computation was t h e P r i m i t i v e Vortex
Theory.
1.0 X X I
i 1 .O I I 1.5
U = INDUCED VELOCITY 2.5 ALONG X-AXIS
WHERE v, = U-W
I I 1 I 1 -- I I I I
2.0 1.5 1.0 0.5 0 - 0.5 4.0 - 1 5 - 2.0
Dl SlANC.E ALONG X-AXIS - X/R .
'. Z
* . .-
Figure A. 10. Variation of the x-~orn~onent of the ~esultant Velocity as a Function of X for a Three-Bladed Giromill.
__--- -- _ 3 - BLADED - --\, . GYROMI LL
FREE WIND VELOCITY STREAM /), R
W ROTOR ORBIT
x 4
Thus a series o f . r e c t a n g u l a r v o r t e x r i n g s whose s t r e n g t h
i s t h e mean v a l u e of v o r t i c i t y a t t h e f l i p p o i n t s forms a nes ted
r i n g of v o r t e x r i n g s extending downstream wi th a spacing between
a d j a c e n t r i n g s o f S = (2m/ANB) where NB i s t h e .number of blades.
These r i n g s induce a v e l o c i t y forward along t h e X-axis of magnitude
u. The wind is blowing toward t h e negat ive a x i s wi th a speed of
W. Since t h e s e two add v e c t o r i a l l y , t h e r e s u l t a n t v e l o c i t y along
t h e X-axis. is Vx = u-W. This is nondimensionalized by d iv id ing
by W s o t h a t
and i f Vx i s nega t ive , t h e wind blows along t h e p o s i t i v e X-axis.
I f Vx = 0, a l l t h e energy i n t h e wind would' be e x t r a c t e d , bu t a s
energy is e x t r a c t e d , , l e s s m a s s flow passes through t h e r o t o r s o
t h a t less t o t a l energy i s e x t r a c t e d . T h e o r e t i c a l l y , t h e g r e a t e s t
energy i s e x t r a c t e d a t t h e Ri tz l i m i t when t h e f i n a l v e l o c i t y i n
t h e wake is one- th i rd t h e wind .speed and hence 16/27 of t h e enerqy
i s recovered.
A t any, given X/R s t a t i o n on any of t h e curves of Figure X A. 10 (e. g. , at - = - - n5, A= 3 . 5 ) t h e ordinate distance f r o m t h e
X K - a x i s t o t h e curve i s equa l t o t h e magnitude of t h e l o c a l re- R X s u l t a n t v e l o c i t y r a t i o along t h e X-axis a t t h e given ?i s t a t i o n ;
i .e . , t h e d i s t a n c e equals Vx/W. A l s o , the distance from t h e
h o r i z o n t a l l i n e where 5 = 1.0 t o t h e p o i n t on t h e curve -
X W (E = -0.5, A = 3.3) i s t h e magnitude of t h e l o c a l induced v e l o c i t y
- - r a t i o n , V/W. The d o t t e d l i n e s show t h e leading and t r a i l i n g edge
of t h e . ro tor . I t is seen t h a t f o r each va lue of A , the r o t o r
e f f e c t s t h e wind speed f a r upstream from t h e r o t o r . A t t h e
l e a d i n g edge of t h e r o t o r , V .. . c W which means t h e "rocking angle" x of t h e b lade must b e l a r g e r than t h e i d e a l theory would p r e d i c t .
S ince Vx/W decreases very r a p i d l y as t h e wind passes through t h e
r o t o r and s i n c e , @ i g u r e . ~ . 9 i n d i c a t e s t h a t t h e r e s u l t a n t v e l o c i t y
r a t i o , Vx/W is almost cons tan t a c r o s s t h e r o t o r i n t h e Z d i r e c t i o ~
a t a given X/R, t h e induced v e l o c i t y changes t h e rocking angle
d i f f e r e n t l y a l l around t h e o r b i t . This is equiva lent t o P r a n d t l ' s
induced angle of a t t a c k i n three-dimensional wing theory. .If t h e
change i n rocking angle can be computed, two-dimensional a i r f o i l
d a t a can be used t o compute t h e l i f t and drag.
It i s noted t h a t a t each value of A , t h e f i n a l v e l o c i t y
i n t h e wake has been nea r ly reached a t t h e downstream edge of t h e
r o t o r . A s A i nc reases t h e r i n g s i n t h e wake a r e packed much
c l o s e r ' s i n c e t h e spacing i s i n v e r s e l y p ropor t iona l t o A . I n
a d d i t i o n , t h e mean c i r c u l a t i o n i n thewake i n c r e a s e s d i r e c t l y as A .
The combined e f f e c t s cause t h e r a p i d decrease of Vx/w a s A i nc reases .
A t A = 3.80., t h e f i n a l v e l o c i t y i n t h e wake i s zero. A s A i n c r e a s e s
t h e curves become smoother because of t h e c l o s e packing. A t low
values of A , V /W f l u c t u a t e s i n t h e wake s i n c e t h e spacing i s q u i t e X
la rge . The a c t u a l flow i s very s i m i l a r t o t h e von Karman vor tex
s t r e e t which causes t h e X component of v e l o c i t y t o f l u c t u a t e (e. g. , examine t h e curves f o r A = 1, 1 . 5 ) .
Since Vx < W a t a l l va lues of X/R, then by con t inu i ty .
t h i s flow must go somewhere, a s l e s s f l u i d i s i n t h e wake than i n
t h e freestream. This f l u i d flows around t h e r o t o r a s it would
flow around a s o l i d ob jec t l and t h e v e l o c i t y ou t s ide t h e wake is',
g r e a t e r than t h e f rees t ream v e l o c i t y . Since t h e v e l o c i t y cont inues
t o decrease i n t h e wake downstream of t h e r o t o r , t h e f l u i d cont inues
t o flow out of t h e wake between ad jacen t vor t ex r inqs . D e t a i l
c a l c u l a t i o n s of t h e y and z components of v e l o c i t y , v and w , v e r i f i e s
t h i s .
When U i s computed along t h e l i n e of v o r t i c e s a t Z = R and
y = b/2, it i s found t h a t t h e r i n g s do no t move a t t h e f r ees t r eam
v e l o c i t y , W, nor a t t h e v e l o c i t y Vx, bu t something c l o s e t o Vx.
There i s a l s o a v e l o c i t y which causes t h e wake t o expand. T h i s i s
very small before t h e flow out of t h e wake dominates. The wake
i s very nea r ly r i g i d .
The wake t r a n s l a t e s a t a v e l o c i t y r e l a t i v e t o t h e r o t o r .
The curves i n Fiqure A . l l a r e f o r one i n s t a n t of time and corres-
pond t o t h e f l i p p o i n t t ime, s o t h e f i r s t r i n g is a t t h e Z ax i s .
A s t h e b lades r o t a t e the . comple te wake t r a n s l a t e s e s s e n t i a l l y
.as a r i g i d body, and t h e d i s t a n c e between t h e p o i n t . a n d t h e ' wake increases ,and t h e l o c a l v e l o c i t y a t a p o i n t decreases .
This is equivalent t o . t h e p o i n t moving upstream i f t h e wake w e r e
s t a t i o n a r y . Whewthe next .blade f l i p s , t h e flow abrup t ly r e t u r n s t o condi t ions a s i n Figure A.11. This is unsteady.flow s i m i l a r t o
. . h e l i c o p t e r b lade f lapping.
The theory .accounts f o r t h i s unsteady e f f e c t by. t r a n s l a t i . n g t h e wake continuously., and because of t h e f i n i t e ramp angle i n t h e lift. reversal smooths o u t t h e abrupt b lade f l i p .
'The p r i m i t i v e theory was used by McDonnel1.-Douglas t o analyze . the performance' o f . t h e girorni l l . The r e s u l t s w e r e i n e x c e l l e n t agreement wi th wind tunne l tests:. Larsen recognized t h e l i m i t a t i o n s of t h e theory and continued t o t r y to . improve it. I n t h e proces's hel .developed an exac t theory inc luding a l l t h ree -
-.dimensional e f f e c t s , ground e f f e c t , and wind s h e a r o r nonuni fom. ' v e l o c i t y p r o f i l e . Blade mutual i n t e r f e r e n c e was included i n t h e
p r i m i t i v e theory a s w e l l . a s i n t h e exac t theory. However, t h e
p r o h i b i t i v e computation time f o r t h e e x a c t theory make i t s
a p p l i c a t i o n imprac t i ca l . Therefore, i n an e f f o r t . t o produce a
more exac t and u s e f u l theory than t h e p r i m i t i v e theory , Larsen
combined f e a t u r e s of t h e p r i m i t i v e and t h e e x a c t theory t o produce. a new approximate theory which he c a l l e d t h e Improved
Pr imi t ive Theory. This theory used axi approximation t o . t h e n e a r
. f i e l d , t h e far f i e l d r i n g approximation, a n d a n approximation f o r the. .widening o f . the . w a k e . .The computation t ime w a s found t o be
only s l i g h t l y g r e a t e r t h a n t h a t of t h e p r i m i t i v e theory , and
t h e r e s u l t s were bel ieved . t o be more accura te . The improved theory
has n o t been v e r i f i e d experimental ly , b u t 'it c o r r e c t s some of
t h e d e f i c i e n c i e s of t h e p r i m i t i v e theory.
This'.i.mproved theory w i l l be descr ibed i n t h e s e c t i o n s which follow.
SECTION A-4
IMPROVED PRIMITIVE VORTEX THEORY OF THE CYCLOGIRO
The improved p r i m i t i v e v o r t e x theory o f t h e cyc log i ro
assumes t h a t t h e wake is a series o f equal -s t rength , equa l ly
spaced concen t ra ted v o r t i c i e s arranged on an empi r i ca l ly widening
wake based on r e s u l t s o f t h e e x a c t theory . The widening i s i n
both t h e spanwise and lateral d i r e c t i o n . Each bound vor tex is
jo ined t o a concent ra ted v o r t e x i n t h e wake corresponding
t o the p o s i t i o n it h a s t r a n s l a t e d from t h e f l i p po in t . The up-
s t r e a m bound v o r t i c e s a r e joined t o concentrated vortices i n
t h e wake on t h e negat ive Z s i d e o f t h e wake on t o p of t h e r o t o r ,
and t h e downstream bound v o r t i c e s a r e joined t o concentrated
v o r t i c e s on t h e p o s i t i v e Z s i d e of t h e wake, o r bottom of t h e
r o t o r . The j o i n i n g v o r t i c i e s a r e assumed t o have a s t r e n g t h
e q u a l t o t h e l o c a l bound v o r t e x s t r e n g t h , and has a spanwise
c l o s i n g v o r t e x co inc iden t wi th t h e concent ra ted wake vortex.
Each vor tex segment i n t h e wake and i n t h e bound vor tex r i n g
sys tem is assumed t o be a s t r a i g h t l i n e . A l l v o r t i c e s i n t h e
wake t r a n s l a t e downstream a t a v e l o c i t y computed from a p p l i c a t i o n
o f t h e momentum theorem. This a r r a y i s an approximation t o t h e
conf igura t ion ob ta ined from t h e e x a c t theory , and does n o t
s a t i s f y a l l t h e requirements o f t h e Helmholtz Vortex laws.
The s t r e n g t h 'of t h e bound' and semibound system can be
computed, whi le t h e s t r e n g t h and l o c a t i o n o f . t h e f r e e v o r t i c e s
i n t h e wake is ,unknown., b u t is found .from an i t e r a t i v e corn-
p u t a t i o n . This is accomplished by computing = and = from t h e
i d e a l theory. The momentum .theorem i s then used t o compute t h e
f i n a l v e l o c i t y i n t h e wake. The wake widening i s computed, and
t h e emper ica l wake boundary determined. One-half the f i n a l
wake v e l o c i t y increment i s added t o t h e f r e e s t r eam v e l o c i t y
t o izompute t h e t r a n s l a t i o n a l velo.ci ty o f ' the wake and t h e
s p a c i n g . o f t h e free v o r t i c e s i n t h e wake. This l o c a t e s t h e
. f r ee ' v o r t i c e s i n . the wake, b u t t h e . ' s t r e n g t h of t h e ' f r e e
v o r t i c e s i's a s y e t unknown.
To compute t h e s t r e n g t h of t h e free v o r t i c e s , t n e mass
flow and momentm- f l u x through ' the cap tu re a r e a a r e computed.
The capture ' a r e a i s ' de f ined a s t h e produck:of the . span and t h e
chordl ine jo in ing t h e t r a i l i n g .edge o f t h e b lades a t t h e f l i p
po in t . The mass flow and momentum f l u x through t h e cap tu re area is computed a t a numb=r ~ f . . ~ o i n t s .aer.oss t h e capture az0.a and
i n t e g r a t e d ac ross t h e . cap tu re . a r e a ; and t h e .mean. value o f t h e
v e l o c i t y increment computed. This .mean .value must be equa l t o - t h e value computed from' t h e ' forces o n . t h e b lades , F X and x, and
t h e 'momentum theorem. The s t r e n g t h . ' o f . t h e f r e e v o r t i c e s i s
ad jus ted , and t h e 'problem i t e r a t e d u n t i l t h e increment o f v e l o c i t y
computed from t h e momntum theorem is wi th in a prescrkbed to le rance
o f t h a t . computed from t h e induced v e l o c i t y computed from t h e f r e e
wake and t h e bound-semi-bound v o r t e x system. When t h i s i s achieved,
t h e wake s t r u c t u r e 'and s t r e n g t h has .been determined. This wake'
s t r u c t u r e is t r a n s l a t e d downstream a s t h e r o t o r r o t a t e s . The
induced, v e l o c i t y a t each p o i n t on the' o r b i t can then be computed.
The l o c a l forces ' on each 'blade a r e then computed inc lud ing t h e
induced v e l o c i t i e s ' o f t h e wake and t h e mutual induced v e l o c i t i e s
due t o t h e boun'd-semibound vor tex system. I t e r a t i o n is requ i red
t o inc lude t h e mutual 'induced v e l o a i t i e s , and t h i s i t e r a t i o n con-
verges r a p i d l y , Once convergence t o .a predetermined t o l e r a n c e
has been achieved, t h e f i n a l performance i s computed. This whole
procedure has t o be' repea ted f o r each 'value of A , w, a , B , and
A used.
Subroutines' w e r e 'wr i t ten which computed s p e c i f i c d a t a
used i n t h e progr'am. Thes'e subrout ines i n some ins tance had
t o be modified f o r use 'of a i r f o i l b l ades o r sp inning r o t o r s and
poss ib le opt ions .
The b lade modulation scheme 'assum*. t h a t p o s i t i v e l i f t
occurred i f ( . ~ + f 3 . ) - < ' 9 - < '(21~+f3) and nega t ive l i ' f t if . . .
B - < JI 5 (IT +B). Since it i s impossible t o f l i p t h e b lade o r
reverse t h e d i re ' c t ion o f r o t a t i o n o f sp inning c y l i n d e r s ins t an -
taneously, a cons tan t deeel'eration-acceleration ramp occurred
a t each ' f l i p p o i n t , B and IT + 6. This occurred over a f i n i t e
phase angle , $, of width 2A. A i s c a l l e d t h e ramp angle. For
b l a d e s , t h e angle o f a t t a c k i s modulated and t h e subrout ine whLch
s p e c i f i e d t h e modulation was t h e subrout ine ALFA. This sub-
r o u t i n e a l s o permi t ted cons tan t geometric angle o f a t t a c k with
p a r a b o l i c v a r i a t i o n i n t h e acce lera t ion-decelera t ion ramp, con-
s t a n t e f f e c t i v e angle of a t t a c k , s i n s u o i d a l v a r i a t i o n o f angle
o f a t t a c k , o r r i g i d b lade ' s e t t i n g a s i n t h e Darr ieus r o t o r .
The Madaras r o t o r used sp inning r o t o r s , and t h e l i f t o f
t h e r o t o r depends upon t h e r a t i o of t h e pkrkpheral r o t a t i o n a l
v e l o c i t y o f t h e c y l i n d e r , U, t o t h e r e l a t i v e wind speed; i. e . U/V.
S ince UR' v a r i e s , t h e r o t o r v e l o c i t y U had t o be modulated. The
subrout ine UPVSR c o n t r o l l e d t h e r o t o r sp in mod~~l.at.i.on w i t h
appropr ia t e dece le ra t ion-acce le ra t ion ramps. Two opt ions were
a v a i l a b l e : cons tant ' U/V o r cons tant U.
The l i f t c o e f f i c i e n t CL and draq coeff ic ient . C a r e W f u n c t i o n s o f t h e ang le of a t t a c k a. The v a r i a t i o n o f CL and
CD f o r 360° angle o f a t t a c k has been found from wind tunnel-
Lests f o r t h e NACA0015 and o t h e r a i r f o i l s . Beyond t h e s t a l l i n
normal flow and reve r se flow, a nea r ly un ive r sa l curve occurs
f o r a l l a i r f o i l s . An empi r i ca l f i t was found t o f i t t h e da ta
to wi th in less than 1 percent . To allow f o r i n p u t , t he l i f t
c o e f f i c i e n t a t t h e end of t h e l i n e a r range and maximum l i f t
c o e l l i c i e n t i n normal flow and reverse flow, t h e zero l i f t drag
c o e f f i c i e n t , and increment o f drag c o e f f i c i e n t between zero l i f t
and end of t h e l i n e a r region a r e a l l t h a t i s necessary. A sub-
r o u t i n e CONS computes t h e cons tan t s used i n t h e subrout ine
TDCLCD which then computes CL and CD f o r any angle of a t t a c k
p o s i t i v e o r negat ive . That is, - 180" < a < 180°. - -
The l i f t c o e f f i c i e n t , CL, and the drag c o e f f i c i e n t , CD,
o f sp inn ing c y l i n d e r s was obta ined . from wind tunnel t e s t s con-
ducted a t t h e Univers i ty o f Michigan. They were found t o depend
upon t h e r a t i o of t h e c y l i n d e r p e r i p h e r a l v e l o c i t y , U , t o t h e
r e l a t i v e wind speed, V, o r U/V, and t h e a spec t r a t i o , A , and 3 36
t h e end. p l a t e r a t i o , e/d. It w a s found t h a t a piecewise .curve
fit could be 'used t o fit t h e test data i n t h r e e regions. For
U/V - < U/VCrit a pa rabo l i c approximation could be used. F o r
< U/V < U/Vmx. a q u a r t i c approximation cou ld be used. F o r U/vcr i t - - U/V . < U/V, CL and CD w e r e ' e s s e n t i a l l y cons tant . max - 'ivcri t i s d i f f e r e n t ' f o r CL and CD. Eleven cons tan t s have t o be
determined f o r both CL a n d CD. These: ' a re i n p u t d a t a t o t h e
program. I n use, U/V is. determined, and . t h e subrout ine MRCLCD
computes CL and CD f o r t h e a b s o l u t e value o f U/V,and t h e s i g n
on U/V determines t h e a l g e b r a i c s i g n o f CL. CD is always
pos i t ive ' .
