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AD004240

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FROMDistribution authorized to U. S. Gov't.agencies and their contractors; SpecificAuthority; Sep 1952. Other requests shallbe referred to WADC, Wright-Patterson, AFBOH.

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AFAL ltr 17 Aug 1979

THIS PAGE IS UNCLASSIFIED

II II/. .

CHNICAL REPORT 52-231 SECURITY INFORMATION

R,__ B-~i:UU-LI ro y

trL-7:

AILERON REVERSAL RESEARCH OF STRAIGHT AND SWEPT WINGS'• AT HIGH SUBSONIC SPEEDSi ''~

CORNELL LB, I-CRPOA

N//

~o3

NOTICES

W~hen Government drawings, specifications, or other data are usedfor any purpose other than in connection with a definitely related Govern-ment procurement operation, the United States Government thereby in-cur s no responsibility nor any obligation whatsoever; and the fact that'the Government may have formulated, furnished, or in any way suppliedthe said drawings, specifications, or other data, is not to be regardedby implication or otherwise as in any manner licensing the holder orany other person or corporation,or conveying any rights or permissionto manufacture, use, or sell any patented invention that may in any waybe related thereto.

The information furnished herewith is made available for studyupon the under standing that the Government's proprietary interests inand relating thereto shall not be impaired. It is desired that the JudgeAdvocate (WCI), Wright Air Development Center, Wright - Patter sonAir Force Base, Ohio, be promptly notified of any apparent conflict be-tween the Government's proprietary interests and those of others.

This document contains information affecting the National defense of the UnitedStates within the meaning of the Espionage Laws, Title 18, U.S.C., Sections 793 and794. Its transmission or the revelation of its contents in any manner to an unauthorizedperson is prohibited by law.

WADC TECHNICAL REPORT 52-231 SECURITY INFORMATION

AILERON REVERSAL RESEARCH OF STRAIGHT AND SWEPT WINGSAT HIGH SUBSONIC SPEEDS

L Goland

Cornell Aeronautical Laboratory, Incorporated

September 1952

Aircraft LaboratoryContract W33-038 ac-21174

RDO No. 459-41

Wright Air Development Center

Air Research and Development Command

United States Air ForceWright-Patterson Air Force Base, Ohio

McGregor & Werner, Inc., Dayton, Ohio100 - January, 1953

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FOREWORD

The research described in this report was conducted at the Cornell

Aeronautical Laboratory, Incorporated, Buffalo, New York, under Air ForceContract Number W33-038 ac-21174, with L. Goland as project engineer and

W. P. Targoff as Section Head. The project was administered by the Dynamics

Branch, Aircraft Laboratory, WADC, under RDO No. 1459-41 "General AeroelasticStudies", with Messrs. I. J. Hykytow and I. N. Spielberg as project engineers.

The experimental work was performed in the 9 x 12 foot high speed wind

tunnel at Cornell Aeronautical Laboratory.

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ABSTRACT

Wing and aileron aerodynamic characteristics are obtained fromexperimental data of wings undergoing the phenomenon of aileron reversal.Wind tunnel tests were conducted on both a straight wing and a 45 degreesweptback wing at Mach numbers of 0.6, 0.7, 0.8 and 0.95.

The test results are presented graphically and compared to theoreticaland empirical aerodynamic characteristics commonly used in reversal calcu-lations. The characteristics suggested for use by References 1 and 2 areshoyn to be in reasonably good agreement with the experimental results.

The title of this renort is UNCLASSIFIED.

PUBLI CATI ON RMI MI

This report has been reviewed and is approved.

FOR. THE COOLýA7DiWG GE'ýEiRkL

D. D. 1cKME, ;olonel, USAFChief, Aircraft Laboratory, Acting

"--'Directorate of Laboratories

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TABLE OF CONTENTS

Page

I Introduction ....... ............... ... 1

II Description of MIodels and Test Equipment . ........... 3

III Instrumentation and Calibration . . .... .............. . . 5

IV Description of Test Procedure . . . . . . . . . . . . . . . .. 7

V Presentation and Reduction of Data . . . . . . . . . ......

