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NACA.

AN ENGINEERING METHOD FOR THE DE TERIIAN’ATION

OF AEROELASTIC EFFECTS UPON THE ROLLING EFFECTIVENESS

AILERONS ON SWEPT WINGS

By E Kurt Strass and Emily W. Stephens

Langley Aeronautical Labor tory.‘i{,s~. Langley Field ,~ac~];~~”~~~’”.~i~/{)

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NATIONAL ADVISORY COMMITTEEFOR AERONAUTICS ‘

WASHINGTON

November 30, 1953

OF

1

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https://ntrs.nasa.gov/search.jsp?R=19930087789 2020-06-29T12:16:38+00:00Z

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NACA RM L53KL4

‘dNATIOIUL ADVISORY C-TTEE FOR

TECHLIBRARYKAFB,NM

ll~lllllllullullllullllll-0144400

AERomIcs

.RESEARCH MEMORANDUM

AN ENGINE3WNG MEI’HODFOR THE DETEWDWION

OF AEROELASTIC E?FE2TS UPON THE ROLLING ElIf?ECTlNENE3SOF

By H.

AIXERONS ON SWEPT WU?GS

Kurt Strass and Ehily W. Stephens

A method is presented for calculating the steady-state rollingeffectiveness of ~lexible sweptback wings at subsonic and supersonicspeeds. The present method was derived by reducing the problem to itssimplest terms. The result is a procedure which possibly is as simpleas can be devised, and which, based on conprisons with experiment,apparently is sti~ capable of providing estimates of the changes inaileron rolli& effectiveness for a wide range of wing-aileron configu-rations within the experimental accuracy.

As an aid to rapid calculation, the results of this investigationare presented in nondimensional form and have been c~c~ted for a tiderange of tapered wings varying from O to 1.0 h taper ratio, for wing-span-body-diameter ratios of O, 0.2, and 0.4, and for ailerons of anyspanwise extent and location. These calculations were made assuming thatthe wings were of homogeneous construction. The direct application ofthe results of this investigation to wings wherein the structural param-eters differ markedly from a homogeneous wing should be avoided. It iS

recommended in these cases that a closer approximation to the actualaerodynamic snd structural values be used and a particular soluticm,also presented herein, be obtained.

Comparisons between the experimental and calculated values are pre-sented for a wide rsmge’of wing-aileron configurations. k illustrativeexample is included to facilitate calculations by this method. in addi-tion, some experimentally determined structural constants are comparedwith those calculated by approximate methods.

-,

—... ..—.—— _.— — —... ,- —. —–— —.——

2

INTRODUCTION

NACA RM L53EL4

b recent years, many methods have been proposed to account for theeffects of aeroelasticity upon the lateral-control characteristics ofswept wings: Because of the complicated interaction of structural andaero@mmic effects, the theories which have been developed are neces-sarily complex. Relatively simple methods for making such estimates forunswept wings at both mibsonic and supersonic speeds are available; how-ever, a comparable method for swept wings which does not involve the useof difficult mathematical procedures and which is relatively rapid andreasonably accurate has not been available. Such a method would be ofparticular importance in preliminary design.

M order to correlate the test results of the more than 370 suc-cessful lateral-contiol test models winch have been flown by the Langley

Pilotless Aircraft Research Division in the course of a general investi-gation of lateral control over a speed range which extended from approxi-mately M = 0.6 to as high as M = 1.8, it was necessaqy to account forthe effects of aeroelastic distortion. Because of the great nuniberandvarie~ of wing-control confQurat~ons, the application of a highlyrefined aeroelastic theory would have been exceedingly tedious. Thepurpose of t~s paper iS to present tk Wtieering method which wasderived and the comparison of the values calculated by this method withexperiment.

The results of this investigation for ailerons are presented in non-dimensional form and have been calculated for a range of tapered wingsvarying from O to 1.0 in taper ratio, for wing-span-body-dismeter ratiosof O, 0.2, and 0.4 and for ailerons of any spanwise extent and location.

An example problem is outlined in appendix A. In addition, some

experimentally determined structural constants are compared with thosecalculated by approximate methods. This

t

SYMBOLS

comparison is-given in appendix B.

AR aspect ratio, b2/S

A dtiensionless angle of twist resulting f?om the component ofthe aerodynamic moment parallel to the direction of flightcaused by unit control deflection,

J;$-L’(Y+=c

m“>

NACA RM Lg3H14 “---”a- 3

B

c

D

E

G

1

J

M

M

P

dimensionless angle of twist resulting from the component ofthe aerodynamic mxnent parallel to the direction of flight

caused by rolling,l:$~(:rk+

=c

dimensionless angle of twist resulting from the component ofthe aerodynamic moment parallel to the elastic axis causedby tit control deflection,

+@(% - 4*P - (k - ‘.)f::~]~

E

dimensional angle of twist resulting from the component ofthe aerodynamic moment parsllel to the elastic axis caused

Youngls modulus of elastici~, lb/sq in.

shear modulw of elastici~, lb/sq in.

moment of tiertia of airfoil cross section about chordplue, in.4

torsional stiffness constant of airfoil cross section inplane parallel to the direction of flight, in.4

proportionality constants

rolling moment (positive clockwise, as seen from the rear),in-lb

accumulated bending moment in a plane perpendicular to theelastic axis (positivewhen bending wing h clockwise direc-tion, as seen from rear), in-lb

Mach number

distributed 10ad, lb/in.

.————. —— — ———. ..—— ——.— — .—. .—

4 L@!!!!9- NACA RM L531U4

s

T

v

b

E

c

‘1

%2

e

k

1

P

~

t

pb/2V

wing area, sq in.

accumulated twisting moment parallel to the direction offlight (positivewhen tending to twist wings in a directionto create positive change in section angle of attack), in-lb

veloci~, ft/sec

wing span, in.

mean wing chord, s/b, in.

wing chord, in.

distance of center of pressure of load due to angle of attackfrom elastic axis (positiveforward), fraction of chord

distance of center of pressure of load due to control deflec-tion fkom elastic axis (positiveforward), fraction of chord

distance of elastic axis &rom leading edge, fraction of chord

distance to any point on the elastic axis, measured from fuse-X

lage center line, fraction of semispan, —b/2

lift per unit length, lb/in.

rate of roll (positivewhen rolling in a clockwise directionas seen from rear), radians/see

dynamic pressure, lb/sq in.

maximum airfoil thiclmessj in.

wing tip helix angle due to unit aileron deflection (rollingeffectivenessparameter), radians

nonscalar torsional stiffness parzuneterjin.211b

control-surfacedeflection, measured in a plane psrallel tothe direction of flight, positive when producing a clockwiserolling tient as seen from the rear, radians

taper ratio, ratio of tip chord to chord at fuselage centerline

slope of deflection curve, radians

~ - -q }------- -----

—

NACA I/ML531U4 5

a

43

%

Cla .

%

twist of wing about elastic axis, radians

fraction of rigid wing rolltig effectiveness retained byflexible wing

sec~ion angle-of-attack change due totion (positivewhen in direction tomoment), radians

sweep of elastic axis, deg

section control effectiveness~ angle of attack causeddeflection

section lift-curve slope, per

aeroelasttc deforma-create positive rolling

wing lift-curve slope, per radian

parameter, effective chmge inby unit change in control-surface

radian

—

c1 rolling-moment coefficient, L/qSb, positive clockwise whenviewed from resr

()cl f additional rolling-moment coefficient resulting from wingflexibility

Subscripts:

A,B,C,D particular types of aerodynamic loading resulting fromstructural deformation

M

P

R

T

signifies that value is for a bending moment paralJel to theelastic axis

load

~tig root, titersection of elastic axis and fuselage

signifies that value is for twisting moment parallel to thedirection of flight

—. ——.. ..—.— .—

. -,,. --—

?- -3!Coogmw NACA RM L53EU4b 7

a aileron

f flexible wing

r rigid wing

a angle of attack

b control deflection

i inboard

o Outbosrd

P roll

1,2 arbitrary reference points

Prime msrks denote that the reference plane is either normal to orparallel to the elastic axis rather than normal to or psrallel to thedirection of flight.

DEV13101?MENTOF EQUATIONS FOR TEE D~TION OF AEROECJLSTIC

EFFECTS UPON THE ROLLING FJ?FECTI’WNESS

OF A.ILERONSON SWEPl WINGS

h a steady roll, the resultant rolling momentzero. In coefficient form this can be expressed aswing:

‘cz~+(i$yP+(C,)f = 0

rewriting equation (1) gives

()pb ()-5c~ - cl f=

Gf c%?

acting on a wing isfollows for a flexible

o)

(2)

—

NACA RM L531D.4 7

The fraction of control effectiveness lost by the wing is

.