The subrout ine 'VSIVCP (Vortex Segrnent Induced Veloci ty
Componen't .at the p o i n t P) computes t h e Car tes ian induced v e l o c i t y
components a t an a r b i t r a r y p o i n t P a s s o c i a t e d wi th a s t r a i g h t .
l i n e vor tex segment o f known s t r e n g t h whose. end. .poin ts a r e known r i n t h e r o t o r a x i s system. It uses w = ,h (Cos + Cos $2 ) ' .
This inc ludes t h e Oseen v o r t e x . f o r p o i n t s which have h ' < RVO.. . - This subrou t ine i s t h e h e a r t o f the program.
The subrou t ine NASVR (Number and S t reng th 'of Vortex Rings)
computes t h e n&er, s t r e n g t h , and .spacing .of t h e f r e e vor tex
r i n g s .which form . t h e wake w i t h 'wake 'widening ..included. . It. inc lpdes
t h e f r e e sys tem and the bound-semibound system, and computes t h e
wake s t r u c t u r e . 'based on. flow through t h e 'capture a rea .
The subrou t ine TRIVCO ( T r a n s l a t i n g Ring Induced Velocf t y
Components 'on t h e Orb i t ) .computes t h e Car tes ian induced v e l o c i t y
components a t each b lade 'on ..the o r b i t a s t h e r o t o r r o t a t e s . The
f r e e wake . i s t r a n s l a t e d downstream and widened a s t h e r o t o r
r o t a t e s . It assumes - the wake s t r u c t u r e computed from NAVSR, and
r e l o c a t e s each 'concentrated vor tex on t h e wake boundary as t h e
f r e e v o r t i c i e g t r a n s l a t e downstream wi th r o t o r r o t a t i o n .
The subrout ine 'TBIVCO ( T r a n s l a t i n g Bound Induced Veloci ty . .
Componen'ts 'on t h e Orb i t ) computes- t h e Car tes ian induced v e l o c i t y
components .of the mutual -induced - v e l o c i t i e s a s s o c i a t e d w i t h t h e
bound-semibound v o r t e x . s y s t e m . a t each p o i n t on t h e o r b i t a s t h e
r o t o r r o t a t e s . This uses t he bound vort i .ces and the r i ngs formed
by jo ining f r e e vor tex locations. .in the t r a n s l a t i n g wake
computed from NASVR including the wake widening e f f e c t .
The subrout ine BRING (Bound Ring) computes the Cartesian
induced ve loc i ty components a t an a r b i t r a r y po in t associa ted with
t h e vor tex r i n g f o m d by-. a bound .vortex, i t s . associa ted f r e e
vor tex i n t h e wake, and the ' t i p - joining vor t i ces , the end points
of each ' segmnt being known. It i s used by.TB.IVCO.to compute
t h e mutual induced v e l o c i t i e s on t h e o r b i t associa ted with the
bound-semibound vor tex system.
The subrout ine R I N G computes the Cartesian induced veloci ty
components assoc ia ted w i t h a f r e e vortex r i n g i n t he wake whose
s t r eng th and end po in t s .of each segment a r e known.. It is used w i t h
TRIVCO t o compute the. induced ve loc i ty components. associa ted with
t h e f r e e 'wake.
With 'minor modification TBIVCO .and .TRIVCO can be modified
t o compute ' the induced veloci ty- a t an a r b i t r a r y po in t ins tead of
t h e o r b i t . An a r b i t r a r y curve o r l i n e can be developed.and the
induced v e l o c i t i e s computed on t h a t path. This has no t been,
included i n t he 'program t o reduce the core memory requirements.
I f it is ,desired it can be done. ' eas i ly . Thd complete f l e w S ie ld
can then be 'mapped f o r one instantaneous posi t ion of t he ro to r .
By computing t h e flow. . f i e l d f o r success'ive ro to r pos i t ions , . . non-
s teady e f f e c t s .could be determined i f desired. It would be an expensive 'and t i m e .'consuming undertaking. It i s n o t bel ieved t o
be of . s i g n i f i c a n t importance i n l a r g e . r a d i i i r o to r s , bu t may be
important i n small r a d i i r o to r s . This has been invest igated i n
a , few examples which is the b a s i s f o r the opinion expressed..
The primary d i f fe rence between the exact theory and the
improved pr imi t ive theory is t h a t i n the-improved pr imi t ive theory
a semi-rigid wake s t r u c u t r e 'based on r e s u l t s of t he exact theory
i s assumed, while i n t h e exac t theory the wake .is formed step-by-
s t e p by computing t h e r e s u l t a n t ve loc i ty and displacement of the
end po in t s o f each ' s t r a i g h t l i n e vortex segment a s t he r o t o r is
r o t a t e d i n . f i n i t e increments. The displacements a r e computed as
the sum o f . displacements along ci 'rcular a r c s .associated w i t h
every vortex segment i n the system. The computing time ' increases
a s n2 + n where, n i s the number of segments i n t he system.
Once t h e induced v e l o c i t i e s have been found, computation of t h e r o t o r performance is r e l a t i v e l y straightforward.
The program uses .a .series. of .nested DO loops t o compute
t h e perfomande ' for each of t h e primary v a r i a b l e s 8, w, A , and
a o r .U/V o r U. Delta, A ' , . t he accelera t ion ramp,is a simple input variable. The i n i t i a l value of 8 , w, A , and a o r u/V
or'.U and the' range on..each 'DO loop a re ' input parameters which
enab.le 'computation to s t a r t : and end at. any se lec ted range o f t he
parameters. The r o t o r geometry and modulation schedule t o be used a r e 'a lso i n p u t var iables . The number of ~ o i n t s on the .
capture 'area -.and the o r b i t , number of, .blades, and length of t he wake ' in number of r o t o r r a d i i .a re 'also. t h e input var iab les . In .addit ion, ' t h e 'neces'sary constants used t o define t he l i f t c o e f f i c i e n t and drag coef . f ic ient functions a r e a l s o input variables. Pr in t ing
options ,are ava i lab le t o res'trict the . output only r o t o r per-
formance, o r ' i f . ,des i red ,deta i led information a t each' po in t on the
o r b i t ; including blade l i f t and drag, r o t o r x force , Z force, torque force, radf a 1 force , induced v e l o c i t i e s due ' t o mutual
in te r fe rence and,wake, @ ' , Or, CL, CD, a, ai, U/V, U, cy l inder rps . and rpm, depending on t h e 'program used.
The f i r s t DO .loop s t a r t s with ' the i n i t i a l value sf @ and
computes the , performance ' f o r a r a n g e o f 8 desired. The second DO
loop,. s t a r t s w i t h , t h e i n i t i a l wind speed and computes the per-
formance over a range o f wind speeds. The t h i r d DO loop s t a r t s with ' the i n i t i a l .value ' o f A and computes the performance over
t h e range- of h . The fourth. 'DO loop, ' s t a r t s with t he i n i t i a l
angle of a t t a c k , & , o r V/V: o r U and computes t he performance over t he range 'of t he var iab le used. -With ' the range of each DO
loop spec i f ied as i npu t .va r i ab l e s , it is poss ible t o r e s t r i c t
each 'DO loop t o a' s i n g l e 'value 'or t o cover any des i red range.
This .allows' f l e x i b i l i t y i n s e l e c t i n g the 'data 'desired as w e l l a s
t he range desired. Once ' 6, w, A , and a , o r U/V,ha .ve been
determined, nominal va lues o f CL and CD are computed t o determine
t h e wake s t r u c t u r e . NASVR i s c a l l e d , and t h e wake s t r u c t u r e is
computed f o r t h e c u r r e n t valueti .of B , w, ' A , a , o r U/V and
c and CD. TRIVCO is then c a l l e d t o compute ' the wake assoc ia ted L induced v e l o c i t i e s .on thg o r b i t which 'need t o be computed only
one t i m e . A DO loop is then used t o compute ' the bound-semibound
induced velocities on t h e o r b i t . Subroutine ALFA o r UgVSR is used
t o compute t h e ' l o c a l va lues o f CL and CD wi th TDCLCD o r MRCLCD
t o inc lude t h e ' induced v e ~ o c i t i e s ' and TBIVCO c a l l e d wibth ' the
c i r c u l a t i o n , r . ," determined i t e r a t i v e l y t o a, d e s i r e d to le rance
a t each p o i n t .on t h e o r b i t . A f t e r convergence, t h e performance,
w i t h t h e in'duced v e l o c i t i e s included, is f i n a l l y computed. The
DO loop r e t u r n s t o complete t h e computation f o r t h e range
s p e c i f i e d . Usually, a i s h e l d .cons tant , and a new value of A
computed. A f t e r t h e X .DO loop has been s a t i s f i e d , ' .control
r e t u r n s t o t h e w DO loop which i s incremented, and . the computation
repea ted f o r t h e range 'of w. Control then passes t o t h e B DO
loop.
The 'ou tput i o i n B r i t i s h ' o r SI u n i t s . The f i n a l ou tpu t
is i n both "un i t s 'while ' the d e t a i l e d d a t a i s i n which e v e r system
h a s been s e l e c t e d f o r computation. Inpu t ' d a t a may be i n e i t h e r
u n i t s , b u t must be c o n s i s t e n t . A l l , i npu t angular d a t a i s i n
degrees , b u t t h e program computes s o l e l y i n r ad ians which a r e
conver ted . t o degree measure f o r output .
Tolerances are 'provided on t h e induced v e l o c i t i e s com-
puted and t h e c i r c u l a t i o n r . These can be a d j u s t e d , b u t a s t h e
t o l e r a n c e s a r e reduced, . t h e computing time i s increased . Usually
1 ,percent accuracy i s -used. Limits a r e placed on t h e number o f
i t e r a t i o n s t o conserve computing time i f convergence does n o t
occur . .. I f convergence does' mot occur, t h e program .progresses t o
t h e n e x t d a t a p o i n t when . t h e l i m i t i s reache'd .and no d a t a is
computed f o r t h a t va lue o f the c u r r e n t value of A . This has
occur red r a r e . l y ~ e n t h e . l i m i t i n g induced v e l o c i t y i n t h e wake
h a s been ,approached. The ' to lerance o n r is .not a percentage b u t
h a s t o b6 i n f t 2 / s e c (m2/sec) . This value i s usua l ly s e l e c t e d
as 1 percent of the man value of I' o r
C- SW L-z---- L GTOL = 200b
This has been found t o be quite satisfactory.
SECTION A-5
BLADE .MQ.DULATION SCHEDULE
A s w a s shown. i n the - i d e a l blade theory, t h e r o t o r c o e f f i c i e n t s
are propor t iona l t o t h e ' l i f t c o e f f i c i e n t , CL , . and t h a t t h i s l i f t
c o e f f i c i e n t must; be reversed i n a l eg rab i c sign a t two'-points on t h e
. o r b i t , 8 and + IT , if useful power ,is t o be ex t rac ted by t h e
r o t o r . The l a r g e s t ' l i f t c o e f f i c i e n t should be used i f t h e drag
c o e f f i c i e n t i s no t t o o l a rge . I f t h e drag c o e f f i c i e n t can be
neglected, the . ' l a rges ' t l i f t c o e f f i c i e n t should be used. Idea l ly ,
t h e maximum power w i l l r e s ' u l t i f t h e l i f t c o e f f i c i e n t is reversed
ins tan taneous ly a t t h e blade. f l i p points. Physica l ly this is impossible s i n c e th& blade a n d t h e r o t a t i n g cy l inder have a moment
o f i n e r t i a about t h e i r a x i s of r o t a t i o n . .A symmetrical a i r f o i l has
ze ro moment about i ts aerodynamic cen t e r i n a s teady uniform flow,
b u t it can be shown t h a t i n . .cu.rveli.near 'flow and nonsteady
o s c i l l a t o r y flow t h a t a p i t ch ing moment e x i s t s . ' T h e r o t a t i n g cylindc has a viscous torque which i s propor t ional t o . square of t h e
angular ve loc i t y due t o . t h e e f f e c t of v i s c o s i t y on t h e exposed
s u r f a c e of t h e cy l i nde r and t h e end cap. he effect of i n e r t i a
usua l ly dominates , .but t h e .aerodynamic torque can be l a r g e and
should no t be neglected. The equat ion of motion. f o r t h e lift
c o e f f i c i e n t r e v e r s a l may be . w r i t t e n a s :
where I is t h e moment ,of i n e r t i a f a . is t h e &ngle of a t t a c k , Q is t h e torque app l ied t o reverse t h e l i f t c o e f f i c i e n t , and Qa is
t h e aerodynamic torque. Neglecting t h e aerodynamic torque, and
i n t e g r a t i n g t w i c e with t i m e when assuming t h e appl ied torque is
cons tan t r e s u l t s i n t h e fol lowing
Q " I a = $, o r a ' = * t 2 / 2 x , p r t = a m , where a is
t h e angle of a t t a c k change. Note a l s o t h a t a =. ~l?/2.1. ~t i s seen t h a t t h e angle of a t t a c k v a r i a t i o n would be .parabol ic with
t i m e , which can be expressed a s t h e phase angle through which
t h e blade moves whi le . t he angle of a t t a c k r eve r sa l i s occurr ing.
The angular ve loc i t y of t h e blade . in .changing ang le of a t t a c k L
and i s seen t o vary with t i m e . Since t h e angle of a t t a c k must go from .a cons tant p o s i t i v e val.ue to a c o n s t a n t negat ive value , t h e blade
.' must f i r s t be accel'erated t o ze,ro. angle . . o f ' a t t a c k , . and the decei-
e r a t e d t o .a cons tant - a . Thus;. an accelera t ion-decelera t ion ramp .must ex i s t . ' Now d t = Rd $/V = .Rd $/(A W) s o t h a t t =
R A / (X'W) = . 21a /Q, where A = t he increnient o f phase angle t he
blade moves' through during acce le ra t ion and ,decelerat ion a t a
cons tant torque which must be : r e v e r s e d i n s ign when a = 0 . Thus, . .
~he'acceleration-deceleration ramp i s i l 1 u s t r a t e d . h Figure A . 1 2 .
E i t he r . t h & ' torque may b e s p e c i f i e d and t he ' ramp angle A
computed, o r the ramp angle spec i f i ed and the . requ i red torque " ,
computed. A s i m i l a r ana ly s i s f o r t h e . cy l inder rpm merely replaces the angle o f a t t a ck 'by the rpm. This simple ana lys i s : neg lec t s t he
aerodynamic t o rque which a l s o increases t h e required ramp angle
o r t h e app l ied torque.
The to rque , ' r equ i red t o reverse t h e l i f t c o e f f i c i e n t f o r a
blade is .qui te sma l l , and amplidyne servos which have an almost
ins tan tan tous and rap id .revers.al c h a r a c t e r i s t i c are ava i l ab l e i n almost any s i z e ' required. However, electric motors' a r e used t o . sp in the ' ro to r s , a n d ' t h e power required ' t o reverse t h e d i r e c t i o n
o f r o t a t i o n can be a very s i g n i f i c a n t f r a c t i o n of t h e power
developed by t h e ro to r . Some power regenerat ion i s . p o s s i b l e dur ing the dece le ra t ion phase; b u t it ,is only a smal l f r a c t i o n .o f t h a t requi red t o accelera te . '
Figure 24.13' is a modulation schedule used i n t h e program t o show the angle o f a t t a c k , a , schedule of the blade f o r one
revolut ion . I n each 'of :the acceleration/deceleration ramp
regions; .A , , t h e ' angle o f a t t a ck va r i a t i on is. a parabola. In
.between blade r eve r sa l , the angle o f . a t t a c k is constant . For
t h e spinning cy l inders , U/V o r U follows the same schedule a s
t h e cy l i nde r p e r i p h l a l ve loc i ty U . = 2 nrn is changed i n ramp
angle i n t e r v a l A , and the rpm he ld cons tan t between r eve r sa l s .
B = ECCENTRICITY PHASE ANGLE A = ACCELERATI ON-DECELERATI ON R A M P ANGLE R = ORBIT R A D I U S
Figure A. 12. Acceleration-Dec'eleration Ramp Angle.
344
uv I S CONSTANT ANGLE OF AlTACK USED V IS. THE CONSTANT VALUE OF v USED
(V/V ) I S THE CONSTANT VALUE OF(V/V) USED v
v 180 360
*PHASE ANGLE - DEGREES MEASURED FROM P (SEE FIGURE A. 12)
Figure A.13. Nondimensional Modulation Schedule for a, V, or U/V.
dCL For t h e b lade CL = da o , where CL i s the+ l i f t
. . dC L=.a c o e f f i c i e n t , da is t h e s l o p e o f t h e l i f t c o e f f i c i e n t versus
a n g l e o f a t t a c k curve i n t h e ' l i n e a r range, a n d a i s t h e angle o f
a t t ack . ' Thus CL f o l l o w s ' t h e same schedule as t h e angle of a t t a c k . '
The s p i n n i n g c y l i n d e r l i f t c o e f f i c e n t was' found i n wind
t u n n e l ' t e s t s t o be a func t ion of U/V, where V is a c t u a l l y t h e
r e l a t i v e w i n d . t o 'the c y l i n d e r , o r the 'wind tunne l speed. On t h e
t r a c k , t h e idea l ' r e l a t i v e speed is VR = W /l + A 2 -2A . , . Sin* .
s o t h a t a c t u a l l y CL = C L ( U / V R ) = CL (U/ [W /1 + X 2 - 2 XSin 9 1 ) .