VI Discussion of Results . . .............. ...... 12

VII References . . . . . . . . . . . . .. . . . . . . . . . . .. 13

Appendix

A. Sample Calculation - Straight Wing ..... .......... . 14

B. Sample Calculation - Swept Wing ... ........ . .15

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LIST OF ILLUSTRATIONS

Figure Page

1 Schematic Diagram of Swept Wing Model . . . . . . . . . . . .. 17

2 Rolling Moment vs Angle of Attack, Straight Ting ........ i.

3 Pitching Moment vs Angle of Attack, Straight Wing . . . . . . . 19

h (a/6 Reversal vs Mach No., Straight Wing * * . . .. . ..*. .*. 20

5 OCL/9a vs Mach No., Straight Wing . . . . . . . . . . . . . . . 20

6 Center of Pressure Location vs Mach No., Straight Wing .... 21

7 Aileron Coefficient,aa/a5, vs ¶ach No., Straight Wing ..... 21

8 Aileron Coefficient, Cm/l86, vs Mach No., Straight Wing .... 22

9 Distribution of C1 due to Aileron Deflection, Straight Wing . . 23

10 Rolling Moment vs Angle of Attack, Swept Wing ......... 2h

11 Pitching Moment vs Angle of Attack, Swept Wing ........ 25

12 (a/6) Reversal vs Mach No., Swept Wing ............. 26

13 cL/aa vs Mach No., Swept Wing .................. 26

14 Center of Pressure Location vs Mach No. Swept Wing . . o o .. 27

15 Aileron Coefficient, aa/86, vs Mach No., Swept Wing .o. . . . . 27

16 Aileron Coefficient,aCm/a8, vs Mach No., Swept Wing e . * ..o. 29

17 Distribution of C1 due to Aileron Deflection, Swept Wing . . . 29

18 Torsional Stiffness vs Roller Position, Straight Wing .o. . . 30

19 Torsional Stiffness vs Roller Position, Swept Wing .. . . . . 31

20 Straight Wing Model Assembly .. .. .. . .. ... . .. 32

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Figure Page

21 Aileron Control Assembly, Straight Wing ............ 33

22 Variable Torsion Spring Assembly, Aileron Control Motor,Schaevitz Assemblies . . . .. . .* * . . * * . . . . . . 34

23 Straight Wing Model Mounted in V1ind Tunnel . . . . . . . . . . 35

24 Top View of Wind Tunnel Ceiling with Straight Wing Model.Installed I . . . . . . . . . . . . . . . 0.. 0. . . .. . . 0 6

25 Top View of Wind Tunnel Ceiling with Straight Wing ModelInstalled II . . . . . .. . * .. . . . * .. .. *. . . 37

26 Swept Wing Model Mounted in Wind Tunnel . . o .. . . . ... 38

27 Top View of Windtunnel Ceiling with Swept Wing Model InstalledI . . . . . . . . . . . . . . . . . . . * . . . . . . . . . • 39

29 Top View of Windtunnel Ceiling with Swept Wing Model Installed

29 Layout of Instrumentation ........ . . . . . . . . . 41

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SYMBOLS

b = wing span perpendicular to plane of symmetry of wing (inches).

c = wing chord measured parallel to plane of symmetry of wing (inches).

C = wing chord measured perpendicular to the leading edge (inches).

5 = model area = j wing area (square ft.).

= angle of attack measured in plane parallel to plane of symmetryof wing (degrees).

J = control surface deflection measured in plane parallel to planeof symmetry of wing (degrees).

J = control surface deflection measured in plane perpendicular tothe leading edge (degrees).

= sweepback angle (degrees).2

A = aspect ratio

M = Mach number.

c = free-stream dynamic pressure (lbs. per square foot).

P e - Reynold's number based on wing chord parallel to plane of symmetry.

U a free-stream velocity (feet per second),

114 " moment about rolling axis of wing (inch lbs.).

M/D a moment about pitching axis of wing (inch lbs,),

L a wing lift (lbs.).

Moa. n moment about the aerodynamic center due to an aileron deflection(inch lbs.).

(C- _C_ 0 wing lift-curve slope (per radian).

Nr-a) 0 two dimensional lift-curve slope of the airfoil section (perradian).

- section lift coefficient (local lift)

s sectional moment-coefficient slope at zero lift caused by an ailerondeflection (per radian).

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d6l ýH l 0 sectional aileron moment-coefficient slope for straight win~g (per racWi

0•01- - two dimensional aileron effectiveness factor.

Icp. = spanvise center of pressure location of one wing panel (fractionof semimpan).

- distance from rolling axis to spanwise center of pressure measuredperpendicular to plane of symmetry (inches).

- distance from pitching axis to chordvise center of pressure ofwing with aileron neutral, measured in plane parallel to planeof symmetry (inches).

0.c. - aerodynamic center location messured in per cent of chord fromthe leading edge.

e.a o- chordwise position of the elastio axis aft of the leading edge(per cent of chord).

L I. - refers to leading edge of wing.

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INTRODUCTION

The aerodynamic loads imposed upon an aircraft in steady, level flight are ofnecessity in equilibrium with the internal elastic stresses. The result ofraising or lowering an aileron is, effectively, to alter locally the airfoilcamber line. The torsional moment produced by this change in camber is re-sisted by the structural rigidity of the wing. A down aileron produces amoment that decreases the angle of attack of the wing, while an up aileronproduces a moment that increases the angle of attack. These induced changesin angle of attack produce airloads which oppose the rolling moment causedby the aileron and thus reduce the effectiveness of the control surface,

As the total aerodynamic torque is approximately proportional to the squareof the forward speed of the aircraft, while the resisting elastic torque isindependent of this speed, the wing deflections will increase with speed,Therefore, at some speed the change in rolling moment due to the wing twistwill be equal in magnitude and opposite in sign to the change in rollingmoment due to the aileron deflection. The aileron reversal speed is definedas that speed at which no net change in rolling moment occurs when the aileronsare deflected.

For the straight wing the rolling effectiveness is dependent upon the wingtorsional stiffness and independent of the bending stiffness. This resultsfrom the fact that bending deformations of a straight wing do not influencethe angle of attack distribution. However, in the case of a sweptback wingit is evident that the bending deformation of the wing would influence theangle of attack distribution. This fact increases the complexity of theswept wing problem as compared to the straight wing problem.