()(p@V)f - C2 ~(1-~) ‘1 - @@)r= 5C25 (3)

For the purposes of this derivation, the following assumptions anddefinitions are used:

(1) The singlesof twist parallel to the direction of flight resultingfrom the application of aerodynamic forces can be calculated by the useof the elementary theories of torsion and bending when correction is madefor the effects of root restraint by a simple empirical method. Thismethod assumes that the wing has an elastic axis and all the aerodynamicforces canbe separated into loads which act on the elastic axis andcouples which act about the elastic axis.

(2) The changes in rolling effactiveness due to aeroelastic effectsare small.in coqsrison with the rigid-tig values. The loads createdby aeroelastic deformations sre small in comparison with the loads createdby rolling and aileron deflection.

(3) The control deflection is constant and is independentelastic effects.

(4)-The chord of the whg varies line=ly with the span.

(5) mere is no yaw or sideslip.

of aero-

(6) Within the framework of these assumptions, a schematic descrip-tion of the spanwise variation of the aerodpamic loads for a typicalwing with the control deflected is as follows:

m:= ‘“due ‘iron,

~Load due todeformation

\due to control

. . .. . .— ~ —. —- .—...——. -. ———— ——. .

8

.—.

NACA RM L53m4

where k = ~. All the aeroelastic phenomena result from the applica-b/2

tion of these loads.

(7) me ltit due to either control deflection or a change in angleof attack acts at the chordwise center of pressure. This assumption isequivalent to assuming that the wing sections are infinitely rigid andcannot distort (camber)under the distributed chordwise air loads.

(8) The incremental lift due to control deflection acts independentlyof the lift because of a change in angle of attack. The wing deformationsresulting from these loads can be superimposed upon each other.

(9) me i.UcreBM loads at any station due to elastic deformationare dependent solely on the angle of attack at that station.

structural Amalysis

Within the limitations h-posed by the first assumption, the angleof attack at any point along the span of a sweptback wing resulting fromloads which act on the elastic axis and couples which act about the elasticaxis can be derived as follows:

Angle of attack resulting from wing bending.- I!romelementary theory,the chsmge in slope between any two points kl’ and ~’ on a wing (see

fig. 1) due to the previously mentioned loading is

M=J@l+~’ Jwhere

(4)

2MNACA RM L5~4 ‘/ 9

thus

where

k’ .”&._= kb’/2 b~2

E’ =E

bb’=—

COG &

P’ =Pcos&

T’ =Tsin~

Substituting these values into equation (5) gives

Angle of attack resulting from wing twisting about the elastic axis.-l?romelementary theory, the change in the angle of twist about the elasticaxis between any two points kl’ and lq’ on a wing due to the previously

mentioned loading is

. . . .—.——.—— . .— .— .— —.— ——. —..

10

where

G’ =G

-J, =Jcos&

Substituting these values into equation (7) gives

NACA RM L53m4

(7)

(8)

For the purpose of this paper it is desirable to express the changesin angle of attack due to aeroelastic deformation as angular changes dueto loads on the elastic sxis and to twisting couples acting about an axisperpendicular to the dtiection of flight. Rewriting eqyation (6) as

gives

kE?5?21E5iiiB

—. .——.

—— -. .

NACA RM L53H14 Ii

Similarly from eqmtions (6) and (8)

so that

which can be written as

.

.,

(lo)

In order that the foregoing beam theory give accurate results forswept wtngs it is necessary to take into account the effect of the tri-angular root portion. One wayto do this is by making use of theso-called “effective root” concept (see ref. 1, for example). If theeffective root is located at k= ~+~ then the resulting expressions

for the angle of attack at any point along the span due to the appliedforces are

(n)

(1,)

.

...- . . . .. —-— ~ .—— —— ———— —.—- —.-——- ---— -

12 s-Com?Il).>”-’

Aeroelastic Analysis

As a consequence of assumption 2 it is assumed that the distortionscaused by the loads resulting from the distortions themselves are negli-gible. The only distortions consitkred are those caused by the aileronloads and the loads due to rolling. !thesedistortions are denoted asfollows:

aA the change in angle of attack caused by the torque resultingfrom aileron deflection

aB the change in angle of attack caused by the torque resultimgfrom rol-g

w the chamge in angle of attack caused by the load on the elasticaxis resulting from aileron deflection

aD the change in @e of attack causedby the load on the elasticaxis resulting from rolling

The roll= -moment coefficients resulting from these distortions aredenoted in a similar manner, CZAY c2B~ C2(7 ‘d C2D”

Rolling-moment coefficietis resulting f?om the elastic deformationscaused by the aerodynamic twistm moments parallel to the direction of

QZ&&” -

Effect of aileron deflection - see figure 2: At any point k thesection twisting moment due to unit positive aileron deflection is

where the lift per unit length, due to unit control deflection, is

Therefore, the general expression for the twisting moment is

(13)

(14)

——

—.— —

NACA RM L53iU4

Specifically:

Region 1 (inboard of aileron)

Region 2 (in way of aileron)

TA=q$z2 J~kod--y@(:)2dkc

13

(m)

Region 3 (outboard of aileron)

TA=O (15C)

Substituting TA into equation (12) gives the angle of attack at any

point on a sweptback wing due to the twisting moment created by theaileron deflection.

where

*%H’= (in region 1)h

L

= P (in region 2)k

f= 0-(in region 3)

g=~.~ .P..-

——. -— . —. ..— —. .—

14 AL NACA RM L53m4

The rolling-moment coefficient due to the spanwise distribution of WA

is

J2q& 1 ~kdk~Ac& ~tiA kR+Ak

CIA._.qsb qsb

S&stitut@ for WA in equation (17) and simplifying gives

(17)

(18)

lMfect of rolling: At any point k the section twisting momentdue to roll is

where the lift per unit length resulting from the roll caused by unitaileron deflection is

(the negative sign indicates that thethe lift due to control deflection).

Ck.kg (19)

lift due to roll is o~osite to

(20)

.— .-

—. —.

I?ACARM L53m4 15

.

and in a manner similar to that wedany point on a sweptback wing due torolling is

previously, the angle of twist atthe twisting moment created by

and the rolling-moment coefficient is

.

Jk

kR+& GJ-1

‘k (22

.

Rolling-moment coefficients resulting from the elastic deformationscaused by the aerodynamicc loads on the elastic axis.-

Effect of aileron deflection: The load P for a unit ailerondeflection is

P=Cl(k< ki)

P=o (k>%)

Ehibstitutingfor P into equation (n) gives the angle of attackat any point k caused by the loads resulting from the aileron deflec-tion. The angle of attack anywhere on a sweptback wing due to the loads

.

—.—..—.— ..————————. -.. —— ———.—.. —

16

O?iby

‘%

L,.=-1rcozll?lDmm NACA RM L53m4

....—.—.—.—-—

created by a positive aileron deflection is obtainedexpression for ~ into e~tion (u).

the elastic axissubstituting the

‘8 COS34

(23)

The rolling-momentthe aileron is

coefficient resulting from the wing bending caused by

L

.

(24)

Effect of rolling: Por the rolling case, the load P is equivalentto the lift per unit length of span on the elastic axis resulting from therolling due to unit aileron deflection.

The angle of attack anywhere on the sweptbaek wing is

(25)

from the wing bending causedand the rolling-mxnent coefficient resultlngby rolling is

.

.—— —

MNACA RM L53m4

)]akpakax

Rolling-moment coefficient due to unit control deflection.-

Loss in rolling effectiveness due to aeroelasticity.- Fromequation (3)

.

()C2 f = CIA+ CIB -t-c~c + CID

17

(27)

(5 = 1)

~eq. (18)) +(eq. (=))+ (eq. (24)) +(q. (26)] (28)l-cp=-

(eq. (27))

Appreciable simplification of e~tion (28) canbe accomplished ifcertain additional qualifying assumptions can be made.

.- .— .——. — .—-—— - .—

, ~-cor?Fm

L .-_!+. .< ;.-. L“--=

NACA RM L53m4

..

These assumptions are:

(10) The wing acts structurally as if it were of homogeneous con-struction and constant thickness ratio; that is, the structural param-eters III and GJ vary as the fourth power of the wing chord.

(n) The lift-curve slope is constant along the whg span and isequal to the value for the wing taken as a whole

(Ch = %).

(32) The ratio of the aileron chord to wing chord is constant alongthe wing span (~ assumed constant).

(13) The distances dl and d2 are constant.

According to the work done by Zender and Brooks and published inreference 1, a good approximation to the effective root for an homoge-neous wing should be consider&1 to be a point located on the elasticaxis where a line drawn perpendicular to the elastic axis passes throughthe intersection of the wing trail@ edge and the fuselage wall (seefig. 1). The spanwise

4Ak=

AR(l+ h)

Reference 2 (page 1~)to the syuhols used in

location of this point can be expressed as

{[ 1}(1-e)cos~sin~~-~(1-~) (29)

gives the followhg expression (altered to conform~he present deriva~ion]

for homogeneous sections similar to airfoils

41J=

1+16~ac2

where

a = cross-section area

I()

kt3= K1ct3 = KIC ~

a = ~(tc)

==

for the-torsional constant

(30)

.

