REG NACA-ARR-L5F23-1945 Lifting-surface-theory values of the damping in roll and of the parameter used in estimating aileron stick forces.pdf

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1、23.!NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSItrI RTIMI, RI: Pi)RTORIGINALLY ISSUEDAugust 1949 asAdvance Restricted Report L_23LI_Z2_-_I_A_-_02_ VAIXIES OF THE DAMPII_IN ROLL AND OF TEE PARAMETER USED INESTINATII_ AILERON STICK FORCESBy Robert S. Swanson an_ E. LaVerne Pridd_VLam_ley Memorial Aero

2、mautical LaboratoryLangley Field, Va., +“_TITUTE 0F TEPHI“C_ (J(YVACTWASHINGTONNACA WARTIME REPORTS are reprints of papers origlnally issued to provide rapid distribution ofadvance research results to an authorized group requiring them for the war effort. They were pre-viously held under a security

3、status but are now unclassified. Some of these reports were not tech-nically edited. All have been reproduced without change in order to expedite general distribution.L - b_Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for Resale

4、No reproduction or networking permitted without license from IHS-,-,-NACA ARR No. LSF23 RESTRICTEDNATIONAL ADVISORY COMMITTEE FOR AEROFAUTIC_ADVANCE RESTRICTED REPORTLIFTING-SURFACE-THEORY VALUES OF THE DANPINGIN ROLL AND OF THE PARAiv_ETER USED INESTI_._ATING AILERON STICK FORCESBy Robert S. Swanso

5、n and E. LaVerne PriddyAn investigation was made by lifting-surfacetheory of a thin elliptic wing of aspect ratio 6in a steady roll by means of the electromagnetic-anaogy method. From the results, aspect-ratiocorrections for the damping in roll and aileron hingemoments for a wing in steady roll were

6、 obtained thatare considerably more accurate than those given bylifting-line theory. First-order effects of com-pressibility were included in the computations.The results obtained by llfting-surface theoryindicate that the damping in roll for a wing of aspectratio 6 is 13 percent less than that give

7、n by lifting-line theory and 5 percent less than that given bylifting-llne theory with the edge-velocity correctionderived by Robert T. Jones applied. The results areextended rio wings of other aspect ratios.In order to estimate aileron stick forces fromstatic wind-tunnel data, it is necessary to kn

8、ow therelation between the rate of change of hinge momentswith rate of roll and rate of change of hinge momentswith angle of attack. The values of this ratio werefound to be very nearly equal, within the usual accuracyof wind-tunnel measurements, to the values estimatedby using the Jones edge-veloci

9、ty correction, which fora wing of aspect ratio 6 gives values 4.4 percent lessthan those obtained by liftlng-line theory. Anadditional lifting-surface-theory correction wasRESTRICTEDProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 NACA ARR No. L5F23

10、 -calculated but need not be applied except for fairlylarge high-speed airplanes.Simple practical methods of applying the resultsof the investigation to wings of other plan forms aregiven. No knowledge of liftlng-surface theory isrequired to apply the results. Yn order to facilitatean understanding

11、of the procedure, an illustrativeexample is given.INTRODUCTIONOne of the many aerodynamic problems for whicha theoretical soutlon by means of llfting-line theorymight be expected to be inadequate is the case of awing in steady roll. Robert T. Jones has obtained inan unpublished analysis similar to t

12、hat of reference 1a correction to the lifting-l:_ne-tbeory values of thedamping in roll that an_ounts to an B-percent reductionin the values for a wing of a_pect ratio 6. Still moreaccurate values may be obtained by use of lifting-surfacetheory.A method of estimating aileron stick forces in asteady

13、roll from static wind-tunnel data on three-dimensional models is presented in reference 2. Thismethod is based upon the use of charts giving therelation between the rate of change of hinge moment withrate of roll Chp and the rate of change of hingemoment with angle of attack Ch_ in the form of theIC

14、hpl which is determined by meansparameter“PCh !Ch !of lifting-llne theory. It was pointed out in reference 2that the charts mlg_it contain fairly large errors whichresult from neglecting the chordwise variation invorticlty and from satisfying the airfoil boundary condi-tions at only one point on the

15、 chord as is done inlifting-line theory. A more exact determination of theparameter _P)Ch is desired. In reference 3 an addi-tional aspect-ratio correction to Ch_ as determinedfrom lifting-surface theory is presented. In orderto evaluate the possible errors in the values of _I(_P_ChProvided by IHSNo

16、t for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA ARR No. L5F23 3as determined by lifting-line theory, it is necessaryto d_termine similar additional aspect-ratio correctionsto Chp.A description of the methods and equipment requi_edto solve lifting-surface-theory

