The effectiveness of rotating ailerons in a subsonic flow is theoretically studied to evaluate their capability in comparison to conventional ailerons. The analysis is based on the cortex lattice approach of Byelotserkovskii (1965) for different wing planforms of small and large aspect ratios. The rolling moment coefficient obtained with the rotating ailerons with a span equal to 22% of the wing span is higher than that for the conventional ailerons of almost double the span. The effectiveness of the rotating ailerons decreases with reduction in the wing aspect ratio, although it is possible to reduce the aileron size for required rolling capabilit

Mozumdar, S

Patel, TS

English

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Investigation on rotating ailerons

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INVESTIGATION ON ROTATING AILERONSS. Mozumrlar* and T. S. Patel**Departmentof AeronauticalEngineeringIndianInstitute of TechnologyBombay, IndiaABSTRACTThe effectiveness of rotati.lg ailerons in a subsonic flow has been theo-retically studied here with a view to evaluate their capability in compa~i-son to the conventionai ones. The }>resentanalysis is based on the vortexlattice approach of ByelotserkovskiiB for different wing planforms of smalland large aspect ratios. The effect of such ailerons on the coefficients oflift and rolling moment has been worked out for their positions corres-ponding to the most suitable positions of rotating flap...IntroductionAn efficient control surface is of particularinterest to an airplane designer. The presentproblem of investigiotion about the feasibility ofrotating ailerons is directed towards an engi-neering solution of improving rolling control ofan aircraft in the subsonic flight regime.Some aerodynamic properties of autorotatingor forcibly rotated cylinders and aerofoils wereinvestigated even prier to the beginning of avi-ation. The following two important properties ofa profile revealed by simple earlier experimentssuggested their promising application in aircraftdesign:1.Ability to autorotate,andZ.Ability to createforce normal to the axis oftherotationandfree-stream velocity.The rotating profile as a lift augrroentingde-vice seems to be one of the possible' aids aboutwhich some workl-7 is already'available in lite,-rature. The concept of rotctting profile as controlsurface elements arose bom thesuggestioRsmade by Crabtreel and NeumarkZ. The 'presentwork,deals with an.estimation of effectiveneSSof'rotating ailerons for ciiffere~t wing planformsusing linear lifting surface theory of Byelotser-kovskii 8.'" Senior Research Scholar (Now at NationalAeronautical Laboratory, Bangalore as Scientistin Aerodynamic Division).** - Assistant Professor. ~. Received Feb. 1978; revision received Sep.9, 1978.Formulation of the ProblemLet us consider the wing as a thin liftingsurfa~e with rotating ailerons placed in an in-compressible fluid flow. In general, the uniformundisturbed flow may be given by ~Fig.l):U 8:Uo cos a.; (1)V;!l'Uo sin a.where Ii and v are the velocity components alongX and Y axes respectively.u.'\i yz.4 3. ~8,/}l8';N.~~8,."/}l8 2: )/ 8 2-}l8 3'-~83'::P84r. ~84(x..,..~. )''I'ira,!}6.-\A,t!IISECTION A AIFig.I. Vortex lattice model of the wing with ro-tating aile ronsIn the present model the wing is replaced bya vortex sur~ce as in the case of linear liftingsurface theory of Byelotserkovskii8. The liftingvortex sheet is then approximated by a series ofn equally spaced bound vortices along its span,the number of which could be as large as practi-cable. Each of these bound vortices is furtherdivided into N elementary pieces by the sections12 JOUR NAL OF AERO. SOC. OF INDIA VOL. 32parallel to the root chord so that the elementaryvortices in the inboard region of