NACA RM L531Dh 19

161 16K1t3c K132—=

2=16—

a’c K@c3 ()K2 C

J=411

Klt2

()1+16—-

K2 c

For NACA 65A~ airfoil sections

K1 = 0.0377

q = 0.651

If

:+.0

then

J+41

The error involved in this approximation

(31)

is small for thin wings. Bythe use of the shplify3ng ’factorsequation (16) canbe rewritten in thefollowing form:

@2$~aA .

-Z&I()16GK1C ~

Let the integral expression

Jk

kR+Ak

—

E!!!!!F

(32)

.——. ...—. —.—— ——. — —-

20

then equation (32) can be simplified and rewritten inform as

NACA RM L53m4

(Y+)

nondimensional

AA) (35)

and

L

(fkR+& A: kd.k+f

]

M:kdk (36)kR k@Wt

The work necesssry to evaluate equation (36) can be shortenedappreciably by approximating the effect of the root restraint.

A typical variationnate k is presented in

of the function A with the spanwise coordi-the following sketch

A

o ‘IIkR I1

.-.

%&

NACA FM L53iQ4

for which

J~+fk

J1

A~kdk+ LA~kdk= mea of shaded portion

l%’ k&Ak c

Now

Wbstituting for c/~ in equation (32) and integrating gives

[ ( )1}

&32(1-X)1- kR+=

.

For convenience in usage, the

21

(37)

(38)

[

1expression for ~ k dk has been

kckR~

of ~, X, and Ak and the values srecalculated for several values

presented in figure 3.

Substituting ecylation(~) into equation (~) gives the completeequation for the rolling-moment coefficient due to the twisting nmmentof the aileron.

.——. .—. — —-——— .— .-— .

22 NACA RM L53~4

(39)

J1

Values for A~kdk for kR= O, 0.2, and 0.4 are presentedkR c

in figure 4. The root correction factor Ak can be obtain~ from equa-tion (29). Figure 5 presents values of @.& for root locations of

‘R = O, 0.2, and 0.4. Then

LA= @AkAk

similarly equation (22) can be written

-qdl~2AR2 ~b ~4

( )(J

1 1

CZB =8

——l+tanz~~ B &kdk-AB

0

;kdk2V GJ kR c kR$ c

(40)

where

.=j-’’$~(+s+s=c

(41)

I1

The values for B: k dk can be obtained from figure 6, those forkR c

pl

ZB/& from figure 7, and those for

1

~ k dk, as for the previous

iui%sc

—.— .—.

NACA BM L53rn4 23

case, f?om figure 3. Equation (24) can be written

where

(43)

[

1The values for c

kR

AC/& from figure 9,

~ k d. can be obtained from figure 8, those forc

[

1and those for ~ k d. from figure 3. Equa-

kn& c

tion (26) can be written

(45)

— —– ———--———- —— ——. . ..—– — —

24

-1

~ CONFID NACA RM L53EL4~:.:...,-- _._.L:

1’-L

The values for D: k dk can be obtained from figure 6, those

%C

J

1

for ~/& from figure 7, and those for ~k dk from figure 3.&E

%@

Equation (27) can be rewritten

(46)

Substituting the expression for c/5 into equation (46) and writing ingeneral terms gives

(47)

For convenience in usage, the terms which me dependent upon thewing-control geometry canbe grouped together as follows:

(48)6(I + x)

Values for eqyation (48) are presented in figure 10, then

Substituting the simplified expressions for equations (18), (22), (24),(26), and (27) into equation (38) @VeS -

lii!3EziEEE3

——

M

NACA RM L53m4

4

-1

25

(49)

Equation (49) is particularly suited to the estimation of the change incontrol effectiveness due to aeroelastic effects upon the free-flightlateral-control test models flown by the Pilotless -craft ResearchDivision. An example application is made in appendix A. For many

Purposes) P~tic~~~ inPrel~ desi~, equation (49) canbe USedwithout nmdification. However, if more precise estimatesit is recommended that equation (28) be used.

APPLICATION AND COMPARISON WITH EXTERIMENT

Selection of Pertinent Parameters

b applying the simplified method to these cases, nomade to determine the detailed aerodynamic psmmeters for

are reqpired,

attempt wasa given wing-

control configuration. For exsmple,-unswept two-dimensiond-wind-tun&values of the control effectiveness parameter c%, the chordwise location

of the center of lift due to angle of attack dl,

tion of the center of lift due to flap deflection

out the calculations. The lift-curve slope c~

finite aspect-ratio wind-tunnel tests of wings of

and the chordwise loca-

d2 were used through-

way estimated from

Sti= pkl fOrm and

.—— —.———— — ————---

26 NACA RM L53~4

thickness ratio in symmetrical lift. The restrictions resulting fromthese broad assumptions are obvious. The accuracy of estimation is adirect function of how well the aerodynamic values resulting from theseassumptions approximate the actual conditions.

Another possible source of error results from the fact that mnyof the test wings were built up of wood and metal in various combina-tions and this form of construction has proved to be subject to relativelylarge variations in stiffness which are difficult to assess theoretically.(The only structural values which were obtained entirely from experimentaldata were the unswept wings; that is, Cases 1-8.) In addition, the methodof attachment of the wings to the fuselage is not the ideal situation vis-ualized by Z.enderand Brooks in reference 1, so that additional uncer-tainties exist. For example, some of the test wings were so stiff thatcomparatively large root deflections were experienced resulting in anappreciable reduction in root restraint. This movement of the wing rootexisted in all the test models. Its relative importance decreased asthe wing stiffness decreased. In order to account for this factor, theeffective root location was determined from experimental data whereverpossible. It was observed that Zender and Brook’s approx~te root loca-tion became increasingly accurate as the wing stiffness relative to thestiffness of the fuselage was decreased.

Comparison of Simplified Method With Experiment

The effect of aeroelasticity upon the lateral control effectivenessas determined experimentally is compared with that estimated by thesimplified method in figures Il.to 19. All of the data obtained to datehave been included, with the exception of three cases wherein unusuallylerge constructional errors were measured and for which proper allowancewould have been virtually impossible without more detailed measurements.

The estimated effect of aeroelasticity is obtained as a fraction ofthe rigid-wing value; therefore, in order to obtain the actual value ofthe rofiing effectiv&ess it is-necessary thatobtained. l?romequation (3)

rigid-wing values be

()pb (pb/2V)f

zr= q

The rigid-wing estimtes which are presented were based upon thetest data which, according to the method of estimation, were the leastaffected by aeroelastici~ in order to obtain rigid-wing values of maxi-mum accuracy. These estimted rigid-wing values were then used in thecalculation of the flexible-wing values. A major assumption of the method

NACA RM L53rn4 27

of estimation is that the changes in rolling effectiveness due to aero-elasticity are small in comparison with the rigid-wing values. However,comparisonsbetween the experimental and estimated values are presentedfor cases where the chsmges in pb/2V due to aeroelasticity exceed theestimated rigid-wtig values. It is impossible to draw a line where themethod is applicable and where it is not. The conditions would verywidely with structural and aerodynamic changes. These comparisons mepresented for their own intrinsic value and sre titended as a guide tothe possible use of this method for design purposes.

All.the data, except those presented in figures 16 and 17, have beencorrected to a common aileron deflection of 5° parallel to the directionof flight. The data presented h figures 16 and 17 sre corrected tocomon aileron angles of 5° and 10°, respectively, measured normal tothe aileron hinge axis. All the data have been corrected to 0° wingincidence by the method given in reference 3. No other corrections havebeen applied. The data presented me for the altitude of the test, w~chvaries continuously throughout the speed renge. The variation of staticpressure with Mach numibercanbe obtained from the ref~renced papers ifdesired.

The geometrical characteristics of the test wings and the referencesfrom which the data for these wings were taken are given in table I. Thestructural and aerodynamic parameters used in the calculations are pre-sented in tables II and III, respectively.

Figure 11 presents a comparison of the.experimental results with thecalculated values for a group of unswept, untapered wings. It should benoted that for the majori~ of the cases the estimated values agree verywell with the measured values, with the ,exceptionof cases 2 and 8 forwhich the measured effect of aeroelasticity differs appreciably from thatestimated. In consideration of the excellent agreement between estimateand experiment in the ssme speed range for the other cases in this group,it appears that some @own model characteristicswere responsible forthe discrepancy. For example, cases 5 and 8 were nominally identicsl.The wings were constructed of laminated white pine. The nondimensional

torsional stiffness constant for c4/GJ as obtained from measured datafor case 8 was only 4 percent greater than for case 5, yet the measuredchange in pb/2V was 67 percent ~eater for case 8 as compared withcase 5. Because the wings were constructed of wood, the probabilitythat the wings warped after they had been measured is very great. Nor-

- every effort iS made to ~~ze the ttibetieen model measurementand flight test in order to avoid this and other troubles. However,experience has shown that the test data from the more flexible built-upwings wheretithe wood was the primary load carrying material are defi-nitely more subject to these indeterndnant deviations.