Aerodynamically, four wing characteristics, the lift curve slope /C

the aileron coefficient ') the moment coefficient at zero lift caused

by an aileron deflection(dkiQ) ., and the aerodynamic center location influence

the aileron effectiveness and reversal speed.

The phenomenon of aileron reversal has been treated by numerous investigatorsand various methods of analysis have been presented. In recent A.M.C. contri-butions by Groth (References 1 and 2) a number of the methods are listed andanalyzed, and methods are proposed for calculating the effectiveness of oon-trols. Also included are empirical values for the aerodynamic coefficients,

Groth concluded that the chief improvement to the simplified calculation wouldbe given by using exact data rather than the empirical values. Consequently,under the cognizance of the Air Materiel Command, wind tunnel tests were con-ducted to obtain data regarding the behavior of these aerodyn~amic character-isticu within the range of the reversal phenomenon. A straight wing modelOf aspect ratio 6 (big. 23) and a 45 degree uweptback wing model of aspect

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ratio 3 (fig. 26) were testsd& at Mach numbers equal to 0.6, 0.7, 0.8 and 0.85.

Both wing models were semi-rigid, having their total flexibility located. inboard

of the root section. The critical Mach number of the airfoil section (MCAk 0008)

at zero lift was equal to 098.

The first report on these studies (Reference 3) presented. the anticipated. experi-

mental test conditions, procedures, and models to be utilized, Outside of a few

minor changes the tests were conducted as described In Reference (3). The nota,-

tion of Reference (3) however, has been revised in conformance with that of

References (1) and (2.

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DUSRIPTION Of XCDRLS AID TABt AIPVI !

A schematic diagram of the model assemblie is shown in Jig. 1, while the actualmodels and methods of installation are clearly shown in Jigs. 20 through 28,

The basic wing models used in these tests were originally used for a high speedflutter investigation (Reference 4). It was necessary to modify these modelsas the original ones made no provision for ailerons. The models were of semi-rigid cantilever design and had the following properties:

Span: root to tip (parallel to L.3.) - 27" (effective)

Chord (perpendicular to L.Z.) - 90

Thickness - 8%

Aileron Gap - 020"

Airfoil type: modified X&CA 0008

Elastic axis aft of L.B. 35% chord

Straight Wing A = 6

Svept Wing A = 3

The wings were of monocoque construction with 24ST aluminum alloy skin; e064skin was used on the inboard half of the wing,.032 being used on the outboardend. A solid 214T aluminum aller spar of rectang•elar cross section was providedon the elastic axis and form ribs were fabricated from 2i4T bar stock, lighteningholes being drilled where practical. The trailing edge was machined from duralstock and the upper and lower skins flush riveted to it. The entire structurewas assembled with machine countersunk rivets driven clear through the wingfrom one surface to the other. A steel end rib and tube were fabricated in onepiece, the rib being riveted inside the above described structure near the root.The steel tube protruded beyond the roet of the wing and was used for mountingthe wing in a universal Joint with spring restraint in a 'sewi-rigids manner.The aileron was of solid steel constructiea and was activated by a steel torquerod (Fig. 22). A motor controlled from the instrument panel rotated the torquerod and thereby deflected the aileron (Fig. 22). The aileron was deflectedfrom its neutral position and rigidly held at 3 degrees by providing a stopof proper dimensions against which the torque rod was caused to *wind up'.(fig. 21) This deflection was increased by replacing the 3 degree stop withone of dimensions corresponding to a 6 degree deflection. The wing me sodesigned that wrinkling of the skin would not occur during the tests and bystatic tests it was shown that the wing structure and tube could be consideredas a rigid body.

The main mounting structure consisted of a 'Tee" formed by means of two 6 inohstructural steel channels bolted back to back. The foot of this OTee" wasbolted to the wind tunnel ceiling as shown in Pigs. 24 and 25 and the two endsof the head were braced by means of steel tube tripods, also shown in the photo-graphs. A universal Joint mechanism (Jig. 1) was mounted on the main channel

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near the wind tunnel ceiling as shown in Fig. 249. The steel tube protrudingfrom the root of the wing was passed. through the center of this universaljoint and held. in place by a pair of look nuts in such a manner that it wasfree to rotate about 'bending and torsional axes passing thr'ough the centerof the universal joint, The universal joint was so designed, however, thatit was capable of taking out any drag loads on the wing,

The two wing types had the same planform area and the same airfoil sectionnormal to the leading :d. e, The aileron span was 40% of the wing span. whilethe aileron chord was Up of the wing chord. Aileron deflections of zero,three and six degrees were obtained while the tunnel was in operation by meansof the irreversible control provided. by the loaded torque rod,

The semi-rigid wings, as shown in Jig. 1 have their total flexibility locatedinboard. of the root section. Variable torsional stiffness was obtained bymeans of movable rollers on two cantilever beam springs. Constant bendingstiffness was provided. by a set of helical springs. Viscous dampers (Jigs.25 and. 28) were utilized in order to eliminate any unstead~y effects thatwould tend to be present due to dynamic instability of the models and tur-bulence in the tuannel. Arrangement of the springs and their controls areshown in the aforementioned. photos.

