1、REPORT 1086-ANALYSIS”OF THE EFFECTS OF WING INTERFERENCE ON THE TAILCONTRIBUTIONS TO THE ROLMNG DERIVATIVESBy WILLIAM H. MICKAEL, Jr.SUMXIARY.-h anai8 oj the efect8 of mung interference on the taii con-tributions to the rolling tability deriratirea oj complete airplaneconj.gurationa i8 made by cafru
2、laing the angularity oj the air.#ream at the rivhkal tail due to rolling and determining therwdting jorctw and momem%. Some of the important factorswhich afiect the remdtant angularity on the wtica.f ia il are wingaspect ratio and sweepbwk, rerticirl-tail panl and consMera-t iun8 associated with ang
3、le of attack and airplane geometry.Some calculated 8idewa8h. re8uIt8for a limited range of wingplan form8 and rerticaL-tail sizes are presented. .Eation8taking into account the positive for positive side force, radiansauaverage value of on the vertical tail$ . . . . . 1“lateral velocity, feet per se
4、condfree-sham” wioc.ity, feet per seconddistance along longitudinrd axis, feetdistance frpm plane of symmetry to spanwise” -loeation of trailing vortice9, feetlongitudinal forcelateral forcenormal forcovariables used in development (fig. 3 (a) Section liftsection lift coefikient - .- 1 V2C2P)(%)r ,s
5、ection lifcurre slope of vericrd tailccl- pb_ pb spanwise loading coefficient for unit 2V -,-c:-(%) v lift-curve slopo of vertical tail, per radianc, L()rollinPvasbc, Y.()lateral-forcO coefficient -; pJ7*Clp y; - . . . .azrc = . ,. . .- . ,- -7=-%“ ahQy,=”!.! that is, the rotat ion is approximatelyp
6、b 1, .equal to 7 .21 b/2 For a tail length of the order of the Wsemispan and for the usual -mlues of pb/2V encountered, therotation of the ortex sheet at the tail location would be1ss than 0.1 radian. The change m sideviash induced qt_ -=_=I.he vertical tafl by thii amount of rotation viouldbe negli
7、gible.CALCUL.4YTO?J OF TES. ANGULARITY OF FLOW AT THE VERTICAL TAILSidewash angIe induced by the rolling wing,-The side-wash, induced by the antisymmetricrd load distribution of arolling wing, is calculated by using the concept of a liftingline with trailing vortices extending downstream to infinity
8、.The load distribution on the semispan is represenhki by anumber of horseshoe vortices with the bound vortices con-centrate ed at the wing quarter.2.: .1 Y,. ), ), .,- - )2 .3 .4 ,6 W1* “-v”Angle of sweep. In considering the angle of sweep in thsidewash calculations, it is assumed thut the loading o
9、f Lhowiug may be codidcred to be concentrated on a sweptlifting lige. Jle bound vorLicea must bc ccmsidcred sincethey now produce a lateral component of induced velocity.The sidewash due to the trailing vortices is calculatd in thesame manner as for a straight Ying) with due considerationgiven to th
10、e distances tim the lifting line to the vertical-tai.1center of pressure at the spanwise location of Lhc Lraiingvortices (that is, 1instead of 1in equation (II). For wingswith conant aspecL ratio, tho antisymmetrical loading de-creases hmccj the strength ;fthe trailing vorticm decreases wiLh increas
11、ing sweep angh?.The. contribution of the bound vortices 10 tho sidcwash atthe vertical ttiil is calculated in much LIM? samo manner astlmt due w the truiling vortices, thti only difference beingthat consideration of LIMswept bound vortices modifies thegeometrical factors in equation (3). The bound v
12、orLiccsbeeomc of increased import.ancc for larger swcop angles, butfor sweep angles as high as 60 and with normal tail lengths,the contribution of the bound vortices to tic effcctivo sido-wash angle is found to be of the order of only about, 10percsnt, In order to establish an approximate method for
13、 estimatingthe sidewash results for swept wings, calculaLions were IUdefor swept wings of severaI aspect ratios and sweep angles.These calculations were compared with results for unsweptProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-AiiALYSIS OF EFF
14、ECTS OF WLN INTERFEREiSCE OX TAIL CC)NTTUBUIT.0X3 TO TIIE ROLLING DEIR”ATIVES 575t-v”til .- - .5t , 0. I I.5 J .4 Fb2 .3.2./.wo .f .2*J(b) A-3d.FGruE6.-Contlmed.wings of the same aspect ratio after.4 .6the unswept-wingresults had been reduced by the ratio of the damping-in-rolIptirameters for the sw
15、ept and the unswept wings. CalcuIatedresults and approximated resulti for 60” sweptback wingswith taper ratios of o-5 are shown in Iigure 7. The method ofapproximation applies fairIy well for the extreme case of60 svieep and better correlation is obtained for wings viithemaIler angles of sweep. It i