——..— -———— — — —..—

28L ‘mq

v..c NACA I@lL53m4

.P... ---..-,--+.

Cases 1 and 2, being constructed of solid metal alloy, are notsuspected of any dimensional change after model measurement. Becauseonly two 3-percent-wingmodels were flown, it is not possible to drawany conclusions as to which of the cases is the probable aberrant one.

A group of untapered wings swept back 45° is presented in figure I-2.As-before, the most flexible case (case 13), which was also constructedof white pine, deviated the farthest from the estimated values. Theremainder of the cases agreed with the estimates within the estimatedexperimental accuracy.

An interesting point is illustrated here in that the method ofestimation indicates that for certain combinations of structural andaerodynamic values, the flexible values sre higher than the rigid ones.This situation results from the fact that for these cases, the loss inda@ngmoment due to roll is greater than the loss in roIM.ngmomentdue to control deflection. If

and

then

($)f‘(R,)r

It is to be remembered that the reduction of available controlrolling moment because of aeroelastic effects seriously affects the timereqd.red to attain a given angle of bank even though the resultant steady-state value of pb/2V may be higher than the rigid value.

In figure 13, for example, the flexible values are considerablyhigher than the estimated rigid values. The magaitude of the relievingeffect of roll on the aeroelastic effects is very well illustrated bycomparison of the experimental results for cases 16 and 17 (fig. 13(b)).In this particular instance, the wings of case 17were approximately 1/7

—

NACA RM L53HL4-

29

as stiff as case 16, yet there was no measurable difference between thetwo cases up to M = 0.9. At M = 1.0, the relieving effect of roll onlypartially overcame the lsrge loss in control rolling moment, the net lossbeing approxhately one-third of the rigid wing pb/2V.

No attempt was made to estimate the aeroelastic effects beyondM= 1.0 because the very unusual aerodynamic behavior of this group ofmodels in this region indicates that the application of simplified aero-dynamics would obviously be unrealistic. The determination of the prob-able aerodynamic loading is beyond the scope of this paper.

The effect of spanwise aileron location upon the aeroelastic behaviorof a given wing is presented in figure 14. The loss due to aeroelasti.city@ greatest when the aileron load is concentrated near the wing tip as infigure 14(b), and least when the aileron load is concentrated near theroot as in figure 14(c). The agreement between the experhental andcalculated vslues is good for the cases presented in figures 14(a) and14(b) andpo?r for the cases of figure 14(c). The poor agreement in fig-ure 14(c) may be due to the fact that strip theory underestimates theeffectiveness of the inboard ailerons and overestimates the effect ofroll.,thus exaggerating the errors inherent in this method.

Some additional comparisons between the experimental and calculatedeffects of aeroelasticity for more or less conventional aileron locations(that is, outboard partial-span ailerons) sre presented in figures 15to 18. W general, the agreement is within the esthuated expertientalerror. A few of the cases are worthy of special mention, among them mecases 29, 31, and 33, which were constructed in such a msmner as to dupli-cate as closely as possible the structural clwracteristics of actual afi-craft. The fact that the agreement of the calculated values with theexperimental is fairly good for these obviously practical cases isencouraging.

The data presented in figure 18 represent an extreme case as far asthe applicabililqyof this method of estimation is concerned. The effectsof minor variables are greatly magnified. For example, the spread betweencase ~ (solid steel) and case 35 (solid aluminum alloy) is apprentlyalmost entirely due to an unintentional built-in wing twist which createda load opposing that due to roll. The wing twist was approximately linearand the ave?%ge for the three wings was approximately 0.4° at the wingtip measured parallel to the dtiection of flight. At M = 1.2, the esti-mated effect of this twist was to reduce the rolling effectiveness of thealuminum wing by 40 percent. It should be pointed out that the incidencecorrection normally used is a “rigid” wing correction and is an entirelyseparate consideration (see ref. 3).

In order to show the probable range of application of the simplifiedmethod, a comparison of the measured changes in rolling effectiveness due

—— —. .— .—.— ..—— —

30 NACA RM L53EL4

to aeroelasticitywith the calculated changes is presented in figure 19.Most of the cases are either within or veqy close to the estimated limitsof accuracy. This estimated limit of accuracy is an average value obtainedfrom past experience and represents the expected degree of repeatability oftwo supposedly identical test models. It should be noted that a high pro-portion of the cases which do not correlate within the estimated experi--mentalerror are cases wherein the measured changes in pb/2V due toaeroelasticity exceeded an arbitrarily chosen value of 80 percent of theestimated rigid-wing value. Of the remaining cases in this category,several were previously mentioned as being of doubtful value because ofprobable dimensional uncertainties or unrealistic aero@xamic assumptions.

CONCUJDING REMARKS

In the light of the foregoing discussion,conclude that this method of estimation, which

it seemshas been

reasonable todeveloped by

-We of certain broti assumptions, is capable of providing esti-mates of the changes in aileron rolling effectiveness for a wide rangeof wing-aileron configurationswithin the experimental accuracy of therocket-model technique for changes up to 80 percent of the estimatedrigid-wing values. The direct application of the results of this inves-tigation to wing-aileron configurationswherein the aerodynamic andstructural characteristicsdiffer markedly from those assumed should beavoided. It is recommended that in these cases a closer approximationto the actual characteristicsbe used and a particular solution beobtained.

Langley Aeronautical Laboratory,National Advisory Committee for Aeronautics,

=eymeld, Vs., August 20, 1953.(Comected April 21, 1954.)

NACARM L531D4

APPENDIXA

31

TYTIC!ALCCMPUTING PROCEDUREUSED IN THE ESTIMATIONOF THE EFFECTS

OF AEROELASTICITYUPON THE STEADY-STATEROLLINGEFFK!TIVENESS

The change in rolling effectiveness due to aeroelasticity for awing wherein the structural parameters closely appro~te those for awing of homogeneous construction is given in eqmtion (49). There sretwo ways in which the equation can be used.

(1) Esthation of rigid-wing values based upon measured flight data.Flight-test data me stistituted into the equation and the effect of aero-elasticity is obtained directly.

(2) Estimation of flexible-wing values ba~e2pon rigid-wing v4ues.

()It is very importsmt that accurate values of — be used.

br

In the fcd-lotig example both methods of estimation sre demonstrated.Case 33 is fairly representative of the computing procedures used through-out this paper. This case is interestingbecause the construction of thetest wings is such that the spanwise variations of GJ and EI of afull-scale fighter type of airplane sre very closely approximated in thetest wings, and for this reason, the measured effect of aeroelasticityshould be very similsr to that encounteredby the actual airplane. Asketch of the wing-control configuration of the example case is presentedas figure 20. In order to obtain the desired elastic characteristics, itwas necesssry to slot the outboard portion of the chord-plane aluminum-alloy stiffener and to orient the grain of be wood approximately45° withrespect to the 38-percent-chordlihe. Grain orientation permits altera-tion of the bending stiffness without appreciably affecting the torsionalstiffness (ref. 4). A special test panel was built and tested with thewood grain at an angle of 45° with respect to the flexural axis. Theresults of this test in conjunction with the data from reference 4 srepresented in figure 21. The flexural axes of all the wings tested wereassumed to be at the 45-percent-chord line. The resulting angle betweenthe gain direction and the assumed flexural axis was approximately 43.8°.The data from figure 21 show that the wood (spruce)was only 22 percentas stiff in bending as it would have been had the grain run parallel tothe flexural axis. The material constants used in the calculations were:

—— ..— .—————

32 @oIJFIpiiiJ-......

NACA RM L531U4

For spruce

E= 1.4 X 106 lb/sq in. X 0.2%?= 0.31 X 106 lb/sq in.

G= 0.09 X 106 lb/sq in.

For 24s-T aluminum alloy

E= 10.8 X ld lb/sq in.

G= 3.91 X ld lb/sq in.

Modifying equation (12) gives:

f

( )1 + tana~ g

f

(& l+tan%gCq. dx- )dx

0 GJ 0 GJ

where at any given spanwise station x the folluwing relationships areassumed:

‘(composite section) = (GJ)(~m. stiff.) + ‘GJ)(wood)

‘r(composite section) = (~) (~m. stiff.) + ‘E1)(wood)

For simplification the identi~ing subscripts can be expressed as

A aluminum stiffener

w wood

Then

1A - cAtA3

E

&&m&

...3

c- -

mlNACA RM L5~4 33

where /

CA chord of stiffener psrallel to model center ltie, ti.

tA thickness of stiffener psrallel to model center line, in.