The sweptback configuration was obtained by rotating the entire mountingstructure about the root of the wing (7ig. 27). Duplicate channels wereprovided where attachments were made to the wind tunnel ceiling to allowfor the straight and sweptback assembly but all other items of the mountingstructure were interchangeable.

With the model mass balanced to zero product of inertia about the bendingand torsion axes, analyses of the straight wing revealed that a structuraldamping coefficient of 0.10 for both the bending and. torsion degrees offreedom completely preclud~es flutter. This damping was provided by theviscous absorbers, However, as a precautionary measure an automaticflutter brake was provided. The flutter brake together with the hydraulicdampers were expected to alleviate any unpredicted vibration phenomenon.However, in agreement with the design flutter analysis, no trouble wasexperienced due to wing vibrations,

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III

INSTRUMENTATION AND CALIBRATION

As a result of the tunnel running at approximately j atmospheric pressureit was necessary to measure the bending and torsion angular deflectionsfrom a point outside of the wind tunnel. These angular deflections, in-veigling maximum rotations of approximately two degrees, were to be deter-mnned within ± .03 degrees.

Schaevitz linear differential transformers were selected as the pickupdeqiceso Units with ± 0.190 inch linear travel were used at a six incharm as shown in Fig. 22, The outputs of the pickoff units were matchedagainst similar units at the operating position (Fig. 29). Indicationof correspondence between the pickoff and dummy units was accomplished bymeans of a null reading meter. As shown in Fig. 29, the dummy unit's corewas moved by means of a thumbscrew, and its position was measured by meansof an Ames dial indicator, calibrated in ten-thousandths of an inch, havinga j inch stroke.

The system was first tested by balancing the alternating current outputs ofthe two Schaevitz units, and indicating null with an AoC. instrument. Therequired accuracy was not obtained because of the broad null experienced.This was a result of phase shift in the connecting cable, which was approxi-mately 100 ft. in length.

The output of each differential transformer was then rectified and filteredat the unit in such a manner that the polarity was indicative of directionof displacement from the center position. These D.C. voltages were thenmatched and the difference signal fed through a D.C. amplifier to a zero-center galvanometer. The output was heavily filtered to eliminate anyelectrical noise due to the vibration of the model which might appear atthe output. A lead was brought out to an oscilloscope (Fig. 29) aheadof the filter to show this vibration. A carrier frequency of 100 cpswas used to permit obseTvation of oscillations at natural frequencies onthe order of 10 cps wh'le minimizing the inductive coupling effects inthe measuring circaits,

To eliminate the effect of zero drift of the D.C. amplifier, a motordriven switch alternately short-circuited the input, then reconnectedthe signal for equal periods, with a frequency of approximately 2 cps.A null was indicated when there was no swing of the galvanometer. Theswith used was a telemetering multiplexing switch.

Experience with the system indicated that precision was limited only byrepeatability in the mechanical portions of the mechanism. Inasmuch asthese parts were themselves quite satisfactory, a high overall accuracy wasobtained, fSee Pacge )

In order to determine the roller position (on which the torsional stiffnessis dependent), the roller carriage drove a potentiometer by means of a steelwire (Fig, 22). This potentiometer, and a dummy located on the control panel(Fig, 29) were connected in a bridge circuit to indicate position in much thesame manner as the angular motion pickups.

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Imnmediately following the installation of the models in the wind tunnel carts,final calibration checks were made. By use of Ames dials (calibrated in ten-thousandths of an inch), weights, and appropriate lever arm mechanisms thefollowing calibration curves were platted.

(1) Dummy Schaevitz deilections versus angular deflections aboutboth the bending and torsion axes. Numerous calibration testswere run and it appeared that ýhe a.ngular deflections could bemeasured accurately to within - .01 degrees.

(2) Dummy potentiometer readings versus torsional spring rollerpositions.

(3) Bending moments versus bending deflections..

(J4) Torsional moments versus torsional deflections at variouspositions of the rollers along the cantilever beams. Fromthese curves the torsional spring constant for each rollerposition was ascertained. Fig. 18 presents a graph of torsionalstiffness versus roller position as used in the straight wingtests. Thr, value of the constant bending stiffness, obtainedfrom curves of (3) above, is also indicated in the aforemention-ed figure. The results for the swept wing tests are similarlypresented in Jig. 19.

(5) The aileron deflection angles, obtained by inserting the 3degree and 6 degree stops, were accurately determined. Thedeflections vere found to be 3.07 and 5.92 degrees for thestraight wing while the deflections for the swept wing were3.12 and 6.00 degrees.

In all the above calibration tests only a very small amount of scatter wasobtained indicating good. mechanical repeatability and high precision.

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IV

DZS0RIPTION Of TOST PROGDURN

Wind tunnel tests were conducted on a semi-span model of a straight wing ofaspect ratio 6 and on a sweptback wing model of aspect ratio 3, at Mach numbersequal to 0.6, 0.7, 0.8 and 0.85. The straight wing tests were conducted duringJuly, 1950 and the swept wing during Septinbe; 1950 in the 8j x 12 ft. VariableDensity Tunnel at the Cornell Aeronautical laboratory.

