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TRANSCRIPT
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DAVID W. TAYLOR NAVAL SHIPRESEARCH AND DEVELOPMENT CENTER ~
Bethesda, Md. 20DS4
A LIFTING LINE COMPUTER PROGRAM
FOR PRELIMINARY DESIGN OF PROPELLERS
by
A:) E.B. Caster
J.A. Diskin
T.A. LaFone
OCT 14 '
L C- jL -'3 .uI
Approved for Public Release;
Distribution Unlimited
SHIP PERFORMANCE DEPARTMENTAL REPORT
NOVIE"MBER 1975 REPORT NO. SPD-595-01
DISCLIMER NOTICE
THIS DOCUMENT IS BEST
QUALITY AVAILABLE. THE COPY
FURNISHED TO DTIC CONTAINED
A SIGNIFICANT NUMBER OF
PAGES WHICH DO NOT
REPRODUCE LEGIBLY.
MAJOR DTNSRDC ORGANIZATIONAL COMPONENTS
OTNSRDC
COMMANDER 00
TECHNICAL DIRECTOR01
OFFICERIN.CHARGE OFFICER-IN.CHARGECARDEROCK - ANNAPOLIS 04
SYSTEMSDEVELOPMENTDEPARTMENT
[ SHIP PERFORMANCE AVIATION ANDDEPARTMENT SURFACE EFFECTS
15 DEPARTMENT 16 )
STRUCTURES COMPUTATIONDEPARTMENT AND MATHEMATICS
17 DEPARTMENT 18
SHIP ACOUSTICS PROPULSION AND
DEPARTMENT AUXILIARY SYSTEMS19 DEPARTMENT 27
MATERIALS CENTRAL
DEPARTMENT INSTRUMENTATION28 DEPARTMENT 29
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'k- ~ Lifting Line Co, utr Program for Dprmna ia~.~jPreliminary Design of Propellers.DpretaFil
-S. PERFORMING ORGc. RtE*dT9V r
SPD-595-017 t% ZOftfS. CONTRACT OR GRAIST NUMBER(*)
X117TIN AE AND ADDRESS 10. PROGRAMd ELEMENT. PROJECT. TASKARIEA & XORK U NIT NUMUIERS
David W. Taylor Naval Ship Research and Tak k 1 5942Development Center Work Unit N~o, 1524-462
Bethesda, Maryland 20084 1500-nolIs CONTROLLING OFFIC:E NAME ANO0 ADDRESS TREBI.Q
Naval Sea Systems Commy~and (S034) /Novembe.-1915-Washington, D.C. 20362 13. NUMBER OF PAGES:.
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16 DISTRIBUTION STATEMENT (of this Reporl)
Approved for Public Release; Distribution Unlimited
17 DIST RIBUTION STATEMENT (of the abstract entered In Block 20, It different fromi Report)
IS SUPPLEMENTARY NOTES
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PropellerLifting LineStress\Design
20. A ftz_ g 4T (Continue on reverse aide It necessary and Identity by block number)
1-his report presents a computer program that can be used for the.preliminary design and to predict t~e performance of single screwpropellers when designed for a presc~'bed hydrodynamic pitch dis-tribution. This design peogram is based on lifting line theory asdeveloped by Lerbs for moderately-loaded fini.te-bladed propellers.Stress calculations using beam theory are also mnade for each design,which take into account the effect of blade skew and rake.Desig4~~c C 9
DD I JAN 7 1473 EDITION OF I NOV 65 IS OIISOLETZ UNCLASSIFIEDSIN 0 102.014- 6601 1 SECUKITY CLASSIFICATION OF THIS PAGE ("oen Date Xnteiedf
v-f o,
UNCLASSIFIEDL AS$% IC1 ION 0 "S AG E" Do'* Eted
Kcalculations can be made for given design speeds where delivered shaftpower is computed (Thrust Option), or for the case when the deliveredshaft power is specified and the corresponding speed is computed (PowerOption). A FORTRAN listing of the yrogram, developed to run on thecomputers at the David W. Taylor Naval Ship Research and DevejopmentCenter (DTNSRDC), is presented as well as input and output obtainedfor two sample designs, one using zhe Thrust Option, and the other thePower Option,
41)
Nw
ii UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE(Whton Dec& Eri.,.d)
TABLE OF CONTENTS
Page
ABSTRACT ....... . . ................. 1
ADMINISTRATIVE INFORMATION ...... ................ 2
INTRODUCTION ........ ....................... 2
PROPELLER LIFTING LINE THEORY . . . . . . ....... 5
DESCRIPTION OF INPUT DATA . . . . . . . . . ...... 6
EFFECTIVE POWER, SPEED, AND SHAFT POWER ... ....... 7
NONDIMENSIONAL RADIAL DISTANCE. . . ......... 8
PROPELLER WAKE ........... . . ......... 8
ADVANCE ANGLE DISTRIBUTION iNPUT OPTION .... ..... 9
HYDRODYNAMIC FLOW ANGLE ................... .10
STATIC HEAD . . . . . ............... 11
BLADE OUTLINE AND EXPANDED AREA RATIO ....... 11
BLADE THICKNESS TO CHORD RATIO .... ............ 12
RAKE AND SKEW ...... .................... .13
SECTION DRAG COEFFICIENT ................ 14
FINAL PITCH INPUT OPTION. . . . . .......... 14
DESIGN AND PROPULSIVE PERFORMANCE PARAMETERS CALCULATED . 15
PROPELLER STRESS CALCULATIONS USING BEAM THEORY . . .19
PARAMETERS FOR MAKING BLADE SURFACE CAVITATION
CHECKS. . . . . . . . . . . . . . . . . . . . . . . . 20
CHORD LENGTHS FOR PITCH AND CAMBER CALCULATIONS . . .23
SPACING BETWEEN BLADES AND FILLETS. ......... 24
ill
Page
PROPELLER DESIGN THRUST AND POWER OPTIONS ........... .. 24
COMPUTER PROGRAM AND SAMPLE DESIGN CALCULATIONS ........ 26
APPENDIX A - PROPELLEk WEIGHT, MASS POLAR MOMENTS OF
INERTIA, AND CENTER OF GRAVITY ......... ... 33
APPENDIX B - AMERICAN BUREAU OF SHIPPING (ABS)
COEFFICIENTS AND THICKNESS REQUIREMENTS . . . 37
APPENDIX C - DESCRIPTION OF INPUT AND OUTPUT ...... 40
APPENDIX D - SAMPLE DESIGN USING THE THRUST OPTION . . 50
APPENDIX E - SAMPLE DESIGN USING THE POWER OPTION . . . 73
APPENDIX F - FORTRAN LISTING OF'COMPUTER PROGRAM ...... 108
F(EFERENCES ........ ........................ .141
IV
I
LIST OF FIGURES
Page
Figure 1 - Typical Velocity Diagram for a PropellerBlade Section at Radius r ... .......... 27
Figure 2 - Diagrams Showing Recommended ReferenceLines and Terminology .... ............ 28
Figure 2a- View of Unrolled Cylindrical Sections atBlade Root and at Any Radius of a Right-HandedPropeller (Looking Down) Showing RecommendedLocation of Propeller Plane ... ......... 28
Figure 2b- Diagram Showing Recommended Reference Lines(Looking to Port) ............... .... 29
Figure 2c- Diagram Showing Recommended Reference Lines(Looking Forward) ..... .............. 30
Figure 2d- Input for Detailed Hub Option .......... 31
LIST OF TABLES
Page
Table 1 - Conversion Factors Between English and SIUnits for Input and Output Parameters . . . . 32
V
NOTATION
AE Expanded blade area, Z h c dr
AE/A0 Propeller expanded area ratio, (2Z/n)f (c/D) dxXh
(A /A Keller's minimum expanded area ratio for elininating backAEAo k bubble cavitation, (2.6+O.6Z)KT/(oO.7[J2+(O.7.n)2J}+K
A0 Disc area, wD2/4
Ap PEstimated propeller projected area,[1.067-0.229 (P/D)i]AE
a(x) Area of section, 2c(x)t(x)fIt(x,x )dx
B(x) Distance of CG from hub face,y cos + x sin(o-e S) x R tan(0-eR) x+DH/
2
(c/R)LE,(c/R)TE Chord lengths measured from leading edge and trailing edgeof blade to propeller reference line
CD Section drag coefficient
CFO Frictional resistance of seLtion
rG Center of gravity
CL Blade section lift coefficient
C P Power loading coefficient, PD/AP/2)xR2VA IC PS Power loading coefficient based on ship speed,
P /[(p/2)iR 2V 31; calculated fxh(1 +c/tan )
(dCpsi/dx) dx
CTh Thrust loading coefficient, T/[(p/2)R 2VA ]
C TS Thrust loading coefficient based on ship speed,T/[(p/2)nR2V2]; calculated f (l - ctanB I)
(dCTsi/dx) dx h
CThP Power loading coefficient, f4 (I W (I - tans)
(dCTSi/dx) dx Xh x
c Propeller blade chord length, c(x)
vi
ICpsi Inviscid power loading coefficient,
(4Z/ s)xG(l-Wx)+UT/2V]
C Inviscid thrust loadina coefficient,CTSi 4ZG[(x/As)-UA/2V]
Propeller diameter
b Hub diameter
F(O') Parameter for calculating the fluctuatingangles of attack, I/[l+21tan(Bi-B)/CL]
f M Camber
g Acceleration due to gravity
G(r) Nondimensional circulation about a blade
section r/(2TrRV)
GF Spacing between fillets
Gz Spacing between blades at the hub
H Static head at propeller shaft centerline
IxoIyo Moment of inertia of blade section aboutx and y axes
J Advance coefficient, V(l-wT)/(nD)=VA/(nD)
JV Ship speed advance coefficient, V/(nD)
K Kellers' constant for predicting minimumblade area of propeller (see p. 22)
2 sTorque coefficient, Q/(n
2D
24h
KT T,,rust coefficient, T/(pn D )
LI Propeller lift distribution per unit spanfor finite element stress calculations
M P Moment of blades, see page 34
vii
MTbMQb Moment due to thrust and torque
Mxo' o Moment parallel and perpendicular tothe nose - tail line
n Propeller revolution per unit time
(P/D)i Estimated propeller pitch ratio at 0.7radius, 0.7tan8I in program
PD Delivered power at propeller, 2rQn
P E Effective power
PS Shaft power
Q Propeller torque
R Propeller tip radius
rpm Propeller revolutions per minute
r Propeller local radius
rh Propeller hub radius
r Local position along the section chord
T Propeller thrust
t Propeller blade maximum thickness t(x),thrust deduction fraction
t(x,x ) Chordwise distribution of section thick-ness (NACA 66 modified thickness form isused)
U A/2V Axial induced velocity at lifting line
UT/2V Tangential induced velocity at liftinq line
V Ship speed
VA Speed of advance of the propeller, V(l-wT)
viii
IV Local velocity along the x axis at any field
point
Vr Inflow velocity at each propeller section,V,/(I -wx )+UA/2VJ4 +LX/s-UT/2VJ '
Wa /V Axial velocity from sources other than the
propeller wake (l-wx)
WB Weight of blades
WH Weight of hub
Wp Propeller weight
wc Circumferential mean wake fraction at eachradius calculated from wake survey
wt/ V Tangential velocity from sources other thanthe propeller wake (l-w x)
WT Propeller effective wake fraction as determinedfrom thrust identity from self propulsionexperiment
wv Volume mean wake fraction
wX Propeller wake fraction, l-[(l-wT)/(l-wv)](l-wc)
x Nondimensional radial distance, r/R
Xh Nondimensional hub radius, rh/R
x Nondimensional distance along section chord, r /c
Z Number of blades
ZR Propeller rake
ZT Total rake, rake plus skew induced rake
ix
Cxi Section ideal angle of attack, 1.54C Lfor NACA a=O.8 meanline in twodimensional flow
amax Maximum fluctuating annle of attack,max ai_(_AB)P(x)
ami n Minimum fluctuating angle cf attack,i-(+AB)F(x)
Advance anqle of a propeller blade section
Hydrodynamic flow angle of a propeller bladesection
r Circulation about a propeller blade section,
C Section drag-lift ratio, CD/CL
9 D Propulsive efficiency, PE/PD=(l-t)CTS/Cps
'Pe Estimated propeller efficiency,CT p/Cpc0R Blade rake angle in degrees
S R Blade skew angle in degrees
A S Advance ratio of propeller based on ship speed,V/(nnD)
Water density
PDensity of propeller material
Pitch angle
a Section cavitation number, 2gH/V2
r
0o.7 Burrill cavitation number,2gH/[{V(lIw x=0. 7 ) 1 2 +{O.7unDj
Tc Burrill thrust loading coefficient,T/[{V(l-wx=0 .7)} 2 +{0.71nD} 2]
x
|ABSTRACT
This report presents a computer program that can be used for
the preliminary design and to predict the performance of single
screw propellers when designed for a prescribed hydrodynamic
pitch distribution. This design program is based on lifting line
theory as developed by Lerbs for moderately-loaded finite-bladed
propellers. Stress calculation3 using beam theory, propeller
weight, moments of inertia, and center of gravity for specified hubs
are also made for each design, which take into account the effect
of blade skew and rake. Desiqn calculations can be made for given
design speeds where the corresponding shaft power is computed
I' (thrust option), or for the case when the shaft power is specified
and the corresponding speed is computed (power option). A FORTRAN
listing of the program, developed to run on the computers at the
David W. Taylor Naval Ship Research and Development Center (DTNSRDC)
is presented as well as the input and output obtained for two sample
designs, one using the thrust option, and the other the power option.
-1
ADMINISTRATIVE INFORMATION
This work was sponsored by the Naval Ship Systems Command,
SHIPS 034, and carried out under the David W. Taylor Naval Ship
Research and Development Center (DTNSRDC) Work Unit No. 1524-462,
Task 15942.
INTRODUCTION
The David W. Taylor Naval Ship Research and Development
Center (DTNSRDC), Carderock Laboratory, was requested by the
Naval Ship Systens Command (NAVSHIPS) to develop a computer
program that can be used as an aid in determining optimum
values of propeller design parameters such as diameter, rpm,
and blade number for naval vessels. This report has the
objective of presenting a computer program that can be easily
used for the preliminary design and for prediction of the
performance of propellers applicable to specific ships.
The main portion of the computer program makes preliminary
propeller design calculations and performance predictions
using Lerbs' lifting line moderately-loaded finite-bladed
propeller theory of References 1 and 2. Once the lifting
1. Lerbs, H.W., "Moderately Loaded Propellers with a FiniteNumber of Blades and an Arbitrary Distribution of Circulation,"Transactions of the Society of Naval Architects and MarineEngineers, Vol. 60, p 73-117, 1952
2. Morgan, W.B. and Wrench, J.W., Jr., "Some ComputationalAspects of Propeller Design," Methods in Computational Physics,Vol. 4, Academic Press Inc., New York, p 301-331, 1965
2
line calculations for the propeller have been obtained, a
computer program based on lifting surface theory must be
used to determine the final pitch and camber of the propeller3
Numerous experimental checks4 on the design procedure used
have verified this procedure.
A computer program for the preliminary design of propellers
having a prescribed pitch or circulation distribution was
previously published in Reference 5. One of the most
important new features of the new computer program is the
power option which computes the speed automatically when the
design power is specified. Other features included in the
present computer program follows:
-A 1. Only one set of basic input data is required for the
preliminary design of a series of propellers with rpm,
blade number and expanded area ratio varied. Any
number of basic sets of data can be specified in
the computer program.
3. Morgan W.B., Silovic, Vladimir and Denny, Stephen B., "PropellerLifting-Surface Corrections," Transactions of the Society of NavalArchitects and Marine Engineers, Vol. 76, p 309-347, 1968
4. Boswell, R.J., "Design, Cavitation Performance and Open-WaterPerformance of a Series of Research Skewed Propellers,' NavalShip Research and Develpment Center Report 3339, March 1971
5. Haskins, E.W., "Calculations of Design Data for Moderately LoadedMarine Propellers by Means of Induction Factors," Naval ShipResearch and Development Center Report 2380, September 1967
3
2. The propeller stress, based on beam theory6 , modified
to account for the effect of rake and skew, is computed for
each design. An input option is used to make stress calcula-
tions for a linear or nonlinear distribution of blade skew.
Parameters required to make blade surface cavitation
checks using the 12t.rrill cavitation charts of Reference 7 and
Brockett's incipient cavitation diagrams of Reference 8 are
calculated on the computer. In addition, Keller's method 9 of
predicting the minimum expanded area ratio based on back bubble
type cavitation, is calculated. The estimated propeller
weight including the hub, and input parameters required for
the lifting surface computer program used to calculate the
final pitch and camber of propeller designs are some of the
other parameters calculated.
6. Eckhart, M.K. and Morgan, W.B., "A Propeller Desiqn Method,"Transactions of the Society of Naval Architects and MarineEngineers, Vol. 63, p 305-370, 1955
7. Burrill, L.C. and Emerson, A., "Propeller Cavitation: FurtherTests on 16 Inch Propeller Models in the Kings College Cavita-tion Tunnel," Transactions of the North East Coast Institutionof Engineers and Ship Builders, Vol. 78, p 295-320, 1963-64
8. Brockett, Terry, "Minimum Pressure Envelopes for ModifiedNACA-66 Sections with NACA a=0.8 Camber and BUSHIPS Type Iand Type II, Sections," David Taylor Model Basin Report 1780,1966
9. Keller, J. Auf'm, "Enige aspectem bij het ontwerpen vanScheepsschroeven," Schip en Werk, No. 24, p 658-662, 1966
4
I w
PROPELLER LIFTING LINE THEORY
The availability of high speed digital computers has made
it now possible to make use of more adequate mathematical models
to represent the hydrodynamic %ction of marine propellers.