That is, i f c o n s t a n t u i s used, CL w i l l be v a r i a b l e around t h e
t r a c k . I f it is d e s i r e d to mainta in cons tan t CL, it w i l l be .
necessa ry t o be c o n t i n u a l l y changing U a s t h e c y l i n d e r progresses
around t h e t r a c k . The ga in i n use fu l power may o f f s e t t h e power
expended t o r e g u l a t e CL. I f U i s he ld cons tan t a t a value which
produces near maximum power over t h e upper h a l f o f t h e o r b i t , t h e .
l o w e r h a l f o f t h e o;bit w i l l go i n t o super c i r c u l a t i o n and opera te
a t t h e maximum CL. Under t h e s e cond i t ions , more net p o w e r may r e s u l t s i n c e none i s spen t i n r e g u l a t i n g CL. As W o r A decreases ,
U, and hence t h e c y l i n d e r s p i n , can be g r e a t l y reduced which
reduces t h e power expended i n rpm r e v e r s a l . The c o n t r o l system
must sense c o n d i t i o n s and automat ica l ly a d j u s t .
The l i f t . c o e f f i c i e n t . f o r t h e spinning c y l i n d e r i s n o t a
l i n e a r func t ion o f t h e speed r a t i o U/V. Thus, i f U/V i s
modulated p a r a b o l i c a l l y wi th $, during l i f t . r e v e r s a 1 , CL w i l l no t
have a pa rabo l i c v a r i a t i o n wi th $.
. SECTION A-6 .
T DEAL .BLADE' VECTOR DIAGRAM.
An i d e a l baade vec tor .d.iagram, which .shows
t h e r e l a t i v e ve loc i t i ' es and aerodynamic ' forces a c t i n g on t h e ,
blade a t an a r b i t r a r y phase angle $, i s presented i n F igure ~ . 1 4 .
The view i s look ing a long t h e a x i s of .mta&ion o u t t h e p o s i t f v e
a x i s . The c i r c l e i s t h e 'path around which t h e b lade moves i n
a counterclockwi'se d i r e c t i o n a t c o n s t a n t angular v e l o c i t y n'=' 2rh.
R i s t h e r a d i u s o f t h e pa th and n .is t h e number of r evo lu t ions
per u n i t t i m e . The p e r i p h i a l . spet5d is V = Q R = 27TPL.R and i s
t a n g e n t t o t h e pa th . The wind speed i s W and i s i n t h e d i r e c t i o n
of t h e negat ive 'X a x i s . The v e l o c i t i e s a r e shown r e l a t i v e t o t h e
blade which may be thought of as be ing ins tan taneous ly a t rest.
VR is t h e r e s u l t a n t aerodynamic v e l o c i t y which produces the 1 aerodynamic f o r c e s of l i f t and drag, where L = C ~ Y S V R ~ i s
1 t h e l i f t and D = CDT P S V R ~ is t h e drag. The phase angle ,* , i.' less than t h e e c c e n t r i c i t y angle , f? , s o t h i s r e p r e s e n t s cond i t ions
f o r a l i f t i n g / t h r u s t i n g r o t o r s o t h a t t h e angle o f a t t a c k , a, i s
p o s i t i v e . The r e s u l t a n t v e l o c i t y , VR, is a t t h e angle 4 r e l a t i v e
t o t h e X a x i s , and t h e drag, D, a c t s p a r a l l e l and i n t h e d i r e c t i o n
of VR. The l i f t , L, acts a t r i g h t ang les t o VR i n t h e d i r e c t i o n
shown, s i n c e a i s p o s i t i v e . If a w e r e nega t ive , t h e l i f t would a c t
i n t h e oppos i t e d i r e c t i o n which it would do for e windmil l , a id
B would be negat ive and i n t h e upper quadrant .
The l i f t and d r a g when added v e c t o r i a l l y give t h e s i n g l e '
r e s u l t a n t . aerodynamic force which i s resolved i n t o components FX.
a long t h e X a x i s , FZ a long t h e Z ' a x i s , FR a long t h e r a d i u s , and
FQ normal t o t h e r ad ius . FX i s t h e l o c a l c o n t r i b u t i o n t o t h e r o t o r
t h r u s t , FZ i s t h e l o c a l c o n t r i b u t i o n t o t h e r o t o r l i f t , FR i s . t h e
l o c a l aerodynamic fo rce along t h e r a d i u s which wi th t h e
i n e r t i a fo rce des igns t h e r a d i a l . blade. suppor t arms i n t e n s i o n and
compression, and FQ i s t h e l o c a l torque f o r c e which is p o s i t i v e
a s shown and would r e q u i r e power t o t u r n t h e r o t o r . The power is
P = FQ.V. Algebraic. express ions w e r e developed i n t h e s e c t i o n on
I d e a l Blade Theory f o r t h e X and Z components of v e l o c i t y , and FX,
- Figure A.14. SIc5eal Blade Elemsnt Vector Diagram of Cyclogiro.
FZ, FR, and FQ. When t h e s e a r e - i n t e g r a t e d around t h e o r b i t t h e
r o t o r l i f t , t h r u s t , torque, and power a r e expressed a s t ime - average va lues as E, E, m, and P = FQ.V. The b lade o r i e n t a t i o n
r e l a t i v e t o X a x i s is given by x = ,(I - a , where X ' i s t h e so-ca l led
"blade rocking angle . " When x i s computed, a cam could be c u t
which would automat ica l ly o r i e n t t h e blade. Ki r s t en showed t h a t
t h e "swinging-sliding block" mechanism wou.ld produce t h e i d e a l
angle (I f o r a l l values o f A , and with 'a servo motor t o follow
t h i s .motion would d r ive t h e b lade proper ly f o r a l l A except
A .= ,1. An e c c e n t r i c cam contoured t o t h e b lade modulation schedule
could s u b t r a c t a from J, t o o b t a i n X . The a x i s o f t h e cam would
be o r i e n t e d a t t h e angle 8 t o c o n t r o l t h e amount o f t h r u s t and
l i f t developed. D i f f e r e n t i a l a c o n t r o l would provide a r o l l i n g
moment about t h e x a x i s s o t h a t a i l e r o n s would n o t be needed.
D i f f e r e n t i a l B c o n t r o l would produce a yawing angle about t h e .Z
a x i s s o t h a t a . r u d d e r would n o t be needed. S tep i n p u t s t o a
would provide . d i r e c t lift c o n t r o l s o t h a t .extreme maneuverabi l i ty
o f t h e veh ic le could be achieved. When B i s negat ive , t h e device
a u t o r o t a t e s , e x t r a c t s power from t h e wind s t ream and becomes a
windmill .
SECTION A-7
REAL BLADE VECTOR DIAGRAM
When the r o t o r develops a n e t t h r u s t and l i f t , FX and E, t h e momntum theorem r equ i r e s t h a t a ve loc i t y increment be given
t o t h e ' f l u i d i n t h e opposi te d i r e c t i o n t o t h e force generated.
L e t t he se increments be WX and W Z , Figure A. 1'5 is a Real Blade
Vector Diagram where WX and WZ have been .added a s shown with a l l . . else t h e same. The r e s u l t a n t ve loc i t y has been changed i n
magnitude and r o t a t e d t o t he d i r e c t i o n $r. This i n tu rn r o t a t e s
and changes t h e magnitude of L, and B, .Compare w i t h . Figure ~ . 3 . .
Note t h a t FX, FZ, FR, and FZ, have a l l been changed i n magnitude.
The t h r u s t f o r ce and r a d i a l force , . FX and FR, have been reduced
i n magnitude, and t h e r o t o r l i f t and torque force , FZ and FQ,
have been increased i n magnitude. Thus, it w i l l t ake more power
t o produce less t h r u s t . Since FX and FZ w i l l vary a l l around t h e
o r b i t , WX and wz w i l l vary a l l around the' o r b i t , and t h e use o f
cons t an t values a s s u m d by many inves t i ga to r s is no t va l i d . When
a c t i n g a s a windmill , FX and FR a r e increased i n magnitude, and .
FQ and FZ reduced. I n both 'cases, t h e presence o f t h e ve loc i t y
increments WX and WZ: reduces t h e des i red performance of t h e ro to r .
The c e n t r a l problem i n cyklogiro theory is t o be ab l e t o p r e d i c t
WX and W Z a t every p o i n t on t he , o r b i t . This l e d t o t h e vor tex
theory ,
F i ~ u r e A.15. Real Blade Element Vector Diagram of Cyclogiro.
SECTION A-8
CIRCULATION AT THE BLADE AS A FUNCTION OF PHASE ANGLE
.Kutta and Joukowsky showed. independently . t h a t a c i r c u l a t i o n
w a s . r e q u i r e d . t o produce a lift force and. formulated t h e Kutta-
Joukowsky l a w as : ; L' = pVr . ,For .a uniform f. in.i te span wing,
t h i s becomes L = pV r b = C L 9, ?, from which r= CL SV/2b .
This c i r c u l a t i o n , . r , i s simulated mathematically b y a bound vor tex
i n t h e wing. F o r a b lade . t r a v e r s i n g t h e o r b i t : the c i r c u l a t i o n
seen t o be a funct ion o f $, t h e phase angle . The maximum value
.occurs when $= , ' - ~ / 2 .and t h e minimum when $= ~ / 2 . These values
are :
CLS C , S 11 -1 1 r - - - X ( l + A ) and r min - - - max . 2 b 2
i n magnitude.
I t i s convenient t o nondimensionalize I' ($ ) by d i v i d i n g by
t o remove ' the e f f e c t o f CL, W , and geometry. The r e s u l t is:
r max
?is funct ion g ives t h e ngndimgnffionali zed ~ l r ~ ~ l a t i ~ n a3 a
f u n c t i o n of phase a n g l e f o r cons tan t l i f t c o e f f i c i e n t a s t h e b lade
traverses t h e o r b i t . It %is p l o t t e d i n Figure A . 3 f o r t h e value of
X = 2 f o r the i d e a l b lade . It i s seen t h a t I' ($) /rmx has con-
s i d e r a b l e change around t h e o r b i t s o l e l y .due t o t h e changing
r e s u l t a n t v e l o c i t y . .'The only way . t h a t t h e bound vor tex can
change a n d . s a t i s f y , t h e Helmholtz Vortex laws is t o shed v o r t i c i t y
t o form a wake which must form c losed paths and be connected t o
t h e bound vortex. The shed v o r t i c i t y i s shed spanwise para1161
t o t he bound vortex. The shed v o r t i c i t y i s shed spanwise p a r a l l e l
t o t h e t r a i l i n g edge o f t h e blade, bends forward a t each t i p and
joined t o t h e bound vor tex t o form a rec tangu la r r ing . Its s t r eng th
.is t h e d i f f e r e n t i a l , , dl'. A s t h e blade t r ave r se s t h e , o r b i t , a .con- . .
t inuously varying shee t would be formed. I f the - shee t w e r e r i g i d , ,
a s P rand t l and Goldstein assumed, t h e s h e e t sh&d from each blade
woul-d form a cycloi'dai , sur face . .The .vortici . ty shed i n t h e shee t
would have opposi te r o t a t i o n t o t he bound v o r t i c i t y .
The nondimensional r a t e . o f shedding with respec t t o phase
angle i s e a s i l y found- t o be :'
1 d r ( @ ) = .- -A Cos @
a$ 2 (1 + X ) / l +.A -2X Sin $
The d i f f e r e n t i a l s t r eng th o f v o r t i c i t y shed i s
and the exac t s t r eng th ',of v o r t i c i t y shed a t pe r iod ic i n t e r v a l s '' i s dr = r ( $ + d$) - r ( $ ) . This w i l l be used l a t e r .
The nondin~erisioaal. ,rate o f . vor tex shedding a t X = 2 is p l o t t e d i n Figure A.2.. I t i s ' s e e n t h a t it is zero a t two po in t s
IT and- on t h e c i r c l e - - IT IT t o , IT . From - 7 1 2 2
3lT . 1 rmax
TT A-M < 0 , and from 2 to. 2 dr(Q) i s pos i t i ve . . . d$
TT The reason is t h a t from + - to.- ' .- 2 3n t h e v e l o c i t y is inc reas ing . 2 It i s seen t h a t there: a r e .two maxim&. P t is' easy to show t h a t
f o r x < 1 the maxima oecurs a t S in $= X ,. and f o r X < 1, it occurs
when Sin $= 1 / ~ . These po in t s ' , a re4 marked' i n . Figure A. 2 a t t h e
t i c k marks, and f o r = 2 occurs ' a t il, = . ~ / 3 = 30 and X = 5a/6
= 150'. I t i s a l s o seen t h a t 30° < * S50° t h a t t h e rate of - - " ' $ < n / 3 a n d shedding changes much 'more rap id ly than f o r - 7 - -
5n/6 S $ s 3n/2 - Figure A . 4 shows t h a t t h e l o c a l s t r e n g t h of v o r t i c i t y shed i n a r i g i d c y c l o i d a l -she@t i s extremely
v a r i a b l e w i t h r eg ions .of p o s i t i v e - a n d negat ive v o r t i c i t y when t h e
l i f t c o e f f i c i e n t .is cons tan t . . I t . a l so shows t h a t t h e p a r t o f
t h e c y c l o i d above t h e ,x a x i s has les's shed v o r t i c i t y than t h e
p a r t o f the e y c l o i d a l s u r f a c e below t h e x a x i s o r f o r p o s i t i v e 2 .
Since t h e - a r e a under t h e curve i s p ropor t iona l t o t h e a r e a between
t h e a x i s .and t h e curve, t h i s ca'n be seen by comparing t h e a rea IT between $= - n/2 t o $= 0 w i t h 'the a r e a from $ = 0 t o $ = - 2
Thus, t h e shedding i s more 'concentrated below t h e x a x i s . This f a c t
w i l l be ' u t i l i z e d l a t e r .
I f the' 'b lade w e r e . f l i p p e d inst-antaneou.s ly. a t ' t h e . f l i p p o i n t ,
t h e l i f t c o e f f i c i e n t would go from CL t o - CL o r from - C t o CL. L T h e ' v o r t i c i t y shed a t b lade f l i p would be twice t h e l o c a l value
i n F igure A. 1 a t $= 0 and' $ = B + IT. Na tura l ly , t h e l o c a l ,va lue
can be any th ing between t h e minimum and t h e maximum depending
upon t h e a c t u a l va lue o f which i s ' b e t w e e n - IT/^ and IT / 2 . The
l i f t c o e f f i c i e n t r e v e r s a l changes t h e s i g n of t h e c i r c u l a t i o n
shed. I f B= - IT/^, a l l t h e shed v o r t i c i t y is t h e same
r o t a t i o n such t h a t t h e sum of t w i c e t h e m i n i - m i ~ m and a l l the
v o r t i c i t y shed wi th phase angle is equal t o twice t h e maximum.
Th i s i s a c t u a l l y t r u e f o r a l l va lues of 0 , b u t t h e va lue shed
a t blade f l i p must b e taken i n t o account. When an a c c e l e r a t i o n - d e c e l e r a t i o n ramp is used i n s t e a d of an ins tantaneous b lade f l i p
it is s t i l l true. instantaneous blade f l i p would c r e a t e d i s -
c o n t i n u i t i e s i n t h e c i r c u l a t i o n d i s t r i b u t i o n which.would mean
h i g h l y concent ra ted v o r t i c i t y . An acce le ra t ion-dece le ra t ion ramp
would r e s u l t i n a cont inuous c i r c u l a t i o n d i s t s i b u t i on , b u t
two reg ions o f . very s t r o n g l o c a l . v o r t i c i t y . I f t h e v o r t e x s h e e t
were r i g i d , t h i s would on ly be a niathematical problem i n e v a l u a t i n g
i n t e g r a l s . u s e d i n computing induced v e l o c i t i e s . D i s c o n t i n u i t i e s
would cause improper i n t e g r a l s which would r e q u i r e s p e c i a l c a r e .
Ac tua l ly , t h e d i s c o n t i n u i t y i s a s i n g u l a r point. . The acce le ra t ion- . d e c e l e r a t i o n ramp removes t h i s d i s c o n t i n u i t y and provides a
cont inuous func t ion .
Mathematically., . the shed v o r t i c i t y is continuous and would:
form a con:tinuous s h e e t o f zero thickne$s i f a real f l u i d v i s -
c o s i t y i s p r e s e n t and 'forms a boundary:.layer on t h e . s u r f a c e o f i
t h e body. Joukowsky showed t h a t a cusp a t t h e t r a i l i n g ' e d g e
c r e a t e d a s i n g u l a r p o i n t which. would be removed by adding a
proper amount o f c i r c u l a t i o n . Von ~ a r m a n ~ ~ e x t e n d e d t h i s t o a
f i n i t e t r a i l i n g edge a n g l e . prandt16' examined t h e viscous flow
n e a r t h e sha rp t r a i l i n g edge exper imen ta l ly , and made approximate
c a l c u l a t i o n s t o t r y t o show t h e fo rmat ion .o f a vor tex a t t h e
t r a i l i n g edge, c a l l e d ' t h e s t a r t i n g .vor t ex , . a s t h e t r a i l i n g edge
s i n g u l a r i t y i n p o t e n t i a l flow was removed physica. l ly . Associated
wi th ' t h i s viscous a c t i o n i s t h e formation of t h e boundary l a y e r
on t h e su r face o f t h e a i r f o i l . This boundary l a y e r i s con-
t inuous ly genera t ing v o r t i c i t y which tends t o accumulate a t . .
t h e t r a i l i n g edge. The r a t e of accumulation i s d i f f e r e n t on '
t h e upper and lower su r face due . t o . t h e v e l o c i t y d i s t r i b u t i o n .