JA ’41A

117s K1ct3 - lA= 0.0377ct3

JW = 4Q

Ax spanwise distance

- 1A

of effective root from fuselage, in.

In figure 22 is illustrated a comparison of the experhental varia-tion of a/T with exposed span with the calculated variation for threedifferent locations of the effective root. The calculated values forb= O overesthate the twist considerably, particularly nesr the wingroot. The agreement is considerably improvedby the use of the effec-tive root location from equation (29) (h= 2.7). AE mentioned previouslythe method of attachment of the whgs to the fuselage may permit appre-ciable movement of the wing root. Because of this fact, the effectiveroot location which gave the best agreement with the experimental datawas the one upon which the calculations were based (M = 1.9). Theoverall agreement is excellent between the experimental data and thecalculated values when based upon the root located at Ax = 1.9.

The foregoing description illustrates the general procedure followedin all of the cases presented. This procedure was necessitated becauseof the extreme difficul~ involved h the procurement of the desiredstructural values experimentally. The variation of a/T with span aspresented is relatively easy to obtain and serves as an expertientalcheck upon the validity of the structural assumptions. The values of thestructural constants thus calculated at the midpoint of the exposed spanwere used in the estimation of the effects of aeroelastici@.

The test whgs of case 33 were not homogeneous but, with the excep-tion of the extreme tip region (k > 0.2), the variation of GJ/EI and

c4/GJ from amem value was less than ~10 percent across the span andsuited for use in equation (49).

L:.:.._3

f-

NACA RM L531114

where at M = 0.8

~= M= 3./@ — (from flight data)144 ~2

AR = 3.4

~ = 43.8°

L& = 1“9‘i” = 0.145 (fig. 22)13.148 in.

Cza— = o.115 (fig. 10)%c~

k S$lil.....,-~--e .,. -,f - :, +-,

. . . . . . . .. ‘, :...’ ”.,S%sL.&.

——

NACA RM L531314

A= 0.44

35

~ = 0.62

kR = 0.19

GJ— = 1.30EI

1

~k

1

calculated

—= 0.0874GJ

J1A~kdk= 0.0375 (fig. 4

kR c

/

1B ~k W = 0.0402(fig. 6

kR c

J’1C ~k dk = 0.0140 (fig. 8

kR c

[

1D; kdk = 0.0130 (fig. 6

kR c

J’1

~kdk= 0.387 (fig. 3kR~ c

$Values obtained by cross plotting

AA 1~= 0.102 (fig. 5)

B

1—= 0.161 (fig. 7)Ak Values obtainedby cross plotting

m—= 0.078 (fig. 9)m

m—= 0.080 (fig. 7)& k’.-.’.. .. . . . . . .

--- .,-. .

A>. ,, .,. .- ..G “d—.— — -.—-

.- —_—— _—-. —- ——

36

t Tcom--

--- -J-----*-

A4=.NC%= (0.145)(0.102)= 0.Olk-8

LB =&g= (0.145)(0.161)= 0.0233

AC = Ak & = (0.145)(0.078)= 0.0113

m=m~= (0.145)(0.080)= 0.0u6

J

1

[

1

J

1A~k&= A~kdk -LA

me *C k@$

=0.0375 - (0.0148)(0.57)

J

1

J

1

/

1B~kdk= B~kdk-AB

&c %’ k~

= 0.0402- (0.0233)(0.387)

= 0.0140- (0.OIJ-3)(0.387)

= o.ol~ - (0.0U6) (0.387)

NACA RM L53m4

~kdkE

= 0.318

~kd.kc

= 0.0312

~kti

= 0..0096

gkdkc

= 0.0085

mL-. ..“’3.... ...-------—

NACARM L5~4 37

S~stituting into equation (49) gives at M =

1 -9= H-(3.80)(102.1)(0.0874) 2.20-0.00025

0.8,for example

( )]- 0.00624 ‘~ -f

r4.070.00374- 0.0@5@)jl=-33.9~.015H2 +0.020%7@)j

Method l.- Estimation ofdata. Prom test of case

effect of aeroelastici~ based upon fl~ble-33

=0.135 at M=O.8

then

1 -~ = 0.k39 or q = 0.561

If it is necessary to estimate the loss in rolling effectiv~nessand rigid-wing values are available, the procedure advocated is asfollows:

Method 2.- I?comestimated rigid-wing values based upon case 32

at M=()

0.8, ~ = o.051 (ba= )ld normal to hinge axis ; sweep of

raileron hinge axis ~ 38.8°; bu (p=allel to model center line) =

10° cos 38.8° = lOOX 0.77’= 7.7’O

()pb/2V = 0.051 _0.00663 radMn/deg = 0.379 rad/rad

5 ~ 7.7

——..—.—. — —. —-— .——. .—

38

Substituting for()

pb/2V into equation (Al) gives~f

NACA RM L5~4

(A2)

1 -~= -33.91~.015772 + (0.020867)(0.379)~ (A3)

Solution of this equation gives q . 0.636.

The difference between the values for q obtained by the two methodsis well within the estimated experimental error of the data.

.

NACA RM L53~4 39

APPENDIXB

CCEE’ARISONOF SOME EH?ERIMEWKHX DEWEFMINEDSTRUC’IVRAT

WITH THOSECALCULATEDBY APPROXIMATEMEITtODS

Cmsms

During the course of this investigation, it was found necessary toconstruct several specis3 test panels in order to obtain structural dabfor design purposes. These were sup@emented with a few additional testpanels primarily designed to indicate the lhits of applicabili~ of theapproximate formulas used in determining the structural constants c4/GJand GJ/EI for use in the aeroelastic calculations. The results of thesetests in conjunction with the calculated values are presented in table IVin the hope that they ~ prove useful to other investigators operatingunder similar circumstances.

The experimental values were obtained in the follm mmner:

EI.- The test panels were simply supported at the ends and a con-centr~ed load P applied at the center. EI was obtaiued from therelationship

p23

‘=mx

where

P applied load, lbs

1 distance between supports, 28 in.

5 maximum deflection of test panel, in.

The load P was applied on, and the deflection b was measured atthe flexural axis of the beam whi-chwas obtained by specisl tests (approxi-mately 0.45c ~ O.1OC).

GJ.- The test panels were rigidly clsmped at one end and a torque Twas a~lied at the other end. GJ was obtained from the relationship

GJ ‘z=—e

_——— _— —— ———...—— .- —

40 fi,- coNFm-

where

T applied torque, in-lb

e angle of twist, radians

1 distance between root and

The calculated values were obtainedtrated in appendix A. In additio~,

. . -dNACA RM L531D4

point of twist measurement, 28 in.

in a manner similar to that illus-most of the test panels employed

metal inlays set into the surface of the wood. The stiffening effectof these inlays in both bending and torsion was determined assuming thatthe curved inlays could be considered as flat plates whose distance fromthe chord plane was equal to the mean effective distance of the curvedinlays from the chord plane where

()1/3

J

x y3~

Mean effective distance = 0 ~

EI.-—

‘(composite) = ‘(stiffener) ‘=(corestock) ‘E1(inlays)

where

Sk&2d)l(inlays) = ~

where

Ci chord of inlay, in.

‘1 twice mean effective distance of outer surface of inlay fromchord plane

‘+2 twice mean effective distance of inner surface of inlay fromchord plane

by.-..

co ‘----.---_.%---

NACA RM L53m4

l(corestock) = 0.03~ct3 - I(stiffener) - l(inlay)

Q. -

‘(composite) = ‘(stiffener) ‘GJ(corestock) ‘GJ(inlay)

‘here ‘(inlays) is computed assuming that the inlays make up two of the

opposing sides of a hollow rectangular section. (This equation is fromref. 2 with the symbols altered to conform to those used in the present.paper.J

J= %(%- J2(%-42cit -i-dltl - t2 - t12

where

tl1

1.*

IIt ‘TI I-T

IItll+- Chord plane lld2II

I — — [-r+%-1’IIIIJ I I

~ Ci

t = tl = thiclmess of inlay, inches

. .—— —.————.Z —

42 NACA RM L53H14

1.

2.

3.

4.

5.

6.

7.

8.

REFERENCES

Zender, George W., and Brooks, William A., Jr.: An Approximate Methodof Calculating the Deforwtions of Wings Having Swept, M or W,A, and Swept-Tip Plan Forms. NACA ~ 2978, 1953.

Rosrk, Raymond J.: Formulas for Stress and Strain. Second ed.,McGraw-Hill Book Co., lhc., 1943.

Strass, H. Kurt, and Marley, lklwsrdT.: Rolling lMfectiveness ofAJ.1-Momble Wings at0.6 to 1.6. NACARM

Anon.: Design of WoodNavy-Civil Comittee

Small Angles of Incidence at Mach Numbers I!romL51H03, 1951.