wing are longerthan those in the outboard region as was done inthe Multhopp's lifting surface theory9.Then, the spanwise positions of those N sec-tions on the wing may be written in the formzp = (b/2) cos (plT/N) . (2)wherebpis wing span;is an integer varying from 0 to N (p=N/2indicates the root chord section).The free vortices from the tips of these ele-mental bound vortices so formed are assumedto be in the plane of the wing, trailing parallelto the plane of symmetry. The rotating aileronsare replaced by a pair of horse-shoe vorticesof given circulationsl,2 having the same magni-tude but opposite sign. The bound part of thesevortices lie along the axes of rotation of theailerons. The trailing vortices are assumed toremain parallel to the trailing vortices of themain wing.The unknown distribution of the strength ofthe elementary vortices representing the wingsurface is determined by imposing the boundarycondition that the res ultant velocity componentnormal to the wing surface doe to the wing vor-tex system, ailerons and the freestream shouldbe equal to zero. This condition is S'atisfied atselected pivotal points on the wing. The positionof the mid-point of each of the bound vortex ele-ments of the wing and the pivotal points are shownin F ig.l. The notation used is as follow s:k serial number of the strips parallel to rootchord(1~ k" N);serial number of bound vortex lines distri-buted along chord (1~ fL ~ n);serial number of the lines on which theboundary condition is satisfied at selectedpivotal points (1~ II ~ n);serial number of the oblique horse-shoevortex (1~ i ~ Nn);serial number of the pivotal points (1~j~Nn).fJ.1/Let ki, kj be the values of k correspondingto the values of i and j. We have theni =kit(fL-1 )N; j =kjt(V-1)N . (3)Here the chord is divided into n equal seg-ments. Each of the elemental surface formed byspanwise and chordwise sections is representedby the Weissinger's model namely. the elementalbound vortex placed along the quarter-chord line "Eof each elemental surface and the pivotal pointfor each elemental surface is located at the mid-point of its three-quarter-chord line. With suffi-ciently large value of n this distribution of vorti-ces and pivotal points practically satisfies Kutta-Joukowsky condition at trailing edge.The coordinates of the mid-point of the i-thelementary bound vortex (xi, Yi, zi) and those ofthe j-th pivotal point (xjoyj. Zj) on the starboardwing will then be given by the following relations:1czil)Czixi=Xoi+4n+(fL- 11'3c . c 'x. =x '+-4~t (V-1).:3.J OJ n n 'Yi =yj =0 ,zi=~[:os(i-(fL-1)N)Ntcos(i-1-(fL-1)J NJZj=~[cos(j-(V-1)J N+cos{j-1-(V-1)]N]wherlczi' Czj wing chords on which the points i and jare located respectively;projections of the leading edges of thesections with the chords czi and Czj onX axis respectively.xoi' XojThe values of zi and Zj on the port side wingwill be the same in magnitude but different insign. The coordinates xi. Xj. n, yj will be thesame as those for the starboard wing. The semi-span of i-th elementary bound vortex is:si =~[cos li-(fL-1 )N] N -cos ti-I {fJ.-1)N] ~JKnowing these geometrical details the in-duced velocity components at the pivotal pointsdue to all the wing vortex elements together withthose of rotating ailerons could be obtained usingBiot-Savart law for induced velocity or from thecorresponding relations for an oblique horse-shoe vortex 1°.The boundary condition to be satisfiec;l overthe wing surface at selected j points will begiven byDo sin at Vjy =0 ,where Vjy is the velocity component at a point j,normal to the wing surface, induced by the systemof wing vortices and rotating ailerons. The valueof sin a may be taken equal to a in radian if theangle of attack considered is very small.(4)(5)(6)I..~.~....-....'.. ~".'..:FEB-NOV. 1980- .', .