17、problems by means ofan electromagnetic analogy is pre_ented in reference 4.An electromagnetic-analogy model simulating a thineiiptic wing of aspect ratio 6 in a steady roll wasconstructed (fig. !) and the magnetic-field strengthsi_iulating the induced downwash ve!ocities was measuredby the methods o

18、f reference 4. Data were thus obtainedfrom which additional aspect-ratio corrections to Chp fora win_ of aspect ratio 6 were determined.Because of the small magnitude of the correctionto _i(_P_Ch introduced by the lifting-surface calculations,it was not considered worth while to conduct furtherexper

19、iments on wings of other plan for_s. An attemptwas therefore made to effect a reasonable generalizationof the results from the available data.Inasmuch as the _heory used in obtaining theseresults is rather complex and an understanding of thetheory is not necessary in order to make use of theresults,

20、 the material presented herein is convenientlygiven in two parts. Part I gives the results in aform suitable for use without reference to the theoryand part II gives the development of the theory.SYMBOLS(ZcICLChC_angle of attack (radians, unless otherwisestated)section lift coefficient _-_ ./wing li

21、ft coefficient _-_-/hinge-moment coefficient /Hinge moment_ q_a2ba /_Rollin C momen t_rolling-moment coefficient - qSb /Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 NACA ARR No. LSF23a opb/2VFC7,-pChpCh_CI,a(_P) ChCC ScbCaCaxYbab/2slope of the s

22、ection lift curve for incom-pressible flow, per radian unless otherwisestatedwlng-tlp helix angle, radianscirculation strengthdamping coefficient; that is, rate of chaPgeof rolling-moment coefficier_t with rateof roll (Tp_-2_ jrate of change of hinge moment with rate ofroll _ _ Ch _, (pb,/_ _I)rate

23、of change of hir,ge moment with angle ofattack k,_“a,-,rate of change of wing lift coefficientwith angle of attack _-_-/Cho_absolute valueof the ratio _ h_)wing chordwing chord at. plane ofsymmetrybalance chord of aileronchord of aileronaileron root-mean-square chordchordwise distance from .wing lea

24、ding edgespanwlse distanca from plans _f s_etry-aileron spanwing semi spanProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA ARR No. I:SF93 8SWFs8s6aAAckMWVqEEFarea of wingweight of airplanestick force, poundsstick deflection, degreesaileron deflec

25、tion, degrees, positive downwardaspect ratioeq_ivalemt aspect ratio in compressibletaper ratio, ratio of fictitious tip chordto root chordfree-stream _lach n_bervertical component of induced velocityfree-stream velocityedge-velocity correction factor for liftedge-velocity correction factor for rolli

26、ngmomenthinge-moment factor for theoretical loadcaused by streamline-curvature correction(reference 5)experimentally determined reduction factor for8KI, K2 constantsSubscript 8:LL lifting-llne theoryF to include effects of viscositytrailing-edge angle, degreesparameter defining spanwlse locationProv

27、ided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 NACA ARR No. LSF23LSEVSCmaxoiecllft_ng-surface theoryedge-velocity correctionstreamline curvaturemaximumoutboardinboardeffectivecompressibility equivalentI-APPLICATION OF METHOD TOSTICK-FORCE ESTIMATIO(SG

28、ENERAL METHODThe values of the damping in roll C_p presentedin reference 2 were obtained by applying the Jonesedge-velocity correction to the lifting-line-theoryvalues. For a wing of aspect 6, the Jones edge-velocitycorrection reduces the values of C_p by about 8 percent.From the data obtained on th

29、e electromagnetic-analogymodel of the elliptic wing of aspect ratio 6, a moreaccurate correction to C_ for this aspect ratioPcould be calculated. The damping in roll was foundrio be 13 percent less than that given by llftlng-linetheory. The results were extended to obtain valuesof C_p for wings of v

30、arious aspect ratios and taperratios. These values are presented in figure 2. Theparameter /1 - M2 is included in the ordinates andabsciss_to account for first-order compressibilityeffects. The value of ao to be used in figure 2is the value at M = O.The method of estimating aileron Stick forces- .re

31、quires the use of the parameter P ChProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Because Cha can be found from the static wind-tunneldata, it is possible to determine Chp and thus theeffect of rolling upon the aileronstlck forces(a) is known. In o

32、rder to avoid measuring ,Chaif p Chat all points to be computed, the effect of rolling isusually accounted for by estimating an effective an_:leof attack of the rolling wing such that the statichinge moment at this angle is equivalent to the hingemoments during a roll at the initial angle of attack.