Aircraft Structures. ANC Bulletin-18, Army-on Aircraft Design Criteria, June 1*.

Slrass, H. Kurt, Fields, E. M., and Purser, Paul E.: ExperimentalDetermination of Effect of Structural Rigidi@ on Rolling Effec-tiveness of Some Straight and Swept Wings at Mach Numbers lWnn 0.7to l.~. NACARML50G14b, 1950.

Schult, Eugene D., Strass, H. Kurt, and Fields, E. M.: Free-FlightMeasurements of Some lHfects of Aileron Span, Chord, and Deflectionand of Wing Flexibility on the Rolling Effectiveness of Ailerons onSweptback Wings at Mach Numbers Between 0.8 and 1.6. NACARM L5~6,1952.

Strass, H. Kurt, and Marley, lMward T.: Rocket-Model Investigation ofthe Rolling Hfectiveness of a Fighter-me Wing-Control Configura-tion at Mach Numbers l?rom0.6 to 1.5. NACA ~ L51128, 1951.

Strass, H. Kurt, Fields, E. M., and Schult, Eugene D.: Some Effectsof Spnwi.se Aileron Lacation and Wing Structural Rigidi~ on theRolling Effectiveness of 0.3-Chord Flap-Type Ailerons on a TaperedWing Having 63° Sweepback at the Leading IHge and NACA 64AO05 Air-foil Sections. NAcARML51D18a, 1951.

NACA RM L55D4 43

1,23-89-1314,15

16,17

18-20ZL-23

24,25Z6,27

?8,29

30,31

32,33

34-36

TABLEI.- GEOMETRICCHARACTERISTICSOF TESTWINGS

o

4;45

45

454545

i;

20

48

61

A

3.73*73*78.0

8.0

4.04.04.04.03.0

5.9

3.4

3.5

A

L.00L.00L.00L..00

.50

.60

.60

.60

.60

.50

.47

-.44

.25

ki

2.19.19.19.13

.13

.14

“?7.14.14.68

.70

.62

.50

1.01.01.01.0

1.0

1.01.0

● 571.01.0

1.0

1.0

1.0

1.2.2.2.2

.2

:;●3.3.25

.2

.2

.3

aCase 19 previously not reported.

NACA airfoilsection

65A00365Ao0965Ao096~AoL2

651A012

65AOG565Ao0665AOC665A006

000X-1.1638/1.14modified); 9 percentat root, 7 percent

at tip64-OXX normalto 38 percent c;11 percent at root,8.~p~~enl tip

to 38 percent c;11 percent at root,8.28 percent at tip

64AO05

Reference

555

Unreported

Unreporteda6

666

7

Unreported

Unreported

8

q!g?:,m—._.——. — —. -——.__——

44 NACA RM L5~4

TABLE II. - m?smmrIol?ALcmwmKmMc2cF’1’mr wltios

ri&picalae.tion thrOu@ wingat mid-span.All

–dimensiom areinincheaI

1’ Core

* ‘ Chord-plane

stiffener

Material of Construction Number of

cse c

core

q/c C.Jc J+/Cu 13J/EI nminally

stiffener identical mdel.a

1 mne Rme

2,7.07--- --- 0.ol~ 1.43

A.lum%aloy1

I?one lime 7.07—-- --- .05461.45 1

z 0.u6°%=d~ Spl-ucerfone ~.q0.10.8 .lx671.W 3None 7.q .1 .8

5.ol~ .p 1

mule6

Hhitepine Hone 7-07------- .G579 .25 10.01steel @-- Hone ?.q .1 .8

7.Olcx).& 2

Iione None8

7.07------- .0371.25 2I?one Whitepine rime 7.07-–- --- ;~tix~.:

91

0.02steel None 7.q .1 .8 210 ITone E.9ech r?one 7.07-—- -- .0377 125 1u. O.o1EM Spruce h ~.q .1 :: .0093 .& 112 0.016ti~ ~ spruce Rone 7.07.1 .oIG1.59 213 None Whitepine None -—---- .0750.25

::2 -------2

14 None Alumimm S.llOy None .CH)1O1.45 115 0.010ew -e 0.(%3allmllllmUoy 4.66.1 .8 .M30.83 116 Rone -------

~~e o.d3al= dlOY ::2 .1 .8.m 1.43 1

17 0.010steel .Oom .85 118 O.dlosteel me o.125allnninwl@-lloy:.g :15.7 .Oom .* 119 I?One Al~ alloy mu ..—--- .a)791.45 120 none -h o.~ allmilllmalloy8.B ------- .1070 .47 121 O.chosteel 2pruce o.125sllmllllmalloy8.~ .19.7 .ti .g9 122 fine Allmllllm.J.10y Hone 8.99------- .~ 1.45 123 Xone wlllogauyo.125eluminumaoy 8.$B------- .L2Sa .46 12b O.ckosteel Spmce 0.125sl~ aoy 8.s .15.7 .mm .* 1v None 2.eecb o.125e.lllmlmmw.oy 8.~ -----– .1070.47X

1tie AlvDinlnnelloy 8.99------- .W79l.kp 1

27 Wne MahO~ 0.125elnllmmalloy8.s-------28

.12m .46 1o.c&steel m- O.m dm!llmmalloyU.37 a a .0039.gl 1

w None Whogmy o.l&aluminum& 11.37--— --- .0931 .31 1w O.ckosteel o.1.&C1.tdnlmem.oy5.85 .1 .8 .ocQ .9

=1

51 None o.~ alundllumamp 5.85------- .d23 1.29 1P O.w steel Spruce O.= aluudmlmellOY7.77 .1 .8 .@7 1.03 133 None spruce3$

0.125el~ w 7.77—----- .oow1.N 1Hane steel m 7.69------- q 1.43 1

35 Hone35

Mlml.lmnalJDy 7.69------- .01361.450.1%3al= ~

1fine l?eech 7.69------- .24m .39 1

acl/c cd c2/c w withspan- aeerefer-e6 fordetaile. ‘-J$&$’bw-p~e stiffeners~= -seereference6 for detaIM.%mrd-plane d.iffener slott.d - see appedix AforWteilE.

L) ------

. . . . . .. .. .

J“-. .’, jd“~

45NACA FM L53~4

TABLE III.- A2s’OMm AmomEAmc cmmmammcs OF TMTWINGS

—.

MpI+f31+2Cases28@ 29Ca9ealand2 C!asea18 to 20

—).6.7.8.9L.OL.2L.kL.6—I

).63.98.7 k.k7.8 4.67.9 4.80L.O4.40L.2 3.58L.43.07L6 2.65

0.49.47.43.31.22.16.16.16

0.20.20.20.100000

-0.02-.02-.02-.18-.40-.ko-.40-.40

I

----3.413*583.843.442.872.752.66

----0.60.56.43.26.24.24.24

----0.20.20.100000

----0.02

-:%-.3.5-.35-.35-.35

----3.413.583.&3.442.872.752.66

----0.63.57.53.27.24.24.24

----0.20.20.100000

-----00-.).6-.38-.38-.38-.38

—

).6.7.8.9L.OL.2L.4L.6—

Case630end31

).6.7.8.91.01.2L.41.6

3.754.27;.&l

4:223;48;.C$.

0.41.%.32.27

0.20.20.20.100000

>.6.7.8.91.01.21.41.6

----3.41;.g

3:442.872.752.66

----0.60.56.43.26.24.24.24

----0.20.20.100000

----0.02.02-.14-.35-.35-.35-.35

2.6.7.8.91.01.21.41.6

3.350.333.63 .%3.91 .=4.18 .283.74 .172.97 .132.73 .132.63 .13

0.20.20.20.100000

-O.(E-.@-.02-.18-.40-.40-.40-.40

-0.02-.02-.CX?-.18-.40-.40-.40-.40

Cases24& 25—0,6.7.8.91.01.21.41.6—

----3.403.603.803.402.902.7’22.68

----0.46

.44

.31

.17

.16

.16

.16

----0.20.20.100000

------0.02-.(E-.3.8-.ko-.40-.ko-.40

I

0.6;;

.91.01.21.41.6

----3.413.%3.@l3.442.872.752.66

----0.60.56.43.26.24.24.24

----0.20.20.100000

----0.02

-:$-.35-.33-.35-.35

0.6.7.8.91.01.21.41.6—

----3.043.173.253.00:.g

2:46

----0.43.39.30.20.15.15.15

----0.20.20.100000

-------0.02-.02-.IJ3-.40-.40-.40-.40

Cases26end27 caEIes34t035Ca6es14and15

T

3.530.370.203.70 .33 .=3.85 .% .203.9 .28 .103.% .1702.75 .16 02.16 .16 0---- ---- ----

----0.20.20.100000

----“o.@

.02-.14-.35-.35-.35-.3:

0.6 ----.7 2.!%.8 3.15.9 3.411.0 3.281.2 2.7’71.4 2.501.6 2.341

0.6 3.78.7 3.*.8 4.22.9 4.571.0 4.101.2 3.191.4 2.e41.6 2.70

0.6.7.8.91.01.21.41.6

-0.02-.02-.02-.lt-.4C-.4C-.4C----- 11

----------—3.600.20 0.02.56 .20 .02.43 .10 -.14.26 0 -.35.22 0 -.35.22 0 -.35.22 0 -.35

----).60.56.43.26.24.24.24

Cases16end17—

0.6.7.8.91.01.21.41.6

-0.02-.02-.OZ-.1[-.4(-.4(-.4(----.