The computer has also released the designer from performing
laborious computations involved in present design methods.
The lifting line theory used in the computer program
presented here is the theory developed by Lerbs (Reference 1)
for moderately-loaded finite-bladed propellers. This lifting
line design method discussed by Cox and Morgan in Reference 10
also permits the designer to accurately account for propeller
parameters such as number of blades, hub size, radial blade-
loading, and wake distribution. Since this theory is discussed
in detail in References 1 and 2, only some of the assumptions
made in developing the theory are mentioned here. The theory
developed by Lerbs' considers the influence of the induced
velocities on the shape of the helical vortex sheet at the
lifting line, but neglects the effect of centrifugal forces
and the contraction of the slip-stream. In addition, the
change in shape of the vortex lines is neglected in the axial
direction, indicating that each vortex line is assumed to be of
constant pitch. However, the vortex sheets are not necessarily
helical surfaces since the pitch may vary along the radius.
10. Cox, G.G. and Morgan, W.B., "The Use of Theory in PropellerDesign," Marine Technology, Vol. 9, No. 4, p 419-429, October 1972
5
The computer program can be used for the preliminary desiqn of
a propeller having a prescribed pitch disIribution. The viscous
effects of the propeller are taken into account by giving as
input the blade-section drag coefficient and chord lengths.
Blade stresses are computed using simple beam theory by giving
as additional input the blade thickness, rake, and skew.
DESCRIPTION OF INPUT DATA
Dimensioned parameters may be input in the appropriate S.I. or
English units, as specified by the user illustrated in Table 1.
Effective power, shaft power, speed (V), number of blades (Z),
diameter (D), rp r, propeller wake (l-w x), and estimate of the
hydrodynamic flow angle distribution (aI) are required input
parameters in order to make nonviscous propeller design
calculation 1,2 The radial distributioo of blade chord lengths
nondimensionalized on diameter (c/D) and section drag coefficients
(CD) must also be specified as input if design calculations are
to account for the propeller viscous effects. Since the computer
program presented calculates the propeller principal stresses
based on beam theory, the radial distribution of maximum thickness
nondimensionalized on chord length (t/c), rake nondimensionalized
on diameter (ZR/D), and skew angle (eS) must also be input parameters.
The blade section cavitation number (o) is a required parameter in
order to make blade surface cavitation checks using the Burrill
cavitation diagrams of Reference 7 and Brockett's incipient cavitation
6
%-1 _V,
diagrams of Reference 8. By specifying the static head (H) as input
data, the cavitation number (a) is calculated on the computer.
Hub dimensions can be input or assumed to be a circular cylinder
of equal length and diameter as described in Appendix A. A brief
description of how these input parameters can be determined will
be discussed in this section.
Effective Power, Speed, and Shaft Power
Effective power and speed are normally obtained from model
self-propulsion experiments. Input effective power (P E and shaft
power (Ps) are defined as follows:
P E = VT(l-t)
PS = 2TrnQ
where n = propeller revolutions
PS = shaft power,
PE = effective power,
Q = propeller torque,
T = propeller thrust,
V = ship speed
(l-t) = thrust deduction, which may vary with
diameter and speed.
7
Nondimensional Radial Distance (X)
This is a reference set of eleven nondimensional radial
distances xi at which all other distributions, either input
or calculated by the computer, are defined as existing. In
general xi = ri/R, with the restrictions
xI =rh/R
xll = R/R=I,
where r. = the distance along the propeller reference line from
the shaft axis to the ith section,
rh = propeller hub radius, and
R = propeller tip radius.
Propeller Wake
The radial distribution of the axial wake (l-w x) which varies
with propeller diameter is also required input data. The circum-ferential mean of the axial velocity distribution (l-w c) is obtained
from a wake survey without the propeller operating. However, the
(l-wc) wake distribution must be corrected for the propeller action.
No completely satisfactory method is presently available to obtain
this correction, but an approximation of the radial distribution of
the wake (l-w x) with the propeller operating is obtained as follows:
8
Wake distribution
(1'W x) = [(l-WT)(l-Wc)]/(1"Wv)[]
where (l-wc) = radial distribution of the circumferential
mean wake from wake survey data,
(l-wT) = effective wake from self propulsion data
(l-w) = volume mean wake, [2/(l-x2)If, (1-Wc) xdx,
R = propeller radius,
r =propeller local radius
rh = propeller hub radius,
x = nondimensional radial distance (r/R), and
xh = nondimensional hub radius (rh/R).
The propeller wake distribution may also vary with propeller
diameter depending on the hull characteristics of the vessel.
Advance Angle Distribution Input Option
The advance angle distribution (tanB) is normally calculated
from the equation V(l-w x)/(nnDx) using the propeller wake (l-wx)
from Equation [1]. For most single screw propeller designs this
approach gives good performance predictions. In a few instances,
it may be desired to utilize the computer program presented to
design and predict the performance of propellers operating inside
a duct or in the vicinity of another propeller as in the case of
tandem or contrarotating propellers where the axial (wa /V) anda
9I
tangential (wt/V) velocities induced by these additional sources
near the propeller plane can be predicted. In this case, an option
in the computer program allows the input of the estimated tanB
distribution which accounts for the axial (w a/V) and tangential
(wt/V) velocities induced by other sources in the following manner:
Equation for Estimatinq tan6 If Input Option Is Used
tanestimated = [(l-w x) +wa/V)]/[(x/xs)-(wt/V)] [2]
where wa/V = axial velocity from other sources,
wt/V = tangential velocity from other sources,
s = advance ratio based on ship speed, V/(nnD),
V = ship speed, and
D = propeller diameter.
It can be seen from Equation [2] that for the case where (w a /V)
and (wt/V) values are specified as zero, the advance angle tanB
is calculated in the usual manner when designing single screw
propellers. If the tane input option is used, the tan6 values
are calculated using Equation ?]. For 'he norral sirlp s',a,
propeller desiqn case, tanR is calculated on the computer.
Hydrodynamic Flow Angle Distribution
The hydrodynamic flow angle distribution (tanBI) can be
specified as input. An option is included so Lerb's optimum
10
tans I distribution6 can be calculated by the computer as follows:
tans, = (tanB/ni)[(l-wT)/(l-,W.x)]1/2 [3]
where n- = propeller ideal efficiency
ni = 0.85 is used in the program, and
tanB - advance angle distribution
Lerbs' optimum tans I distribution usually results in optimum pro-
peller efficiency. If other factors such as cavitation, strength
and vibration are considered, the input of an alternate tans I
distribution may be desired.
Static Head
The static head (H) at the shaft centerline is
required input. This parameter (H) is defined as Hs+H a-Hv, where
H is the shaft submergence, Ha is the atmospheric pressure, and
Hv is the vapor pressure of fluid which is normally small compared
with H and may be neglected. The static head (H) is used to
calculate the section cavitation number (a) in Equation [25] and
the Burrill cavitation number 00.7 of Equatiun [30].
Blade Outline and Expanded Area Ratio
The blade outline (c/D) and expanded area ratio (AE/AO) must
be input for the design. An expanded area ratio (AE/AO) is
calculated on the computer according to:
11J
AE/A= (2Z/z)fh c/D dx
where c/D = nondimensional chord length, and
Z = number of blades
If the (AE/AO) input value differs fron the one indicated
in equation [4], adjusted (c/D) values used for the design are
calculated as follows:
(c/D) adj=(C/D) input (AE/AO)calc/(AE/AO)design
The final blade outline and expanded area ratio should be chosen
to give satisfactory propeller strength and cavitation characteristics.
Blade Thickness to Chord Ratio
The input of maximum thickness to chord ratio (t/c)
values allow an estimate of the propeller principal stresses
(see The Propeller Stress Calculations Using Beam Theory section
discussed later) based on beam theory6 to be calculated durinq t~e
preliminary design stage of the propellers. From a rough estimate
of the blade outline (c/D) for the final design and an estimate of
the radial distribution of thickness (t/D) based on fatigue
6strength , the following equation can be used to obtain initial
(t/c) input values:
Blade Thickness Ratio:
t/c = (t/D)/(c/D)
where t/D = radial distribution of thickness (can be estimated from
Reference 6).
12
Rake and Skew
Nondimensional rake (ZR/D) and the skew angles (Os) for a design
are specified to permit adequate predictions of principal propeller
stresses using the beam theory method described in Reference 6
and discussed later in the propeller stress section of this report.
The rake (ZR) is defined consistent with Reference 11 (see Ficures
1 through 2d) as the distance from the propeller Diane to thp genera-
tor line in the direction of the shaft axis. Aft displacement is
considered positive rake (see Figures 2a).
Since the skew angles (eS) significantly affect propeller
unsteady forces, a computer program based on the unsteady
propeller lifting surface theory of References 12, 13, 14, and 15
can be used to select the skew angles (es) for the propeller
design. The input skew angles (eS) in degrees are defined as
the angular displacement of points on the blade reference line
from the propeller reference line in the projected view.
11. Cumming, R.A., Dictionary of Ship Hydrodinamics - PropellerSection, 14th International Towing Tank Conference 1975,Report of Presentation Committee, Appendix VII
12. Tsakonas, S., Breslin, J., and Miller, M., "Correlation andApplication of an Unsteady Flow Theory for Propeller Forces,"Transactions of the Society of Naval Architects and MarineEngineers, Vol. 75, p 158-193, 1967
13. Breslin, J.P., "Exciting-Force Operators for Ship Propellers,"Journal of Hydronautics, Vol. 5, No. 3, p 85-90, July 1971
14. Jacobs, W.K., Mercier, J., and Tsakonas, S., "Theory andMeasurements of the Propeller-Induced Vibratory Field,"Davidson Laboratory Report SIT-DL-1485, December 1970
15. Tsakonas, S., Jacobs, W.R., and All, M.R., "An Exact LinearLifting Surface Theory for Marine Propeller in a NonuniformFlow Field," Journal of Ship Research, Vol. 17, No. 4,December 1974
13
Section Drag Coefficient
In order to account for viscous effects when predicting the performance
of a propeller, the section drag coefficient (C0 ) must be specified as input.
A section drag coefficient (CD) value of 0.0085 usually gives reasonable
estimates of model propeller drag for propeller shapes normally used at DTNSRDC
in the past. For propellers having very thick blades, the following equation,
available as an input option on the computer, and derived as a function of
maximum thickness (t/c) values using experimental data from NACA 66 type
sections, 16 ,17 will give a better estimate of the section drag coefficient (CD):
Section Drag Coefficient:
C = CFO [l+1.25(t/c)+125 (t/c) 4
where CFO is the friction resistance of the section, e.g., CFO = 0.008 for
Reynolds number of approximately 106 and CF 0.004 for Reynolds numbers of
approximately 1O8.
Options for using alternate nonlinear CD distributions, or a constant CD
distributions are also available.
Final Pit..n Ratio (P/D) Input Option
The final pitch-diameter ratio (P/D) distribution defined as
rxtan where is the pitch angle is normally not known
during the preliminary design stage of the propeller. Because
of this hydrodynamic flow angle (e) from lifting line
16. Abbot, Ira H. and Von Doenhoff, Albert E., "Theory of Wing
Sections Including a Summary of Airfoil Data," Dover PublicationsInc., New York, Library of Congress Catalog No. 60-1601, 1949.
17. Hoerner, S.F., "Fluid-Dynamic Drag," Published by the author,
Midlard Park, New Jersey, 1965.
14
calculations is substituted for the pitch angle ( ) in the
bending moment calculations when making stress calculations
using beam theory and when predicting clearance between blades
and fillets at the propeller hub, If the final P/D values are
known, they can be used.
DESIGN AND PROPULSIVE PERFORMANCE PARAMETERS CALCULATED
In order to simplify propeller design calculation pro-
cedures, the design thrust and power of propellers are usually
considered in nondimensional form. The nondimensional design
thrust loading coefficients (CTS and CTh) and design power
loading coefficients (C PS and C ) are calculated on the computer(Cpp
in the following manner:
Thrust Loading Coefficients:
CTS = T/[(d2)]nRR2V2 or CTh = T/[(p/2)nR 2VA2 [7]
Power Loading Coefficients:
C = PD/[(p /2)TR 2V 3 ] or C = P D /[(p/2)rP2V A3] [8]
where V = ship speed,
VA = speed of advance of propeller, V(l-wT), and
p = density of fluid
Lerbs lifting line theory is used to determine the
propeller lift coefficient (CL), circulation (G), hydro-
dynamic flow angle (a), axial induced velocity (UA/2V), and
15
I
tangential induced velocity (U T/2V). These lifting line calcula-
tions take into account propeller viscous effects by specifying
as input in the computer program the propeller section nondimen-
sional chord length (c/D) and section drag coefficient (CD). A
method for obtaininq values for c/D and C is discussed in the
Description of Input Data section of the report. Design parameters
such as thrust loading coefficient (CTs), thrust power coefficient
(CThd, power loading coefficient (Cps), propeller efficiency (rnp),
and propulsive efficiency (nD ) are calculated for each propeller
in the following manner:
Thrust Loading Coefficient:
CTS=fP (l-EtanBi)(dCTs/dx)dx=T/[(d2)/nR2V2 [9]
Thrust Power Coefficient:
CThP= I h(lW)(lEtanai)(dCs/dx)dx=(l-WT{T/[( c /2)iR2V2]} [10]
Power Loading Coefficient:
Cpse=fh (1+ Vtan)dCp /dx)dx=P /[( /2)R 2V 3 ] [11]
Estimated Propeller Efficiency:
"Pe: CThp/CPs , TVA/(2rQn) [12]
Estimated Propulsive Efficiency:
nD=(l-t)CTs/CPs=PE/PD [13]
16
f
where CL = section lift coefficient from lifting line theory
CTs i = nondimensional inviscid local thrust loading coef-ficient, 4ZGx/xs)-UT/2V]
Cpsi = nondimensional inviscid local power loading coef-
ficient, (4Z/s)XG[(I-Wx)+UT/2V]
G = nondimensional circulation from lifting line theory
UA/2V = axial induced velocity from lifting line theory
UT/2V = tangential induced velocity from lifting line theory
The calculated prapeller thrust (T) is obtained by substituting
the CTS calculated in Equation [9] into Equation [7] and the
delivered power PD is obtained by substituting CPS computed
using Equation [11] into Equation [8].
( Other parameters useful in designing and evaluating the
performance of propellers include the advance coefficient (J),
ship speed advance coefficient (Jv), thrust coefficient (KT),
torque coefficient (KQ), moment due to thrust (lTb), moment
due to torque (14Qb), moment parallel to section nose-tail
line (M xo), moment perpendicular to the nose-tail line (M yo) and
the blade loading distribution (LI). These parameters are
calculated as follows:
Advance Coefficient:
J=V(lIT)/(nD)=VA/(nD) [14]
17
Ship Speed Advance Coefficient:
J =V/(nD) [15]
Thrust Coefficient:
K = n2 D4 )=W S/)jV2 [16]
Torque Coefficient:
KQ=Q/( rn 2 D5)=(C PS/16)J V [17]
Moment Due to Thrust:
M b(X= 'TrRV 2/(2Z)]fl (x-x )(1- Etane?)[dCTS/dx]dx [18]T 0X h 0 i
Moment Due to Torque:
M~~~~~ ~ ~ (x)[ r (Z]l(- (tanB + E)[dCT /dx]dx [19]MQb(X)Pr 0 2 (Z)! X- 0
Moments Parallel to Section Mose-Tall Line:
M xo (x o)=H Tb cos+m Qb sino [20]
Moment Perpendicular to Section rNuse-Tail Line:
M y (x o)='. Tbsin -MMQbcoso [21]
Blade Loading Distribution:
LI(x)-(l1/Z)pcV r2 CL[22]
where x,x0 propeller nondimensional radial stations,
r/R and r 0/R
o= propeller pitch angle (input or aI
V r= section inflow velocity, V/[(l..w )+U 2V]'+[(X/x )U T/2V]~
Appendix A presents procedures for calculating propeller weight,
center of gravity, mass polar miments of inertia and radius of
gyration and Appendix B shows how the American Bureau of Shipping
CABS) coefficients and thickness requirements are calculated. Other
18
calculations made include stress calculations based on beam
theory, parameters for making blade surface cavitation checks,
chord lengths for making final pitch and camber calculations,
and the prediction of spacing between blades and fillets at
the propeller hub.
PROPELLER STRESS CALCULATIONS USING BEAM THEORY
A propeller blade must contain enough material to keep the
stresses within a blade below a certain predetermined level.
This level depends on the material properties with regard to
both steady-state and fatigue strength and to both mean and
unsteady blade loading. The material selection controls the
( allowable stress level and the blade chord, thickness, rake
and skew are the main parameters which control the blade stress
for a given blade loading. The principal stresses in the
propeller blade are computed for each propeller. Both hydrody-
namic and centrifugal loadings are considered. In this stress
calculation procedure, the propeller blade is represented as a
straight cantilever beam of variable cross-section without camber.
Experimental results show that the neutral axis of an airfoil
section lies approximately along the mean line so camber is not
considered in the stress calculations presented. Only the
maximum principal stresses calculated at the mid-chord of each
section are printed as output in the computer program. Stresses
19
for the final design should be calculated by finite element
techniques if rake and skew for the propeller differ from
usual propeller shapes.
PARAMETERS FOR MAKING BLADE SURFACE CAVITATION CHECKS
Brockett's theoretically derived incipient cavitation charts
of Reference 8 can be used to predict the blade surface cavita-
tion characteristics of each propeller once the lifting line cal-
culations have been completed. The two-dimensional camber to
chord ratio (fM/c), ideal angle of attack in degrees (ai), section
cavitation number (a), nondimensionalized with the section inflow
velocity (V r), and the maximum and minimum fluctuatinq angle of
attack (max' am in) in degrees are parameters that must be deter-
mined before Brockett's incipient cavitation charts can be used.