16、s therefore suggested that thesidewash results for swep t wings be approximated by reducingthe unswept results by the ratio of the swept- and unswept.-wing damping-in-roll derivatives-T multiplying resuh% u+ A = O“by rafio of.7%JA.60 o %p=o (from refe-nce - .,. .6 - I I1I.5.4 -* 2.3.2 .f I “ . / , )
17、I .-H10 .i .2 .3 .4 .5-%L+FIGURE7.-Conrpwlmn of cakuk.ted efdewwh rqsufts fortm.llhr.svortfces with appmx!matd results.attack by the equationA-60 wnefderhE bound and18-o* T1O”(14)fhe displacement of the trailing vortex sheet at the tailexpressed as a function of the angle of attack ish,-= tanb/2 b/2
18、 ()% (15)In discussing the displacement of the vertical tail, it isconvenient to refer to a particular station on the tail, saythe tail root. The displacement of the tail root is in a down-ward direction with respect ta the longitudinal axis for positiveangle of attack and is given bytan ab/2!3-.,-
19、y .- -.,-,.%-*- ,.:. .=.-. .- ., %1i+.5- %;4 -! ,A-l a=OO.JA-l +.plane of the longitudinal asis, there will ahvap be a reduc-t ion in the positive value of the etktive sidewash angle onthe tail. This reduction occurs because the sidewash is zeroon the vortex sheet and becomes negative below the vort
20、axsheet; thus, a negative increment is introduced -when thevortx sheet is shifted upward on the tail. For vorttx+heetlocations bdovr the longitudinal axis, a slight decrease in thepositive sidevmsh distribution occurs. These considerationsare iktrated in ligure 10.When the tail root is above or belo
21、w the longitudinal axis,with the vortex sheet in the plane of the a.ti, the effect onthe angularity distribution at the tail is simply that ofshifting the angularity distribution down or up by theamount of the displacement. of the root. .k displacement ofthe tail root above the reference axis has th
22、e same effect as avortex+heet displacement below the atis and vice versa.Other factors, -l?or wings with flaps, the additional loadingclue to flap deflection is symmetrical and the contribution tothe sidevmsh should be negligible according to the sameargument as that for the additional angleaf-attac
23、.k loading.However, the additional loading due to flap deflection in-creases the dow-nvrash behind the wing in the same manneras the angle-of-attack loading increases the downwash.This effect is difhdt to estimate but. ould be accountedfor when possible by using experimental values of the changein d
24、ownwash angle with flap deflection.It can be seen from expressions in the preceding sectionsthat although changes in t.d length had little tiect on thesidevmsh calculations such changes are of importance in,272483-663S1, t3 Il!lb/2.4 Ill II I .4- -.3 -2 -./ o .1 .2 .3 .4*m.-FIorrz 10.-The varlsclon
25、ofddewash+ngle dhtributfcm on tha m?ztk?alMl with pcsItIonofthe M root and tb9 tmm vort.m skwet. -6 u-W.determining the resultant angularity distribution on thevertical tail.APPHCATIOThe vertical-taiI contribution to the lateral-forcedue-to- “-roII coefficient maybe expressed in the form .-ac= aav(W
26、t= a -2Vand the corresponding exprmions for yawing moment androIIing moment due to rolI we obtained by multiplying theMera.1-force expression by the proper moment arm. Thegeneral expre9sione for thd application of the angularityresults obtained herein to the calculation of the vertical-t ati _contri
27、butions to the rcdling derkatives arewherea -m =+ (R C09 ai: sin a)+-+a$.(16)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-578 REPORT K186-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSand the distances lt and h refer to the section centers ofpressure
28、. If the distribution of the verticaI-tail section lifhcurve slope for the particular flight attitude is knovn, theintegrals in the preceding equations can be evaIuated bygraphical means by using a sufficient number of points overthe vertical-tail span to give reasmably smooth curves, Inthe usual ca
29、se, the section-lift-curve-slope distribution is notknom and, also, the preceding method is somewhat Iengthy.Past experience has shown that it is more convenient toreplace the section M%urre slope by a constant., the vertical-tail lift-curve slope, and to find an average tail angle ofattack due to r