0.20.20.20.10000----

3.533.703.853.93.50

%----

0.37.33.32.28.17.16.16----

.

———. ———_. —.. ——— .—— —

46\“

--Cmmll.’ “,”

,,: .,’ -:- -‘ -. +:*-.AT.-.A,*;......*;. . -. --

NACA RM L53EL4

TABLE-ZIZJ_7RUClL!If?ALCQtXA/UZJFORA VLIPlfTYOFTYPESOf WINGCOA$L?UC7/O/Y

72s/paLt.-/

/

2I

3

4

r./25alum.Ji+ffezw

//- .azoJ-?&/ /ti/uy

Pa====7-

Wood grain45° /0 L.f.

I

Airfoi/ =cfion

ti/AO/2

65AO09

65AO09

65AO09

65AO09

65AO09

65AO09

65AO09

65AO09

65AO06

.09s/Qb

65A009

[>

7-x/o83’9

42’5

709

/?’07

376

233

/03

4a

474

/56

639

/?2

~rlmt

7X/6882

488

8/0

/76

324

90

39

496

557

/90

625

4/

‘0/

5

6

7

8

9

/0

//

/2

Nofe ’ Core /> mahogany ; c = Z07/ inches ; all dlmen~ions are M Inches.

~

&.@L05

/./5

/.15

B5

.86

39

.%

/./7

L27

L22

98

1.87

7XI0.9/9

456

854

227

40Z

250

/23

461

466

/66

586

—

‘cu/a,

Vx/0885

473

4003

/73

386

/63

S’3

483

49/

/89

640

!aJ

/04

/./8

.76

.96

.65

.27

/.05

M5

/./4

/09

—

-.Z31

NACA RM L53m-4

—}. / I,.

t!lT

7

1-”1

Figure 1.- The configuration considered in the structural analysis, showingplanes of action of applied moments.

.— -—. .—— — —.— —

48 NACARM L531114

4

+----+

<

<

l--

\,\

Figure 2.- The configuration considered in the aeroelastic analysis.

NACA RM L53~4

,4

,2

,0

.6

.2

.6

.4

.2

I

—

—

——

—_

(a) kp =0.4.

a-Loo.75.50,25

0

:/. 00i .75.50

..25

0

0

0 ./ .2 .3 .4

@oof correction k’cremed, Ak

Figure 3.- Root correction factor for nondimensional rolling moments.

-

.— ——— .—— —.. —. —-. ——

50

f A # kdk

NACA

.081 I I I I I I I I I I I I I I I I IA I

.04BI

o .2 .4 .6 .8 Lokj ; kO

(a)kp =0.4../2 “

.08

-4##Ha1 1 I I I , 1 1 1 — 1 1 “ . ,

0 ..2 .4 .6 .8 /.0k,”j kO

@kp =0.2.

.20

./6 I I I I I I I IN I I I I I I I/.:0, , , , I , , , I . 1 , I a , ,ffm-.

A###d.08Il$EM

RM L’53rn4

.04

0 .2 .4 .6 .8 LO

Figure 4.- Nondimensional rolling moments resulting from the deformationscaused by the torques of the aileron loads about the elastic axis.

kdkat~.

NACA RM L531U4 51

.6

.4

.P

o0 2 .4 .G .8 10

.4,4’0

(a) kR = 0.4.

.8

.6

.4

2

0

(b) ~ = 0.2.

Figure 5.- Root correction

Lo

.8

.6

.4

.Z

o0 .Z

for nondimensional angle of twist, A.

—.——— ——. . — —- -—. — -.

o

6.-“=-mn.sio=

I/ r-l--l

NACA RM L53EU4

.3

.2

./

o

.5

.3

“%?.2

.1

.2 .4 .6 .8 /.oA

/1 I l-r I I

-i’ fl-krlllllllY 1 I I I I I I 1 I I I I

/ -/ 1 I I 1’=%%=-/

1, .,1

0 .2 .4 .6 .8 /.o.A

Figure 7.- Root correction factors for nondimensional.anglesof twist, B and D.

53

.-— —. .—. —— .—.

54 NACA RM LS3EL4

A/.00

[/-.75.02

fC ~ kdk

o ..2 .4 .6 .8 Lok;j,40

(a) k-- =0.4.

A

J’C~kdk .

f C 5 kdk

04

. Eli

02

, ,I

1 I I I I I II I , 1-

0 .2 .4 .6 .8 /.0k;;ho

(b)kp=0.2.

.08

.06

.04

.02

0 ..2 .4 .6k; j k.

(c)kg =0. w

Figure 8.-Nondimensional rolling moments resulting from thedeformations caused by the aileron loads on the elastic axis.

NACA RM L~~4

Figure 9.- Root

.— -

—

(a) ~ = 0.4.

,3

o

5

.4

.3

AcA—k

./?

./

A=100

.75\

.50 \\ . \ \.

.25

0

(b) kR = 0.2.

55

0

correction

1~ko=iiki—-

(c) kR.

factor for

At!— at k+

o.

nondhensional angle of twist, C.

N!-—atk.

.—— ——— ---__- ——-

56‘i-Q&@ N.ACARM L53EL4

.24

.4?0

./6

.08

.04

Figure

and

\_

\

\\

\ \ \

\

\

\

\ \\

o .2 4 .6 .8 10

lo. - Variation of nondimensional rolling moment with spanwise extent

%81k.

C25 %8location of the aileron. — =—atki-— at ko.

~CLa ki

@La %c&

-.r.J

!hNACA RM L53rn4 57

pb2V

●/2

.08

,04

0

-.04

Experimer7t Co/cff/uted

n

.—— —.— Refereme

—- cl

o0.0/84

.0556

ITD’7777n

I I t-+ VW I I

(a)WCA 65Ao03airfoil section.

Figure 11.- Effect of decreasing wing stiffness on the variation of rollingeffectiveness with Mach number. AR = 3.7; A=OOj ~=1.oj ~a=50jki =0.19; ~ =1.0.

—.—— . . . . ——— —— .—. ——.— .—- — .—

58-.. -. .—. ”’,*-

- j CONF*-. ..-A’d. -NACA RM L53rnb

J 2

.08

.04

0

704

Experiment (22kw[0/ed

n

——— —— Refeyence

—— — ❑

—. —— 0

0.0067

.0/58

.0579

m7)/////)//

I

\1 /\ /

<“>’\I\l

5/ J ‘w

——

! , I 1 1 1

. /

)1

.6 .8 Lo L2 /4 L6

M

(b) NACA 65Ao09 airfoil section.

Figure 11.- Continued.

NACA RM L53H14 59

Experiment

——— —.

—— —

—.— —

H&f

Colcuh+ed @ A~,n o

❑ o. 0/00

o .037/

A .0603

nI I

/9////////1

.08

Pb .042V

o

i-

EHiit /4CQse‘\ 6

\ la 7‘\ I 8

% f’ / 1- ._

\,“~{~.—_ -.\ —-1 I I I I I [ I 1=$=.6 .8 10 /.2 [4 /6

m

(b) Concluded.

Figure il.- Concluded.

——. .— —.—

60

d 8

.04

pb2V

o

724

.

n o

——_ __ Reference a 0067 104

——_ El .0377 .25

x-I--F+’” “\

I I I-_

Figure 12.- Effect of decreasing wing stiffness on the variation of ro~lingeffectiveness with lhch number. AR=3.7; A= 45°; A =1.0; 5* = 5 ;NACA 65Ao09 airfoil section; ki = 0.19; ~ = 1.o.

NACA RM L53m4

.08

,04

pb2V

o

. .

n o

—— ..— ❑ 00093

—— — o .0/6/———_ A .0750

Q84

● 59

.s?5

61

II I I I1

I I I I I I

I I I I I I + I I &:04

.6 .8 /.o L2 L4 16

M

Figure 12.- Concluded.

.—. ——.. .—— —— ...— ..— — .—— —.

62 $ypf%am*.-“--

n o

——— —.- Reference 0.00/0 L45

(a) A = 1.0.

Figure 13.- Effect of decreasing wing stiffness on the vsriation of rollingeffectiveness with Mach nwber. AR . 8.0; A . 45°; NACA 651AOU airfoil

/

!1‘

section; 8a = 5°; ki=O.13; ~ =1.0.