Because. o f t h i s , a c r i t i c a l accumul.ation is reached a l t e r n a t e l y
on t h e .upper and lower s u r f a c e which i s p e r i o d i c a l l y shed. This
means two th ings : t h e bound v o r t e x s t r e n g t h f l u c t u a t e s about a
mean value, and t h e vor tex s h e e t i s n o t shed cont inuously, b u t
i n d i s c r e t e f i n i t e ' increments o f a l t e r n a t i n g s i g n . Carefu l wind . .
t ' m n e l measurements and flow v i s u a l i z a t i o n techniques have
v e r i f i e d t h e s e deduct ions . f o r s teady s t ream flow. The von Karman 68
v o r t e x s h e e t behind c y l i n d e r s i s t h e c l a s s i c example. When
t h e s e concepts are a p p l i e d t o t h e varying c i r c u l a t i o n and shedding
o f t h e cyclogi ro , it may . a l so be 'deduced t h a t t h e v o r t e x s h e e t
shed i s n o t continuous, b u t i s a c t u a l l y . a. series o f d i s c r e t e
f i n i t e v o r t i c e s shed p e r i o d i c a l l y . The frequency and s t r e n g t h of
t h e s e d i s c r e t e v o r t i c i e s is unknpwn, b u t provides phys ica l argu-
ments f o r us ing a d i s c r e t e vor t ex wake a r r a y t o model t h e real
wake. Such a model w i l l . be d iscussed next . '
SECTION A-9
SEMTRIGID WAKE, STRUCTURE
Associa ted w i t h each d i f f e r e n t i a l segment o f a vor tex
f i l a m e n t is an induced v e l o c i t y f i e l d which extends t o i n f i n i t y ,
and which i s given by t h e Biot-Savart Law. The t o t a l induced
v e l o c i t y a t any p o i n t i s obta ined by i n t e g r a t i n g t h e c o n t r i b u t i o n
o f each element over a l l t h e vor tex f i l ament s i n t h e f i e l d .
P r a n d t l showed t h a t when t h e t o t a l induced v e l o c i t y is combined
v e c t o r i a l l y w i t h t h e f r e e s t ream v e l o c i t y , an induced angle o f
a t t a c k r e s u l t s which changes t h e angle o f a t t a c k , and hence l i f t
coe f f i c i en t ,which an a i r f o i l i n t h e r e s u l t a n t flow produces. This
i n f l u e n c e s t h e c i r c u l a t i o n about t h e a i r f o i l and t h e v o r t i c i t y
shed i n t h e flow. Differentia-integral equat ions can be w r i t t e n
which must be so lved t o o b t a i n a s o l u t i o n . These equat ions may
be t i m e dependent. P r a n d t l assumed a s t eady flow wi th a flat
t r a i l i n g r i g i d v o r t e x s h e e t f o r an i s o l a t e d wing wi th a con-
t inuous d i s t r i b u t i o n o f v o r t i c i t y i n t h e s h e e t . P rand t l found
t h a t an e l l i p t i c - spanwise loading f o r t h e bound v o r t i c i t y
s a t i s f i e d t h e i n t e g r a l s f o r l i f t and d rag o f a wing and r e s u l t e d
i n t h e minimum d r a g f o r t h e r e s t r i c t i o n s imposed.
I t is p o s s i b l e t o w r i t e similar equat ions- f o r t h e
c y c l o g i r o . i f the wake i s a s s w d t o be. ' r i .gid c y c l o i d a l su r faces ,
b u t t h e 'equat ions a r e 'time 'dependent.. . A t one . p o s i t i o n , of t h e r o t o r ,
t h e equa t ions are. ' t i m t ' independent ,' .bu t t h e . equat ions cannot 'be
s o l v e d i n c losed form. ' I t 'is p o s s i b l e . . t o compute ' t he induced
v e l o c i t y a t any p o i n t i n t h e f i e l d by. assuming f i n i t e filaments
i n the . spanwise 'and s t reanwise ' d i r e c t i o n , and approximating t h e
r i g i d c y c l o i d a l s u r f a c e by - a mesh o f f i n i t e l e n g t h segments t o
form polygonal a r c s . Numerical: in tegra t i -on: .is. then 'performed
adding t h e increments of induced v e l o c i t y a t .a p o i n t v e c t o r i a l l y .
Spanwise d i s t r i b u t i o n can be 'handled by ,us ing a , f i n i t e 'number
o f c o n t r o l p o i n t s a c r o s s . the span.. Convergence is achieved by : .
i t e r a t i o n . To set up t h e problem, t h e shape o f t h e wake and t h e
v o r t e x s t r e n g t h 'of each. segment ' in t h e network must be known.
The shape can be 'assumed t o be cyc lo id f o r t h e wake su r faces , and
t h e s t r e n g t h c a n be computed f r o m t h e bound v o r t e x c i r c u l a t i o n 356
l i s t r i b u t i o n with phase angle , inc luding l i f t c o e f f i c i e n t r e v e r s a l
and accelera t ion-decelera t ion ramp e f f e c t s . This i s accomplished
by us ing f i n i t e increments of phase angle. The v o r t i c i t y shed
a t each increment of phase angle becomes; Ar = r ($ , + d$) -r ( $ 1 . The spanwise loading can be approximated by us ing f i n i t e inc re -
ments i n t he bound v o r t i c i t y . which approximates t h e e l l i p t i c a l
loading o r t h e Shcenk loading .to .es t imate conditions. . ~ t e r a t i o n
would produce t he f i n a l .loading..The .experimental evidence t h a t
t h e v o r t i c i t y shed from a wing is f i n i t e pe r iod ic increments
r a t h e r than continuous v a r i a t i o n tends t o suppor t t h e assumption
of f i n i t e element ana ly s i s .
I n p r i nc ip l e , a . f i n i t e system of: simultaneous equat ions
could be w r i t t e n t o f i n d a sol .ut ion.which would be solved by
matrix techniques. The number of equat ions would be enormous,
a n d . i n v e r t i n g t h e mat r ix would probably s a t u r a t e t h e l a r g e s t
computer known, and , i f it d id not,would r equ i r e so much com-
pu t a t i on tine t h a t it wo.uld.:not be f e a s i b l e . An a l t e r n a t e .
approach 'would be t o s t a r t t h e r o t o r impulsively and'compute . .
t h e v o r t i c i t y shed and t r a c k .its l o c a t i o n i n t h e wake; A f r e e
vor tex moves a t t h e l o c a l ve loc i t y i n the flow which i s t h e
vec to r sum.of t h e f rees t ream v e l o c i t y and t h e induced v e l o c i t y
a t a po in t due t o . a l l t h e f i n i t e 'segments i n t h e flow. This
inc ludes a l l nonsteady" e f f e c t s , and would genera te an approximation
t o t h e t r u e wake. I n i t i a l l y , t h e computation t i m e is q u i t e small,
b u t a s t he number of vor tex segments i n t h e f low. ' increases t h e com-
put ing t i m e i n c r e , a s e s a s n2 + n where n i s t h e number of seg-
ments i n t h e flow. I n t h i s approach, it would be. necessary t o
cont inue t h e wake genera t ion u n t i l the induced ' ve loc i ty a t po in t s
on t h e o r b i t . approached a ' l i m i t . This r equ i r e s enormous
core memory o r mass s t6rage . and computing t i m e f o r ' the . s imp le
case of uniform .loading.
Since t h e v e l o c i t y i n t h e wake gradual ly decreases from
f r e e stream value. . f a r .upstream. t o . t h e .va lue computed from t h e momentum theorem, \he wake does not t r a n s l a t e a t uni.form ve loc i t y , bu t
tiden's a s t h e ve loc i t y . dec r ea se s t o s a t i s f y con t i nu i t y . The r i g i d
wake ignores t h i s e f f e c t , while t h e wake genera t ion technique
inc ludes + h i s e f f e c t . 357
It .was decided. to . .constx.uct a .semirigid .wake t o i nves t i -
g a t e t h e e f f e c t o f stre'mwise .reduction of t h e wake 'veloci ty. It was assumed t h a t t h e . ve loc i t y pass ing through ' the r o t o r decreased
l i n e a r l y from fre,e'Stream ve loc i t y 1. SR upstream t o t h e f i n a l wake
v e l o c i t y 1.5R downstream from t h e 'center of t h e ro to r . Wake
widening was neglec ted s i nce the$e computations were made on a
small programnable cal 'culator . he shed v o r t i c i t y was assumed
t o move a t t h e l o c a l ve loc i t y from t h e point of shedding t o 1.5R
downstream a f t e r which i t moved a t constant ve loc i ty . I n t h e
varying ve loc i t y region, t he wake would d i s t o r t , while a f t e r
1.5R downstream it would be r i g i d . Induced ve loc i t y e f f e c t s of
t h e wake on i t s e l f w e r e Ignored s i n c e t h e wake was assumed s e m i -
r i g i d . The e f f e c t s of l i f t r e v e r s a l and accelera t ion-decelera t ion
ramp of A * lSO wi th yarying angles of a t t a ck were included. The
shed v o r t i c i t y was assumed t o o r i g i n a t e from t h e t r a i l i n g edge
of t h e blade a s t h e b lade was modulated around t h e o r b i t always
o r i e n t e d a t t h e i d e a l value of $, Since t h i s was fox t h e wind-
m i l l s t a t e , f3 was assumed t o be -~r/2. Three blades w e r e used t o
show mul t ib lade e f f e c t s . The r o t o r was r o t a t e d i n . increments of
S o , and A = 2 w a s used. A uniform loading was assumed s o t h e wake
was e s s e n t i a l l y two dimensional. For comparison purposes, i d e a l
wakes w e r e cons t ructured with a d i g i t a l computer and p1,otted by
Calcomp. These w e r e f o r X = 0.5, 1, and 2 and blade angle .of
a t t a c k -a 0 + 1 2 O and constant .
Figures A. 16a and A.1.6b i l l u s t r a t e t h e i d e a l wake f o r A =
2.0, 1 .0, and 0.5 f o r a = O O . I t is seen t h a t t he se a r e respec t ive ly -
p r o l a t e cyc lo ids , cycloids. , and c u r t a t e cycloids. These a r e r i g i d
wakes and t r a n s l a t e a t t h e freestream speed. Note t h a t t h e i n t e r -
s e c t i o n s of t h e su r f ace c r e a t e cells which would make .any p o t e n t i a l
mult ivalued and mu l t i p l e connected regions. ~ i g u r e A.17a and A.17b
i l l u s t r a t e t h e i d e a l wake f o r X = 2.0, 1.0, and 0.5' f o r a = , + 1 2 O .
These a r e cyc lo ida l l i k e su r faces , bu t s i nce t h e wake emenates from
t h e t r a i l i n g edge, t h e r e s u l t i n g shapes a r e d i s t o r t e d from cycloids.
It must be expected t h a t blade modu1,ation w i l l d i s t o r t t h e su r face
genera ted from a cyc lo ida l motion of t h e p ivot . Each a r c f o r each
b lade i s s i m i l a r , bu t t r a n s l a t e d from t h e previous blade by a f ixed
d i s t ance . The i n t e r s e c t i o n again produce c e l l s .
F i g u r e A. 16a. I l l u s t r a t i o n of t h e I d e a l wake for X = 2.0 , 1 .0 , and 0 .5 for a =0° ,
IDEAL.WAKE - PATH OF BOU*D VORTEX
Figure A.16b. Illustration of the Ideal Wake for X = 2.'Of 1.0, and 0'.5 for a=Oof
DISTORTED RIGID.PSEUD0-CYCLOID.VORTICITY SHED FROM TRAILING EDGE OF BLADE
CONSTANT BLADE ANGLE OF ATTACK OF +12O
F i g u r e 1'7a. I l l u s t r a t i o n o f t h e I d e a l Wake f o r A = 2 .0 , . 1 . O , a n d 0 .5 f o r a= +12O.
Figure ~ . 1 7 b . I l l u s t r a t i o n of the Ideal Wake f o r A = 2 . 0 , l.O,and 0 .5 f o r a= + 1 2 O .
Figure A . 18 i s t h e ' semir igid wake wi th ' d i s c r e t e vor t ex
shedding every 5' .of ro ta . t ion f o r A = 2 with 'blade 'modulation,
A= 15', and a = i .2 ' . This wake i s n e a r l y a p r o l a t e c y c l o i d w i t h
d i s t o r t i o n evidence n e a r t h e blade f l i p po in t s o f kg. Each
vor tex shed i s i n d i c a t e d by a smal l arrow headed c i r c u l a r a r c
which shows . the ' d i r e c t i o n o f t h e vor tex r o t a t i o n . The vor tex s t r e n g t h is
rough1.y propor t ional . t o the s i z e o f t h e symbol. The bound
v o r t i c e s a r e a l s o shown', and t h e bottom b lade i s ins tan taneous ly
a t zero angle o f a t t a c k . The l i n e jo in ing each symbol r e p r e s e n t s
t h e t i p jo in ing vortex. Note t h a t a t each f l i p p o i n t t h e r e a r e
s t r o n g concent ra ted v o r t i c e s shed a s t h e angle of. a t t a c k i s
reversed , and t h e upper and lower concent ra ted v o r t i c i e s occur
a t nea r ly t h e same value of x. I n between t h e concen.trated
v o r t i c e s i s t h e d i s t r i b u t e d v o r t i c i t y which is very weak, t h e
1 a r g e s t . i ~ only 1.5 pe rcen t o f t h e concent ra ted v o r t i c i t y which
would occur w i t h ins tantaneous b l a d e f l i p and occurs when $ = 30°,
and occurs approximately .one-third between t h e x . a x i s and t h e
bottom of t h e r o t o r . There i s more d i s t r i b u t e d v o r t i c i t y
l o c a t e d i n t h e lower one-third of ' the wake than i n t h e upper two-
t h i r d s o f t h e wake., and is more c l o s e l y spaced.
The in f luence o f t h e slowing down of . t h e wake can be
i n f e r r e d from t h e width and s p a c i n g . o f t h e lower loops. The
end of slowing down region .is the v e r t f c a l dashed l i n e . Down-
s t ream of t h a t t h e wake ve, loci ty i s two-thirds o f free-stream. * The wake should be '-$rider t o s a t i s f y c o n t i n u i t y b u t this' was
omi t ted i n t h i s simple c a l c u l a t i o n . I t i s seen t h a t t h e lower
loops compress and become narrower a s t h e wake slows down.
One loop i s i n both regimes. The l a s t two a r e t h e same shape
s i n c e t h a t region is r i g i d and t r a n s l a t e s a t a uniform v e l o c i t y .
I t is no t i ced that t h e concent ra ted v o r t i c i t y on t h e
upper. and lower h a l f occur a t n e a r t h e same value of x. The con-
c e n t r a t e d v o r t i c i t y on the lower h a l f i s one-third the con-
c e n t r a t e d v o r t i c i t y on t h e upper h a l f , and the sum of t h e
d i s t r i b u t e d v o r t i c i t y is two-thirds .of t h e upper and o f oppos i t e
r o t a t i o n f o r this v a l u e of A = 2 . Each 'segment .on t h e wake is
Figure A.18. Semi-Riad Wake Array with Distributed ~ c r t i c i t y Shed Every 5 O oE Rotation.
inducing v e l o c i t y on every 0the.r p a r t o f t h e flow.. Since. t h e
wake i s r i g i d except f o r wake .slowing' down, the wake does n o t feel
t h i s e f f e c t . I f t h e wake were f r e e , this induced e f f e c t would
cause t h e wake t o d i s t o r t cont inuously. The 'concentrated v o r t i c i t y
would cause t h e d i s t r i b u t e d v o r t i c i t y t o r o t a t e around the con-
c e n t r a t e d v o r t i c i t y i n s p i r a l l i k e pa th and gradual ly coalesce
i n t o two concentrated v o r t i c i t y 'of equal s t r e n g t h b u t oppos i te
r o t a t i o n . The upper h a l f o f t h e wake would wrap around the upper
concentrated v o r k i c i t y and be ing o f opposi te . s i g n reduces t h e
s t r e n g t h t o two-thirds t h e i n i t i a l . value. The lower loops of t h e .
wake .would wrap around t h e lower concent ra ted v o r t i c i t y and be ing
o f the ' same s i g n would add t o . t h e s t r e n g t h . The n e t r e s u l t is
t h a t two concent ra ted v o r t i c e s of equal s t r e n g t h would form.
The f i n a l s t r e n g t h o f t h e s e two concentrated vor t i ,ces would be
t h e mean of t h e concentrated v o r t i c i t y shed a t each b lade f l i p f o r
t h e p a r t i c u l a r . value o f . 6.. This mean . s t r e n g t h occurs due t o t h e
ro l l ' up and t h e a l g e b r a i c s i g n o f t h e d i s t r i b u t e d v o r t i c i t y . TO. s a t i s f y t h e Helmholtz vortex. Paws a l i n e o f v o r t i c e s must j o i n
a t t h e t i p s , and a l s o j o i n each . 'pair o f concent ra ted . vor t ices . .