~;": f'~;J, '.i;"~ .?l ., If Vljy is the Y -component of the induced:t" velocity at a Roint j due to the i-th elementalvortex then. e~idently.INVESTIGATION ON ROL~~ING AILERONSNnVjy = ~ Vijy .i=I (6)Solution of the ProblemIt is obvious that we are dealing with anti-symmetric load distribution on the wing arisingout of operation of ailerons. Therefore. theBoundary condition (6) is satisfied at all Nn pivo-tal points on the wing surface. This conditionthen results into a system of Nn Unear algebraicequations which are solved simultaneously usingGauss Sideal method and all Nn unknown vortexstrengths on the wing are determined.Aerodynamic ForcesThe lift L endrolling moment Mx producedby the main wing and rotating ailerons are com-puted using Joukowsky's theorem. The lift androlling moment produced by main wing alone willbe given by the following relations respectively:NnLw =PI. 2Siri(Uo cos a.+wxi)cOS a. .i=I(7)NnMxw=-Pl. 2Sirizi(Uocosa.+wxi) .i=Iwhere Pis density of air and wxi is the x-compo-nent of velocity at a point (xi. Yi. zi) on the winginduced by the wing vortex system and ailerons.The resultant lift and rolling moment forthe complete systemof wing and ailerons aregiven byL =Lw+La ; Mx =Mxw+Mxa ' (8)where for ailerons we haveLa =ZPfa.sa[(uarua-) cos a.+(va+-va-)sina.) .Mxa =-2prasa(ua++ua-)za .(9)where (ua+'ua-) and (va+'va-) are the velocitycomponents chordwise and normal to the wingsurface at the mid-points of the axe~of up-goingand down-going ailerons respectively; sa is ai-leron semi-span; za is the distance of the mid-points of ailerons from rolling axis. The cor res -3ponding aerodynamic coefficients may be expre~sed in the following form:2L .CL =pu~S'4M.2L,Crnx =U2Sb '0 (10]where S is the planform area of wing.Numerical CalculationsCalculations of the above aerodynamic coef-ficients for various wing planforms at differentval~s of angles of attack and rotational speedof ailerons have been carried out on EC-I030computer at Indian Institute of Technology,Bombay.The vortex distribution over the wing hasbeen carried out for N =16 and n =4. The aile ronchord ca is 25% of the wing chord car corres-ponding to p=4 in equation (2). The aileronsextend in spanwise direction from strip number5 to strip number 3 on the starboard part of thewiig and from strip number 12 to strip number14 on the port s ide of the wing. The posi tion ofaxes of rotation of ailerons is given by 6x =0.05car' -6y=0.13car (see Fig.I) along X andY axes which 'ire reported to be the best positionof flap axisl. The circulation G. of the rotatingailerons is represented byl0:T'" 1 E.u = '411'CarUo(11)wher.eEUK'==Kf..U/U );- 0=peripheral speedof the rotatingailerons;=effectiveness coefficient depends on thegeometrical parameters of rotating pro-file, taken equal to 0.25 based on experi-mental resultsl0 for conventional profiles.The calculations of aerodynamic coefficientsCLand Cmx using relations (10) are carried outfor the values of a.varying from 3° to 15° a.ndthose of the ratio U/Uo =1,2.3, & 4 for the wingplanforms of aspect ratios 7 and 3 with taperratios of 1 and 0.5 for each wing planform. Theresults so obtained are shown in Figs. 2,3,4 & 5.Discussion of the ResultsThe rotating ailerons seem to be promisingrolling control surfaces.. The curves in Figs. 2-5 suggest that the rolling moment coefficientobtained with the rotating ailerons of the spanequal to 22'10of the wing span is higher than that4...SWEEPII4C.O'l'JOURNAL OF AERO. SOC. OF INDIASWEEP1/'C.30.CLO'O'CUi0'01, I 12at(OEGJ11 8 12at(OEG.)0 , 16U/Uo.1 LU/U&:-~O,'t 0 0 ~Cm. Cm.0'2 0--0 2~3~,~(b)Fig.2. Curves of CL Vs a.andCmx Vs a.withu/uo=1,2,3,4for thewing of AR =7,taper ratio =1.O'CLO.20 0--0SWEEPI/i..c=30.CL0'3 30--0--0--0--<>16 8 12at(DEGJ160,' ,~0 ,(. )1. .SWEEPI/'C = 0U/Uo.1 IU/U~0"1c:5--o--<>--<>-Cm. Cm.0'22~30--0--:>--<>--0l'0"10.2'0' , 8 12at(DEGJ0--0--0--0--<>~~Cb)Fig.4. Curves of CL Vs a.andCmx Vs a.withu/uo=1,2,3,4 for the wing of AR =3,taperratio=1.00'3~0,'(a)1.SWEEPI"C =o.,.o.CLO'0-0-VOL. 32SWEEPI/'C =30.ClFig.3. Curves of CL Vs a.Cm Vs a.withxU/Uo=I,2,3,4 for the wing of AR=7,taper ratio ==O.5..0'8~SWEEPI/'C . 