NACA RM L53rnk 63

.08

.04

pb2V

o

-.04

n o

—.—_ .— ZPferencp 00004 1.43

—— — cl .0030 .85

[ 3

TI I I

., I

\\

\\

I 1 I I t 1

CasP“/61?

.8 .8 Lo 12 M 16M

(b) A = 0.3.

Figure 13.. Concluded.

—. .—. —— — -.. — — ——--— —.. .

64 b- .J...-—...

. . IAL“ NACA FM L53~4

/o&-27

-t”——. - ——

1ReFere ce 0.0080 0.98

—— — ❑ .0079 L45—.— — o ./0 70 .47

(a) ki = 0.14;~ = 1.0.

Figure 14.- Effect of decreasing wing stiffness on the variation of rollingeffectiveness with Mach nmiber. AR . 4.0; 4/4 = 45°; NAcA 65Ao06 airfoil

section; ba = 5°; ~= 0.3; A = 0.6.

‘1~coyIgmnQ

.-.—.- --

-. —..=

NACA RM L53HL4 65

o0.0080

.0079

./290

0.98

/.45

n

—— —_. _ Peferpnce

—. — ❑

—-— — o .47

Cu.se

.08 ~ -22

.M/////’/////////

~b {> /Zv

o\

<) \\ — . — ~ - .—

-.04.6 .8 [0 /.2 14

M =ki9+6

(b) ki = 0.57;~ = 1.0.

Figure 14.- Continued.

——— —

66 NACA RM L53HL4

pb

Zv

nu o

——— ——. . Reference Oa%lo 0.98

——cl ./070 .47

(C) ki = o.lk; ~ = 0.57.

Figure 14.- Concluded.

NACA RM L53EL4 67

pb2P

,08

.04

0

-.04

n o

—-—— -— Reference 00079 L 45

—.— •1 ./2 90 .46

Cbe

~ -26-27

(//////////////

[1 \ .-*.

[ --“

‘— __( )

\\LJ\

\\

T

.6 .8 Lo AZ M L6M

Figure 15.- Effect of decreasing wing stiffness on the variation of rollingeffectiveness with IQch number. AR . 4.0; +/4 = 35°; NACA 65AO06 airfofi

Casection; ba = 5°; ~ = 0.3; A = 0.6; ki = 0.57; ~ = 1.0.

—.— _-.-——z—— —. —-.—— -———.-—

68 L.-.4.

comE@rr NACA RM L53HL4

/obf?v

——— —— Reference 0.0CY9 0.9/

—— — •1 .093/ .3/

L2?JP

.Gw /

() //////////////

o

-.04.6 .8 [0 /2 L4 L6

M

Figure 16.- Effect of decreasing wing stiffness on the variation of rollingeffectiveness with Mach number. m = 3.0; ~/4 U 45°; ba = 5° (IIOITld

to hinge line) ki . 0.678;~ . 1.0;~. 0.25;NACA airfoil sections

0009-1.1638/1.14(modified) at the root, 0007-1.16 38/1.14 (modified)at the tip.

NACA RM L53EQ4 69

.08

0

-.04

Expemhenf Calculated

n

——— —. Ri+i%ence—— — •1

~4()GJ#~

o

00022

.0423

I

(a) ~ = 5.9; ~/4 = 20°; h = 0.47; ki = 0.70; h = 1.0.

Figure 17.- Effect of decreasing wing stiffness on the variation ofrolling effectiveness with Mach number. ba . 10° (normal to hinge

line); ~ s0.2; NACA airfoil sections normal to 38-percent chord line

(64-Oil at root, 64-08.28at tip).

——--- .— .—— -— . — .——A— . .—

70 ‘rcxmm~...‘A-—--’

NACA RM L53rn4

.08

.04

/oh

2V

o

704

n o

—— —.. Reference 0.0047 Loo—.— ❑ .0874 A30

Case

Id /////////////

El

\

(b) m = 3.4;4+4 = 47.5°;A = 0.44;ki = 0.62; ~ = 1.0.

Figure 17. - Concluded.

E.ON-FImy ‘w“..>..- .-..—-4-....*”>.

NACA RM L53ED.4 n

.08

.04

0

-.04

n o

——— .— A++rence 0.0053 /43

[ 1

❑ @ flo Wn)—-—

u’(No +wist) .0/36 /.45

—.— — o ,24(7 ,39

L2ve

I I

/

3435

—

///////////////

‘\

,

T.6 .8 Lo L2 L4 /6

M

Figure 18.- Effect of decreasing wing stiffness on the vsriation ofrolling effectiveness with Mach number. AR . 3.5; A=o.25;

&/k = 61°;NACA 64AO05 airfoil section; ba . 5°; ~= 0.3;c

ki = 0.5; ~ =1.0.

.— .—.._.—— ——

72

.04

.02

0

(-)pb% fx.-.02

-.0+

:06

\ ‘----- --”- -—NACA I?ML53EL4

Lit?& of p6rfacf corre /0 +/on

Es fimufed0 xperin7en+a/error

/

-.08 ;06 -.04 702 0. 02 .04

()pbd2?7 cQ/= .

(a) M = 0.7.

Figure 19.- Comparison of the measured change in rolling effectivenessdue to aeroelasticitywith that calculated by means of the simplifiedmethod. I?umiberinside symbol denotes test case.

k“‘ONFIDENTm--~r-—--,.,--—-,

NACA RM L5yak 73

.04

.02

0

-.04

-.06

-.08

/

()pbAZT Cult.

(b) M = 0.8. (Flagged symbol indicates that measured change in pb/2Vdue to aeroelasticity~ 80 percent.)

Figure 19.- Continued.

.—— —.. —_—_— -. — —— —.— —

74

.04

.02

0

704

-.06

b=m?i$p,-*..>

o’- NACA RM L53HL4

Line of perfe c + c orrelh?on

\

Es fimafed

expwimen falerror

:08 ;06 :04 :02 0 .02 .04

()‘$$ talc .

(c) M = O.9. (Flagged symbols indicate that measured change in pb/2Vdue to aeroelasticity ~80 percent.)

Figure 19.- Continued.

tE-5F@—-...-.

c “D -’L:,‘;‘6. “

NACA RM L~5EL4 75

.04

.02

0

708

Lineof parfec+corrdotion

Estimat%dexp~rimenfulerror

z08

(d) M = 1.0.

:06 704 :02

()pbA27 ca/c.

o .02

(Flagged symbols indicate that measured change indue to aeroelasticity? 80 percent.)

Figure 19.- Continued.

.04

pb/2V

.——. —. .— .—— — —— . .

76 NACA RM L531U4

.04

.02

0

704

706

:08 706 z04 :02 0 .02 .04

()

bAZ% talc.

(e) M = 1.2. (Flagged symbols indicate that measured change in pb/2Vdue to aeroelasticity z SO percent.)

Figure 19.- Continued.

NACA RM L53~4

.04

.02

0

-.04

-.06

-.08

Esfjma fe a’

F - @

@experlme n fal

error

10

,r

/

-.08 . :06 704 702 0 .’02 .04

()/oh’27 Cult.

(f) M = 1.4. (Flagged symbols indicate that measured change in pb/2Vdue to aeroelasticity ~ 80 percent.)

Figure 19.- Continued.

o

—- —.— —-— —-—

NACA RM L55rnh

()pb527 @x.

.04Line of perfec / corrc ‘u~!-IJ–

.02

0

Estima fedmpwim0n7%l

702error

-.04

706

-.08:08 ~06 :04 702 0 .02 .04

~@() 2V talc.

(g) M = 1.6. (F~ed symbols iticate that measuxed change in pb/2Vdue to aeroelasticity Z80 percent.)

Figure19.- Concluded.

(a) External details.

Fi@me 20. - Description or example wings (case 33). AirfoLl section is

N&CA 64-ou. at the root, 6-4-08.28at the tip norud to the 3i3-percent

chord line. (~dh=BiOnB are h inches. )

—

80 B-.>.-.....—

/ \ //

/[

At-----

(b) Details of

Y

NACA FtML53H14

L

chord-plane stiffener.

(c) !lypicalsection (gra~ng; wocd approximately normal to model centernot to scale.

Figure 20.- Concluded,

cK..*W”*:.,..,.-.,-:-----’3..,:___

lMNACA RM L53HL4

A@ &z?dem 4exwz2/a.vj tm7’qmA7

Figure 21.- Effectof grain orientation upon Young’s modulusfor wood.

of elasticity

—- ———— -— .—— -—. -—.—-

82 NACA RM L53rn4

6 x/O-4 1 I I I

5

4

3

z

/

o z

Figure 22.- Comparison of

4 6

measured and calculatedof wing twist.

8 /0in.

spanwise variation

NACA-bI@uy - 7-15-S4 -360