The l i n e , j o i n i n g thg concen t ra ted p a i r would have vanish ing
s t r e n g t h 'as t h e ro l l -up continued.. The f i n a l ro l l -up would occur
f a r downstream b u t c a l c u l a t i o n s from genera t ing t h e wake shows
t h a t it s t a r t s very r a p i d l y and by one t u r n o f . t h e r o t o r ro l l -up ,
i s w e l l developed. Thus ,, t h e r e is a nea r d i e l d . f a r - f i e l d s t r u c t u r e
with an in termedia te region.which t r a n s i t i o n s from one t o t h e
o t h e r . Spanwise load d i s t r i b u t i o n would concent ra te t i p j o i n i n g
v o r t i c e s near each .blade t i p . This concent ra t ion would tend t o has ten r i n g formation which would r a p i d l y d i s t o r t t h e o r i g i n a l
r ec tangu la r r i n g p a t t e r n s t o elongated. ova l s and perhaps f i n a l l y
t o t o r o i d a l r i n g s . This is specu la t ion based .on the t r a i l i n g
vor tex system of wings and some experimental evidence of the
f a r wake o f p r o p e l l e r s .
The f a r wake s t r u c t u r e has been deduced earlier from s t u d i e s
o f vor t ex motion and used t o develop t h e "Pr imi t ive Vortex Theory
of t h e Cyclogiro." I t was ,used t o exped i t e t h e i n i t i a l r e sea rch
on t h e giromilk. , and tests have i n d i c a t e d i t s usefu lness . . I t
w a s t h e s t a r t i n g p o i n t f o r cont inued. work. . - The e x a c t theory of
wake genera t ion w a s developed,. and v e r i f i e d t .hat t h i s s t r u c t u r e .
e x i s t e d . i n ' t h e f a r f i e l d . . The p r i m i t i v e theory. was then modified
t o inc lude wake. expansion - a n d b e t t e r modeling o f t h e near f i e l d .
Th i s h a s r e s u l t e d i n . improved .convergence.- b u t some except ions s t i l l
occur . This theory i s p r e s e n t l y be ing modified t o inc lude b e t t e r
n e a r f i e l d modeling t h e expense o f longer computing t ime. This
w i l l use c y c l o i d a l l i k e wake nea r t h e r o t o r combined wi th t h e
f a r f i e l d s t r u c t u r e . Wake widening is included.
, SECTION A. 10
WAKE MODEL FOR IMPROVED P R I M I T I V E THEORY
The p r imi t ive theory used a series o f . r e c t a n g u l a r vor t ex
r i n g s f o r t h e uniformly loaded b lade , s t a r t i n g . in t h e .immediate
v i c i n i t y o f t h e r o t o r . The r i n g s were of equa l ' s t r e n g t h and
equa l spacing and t r a n s l a t e d . ' a s . t h e r o t o r r o t a t e d a t a v e l o c i t y
equa l t o t h e ' f r ee s t ream v e l o c i t y p lus t h e mean induced v e l o c i t y
computed a t t h e . cap tu re are.a. .No wake expansion was considered.
The induced 've loc i ty a t t h e cap tu re a r e a was computed by t h e
momentum theorem. from t h e fo rces on t h e blade'. The x component
of v e l o c i t y on t h e o r b i t was assumed t o be. t h e induced v e l o c i t y
a t t h e c a p t u r e . a r e a c o r r e c t e d by a s i n e func t ion of I/.J t o reduce
t h e upstream s i d e and . i n c r e a s e t h e downstream s i d e t o allow f o r
v e l o c i t y decrease through t h e r o t o r . This c o r r e c t e d t h e angle of
a t t a c k , and i t e r a t i o n performed u n t i l t h e c i r c u l a t i o n on t h e
o r b i t and t h e mean i n d u c e d - v e l o c i t y computed from t h e momentum
theorem converged. .The r i n g spac ing . w a s then determined and t h e
induced v e l o c i t y on t h e capture a r e a computed from t h e wake and
t h e bound vor tex system, .was i t e r a t e d u n t i l it converged t o t h e
value computed from t h e momentum theorem by a d j u s t i n g t h e s t r e n g t h
o f t h e v o r t i c i t y i n t h e wake. The wake w a s then t r a n s l a t e d a s
t h e r o t o r r o t a t e d and . ' t he performance computed. Subrout ines were
used t o compute var ious s t e p s i n t h e ca . lcu la t ion . - The exac t wake .generation showed t h a t t h e wake widened i n
t h e spanwise and l a t e r a l d i r e c t i o n , t h a t t h e f a r f i e l d s t r u c t u r e
was generated q u i t e c l o s e t o t h e r o t o r , b u t t h a t nea r t h e r o t o r t h e
c y c l o i d a l s t r u c t u r e s t i l l e x i s t e d . I t was decided t o incorpora te
a s many o f t h e s e f e a t u r e s i n t o a modified p r i m i t i v e theory a s
poss ib le , b u t t o keep the ' computing t ime a s s h o r t a s p o s s i b l e .
Figure A . 1 9 i s a ske tch obta ined from c a l c u l a t e d r e s u l t s
f o r an eight-bladed r o t o r which incorpora tes most of t h e s e f e a t u r e s .
The c i r c l e i s t h e r o t o r o r b i t and t h e bound v o r t i c i e s a r e small
c i r c l e s on the o r b i t . The wake boundaries a r e t h e curved l i n e s
Figure A.19, Wake Structure Assumed for the Improved Primitive ~,ortex'~heory.
extending downstream from t h e cap tu re a rea , and t h e r i n g s o f
concentrated v o r t i c i t y a r e ind ica ted by c i r c l e s on t h e boundary
and diagonal l i n e s jo in ing p a i r s o f concent ra ted v o r t i c i t y on
t h e boundaries. The shape of t h e boundaries i s determined by
an emperical f i t t o t h e wake expansion based on c o n t i n u i t y and
t h e f i n a l v e l o c i t y i n t h e wake computed from t h e momentum theorem.
The sidewash due t o t h e r o t o r l i f t fo rce has been included and
tends t o cause t h e wake t o de . f lec t t o t h e s i d e oppos i te t h e
d i r e c t i o n o f t h e r o t o r l i f t force . Spanwise widen i s a l s o
incorporated, , b u t is symmetrical. A s t h e r o t o r r o t a t e s t h e wake
is t r a n s l a t e d downstream.
The bound vor tex system and t h e t i p v o r t i c e s jo in ing
t o t h e wake t o s a t i s f y t h e Helmholtz Vortex laws presented a
problem. I f t h e c y c l o i d a l su r faces w e r e incorpora ted , many
vor tex segments would be needed t o s imula te t h e s e s u r f a c e s , and
t h e computing t ime, e s p e c i a l l y wi th t r a n s l a t i o n , would be excess ive .
Examination o f Figure A.19sugges.ted a s o l u t i o n which only p a r t i a l l y
s a t i s f i e d t h e Helmholtz vor tex laws; but 'which requi red very ,
l i t t l e computing t ime. This w a s t o jo in t h e bound v o r t e x t o t h e
f r e e concentrated vor tex which was shed when t h e bound vor tex was
a t t h e . f l i p p o i n t by a s t r a i g h t l i n e vor tex segment of s t r e n g t h
equal t o t h e l o c a l bound vor tex s t r e n g t h , and t o ' add a vor tex .
t o t h e f r e e concent ra ted vor tex t o form a c losed r i n g . The s t r e n g t h
of t h i s semibound r i n g va r i ed cont inuously a s t h e . r o t o r r o t a t e d
and vanished. a t t h e lower f l i p po in t . ,The f r o n t bound v o r t i c c c
were joined t o t h e upper h a l f o f . t h e wake, and t h e lower bound
v o r t i c e s t o t h e lower ha l f of t h e wake. This was super io r t o t h e
way t h e bound v o r t i c e s had been t r e a t e d i n t h e p r i m i t i v e theory
which d i d n o t connect them t o t h e wake. This model has . t h e d e f e c t
t h a t t h e jo in ing vor . t ices a r e cons tan t s t r e n g t h and t h e f i r s t few
f r e e concentrated v o r t i c e s a r e too s t rong . This induces too high
v e l o c i t y on t h e o r b i t and tends t o degrade t h e performance.
However, it grea t ly reduces t h e computing t ime and seems t d g ive
' s a t i s f a c t o r y r e s u l t s . The program was run t o check the McDonnell-
Douglas tests of three-bladed g i r o m i l l and t h e agreement was
e x c e l l e n t .
The s e c t i o n p e r t a i n i n g t o t h e Madaras system fol lows.
369
SECTION A . l l
APPLICATION TO THE MADARAS ROTOR PLANT
The vor tex computer program was used t o compute t h e perform-
ance of a series of Madaras p l a n t s t o determine e f f e c t s of mutual ,
i n t e r f e r e n c e between r o t o r s a s a funct ion of t h e design va r i ab les .
The v a r i a b l e s i n v e s t i g a t e d were: t r a c k r a d i u s , R; wind speed, Vu;
t i p speed r a t i o , A ; c y l i n d e r r o t a t i o n speed r a t i o t o r e l a t i v e wind
speed, U/V, r o t a t i o n a l speed, U; ramp - angle, 8 ; e c c e n t r i c i t y , p;
and number of c y l i n d e r s , NB. The cy l inder chotien had a p ro jec ted
area of 2000 square f e e t , an aspect r a t i o of 6 , w i th an cnd eap
r a t i o , e/d, of 2. This gave a c y l i n d e r diameter of 5.56 m and
a h e i g h t of 3 3 . 4 m. The va lues of R i n v e s t i g a t e d w e r e R = 457 m,
610 m , 762 m , 915 m, and 1196 m, The wind speed ( V ) was v a r i e d W
from 4 . 5 m / s t o 13.5 m / s i n increments of 1.1 m/s . The t i p speed
r a t i o , A , was v a r i e d from 0.8 t o 2.5 t o f i n d t h e peak power output
of t h e c y l i n d e r s . U/V was v a r i e d from 2 t o 6 i n increments of 0.5
t o determine an optimum, U was va r i ed from 46 t o 61 m / s i n inc re -
ments of 7.6 m/s . Ramp angle , A , was checked a t 15O, 30°, and G O 0 ;
however, most d a t a was computed only a t 30° and 15O. Ramp angle
is t h e angle dur ing which t h e c y l i n d e r r o t a t i o n is a c c e l e r a t e d from
f u l l s t o p t o f u l l speed, and v ice versa . The e c c e n t r i c i t y angle ,
B , was checked a t -85O, -87,5O, and -90°; but -8S0 was used f o r
most c a l c u l a t i o n s .
The number of c y l i n d e r s w a s v a r i e d from 1 t o 18 i n incrdments
of 1. The wake l eng th was a r b i t r a r i l y set a s be ing 5 r a d i i .long.
I n computing, p o i n t s were s e l e c t e d on t h e t r a c k a s near t o lo
a p a r t as poss-ible, The program used a s an i n p u t t h e number of
p o i r ~ t s un t h e o r b i t , N 2 , which i s an i n t e g e r . N2 = l a r g e s t i n t e -
g e r i n t h e r a t i o [(- 360 ) 1 x NB + 1. I f NB is an i n t e g r a l mul t ip le NB
of 360°, t h e p o i n t s are lo a p a r t . Th i s i s a c h a r a c t e r i s t i c of t h e
program and must be followed e x a c t l y o r spurious r e s u l t s occur.
The number of p o i n t s on t h e cap tu re a r e a can be any number equal
t o o r less than 201, but must be i n t e g e r s . The number of cy l inder s
must be i n t e g e r s , bu t may be odd o r even. The wake length i s
expressed i n terms of t h e number of r o t o r diameters (NR) . ~ h ' e wake
extends both upstream and downstream. It is characterized by an
input parameter of NR which must be integer. The data was com-
puted for NR = 5, but NR = 10 would have been preferred. NR = 5
was used to reduce the computing time with only .a small loss of
accuracy.
Preliminary runs for a 6-cylinder plant were run for
4.5 < - VW - < 13.5 m/s on R - 457 m radius track with 0.1 < A < 1.5 - - and A A = 0.1 and A = lSO, with 2. < U/V < 6. with A U/V = 0.5 at - - 8 = -85" to find the value of A = 1.1 and U/V = 5.5. The value
of u/V was modulated to maintain U/V at a constant value for all
values of orbit angle except when reversing the rotation. The
computations showed that the rotor was self-starting in the wind,
and generated about 1.1 MW per rotor at peak power. We also
learned that at each wind speed,peak power occurred at a track . 'P
speed of V = 10.5 m/s.
A computation of the power required to accelerate and
decelerate the rotors with a ramp angle of A = 15' showed that
very large electric motors would be required. Therefore, the ramp
angle, was increased to 30' and the data recomputed. Only a small
loss in gross power generated resulted, .but the power to spin the
rotors in acceleration-deceleration was reduced to approximately
1/4 that required fbr A = 15'.
Operation at constant U/V meant that a costly cylinder rpm
control sensing and,regulation system would be required, and that
cylinder spinning power would be variable around the track, since
V is not the track speed but the resultant aerodynamic velocity.
Since the electric motors would operate more efficiently at con-
stant rgm and the control system would.be simplified, it was de- cided to operate at constant peripheral speed, U.
The program was run again with 6 cylinders on a 457 m track
with 4.5 < W < 13.5 m/s, AW = 1.1 m/s; 0.1 < X < 1.5 with A X = 0.1; - - -. - and A = 30°, and B - -8.5". Examination of detailed data showed th.at
as V and 3\ decreased, the cylinder approach.ed super ci.r.culation W
over part or all of the orbit. If U were reduced proportionally to Vu
as Vu reduced, supercirculation would be avoided and a small gain
in power would result. More importantly, the acceleration-decelera-
tion power reduces as U is decreased by the cube of the speed ratio,
and an increase in the net power would result. The program was not
written to accomplish this except by changing control cards. This
,procedure would be too time consuming, so it was elected to perform
all the runs at a constant U. The program could be altered later
to include this option as time did not permit altering the program
or changing U during one run by control cards.
A conference was held to outline the range of variables to
be investigated as minimum objectives. Since an excessive number of
computer runs would be required i-f a l l combinations were s l u d i e d , if
was decided that certain variables would be investigated to try to
find an optimum, and then held constant while the next variable
was optimized, and then held constant. This procedure would be
continued until all variables had been investigated. Although the
number of runs required was reduced greatly, we recognized that
a true optimum would not be reached.
Starting with the 457 m radius track, the number of cy- linders was increased from 1 to 8 in increments of 1. It was found
for 0.8 - < h - < 1.3 that the power generated increased linearly with NB up to 6, and then began to depart from a linear increase with
power increasing more slowly as the number of cylinders increased.
Thus, there is a maximum in power generated as NB increases, A maximum has not been reached, but cylindcr mutual interfereme
effects were beginning to be significant as the number of cylinders
increased beyond 18. Above A = 1.3, the loss in power per rotor
increased markedly as NB increased, w i t . h maximums occurring st.
different values of A as NB was increased. This indicated that
there was a minimum spacing between cylinders below which cylinder
mutual interference was important. This spacing occurred when R1
Sin (180°/NB1) = R2 Sin (180°/~B2), with R1 = 457 m and NB1 = 6.
Thus, as R is increased, NB2 could be computed for a given R2. 2 It would be necessary to investigate NB > NB2, when R2 > R1, since
below NB2 the o~lhder mutual interference would be negligible. hi^ . ,
would reduce the computationneeded to investigate larger radii
track.
The time available to accelerate and decelerate the cy-
linders in rotation increased directly as R for fixed A. This has
a significant effect on the power required for deceleration-
acceleration,, and since this power is a significant portion of the
gross power generated, anything which can reduce this power has
potential pay-off. Increasing R appeared attractive, so R. was
increased from.457 m to 1220'm in steps of 152 m. At each value of
R2 several. values' o f numbe'r of cylinders, NB, were ch~sen and the
perf ofiance 'was computed.
The peak power per rotor at each value of V was plotted W
and labeled for each value of NB versus the Radius, R. Selected
values of NB were computed at each value of R so that trend lines
could be established. At fixed VW and NB, the peak power increased
monotonically with increasing R, and a8ympto.tically appg~ach.e$
limit. The rate of increase decreased as R increased. Physically,
this meant that as R increased with fixed rotor spacing, the blade
mutual interference effects decreased. until only a few adjacent
cylinders affected one another, and those on the far side of the
orbit had vanishing effect. As NB increased beyond that for
critical spacing, the peak power per rotor decreased indicating an
increase in mutual blade interference, As NR was increased, the
trend lines of peak power per rotor were essentially parallel but
below one another.
It was obvious that increasing R was beneficial. However,
the track length increases directly with R increase, and if track
costs are found to be a significant portion of the cost, the larger
radii may not be an attractive trade-off since the beneficial effects
of increase.in.power with increase in R would be offset more by the
increase in cost.
It was decided t o i n v e s t i g a t e t h e in f luence of l a r g e r num-
bersof cy1inder.s on t h e performan.ce .at R = 457 m, Data was then
r u n f o r R = 457 m w i t h NB = 9 , 10, 11, ,12 , 13, 1 4 , 16, 18. A s
NB increased , X f o r peak power a t each wind speed decreased, s o
f o r NB = 14. , 16, 18 it w a s nec'essary t o cover t h e range of 0.6 - < A - < 1.5, w i t h A X = ,0.1. It was found t h e power a t each wind speec
neqred a maximum as. NB approachsd 18, Although a maximum was n o t
de f ined t h e r e wasonlyamargina l i n c r e a s e i n power f o r NB = 18 over
t h a t f o r N = .16, s o no l a r g e r va lues of NB were used, I n a d d i t i o n
computing t i m e would inc rease p r o h i b i t i v e l y .
The power r equ i red to d e c e l e ~ a t e - a c c e . l e r a t e t h e rotor was found t o be c r i t i c a l a t R = 457 m. The s imples t method t o reduce t h i s would be t o i n c r e a s e A . However, an i n c r e a s e of A t o 60' re- s u l t e d i n a s e r i o u s l o s s i n power generated, It appears t h a t
A = 30° i s t h e l a r g e s t A t h a t can be t o l e r a t e d . Decreasing U i s as e f f e c t i v e as i n c r e a s i n g A . An examination of d e t a i l d a t a a t
U = 54 m / s , shows t h a t a t t h e lower wind speeds, t h e cy l inder i s
i n s u p e r c i r c u l a t i o n , and U can be g r e a t l y reduced. A t Vu = 13.5
m / s , t h e c y l i n d e r i s i n supercircnlat.j . ,on on a small p a r t of t h e
o r b i t , s i n c e X for peak power i s about un i ty . A decrease i n U
could be t o l e r a t e d wi th almost n o . e f f e c t on the power generated,
b u t if decreased t o o much t h e power wou3.d he reduced. The super-
c i r c u l a t i o n phenomenon w i l l be d iscussed i n more . d e t a i l l a t e r .