00-CL0-'0-20 8-10 at(DEGJI .U/U.1 . IO"'~,SWEEPI/4C.. 30..CL16 , 8 12CIC(DEG.)160U/U8o1:. 0 -')0-020--0--0--0-<>3~~( b)Fig.5. Curves of CL Vs a.and Cmx Vs a.withUluo ==1,2,3,4 for the wing of AR =3,taper ratio ==0.5., 8 12 16 0 , 8 12 16at(DEG.) (DEG.)0, . - "U/ IU/U°'[Cm.''.'f20.2 3 340-0---0---<>-0,0'31-0". (a) (b)Cm'l2Cm.0.230--0--0--0--00'3t '0--0--0--0--0D" (a )r>:iFEB- NOV 1980 INVESTIGATION ON ROTATING AILERONS 5for the conventional ailerons of almost double thespan. The conventional design value of rolling~oment coefficient for. most of the subsonic air-planes is about 0.05 to 0.611. It is possible toachieve this value of Cmx with rotational speedof ailerons less than the flight speed and aileronspan of about 20%.It is seen from the results that the effective-ness of such ailerons decrease.s with reductionin the wing aspect ratio. The value of Cmx pro-duced by these ailerons also reduces with in-crease in wing sweep. However, this effectseems to be milde r for rotating aile rons thanthat for the conventional ones for which Cmxdrops to about 82% at sweep of 30. from itsvalue for zero sweepll. These results indicatethat there can be significant improvement in rol-ling capability of aircraft for a given wing plan-form and size of ailerons. In other words, it ispossible to reduce the aileron size for requiredrolling capability.The results of calculations presented inFigs. 2- 5 shows that lift remains practicallyconstant during operation of ailerons. Experi-mental evidences indicate that the drag of downgoing part of wing is considerably high comparedto that of other half of wing if rotating aileronsare usedl. Thus, it gives pro-yaw characteris-tics.The work about effectiveness of this type ofailerons with non-linearity effect, structuraldeformation of wing influencing aerodynamiccharacteristics, compressibility effect etc. isbeing carried out.References1. Crabtree, L. F., "The rotating flap as a highlift devicell, ARC CP No. 480, Great Bri-tain, April 1957.2. Neumark, S., "Rotatingae,rofoilsandflaps",J.Roy.Aero.Soc., Vol. 67, No.1, 1963,pp:47.3. Ryabushinskii,M. D., "Investigationofarotating flap as a device for increasing liftof wing", Compt. Rend. A cad. of Sci., 1957,224, No.13, pp.1687-91 (French).4. Patel, T.S., .Calculation of lift force onthe wing with a rotating flap", AviationalTechnique, Izvestia VUZ, USSR, Kazan,No.4, 1970, pp. 10-15 (Russian).5. Patel,T.S., IIGround-effect on,thethinaerofoil with rotating flap", VINITI, Aca-demy of Sc., USSR, No. 4993-72, 1972(Russian).6. Patel, T.S.,' .Wing profile with a rotatingflap in non-uniform flow near wall", Mecha-nics and Mathematics, MSU, Moscow, No.1,1973, pp.16-23 (Russian).7. Patel, T. S., IIWing profile with a rotatingflap in shear flow", Vestnik-Mechanics andMathematics, MSU, Moscow, No.2, 1974,pp. 97-105 (Russian).8. Byelotserkovskii, S. M., nThin lifting sur-face in subsonic flow of gas", Nauka Publi-cation, Moscow, USSR, 1965 (Russian).9. Multhopp, H., "Methods for calculating thelift distributionof wingsn, ARC R & MNo. 2884, Great Britain, 1955.10. Patel, '1'.5., "About the effectiveness of arotating flapll, Ph. D. Theais, Departmentof Aeromechanics and Gasdynamics, MoscowState University, USSR, 1973 CRussian).11. Badyagin,A.A., etal., "Design of Air-planesn, Mashinostroyenit:Publication,Moscow, USSR, 1972(Russian)..

Investigation on rotating ailerons

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