1、REPORT No. 54SEFFECT OF TIP SHAPE AND DIEEDRAL ON LATERAL-STABILITY CHARACTERISTICSBy JOSEPHA. SHORTALSUMYTt?8t8 were wndueted in the N. A. C. A. 7- by 10-jootwind iunnd to determine the e$ect of wing-tip 8hapeanddihdnd on sonw of the aerodynamic characteri+diwofClark Y wing8 that aect the performan
2、ce and lateral8tthe speed-range ratio was increased about 3 percentand the climb criterion about 9 percent. Althoughthese percentages are within the experimental error,it is believed that they indicate a definite trend. Thetiect of these two similarly shaped tips of differentkmgtb is in fair agreeme
3、nt with previous systematictests of the eflect of plan form as shown in figure 6,The improvement in rate-of-olimb criterion is explainedby the fact that the span load distribution for thewings with rounded tips approaches the ideal, whichresults in a lower induced drag.1.41I I c,._ . 1 12-.k- .- A+
4、,1.2 ! I -a-mm+. “)1.0 20=n- .L-.8$F w= ,6G=.6 - 12I ()D mzo Re ferenccZ.4t-tx . 4-H8A _ Present+e3is,.2 - 40 .8 1.6 2.4 3.2 0Ep lengih/Rod chordfiGuEc%6.Effex OftfpfexhoncL_ and (LID)X,.EfTect of elevation shape,-The eilect of elevationshape of the one-chord length tip on the perfon.nancecriterions
5、 is shown in table I. The results of thwetests are in agreement with previous unpublished Navytests in that, although the effect of elevation shape onthe performance criterions is not great, there is a cer-tain advantage in raising the extreme tip at least whigh as the midpoint. The tip adopted by t
6、he Armyas their standard rounded tip is the longer roundedtip with the masirnum ordinate points on the uppersurface in one plane.Effect of aspect ratio.-The wing with aspeot ratio8.39 was made by adding the Army tip to the rectan-gular wing of aspect ratio 6, which makes the tip por-tion a smaller p
7、ercentage of the span than the wing ofaspect ratio 6 with the reduction in maximum lift coeflicientawas proportional to the reduction in the projected area.The minimum drag coefficients, however, increasedslightly in every case except with the Army tip with93 percent sem.ispan dihedral. The coeffici
8、ents usedwould be expected to remain constant except for inter-ference effects at tbe juncture of the portions of thewing forming the dihedral angle. In all casea theeffect was no larger than about 5 percent. Since themaximum lift coefficient wna decreased and the mini-mum drag coefficient was incre
9、ased, the speed-rangeratio was reduced about 10 percent for extreme dihe-dral angles except for the wing with Army tip and93 percent semispan dihedral, for which the ratioremained practically constant. I?or dihedral anglesnormally used (5 or less), however, the effect isnegligible. All the dihedrals
10、 reduced the rate-of-climb criterion by a alight amount.AERODYNAMICCHARACTERISTICSAFFECTINGLATERALSTABILITYIn order ta make a complei% determination of theasymmetric motions and the lateral stability of an air-plane, there are reqed nine resistance derivativesdetemnined from the rate of change of ro
11、llii moment,of yawing moment, and of cross-wind force with cross-wind veloci, with roll velocity, and with yawingvelocity. The results are presented in such a mannerthat a direct determination is possible of four of thederivatives, namely, the three computed from the rateof change of rolling moment,
12、 of yawing moment, andof cross-wind force with cross-wind velocity, and theone computad from the rate of change of rolling mo-ment with rolling velocity. Although these four fnc-tors are the important ones affected by the wing shapestested, it is considered outside the scope of this reportto make de
13、tailed latmal-stabili calculations in whichassumptions for the remaining fact-era would be re-quired. C?msequently, only the quantitative effecof the wing shapes on the four abovmentioned factorswill be discussed.Efleot of plan form.lhn a wing is yawed, thespan load distribution is considerably chan
14、ged and arolling moment results that may become very large athigh angles of attack. The particular changes thatoccur are clearly shown by means of pressure-distribu-tion test9 in reference 10. The particular plan formof the wing has an appreciable effect on the results asshown in figure 7 where the
15、rates of change of rolling-()amoment coefficient with ae of yaw oh givenfor three wings of the same elevation shape but havingdifferent plan forms. The effect is pronounced at anangle of attack of 10, which corresponds to a lift co-efficient of about 1.0, where the rate of change given by-.()d d# o0
16、001I.- I rounded f,p.- I o-Three- qvorfers- 4 - 4 r-c-hord length-.003 rounded fip. 1 w-8 0.8 16 24 32 40Angle of oftock,d ,degreesFIaum plac-ing the maximum ordinate points on mean lines in oneplane vrnsequivalent to giving n wing with the krmytip (maximum ordinate points on upper surface in onepla