A s i n g l e c y l i n d e r w a s run on t h e R = 457 m t r a c k s i n c e t h i r
run enabled a comparison with a s i n g l e c y l i n d e r opera t ing i n un-
d i s t u r b e d flow. The single c y l i n d e r experiences no in te r -cy l inder
mutual i n t e r f e r e n c e , bu t has self- induced i n t e r f e r e n c e wi th t h e t i 1
j o i n i n g vor tex and t h e wake. These e f f e c t s a r e usua l ly omitted i n
a undisturbed flow a n a l y s i s , b u t are a c t u a l l y p resen t .
The power generated by a s i n g l e c y l i n d e r on a 457 m r a d i u s
w i t h U = 54 m / s and A = 30° i s shown i n Figure A,.2O f o r 5 different
v a l u e s of Vu a s a func t ion of A. I t i s t o be noted t h a t as Vu
i nc reases , t h e va lue of X corresponding t o maximum o r peak power
decreases. ' I t i s i n t e r e s t i n g t h a t t h e t r a c k speed a t which t h e
maximum occurs i s approximately 10.9 m / s f o r a l l va lues of Vu.
Fisure A,'?*3. Gross Power Output versus X for various Wind Speeds, One Roto'r Spinning at 183 rpm, 915 m Diameter Track.
3 r 1.2 AR = 6 - e/d= 2
2 Rotor Diameter = 5.6m I- Rotor Height =33.4m - t- Rotor Speed = 183RPM 3 o Track Diameter =915m
0
0 0
A = v , /v,
T h i s f e a t u r e i s a d e s i r a b l e f e a t u r e for .synchronous genera tors .
Also of i n t e r e s t is t h e f a c t t h a t each va lue of Vu, t h e t r a c k
speed V t a t which t h e power developed becomes zero i s approximately
26 m/s . T h i s shows t h a t t h b system is s e l f l i m i t i n g , t h a t it can-
n o t run away, and t h a t an e s s e n t i a l l y cons tant optimum t r a c k speed
e x i s t s f o r a l l : wind speeds. when t h e e f f e c t of t r a c k r e s i s t a n c e ,
motor power l o s s e s , and genera to r power l o s s e s a r e included, t h e
maximum t r a c k speed t h e r o t o r w i l l reach w i l l be always less than
t h i s l i m i t i n g speed Based only on rotor c h a r a c t e r i s t i c s . The
reason t h e speed f o r peak power and t h e l i m i t i n g speed are essen-
t i a l l y cons tan t speeds can be t r a c e d t o t h e f a c t t h a t U had been
The wind t u n n e l t e s t s r epor ted i n Sect ion 3 showed t h a t
CL and CD of a sp inning c y l i n d e r a r e a funct ion of ( U / V ) , where U
is t h e c y l i n d e r p e r i p h e r a l v e l o c i t y , and V is t h e r e l a t i v e aero-
dynamic speed. When t h e r o t a t i n g cy l inder is moved on a c i r c l e
i n a uniform flow, i d e a l theory neg lec t ing induced v e l o c i t i e s show
t h a t Vu i s a c t u a l l y VR = W 41 +hL - 2ASin$, and (U/V) a c t u a l l y
is (U/VR). The tests a l s o showed f o r , A = 6 and e/d = 2 , t h a t when
(U/VR) = (U/VR) crit = 6, C and CD reach t h e i r maximum values ; and L when (U/V) (U/VR) crit t h e CL and C a r e e s s e n t i a l l y constant:. D The reason f o r t h i s i s t h a t a t (U/VR)cri t , s u p e r c i r c u l a t i o n occurs
on t h e cy l inder .
S u p e r c i r c u l a t i o n i s a t e r m used t o i n d i c a t e t h a t t h e s t a g n a t i o n
p o i n t i n t h e f low around a body has moved o f f t h e body and occurs
i n t h e f l u i d n e a r t h e body. This is i l l u s t r a t e d i n ~ i g u r e A. 21.
Figure A.21a i l l u s t r a t e s t h e s t r eaml ines a s s o c i a t e d wi th p o t e n t i a l
f low around a c i r c u l a r c y l i n d e r without c i r c u l a t i o n . Figure A.21b
i l l u s t r a t e s t h e real f l u i d taken from photographic techniques used
t o v i s u a l i z e t h e flow a s r epor ted i n Reference 62. When a vor tex
i s placed a t t h e c e n t e r of t h e c y l i n d e r t o add c i r c u l a t i o n , t h e
s t r eaml ine p a t t e r n changes, a s i n Figure A . 2 1 ~ and A.21d. The
s t a g n a t i o n p o i n t s occur where t h e s t r eaml ines come normal t o t h e
c y l i n d e r a t t h e p o i n t s S. For real flow, s t agna t ion p o i n t occurs
on t h e upstream s i d e of t h e c y l i n d e r , but a wake e x i s t s on t h e
Figure A. 21. I d e a l 'and R e a l Flow Around a C i r c u l a r Cyl inder f o r Various C i r c u l a t i o n from 0 t o a S u p e r c r i t i c a l Value.
downstream s i d e . The wake reduces t h e l i f t magnitude f o r a given
r a t i o o f U/V s o t h a t t h e l i f t generated i s less than p red ic ted by
theory . F igures A.21e and A.21f i l l u s t r a t e t h e c r i t i c a l value
of c i r c u l a t i o n which causes t h e two mathematical s t agna t ion po in t s
t o coa lesee i n t o a s i n g l e s t agna t ion p o i n t a t t h e bottom of t h e
c y l i n d e r .
I f t h e c i r c u l a t i o n i s g r e a t e r than t h e c r i t i c a l value t h e
s t a g n a t i o n p o i n t moves ou t i n t o t h e f l u i d , and t h e cy l inder i s
surrounded by a l a y e r of f l u i d which r o t a t e s around t h e cy l inder
i n s i d e t h e c losed loop. E f f e c t i v e l y t h i s has changed t h e c i r c u l a r
c y l i n d e r i n t o a t e a r d r o p cy l inder . Mathematically, S i s a s i n -
g u l a r p o i n t , and s i n c e t h i s occurs ou t i n t h e f l u i d , some resea rchers
b e l i e v e t h i s could n o t occur i n r e a l i t y . This b e l i e f is not t r u e ,
because a t S t h e v e l o c i t y is ze ro , and a s shown i n Figure A.21ht
t h i s s i t u a t i o n i n a r e a l f l u i d was photographed . .. by Prandt l . This
s i t u a t i o n occurs on a r o t a t i n g cy l inder because of v i s c o s i t y . When
t h e c i r c u l a t i o n i s s t r o n g enough t o be g r e a t e r than t h e c r i t i c a l
v a l u e , it i s r e f e r r e d t o a s s u p c r c i r c u l a t i o n . It can be c r e a t e d
by r o t a t i o n on a c i r c u l a r cy l inder , o r by blowing j e t s on a i r f o i l s .
It does e x i s t .
V i scos i ty i s n o t powerful enough t o i n c r e a s e t h e f l u i d v i s -
c o s i t y s u f f i c i e n t l y t o cont inue t o cause the ' l i f t c o e f f i c i e n t t o
i n c r e a s e a f t e r some va lue of U/V. For t h e c y l i n d e r t r a v e l i n g a t a V.t t r a c k speed Vt , (U/VR) crit = U/ [V 41 + A 2 - 2ASin$ 1 where A = - .
W v W
It i s seen t h a t ( U / V R ) ~ , ~ ~ o r s u p e r c i r c u l a t i o n can occur a t po in t s
on t h e o r b i t depending upon U , W , A , and $ . Of p a r t i c u l a r i n t e r e s t
i s when $ = - ~ / 2 s i n c e t h i s corresponds t o t h e maximum value of VR T7 - - U which makes (U/VH) a minimum. Then, (U/VR) crit + . If
U i s a cons tan t , e i t h e r Vu o r A can be solved f o r , k!:nce V) 0) =
u/ [ (1 + 1 (U/VRcritl , and Acrit = u / [ v ~ ( u / v R ) crit] -1. 1t i s
seen t h a t a s Vu i n c r e a s e s , t h e va lue of A a t which s u p e r c i r c u l a t i o n
occurs b t t h e upper f l i p p o i n t decreases . The s i g n i f i c a n c e of Acr i t
is ' t h a t f o r each va3ue of V foa A < A c r i t , t h e c y l i n d e r has super- W
c i r c u l a t i o n - o v e r t h e whole o r b i t , and CL and CD a r e e s s e n t i a l l y con-
s t a n t a t t h e maximum values around t h e whole o r b i t . When A > A c r i t ,
p a r t of t h e upper o r b i t ( reg ion of advancing c y l i n d e r ) has (U/VR) c
(U/VR) c r i t t and t h a t por t ion of t h e o r b i t has CL and CD less than t h e maximum, bu t v a r i a b l e with $. The va lue of $ a t which
i s reached on t h e o r b i t can be shown t o be $crit - ( U / V ~ ) c r i t - 2
S in { + ' - (U/W)/U/VR) I . The minimum value of CL and 2 A -- - CD on t h e o r b i t occurs a t $ = - 7r/2 and i n c r e a s e s t o t h e maximum
value a t $crit. I f U i s a cons tan t = 53 m / s , and (U/VR)crit = 6 ,
then qcrit = 0 f o r Vu = 8 .9 m / s . Thus, f o r a l l Vu < 8.9 m / s t h e
c y l i n d e r i s i n s u p e r c i r c u l a t i o n f o r t h e complete o r b i t . This
means u n t i l X = X c r i t t C and CD a r e c o n s t a n t a t t h e maximum values. L A s X i n c r e a s e s beyond Xcri t t h e p a r t of t h e upper o r b i t f o r which
s u p e r c i r c u l a t i o n does no t e x i s t i n c r e a s e s and CL and CD on t h i s
p a r t of t h e o r b i t decrease with inc reas ing A. CL and CD a r e a
minimum a t $ = -n/2 and gradual ly inc rease u n t i l $ = qcrit a£ ter
which CL and CD become cons tan t . Since t h e upper p a r t of t h e o r b i t
produces t h e most power, t h i s means t h a t t h e rate of i n c r e a s e of
t o t a l power with i n c r e a s i n g X decreases below t h a t which would
occur i f CL and CD w e r e cons tan t . C S VR
The c i r c u l a t i o n i s I' = L 2 b s o t h a t it i s p ropor t iona l - .-
t o t h e product CL VR. But, VR = vu/l + A ' - 2 XSin$ , s o t h a t
V i n c r e a s e s wkth inc rease of A . The v o r t i c i t y i n t h e wake is'?i' R p ropor t iona l t o r and t h e r dens i ty in t h e wake i n c r e a s e s with X
s i n c e t h e r e a r e more c l o s e l y packed s u r f a c e s o r vor tex r i n g s a s X -'
i nc reases . The induced v e l o c i t i e s a r e p ropor t iona l t o I' and t h e
number of r i n g s i n t h e wake. Thus, a s A i n c r e a s e s t h e induced
v e l o c i t i e s i n c r e a s e i n magnitude, and t h e s e reduce t h e magnitude
of VR. The n e t e f f e c t i s t h a t t h e power generated i n c r e a s e s wi th
i n c r e a s e i n X u n t i l t h e induced v e l o c i t i e s become s i g n i f i c a n t , and
then t h e power generated decreases . A t some value of X f o r t h e
given value of Vu, t h e peak power i s generated. For A g r e a t e r
than t h i s va lue , t h e power generated decreases . The e f f e c t of
cons tan t U i s t o reduce t h e e f f e c t i v e CL a s X i n c r e a s e s , and t h i s
reduces the power generated Er'om that which would be generated if
CL were constant in magnitude. This causes the peak power to occur
at a constant. V and a more rapid decrease in power generated once
the peak has been passed. The mechanism is complex and the results
are not easily predictable, but come from detailed calculation.
The shape of the power generated versus A curves can be more readily understood. Since the power generated is proportional
to the cube of the wind speed, increasing wind speed should have a
powerful effect on the peak power generated. For example, an 8.9
m/s wind speed should generate 30% of the power developed at 13.4
m/s at the same value of A. Thus the peak power for 1 cylinder
at A = 1.2 would be expected to equal 0.33 MW at 8.9 m/s, since a
wind of 13.4 m/s generates 1.11 MFJ. However, the computed power
at 8.9 m/s at A = 1.2 is 0.39 MW which is greater than would be
expected. The reason for this is that at 13.4 m/s the ideal value
Of: qcrit is 1.6'. Consequently, the effective lift coefficient
at 13.4 m/s is less than the effective lift coefficient at 8.9 m/s
since for winds of 13.4 m/s, less of the orbit has supercirculation
than for 8.9 m/s winds. This reduction in effective lift coefficient
causes the power to increase less rapidly than the cube of the wind
speed. Therefore, tk:~ more rapM decrease of power above peak
power as wind speed increases is associated with the reduction in
effective CL as A increases due .to less of the orbit being in supercirculation. Based on these no l o s s computations,if constant u/V could be used rather than constant I1 more power could be generated at all X and W, than for constant TJ. Theso two kypcs
of operation will be studied to determine which yields the most
uet power per dollar.
As mentioned before, as the number of cylinders is in-
creased, mutual cylinder interference effects begin to have im-
portance when NB > 6. The reason for this is that the spacing
between the cylinders is h = 2R Sin (180°/NB), where h is the spacing. The induced velocity in two dimensions is Vu = r/(2rrr),
where r is'the radius from the bound vortex to the point in ques-
tion, since the spacing, h, reduced with.increasing number of
cyLinders. Thus the induced velocity on neighboring cylinders
increases as the number of cylinders .is increased. The total
induced velocity felt by a cylinder is the vector sum of the induced
velocity associated with each cylinder on the orbit and its
associated semi-bound .vortex ring. This sum increases in magni-
tude, and its direction changes as the number of cylinders increases.
Those cylinders nearest any given cylinder have the major effect,
as the radius r is less. If each cylinder had the same lift
coefficient and velocity, the direction of the mutual induced
velocity would be radially outward on the upstream side of the
orbit, and radially inward on the downstream side of the orbit.
Because of the variation in velocity and lift coefficient around
the orbit, the direction is not radial, but may be reasonably close
to radial. It will still be outward on the upstream side and in-
ward on the downstream side for a windmill and opposite for a #
propulsive device. This.mutua1 blade interference has profound
effects on the shape of the power generated versus X curves.
Figure R . 2 2 is a series of power generated versus X curves for a series of wind speeds for a 14 rotor plant having 33.4 m high by 5.6 m diameter r~tors, The cylinders operate on a
circular track having a 457 m radius at a rotati~n speed, U,
of 53.1 m/s. Note that only CD losses of the cylinder are included
in this data. It is seen that the value of A for peak power in-
creases as wind speed increases, This means that the track speed
for peak power is no longer constant, but increases as wind speed
increases. The reason for this is that the mutual interference
becomes less as wind speed increases. This means that synchronous
generators geared to the car wheels would not generate constant
frequency. If dc current or an induction generator were used, this
would not be important.. In additi~n,the decrease of power beyond
peak power is much more rapid at the lower wind speeds. As wind
speed increases, this effect is less pronounced, since the mutual
induced velocities are a smaller fraction of the total velocity,
and do not effect I' and VR as much. The peak power per rotor is
less than that for a single cylinder as would be expected, since
14 - ROTOR PLANT - rn /s
"w2 -
-
-
-
-
-
I I
FigureA.,22. Average Gross'Powex 'Output from a Madaras Plant of Fourteen Rotating cylinder^ versus h for Various Wind Sp'eeds. Fourteen Rotating Cylinders, Aspec't Ratio = 6, e/d = 2, Cylinder Area.. = : 186m2, Diameter = 5.. 6m, Track Radius = ; 457m, Cylinder Rotating at ,183 rpm.
t h e magnitude and d i r e c t i o n of t h e r e s u l t a n t v e l o c i t y a t each
po in t on t h e o r b i t has been changed.
Figure A.23 p resen t s t h e d a t a when t h e p l a n t s i z e has been
increased t o 16 of t h e same s i z e d c y l i n d e r and t r a c k radius . The
c h a r a c t e r i n t h e curves i s t h e same as f o r 1 4 cy l inder s . The t o t a l
power has increased while t h e power p e r r o t o r has decreased. The
value of X f o r peak power has reduced a s w e l l a s t h e l i m i t i n g value
of A . The primary advantage of 16 cy l inder s over 1 4 .is t h a t t h e
problem o f ' c o n n e c t i n g t h e r o t o r s i n an endless t r a i n is e a s i e r ,
b u t t h e p l a n t c o s t i s h igher s i n c e more c y l i n d e r s must be used.
Figure A.24 p resen t s t h e d a t a when t h e number of c y l i n d e r s
has been increased t o 18. The peak power has been increased only
s l i g h t l y while t h e power generated p e r r o t o r has decreased again.
A l l t h e comments f o r t h e 16 c y l i n d e r r o t o r apply. This appears
t o be about t h e maximum power which can be generated i f t h e t r e n d s
cont inue. No f u r t h e r i n c r e a s e i n number of c y l i n d e r s has been
run since t h e ga in i n t o t a l power i s marginal, and computing t ime
i n c r e a s e s r a p i d l y wi th NB and w a s p r o h i b i t i v e . The power pe r r o t o r
is only 0.7407, than t h a t f o r a s i n g l e r o t o r c y l i n d e r a t 13.4 m/s .