These parameters are calculated as follows:
Section Maximum Camber to Chord Ratio for NACA a=O.8 Meanline:
fM/c=0.0 679 C1 [23]
Section Ideal Angle of Attack in Degrees for NACA a=O.8 Meanline:
ai:I.5 4 CL [24]
Section Cavitation Number:
a:2g(H-xR)/Vr2 [25]
where g = acceleration due to gravity
H = static head at shaft centerline (see section
on Static Head).
The maximum and minimum fluctuating angles of attack
20
........ .... ,t' : m 7 - .
(amaxamin) in degrees are calculated using the method derived
by Lerbs and Rader in Reference 18. These calculations can be
made using the following equations:
flaximum Fluctuating Angles of Attack:
amax=ai-(-As)F(x) [26]
Minimum Fluctuating Anqles of Attack:
c'min"i-(+AB)F(x) [27]
where -AB = Maximum effective angle of attack in degrees
(from wake survey data), and
+aB = Minimum effective angle of attack in degrees
(from wake survey data).
The parameter F(x) in Equations [26] and [27] is dependent
on the hydrodynamic flow angle (aI), the advance angle (a) and
the lift coefficient (CL), and is calculated on the computer
using the following equation:
F(x)=I/[l+27rtan(a i-0)/C [28]
The Burrill Cavitation Charts 7, can also be used to give an
approximate check on the cavitation performance of propellers.
Burrill's thrust loading coefficient (T c) and cavitation number
(00.7) at 0.7 radius defined as follows are parameters that
must be known to use these cavitation charts.
18. Lerbs, H.W. and Rader, H.P., "Uber de Auftriebsgradienten vonProfilen im Propeller Verband, Schiffstechnlk, Vol. 9. No. 48.p 178-180, 1962
21
Tc=T/{(p /2)Ap[{V(l-Wxo.w J 2 +f0.7xnD} 2] [29]
Burrill Cavitation Number at 0.7 Radius:
ao.7 =2gH/[{V(l -xwe. ) 2 +0.7nD} 2] [30]
where A. = propeller expanded area, fRc dr,
A0 = propeller disc area, nD 2/4,
Ap = propeller projected area, [1.067-0.229(P/Di]A , and
(P/D)i = propeller pitch ratio at 0.7 radius input or
estimated as 0.7ntans I.
Keller's method9 of predicting the minimum expanded area
ratio of the propeller is also calculated on the computer. The
minimum expanded area ratio, based on eliminating back bubble
type cavitation, is computed as follows:
(A/A) KT' 6+.6)K2 2(AE/AO) K= KT (2.6+. 6 Z)KT/{O.7[J +(0.7n) 1 [31]
The constant K=0.15 was used in this program. Many possible
alternate values of K may be desired, for example: K=0.2 is
used for single screw ships with bronze propellers having rake
of approximately 10 degrees, K=0.l0 is used for twin screw ships
with copper-aluminum propellers, K=0.15 is used for twin screw
ships with bronze propellers and for single screw ships with
copper-nickel-aluminum propellers, and K=O to 0.05 is used for
propellers for fast ships such as destroyers and frigates. If
a different value of K is desired, the expanded area ratio cal-
culated in equation [31] should be adjusted to account for changes
in the value of K.
22
CHORD LENGTHS FOR PITCH AND CAMBER CALCULATIONS
The final pitch and camber for each propeller can be calcu-
lated using computer programs presented in References 3, 19, 20,
21, 22, and 23. The programs require as input the section chord
length, (c/R)LE and (c/R)TE nondimensionalized on propeller radius,
in terms of the skew angle (es), hydrodynamic flow angle (aI) and
blade outline (c/D). The parameters (c/R)LE and (c/R)TE measured
(- from the leading edge and trailing edge to its reference line,
respectively, are calculated in the following manner on the
computer:
19. Kerwin, J.E., "The Solution of Propeller Lifting-SurfaceProblems by Vortex Lattice Methods," Department of theNaval Architecture and Marine Engineerinq, MassachusettsInstitute of Technology, Cambridge, Massachusetts, 1961
20. Kerwin, J.E., and Leopold, R., "Propeller Incidence Cor-ection Due to Blade Thickness," Journal of Ship Research,Vol.7, No. 2, 1963
21. Cheng, H.M., "Hydordynamic Aspects of Propeller Design Basedon Lifting-Surface Theory: Part I - Uniform Chordwise LoadDistribution," David Taylor Model Basin Report 1802, 1964
22. Cheng, H.M., "Hydrodynamic Aspects of Propeller Design Basedon Lifting Surface Theory: Part II - Arbitrary ChordwiseLoad Distribution, " David Taylor Model Basin Report 1803,1965
23. Kerwin, J.E., "Computer Techniques for Propeller Blade SectionDesign," Transactions of the Second Lips Propeller Symposium,Drunen, Holland, p 1-31, May 1973
23
Chord Lengths Measured From Blade Leading Edge:
(c/R)LE=Xes/(57.296 coso)-c/D [32]
Chord Lengths Measured From Blade Trailing Edge:
(c/R)TE=Xes/(57.296 coso)+c/D [33]
(eaI is used when pitch is not input)
SPACING BETWEEN BLADES AND FILLETS
Propeller designs should have enough clearance between
blades at the hub so fillets are properly applied. Hill,
Reference 24, derived the following equation, which is used
in the program to estimate spacing between blades at the hub
without fillets:
Gz = (2r rh)/Z - (th/sin) [34]
where € input pitch or 81
Based on a number of full-scale propellers built with standard
fillets, Hill's blade clearance equation was modified in the
following manner to estimate spacing between fillets at the hub
during the preliminary stage of the design:
GF =(2?irh/Z) - (l.9th/sin ) [35]
A layout of blade sections is recommended as a final fillet
clearance check.
PROPELLER DESIGN THRUST AND POWER OPTIONS
The thrust option can be used to make lifting line calcula-
tions for propellers required to produce a given thrust at
24. Hill, J.G., "The Design of Propellers," Transactions of the Society
of Naval Architects and Marine Engineers, Vol. 57, p 143-170, 1949.
24
specified values of speed and rpm (this is accomplished by adjust-
ing the input tan 8I distribution), or the power option can be used
if the propeller is required to absorb a specified power at a given
rpm (in which case the speed is determined).
From each calculated power, a new value of speed (assumed to
vary as the cube root of the ratio of the design and calculated
power) is obtained and its correspondino effective power is obtain-
ed from the effective power input curve. Design calculations again
produce a new calculated power, and the process continues until the
closeness criteria of design calculated power is satisfied (two
iterations are normally sufficient). Smaller increments of input
speeds in general cause faster convergence.
(Once the basic shape of the distribution is defined (see the
Hydrodynamic Flow Angle Distribution section) the final tanB I
distribution K4 tanB I is determined using the thrust or power
options, making lifting line calculations of three nondimensional
thrust loading coefficients (CTs)l, (CTs)2, and (CTs)3 that cor-
respond to three hydrodynamic pitch distributions, K1 tanB I, K2
tanB I, and K3 tan8 I where K1 = 0.975, K2 = 1.0, and K3 = 1.025.
Once these calculations are obtained, the following system of
equations are set up:
(CTs)l = A+BKl+CK2
(CTs)2 = A+BK2+CK 22
(C = A+BK +CK 2
25
from which values of A, B, and C are obtained. Then, values of A, B,
and C are substituted in the following equation to obtain the value of
K4.
2CTs = A+BK4+CK4
where CTs = design thrust loading coefficient (Equation (7)).
COMPUTER PRCGRAM AND SAMPLE DESIGN
CALCULATIONS
Liftina line theory of References 1 and 2 has been used to
derive a computer program for the preliminary design of propellers
using high speed CDC computers at DTNSRDC. A core size of approxi-
mately 60,000 octal is required for the program. The average run-
ning tine for a design based on thrust is 25 seconds and 100 seconds
are required using the power option. As mentioned earlier, Appendix
A presents procedures used to calculate propeller weight, center of
gravity, mass polar moment of inertia, and radius of gyration.
Appendix B shows how the American Bureau of Shipping (ABS) coefficients
and thickness requirements are calculated. A detailed description of
the input and output formulas for the computer program is ptesent in
Appendix C exercising most of the available options. Design calculations
are presented in Appendix D for a sample design using the thrust
option and results using the power option are shown in Appendix E.
A Fortran listing of the computer program is presented in Appendix F.
26
..-..- ~ ~ :...." ...- :-- : =:" "":= - ;. :
Vx (, 0
(r-V0 (r.0)I
Figure I -Typical Velocity Diagram (or a Propeller Blade Section al Radius r(The diagram is drawn Yft., all quantities positive and the velocity vectors represent the velocity of
the propeller blade u'ction relative to the fld)
27
0z
MUD, wIw < z
ccr
w4~~ 044f- ~ %I -W-3:C
4~ uw 0oW CCLLAc 7ui Z n Ww<sJ U U C
-j -jz < :. 2 t
g U. WCL LC~ Wa
0 z
-a - - z
~w C)JL
S0 0cr.
w 1IL w
0 I
28w
BLADEREFERENCE
LINE / GENERATORLINE
I
---- PROPELLER REFERENCE LINE(PROPELLER PLANE)
REFERENCE POINT OF/ BLADE ROOT SECTION
PROPELLERHUB
FORWARD-.4..HUB DOWN
RADIUS
_SHAFT
AXIS
Figure 2b - Diagram Showing Recommended Reference Lines Looking to Port)
29
PROPELLER REFERENCE LINEzAND GENERATOR LINE
BLADE REFERENCE LINE(LOCUS OF BLADE SECTION
REFERENCE POINTS)
PROJECTED BLADEOUTLINE
TRAILING EDGE
LEADING EDGE
PROPELLER HUB REFERENCE POINT OF ROOT SECTION
SHAFT AXIS
NOTE: THE SKEW ANGLE. Qs. SHOWN AT RADIUS r IS LESS THAN ZERO.
Figure 2c Diagram Showing Recommended Reference Lines (Looking Forward)
0 )30
PROPELLERREFERENCE LINE
-~ I
-u
W 0o
- _ _ _ _ _ _ _ _ _ _ _
_________________ - HUBLEN
FIGURE 2d -INPUT FOR DETAILED HUB OPTION
31
TABLE 1
List of dimensioned input and output parameters used by
computer program based on English and SI units
Parameter English Units SI Units KSI (I )
Shaft power (P ) hp KW 0.7457
Effective power (P E hp KW 0.7457
P ibm/ft3 kg/m3 16.01846
V knots 2) n/s 0.514444
V ft/sec knots (2) 0.5924
D ft m 0.3048
H ft m 0.3048
2 4 3P lbf sec /ft kg/m 3 515.3788n rev/min rev/min (3) 1.0
T, weight lbf N 4.44822
V ft/sec m/s 0.3048
LI lbf/ft N/m 14.5939
MTb in lbf Nn 0.112985
MQb in lbf Nn 0.112985
M in lbf Nn 0.112985xo
M in lbf Nn 0.112985yo
Max Stress ibf/in 2 Pa 6894.757
SKEW deg deg (3) 1.0
RAKE deg deg (3) 1.0
Mass polar moment Ibm in2 kgm 2 0.00029264of INERTIA
(i) Multiply English Units by KSI to get SI Units.(2) Computer program uses knots in both English Units option
and SI Units option.'PI These are not SI Units but are permitted to be used in the
SI sy-.:m according to International Standards Organization (150)Standard No. n
32'
APPENDIX A
PROPELLER WEIGHT, MASS POLAR MOMENTS OF INERTIA, AND CENTER
OF GRAVITY
The approximate propeller weight (W p) and location of center
of gravity (CG) from the propeller center line is also calculated
for each design. In order to make these calculations, the density
of the material (p) must be specified as input.
Hub dimensions can be input, or a solid circular cylinder of
equal length and diameter, with propeller center line at the mid
length of the hub can be assumed. If the cylindrical hub is assumed:
Wp = W+W H
where WB = weight of blades, OpZfl a(x)dx
WH :weight of hub, (irppDH/4),DH = hub diameter
a(x) = area of section at radius x, 2c(x)t(x) f I t(x,x )dx,
c(x) chord length of section at radius x,
t(x) = maximum thickness of section
t(x,x) = Chordwise distribution of section thickness (NACA 66modified thickness form is used in program)
x = nondimensional coordinate alona the section chord, (r /c),and
= density of material considered
33
'Iif calculations are desired for a noncylindrical hub, the follow-
ing dimensions are input:
DFH = forward hub diameter,
DA = aft hub diameter,
LH = length of the hub,
DFB = forward bore diameter,
LRL = distance from aft end of hub to propeller reference line
The hub is then treated as consisting of two frustrums of cones,
joined at the propeller reference line. Again
Wp = WB +WH,
but now
WH = WAF+W FF-W b
where WAF = weight of solid aft frustum, (lTp p/3) (DAHDH+DH+DL)/4
WFF = weight of solid forward frustum,
(-r p/3) (D2+DHDFH+DF2 )/4
Wb = weight of bore, (np p/3) (D2B+DABDFB+DFB2)/4
The propeller center of gravity (CG) with respect to the blade
center line, where plus values represent the distance ahead of the
center line and negative values aft of the center line, is calculated
in the following manner (see Figures 2b and 2c):
Center of Gravity:
CG = M /Wp p
where Mp moment of the propeller, P pZfx a(x) B(x) dxp3 h
34
where Mp = moment of the propeller, p Zfh a(x) B(x) dx
ph
B(x) = distance of center of gravity from propeller reference
line,j + +i
x = the distance of the center of gravity of the section alonq
the chord line from the position of maximum thickness,
y = the distance between the center of gravity of the section
and the chord line of the section, measured perpendicular
to the chord line,
ri = the radial distance from the shaft axis to the section,
R= rake angle in radians of the section,4-,
S= skew angle in radians of the section, and
4 = pitch angle in radians of the section (:=I is used
when pitch is not input).
Then x = the component of the center of qravity adjusted for
pitch, xsin q +ycos 4;
y = the component of the center of gravity adjusted for skew
(=- vrtan4 ) and rake (=- c ri/R); and
i = the component of the center of gravity alonq the shaft
axis of the specified hub, aft of the propeller reference
line taken as positive.
35
U L
If the standard hub is selec-ted,
6 m= mass polar moment of hub W WH DH 2/8
otherwise,
H PM Tigp ( PM FPM- B PM) /10
where A PM = aft mass polar mom~entLL 4 3 2 jIf 4I~)1
L L(D H +DHP D Ali+DH D AH hIfDAl"+AN)1
Fm= forward mass polar moment =
(f4 3 +D2 3 4C IL RL )(D H +DH D FH+11 DFH-+D H DFH +D FH )116
BP.,1 = mass polar moment of bore =
1(D4 +D3 D D2D 2 +DD3 D4 )1HL(DAB AB DFBDABDFB DABDFB 0FB )l
zpl= mass polar mioment of blades
Z c Xh xe (x) dx
Then P P~m = propeller mass polar moment=
Z P +11 M
and K z = radius of gyration of blades
?:1 B
K = Radius of gyration of hub
PM' H
K= radius of gyration of propeller
v' P /W,
36
APPENDIX B
AMERICAN BUREAU OF SHIPPING (ABS) COEFFICIENT AND THICKMESS
REQUIREMENTS
The minimum blade thickness at the one-quarter radius is
defined in Reference 25 by:
tl =K 1APs/(C'NCZn) + CSBZR/(4C NC)
and T2=K1I.APS/(CNCZn) + CSBZT/(4CNC)
where PS = shaft power at the maximum continuous rating,
n = propeller revolutions per minute rpm at the maximumcontinuous rating,
Z = number of blades,
ZR = rake, positive aft, at the blade tip.
Z T= rake and rake plus skew induced rake, at the bladetip, positive aft taken as positive,
and
C = as/(11st 0.25) section area coefficient at the one-
quarter radius
CN /(UfWst 20.25) = section modulus coefficient at the one-
quarter radius
A =l+(K 2/tan4 0 .7)+K 3tan4 0.25
B =(K4(AE/AO)/(Z) (n/lO0)2 (D/20)3
C =(l+K 5 tan 0.25)Wsf-B)
where K 1 through K5 are constants which depend on the system of
units employed
25. American Bureau of Shipping, "Rules for Building and Classing
Steel Vessels," p 621, 1972.
37
as = area of expanded cylindrical section at 0.25R :
2c0 25t0 25 f t(O.25,x) dx,
WS = expanded width of cylindrical section at the one-quarter
radius,
t0.25 = maximum thickness at the one-quarter radius,
10 = moment of inertia of the expanded cylindrical section at
one-quarter radius about a straight line through the center
of gravity parallel to the chord line,
UF = maximum normal distance from the moment of inertia axis to
points on the face of the section,
c0.25 = section chord length at 0.25R,
n 2 4 A = the pitch angles at the one-quarter and seven-
tenths radius (or BI if 4 not input),
t(O.25,x) = chordwise distribution of section thicknesses at the
0.25 radius
AE/AO = expanded blade area divided by the disc area,
D = propeller diameter,
f = material constants in length/weight as a function of w
38
w = a nondimensional parameter associated with the i1aterial type
as illustrated in the table below.
Type Materials Units
2 Manganese bronze 0.30
3 Nickel-manganese bronze 0.29
4 Nickel-aluminum bronze 0.27
5 Mln-Ni-Al bronze 0.27
6 Cast iron 0.26
If CN 0 0.1, the thicknesses ti and t2 are recomputed with
CN=O.1.
39
APPENDIX C
DESCRIPTION OF INPUT AND OUTPUT
Data are input to the program in unformatted groups. Within
each group the data must be in the order specified, and each
value must be separated from all others by a blank or comma.
