1、REPORT 1056THEORETICAL ANTISYMMETRIC SPAN LOADINGFOR WINGS OF ARBITRARY PLAN FORMAT SUBSONIC SPEEDSBy JOHN DeYOUNGAmes Aeronautical LaboratoryMoffett Field, Calif.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-National Advisory Committee for Aeronau
2、ticsHeadquarters, 172_ F Street NW., Washington 25, D. C.Created by act of Congress approved March 3, 1915, for the supervision and direction of the scientific studyof the problems of flight (U. S. Code, title 50, sec. 151). Its membership was increased from 12 to 15 by actapproved March 2, 1929, an
3、d to 17 by act approved May 25, 1948. The members are appointed by the President,and serve as such without compensation.JEROME C. HUNSAKER, Sc. D., Massachusetts Institute of Technology, ChairmanALEXANDER WETMORE, Sc. D., Secretary, SInithsonian Institution, Vice ChairmanDETLEV W. BRONK, PR.D., Pres
4、ident, Johns Hopkins Univer-sity.JOHN H. CASSADY, Vice Admiral, United States Navy, DeputyChief of Naval Operations.EDWARD U. CONDON, PH. D., Director, National Bureau ofStandards.HON. THOMAS W. S. DAVIS, Assistant Secretary of Commerce.JAMES H. DOOLITTLE, Sc. D., Vice President, Shell Oil Co.R. M.
5、tIAZEN, B. S., Director of Engineering, Allison Division,General Motors Corp.WILLIAM LITTLEWOOD, M. E., Vice President, Engineering,American Airlines, Inc.THEODORE C. LONNQUEST, Rear Adlniral, United States Navy,Deputy and Assistant Chief of the Bureau of Aeronautics.HON. DONALD W. NYROP, Chairman,
6、Civil Aeronautics Board.DONALD L. PUTT, Major General, United States Air ForceActing Deputy Chief of Staff (Development).ARTHUR E. RAYMOND, SC. D., Vice President, Engineering,Douglas Aircraft Co., Inc.FRANCIS W. REICHELDERFER, Sc. D., Chief, United StatesWeather Bureau.GORDON P. SAVILLE, Major Gene
7、ral, United States Air Force,Deputy Chief of Staff (Development).ItON. WALTER G. WmTMAN, Chairman, Research and Develop-ment Board, Department of Defense.THEODORE P. WRtGHT, SC. D., Vice President for Research,Cornell University.IIu6u L. DRYDEN, PH. D., DirectorJOHN W. CROWLEY, JR., B. S., Associate
8、 Director for ResearchJOHN F. VICTORY, LL.D., Executive SecrttaryE. II. CHAMBEHLIN, Executive O_cerIIENRY J. E. REID, D. Eng., Director, Langley Aeronautical Laboratory, Langley Field, Va.SMITH J. DEFRANCE, B. S., Director Ames Aeronautical Laboratory, Moffett Field, Calif.EDWARD R. SHARI, SC. D., D
9、irector, Lewis Flight Propulsion Laboratory, Cleveland Airport, Cleveland, OhioTECHNICAL COMMITTEESAERODY._AMICS OPERATING PROBLEMSPOWER PLANTS FOR AIRCRAFT INDUSTRY CONSULTINGAIRCRAFT CONSTRUCTIONCoordination of Research Needs of Military and Civil AviationPreparation of Research ProgramsAllocation
10、 of ProblemsPrevention of DuplicationConsideration of InventionsLAN(_LEY AERONAUTICAL LABORATORY, AMES AERONAUTICAL LABORATORY, LEWIS FLIGHT PROPULSION LABORATORY,Langley Field, Va. Moffett Field, Calif. Cleveland Airport, Cleveland, OhioConduct, under unified control, for all agencies, of scientifi
11、c research on the fundamental problems of flightOFFICE OF AERONAUTICAL INTELLIGENCE,Washington, D. C.Collection, classification, compilation, and dissemination of scientific and technical information on aeronauticsProvided by IHSNot for ResaleNo reproduction or networking permitted without license f
12、rom IHS-,-,-NOTICETHIS DOCUMENT HAS BEEN REPRODUCEDFROM THE BEST COPY FURNISHED US BYTHE SPONSORING AGENCY. ALTHOUGH ITIS RECOGNIZED THAT CERTAIN PORTIONSARE ILLEGIBLE, IT IS BEING RELEASEDIN THE INTEREST OF MAKING AVAILABLEAS MUCH INFORMATION AS POSSIBLE.Provided by IHSNot for ResaleNo reproduction
13、 or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-THEORETICAL ANTISYMMETRICREPORT 1056SPAN LOADING FOR WINGS OF ARBITRARY PLAN FORMAT SUBSONIC sPEEDS 1By JOHN _DEYoUNGSUMMARY,4 simplified lijting-su
14、_:face theory that includes effects ofcompressibility and spanwise mriation of section lift-curve slopeis used to progde charts with which a ntisgmmetric loading dueto arbitrary antisymTnetric angle q attack can be .found =orwings hagng symmetric plan .forms with a constant spanwisesweep angle of th
15、e ouarter-ehord line. Consideration is givento the flexible win9 in roll. Aerodynamic characteristics due torolling, deflected ailerons, and side._lip of wings with dihedralare considered. Solutions are presented for straight-taperedwings for a range fff swept plan Jorms.INTRODUCTIONReference 1 has
16、been for many years the standar(l referencefor estimating the stability and control characteristics ofwings. The lifting-line theory on which this work wasbased gave generally satisfactory results for straight wingshaving the aspect ratios considered ; however, the use of wingsweep combined with low
17、 aspect ratio has made an extensionof this work desirable. Lifting-line theory cannot ade-quately account for the increased induction effects due tosweep and low aspect ratio; consequently, it has been foundnecessary to turn to the more complex lifting-surface theories.Of the many possible procedure