In order to attain these high subsonic Mach numbers in the C.A.L. wind tunnel,the stagnation pressure was reduced to j atmospheric. At each Mach number eachwing was tested at a constant Reynolds number, which ranged from R = 1.13 x 106to 1.22 x 106 for the straight wing and from R. - 1.60 x 106 to 1.72 x 106 forthe swept wing. The average operating dynamic pressures and velocities are listedbelow for the various Mach numbers.

N (lbs. -er square foot) U (feet yer second)

o.6 192 675

0.7 228 783

0.8 265 887

0.85 283 950

The greatest deviation of dynamic pressure during a test amounted to 2%.

The straight wing was initially installed in the tunnel at an angle of attackof -0.2 degree while the initial angle of the swept wing was -0.4 degree.The error in flow alignment in the tunnel was negligible. At a given Machn~umber the angle of attack was controlled simply by varying the torsionalstiffness. The torsional and bending deflections were recorded at thevarious angles of attack until the reversal condition was approached. Tromthe above deflections and the spring calibrations, the rolling and pitchingmoments were determined at the various angles of attack. The test procedurewas as follows.

At zero air speed the torsion spring rollers were set at the maximum stiffnessposition and the aileron was set in the neutral position. The zero readingswere recorded. The tunnel speed was increased to M - 0.6. Readings werethen recorded as the torsional stiffness was reduced, which increased themagnitude of the angle of attack.

The torsional stiffness was again set at its maximum value and the aileronwas deflected to 3 degrees and the above procedure was repeated. Test datawere similarly obtained at M = 0.7, 0.8 and 0.85. The tunnel was then shutdown and the 6 degree aileron stop was inserted and the procedure repeated.Throughout the tests numerous checks were made on the repeatability of thesystem which proved to be extremely accurate. The torsional and bendingdeflection readings were converted to moments during the tests in order torecognize the reversal phenomenon which occurred when MP - 0.

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PRJSENTATION AND RXDUCTION 07 DATL

Data were directly obtained in the form of deflection measurementsabout the bending and rolling axis, and potentiometer readings indicating theposition of the torsional spring roller assembly. From the calibration curvesof Schaevitz deflections versus angular deflections, potentiometer readingsversus roller position, and the bending and torsion spring calibration curves,the corresponding rolling and pitching moments at various wing angles of attackwere determined.

It is recalled that in the swept wing case, the wing angle of attack is a functionof both the torsional and bending angular deflections. For the small deflectionsdealt with herein the relationship is simply a = MT co5r-z(1 5ir) e where,1. and a,6 are the torsional and bending deflections respectively. The positive

directions of these deflections are indicated in Fig. 1. The moments for thestraight wing are presented in Figs. 2 and 3 while those for the swept wing areshown in Figs. 10 and 11. By assuming a spanwise distribution of lift due towing angle of attack and aileron deflection the above data may be utilized todetermine the four aerodynamic coefficients which influence the reversal phenom-enon. For the additional (angle of attack) span loading characteristics of boththe straight and swept wings the familiar Weissinger method was used. Despitethe limitations of a lifting line method such as Weissinger's the good agreementfound between experimentally and theoretically determined characteristics warrantsconfidence in the use of this method to predict the spanwise distribution (Ref-erence 5). To determine the spanwise distribution on the straight wing due toan aileron deflection Reference 6 was used, in which simple computing forms areincluded for determining this distribution by the Lots method. Use of this methodpermits the effect of ten semi-span stations to be considered, and the comparisonsbetween a number of theoretical and experimental results have been shown to beextremely good. The resulting distribution for the straight wing at a = 0 is•Nown graphically in Fig. 9. The distribution for the swept wing with an ailerondeflected was determined by use of Reference 7 which is based upon the Weissingeriwethof. and permits the effect of 4 semi-span stations tc be considered. Thisreference permits the span loading to be rapidly predicted for wings havingarbitrary values of sweep and aspect ratio. Considering the compressibilityeffects (on equivalent aspect ratio and sweep as explained below) at the testMach numbers, and the accuracy of this method, it appeared to be the mostpractical for use in the present analysis. It is recalled here that the liftdistribution of an airfoil at a given Mach number is obtained by calculatingthe lift distribution in incompressible flow of an equivalent airfoil thelateral dimensions of which have been reduced in the ratio :1- M. 1 . Theaspect ratio is thus reduced in this ratio and the tangent of the sweep angle

is increased by ./V/-'--M• . Thus, the equivalent airfoil aspect ratio andsweep angle varies with Mach number. The resulting distributions for theswept wing at a = 0 is shown in Fig. 17.

The above methods have been widely accepted as capable of determining theloading characteristics with accuracy.

With the above conditions, the four aerodynamic characteristics may be deter-mined from the test data by the following equilibrium relationships.

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Straight Wing

dC-5 7 ,Jý M,

cl .(ea bz( (1 (2)c Mý

where is the spanwise location of the center of pressure obtained from

Reference 5, and the term (.148) accounts for the distance from the wing root

to the roll axis (Fig. 1). (M,/IM)is the ratio of pitching moment to roll-

ing moment at a given angle of attack given by Figs. 2 and 3.