Variable names beginning with I,J,K,L,M, or N require an integer
input, but other variables which happen to have integer values
do not require a decimal point. Zeroes must actually be keypunched.
Beyond this there are no restrictions on how many or few data
cards are needed for a group, except that each group must start
with a new card. The input required is as follows:
(
i 40
Group Parameters Description of Input
I IDD Number of data sets(each of the groups
2 through end form a data set)
2 UI,UO,Title Use SI in columns 2,3 to pecify input
in SI units. Use SI in columns 4, 5
for output in SI units. The remaining
66 columns are available for identifi-
cation of input data.
3 SHP[FL/T] Desinn shaft power or 0 if the thrust *
option is desired
TANBI Use 1 unless use of an exact (not ad-
justed by program) tanB I distribution
is required, then use 0 (see hydrodynamic
flow anqle distribution
TANB Use 1 to input tanf distribution, or 0
for machine calculations accordinq to (2)
XPS Use -l to input a skew distribution, or
input the skew at the tip for a linear
skew distribution (both in degrees)
RAKE Use <RAKE< 0.01 to input a rake/D *
distribution or input the rake/D at
the tip for a linear distribution
POO Use PDO 0 to input a P/D distribution,
otherwise i xtanB I is used as an approxima-
tion
* As used within the Fortran Program
41
2 "' ,/ i ,
Group Parameter Description of Input
CD Use CD>lO to input the radial distribution of
drag coefficients (CD); O<CD<lO to input a con-
stant drag CD=CD at all radial stations; CD-O
causes the computer program to calculate the
radial distribution of drag coefficients using
the equation CD=O.OO8[l+l.25(t/c)+l25(t/c) 4];
-IO<CD<O causes the computer program to use a
constant frictional resistance CFO=ABS(CFO) in
Equation 6 CD=CFo0l+l.25(t/c)+125(t/c)4
CD<-lO to input the radial distribution of
frictional resistance (CFO) values to be used
in Equation 6.
3 TYPE For ABS minimum blade thickness calculations
coefficients use the number corresponding to
the material type in the blade thickness
section. Use TYPE=O to suppress these calcu-
lations
HUB Use HUBtO to input actual dimensions of 11UD,
or HUB:O to use solid cylindrical hub in
relevant calculations
4 DIAM[L] Propeller diameter
EWAKE Effective wake (l-wT)
ETHRUS Thrust deduction (l-t)
42
Group Parameters Description of Input
IIEAD[L] See section on Static Head, at the shaft
centerline
DENIM/L3] Density of propeller materials
RHO[M/L3] Density to be used for water
5 IVV Number of velocities input
VEI[L/T] 1VV velocities
EHP[FL/T] IVV design effective power values, corres-
ponding to the input velocities
5 IZZ Numoer of different blade numbers input
JBL IZZ values of blade numbers
IEA Number of expanded area ratios input
EXX IEA values of AE/Ao. A value of 0 input as
the first AE/Ao will result in calculations
being done exactly at the design AE/Ao. If
this default is used, calculations will not
be done at other values of A E/A in the
list that happen to be within 0.005 of the
design AE/Ao.
IRPM Number of different rpms input
XMM IRPM values of revolutions per minute
43
Group Parameters Description of Input
(The remaining five radial distributions have eleven values each)
X3 Values of r/R at which other radial
distributions are defined
X4 Propeller wake (1-wx )
X5 Hydrodynamic flow angles (taneI). If zeroes
are input, Lerbs optimum is calculated as a
default distribution
X6 Section chord lengths (c/D)
AZZ(25) Thickness to chord ratios
(Groups six through ten which are specified in group three are
defined at the eleven radial stations)
6 AZZ(24) Blade skew angles, degrees (if XPS<O)
7 3(7) Section drag ccefficients (if CF>0)
or frictional resistance of section
CFO (if CD<N-l0
8 B(8) Tangents of advance angles (if TANB>O)
9 RAK Rake/D, aft positive (if O<RAKE<0.0)
10 P Pitch, P/D (if PD>O)
11 FWDDIAM[L] Dimensions, as indicated in Figure d
(if HUB0)
AFTDIAM[L]
HUBLEN[L]
FDBORE[L]
ADBORE[L]
DISREFL[L]
44 '4
A Description of the Output Generated by the Program Follows:
Program Output Description
G Nondimensional circulation
UT/2V Tanqential velocity induced at lifting line
UA/2V Axial velocity induced at lifting line
DCTSI Local nonviscous thrust coefficient (Defined in
Equation (9))
DCPSI Local nonviscous power coefficient (Defined in
Equation (11))
VR [L/T] Section inflow velocity, equation (22)
CAVV Section cavitation number, Equation (25)
CPTI Nionviscous thrust power coefficient (Equation (10)
when r-0).
CPSI Nonviscous power coefficient (Equation (11)
when c =0)
ETAI Estimated nonviscous propeller efficiency
(Equation (12) when (=0)
CTSI Nonviscous thrust coefficient (Equation (9) when
E =0)
CPT Thrust power loading coefficient (Equation (10))
CPS Power loadinq coefficient (Equation (11)).
TETS Projected skew angle in degrees
RAKG Rake/Diameter
PE Effective power
4 )45
Program Output Description
PS Shaft power
ETA Estimated propeller efficiency (Equation (12)
CTS Thrust loading coefficient (Equation (9))
CL Section lift coefficient
ALI Section two-dimensional ideal angle of attack
in degrees for NACA a=0.8 meanline, Equation
(24)
FM/C Section two-dimensional maximum camber ratio
for NACA a=O.8 meanline, Equation (23)
CD/CL Section drag-lift ratio (c=CD/CL)
F(X) Parameter for calculations section fluctuating
angles of attack, Equation (28)
LI[F/L] Propeller blade loading distribution Equation (22)
(C/R)DLE Chord lengths for lifting surface pitch and
camber calculations, Equation (32)
(C/R)DTE Chord lengths for lifting surface pitch and
camber calculations, Equation (33)
T/RD Ratio of section thickness to radius
PC Estimated propulsive efficiency, Equation (13)
PS[FL/T] Calculated shaft power delivered at the propeller,
Equation (13)
DESIGN [F] Design thrust
CALCULATED [F] Calculated thrust, Equation (7) and (9)
46
Program Output Description
AEPA [L2] Area of section
XBAR [L] Longitudinal position about x axis parallel
to nose-tail line from centroid
YBAR [L] Vertical distance about y axis perpendicular
to nose-tail line from centroid
IXO [L4] Moment of inertia about y axis perpendicular
to nose-tail line
MXO [FL] Bending moment about the x axis, Equation [20]
MYO [FL] Bending moment about the y axis, Equation [21]
MTB [FL] Bending moment due to thrust, Equation [18]
MQB [FL] Bending moment due to torque, Equation [19]
MAX STRESS (F/L 2] Aaximum stress
WEIGHT OF BLADES [F] Equation [32], WH=O
WEIGHT OF PROP (BLADES
+DESIGNATED HUB) [F]
(CENTER OF GRAVITY OF Appendix A
PROP/D)
(CENTER OF GRAVITY OF Appendix A
BLADES/D)
KELLERS MINIMUM EAR Equation [31]
SPEED COEFF(JS) Equation [15]
47
A3Program Output Description
Advance Coeff (JA) Equation [14)
THRUST COEFF (KT) Equation [16]
TORQUE EOEFF (KQ) Equation [17]
PROPULSIVE EFFICIENCY Equation [13](PC)
BURRILL THRUST COEFF Equation [29](TC)
BURRILL CAVITATION Equation [30]COEFF
CLEARANCE AT HUB BETWEEN Equation [34]BLADES/D
CLEARANCE AT HUB Equation [35]
BETWEEN FILLETS/D
MASS POLAR MOMENT OF 2INERTIA OF GLADES [FL 2] Appendix A
TOTAL MASS POLAR 2MOMENT OF INERTIA [FL 2]
RADIUS OF GYRATION OFBLADES/D
RADIUS OF GYRATION OF
HUB/D
TOTAL RADIUS OF GYRATION/D
ABS MINIMUM THICKNESS Appendix BCONVENTIONAL RAKE
CONVENTIONAL + SKEW1INDUCED RAKE/D
VALUES USED INDETERMINING THICKNESS
4848. .
Program Output Description
SECTION AREA COEFFICIENT Appendix B
SECTION MODULUSCOEFFICIENT
AREA OF EXPANDED 2CYLINDRICAL SECTION [L2]
49
APPENDIX D
SAMPLE DESIGN USING THE THRUST OPTION
50 ,.
OPTIONS EXERCISED IN APPENDIX D
Power or thrust T
Calculations with input tana I N/A
TanB I (Lerbs or input) Input
Tane (Calculated from (l-w x) or input) Input
CD (constant, variable, or calculated) Const
Multiple RPM No
Multiple Z No
Multiple AE/AO No
Check AE/AO of input C/D and modify No
Skew (Linear/Nonlinear) L
Rake (Linear/Nonlinear) L
P/D (input or approximated by nxtans1) Input
ABS coefficients No
Hub geometry Input
Input Units SI
Output Units SI
51
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AAPPENDIX E
SAMPLE DESIGN USING POWER OPTION
(7 I i,73 "A
OPTIONS EXERCISED IN APPENDIX E
Power or thrust Power
Calculations with input tano I N/A
Tans, (Lerbs or Input) Lerbs
TanB (calculated from (l-w x) or input) Calc
CD (constant, variable, or calculated) Calc
Multiple RPM Yes
Multiple Z Yes
Multiple AE/AO Yes
Check AE/AO of input C/D and modify Yes
SKEW (Linear/nonlinear) NL
RAKE (Linear/non7inear) NL
P/D (input or approximated by wxtanai) ApproxCalc
ABS Coefficients Yes
Hub Geometry ApproxCalc
Input Units English
Output Units English
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APPENDIX F
FORTRAN LISTING OF COMPUTER PROGRAM4
108
PPOG'RAM GMAIN(INPtIT=256,OUTPUT=512, TAPr'=INPUT,TAPC6=OUTPUTH
DIMENSION CH3RO(11) ,THICKNS(11.),CAMtEP(tt) ,PITCH(11) ,SKEWP(11)
DIMENSION I(38,3P) ,DENS(61,62(181)dR3(1'1l)
2 8B15 (1 P )#AZ (11,I ), BHt11iIt) ,C.(12,t?),Cr(12,12)DIME-NSION X3(tl1,X4(tj),X5(1it)11),VL9),EHP(9),qLA(9),EXXI9)DIMENSION AZI(IJ,38),ASHP(q),XM()CAV(q)cAE(),F(l),F1j(llIDIMENSION VEL.1 (9) ,EHPI (9) 9AX(I1) 9RAK(11 )YTRI it 11PXT~fl),SX(7)DIMENSION VSU9RSQ(II),VSU10(Il)DIMENSION ARE-A(7),XBAP(7),YRAO(7),AYEXO(7),AYEYO(7),EMXO(7),EMYO(7
1),FMT8 (7) 9EMOB (7) *STRMAX (7)DIMENSION W(13),FMMX(13),YTX(13),TX(11),CV(11),FMX(11),Jc!L(11),
1 ARPMI(I1),PM0X(II) Q1)S(),1)DIMENS.ION TABS(6)DIM--.NFION t4V (9) OME(9) 904X(9)COMMON /UNITS/ SIUIUOCOPIMON/CWEIG-iT/X ,CHORD,THICKNS,CAMREq,PTTC4, SKEWP,DIAM, U ,OE'I, AIKE1,PI,P,PP8,OPg,PPII,EWAa(E,VS,RPSSIGMAFAQ,rtT,PProO2 ,FWOOIAMArDIAMNUBLEN,FDBOREAD8OREif)S~'FLCOMMONl 'l, 132,83, ni Rh9I*A9H
COMMON CCoNU11i),CCTHO0(11),CCTH4R(11),CCFORt)COMMON PPiqPD2,PP3*PP,PP5,PPF)9PPl3COMMON SN(73),CO(73)
DIMENSION XR(20) TANBETr(7o) r,(20),XSL (;P),(ST(2fl),WAKr(?O)
OIMrNSION TLES(10,2)PEAL NqNIqI4PUTvLFBSLIN~,NLINRDAT! iAPU*E~ARF / 8H DESIGN ,8H4 INPUT/
9ATA FM.'X 1.0,. 2712, .442,.'~qQ3, . 9 63c ~ Q,)13,1.,. 97%, * 8R92, .7a27,1 .35fib,.17139.C/
flAT4 YTY ':.C6.q7.4.67
DATA DENS / I.5I86, /3$1jslLIATA TABS /IC'4ABS MINIMU -;Ij4H T14ICKNrCz ,1'HS TN INCI"E
2 I.HS (USING P 910H4 ,ICHDAThTr,S,UBS,VBSiXOS / iCH/D=P?XTAriB *1114T)-
2 1GII/D INPUT)- ,10H/DATA SHPP,S'4PTI ,SHPT2,OEN1,OErN2,OE N3,ZS,?Aq,rQ P4SrOMMA,Ar)r)J
1 /rH 53P':,7H THRUST97'I OPTIDNJ,tOH, OrEN"TTY ttgO'0F POOP(LP,2 8HM/FT3V= ,3H 7=,5H EAR=95H4 OPM=,2H9 131H AgJtU'TEn'
DATA TLES / iOH x .104 1-wY lSH d/O2 104 T/C 910H4 TANR3I .1014 TA4-13 1014 TETS(DES) .10H RA'(G/l .10H P/fl4 ICH CO 9 1C'1H /
DATA I P~L-B*I~NIN,)TrTC~TCL /104~ INPUT2 ICH LERBS 910H4 LINFAP ,10HNfNLITrA03 1CHPIYTANOI 910HCONSTANT ,1OHCALI;ULATED /
DATA SI /2HS1/DATA UVE / 7HFT/SEC)/DATA EXAURPM / 514AE/AG 99I4(PEV/I4IN)DATA UEI19UEF, USL /'.N(IN) ,d.H(FT) , (&H('4) fDATA VL,PE f 2HV( , 3HPE(/DATA ULEUL3 / 8H(LBF/FT) 9 8H(N/M)/DATA USV9UEV / 6HM/SEC) 96HI(NOTS)/
109
DITA LVSP,UEP / 3H'(W) , 31*4P)IDA&TA UE09USD / L HCSLUG/FTS) ,IOH(ICG/M3)DATA ULE4ULSULE2tJLS2UN,UItLUPAUPIM2 /5HCINz.)95I(r*-)9
)ATA UFEtUFS / '5H(LBF1 ,5H(N) /DATA 4J129U03 /l3HOF PROP(KG98H/M3)z /r3ATA PSiIIU07 /13H(LBM-INZ)z ,1GH(KG-MZ)=OCIA GRI,GRZ / 9HRAOIUS OF 9'H GYRATIONflATA EFT,UO'. / LHFT.=,4HM1.z3ATA EIN,J05 /5HINCH1,5HM))ATA EINS,UOb /7HINC-4ES= ,7HMETERS= /3%TA E.IV,SIV /6H RP4: ,6MqAD/S= /34ATA PINS,J08 / ?HINCHES) 97HMETERS)/n&TA PINS,U09 / 6HI4NES , 6HM--TERS /DATA LFPtUIO /.4FT): 4HM)=
EL2=1. EL I/EL Ir-F: ./.30418
JC :11OKI=1. 6S 78
P1 =3.14159265
1'0 11 I1973
31 C)(11=:.OS(AC)
10 1'.72 NDIA=1,rlDSJM=6 ./P12READ(5,10108) JI,UOQPAt)5,*) SHP, TAN8I,TANB,XPS,RAK(E,POOCD,TYPE,HUBDOtAO (5,11 OIAMEWAKE,ETHRUSHEAD, OEN9PHO
I(J-3L(I),1:1,IZZ),IEAv (EXX(I)91:1,IEA),IR0M, (XMM(I)tI=1,IRP-i)
I I:1,JCV ,tAZZ(I ,Z5) ,Iz19JC)
IFOWS.D .. iO.)ED(,4 REAZZ(5,1 ('3(19J) ,:,
L(CTANB.GT.O.J RLA(5,)l (83(I,8)oI:1,JC)Jr(0AF.GT...AND.RA(E.LE..o1) READ(59*) (RAK(I) ,I:IJC)IrPrhJ.GT.3.) REA(,') (P(I),I1,1JC)I- (HIJB.NE.~O. REAO(5,') FWDD1A~1,AFTOIAMHU3Lt.N,FOBORE,AOORE,
I nISPEFL
c N! DATA 4EAD AI4YWHERi BEYOND THIS STATEMENT
IF(UI.NE.SI) PF=OIAM*12.IF(RAIE.GT.O.oAND.RAKE*LE.,Oi) GO TO 14.0
PAKE=PAKEIRFGO TO 14.2
110
140O 0O £41 I=iJC
1.42 UOEN=UEOI0EN=OENIF(IOEN.LT.,2) 10EN=4IF(IIJEN.LT.7) IENODENS(IOEN)UL=UEFV U tiE VPU:UEPIF(UI.NEeSvI) GO TO 2413
IF(IDEN.LT.7) DEN=OEN/DSI
UDEN:USnUL=USLV U:US VPU:USP
24.13 WIPITE(bvi]0461 100IF (SHP. EO,..) WPITE(6ti0020) SIHPT1,SHPT2dr.'=N1,OEN2,DEN3,OE-N
IF(SHP.NE.o0) WRITE(6,i0021) PU, SHPqflEN1,0EN2,DEN3,DEJ
WRITE(6,10027) VLpVU,(VEL(I),I=19IVV)
WPI TE (6 , 10045 ) PE,9PUt (E HP (I) v,1 1VV)WPITE (6.,10028) UL9 OIA M9EWAKEq-THqUS, UL9H=-AD9UnlEN, RHO
IF(TYP-E.LT.2*) TYPE:I.