This p l a n t produces n e a r l y t h e maximum power.
THE EFFECT OF RAMP ANGLE ON THE POWER PRODUCED
The ramp angle ( t h e angular d i s t a n c e during which t h e
cy l inder i s spun-up) was i n i t i a l l y chosen t o be I S 0 , b u t spin-up
power was excessive. The ramp angle was then increased t o 30° as
c a l c u l a t i o n s showed t h i s may be acceptable , e s p e c i a l l y a t t h e
l a r g e r t r a c k r a d i i . When t h e r a d i u s was he ld t o 1500 feet t o reduce t h e t r a c k c o s t , t h e number of c y l i n d e r s w a s increased and
t h e d a t a computed. It w a s found t h a t a t t h e h igher wind speeds,
t h e spin-up power was again becoming a l a r g e f r a c t i o n of t h e t o t a l
power generated. Calcula t ions showed t h a t a 60° ramp angle 'would
be d e s i r e d t o reduce t h e spin-up power, s o t h e ramp angle was
increased t o 60°. and t h e d a t a computed a t near t h e peak power
a t X = 1 . 2 for t h e 16 c y l i n d e r r o t o r . The r e s u l t s w e r e d i s a s t r o u s .
The power generated was only about two-thirds of t h a t generated
L
I4
I2
10
Z Y 8 e
6
4
2
0 0.2 0.4 0.6 0.8 I .O 1.2 1.4 1.6
X= v/w .gure A. 23 . Average Gross Dover O u t ~ u t from Nadaras Plant versus
X fo r various Wind Speeds. Sixteen Rotating Cylinders, Aspect Ratio = 6 , e/d = 2 , Clyinder Area = 186m2, Diameter = 5.6m, Track Radius = 457m, Cylinder Rotating a t 1 8 3 r p m .
VW= M/S 16 ROTOR PLANT
0 - a 1 -
Figure.A.24. Average Gross Power Output from Madaras Plant versus h for Various Wind Speeds., Eighteen Rotating Cylinders, Aspect Ratio = 6, e/d = 2, cylinder Area = ~ $ 6 ~ 2 , Diameter = 5.6m, Track Radius = 457.1~~ Cylinder Rotating at
a t t h e same value o f X when t h e ramp angle was 30°. This r e s u l t
w a s a n t i c i p a t e d a s t h e upper h a l f of t h e o r b i t produces t h e major
c o n t r i b u t i o n t o t h e power, and one- th i rd of t h i s had been a t
reduced CL d u e , t o t h e l a r g e ramp angle.
It may be p o s s i b l e t o opt imize r a m angle power l o s s with
spin-up power l o s s by varying t h e ramp angle over a wide range
i n smala increments. This has n o t been done due t o t h e p ress
of t i m e and t h e long computing time^ f o r l a r g e number of blades.
There w i . 1 1 probably be a d i f f e r e n t optimum condi t ion a t each number
o f r o t o r s and wind speed. This would r e q u i r e l a r g e amamts of
t i m e and funds f o r computer a n a l y s i s , and i s iecommended i f t h e
Madaras system i s ftnded f o r f u t u r e research ,
APPENDIX B
COST 'ESTIMATE DETAILS
APPENDIX B
COST ESTIMATE DETAILS
B.l PLANT COST
A. LAND'
B. SITE PREPARATION AND EARTHWORK
C l e a ~ S i k e , 70 Ac @ $750.00 Layout Work Fencing, 11,500 If @ $10.00
TOTAL SITE PREPARATION AND EARTHWORK
SITE BUILDINGS MID VIADUCT Assembly Building, 100' x 160'
See attached sheet Control Building., 30" x 50'
1,500 sf @ $50.00 Access under Track:
Excavation, 5,500 cy @ $2.60 Concrete, 1,015 cy @ $137.00 Roadway, 295 sy @'$15.25
TOTAL SITE BUILDINGS AND VIADUCT
To be Considered Separately
UTILITIES, ROADWAYS, TRACKS AND TROLLEYS
Utilities: Perforated Drains, 61,000 If
@ $6.85 $417,850 Catch Basins, 160 @ $75.00 140,000 Corr. Metal Pite 24" dia.
16,000 If @ $15.00 240,000 Corr. Metal Pipe 12." dia.
10,000 .If @ $7.50 75,000 Corr..Metal Pipe 8" dia.
6,000 If @ $4.35 26,100 Excavatiun & Backfill,
24,000 cy @ .$3.60 86,400 985,350
Roadways : Concrete, 3 4 , 7 0 0 . ~ ~ @ $15.25 $529,200 Gravel, 20,.315 cy @ $8.00 . 162,500. 691,700
Tracks : Subgrade Compaction, 170,000: sy
@ $:20 $ 34,000 Testing 50,000 Cuts & Fills, 143,000 cy
@ $2.60 371,800
Borrow Fill, 160,.000 .cy @ $8.00 1,280,000
Fine Grade, 170,O.OO sy @ $.30 51,O'OO 1,786,800
Roadbed Concrete, 10,500 cy
@ $52.25 $ 548.,7'00 Reinforcing Steel, 945 tons
@ $660.00 623,700 Joints, 41,000 If @ $6.00 24,600 Finish & Cure, 24.3,700 sf
@ $2-25 61,'OOO 1,258,000
steel Track Bolts, 15,235 @ $30.00 $ 45'7,050 Track Plates, 4,200 tons. -
@ $660 3,150,000 Grout, 317 cy @ $1485.00 470', 800 4,077,850
Trolleys Poles, 380 pc @ $1100.00 383,800 Joists, 230 ton @ $700.00 161,000 Support Angles, 115 ton . . . .
@ $1200.00 138,000 Collector Track, 13,180 If
@ $40.00 527,200 Trolley Brackets, 28 pc
@ $1200,00 33,600 Trolley Shoes, 84 pc
@ $570.00 47,800 Pole Excavation, 24-0.. cy ...
@ $100.00 24,000 Pole Foundation Concrete,
24'0 cy @ $45.00 10,800 Pole Anchor Bolts, 1,520 pc
@ $25 38,000. 1,321,280
Puwer Cull~ectien Systcm 1000 amp Aerial Cable,
6,000 If @ $69.00 414,000 1000 amp Taps on Tr.olley 6,100 Poles, 150 pc @ $225.00 41,250 461,350
Wind Sensors and Poles Wind Sensors, .24 pc C! $650.00 15,600 Sensor Poles, 24 pc @ $275.00 6,600 Underground Cables, 20,000 If
@ $2.25 45,000 67,200
TOTAL UTILITIES, ROADWAYS, TRACKS AND TROLLEYS $10,649,530
E. ROTOR AND CAR
Wheel and Suspension System: (see attached sheet) 28 pc @ $220,565 $6,175,820 (includes generator and speed increaser)
Couplings and Train Assembly Cables, 25,000 lb @ $5.00 125,000 Cable Sockets, 56 pc @ $1000.00 56,000 Cable Pins, 56 pc @ $100.00 5,600 Positioning of Cars on Track 50,000 Rental of Prime Mover 83,000
Car F r a n e and Housing (see attached sheet) 28 pc @ $167,230) 4,682,440 (includes spin motor and speed increaser)
Rotor Tower (see attached sheet) 28 pc @ $94,960 2,658,880 (inoludes bearings, sliaftlng, lube system)
Balance Rotor 28 pc @ 2500.00 70,000 Generator Controls & Wiring:
Generator Control Center 36,500.00 Generator Wiring 1,230.00 Spin Motor Wifing 600.00 Lube Pump Wiring 1,270.00 Car Lighting 920.00 Telemetry and Controls 37,500.00 Grounding 2,500.00 Car Power Wiring 1,050.00
28 PC x 81,570.00 $2,283,960
TOTAL ROTOR AND CAR $18,850,420 .-- B'. PDWER AND CONTROL SYSTEMS
Power Factor Correction 2000 amp Disconnects Control, Computers, Displays
TOTAL POWER AND CONTROL SYSTEMS
B,? SUMMARY
DIRECT COSTS
Construction * E i t e Prepar-a L i o l l *Buildings & Viaduct -Utilities *Roads 'Tracks & Trolleys
Total Construction
Mechanical *29 Rotor Cars (includes 1 spare)
Total Mechacical
TOTAL DIRECT COSTS (no land)
Land Net Acreage = 70 acres 390
INDIRECT COSTS
a Land none
a General Consturction Indirect Cost (24 months)
'Insurance on Labor, Workmen's Comp., FICA, Unemployment: 16% x 3,600,000 $ 576,000 'Office Expense: 3% x 13,243,930 397,320 'Field Personnel: Project Mgr. 80,000 Field Engr. 200,000 Supervision 56,000 Timekeeper 40',0'00 380,000
*Overhead 5% x 13,243,930 (direct) 662,200 'Profit 3% x 13,243,930 (direct) 397,320 *Temp. Heat & Electric 110,000
a Total General Construction Cost $ .2',522,840
.*.Indirect Construction Cost = 19.05% of Direct Construction . L- , Cost
a Mechanical Construction Indirect Cost (36 months)
*Insurance on Labor 18% x 890,000 $ 160,000 'Office Expense 4% x 19,940,700 797,630 'Field Personnel Project Mgr. 165,000 Field Engr. 150,000 315,000
'Temp. Heat & Electric 160,000 'Small Tools 100,000 'Overhead & Profit 15% x 19,940,700 2,991,110
e Total Mechanical Construction cost $4,523,740
.',Indirect Mechanical Cost = 22.69% of Direct Mechanical Cost
TOTAL PROJECT COSTS --
LAND
GENERAL CONSTRUCTION a Direct a Indirect
a Total Construction
To be considered Separately
MECHANICAL CONSTRUCTION a Direct $19,940,700 a Indirect 4,523,740
a Total Mechanical 24,464,440
CONSTRUCTION FINANCING
11 -7% Total nj.rect ($32,511,400)
TOTAL COST
B.2 ANNUAL CHARGES (less Land Cost)
Mortgage 'Payments $39,420,.060 @ 8.75% per annum $3,449,260 ~epreciation $39,420,060 @ 30 years 1,314,000 Taxes: Real Estate 221,000
Income '3'0'0', '0'0 0
TOTAL ANNUAL CHARGES 5,284,260
Total Annual Charges - 12.2% PlanL Cask (excluding Land)
OPERATING COSTS
Wages
S e c y . & Billing Clerk 13, 000 Station Manager 50,000 Outside '~abor 50,000 Ef ectricians (2) 25,000 Millwrights (2) 25,.000 Labor 11lsurance '& Taxes 3'0 ,'0'00
Utilities
Heat & Lights: Control Building 3,000 Assembly Building '8 , '00 0
Expendable Parts
Bearing (616) 60 @ 35QQ $21,000 Wheels (224) 8 @ 3000 24,000 Reducers (140) 4 @ 15000 60,000 Lube Oil Pumps (56) 2 @ 1500 3,000 Couplings (392) 16 @ 450 7,200 DC Brushes (56) 56 @ 600 33,600 Contractors (504) 504 @ 80 40,320 Track Shoes 184) 84 @ 300 25,200 Collector rail^ 113,180) 1200 @ 40 40,000 262,300
Insurance Misc'ellaneous I terns
TOTAL OPERATING COSTS $95fi, 300
.*. Total Operating Cost = 2.2% of Plant Cost (excluding Land)
B .3 DETAILED. COMP0NEN.T. BREAKD0WN.S
ROTOR CAR WHEEL AND SUSPENSION SYSTEM ( f o u r t r u c k s )
S t r u c t u r a l Fr 'ames 4 PC @4,0,00:.~00 Whee l B e a r i n g s 1 6 PC @ 1 8 5 0 . 0 0 Wheel's 8 PC @ 3000'.00 B o l t s & N u t s 64 PC @ 4 .00 A x l e s . , 8 'PC @ ' 450'.00 Keys & S e t 'Sc rews 8 PC @ 30'.0@ R e t a i n i n g R i n g s 8 'pc @ 80'.00 S p r o c k e t s 8 PC @ 200'.00, C h a i n i 2 5 l f @ 1 0 . 6 0 F a l k C o u p l i n g 160T10 4 PC' '@ 820'. 0 0 Keys &' S e t S c r e w s 8 PC @ 20.00 S u p p o r t P i n s .12" d i a . 4 PC @ ' 600.00 R e t a i n e r R i n g s 8 PC @ 1 2 0 . 0 0 F a l k S p e e d I n c r e a s e r 4 PC @ 1 2 , 5 0 0 . 0 0 F a l k ' C o u p l i n g 120T10 4 P C , @ 2 7 0 . 0 0 ' Keys & S e ' t S c r e w s 8 PC .@ 1 0 . 0 0 ' .
I n d u s c t i o n G e n e r a t o r 250 kW 4 pc @ 1.5,000.00 B o l t s : & N u t s 40 PC @ :'3.'00', C a m r o l Guides ' . 8 PC @ ' 150. '00 ,
B o l t s & N u t s 8' PC @ 1 2 . 0 0 S u p p o r t P i n C B e a r i n g s 4 .PC @ ' 4500.00. A s s e m b l y labor o n s i t e
TOTAL $ 2 2 0 , 5 6 5
ROTOR CAR FRAME AND HOUSING
Main G i r d e r s G u s s e t P l a t e s . S t e e l Tubes ' F i e l d W e l d i n g 3/4," , F i e l d W e l d i n g 3/8" B o l t s & N u t s Gaskets. S t r u c t u r a l T u b e s and
1 / 8 " P l a t e S k i n . O C Motor & C o n t r o l s ~ e d u c e r C o u p l i n g 140T10 C o u p l i n g 130T10 C a r lo or T u b i n g C a r F l o o r G r a t i n g B o l t s & . ' N u t s S e t S c r e w s & 'Keys C o n c r e t e ' B a l l a s t F i e l d A s s e m b l y L a b o r
TOTAL
ROTOR CAR TOWER
S t e e l T u b e 7 2 " d i a . 2 2 , 0 0 0 l b @ $ . 7 5 C o n e B a s e 5 8 , 0 0 0 l b @ S.35 G u s s e t P l a t e s 1 0 , 0 0 0 l b @ $ . 3 5 B e a r i n g s 6 PC @ 2350 .00 C o u p l i n g s 4 PC @ 4 5 0 . 0 0 Key & S e t S c r e w s 1 0 PC @ 4 0 . 0 0 B e a r i n g S u p p o r t U p p e r 5 , 4 0 0 l b @ $ . 3 0 L a d d e r 1 0 2 I f @ 3 0 . 0 0 B e a r i n g S u p p o r t Lower 3 0 0 l b @ $ . 4 5 1 3 5 8" S h a f t i n g 99 I f 1 1 , 2 0 0 L u b e O i l S y s t e m 2 PC @ 2 5 0 0 . 0 0 5 , 0 0 0 B o l t s & Nuts 24 PC @ 7 . 0 0 1 7 0 S h a f t B e a r i n g S u p p o r t s 1 , 5 0 0 l b @ $ . 4 5 6 7 5 O i l S e a l s 5 5 I f 1 , 4 0 0 O i l R e t a i n e r s l u m p sum 2 , 5 0 0 F i e l d L a b o r 1 2 ,'6'00
TOTAL $ 9 4 , 9 6 0
ROTOR AND END CAPS
Alumin,um . T r u s s e s T r u s s . A s s e m b l y C o r r u g a t e d Alum. S k i n S c r e w s C o v e r . P l a t e s . R i n g G e a r & R e t a i n e r R i n g G e a r S u p p o r t s Lower B e a r i n g R e t a i n e r Upper B e a r i n g Lower B e a r i n g Upper B e a r i n g R e t a i n e r E r e c t i d n L a b o r
TOTAL $ 9 4 , 9 9 0
APPENDIX C
ROTOR STRUCTURAL WEIGHT AND INERTIA SCALING EQUATIONS
APPENDIX C
ROTOR STRUCTURAL WEIGHT AND INERTIA SCALING EQUATIONS
The procedure f o r s c a l i n g r o t o r weight and mass moment of
i n e r t i a f o r v a r i o u s geometr ic changes i n r o t o r and end cap s i z e
w a s a two s t e p proces 's .
F i r s t , a d e t a i l e d r e f e r e n c e s t r u c t u r a l des ign w a s developed
f o r t h e fo l lowing c o n d i t i o n s .
Design geometry d e s c r i b e d i n Paragraph 4 . 1 .
Design wind -and o p e r a t i n g c o n d i t i o n s desc r ibed i n Paragraph 4 . 1 .
e Des'ign l i f e , environmental , and system c r i t e r i a d e s c r i b e d i n Paragraph 4 .1 .
Design l o a d s desc r ibed i n Paragraph 4.2 and a l l sub- paragraphs the reunde r ,
a S t r u c t u r a l c o n f i g u r a t i o n a s desc r ibed i n Paragraph 4.3 and a l l subparagraphs the reunde r .
Second, s c a l i n g e q u a t i o n s based on v a r i a t i o n s from t h e
r e f e r e n c e geometry and o p e r a t i o n c o n d i t i o n s w e r e genera ted . These
e q u a t i o n s , p r e s e n t e d below, were t h e n programmed i n o u r Madaras
System Performance S imula t ion Program i n o r d e r t o p rope r ly account
f o r t h e effects of ro tor geometry arld spin c o n d i t i o n v a r i a t i d n s
on system performance. i
C. 1 CYLINDER WEIGHT
The weight o f c y l i n d e r s having a c o n s t a n t p r o j e c t e d a r e a of
2000 f t 2 i s
- 1.75
W CY 1 where,
W CY 1
= weight of c y l i n d e r i n l b s
r c y l = r a d i u s of c y l i n d e r i n f e e t
RPM = maximum r o t o r s p i n r a t e i n rev. p e r minute
= weight of c y l i d n e r having a s p e c t r a i o o f 'REF 4.0 = 18,889 l b s ,
C.2 CYLINDER WEIGHT PER U N I T HEIGHT
I n o r d e r t o be a b l e t o p r e d i c t t h e weight .of a c y l i n d e r . -
having an a r b i t r a r y p r o j e c t e d a r e a it i s d e s i r a b l e t o develop a n
exp res s ion f o r c y l i n d e r weight pe r u n i t of h e i g h t .