The aileron coefficients may be determined by use of the spanwise load distri-bution of Fig. 9 and the relationships:

a _ _ 57-. M,,o. : -d -r (dOC/ / d) d ý5[Area of F~q. T.I4 "•./ (3)

aJ. a. 0 d ( CI /L ... of 4

d (TILý a1 O-LC j

where , is the spanwise location of the center of pressure for an ailerondeflection at a = 0, and where MP. 0= I MR, o are the correspondingtest values of the pitching and rolling moments. In the formulation of Equation

(4) it has been assumed that OCldý: 0 outside of the aileron span, since no

spanwise distribution of this factor is known and, therefore, the factor 2.5appears (aileron span 0.4 of wing span).

The determination of the coefficients for M = 0.6 is presented in Appendix Aas a representative example of the reduction of the test data for the straightwing.

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swept Wim

Similar to the treatment of the straight wing, the aerodynamic characteristicsof the swept wing may be determined from the following equilibrium relationships:

acL 5 i7..3(dM1/,x), (e)

and

o. c. e.o. -(.146 + (6)

where •* is the spanwise location of the center of pressure obtained fromReference

As difficulty was encountered in controlling the angle of attack of the wingwith the aileron in the neutral position no data were recorded for Jf= 0 .

Nevertheless, the slope of the pitching and rolling moment curves (d04p/d.t)

and (00/4/dz)j with d - 0 may be assumed the same as those determined at anyconstant aileron deflection and, therefore, these values may be obtained fromthe curves of Figs. 10 and 11.

The aileron coefficients may be determined by use of the relationships,

"/•,°/I. M0 cosM.-.- L (7)

Mo• Mac SIn t+L (8)

wh-e M. C. 0.aC • ,

- [. Fr e a of Fig. f 7] -5 (9)dL

1(.48#7a) b 2z

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svept Vi, - contd.

In the aforementioned expressions Z is the spanwise location of the centerof pressure due to an aileron deflection at a - 0. This location is indicated

in Fig. 17 which shovs the epanvise distribution of the lift at a- = 0 for thetwo extreme cases of M = 0.6 and. 0.85 as determined by use of Reference 7.The factor 0.4 is again introduced as previously explained. With the two simul-

taneous Equations (7) and (8), the values of dCm/ad and da/e)J may be ascertained.

The determination of the coefficients for M = 0.85 is presented in Appendix B

as a representative example of the reduction of the test data for the swept wing.

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VI

DISCUSSION OF RESULTS

The test results for the straight wing are shown graphically in Figs. 4 through9, while the swept wing results are shown in Figs. 12 through 16o

In general, it is noticed that below the critical Mach number, the empiricalvalues of the aerodynamic characteristics presented in References (1) and (2)agree favorably with the test results, Above the critical Mach number theexperimental results differ from the predicted values. The critical Machnumber of the straight wing is approximately Oo while that for the sweptwing is above og 5 ,

The value of (c/d) at reversal, as shown in Fig. 4 agrees favorably with thevalue predicted in Reference (3) by use of a highly simplified method. Simi-

larly, for the swept wing, agreement also appears favorable as shown in Fig, 12o

It can be seen from Figs, 5 and 13 that the lift curve slope predicted by useof the Weissinger method (Reference 5) is in good agreement with the testresults, However, while predicting the total lift accurately it may be noticed(Figs, 6 and 14) that appreciable discrepancy exists in the chordwise locationof the aerodynamic center, The Weissinger method, being a modified liftingline method, assumes the aerodynamic center at 0,25 chord. The test resultsindicate a slight tendency of the aerodynamic center to move forward withincreasing Mach number, This tendency is in agreement with a recent paper(Reference 9) which is more accurate for predicting chordwise pressure distri-butions of low aspect ratio wings than is the Weissinger method. Fortunately,however, the error in chordwise position of the aerodynamic center seems tohave small effect on the determination of the reversal speed and appears not tobe a serious argument against use of this method for reversal calculations, Infact, Reference (1) indicates that in the first apprcxCiia'ion the distance( e. a - a. c. ) may be assumed to be zero, An illustrakive example in the afore-mentioned reference indicates that the reversal speed as determined with thisassumption is conservative by less than J% for every VA) of chord which the elas-tic axis lies behind the aerodynamic center.

The variations of the aileron coefficients dazdd and 6Cm/6j with Mach numberare shown plotted in Figs, 7 and 9 for the straight wing, while Figs, 15 and 16show the swept wing variations. The effect on the reversal speed of usingthe empirical rather than the exact aileron coefficients is discussed inReference (2) and an example therein indicates that large errors may be intro-duced by use of the empirical values, especially in the transonic region,

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VII

RETZR2hINCES

1. Groth, E, E7,_LUATION OF METHODS FOR CALCUTLATING THE ROLLING EFFECTIVE-NESS ANVD AI.2fRC.T REVERSAL SPEED OF A STRAIGHT WING A.M.C. MCREA54595-8 (uoskmber 1948)