VU:UE VP U:UE PUOEN=iJEDUL:'JEFESI=EINFSI=EFPANV=E AVSNIP:PINSSNIR:PINSIF(UO.NEoSI) Go TO 143
VU=USVPU:USPU OFN: USOUL :JSSt'lIr-P U09SrIIP:Ui3ANV=SIVOEN2=U32OEN3:Ul 3FSI=U1:ESI=VC15
143 IF(UI.NEeSI) GO TO 14.9
C OPTION FOP SYSTEM INTFRNATIONAL INPUT uJNITS
SPSHP*PWRDIAM:C'IAM*ELFHFAD:HEA0*EL FRHO=RHOPRHO I00 14l: 1=1,IVVVEL( 1) =VEL (1) VS I
t45 EHP(I)=EHP(I)*PWRIF(HUB.EOsO.) GO To 146
FWODIAM=FWO) IAM*ELFAFTO IAM=AFT I AM*ELF
FOBORE=FDOROE*ELF
A OBOR[ = ADBORE'ELF1 0 ISPEFL2OISR(EFL* ELF
146 IFIRAKEGT, 0..AND. RAKE Lvo .Ot) GO TO 147RAKE :PAKE*EL IGO TO 1t49
14.7 00 148 IlJC14.8 RAK(I)=PAK(I)*ELI14c) CONTINUE
IF(XPS.GT-0.) X(PS=XPS'JBL(i) f3639nlA=OIAM
1315-3 TLES(I,2)=INPUTTLES(7,2)-TLES(4)rLINRIF( g5(t).EO.09) TLES(5,2)=LP'3CIF(TANS.EQ.0-) TLES(6,2)zCALC
IF(XPS.LT.O.) TLES(7,2)=NLINRIF(PAKE.GTo0eoANOsRAKELE-0) TLrSf~,7)=MLlNq
IF(C.O.EO*0.) rLES(10,2)=CALC
WPIIE(6ti0041.6 100
1004.6 FORMAT(IF ,4X,1'., BASIC D SIG4(S) A;Kzr) FOR*
IOE N=ENIF(IOEN.1To2) IDEN=1.IFIIOEN-LT.7) OEN=0ENSIfN)IF(IOENGE,,7AND*UI*EO*SI) fl' No--N*35I
IF(PHO*EOo) RH.O1-9905
PSC=144'*s3605*OIAM*OIAMl'2PlAN= PI)/ (PI*X3(l))
DUN=9FNDAEH=HEA-O
IF(UO.N;-:.Sl) GO TO 1l5CAIO=AlD/ELF0UNO0UN/DSIOAfY:O9AEH/ELFOHR=OH/RHO3I
130 C ONT I NUE00 1 1=199CAV( I) :VE-L(t)CAE (I) = HP (1)IF(SHP) 103,102,103
1.33 PVEL=VEL(3)PEIIP=E'P (3)
102 CONTINUE
@LAS=JPL II)IF(XPS.GEo0.i GO TO 7
nO 26 I=1,JC
7 EXXS:2*.BLAS /PI4SIMPUN')(39,(6qjC)10,.03 FORMAT(H ,2A2,66H
2)JEA=0IFkEXXW#)NE.Co) GO TO 1000'.
EXX(IEXXSJEA=1
10104 IF(CO.GE*1O.) GO TO 90T?4t6(2911CFO=.1008
IF(CO.GT*-10. eANO.CO.LT.0.) CFO=-CD00 10037 I1,JCIF (CO.LE.0.) TM~i.+i.25AZZ(!,25)125.*AZZ(1925)4IF(CO.LE.-lO.) CFP=8(I,71
10007 B(IT)=CFO*TH93 00 15 I=1,JC15 AMZ1 ,23) =X3 (I)
00 16 I=3,JC16 AZZ(l-lt19)=X3(I)
AZZ(1,19) =X3(l)DO 4 I=1,11
PXTBI (1) =P(I)AZZ(I,36) =AZZ'(It25)
4 AZZ(It37):AZZ(I923)00 13071 IE1,tIZZ3(9 ,2) =JBL(IE)XSX=XPS*( 360. 0/B (9,2))AS1=XSX/(1.0-X3(l.))AS2=XSX-ASi.00 IJ073 KE=19IEATLES(3,2)=TLES(4q2)=INPUTE 6P U:EARFERA=AES( EXXS-EXX(KE)) -
I7(ERA.LT.,005.AN0.KE.GT~i.ANO.JEA.EQ.') GO TO 10070IF(ERA.LE..005) EARU=EARO
00 10069 IRP=1,IRPMKI=0RPM=XMM(CIRP)EAR=EXX (KE)00 100 I=LJC:3 (1,93) =X 3 (IDB(1,4)=X4(I)
00 112051 LE=1,JC1)051 B(LE,6)=(BLAS*EAR*X6(LE) )/(8C9,2)*EXXS)
93DEL=A9S( B(3,6)-X6C3) )IFABOEL.GT**0001) TLES(392) =AD0J
00 10,'52 LE=1,JC13352 AZZ(LE,251 =AZZ(LE,36)*B(LE,6)
)O 30 I=199VEL(I) =CAV (I)
30 EHPi'):CAE(I)
IF(SH0.NEo 0.) GO TO 5100 53 I'kYitIVVVELI(IG) =VEL(IG)
53 EHPI(IG)=EHP(IG)GO TO 21
51 VELi(i)=PVEL)
113
74i
21 00 5 risii1AZZ(I,24lzASI*X3(I)-AS2SKZzABS(AZZ(Iv2.I)IF(S'(Z.LT..OOCl) AZZ(1924190.IF(XPS.LT. 0.3 AZZ(Iq2'slAZZ(Tv38)
AZZ(Is3S1zAZ7 (I,24)PZZ(I,25)=AZZ (I,3fi)
5 l17Z(I,?31=AZZ(Ij3?)IF(SHP.EO*0..OR.IV.EQ911 GO TO 1S
')O 114 J=1,IVV411 (A =VEL (J)
itu R3 (AJ3HP U)Sl=VEL1( IV)CALLOI SCOT (SiSlBilV%383,-120,JC,0,S2I-HP1(TV)=S2
NNzGRJ1I.JB B J
JEE=TAN3IJDO=00JJO=.666667*F-OAT (JC)
R (29,1) =CO-!A3, 1) TAN8
P(7,1)=:000
P( 1,2)=*i(2,2) :1.0q(P~,2) :PHO
PSL=37, 21/ 0 14t59265*B t5 2) 3 ,P2 1)
IF(AN9.GT.0.) GO TO 101n0 1',035 I=iJC
101 AJJ=I.CIF( 9(i,5).GTo6'.) GO TO 10019IF( fl(5,1)*LEoG9.) ~5j:(r,
101J9 NN=N?441PAKOP=1IF(PAKE.LEo.O*ANDoRAI(EoGT.o0) GO TO I90RF
00 3'. 1=1,1i
1031~5 VK=B (7,2) /1.6878IF(,(I.GT.0)l GO TO 85AJ.i:1.k CWWITF (f , 10025)PHSzSt4P
114
00 152 ritV9IF(IJO.EQ*SI) GO TO 151
ON4E I)zEHP (I IGO TO 152
151 OIV(I)=VEL(I)/VSIONE(II=EHP(1) /PWR
152 CONTINUIEwprTE(6,130'8) UI,0OIF(SI4P.NE*.. WRITE(6ti0021) PU, PHS qOEN1,*0N290EN3,0UlNIF(SHP.EO.0.) wRITE(6v1002O) SHPT1,SHPT7,OE-Ni,3FN2,iEcN3tOUNWRITE(6910027) VLVU,(omvq1h11,19v)
WRITE (6,1028) UL, AIOEWAKEz,PETHRUSULolE4U')FNOR
2 AI.,'=*,F8.I., jRHO',A1O,~x, IXF9q'., )
WRITE(6,910031) EXA, (EXX(DI!-19IE-A)
10025 FOPMAT (111)10'123 FORMAT(/,2A7,2AlQA89FiO .4,1)10021 FORMAT(/,* PS (#,A3,,'z',1PE12.4,2Ai0,A~&2PF0.'.,/)1303 FOPMAT(2X,*ZQX,913)10031 FOQMAT(ZXA~q5E, 1P9El2.'i)1i]C32 FORMAT (2X,#Nw ,A9,IP9E12.'.)10027 FORMAT (2X,A2,A6,2X,lP9E12.4)13:45 FORMAT(2X,2A3,4XIPE2..)
WRITE(6,10100) (TLESU,1l)qP11,1O)WRITE (6,1010-1) (TLES(Iv2) ,1,10)
10103 FORMAT(/,1X, 10(3XAl0))13101 FOPMAT(IX, 1O(3XAlC),/)
DO 10111 I11,jc
SRK=RAK (1)/)IA/12.10111 WPITE(6,10102) X3(I),X411),R(I,6) ,A7Z(It,) ,VI,5),3(TI,'),
2 AZZ(I,21.) ,SR,P(l) ,B(I,7)1310 2 FOR HAT (lP10r13* 4)
85 9)Q IC090 I=1,JCAZZ(I, 25)=AZZ( I, 25) 'Bf(1,6)
13095 P(I,33)=B(I,5) 'AJJIF(JEE..LE.0) GO TO 4i?
00 2C9 IOC=1,300 2CI I:1,JC
201 Ft(I1,3 0 = 3(193O0 )*A JJej4(1)=975
9 14(42):1*000c11.(43)=1.025no 215 IJ=41,'.3IJT=!J41Jp=IJ .S00 216 I=1,JC
CALL SUBr14(*JTI=PP7114(IJP) =PPS
215 CONTINUEJK=44
115
-iA
TTT=P(6921/ ((8 M2)8(3,2)623@14L5927*t(7,9>)"2) /A.I IF( B(1,2).GT.0. GO TO 10JK=18TTT=TTT*550*18(792)
CC (l,l1)=814(JI(*I)00 11 J=193K=3# (J-1) 4181t5 ('C+I() 81'.(4C GJ)**(I-I)
CALL SIMEO(3.CtCC)
11))48 (Ili 49 1:1,JC
147 JE,=0CALL SURPP11=915 (181) *ET I4RUSPF12=EH01(IV) ,PPlITHP=P (6,2)
AS14P (IV)=PP12!F(SHP) 55,1035C,55
1. ~ 55 COWiINUEKI=KI 1IF (KIGE.6i Go TO 10050
2~ NI:.33( IF(TV.EOQ.1) GO TO 823NIAtLOUG( VECLltTV-i)/V--L4(IV) )/ALOG( A'cH0(1V-t)fAS14O(IV)
AVL=VFL1(IV41JII'(AVL.GT.CAV(5) .OP.AVL.LT.CA'J(1)'. WRTrfE,9??) t&VL
q22 FOPtAT(////1X,*ESTI1iT;O VELOCITY VALU-- T14 IT=RAT1ON FO OrSIPEOD1",H0 IS NOT WITH~IN RANGE OF TNP'JT VFLOCPVY VALUES ... */15X,...PqOGR2AM CANNOT EXTRAPOLATE FOR COROCESPONOINr, VHP, ESTIM~ATED VzLOCTTY3VALU: = IPFIO,.4)IV=IV41GO TO 21
rHP(IX)=EHPl( IX)1004.9 VEL(IXh=VELi(IX)
00 4CU^50 I:1,JCAZ7(1,26)=8 (,1l4)AZZ( 1,27)=9(I,5)BI:A ZZ (1,27)IF(PDOGT.0.) S1= P(I)/PI/X3(1)
AZZ(1,29):C11413(I ,6)AZZ(I, 3C)=B(I, 6)AZZ(1I, l)9 (I, 4)AZ7(I932)=B(I, 12)AZZ(I,,33)=fM (,13)A ZZ7(1 , 341 AZZ ( 1,25) 4 2. C
450A X (I)=A ZZ 1934 )IF(AZZ(11,25)*NE.O.) GO TO 5555
116
--1 V
SLPx (A ZZ19934) -A ZZ(69340) ),(AZZ(923)-A V US* ?) 1Y INT=:AZZ (9934)h-(AZZ(9s 23)'PSLP)A ZZ(10 934) =(SLP*AZZ(10 923 1 )+Y INT
AMZ11,341)ZGLPA ZZ(119231 ).YINT5555 D0O~52 K:2b,34
00 40051 JsI,11s11() =B(J,3)
SI:AZZ (I ,23)CALL o 1ScQT(Sj,8jll83,R3,-J'20JCOS
2)140052 AZZ(I,K)=S2
0O 505t i=1,JcAZZ(I, 21zB(I ? )
;31=8(1921)
8(I,22)=B(I,38)13( 1, 23) :13 (1,)4(I,24):AZZII ,24)
T(I,)=AZ(1,25)A1.
Txr (11) =8( 19215)I~ie
C OPTAII4 DATA AT "'nOen CAMTI CTATIOnm' Vlq ';T~SS PPOGQAH
00 r.10[80 Iz1ioO:AZZ (I,19)C-0 50.31 K=20.24
50030 CALLCALL OISCOT(DOB(i ,3) ,PP,-120 ,JCO ,Cy(!))
CALL OISC0T(D,DB(1,3),B(IS5 9 ,(1918),-?0,JC,0,oAZZ(I,1S))
50',B CONTINUE00 :1090 1=1,10
50'931 P(II'CX(I)
CALL STRFSS (fZZ, AREA XA0YAAIX9A-O -X) MOE~qM09T1 A Y ,PA, P A KO
c THE FOLLOWING STATEMENTS HAVE REEN An'P IN opnOEP TO SEND THE R
C VALUES TO SUBROUTINE WrIGHT. CHORDTPIC'(NESS, AND CAMBEq ARE I
C PITCH AND SKEWR APE IN RADIANS*
VS=VKH. 6878n0 999 I#JCIF(P!JO*GT*0.) Pt1)=PXTBI(T)
IF( X(I).GTe .65 *AND* X(I).LT* .75) SIGmAzB(I,19)
CHOP0( I):8(,6)DIAMTHICKNS(I)=AZZ (I,31d#D0IAtM/2ePITCH(I)=ATAN(8(I95))8BJ( I) ATAN (3(1, 8))rx (I)=c,0IF(CuL1(I)9E0. 0.) GO TO 29
FX(I)=1 .O/(I.0+(6e2832*TAN(PITCH(l)88FJ(T)) CLIII))
2~ CONTINUE
IFZP9O.GT*0*) PITCH(I)ZATAN(1J)SKFWR%*T) :A7Z(I ,38)/57.?951
117
'7- 6
AV = 1(q4) 46(1,121) 2
vSuqrFSO M VS"626(AV *9V 1VSUB6t(1) =SORT (VSUqPSO(1) )
Qq9 CAMB!R(I)z,0679*R(I,1si~oTAmPPS=RPM/60.00 996 rzit,Z
PxT8 (ii )P1' 1.3) '8(1,8)q6 CONTINtic
EAlz(EAR*3. i4159f0IA**2)/4.OAL=3.1i59*0. 76(7,5)AP=EAI' I i.67-P.229*AL)VA: VS 'P (7,')VRSORT(VA'42(O.?'3.1'159RPS~or1U'2)TC=2.0O'9(692)/f RH0'AP*VR**2)SIGMA7= (64*L.HEAO)IVR**2WRrT-- (69 10342)
10 . FOPMAT (I HUVD=VUIF(Uo.NE.SI) UVRZUVEWPITE 6,7e) UVP
9O 79 1=1911
VPEI=VSUeR(I) VSSRI.0.
I B8(I,17),.vQsit9(r,9)
WRIT:(6977) PPjPP34PP4,PP2,PP5WPITI:(6981) Pf~P,PPaqPP9qPP7qppl)
131 O=UL EIF(UO.EO.Sl) LO=ULSWIWITE(6,76) ULO
gn0 7 I=1,11
IF(UO.EQ.sI) SLI=SLI*14*.593973 WPITE(6,2001461 riI3vCW(1CTOIl CwT,~C()F(1
WRT~ (6, 10042)f1NV=:'AVPI2=PP12PT H: THR
UTO0:U FEfITHF: 4THRUST=UPI N2VL S=3 (7, 2)
U02=ULE2IJ 04: ULI E4UMO=UILUST-?=I PIN2IF(UO.NE.SI) GO TO 10C( U02zULS2U04=ULSI.