33、The effective angle of attack is equal to the initialangle of attack corrected by an incremental angle (A_)Chthat accounts for rolling, whereThe value of (A_)Ch is added to the initial a forthe downgoing wing and subtracted from the initialfor the u_going wing. The va_nes of Ch correspondingto these

34、 corrected values of a are then determinedand are converted to stick force from the known dynamicpressure, the aileron d_mmnsion_, and the mechanicaladvantage.The value of pb/2V to be used in equation (1)for determining (Aa) ch is (.-.asexplained in reference 2)the estimated value fok“ a rigid unyaw

35、ed wing; that is,f_2V- C_pThe value of C_ to be used in Calculating pb/2Vshould also be corrected for the effect of rolling.The calculation of pb/2V is therefore determined bysuccessive approximations. For the first approxi-mation, the static values of C_ are used with thefrom figure 2. From the f_r

36、_t-approzi-value of C_pmation values of pb/2V, an incremental angle ofattack (Aa) c_ is estimated. For all practical purposes,(ap) c_ : (aP)ChProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 VACA ARR ?o. LSF23and from equation (i),(A_) C_ _= (C_P)ch

37、 _VSecond-approximation values of C_ can be determinedat the effective angles of attack _ + As and _ - Aa.The second-approximation value of pb/2V obtained fromthis value of C_ is usually sufficiently accurateto make further approximations ur_ecessary.In order to estimate the actual rate of roll,valu

38、es of pb/2V for the rigid unyawed wing must becorrected for the effects of wing flexibility andairplane yawing motion. A_n emf:irical reduction factorof 0.8 has been suggested for use when data on wingstiffness and stability derivatives are not availableto make more accurate corrections. Every attem

39、pt shouldbe made to obtain such data because this empiricalreduction factor is not very accurate - actual valuesvarying from 0.6 to 0.9. The improvement in thetheoretical values of C_ obtained by use of lifting-surface theory herein is _ost if such an empiric_l“ factoris used. In fact, if more accur

40、ate corrections forwing twist and yawing motion are not made, the empiricalreduction factor should be reduced to 0.75 when the morecorrect values of C_p given in figure 2 are used.(_) presented in reference 2The values of p Chwere obtained by graphically integrating some publishedspan-load curves de

41、termined from lifting-line theory.Determination of this parameter by me_h_ of the lifting-surface theory presented herein, however, gives somewhatmore accurate values and indicates a variation of theparameter with aspect ratio, taper ratio, aileron span,F_.Mach nu_.ber, CI_ , and the parameter(Oa/c

42、In practice, a value of (_ equal to thelifting-line,theory value of (_p) n_ _ appendix)“,. t _._T _.jtimes the ,7ones edge-velocity correc_lonparameter Ac + 4 AcE c + 2 is probably sufficientlyAc + _ AcE c + 4accurate. The incremental angle of attack (Aa)Ch is thenProvided by IHSNot for ResaleNo rep

43、roduction or networking permitted without license from IHS-,-,-NACA aPJ + iValues of Eec and Eec are given in figure 16.Values of C_P ,/1 - M2 determined by usinga oare presented in figure 2 as a function of Aa/aoEecProvided by IHSNot for ResaleNo reproduction or networking permitted without license

44、 from IHS-,-,-NACA ARR No. L5F23 27where Ac - A /I - _2 and ao is the _ncompress_bleslope of the section lift curve per degree.Hinge-moment parameter Cho.- In order to deter-mine Chp for other aspect ratios, it is necessary toestimate the formulas for extrapolating the streamline-cul_vatur e correct

45、ionsof (ACha) SC forreference 3.ACh_( U.)SC andA = 3 and A = 6Values ofAChp) . ValuesSCare available inA 51 might be expected to beCh SCapproximately inversely proportional to aspect ratio andr._u_a in the form ACh SC A + gan extrapolation fo _“ =is therefore considered satisfactory. The values of K

46、Iand K2 are determined so that the values of _-,(ACha_sCfor A = 3 and A = 6 are correct. Values of“ K I t andvary v,ith aileron span. The values of K2, however,for all aileron spans less than 0.6 of the semispan arefairly close to _.0; thus, by assu_ling a constant valueof K2 = 1.0 for all aileron s

47、pans and calculatingvalues of KI, a satisfactory extrapolation formulamay be obtained. It is impossible to determine such aformula for #ACh_ _ because rcsults are availablePl Suonly for A =6; however, it seems reasonable to assumethe s,_me form for the extrapolation formula and to use. o. ova uoo /

48、SCof KI can, of course, be determined from the resultsfor A = 6.K2Although no proof is offered that these extrapolationformulas are accurate, they are applied only to part IIof equation (9)(values of A(Chp)LS) which is numerI-cally quite small, and ere thereore considered justified.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-28 UACA ARR No. L5F2ZCONCLUDING EEZARK$From the results of tests made on an electromagnetic-analogy model simulating a thin ellipt