18、s, a simplified lifting-surface theory proposed by Weissinger and further developedand extended in reference 2 has been found especially suitedto the rapid computation of characteristics of wings ofarbitrary phm form. Comparisons with experiment havegenerally verified the theoretical predictions. In
19、 reference2, this method has been used to compute for plain, unfiappedwings, the aerodynanfic characteristics dependent on sym-metric loading. The same simplified lifting-surface theorycan be extended to predict the span loading resulting fromantisymmetric 2 distribution of the wing angle of attacl_
20、.From such loadings the damping moment due to rolling,the rolling moment due to deflected ailerons, and the rollingmoment due to dihedral angle with the _ing in sideslip canbe determined. A recent publication (reference 3) makesuse of the simplified lifting-surface theory to find span-loading charac
21、teristics of straight-tapered swept wings in rolllind loading due to dihedral angle with the wing in sideslip.Experimental checks of the theory for the damping-in-rollcoefficient and rolling moment due to sideslip were veryfavorable. The range of plan forms considered in reference3 is somewhat limit
22、ed and aileron effectiveness was notincluded. The loading due to aileron deflection normallyinvolves excessive labor when computed by means of thesimplified lifting-surface theory; however, development ofthe theory, presented in reference 4, that deals with flap andaileron effectiveness for low-aspe
23、ct-ratio wings provides ameans by which the simplified lifting-surface method can beused to obtain spanwise loa(ting due to aileron deflection.It is the purpose of the present analysis to provide siml)lemethods of finding antisymmetric lea(ling and the associatedaerodynamic coefficients and derivati
24、ves for wings with sym-metric plan forms limited only by a straight quarter-chordline over the semispan. .Means will be presented for findingquickly the aerodynamic coefficients of simon loading due torolling, of span loading due to deflected ailerons, and ofspan loading due to sideslip of wings wit
25、h dihedral. Flexiblewings, when the flexure depends principally on span loadingas in loading due to rolling, can be included in the analysis.AbCCaCarCZ(%,CzC%1CCl C atJdr,NOTATIONwing span measured perpendicular to the plane ofsymmetry, feetwing chord, feet 3aileron chord, feet 3mean wing ehord (_),
26、 feet 3(local lift,)local lift, coefficient q_(induced drag_induceadings for the flexible wing as determined.Deflected ailerons.-Where the spanwise distribution ofthe angle a, is to be considered equivalent to antis3qnmetricaileron deflection, it must suffer a discontinuity at the span-wise end of t
27、he control surface. The loading when such adiscontinuity is present can be duplicated by a properdistribution of ant|symmetric twist. In appendix C, theant|symmetric twist distribution required by the presenttheory to give accurate span loading distribution due toailerons is found with the aid of ze
28、ro-aspect-ratio wing theorygiven by reference 4. To minimize the computation involved,it is convenient to consider both the case of outboard andinboard ailerons.1. Outboard ailerons.-With m=7, three different aileronspans can be conveniently defined for the outboard ailerons.For the aileron spans n_
29、, measured from the wing tip inboard,the ant|symmetric twist (|istribution required per unitdeflection of full-wing-chord ailerons, _/8, is given by_aseor_a 3I0.1691.003.0t7.006II0. 4440. 971996 014ol0, 998 I(s)IJ_board aileron._.-With rn= 7, three (lifferent aileron spanscan be conveniently defined
30、 for tlw inboard ailerons. Forthe aileron spans _, measured from the wing midspan out-board, the antisym_metric twist distribution required per unitdeflection of full-wing-chord ailerons, a,/_, is given byCase_aor Ioe3IV0. 5560. 044-.017I, 0870.8,310.013 96t1. 095vII.O001.0169791 101(9)Sideslip of w
31、ings with dihedral. For calculating the roll-ing moment caused by dihedral angle for the sideslippingwing, the effect of the skewness of the vortex fiehl in alteringthe effects of the dihedral angle will be assumed to be small(as assumed in reference 3). The problem then simplifies toProvided by IHS
32、Not for ResaleNo reproduction or networking permitted without license from IHS-,-,-THEORETICAL ANTISYMMETRIC SPAN LOADING FOR WTN_GS _ OF ARBITRARY PLAN FORM AT SUBSONIC SPEEDS 13finding tile rolling mon!ent due to ant isymn_etric angle ofattack with tile unskewed vortex field. The solution to thisp
33、roblem is the same as for the ailerons which has aheady beensolved.The antisymmetric distribution of angle of attack for thesideslipping wing with dilw(hal is given by(10)whereo_ effective angle-of-attack distributionangle of sideslip measured positive in the counterclock-wise direction from the phm