118
UMO=UNMU STP= :P AUST=UPAUt~mUS IU TO U FSV2xUSVVLS=VLS**3048P12=P12/PWRRTH=RTI4/UWT8 rHP= 9THR/U6,T
160 WRItE (6,10044) PP11,pPU# P1.29ET4RUSq EWA KF, VL,UEV, VKUTO RTH, J'3 (IE)2 PRPM,EARU,--XAtEAR*VLPV29VLSUTCJtOBTMR
IF(UO.EQ.SI) WRITE (6q,10j IJJ2,u8,uBU04,104,UPO,UMO,UMO,U40,USTIFfUO.NE.SI) WPITE(6,20009)IF(UO.!iF*S1)r MIRITi6,200)~ U02 ,UBf,,IO4,UO4,,UMOUMO,UMO,U1o,UST
77 FORMAT (4X,* PTI=U,1PE10.4,p4l(,CPSIx0-,1PE1C.4,4x,#ETAI=4,1PEIC.4,2 4X,'CTSI' ,1 PF1O e4,4X,'CTSI/CPSI=',I1PEIO. 4)
7q FORMAT(6X,* X'*,8X,'TANBI',7X,*TIN 8, ,9X**G*,qY,*UT/2V*,7X,2 'JA/2V',?X, 'OCTSI,97XDCSI,5~,'VR(,A7,5X,'CAVV*)
83 FORMAT(lPl0Ei~oh)81 FORMAT(5X,'CPTz',IPEiC*49 5X,'CPS:V,1PE10.4,,5X,#ETA:2, IPEIC.4,5X,
2 CTS=%1IPEIC.4,t6X,'CTS/CPS=8 e1PE10.4j76 FOPMAT(5X** X#*,RX,#CL9 ,6X,'ALI(OEG)#5X,*FM/C-'A,7X,#COCL#,7X,
2 4F(X) ';XL'A,~'ET~~)'K'(C f00)LI7,4,'*(C/0O)TE',6x93 *T/o# )
2 3 ',4 - f%; A T I PE'~ 3,9 1 P10 E 33 1
2 91PE1O.4 92 3X,*1-WTT=:,1PE20.,4,3XA2,A8,~r:$,1PE10.4,?x,.DOcSIGN TH',A5,:$,,3 IPE1C*49/,4X,'Z=*,I',9XNRVI~)$ P04 A8,A5s*=*9IPEIO,4v3XtA2,A7, z 9 1P~1'3.43WCALCULATED Tm~v5 A5 t 4 * 9 PEIO0.*4)DO 74. 1=1,7SX(IJ :AZZ(I, Iq)APR=APEA (1)XPP=XBAR( 1)YPP: YBAR (I)XOI=AYE XO( I)YOI=AYEYO(I)XOM=EMXO (I)YOM:EMYO(I)T;3M E MSS (I )OFIM=EMOI3 (1)STRM=STRMAX( I)IF(UO.NESI) GO TO 74A PR=A PR'EL2XPR=XPP/ELIYPP=YPR/ELIXOI:XOI*EL2P EL2YOI:YOI'EL2*EL2XOM: XOM/SIMYOM:YOM/SIMTEM=TFAM/SIMO MQBM )84/ SIS TR M=ST RM 6594 s 7 57
74 WPITEI6,20C47) SX(I),APRXPPYPRxoIYt)I,X09,Y9TRM0t4,STRM20047 FORMAT(IPEIO.3,IPtEil.3,IP5Ei2.3)
119
20009 FOMTI149Y9X*RA9W*8RtW*qR9X*X*8tlo
?0Ofl FORMAT (15Xt,45 ,6XqA4,7XqA4.,6X, A596X9A5 qfXA3,4X9A8,.XA8q4X, A 93X2 A9)
10010 FORMAT(1H1,4.X,'X',?X,*AqEA*,A5,4X,*X8lAQO A4,?X,9YqAQ*,A4,2,*X)2 ,AE~ , 3X ,*IY0',A5,I.X,'MXO',AR, 1X,"MYO'.AftI,1'M'TR*,AR,1X,'MO9',A8,3 OMAXSTRE.SS*,oA9$
WRITE (Oo 10042)WPITE (6, 10042)WPITL, (E,10011)00 73 1=1911
SRK=RA,((I) ')IA/12.WPITE (6*100121 8(Ip3) ,SRKv0YT93I(I) PXTD(T)
73 IF(POO.GT.0o) PXTBI(TlsP(D10011 FORMAT(5X,'x*,8XvsRACG/Dx,IX, 23H4 P1 YVANII DI WTAN.10~t2 FORMAT(1PEl0.3,lP3E11.3)
CALL WE IGHT(JCSIGMA7,HUBPMCWEIGTRWctG4TH,A()SEAI=SIN( PI1'CH(1) )
F ILASP AC=HUBS P A C -TSIFILSPAC=PLASPAC-.9*TPIjWPITE(e,998) TC,SIG4A78LS=5LASPAC/ 0IA/12.lLE=FILSPAC./ OIA/12.
tJF=: FT
IF(UO.NE.SI) GO TO 158
151 CONTINUEWRITE(6,9941 RLS, FILS
991 FOF'MtT(/2X,'9URRILL THRUST CO=FF T~4cq4/?Y4U0L CAVIJTATICN COEFF SIGMA(O.7)=*,ECs,#)
99,4 FO~tAT(/23X9*CLEARANCF AT HUR RETWEE-N L/ ', 0 1. //2 2EY,'CLEARANCE AT HUB 9ETWEE-N FILLFTS/'nz$,1DE12.4)00O 122 I=1,11APPmI(I)=93(1, 6) *AZZ(I,25)*PSC
12? PMOX(I):ARPMI(I)*X(I)4'2
TPHTN=PMOFIR4 P'*4CPADOGi3:SORT (PMOFIB/WEIGHTR)/12*PAOOGH=SORT (PMHC/WEIGHTH) /12.F:ADOGT=SORT (1PMINf (WE IGHTB4-WEI'14TH) )/12.PMS=PMOF113TPS=TPNIINGPS=RAOOG/) I AGPI4: RAQOGH/D IACPT=PADOGT/oIAIF(UO.NE.SI) GO TO 171i)MS=PMS**0002926.TPS=TPS#.000 29264
171 WPITE(6,9951 UMIPMS*UMTTP.;,GPL,GR2, GPlqGG2, GRH,2 GRI,GP2, GRT
995 FORMAT (IHI,19X,fMASS POLAR MOMENT OF INF0TIA OF BLArOES *,Al),1.2 E13.6,//,20X,'T0TAL MASS POLAD MOMENT OF IP4ERTIA *9A1CEl3o6,//,
3 2CX,2A99f OF BLADE/Ov# ,Fqs4,//20Xo2Aq,* OF HUR/Ox oz#s
120
4 //920Xip*TOTAL *,2A9, 4/O:,F9*41C THIS SECTION CALCULATES THE ASS COEFFICIENTS
IF(TYPE.EO.0.) GO TO 570PAO=C 025
IF(8(1,3)eGE*0*25) RAO'8(1,31#*05IF(B(2s3)eE0025) GO TO 590n0 510 J=1,liB1I(J)=:P(J,3)
51J 93(J)=PXTBI(J)S1=9 25IF(B(193)*GE90*25) Sl:RAOCALL DISCOT (SI ,SIBil,6.3,83,-120,JCOS2)PTWOFIV=S200 513 J=1I1i
513 93(J)=8(J,6)*OIAM'i2.oS1=.25IF (6(1,3) .GE.O.25) Si=RAOCALL OISCOT(S1,SIB11,63,83,-120,JCOS2IOUPtLU=S2no 51.6 J:i,11all (J)tR (j,31
516 B3(J)=ARPMI(J)Si=.25IF (6(1, U.GE. 0.25) Sl=RAOCALL DISCOT (S1,S1,811,83,B3,-l?OJCOS')ATWOFIV=S2no 5E9 J=1911RII (JI 9 (J,3)
56~ 9"3 (J)=THICKNS (J) 12*0S1=. 25IF (8(1,3) .GE.O .25v Sl:RAOCALL ICTS SI,8,31CJ,;7TMAY=S2IJF=G. 5*TMAXGO TO 592
593 PTWOFIV=PXTBI(2)OU8LU=A(2v6)*oIAM#12. 0AT WOF IV= APPMI ( 2)rMAX:TP)ICKNS(2 )12*0UF=C. 5*TMAX
592 CONTINUEIF(8(7,3)sEO.0.7) GO TO 59600 595 J=1911
595 R3 (J) =P)TBI(JMS1=. 7CALL 0DISCOT B I 9SI9011983 9839-120,9JCip GS~lPSEVEN=S2GO TO 597
596 PSEVEN=PXTBI(?)59? CONTINUE
RAKE2=PAK(11) +OIAM'AZZ(i,938) 'P(11)/3C.D0 519 J1i97011(J) SX(J)
519 R3 (J) =AYEXO (J)Sl=*25
121
IF (SX ( 11GEeOs 2S) S1=SX(t )4a+3 CALL OISCOT(SI ,Sipl11,83,,3-1?07,0,S2)AY 0= 2
FINT(TYPE/2)*68.+INT(TYPE/3)*5,-INJT(T.YPE--/4)536.-INT(TYPE/6)*127*
CS= AT WOFIV/ (OUBLU*TIIAX)CN=AYO/ CUP 'URLU*T4AX*2)
AA=1. 0+6. 0/PSE VEN+4*.3*PTWOFIiJ
CA=(1.Ge1.5*PTWOFTI)(OULU'F-IAIANEW:13.*SQRT(AAPP12/(CARPMPI(9,2)) IBNEW=CS*BA/t. /CASTHICKt= ANEW/SPT(CN)4'BNEW/CNRAK(11)ESTHICK2=ANEW/SOPT(CN) +8NEW/CN*RA'(E2
WRITE(E-,530) RAOS3 FORMT (///29Xt'AS COFFFICIFNTS (CALCIILATE1 AT THE#,F4o29* PADIUS
1)')TA8KIE1=TBSTA9S Q)=UBSIF(PDO.GT.0.) TABS(5)=VRSIF(PDO.GT.0.) TABS(b) =XBS8S1=9THICKlfD IA/i2*BS2=i3TwICK2/0 IA/12.ATF=ATWOFIVIF(UO.NE.SI) GO TO 172ATF=ATF**0006.516
172 WRITE(F,,541) TAPS,8Si,BS2,,~A;,CA,CS,rNSNTRATF5141 FORMAT(//20X96A10,
2 /&.OX*IJSING .0S RAKE =CONVLNTIO4AL PAKEq T/D: *EiG*4/'.0X*USI( BNG ADS RAKE = CONVENTIONAL + SKEW-TNOUCcO PA'KE, T/I= 'El *42 //2 X*VALUES USE') IN nE-TERMININrG THICKNESS-3 A= *E12.6/62X*;3 $Ei2.6/62X*C= *,E1'.6//lCX*SECTION AREA COEFF41CIENT C3= *El0.L//20X'SFCTION MODULUS CIFFFICI?7NT CN= *=I5.4//2CX#AREA OF EXPANDEW) CYLINDRICAL SrCTIP'4 IN SO.#,A695X,*AS=*g6 F1U.4)
CN=. IRTHICKI= ANE-W/SOQT(CN)48N W/CN#*RAK(ii)nTHIC'(?=ANEW/SOPT (CN) +BNEW/CN*P.",C?BS2=BTHICK2/O IA/i?.(S18T HICKI/D0IA/i?.WPITE(6,543) TABS98SiRS2
EL. FORMAT (//////920X,'FOP CN=*1*9/92OX96MO9,2 /'.C'X*USING AEIS RAKE =CONVENTIONAL RAKE,9 T/0= *PE10.4/L.0X*USIBNG AeS RAKE =CONVENTIONAL +' SKEW-INOUCFD PllKE, T/fl *EIC.4)
57: CONTINUEBLAD:iL~q(t,3) -8(1,3)DEL TA=PLAOEL/S.O)ELTAI=DELTA/2e00 132 1=1911XR(I)=B(I*3)TANBF.TI(I)=8(I ,5)G(1) =8(1,14)
XST(I) =AZZII929)WIAKE (II=3 (I,")* I UVELA(I)=B(Iqi2)THICKR(I)*AZZ (,3'.)
122
t32 CONTINUEXRf12) =XR(1).DELTAlXR (13) zXR (L)4OELT A00 130 1=14,19XR(I)=XR(I-1J +OELTA
130 CONTINUEXP(20) =XR(19) +DEL TAI00 131 1=12920CALL DISCOT(XR(I) ,XR(I),XRTANBET1,XR,-044,1,0,t~TANqETI(I)ICALL OIS'OT(KR'(I),XR(I),XRGX,-04a,1,0,G(I)ICALL DISCOT(XR (I) ,XR(I),XRXSLXR-I.5.,11OXSL(I)CALL DISCOT (XR (I) ,XR(I) ,XRXSTXP,-OI.4,1t,~,XST~ 1))
CALL OISCOT(XR(IPXR(I3,X~,WAKEXR,-04i,1tWAKF(ri)CALL OISCOT(XR(I) ,XR(I),XRUVELAvXR,-044,1j,0,UVC'LAqI))CALL OISCOT(XQiI),XR(I),X,THICKRXR04,11,0,gTIC(R( I))
XST(I) =XST(I)*OIA46.THTCKR(I)=THICKR(I)*DIA*6.
131 CONTINUEUPITE -(6,133)
133 FOPMAT(1H1,//f/,10X9RADTAL ORPLE DATA FnR INPUT INTO DESIGN PIROGgZA'S(q RA)IAL STPIPS ASSU4Fn)*,///)
WRITE(6,134) SNIP,SNIP,SNIP13'4 FOPHAT(ICX9*'KR*95X9*TAN BETA T,98XG*,q7X,XSL*,A7,p5XXST (*,A7,
2 5X,'1-WX~, 8K,#UA/2VS',5X,*THICKNESS'*,A7,/)00 17'. I=12920SSL=XSL (I)EST= XST (I)STHreTHICK(R(I)IF(UO.NE.SI) GO TO 174SSL=SEL/ELISST=SST/EL ISTHF=STHP/EL I
17'. WPIIE(69135) XR(I),TANRFTI(I),G(I),SSLS;ST,WAKE(I),UVcLArI) ,STHP135 FOPHAT (4X,F10.5,3X,F10.5,3X,E243XF'7.5,4.ri'.5,1XFlC.,'.x,cI
XSL (11 )=XSL (11I )'01A*6.
SSL=XSL (11)SST=XST (11)IF(UO.NE*SI) Go To 175SSL=SSL/ELISST=SST/ELI
175 WPIIE(6,136) XR(11)tSSL,SST136 FOPMAT ('X,CO.5,31X,F1G.5,'.X,F10.5)
IF(SHP.NE.0.) GO TO 10069IV=IV~ 1IF(IV.LE.IVV) GO TO 21
10J59 CONTINUE10070 CONTINUE101071 CONTINUElOG72 CONTINUE
STOPENO
123
SUBROUTINE SUB
COMMnON/C WE rG.4T/XICHOR~o THCNSCAIBrE,DTTCI,SKER,lI AM, 77,01FN1,PAY(,PPI,PP7,PP8,PP9,PP11,EWA~C,VSRPS'IIMA, AQ,8TPPO2 ,Fwo0CrAM.Ar r orAM HUBLEN90OnRE 9ADOOE 9 lrSq'
2IESO ,Oj (8),Z(II), 8(1811,8(141b),C?12
COMMON 8, 82,839 RuliCocc, ID, JB JCJOJOOJEE9CLi(ll)COMMON CCONE(11),CCTWO(ui),CCTHP(it),CCFOP(ii)COMMON PP1,P02 ,PP3vPPI.,PP59PP6,PP1C
COMMON~ SN(73) ,CS(731
no 2C021 I=I*JC
AAH 8(N,3)/B(I,3) 'AAGAAQ=13 (1,5o)IF (AAH-AAG) l6iOj, 10C18, 100 19
83(t1r -zA 182 ( Vr.0 TO 23021
T= SOcT (S)
W=SVT (V)tiE =T-W
IJ=E XP ( A!
60=. 25(=1./(2.*8(9,2)'AAG))'((V/S)AD)
JF (AAH-AAG) 103 21,o100 21,10023
P2 (I) =2. R( 9,t2) 42AAG*AAH* ( 1 9AAG/AAUI *2A
r;o To ?0021
20021 CONTINUE23142:s FOPMAT(gF12.I.)
010 2 I=1,JC
n0 3 ri1,37
rALL OISCOT(31,SI,BII,83 1133 9-i2OJC#,,Sl3 R1s(I)=s3
0)0 5 I1937Si 54(.+8( 1)97 I 9(t3 C(T
CALL OISCOT (S1 t,I 1 32 .32 , -121, JC,,
124
~~~~~~'~Z7 77 T
5 1(IS00 4 1=1937
R311) = pis(1)00 10022 Lz1,35N1=37*LN2=37-L82 (NI ) =82 WN)
10022 B3(Nl)=S3(N2)C2:Z. /72.NP=72NH=3bXNP=NPS= C 0G
00 20 I=1,NPS=S+B2 (I)
23 SL:SL*F-3(I)8 (1, 9) S /X NPR (1, 10) =SL/XNP
00 4C. I=1,NH
SI :0.000 3: J=I,NPK=(J-1) 1K=MCO (',72)4i
3Z SI:SL +33(J)*CS(K)L=I~1B(L99)=S*C2
43 B(IiC)=SIUC2
IF'(CPH4I.LT.-1.5 ) CPHI=-1.IF(CPIoIGT.1.) CPIIo1
B(JC,1i)=3.iI.15927CON3= 3 .14159200o IC025 74=19,JCSMP:SIN(FLOAT (I)'8(N,1i))CMP=COS (FLOAT( 1) *6(N,1i))IF(N-i)10027, 10026,10027
13C^27 IF(N-JC)10028,10C29,1002810026 AZN:. 0
ctZN=. 0N2=-I+ I00 2LG26 KiN2IF(K-JCI 10070,10070,20026
10Z73 AZN=AZN+CON3*FLOAT()8((,)6ZN=8ZN+C0N3*FIOAT (I)8(Kql0)
20026 CONTINUE
RZL=oOIF(N2-JC) 10060 ,10030,1G030
10063 NI=N2+ino 2C036 M=N1,JC
125
AZL=A7L4FLOATtL) '8(M99)*CON3
20036 fZLBZLFLOAT(L)BS(Mi0)*CON310290 TO 10030109AZN:.0
BZN:. 0N2=I41DO 2CO29 K~1,N2CKP=COS(FLCAV (K-l)'R(Nqil))IF IK-JC) 100719,100719 2OC29
10071 AZ=Z-O3CPFOA()BK9*VKBZN=BZN-CON3'CMP*FLOAT(I)*R(K,1G)'CKP
20rv29 CONTINUEAZL=. 0BZL= . 0IF (N2-JC) 10 061,v1tC030,91C0 30
10061 N1=N2+100 2CG39 M=N1,pJCL="i-1CKP=COS (FLOAT IL) '8(N,11))AZL=AZL-CON3 C MP*FLOAT (L ) *3(M, q) *'CKP
20'39 P7L=BZL-CON3*CMP*FLOAT (L)*B('4,10)'CKPGO TO 10030
12:28 AZN=.3PZN:. QCONl=3.i'.15927/SIN(B(N,11))N2:I~i00 2 322P! K1,tN2CKP=COS(FLOAT (K-1)'B(N,11))IF (K-JC) 100 72,910072 20 C2 8
10372 AZN=AZN+CONi'SMP*B(K99)*CKP63ZN=BZ N4CONl*S MP*B(Kt IC) *CKP
2 T2 3 CONTINUEAZL=. .FSZL= . 0IF(N2-JC)10G62,IC*030,10G03C
13'62 N1=N2+1')O 2C)38 M=N1,JCL=M-lSKP=SIN(FLOAT (L)'BfN,11) )AZL=AZL*CONi*CMP*B(Mv9l)SKP
20G3'3 PZL=CZLfCON1'CMP*B(M,1C)*SKPIOG33 AZ(IN):AZN4AZL
9H QI,N) =BZN+3 ZLi0C25 CONTINUE
00 1C031 I~iJCDO IC031 J=I,JC
CC 1 (I,1J)=FL(i.3(1 ) (( ,5)3(T, 8)-Ji.))