2. Groth, 11. DZ.LmiAINATIoN OF THE ROLLING EFFECTIVNESS AND AILERONB £7EREo1 SP OZ J•• F JX LASTIC SWEPT WING AoM.C, MCB.XA5 4595-8--0(October 1949)

3. Goland., L. INTIIM REPORT ON AILERON REVIRSAL RRSEIuRCH CornellAeronautical Laboratory Report SB-569-S-1 (August 1949)

4. Curtiss-Wright Corporation Report No. H-47-3 (September 1947)RESTRICTED

5. DeYoung, John THEORETICAL ADDITIONAL SPAN LOADING 1,kRACTERISTICS O0WINGS WITH ARBITRARY SWEEP, ASPECT RATIO, AND TAPER RATO TN 1491(December

1947)

6. Pearson, H. A. SPAN LOAD DISTRIBUTION FOR TAPERD WINGS WITH PARTIALSPAN FLAPS NoA.C.A. Report No. 585 (1937)

7. Stevens, Victcioc I THEORETICAL BASIC SPAN LOADING CHARACTERISTICS OFWINGS WITH ARLYA,ýRY S%•EEP, ASPECT RATIO, AND TAPER RATIO N.AoC.A.TN 1772 (Q , rnber 1948)

8. Lawrence, H. R. TT LIFT DISTRIBUTION ON LOW ASPECT RATIO WINGS ATSUBSONIC SPEEDS !.A.S. Preprint No, 313 (1951)

9. Glauert, H. A3F.0,1)OIL AND AIRSOREW THEORY Cambridge University Press(1942)

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.APPnD IX

A. Straight Win

The aerodynamic characteristics are determined below for M= 0.6.

From Fig. 2, the rolling moment is -450 in.lbs. at J- = -1 and 6 = 0. Thespanwise location of the center of pressure for this Mach number is given inReference 5 as = 0.454. Applying Equation (1),

)CL -5 Z7 J(40 -5 45)- 4.90 per rodan.dao •Tf9Z) 1. 69 (.146 , .4,5,4.) Z-7

The corresponding pitching moment at c = -1 and d = 0 is given in Figs. 3as 35 in. lbs. Thus from Equation (2)

9c o.ý-50 k 1 4).46 +.4,54) 0.

The rolling moment due to aileron alone (ax 0, d 0 - 07) is 350 in. lbs.as shown inlig. 2. The area of Fig. 9 is 0.336 and = 0.596. The ty

dimensional section lift coefficient (dc ./,cx) can be accurately determined

from the wing lift coefficient by the expression,

i /a C')JCL am_ _ /.0

where the parameter -r (which accounts for taper ratio) is given in Fig. 88 ofRef. 10 as equal to 0.17 for the subject wing. Applying the above expressionthere results

Mc_,) = 7, 05

and finally Equation (3) yields-

-_ 7. b (.3,5o) 0.4'Z4Mcf 7"0-: (J. 0 .7)19Z ( f. 6 o0.J 36 (0., -44) - 7

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The corresponding pitching moment due to an aileron deflection alone ( a = 0,f= 3.07) is -23 in lbs. (Fig. 3). Accordingly Equation (14) gives

f-. 1) 7-05 (4.-24) 0-,ý6 -7-3IP 1fd 92(1.69)97 :07J

-- 0.72 per rodi'an

B. we in

The aerodynamio oharacteristics are determined below for M = 0.,8.

From Fig. 10 at M u 0.85, the average slope of the rolling moment curves is

(dMt/ldo 6 = 290 ir. lbs. per degree. The spanwise looation of the center of

pressure is = 0.48 (Reference 5). Consequently, fquation (5) yields,

dc" -6 57. -290) ,o J 00 per roodiwnam ~ +3Y6Wj #14d) 1M/

(dO1d/c),f and (dk44,/da) are equal to 236 ins lbs. per degree and 290 in, lbs,

per degree respectively (Tigs. 10 and 11). Reference 5 show% that . 0.48.Thus, according to Zquation (6),

a.cC. O0,.7 -(0.46 0.4.58)[/ 1 - i-91 0/.

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BY use of Equatiens (9) and Jig. 17 there ic ebtained,

M,.." 0. 4 0 - •6 Z31. (

w. • ' ,1 • ÷ O / )f , ( 4, •.r•:•) '6 a-. 6(707')§6] 8 (GQ*ý7 -d 7.3 1

14-/45 - (31- .1,65) 12,7 - W.4

By use of ti.•ation (7) and (8) and Jigs. 10 afx X C , d )

/94 IZ74 "" ,

and these simultanieous equatitýinc ~±& rYield

z 0,450dd

S- - 0,268

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Wind Tunnel CeilinqlCoil Spring ForBending Stiffn~essU

Torsion 5prings

RollerPI TCHINGRoler--G AXIS5

B ENDING '

A XI,5

U~niversal Join t

I2OLLIN.G .4,YIS

Line

Coil 5prings Hiinge Line

Po//t-sForVarinqAll Dimens5ions AreTorsion Stiffness in Inches.