34、e of symmetryF dihedral angleThe wing parameter Y is not affected by compressibility.Equation (10) is approximate for small values of _ and I.For unit flF over the span of the ailerons considered,_I_=(i (11)can be substituted for“ 6 in equations (8) and (9).APPLICATION OF METHODFor the eases of anti
35、symmetric angle-of-attack distribu-tions resulting from rolling, aileron deflection, or sidesli I) withdihedral, it is possible to present a set of simultaneous equa-tions which are required for the solution of the load distribu-tion for an arl)itrary plan form. With the loading known,integra.tion f
36、orrnulas can be given to determine aerodynamiccoefficients.The loading-distribution coefficient Gn determined fromthe soh|tions of the simultaneous equations, are functions ofp, which has been shown in a preceding section to be afunction of wing geometry, compressibility, and section lift-curve slop
37、e. The aerodynamic c()emcients are integrationsof the load distribution and, therefore, will also be a functionof wing geometry, compressibility, and section lift-curve-slope parameters. Application of the method to the generalsolution for arbitrar 3, chord 2.In using da/da here, it should be nated
38、that the assumption is made that the effeetivairfoil section is taken as being paralh,l to the plane of symmetry and that the sect!onapproaches a two-dimensional section The validity cf this assumption can be questionedhowever, imlted checks with experiment show it to be at least approximately corre
39、ct.Theory -d_4 .08 . IBJ, !/Jel,ronge gop- -I0 to I0 _eo/ed- 0 to 20 seoled“ -I0 to I0“ open0 .16 ,_0 .24 28 32tFV;IRE 3. Variation of lift-effectiveness parameter with aih, ron chord ratio, t_. Averagetrailing-edge angle about 10; _/-_ped that applies to each givenaileron span. Equation (C10) and t
40、able C5 give(2+where for each of the cases of equations (18) and (19) iheh, values are given byI Case I II IIl IV V VI. -0, 70-7, i /_ 1+I I +I_, “199 _ i :196 :_0_ 197 9S(b) Conslant fltwtion oJ wing-chord ailerons.-For constantfraction of wing-chord ailerons with aileron angle measuredparallel to
41、the plane of symmetry, the aileron effectiveness isgiven by_Ca-da(_Cn_ (21)(c) Arbitrary spanwise distribution oJ aileron chord.-Thedeflection of ailerons for which t varies spanwise on thewing can be considered as an equivalent wing-twist distrit)u-tion. The effective antisymmetric twist of the win
42、g isgiven byda_ (22)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-THEORETICAL ANTISYMMETRIC SPAN LOADING FOR WINGS OF ARBITRARY PLAN FORM AT SUBSONIC SPEEDSwlwre dc_/d8 is now a hmetion of spanwise position. Theanlis3-mmetric angle-of-attack distri
43、bution given l)y equal ion(22) can be divided into spanwise steps of constant angle ofattack and the total rolling moment can t)e found t)y thesummation of the rolling moment due to ewh _panwise step.The rolling moments of the spanwise steps are obtained froma curve of rolling-momcni coefficient 13C
44、6/K,_ as a functionof unit antisymmetrie angle of attack hom the wing root.outboard. This step method is the procedure used inreference 1.A curve of _6/_ as a function of unit anlisymmetrieangle of attae obtained from the solutionof ease III of equation (18), applying the relations (dis-cussed later
45、) existing 1)etween int)oaM and outboard ailerons.The rolling moment due to the twist given by equation (22)can be obtained, by a method otlwr than the step method,from the integral given byK_. _. d5 (ln - dn (23)which can be integrated numerically by taking the graphicalslopes of 13Csa/K,o which is
46、 a function of extent of refit anti-symmetric angle of attack from the wing root outl)oard.4. Spanwise center (_ pressure and induced drag.-Spm-wise center of pressure and induced-drag integration formulasfor loading due to ailerons are not given; however, equations(16) and (17) can give approximate
47、 integrations of the load-ing to obtain center of pressure and induced drag.5. Additional consideration._:(a) Rehttion between aerodynamic characteristics for out-board and .inboard alleron.-The spanwise loading distribu-tions due to outboard and inboard .dlerons bear a simplerelation to each other.
48、 Since loading is linearly propor-tional to angle of attack, loadings are directly additive.Then, for outboard and inboard ailerons with the spanwiseends of the ailerons at the same span station,Gmho_m= G (_= l) - G,mb,a,l )Ct_ = C5 - C%utbo_rd (24)inboard (_a = 1)r/ainboard _ 1 - 77aoutboardThese r
49、elations do not apply for v_.,. and C_)_ since thesecharacteristics are not Iinearly: proportional to loading.(b) Differential aileron, a_gles.-The effect of a differentiMbetween aileron angles can be taken into account by con-sidering the C_5 of eqeh wing panel as one-half the antisym-metric results of equations (205, (21), or (235. The totalwing