CALL SIMEO(JCCCC)0O IC,035 I=IIJC
D0 IiO35J,JC
10335 8(I,14)=CC(J,1)*S~T!(FLOAT(J)*B(I11))/i(I,4)4B(I,14)
126
lip,
A S(JC* I W 0c20001 00 IC036 1*1,JC
12)
1*8 (992)iTT=ATAN(6(I9S8)BTI=ATAN(B(195))P(I,18)=2.'3.1415927'8(It14)*COSIBTI)1(1./B(I,3)-B(1,13)8( It19)=64*10 (8(4,2)-8(I,31*9(392) /2*)*(SlN(nTTl/(8(I,4)*9(71p2)
1'COS(!3TI-BTTI)) )#2IF (I-i)9,9,6
6 IF(I-JC)1099
GO TO 1110 CONTINUE
It CONTINUEP3 R(It 22)=9 Q 920 ) 8(194)
1338CONTINUEPP1:SIMPUN(9(Iv3)v8(Ivi63,JC)
PP2=S IMPUN (1 3) ,B(i, 15) ,JC)PP3:=S I MPUN (B ( 1, 3) 98 Q1,17) )JC)I
PP4=PPI/PP3PP5=PP21'PP3PP6=SIIIPUN(8(I93),B(1,22)qJC)PPT=SIMPUN (8 (1,3) ,B(1,20) ,JC)PP8=S IMPIN (8 ( 1,3) , (1, 21) ,JC )pp c~ppe6/PP 8
PP IC=PP7 /PP8
JCI=JC+1-I0O 1Z'3"O L=19JC
IF(O(O) 860,860,871fkl XO~t.O
GO TO 561871 CONTINUE
861 CONTINUEB2 (L) =)XO*B(L, 2 0)
R(192b)=.0R(I,27)=.0P(I,28)=*0GO TO 10039
8(I,26 =SIN UN (8(1,3) ,B(li16) JC)*E4(8,2)*9(3,t2) ##2*(792)**3/(16.*1 B(S921'8(9,2)3TI=ATAN(B(I95))S8I=SIN(8TI)
127
;3(I,28)=B(I,25) #CI8 (I*,26)*CR I
10039 CONTIMUE00 2C6 I=IjC
IF(JEE*GT.0) GO TO 10081
00 1&04.9 11.,JCIF(e(I,6l) 702,702,703
792 CC1=CoCGO TO 704
734 CONTINIIECLI(I)=CCIrC2=1. 54*CCICC 3=0 679*CClIF(CCI) 701,700,701
70C CC4=c 0C"(I,38)=CC4GO TO 52
7:1 CC4=B(I,7)/CCIfl( 1383 =CC4
52 CCONF(I)=CClCCTWO(I)=CC2CCTHP(I)=CC3 SU4ROUTINE SIMEO(JCCCC)
t10O49 CC FOP (I) =CC410081 CONTINUE- C ---- NEW VERSION RY JACK DISKIN -- X71'.5C20041 PETU;N
END DIMENSION B4(12)vC(12912)hCCQ12912)N PD=J CJCIXJC41CC(JCI, 1)0.o00 80 I1i,J"CUIJCI3 =-CC (1,1)00 78 J=29JPI
00 89 K=2,JC00 86 1,MPO
00 86 J=I,JCI86 PYA(I) BA(I + C(K,J)*CC(I,J)
MPOM PD-IDO P9 J~i,JCIZ=CC(1,J)/SA (1)DO 89 I:1,mpD
59 CC(IJl:-Bh(I+13#Z 4CC(I+1,JJ00 99 J1,qJCI
99 CC(J,1)=CC(1,J)RETURNEND
128
SUPROUTINE DISCOT (XAZATASXTABYYABZ, NCNYN7,ANS)
DIMENSION TA8X(l) ,TA8Yqj~vTA87(l)9NPXq37)9N0Y(37)vYY(37)
C MERGE OF OISCOT9OISSE~,AND LAGRAN USING BUILT IN CONSTRAINTS
NLz2IF(NC.Eg.-44) NLz3
NUPP=NY -NL00 15 lIINLvNUPPNLOC=IIIF( TARX(ri)eGEXAI GO TO 20
15 CONTINUENUPPzNUPP-NL 42GO TO 99
23 NUPP=NLOC-NL.4NU=NUPP4I300 25 JJzNUPPNUNOIS=JJIF( TABX(JJ) *E~o TARX(JJ41il GO TO 3nl
25 CONTINUEGO TO 99
33 NUPP=N0IS-I0IF(TARX(NDIS) .LTeXA) WUPPzNOIS+i
99 SUM=C.CN N=NU PPN=NN+ ID00 3 I=NNNPROC=TAFIY(I)00 2 J=NNqNA=TA8X(I)-TA8X(J)IF(A.'EQOO) GO TO 2B=~(XA- TABX(JI )/APROD=PROD *8
2 CONTINUE3 SUm=SUM+PPOO
AN S=SURETURNEND
129
:1SUBROUTINE STRESS (AZZAREA,XKBAR,YRARAYryd),AYEYD,EM1XOEMYOEMTB9eM108,STRMAXvRAK*RAKOP)DIMENSION CHDQD(11),THICKNS(11) ,CAMBER(l1),PITCI4(11),SKEWQ(tI
COMMON/CWEIGHT/XI ,CHORO,THICKNS',CAM8E-PPITC4,SK(EWR,OIAMZZDEN1,RAKL,FI,PP7,PP8,PP9,PPii,EWAI(EVSRPS,' TrMAEAP,RT,P,Pno2 ,FWDDIAMAFTDIAM,HU8LENFEBOOEAD8OREDTS~rFL
COMMON /UNITS/ SIUIUOOTMENSION R&K(1i)DIMENSION AZZ(11,36)DIMENSION XE(20)DIMENSION HA(20)P4Ai(20) ,PHI(203),PNI2(201)XLI(23),TI(2C),O1(2C),CP
1II(2C ) SPHI (20) ,X4.(20) ,AE(20 ),qE (20) ,PE(23?DIMENSION A(13llB(13)tC(131,fl(i3)gE(13),F(13),G(II),H(13),0(13) ,
XP(13) Q( 13) R(13) ,S(13)tT(4 1',,U(13),V (13) ,W(1) ,Y)(%13) ,Y(13) ,Z(13I0IMENSION RI(7,IF,), Si(7,I6)DIMENSION CE'JTST (7), CENT'IO (7)DIMENSION FMXt7),TX(7),FMMX(13),YTX(13)!Z'(4(i3),XU)(1G)DIMENSION VOL(7),CENT4(7),A1(7),A2(7),x~naLA,(7)CNTS2(7?),82(13).X F5(13) ,P2(t3)q02(i3) ,AA(lG) qgq(t0) PCENT42(7) ,CENTMS(7),X TSIEW(7),TSKEW2(7),ASKEWi(7),ASKEW2(7)DIMENSION V2(i3),02(l3hqF2(13)DIMENSION ALP HI A(7)DIMENiSION XMT(10) ,XL(IC),XMII0),XT(iO),9TM(10),STLT(i0)fIMENSION AREA(7),X9AR(7),YBAR(7),AYE-XO(7),AYEYO(7),FMXO(7), MYO(71k ENTO (7) ,EM093(7) ,STRMAX (7)
DATA AF,AT,ATX, ATF,ATFF,AFXX, ATTT,GPA V/I *4O-t95, *72099, .3L1, .r8C32
2,.5'3219*40733got2714932o14/
C * * I--MPLE REAM APPROXIMATION INCLUDINGC * * * PENOIN39 CENTRIFUGAL AND TORSIONAL POR"ESs
PI=3. l4.15926536ATXY=. 2020ft4
NN~ljli FCPMAT (8F9*6)
ZZ=AZ7 (c),2)VS=AZZ (7,2)DIAM=AZZ(3,21OIACDIAMVEL=600 * AZZ( 5,2)ISFC:0AZZ(lC,20)O. 0A7Z(10,2t)=Br (1.)
O(I) =AZZ (1,20)T (I)=A Z Z(I, 21)E(1)=AZZ(I,22)C (I)=A77Z(1,23 ) 1A*12@ 0SKEW(I)C(I)/2.O-AZZ(I,24)'OIA'12.C/2.C
10ZO XU(I) =AZZ (1,19)00 3C. J=297
30 AZZ(J925)=AZZ(J+it,2,)DO IC01 1=1,7Kilt.-I( J=K/i3
130
UfK)ui-U(Ii7tX(I IzAZZ (1,25140IA*12* 0FMX (I)xo0679#OIA#AZZ( IIS)Y BAR( I) =*0679*DOI A*AZZ 41918)FMX(l)=O.oA (I) =C( I) *TX £ 11 *ATY (1)=C( I)* ATX/ATV (I)=FMX (I)' ATF/AT/2o
H(I)=C( I)"*3TX(I)'ATXX - A(I)'X(I)*X IT)1001 CONTINUE
C CALCULATE THE VALUE OF F1 FROM INFUT VALUES.26 Fj=1. 9905'(OIAM/ 2.O)"3'VS"*2'PI*6./ZZ
FFI=F 1,F(PDOGT,09) GO TO 52
00O 215 1=1,10215 P(I) =T(I'*PI*XU(I)52 NN=NN+l
C .... so ... '" COMPUTE " ow. . . ."a- -- 04"o- -- *
C CALCULATIONS FOR CONSTANTS USED IN DETERMINATION OF TOPQUF AND THRUSTC CALCULATIONS OF BENDING MOMENTS FROM THRUST ANI TORQUE.
00 360 15=192F1=FFIoAnt=OIAM#0o5*12s0IF (IE-2) 55,56,56
55 00 210 I=1,iCPE (I)=P(I)AE(I)0(I)'(l-E(I)*T(I))
TE (I) z M/(31IX I
PHI(I)=ATAN(T (I))
SPHI (I) =SIN(PHI (I))HA(I)=(SKEW(I)I'(CPHI(I)/(RA~l'XU(TI))YU1(I) =XU(I)vCOS(HA CI))
GO TO FS56 00 57 1=1,10
P(1):PE (I)57 S(I)=3EMI58 F1=F1/eC.0
00 69 I=197
IF Q15- 2)62,63,96362 XO=XUI(I)
GO TO 6463 XO=XU(I)64 13=0
00 68 12=lIo,113=13+1IF Q5- 2) 659,6b,966
65 X4(13)=(XUi(12)-XO)(E (13)--XU(I2)GO TO 67
66 X4 (13) (XU (12)-XO)
131
XE (13)=XUJ(121
67 T I (13)=X4(131)'AE(I12)
TI I)SIMPUN(XE,T1,I3)
6q OII):0(I)FFtCC LOOP W141CIH APPROXIMATES STRESS )Ur TO TOPSIO4 R:SIJLTIN,
C FPOM SI(FWC XT (1) =LIFT FORCE ,XMT(I)= MOMENT 011c T) Li-,.
XA=C(I )/2.OYH=TX I T) /2o.000 222 J=IqX(L(J):A9S(SKEWIJ1345*CIJ))XL (J) =XL (J) -ABS (SKEW (I )- ,54C1 tI
)(M (J) =YT ( ) *XL (J)XMTII)~xmT I) +xm(J)
2c'2 CONTINUESTII) :MT (I) '2. /(PI'XA'X-1"2.)
STI T (I I XMT (I)'2. 0/ (Pr'x'9XA"'. 0)GO T ' A4C
ST1-T I =C*Cz."54nl CONTINUE
III CONTINUEi53 FOm.TIG2 ttX,1OX,4HTAUM,i2XteNTAUL%1,IOY,7H'4 SUB T)
', 0 OPMAT(I1H,20X,4Fiq,6)600 FOPMAT(IHi95OX,32HS.MEAPINr, STRESSES V)UE TO) TORSION)
C
C LOOP WH4IC'4 GALCJLATES VOL. Or SFCTIO:4S*VOL TOT=0.*030 24.1 I=196
241 VOLTOT=VOLTOT+VOL(I)VOL(7)=A(7)f(i-xu(7w)orAM/57,
243 VOLTOT=VQLTOT+VOL 17)C LOOP WHIICH~ CALCJLATES CENTPIFUGAL FORCE AN') ST-SS,.
1F (19-2) 244,21.(,246?44. 00 245 1=196245 AIII)=XU1II)'( (xuit141)-xu1(Il/.C)
A1(7)zXUIA7)4((XUI(10)-XUI(7))/2,0)GO TO 248
246 CO 247' 1:1,6247 Ali)=xufI)+I Ixu~iIi)-xuti))/2.C)
Al 17)=XU(7)+((XU(1O)-XU(7))/2.0)C LOOP TO TPANSFER CONSTANTS FOO DETFPMrNING X~nAPo
248 00 236 I1,74 X28ARIM - 0.0
132 1
C LOOP TO CALCULATE RADIAL CENTROID (X28AR )00 251 1=1,7X2PAR(Il x( (A2(i)4A2(2)4A2(3)4A2(4)4A2(5)4A?(6)tA2(7II / VOLTOT IX~ (DIAMi'29O)
AM() =0.0C UNCORPECTED FORCE AND STRESS FOR OUTPUT OF ANSWERS WITHOUT THE EFFECTC RAKE AND SKEW TAKEN INTO CONSIDERATION*
264 CENT4(I) 0EN#4oO#PI##2#VEL*62'VOLTOT*)X28AR(I)/(360O00GRAV)CENTST(I) zCENT4(1) / AMI
251 VOLTOT =VOLTOT - VOL(IC LOOKING AT THE EFFECTS OF RAKE AND SKEW IN TH4E OROPrLLEq*
DO 2b3 1=1,10AA(!)=PI*XU(I)
263 88(l) = SORT(AA(1)442+P(I)**2)DO 267 T=197TSKEWi (I) = (C(I)/2oC - SKEW(T)) * AA(I)/qSfl)KK =£
146 IF(X28AR(I)-XU(KK) 'OIAMI290) 149-m1499i5l151 'K'r KK4I
IF (KK- 10) 146, 1 4 9 11£49149q TSKE~r2(T) = (C(KKI/290 - SKEW(KK)) * AA(KK)fgg(KK)
ALPHIA(I)=ATAN(TSKEW2(I)/(X23AR(I) * 12sC)CENT42MI = 'ENT4(I)*COS(ALPHIA(I))
CENTMS(Il = CENT42(I)*(TSKEW2(I) - TSKEWII)CENTS2'() = CENTI.2(I) / AMIASKEWiI ()=(TSKEWI(I)'P(I)/AA(I)) + RAK(I)ASKEW2(I)=(TSKEW2(I)*P(I)/AA(I)) + PAK(KK)
77 CONTINUE267 CENTMO(I) =CENT'.2(I) *CASKEW2(I) - ASKEWil (I)
no 281 r=1,7O(T) = (T(I)4CENTMO(I1))AA(r)4(fl(I)-CEN'MFZ(I))'P(i)f8(r)
02 (13=(T (I)*AA (I) ii)*P() / 86(1)?Mt E2(I3=(T(I)*P(I)-Q(I)'AA(I)) / B6(I)
C PROGRAM CONTINUES.n0 350 1=1,7K(=1S (13=:Z (K3=U(7)F2=FMX(I)4.4962*TX(I)-Y(1)
00 31'0 L~i,K9L=(C I)*Z(L)-X(I)) 'E (I))/H(I) +F2'O (T)/G(1) 4CFNTS2 (I)
V2(L) =ABS(B2(L))300 V(L3=ABS(B(L))
F3=V(i)F4 = V2(1)
F5(I) =02(1300 32G L1i,KF(I)'V (L)
3Z3 F5(1)=V2(L)F5MI = 000
340 Pi'1)=-X(I)*E(I)/H(I)-(C(I3*S(1)-Y(1) )D(I)/G(I)+CENTS2 MI -
02(I3=(C.(1)-X(I))#E2(I)/H(I)-(-Y(l))'02(T)/G(I)4CENTST(I)350 0(I):(C(I)-X(I))*E(I)/H(1)-(-Y (I))'0(I)/(,(I)4CENTS2 (1)
133
-~*1 7.
4w.
E?4X)0 ( I I =0(11
STPMAY, (I I=AZZ( I,1
103 Emoq(I)=O(I)IF(IL-2) 351,352,352
351 CONTINUECALL PPNST'R (Fgpgo,STM,STLT,AZ?) U
C~0 .... P RTNT 0 U TIPU .4***'
~2. GO To 363352 ummYZDUMMY
NN =NN41
360 NN=N4N+iqETt.QN( END
* (. 134
........... ..........