2 For c y l i n d e r s having a 2000 f t p r o j e c t e d a r e a ,
W r 1000 - c y l c y l
where h = c y l i n d e r h e i g h t i n f e e t .
C.3 CAP WEIGHT
The weight of t h e cap i s given by
r = r a d i u s of cap i n f e e t cap
CAP = weight of cap f o r c y l i n d e r having a s p e c t r a t i o o f 'REF 4.0 and cap r a d i u s t o c y l i n d e r r a d i u s r a t i o of 1 . 5 = 3127 l b s
C. 4 MASS MOMENT OF I N E R T I A
The m a s s moment o f i n e r t i a of t h e r o t o r w i t h r e s p e c t t o t h e
geomet r ica l a x i s i s expressed a s
' ro tor = I CY 1 + I cap
I - ... , rn (0 .81 rcyl) 2 CY 1 CY 1
where,
1 = ,mass moment of iner t3 .a i n s l u g - f t 2
m = mass i n slugs.
. M I N I M U M WEIGHT CUT-OFF
The e q u a t i o n s p re sen ted above a r e based on p e r t u r b a t i o n s about
t h e p r e v i o u s l y d e f i n e d Maderas d e s i g n p o i n t . The accuracy of t h e s e
e x p r e s s i o n s f o r l a r g e d e v i a t i o n s from t h i s p o i n t have n o t been
t e s t e d . However, i t is obvious t h a t t h e r e w i l l e x i s t some minimum
weight f o r b o t h t h e cap and t h e c y l i n d e r . T h i s weight w i l l be
i n f l u e n c e d by minimnm gago requireme11Ls for m a t e r i a l handl ing ,
damage r e s i s t a n c e , and s t r u c t u r a l s t a b i l i t y .
A minimum w e i g h t of 9,500 l b s lor c y l i n d e r s having a p r o j e c t e d 2 a r e a o f 2000 f t i s recommended. The minimum weight f o r o t h e r
c y l i n d e r s i z e s i s g iven by
wmin - (A,;:: j ) 9500 CY 1 - 21)110
where
ACY1 pra j - p r o j e c t e d area nf cylindcy.
A minimum weight f o r t h e r o t o r cap has no t been def ined . The
cap weight c a l u c l a t e d us ing t h e equa t ions of S e c t i o n 111 w i J . . l be
used f o r a l l c y l i n d e r s i z e s and geometr ies .
REFERENCES
G. Magnus, "On t h e Def l ec t ion o f a P r o j e c t i l e , " ( a ) "Abhandlung d e r Akademie d e r Wissenschaf te rn , " B e r l i n , Germany, 1852. Engl i sh t r a n s l a t i o n i n T a y l o r ' s S c i e n t i f i c Memoirs, 1853. ( b ) "Poggendorffs Annalen d e r Physik und Chemie," Vol. 88, No. 1, 1853.
C.F. H i r s h f e l d and J . D . Madaras, The Madaras Rotor Power P l a n t and Its Development. P a r t I . Progress Report Dea l ing wi th t h e Resu l t s o f t h e F i r s t P a r t o f a Three-Stew Develop- ment - Program, Madaras Rotor Power Corporat ion, D e t r o i t , *
Michigan, January 19 31.
Madaras Rotor P r o j e c t - Correspondence and Meeting Notes, E d a r a s Rotor Power Corpora t ion , D e t r o i t , Michigan, December 19 38.
E .C . S tone , C.F. H i r s h f e l d . and J . D . Madaras. Rewort on T e s t o f a F u l l s i z e Madaras wind Rotor Conducted a t ~ i r l i n g t o n , New J e r s e y ' - 1933, Madaras Rotor Power Corpora t ion , D e t r o i t , Michigan, A p r i l 19 34.
Pe r sona l communications from M r . Russe l l F. Hardy, Chief Engineer o f Madaras Rotor Power P l a n t and l e t t e r from P r o f e s s o r John D. Akerman, S t r u c t u r a l Consu l t an t on Madaras P r o j e c t .
La f a y , "Sur 1 ' Inve r s ion du Phenomene de Magnus , " Comptes Rendus, Vol. 151, 1910.
Lafay, "Con t r ibu t ion Experimentale a 1"Aerodynamique due Cyl indre , " Revues Mechanique, Vol. 30, 1912.
I
A. B e t z , "Der Magnuseffekt, d i e Grundlage d e r F le t tnerWalze , " V D I , 1925r p. 9 . Engl i sh T r a n s l a t i o n , NACA T M 310, 1925.
L . P r a n d t l , "Magnuseffect und Windkraf t sch i f f, " D i e NaLurwissen- s c h a f t e n , 1925, p. 93. Engl i sh t r a n s l a t i o n , NACA T M 367, 1926.
A. F l e t t n e r , Mein Weg zum Rotor, Le ipz ig , 1926. Pub l i shed i n Engl i sh under t h e name The S t o r y o f t h e Rotor, by F .O . W i l l h o f t , 68 Beaver S t . , New York.
A . Thom, "The Aerodynamics o f a Ro ta t ing Cy l inde r , " t h e s i s , Un ive r s i t y o f Glascpw, 1 9 2 6 .
A . Thom, "Experiments on t h e A i r Forces on R o t a t i n g Cy l inde r s , " ARC R and M 1018, 1925.
A. Thom, "The P r e s s u r e s Round a Cyl inder Ro ta t ing i n an A i r Current. ," ARC R and M 1082, 1926.
A. Thorn, "Experiments on t h e Flow P a s t a Rotat ing Cylinder, "
ARC. R and M 1410, 1931.
A. Thorn and S .R, Sengupta, " A i r Torque on a Cylinder Rotat ing i n an A i r Stream," ARC R and M 1520, 1932.
A. Thorn, " E f f e c t s o f D i s c s on t h e A i r Forces on a Rotat ing Cyl inder ," ARC R and M 1623, 1934.
E.G. Reid, T e s t s of Rotat ing Cylinders , NACA TN-209, Nat ional Advisory Committee f o r Aeronautics, Washington, D.C . , December
J.T. Matthcws, Low Speed-Wind Tunnel T e s t s t o Determine t h e L i f t and Drag o f a Cylinder Rotat ing wi th in End P l a t e s , Aero Report 977, The David Taylor Model Basin Aerodynamics Laboratory, Washington, D.C., A p r i l 1960.
R.T. G r i f f i t h d and C.Y. M a , . " D i f f e r e n t i a l Boundary-Layer Separa t ion E f f e c t s i n t h e Flow Over a Rotat ing Cylinder, "
Aeronaut ica l Journa l , V o l . 73, p. 524, June 1969.
W.M. Swanson, "The Magnus E f f e c t : A Summary o f I n v e s t i g a t i o n s t o Date, " J o u r n a l o f Bas ic Engineering, p. 461, September 1961.
Personal conmunication - L e t t e r da ted February 25, 1977, Dean R'., S t u a r t , Department o f Mechanical Engineering, Univers i ty o f Waterloow, Ontar io, Canada.
E.A. S t a l k e r , "The Ex t rac t ion of Energy from t h e Wind, " Journal of t h e Aeronaut ical Sciences, Vol. 2 , p . 162, July 1935.
R.E. Powe, H.W. Townes, D.O. B lackke t t e r , and E.H. Bishop, Technical F e a s i b i l i t y o f a Wind Energy Conversion System Based on t h e Tracked Vehic le-Air fo i l Concept; NSF/RANN/SE/ G I 39415/PR/73/4, Annual Px-ogress Report, Univorcity of Montana, January 1.9 74.
E .E . Lapin, V e - r t i c a l A x i s Windmills - Wing .Driven and R o t o r Driven, ' Unpublished Manuscript, October 19 76.
C.F. Hi r sh fe ld and. J . D . bladaran, The Madafati Rotor Power P l a n t and Its Development. P a r t 11. Aerodynamic Theory as Applied t o Madaras R o t o r P l a n t , Madaras Rotor Power Corpora- t i o n , D e t r o i t , Michigan, January 1931.
F.W. Pawlowski, C o n ~ i d e r a t i o n s of Puwer Output and Aerodynamic Ef f i c i ency o f the Madaras Wind Rotor, Madaras Rotor Power Corporat ion, Detroit , Michigan, October 1930.
F.W. Pawlowski, Report on An E x p e r i m n t wi th a Screw-Type ~ i n d m i i l , Madaras Rotor Power Corporat ion, D e t r o i t , Michigan, November 19 30.
F.W. Pawlowski, Experiments w i t h a P a i r o f Savonius Rotors , Madaras Rotor Power Corpora t ion , D e t r o i t , Michigan, November 1930.
U t i l i z a t i o n o f Madaras Wind Rotor P l a n t f o r Genera t ing ~ l e c t r i c a l Energy, Duquesne L i g h t Company, P i t t s b u r g h , Pennsylvania.
Economics. o f Wind Rotor P l a n t I n s t a l l e d by P r i v a t e I n d u s t r y , Madaras Rotor Power Corpora t ion , D e t r o i t , Michigan, December 1932.
O u t l i n e o f T e s t o f t h e Exper imental Wind Rotor a t Bur l ing ton , New Jersey, Madaras Rotor Power Corpora t ion , D e t r o i t , Michigan, J u l y .19 33.
E.A. Hester and F.D. Campbell, P rog res s Report on T e s t s Made a t t h e Exper imental Wind Rotor a t Bur l ing ton , New J e r s e y , Madaras Rotor Power Corpora t ion , D e t r o i t , Michigan, J u l y 19 33.
J . D . Madaras and E h . H e s t e r , Report on T e s t s o f a F u l l S i z e Madaras Wind Rotor Conducted a t Bur l ing ton , New ~e r sey -1933? , Appendix B. Sec t ion I. D e . s c r i ~ t i v e Matter, Madaras Rotor
J . D . Madaras and E.A. ester, Report on T e s t s o f a F u l l . S i z e Madaras Wind Rotor Conducted a t Bur l ing ton , New J e r s e y -1933. Appendix B . Sec t ion 11. Photoqraphs , Figures , Curves, and Tables , Madaras Rotor Power Corpora t ion , D e t r o i t , ~ i c h i g a n , March 1934.
J . D . Madaras, The Rotor T e s t s a t Bur l ing ton , New J e r s e y , Ma.daras Rotor Paer Corpora t ion , D e t r o i t , Michigan, A p r i l 19'34.
Miscel laneous photographs o f t h e Madaras r o t o r system.
F. R. E l d r i d g e , Wind Machines, MTR-69 71, The Mi t re Corpora t ion , Octcber 19 75. Na t iona l Sc ience ~ o u n d a t i o n No. ~ s F / ~ ~ / ~ - 7 5 - 0 5 1 .
R.L. Thomas and J . E . Sholes , P re l imina ry R e s u l t s o f t h e Large Exper imental Wind Turbine Phase o f t h e Na t iona l Wind Energy Program, NASA TM X-71796, NASA L e w i s Research Cente r , Cleveland, Ohio, October 1975.
R.V. B r u l l e , F e a s i b i l i t y I n v e s t i g a t i o n o f t h e G i romi l l f o r Generat ion o f E l e c t r i c Power, Midterm Report , April-November 1975, Energy Research and Development Admin i s t r a t i on , November 19 75.
Er ich J. P l a t e , Aerodynamic C h a r a c t e r i s t i c s o f Atmospheric Boundary Layers , U.S. Atomic Energy Commission, O f f i c e o f ~ n f o r m a t l o n S e r v i c e s , AEC C r i t i c a l Review S e r i e s , 1 9 71.
49.
SO.
Theodorsen, T. and A. Regie r , NACA Report 793, 1944.
N a t i o n a l Bureau o f S t anda rds , "American N a t i o n a l S t a ~ d a r d B u i l d i n g Code Requirements f o r Minimum Design Loads i n B u i l d i n g s and Othe r S t r u c t u r e s , " J u l y 20, 19 72.
Ko,rneich, T.R., Proceedings o f t h e Th i rd B i e n n i a l Conference and Workshop on Wind Energy Conversion Systems, Volume 1, September 19 t o 2 1 , 1977, Sponsored by t h e United S t a t e s Department o f Energy.
Coty, U.A., Wind Energy Miss ion An'a lys is , September 1976, ERDA r e p o r t SAN/1075-l/l.
Hightower, S t a n l e y J . , "A Proposed P lan f o r I n t e g r a t i o n o f Wind Turb ine Gene ra to r s w i t h a ~ y d r n e l . e c t r i c ' S y s t e m , " P re sen ted a t t h e Annual Meeting o f t h e Missour i Basin Systems G.rrou.p, Sioux F a l l s , S.D., March 9 , 1977.
B. Glen and E. Barbour, "A Guide t o Using I n t e r e s t F a c t o r s i n Economic A n a l y s i s o f Water P r o j e c t s , " Engineer ing and Research Cen te r , Bureau o f Reclamation, December 1970.
Congreve, W i l l i a m , l l A e r i a l Car r iage , ' Me'cAan'i'cs' 'Ma'cJaz'ine, Vol. 9 , No. 240, March 22, 1928, pp 129-134, and A p r i l 12, 1928, ,
pp 186-187.
Foshag, W.E. and G.B. B r e s h l e r , USAAVLABS Techn ica l Report 69-13, U.S. Army Av ia t ion Material L a b o r a t o r i e s , F o r t E u s t i s , V i r g i n i a .
Voi th-Schnieder , E i n Neven S c h i f f r a n t r i e b , Esch i f I b d u and S c h i f f a r t , V o l . 30 , No- 8 , A p r i l 1 7 , 1929, pp 137-190.
K i r s t e n , F.J.K., P r o p e l l e r U.S. P a t e n t N o . 1432700, October 17 , 1922. See Reference 48 f o r complete l i s t i n g o f K i r s t e n s p u b l i c a t i o n s .
Wheatley, John B . , " S i m p l i f i e d Aerodynamic Analys i s of t h e Cyclog i ro Rotating-Wing System," NACA ~ e c h n i c a l Note 467, August 1933.
Heuver, H.M. and Robert E. Wage, "And ly t i ca l Study of t h e Performance of a Cyc lo ida l P r o p e l l e r and P re l imina ry Survey o f a F i g h t e r Type Design, Memorandum Report No. ENG-Sl/P706-84, AAF M a t e r i a l Cen te r Command, Eng. Dw. Wright F i e l d , Dayton, Ohio, J u l y 22, 1943.
Hage, R. E. , "Summary of t h e Development Work o n . a Cyclog i ro Type of R o t a t i n g Wing A i r c r a f t , " Memorandum Report No. TSEA2-4203-4-1, AAF A i r Techn ica l S e r v i a r Command, Wright- P a t t e r s o n A i r Force Base . , Dayton, Ohio, August 16 , 1945.
54. Be tz , A . , and L. P r a n d t l , I1Gbktinger Nachr ich ten ," p 193, 1919.
55. Golds te in , S . , "On t h e Vortex Theory of Screw P r o p e l l e r s , " Proc. Roy. S'ci. A , 23, London, 1928.
56. Theodorsen, T., Theory of 'Prop 'e l le ' rs , McGraw H i l l Book Co. I n c . , New York, 1948.
57. P r a n d t l , L., " A i r f o i l Theory," (German) , P t s . I and 11, Nacht i ges W i s s . Gb'ttingen, p 151, 1918, and p 107, 1919.
58. Helmholtz, Ueber I n t e g r a l e d e r ~ydrodynamischen glieehenungen welche dem Wirbelbervegungen en t sp rechen , C r e l l e , l v . (1858) [Wiss, Alh. i 1011.
59. B r u l l e , R.V. and W.A.Moran, "Gi romi l l Wind Tunnel T e s t and ~ n a l ~ s i s , I 1 COO-2617-4, McDonnell A i r c r a f t Co, , P.O. Box 516, St, Louis , MO. 63166, October 1977.
60. Oseen, C.W. Ark f Match Astron och Fys. 7 (1911) ; Hydromechanik, p 82, Lupzig 1927. ,. ?
61. Taylor , G . I . , Rep. Memor Aero. R e s . Coun., No. 1381 (1930) , c.:~ . .
and J. Loudon Match Soc. 5 (1930) 224-49. ,t ;. >,:! .I. , ,
62. P r a n d t l , L. and 0. G. ~ i e t j i n e , Applied Hydro-and Aeromechanics , McGraw- ill Book Company, Inc . , New York, 1934.
\ 7
"
63. Ku t t a , A u f t r i e b s c h a f t e i n Strominden F lus s igku ten , I l l u s t r i e n t s Aeronautiabke, Mi t t l e lungen , p. 133, J u l y 1902.
>I ' ? v?, f ' - "
64. Joukowsky, T ransac t ions of t h e p h y s i c a l S e c t i o n of t h e I m p e r i a l + !:L
S o c i e t y o f t h e F r i ends of N a t u r a l Sc i ences , Moscow, Vol. X I I I , No. 2.
65. Joukowsky, "Ueber d i e Konturen d e r Tragf lachen d e r Drachen- f l ugen , " Z i l t s ' c h r i f t f u r F lug technik und M o l o s t u f l s c h i f f a r t , Vo. X X I I , N o . 2 , November 26, 1910.
66. Karman, Th. von, and E. T r e f f t z , Po ten t i a l s t romung urn gegebene Tragfaschen q u e r s c h n i t t , Z.F.M., 9 , p 111, 1918.
67. P r a n d t l , L. , C. Wiese l sberger , and A. B e t z , "Ergebsn isse d e r Aerodynamishen Ver suchsans t a l t g o t t i n g e n , 11,. p 28 , (Munchen and B e r l i n , 1923) .
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