30、olling that can be apphed at Lhe calculatedcenter of preemre of the vertical td. The average inducedangle due to the rolling tail has been assumed in reference Ito be simply that calculated at the center of pressure. Thereau()remains only to find an expression for and then the $7EDtail contributions
31、 can be found from. t.he.following equations,-.which arc similar to those of reference 2:“ au;(1Cos a ( )11, sin a)+ t) ; 08(O=)l=(C%)r (1 COSal, sin a)1?LY( )1; (1 Cos CZ-1*sin a)+ #J 2V *,(17)al()Vahw.s for can be found by using the sidewash2V resuILs presenkd in figure 6. ResuIts of calculatio fo
32、rau() (corresponding to wing aspect ratios of 3.5 and 6.0a.p!2V .,and for taper ratios of from 0.5 to 1,0). a-l. .sheet positions above the reference asis or for the taiI rootbelow the reference axis at zero angle of attack can Im madogl thus,au()the more simple application using a constant. - -p- g
33、ives27 the hctter results, for the pmtic,ulm modeI inveetigatcd,The comparison of calculated and measured results forthe swep_- .-: =“0 “- - . 0)- - / -/ -2 -.2. .1(cnJt - - - -, _-0 . - .- -1I - Yi ,(*4* .cI1)-.1./(Cl$t 480,+!-: .- - ol(a) b)-.b 4“ 8 t2 -./d, de9 o 4 8 12d, Cfeg(a) Model ofreferenc
34、a 2. A-4.% A-G% X-OS A-O.#j-O.9S.-.J-. .-.- -.Fmx MCornson of mass d cdcdet+d dues of W till amMbutIoIu to W dlhg ddti-. Htitd Ofi.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-580 REPORT 1086-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSThe tdculate
35、d results presented in the figure were obtainedfrom sidewash calculations considering the bound and trail:ing vortices of the swept wing, but approximated resultsobtained by means of the method suggested previously inthe report. gave essentially the same results as those presentedin the re.Calculate
36、d vaues of (Cmp), for a rectangular wing ofaspect ratio 6.0 at zero angle of attack are presented infigure 13 as a function of the ratio of verticaJ-taiI span towiug span. Measured values for (Cmp), for a sting-mounted.14 ., ,0Winq- on feki poinhn Wing-offtestpoints“ Wing-on calculatedvalues-Wing-of
37、f calculated valuesmodel with a small-diameter stick fuselage and two dilTercntvertical tails are also given in the flgurc. This comparisonillustrates how the values of (C=,), may change sign withchange in vertical-tail sptin and also gives an indication ofhow the calculated and measured resuhs comp
38、are when themeasured results are subject to very nearly the same condi-tions as those assumed in the calcndat.ions.CONCLUDING REMARKSThe tiect of wing interference on the tail contributionsto tho rolling derivatives of complete airplane configurationsis detiiinined by calculating the tiir-stream ang
39、ularity at thevertical tail in rolling flight and finding the resultant forcesand moments, The important factars in t-he determinationof the angularity distrilmion on the vertical tail are wingplan form, vertical-tail span, and considcrat.ions associatedwith angle of attack and airplane geometry. co
40、mparisonof the calculated and cxpcrirnental rcsults indicates that aconsideration of wing interference can be expected to be ofsuch importanfic as to change the sign of the calculatedvalues and that fair agreement with the available experi-.08.06 - “. T /,.04 Q , ./; /,6/“.C22 / /,H n .0 + w-,020 .t
41、o .6 . .20 .25 ,30IFIGURE18.ComparLwn of c.akulated with expxfmenkd VUIufafor a stick-fmdago modeLA- &-0, a+.IJANGLEY AERONAUTICAL LABOItATORY,NATIONAL ADVISORY COMMITTEE FOR ERONAUTICS,LANGLEY FIELD, JTA., January 84, 1961.REFERENCES.1. Bad.mr, lillard J.: Effect of Some Prescnt+Day Airplane Design
42、Trends on Reauirementi for Lateral Stablity. NACA TN 814,1911: -2 Letko, iVilliam,and Riley, Donald R.: Effect of an Unswept Wingcinthe Contribution of Unswept-Tail Configurations to the LOW-Speed Static- and Rolling-Stability Derivatives of a MidwingAirplane Model. NACA TN 2175, 195o.3. SiIvarstiin
43、, Abe, Katzoff, S., and Bullivant, W. “Kenneth: Down-wash and Wake Behind Plain and FYappcd Airfoils. NACA Rcp.651, 1939.4. Spreiter, John R., and Sacks, Alvin H.: The Rolling Up of thcfiaihz Vortex Sheet and Its Effect on the DownwaYhBehindWfigs.- Jour. Aero. Sci., vol. 18, no. 1, Jan. 1951, pp. 21
44、-32, 72.5. Bird, John D.: .me Theoretical Low-Speed Span Loading Char-acteristic of Swept Wings in Roll and Sideslip. NACA Rep.969, 1956. (Supersedes NACA TN 1839.)6. ToII Thomas A., and Queijo, M. J.: Approximate Rclationu and&arts for Low-Speed Stability Derivatives of %rcpt Wings.NACA TN 1681, 1948.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