Fig.l-5CH-EM4ATIC DI1AG/ RAM OFS5WEPT WING6 MODEL

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- -- - RESTRICTED--

0.85-1000F

-

0.8 _ _ 60

0.7

0.6 307

5000

4 10.10 016.5920

00

~1- 0 010

- - - - - - - - - - - - -

-05 -.'.0A,,~~~Ie of4 00aok,~(e ' e)

ROLLNG MM~NTvs AGLE F ATAC00ZTAH WINGCalRESTRICTED

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zo S3YM BOL-- fO -' -0-

.---- 6-3.070

TF5 T POINA/T5 A T - - - - - - -

M-0.6 a M-0.8M=0&.7 c3M'O85 1

-150 For j6Q 00 3.07 0 - _ - -3__

andic 5.92' -3

.0

Mtoao - 9 -0 ol -01*-

A 1-

oo-

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-_ Predicted Value (Re{.3) fxperimental

0,6 0.7 0.8 0,9

Mach No

Fig, 4 - \1 vs, M4 CH NO,P e versa l

5TIAICt-T WING

-ý - - .pe~rimerntal -

, /

4,4 - 00 - 0. -0

00'0

0,6 o 7 old•,

Match No,

F/9, 5- vs MACH NO,

S7TQAIGHT WING

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Sz Weissinqer (Ref. 5).'24_

_ _ _ __ _ __

Reference 8"-4 K• .20 _. _ '"-'--_

Exper'imental-

C.- - .,6 __"

o ~ .08 NO TE -cO -

Mach No.Fig. 6-CENTEP OF PRE57URE LOCATION vs. MVACI NO.

,5TRAIGMT WING

4 Experimental

,2,

0.6 0.7 00.Mach No.

Fig 7 - A ILERON COEFFiCIENT, vs. MACI-I NO.

ST•,AGI-IT WING

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1-.o. (57.3)-1.0 .._ ""__!_-

Ex eper m en ta

S-.6 - - - __

-4- [ i

- .2 - -.- 4-

0 0,7 - - - -,-

0.9Mach No.

Fig. &-A/ILERON COEFFI/C/NT,' ;MACM NO5TRAIGHT WING

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i ii

•cLý

* _ V

- - 2

iC

LQ

S/ cv

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\ M.

-- I TT POINT5 AT

160 -A = 0.6

M-.85 o M =0.7__a A 4- 0.a

a M -0,85140 \\ OP j 3. 12eand Co'

120

86080

60-

""" \ 14,0 -•

VN

10I t

0 - - - .

An q/e of Attck, cQ (Derees)

Fi. 10- 1R0LLING MOMWENT vs ANGLf OF ATTACKS WCP7T W/IA0

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-200 _ __ _ _\~ \

M =.8- M=.85 TE-T POINTS AT

M -O0.6-180 - - o M- O.7

A \ M0.8\ " _ M: 0.85

FOR 5=3.I2*ad 6'

IM-.6

Z

q)3

oZ -120__

.•t~ \ \

0~

-60- N

-40 -A __

3\\

0.1 .2 -.3 -. 4 -.5 -.6 -. 7 -8

Angle oif Attack, a (Degrees)

Fiy. I1- PITCHING MOMENT vs. ANGLE OF ATTACK--.5WEPT WING

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-- -- - - - Predicted Value (2ef 3)

V -45 __e• ~~Ex per imenta l_.-

0,6 0o7 0,8 0,9Mach No.

Fi, 122- (Ad)Reversal s

SWEPT WI NG

3.-32

P.xoerime nta/- ..-

.- -' heoretlcol (/lef 5)

"4 ,

Old 0,? 0,8 0.Mach No,

Fig, 13- -C vs MACH NO-3v

sWEPT WING

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fly,• Experimental

o ) ,08

u NOTEJ- •.0

r: _-- - -Wi5ner(eT5

0.6 0.7 0.8 0.9

Mach No.

Figq, 14- CENTER OF PRE-55URE LOCATION vsMA1CH NO.5 WEPT .WIN\G

._

. o --- - - - _ _

Experimental

0.6 0.7 0.8 0.9Mac h No.

FIg. 14- AILENRON COEFFICIENT) LN MACH NO.

SWEPT WING

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-0.6

-0.4"•fExperimental

43 1O56 Mo---- - .- , --- o

(Based on f.ef 2)

0.6 0.7 0.8 0.9

Mach No.

Fig. 16-AILEI2ON COEFFICIENT,*m-- v,5. MACH NO.

S WEPT WING

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-.4

K

K

h�-

F-..

II

C _ 1 4-H

K ___ __

N 0 0

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0

)K

"fir%

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liP,

\lnc0

4- V

-~L LJ- - - -

L-J

.4Q,9 O.1U00d - - --90 J 1/2

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ul

0

E-1

!0

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0

E-

0

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VARIABLE TORlSION SPRING ASSEMBL,AILERON CONTROL MOTOR, SCRA.EVITZ ASSEMBLIES

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F ig., 23STRAIGHT WING MODEL MOUN1TED IN WIND TUNNflEL

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E-4

-1A

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tIT

k 4

V%0

Tki U

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F ig, 26SWEPT WING MODEL MOUNTSD IN WIND TVfl'EL

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DCCTDUrTofl

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k I

AMi

211

70~

'00

39i

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oilo

-I

t~i

4LH

lk-

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140

E-4

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