SUBROUTINE PQNSTR (~Yq~~q~4~DIMENSION AZZ(il ,38)
DIMENSION XX(1 C),YY(IO)qZZ(IO),Sj(£O),S'(£CtCC CAL CULATION OF PRINCIPLE STRFSSFSC DUE TO TORSION ANO SENDING*C
DIMENSION xI2(iO),X13(1O)00 333 Kzis7
333 CONTINUE
nlo 444 L=197XXX=XXX+O *00 555 M=193IF(M-2172922, 33
72 X(I1XX(L)
XO=0O-4*. XI2(L)CC=(AFBS0(D) )p' 5GO TO 44
GO TO 66
66 D)D=(AR~fXIi))*'2.0
CC=(AgS(XO))*fo54'4 SIGMAI=(XIICC)/2.0
SIGMA2= (XII-^ZC)/290AZZ (1,4)=XXXAZZ(L,M+ IC) =SIGMAI
555 AZZfLI1G20)=SIGMA2444 CONTINUE7 0J FOQMATQ(H,2OXF12.2,6Xp2E20#6)~5 FOPMAT (1HC,33X,IH4X~l2X,6HSIGMAi,£OX,6HSTGMA,,136 FORMAT IH0,2X,9q14STPESSES AT EACH X STATION 10c GIVC'N INi TUE FOLLO
xwING OPDEP# mIOCHORD, LEAn)ING rOGE, TPATLtNG EIGE.RETURNEND
47 ~ ~~~~~136 ___________
FUNCTION SIMPUNIEYNiC FORTRAN IV FUNCTION FOR SrNPSONS RULE INTEGRATIONC ARBITRARY NO. AND LENGTH INTERVALS KoMEALS NSRDC CODE 842 10-5-67
DIMENSION X(21,Y(2)IF(N-2) 7, 5,1.
5 S=(Y(1)4Y(2)) '(X(2)-XfI))/2*GO TO 6
4. M=N-18 IF(M-2) 9,10,11
11 M=M-2GO TO 8
9 S=(X((2)-X())16.*(Y(1)6(3-(X(2-X(1) P/(X(3)-X(1))).Y(2)'(3.4(X(2I
2))))L=3GO TO 12
to S=00~L=2
12 M=N-100 1 K!L9M92IF(ABS(X(K-i)-X(1)).GE.ARS(X(KJ-X()) GO TO 3IF(APS(X(K41)-X(i)).GT.ABS(X(K)-X(1))) GO TO 1
3 WRIrE(692) K(X(K-1bqY(K-l),X(K),Y(K)qN2 FORMAT(* NON MONOTONE X(SIMPUJN)4,I4,2X,1P2Ei2.4,5X,2E12.4,5XI4)
7 S=00GO TO 6
i S=S. (X(K41)-K (K-i))/6.'(YIK-1)*(3.-(X(K~i)-XtK-1))/(X((K)-X(K-1))) 4
6 sIMPUN=SRETU,?NENO
137
suRRoUTIN WE-IGHT(JC,-IGMA7,HUA,PMHC,WETGCH-q,WcilHTH,RAK)
C W&ICHT COMPUTES THE WEIGHT AND CENTEO IF GRAVTTY. THfE VALULS FC CHOP(), TH[CKNS, CAMBER, PITCH AND SKFW0 'SIME FPOM GMAIN. OA ,c DEN, RAKE AND PI ARE SET IN STRESS. OTHX-P VALUES' AC COMP,,TEr)c MAKING CEPTAIN ASSUMPTIONS.c THE ARRAY RAK USED FOR RAKF COME FOOM 'vM4TN
DIMrNSION P(13),BT(11I,RAK(11)COMMON /UNITSI SIUIIJO
COMMON/CWEIGHT/X,CHORDTHICKNS,CAMBEQ,PTTCH, ,K-WDO)TAM,Z7,rOENDlgAKEI ,PlICTSCPSE-PPCWAKEVS,RPSSIGMA,EAP l,P,Pf)02 ,FWOOIAM,A TorAM,HUBLEN*FOBOOEADOREOTSRFLDIMENSION CHORD(lI),THICKNS(1IhtCAMBEP(il),PTCrH(Il) ,SKEWP(1I)
OIMENSION DISTHF138),A(38)DIMENSION R(g),jPMT(9)DATA CNSTNT1,CNSTNT2,CNSTNT3/.365,.*PC7,.':?I/DATA THRI,TI462qTHB3,TH94 /614 CYLINE.I*TlCL96w IFST96HGNAT'l/DATA UFEUFS / 5H(LBF) ,5H(N) /DATA tlrIUE,USL /4H(IN) 94H(FT) , f.H(m)/
C ***VALUES COMPUTED AND DATA OUTPUT**C THE HUB DIAMETER IS ASSU4ED TO BE THE eI4METEO TO THF FIDIT RAOC RATIO TO BE CONSIDERED AND THE HUB A"ZSUMZEO TO 8=- CYLINDOICAL9C THE HUB LENGTH IS ASSUMEO TO EQUAL THE HIfl lITMETrR ANr) THEf DISc TH~E PEFERENCE LINE FROM THE HUI FACF T' TAKN AS HALF THE HUB~ L( C IN~PUT DATA AND ASSUMED DATA WPITT:N ntJT.
CGR(XY,H)=H(X'X+2'XY+3Y'Y)/(XY'X4K'V4Y /c.VOL(XtY,H)=H*(X*X4X*YY'YI/3oPMF--(Y,Y)=XXX'XXGX''KY4X'X'V'Y4X'yYYYYY'YYATH=TH~liOTH=THR2IF (HUE6,.NEa..) AT H=THB3IF(FUP.NEGO*) BTH=T4
HU8DIAt=X (1 )DIAMIF(HUrlNE.0.) GO TO 50
0ISRE FL=HUROIA4/?.HUSL E N=HUBO IA MCE N GRVHH ~U 3LEN/2.GO TO ?7C
5; FWDRAD=PWDOIAM/2.0AFTPAO=AFTOIAM/2. 0HURRAD=HUBOIA M/2. 0FRRORE=FOBORE'/2*ARAOkE=ADBORE /2.
C "'"WEIGHT CALCULATION"**273 0O IC I=I,JC10 A(I) :CHORO(I)*THTCKNS(I)
C W-.IGHT OF THE BLADES;3SAI=SIMPUN(X, A,PJC)WEIGHTe=CNSThTl'CIAM'DEN'Z7'nSAI
C WFIGHT OF THE HUBC IF(HUlB.EO09) GO TO 20C20 1 HPOORE:ARBORE +0ISREFL ( FPOD0E-AP;3t)RE) /wUlL TN
138
WSIaPI'OEN*PVOL( AFTRAOI4USRAOOISREFL)WilaI* OEN'PVOL t AftRO REHRBORE 9 DISREFL I
IF(HRBORE.EQ.ARBORE) HR8OREzAR8ORE.o0Q0!1901AFMxWSi'CGR(AFTRAOHUBRAODISQEFL)-W81'CGR(AR8OPE,HQBCREOISPEFL)OS:IURLEN-OISREFLWS2:-PI'OEN'VOL (HU'JRADFWORAOOS)WE82PI*DEN#VOL (HRBORE,FRBORE .OS)WFR2zWS2-WB2FWMOITSREFLWFR2WS2'CGR(HUBRA0,FWRAO,lS)IF(FRBORE.E39HRBORE) FRBOREzHRBORE~.OOOO3O10FWM=FWM'-WB2'CGR (HRBORE, FRBOREOS)WE IGHTHzWFRI GWFR2CENGRVH= (AFM+FWM)/WEIGHTH
GO TO 202203 WEI GHTI=P I *HUB 0 1AM*2t4ULENIN/4202 CONTINUE
C W: IGHT OF THE PROPELLERWE IGHTP= WEIGHT BtW EIGHTH
C *9CENTER OF GRAVITY CALCULATION****00 2 I=19JC
23 0ISTHF(I)=CN3TNT2*CAMOER(I)#COS(PITCH(I))4CNSTNT3*CHOR0(IJL'S IN(PITCH(I)) *OISREFL
C THE EFFECT OF RAKE AND SKEW APE AOOE3 TO THF r1ISTANCE OF THE CEC GQAVITY FROM THE HUB FACE FOR EACH SFrTION.
00 3C I=t,JC
3S A(I) =CHOR0(I)'THICKNS(1)'0!STHF(I)
CE NGPV3=BSA2/BSAICENGVP=OISREFL-CENGPV3
C CE NTER OF GRAVITY CONSIDERING RAKE AN!' SKCWCFNGPV1I (WEIGHTB'CENGRV34WEIGHTHCENGPVH) /WE-IG'4TPCE NGPVFOrISRE--FL-CENGRVL
IF(HUB.EQ*Uol Go TO 250
PMA=OISREFL'PMFR (HUBRAO,AFTPA))PHF=OS*PMFR( FWDPAD,HUBRAO)PM9=HU8LEN*PMFR (FRBOREvARSORE)PNH^Z= CP#(PMA4PHF-PMB)
GO TO 251250 PmHC=WEIGHTH*HURRAO"f2*72251 CONTINUE
C ***RESULTS OUTPUT**SIF=.*301.8UB=WE IGHTBUP:WE IGHTPCFL:CENGRVF/DIAMC8L=CFNGRVB/O lAMBA=HUUBLEN/OI AMBB=FWDDIAM/DIAMBCzAFT0IAM/) lAMBOz:OISREFL/ I AMBESHUBOIAM/ I AM
t 39
OF= FDRORE/OI AMBG=AOSORE/0IA MSW=UFEIF(UO.NE.SI) GO TO 531SW=UFSU5J =U9*4.448222!iF1-UP*4. 482?2
531 P-TNT 1u49SW.UB,ATHBTHSWU09 CFL, -,LIF(HJP.EO.O.) GO TO 55PRINT 108, 8A9B8tBCBO'QE,9F,B;GO TO 53
5i CONTINUEPPIt"T jiC9 BE,BAsBD
53 CONTINUE
C MINIMUIM EXPANDED ARFA PATIO CALCULATTONStAJS-'V3/ ( RPS*OIA1)AJA=WAKE*AJSSAKT=PI #CTS*AJS**2/geAKO:PS*AJS**3/eEAPMIN=(2.6G6ZZ)AKT/(SGA7(AJA*2(7DI"))4.15PRINT i5sEARMIN,AJSAJAAKT9AKO, oC
134 FQPM4T( //23X9*WEIGHT OF SLAOES* ,A5,'=4j,*15.4//2CX,'WEIGHT OF PIROP (BLADES +*2A6,' HUB)* tAS,':' ,Ft3.4//20X,'CrNTER OF GRA2VITY OF PROP REFERENCED FROM 41DCHORO) 01 2111T SECTION (- FWD, + AF
IT) /D= ' ,P9e6//2oXv#CENTE0 OF GRAVITY IF 'LA9-FS crc~NCE9 FROM4 MID:HO9I) OF ROOT SECTION (- FW0, + AFT)/I* ,F9.15)
1j-3 FOPMC.T(/2CK,'KELLERS MINIMUM zEAP=*9E1C941//2-'XvwSPEEO COEFF V/(NO) JS~f',Eic.41//2:X,'ftDVANCE CO--FF V(21-wTT)/(NO) JA=,qE1O.4//2CX9*OESIGN THQ'JST COF K=*;31C .'./20X,'T3ROJE COEFF I(Q:= EiO.L,//4 2CX,'PPOPULSIVE EFFICIENCY rTAfJ=*,E1).4)
111 FOPMAT(/2CX*'HUS DIMENSIONS/9D, 8( ,' 141)9 ')!All =r9s4/47ytwUB L1LNGT" =',F9.'./47X,'MIOCHOR) OF POOT SECTT')N TO A'rT -NO O' HUt3 *,F29o 'L0
IC 1 FOPMAT (FF8o 4)107 FOFrI( //20X,*WEIGH' OF 9LAnO-S* ,A5,'=, F15.Ij//20X,*WCTGHT OF P
1POF (gLAflES + TAPERED HUB)* ,A-)t=*,F15@4 //20X,*CENTER OF GRA
2VITY OF PROP RUFRENCEO FROM MTDCHOQO OF 01OT SF-CTION t- FWfl, 4 AF,9$.4//20XCENTER OF GPAVITY O'F "LAP 0DEFEro-NCF FROM
I. MIDCHORO OF POCT SECTION (- FWQ, + AFT)/I* ,F9.L)109 FOOMAT(/20X,*HUR OIMENSIOf4S/n* 11,L-GH*Fq44)9F DIA
1M',j'fF9s4/47X,#AFT DIAM=*,F9,4/.7XtmiDCmnlRo OF POOT SECTION TO tFT2 ENO OF HUR=r#,F9.4/47X,*Huq OTAM AT MIO'WHe)PI OP L'OOT S*--CTION=*,Fg.3'./47Xt'FWD oIAKI OF 9lOR=*,Fq.4/47X,*AFT n1IA4 OP 3O'=*,F9s4)k FT UR~NENn
140
REFERENCES
1. Lerbs, H.W., "Moderately Loaded Propellers with a FiniteNumber of Blades and an Arbitrary Distribution of Circula-tion," Transactions of the Society of Naval Architectsand Marine Engineers, Vol. 60, p 73-117, 1952
2. Morgan, W. B. and Wrench, J.W., Jr., "Some ComputationalAspects of Propeller Design," Methods in ConiptationalPhysics, Vol. 4, Academic Press Inc., New York, p 301-331,1965
3. Morgan, W. B., Silovic, V., and Denny S. B.,"Propeller Lifting-Surface Corrections," Transactions of theSociety of Naval Architects and Marine Engineers, Vol. 76,p 309-347, 1968
4. Boswell, R.J., "Design, Cavitation Performance and Open-WaterPerformance of a Series of Research Skewed Propellers," NavalShip Research and Development Center Report 3339, March 1971
5. Haskins, E.W., "Calculations of Design Data for Moderately LoadedMarine Propellers by Means of Induction Factors," Naval Ship -_
Research and Development Center Report 2380, September 1967
6. Eckhart, 1l. K. and M1organ, W.B., "A Propeller Design Method,"Transactions of the Society of Naval Architects and MarineEngineers, Vol. 63, p 305-370, 1955
7. Burrill, L.C., and Eme-son, A., "Propeller Cavitation: FurtherTests on 16-Inch Pror ir Models in the Kings College CavitationTunnel," Transaction'. the North Eact Coast Institution ofEngineers and Ship Builers, Vol. 78, p 295-320, 1963-64
8. Brockett, T., "Minimum Pressure Envelopes for ModifiedNACA-66 Sections with NACA a=0.8 Camber and BUSHIPS Type Iand Type II, Sections," David Taylor Model Basin Report1780, 1966
9. Keller, J. Auf'm, "Enige aspectem bij het ontwerpen vanScheepsschroeven," Schip en Werk, No. 24, p 658-662, 1966
10. Cox, G.G. and Morgan, W.B., "The Use of Theory in PropellerDesign," Marine Technology, Vol. 9, No. 4, p 419-429, October1972
141
11. Cumming, R.A., Dictionary of Ship Hydrodynamics - Propeller
Section, 14th International Towing Tank Conference 1975,Report of Presentation Committee, Appendix VII
12. Tsakonas, S., Breslin, J., and !liller, M., "Correlation andApplication of an Unsteady Flow Theory for Propeller Forces,"Transactions of the Society of Naval Architects and MarineEngineers, Vol. 75, p 158-193, 1967
13. Breslin, J.P., "Exciting-Force Operators for Ship Propellers,"Journal of Hydronautics, Vol. 5, No. 3, p 85-90, July 1971
14. Jacobs, W.K., Mercier, J., and Tsakonas, S., "Theory andIeasurements of the Propeller-Induced Vibratory Field,"Davidson Laboratory Report SIT-DL-1485, December 1970
15. Tasakonas, S., Jacobs, W.R., and All, M.P., "An Exact LinearLifting Surface Theory for Marine Propeller in a NonuniformFlow Field," Journal of Ship Research, Vol. 17, No. 4,December 1974
16. Abbot, Ira H. and Von Doenhoff, Albert E., "Theory of WingSections Including a Summary of Airfoil Data," Dover Publica-tion Inc., New York, Library of Congress Catalog No.: 60-1601,1949
17. Hoerner, S.F., "Fluid-Dynamic Drag," Published by the author,Midland Park, New Jersey, 1965
18. Lerbs, H.W. and Rader, H.P., "Uber der Auftriebsgradienten vonProfilen im Propeller Verband," Schiffstechnik, Vol. 9, No. 48,p 178-180, 1962
19. Kerwin, J.E., "The Solution of Propeller Lifting-Surface Problemsby Vortex Lattice Methods," Department of the Naval Architectureand Marine Engineering, Massachusetts Institute of Technology,Cambridge, Massachusetts, 1961
20. Kerwin, J.E. and Leopold, R., "Propeller Incidence CorrectionDue to Blade Thickness," Journal of Ship Research, Vol. 7,No. 2, 1963
21. Cheng, H.MI., "Hydrodynamic Aspects of Propeller Design Based onLifting-Surface Theory: Part I - Uniform Chordwise LoadDistribution," David Taylor Model Basin Report 1802, 1964
142
-Its
22. Cheng, H.M., "Hydrodynamic Aspects of Propeller Design Based onLifting Surface Theory: Part II - Arbitrary Chordwise LoadDistribution," David Taylor Model Basin Report 1803, 1965
23. Kerwin, J.E., "Computer Techniques for Propeller Blade SectionDesign," Transactions of the Second Lips Propeller Symposium,Drunen, Holland, p 1-31, May 1973
24. Hill, J.G., "The Design of Propellers," Transactions of theSociety of Naval Architects and Marine Engineers, Vol. 57,p 143-170, 1949
25. American Bureau of Shipping, "Rules for Building and ClassinqSteel Vessels," p 621, 1972.
143
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