17、ne) a negative dihedral angle of 1”; whereas placingthe straight portions of the lower surface in one plane.010dCc()Woo0-.001()dCaqvo-.002-Xx23 _8 o 8 16 24 32 40Angle ofattack,ti,degreesFIGUnE lLEflect of efevaton sham of a On with the dihedral axis at the 50-percentpoint (fig. 16), the values are
18、increased up through20 angle of attack; and with 93 percent of thsemispandC,in use (fig. 18), the increase in(1. due to dihedralis reduced to zero at 19 are of attack. This actionis explained by the manner in which a rectangular.60.40.20(%)00-a-.40-8 0 8 /6 24 3? 40Angle of otiock ci,degreesFIGUBIJ
19、15.Effect of dfhdrd Of 24 t SW,O of wfth A1roY tfp Onrata of ohange of mllfng-mornent cWTidant wfth rate of MU.Mu.- -.+n-1/wing stalls. The burble starts at the center sectionand spreads toward the tips, the tips remaini un-tiected for several degrees after the center+ectiondc()flow breaks down. The
20、 effect of dihedral on d+ ,.LW7.CU6.cu5.Lw4HdCl IW.C3.m2.(X7Io -8 0 8 16 24 32 40Angle of ofto, & ,deqreesFrom I&Efkct of dffmdml of Ml fxxcent mrean of wfng wfth Army tip onrata of chenga of mfffng-memant mefCdent wfth angle of yaw.and dC.()dtJ , sho in es 14, 17, and 19, althoughnot large, is fair
21、ly consistent for the three dihedralaxes used. The values of () , were reduced for thewing alone as would be experted but the values ofProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-= .156 REPORTNO. 548 NATIONALADVISORYCOMMIITEEFOR AERONAUTICSde() ,
22、 the direction&stability criterion, became. .dC,()more positive. The vrdues of were decreased%7 .somewhat when the dihedral &s & at 25-Dercent.semisprm (fig. 15) and the dihedral angle wm greater.OJO()%dv o0-.00/H$0-.LW2:003Ae of offack,& ,degreesFIQIJBE 17.Eff of dfhedral of ECt smnbpen of W with A
23、rmy tIp onMO of clmnge of crass-wind form and yowfng-moment cmfffclmts with engle ofyaw.than 15. For the other dihedral+mis locations, thevalues were hardly affectid for the angles up to 15.When the wing with square tips was given dihedral the“UWOf(%,(%,(#), nd() emo.Cm.005.004.003.Lw2.mlo -8 0 8 16
24、 24 32 46Angle of atf&, degreesFmwm M.-EM of dlhedrrd of W prcnnt se.umr of wing wfth &my tlp onrab of clmnge of rollfng-moment m311M3nt wftb eagle of yaw.affected h about the same manner as were the valuesfor the wing with the Army tip, except that the valuesof dC:() o due to dihedral revemed in ef
25、fect at 18angle of attack and considerably reduced the totaldCJ forthe .() d+ . (S& figs. 20 and 21.)-.A more direct comparison of the effects of the dihe-drals tested V& made by computing the increments ofFmumr 19.EtWt.of dfhedrd of W percent SembJMII of wing with Army tip onrete of efmnge ofcicus-
26、wfnd fome end yawfng-moment coolllolents with ong.le ofyew.()f+%. for 0, 10, md 15 angles of nttack andplotting them against dihedral angle in figure 22. lt.W7.mI 1 I M 1 I 4.ms.m()C&W O.m0020010-8 0 8 16 24 32 40Angle of attcck,d ,degreesFIQOEE ZU-Effmt of dihedrel of 93 t smdspm of a rwtengnfar WI
27、OE on mtoof change of rollfng-mommt cmftlofont with W Of yew.may be seen that the increments with the rectangular!wirgare practically the same as for the wing with thoArmy tip w-henthe same percentage of the semkpan isProvided by IHSNot for ResaleNo reproduction or networking permitted without licen
28、se from IHS-,-,-IWFECI?OFTIP SHAPEANDDIHEDRALONLATERAL-STABIJ_JTYCHARARISTICS 157used in both cmes. This agreement is an indicationthat the effects due to a dihedral angle with practicallythe full semkprm in use may be added directly to thebasic 0 dihedral curves regardkm of tip shape.-8 0 8 16 24 .
29、3? 40%gle o-fotto& d ,%greesOUFIE 21,Efltzt Of dih6dd Of W 0311t of rwkarmwfngonmteof ohmge of mces.wind form and yowfng-moment cmlllcfonts wfth ongle of yaw.hencreme”k(%)0“Cwoenthe-mselvesto further evaluation since they vary as a straightline with the rtngleof dihedral I up to an angle of 16.An av
30、erage curve has been draw-nthrough the sets of,points and the equations of the curmw have beendetermined to be()$%0 =0.000333K0.0001181i?sd do.()a A w .= O”OOOO=where Kis the fraction of the semispanin use.These equations may be used with sticient accu-racy in detwminhg the effect of dihedral of any
31、 fractionof the semispan of a rectangular wing of Clark Y orsimilarsection hav an aspectratio of 6with the Armytip. These values, of course, must be added to thebasic values for the wing with 0 dihedral. If the()entiresemispanhas dihedral,Kbecomes l.0,# A # dc ()=0.000215, and -$ A -& ,=0.000024. Bl
32、enk (ref-erence 6) found correspondo values of 0.000204 and0.000030 for a rectmgnlar W with square tips.Comparison of oalonlated and experimental results.When a wing with a dihedral angle 1?is yawed throughan angle+, the new wing chord along thd wind directionis c“=cos +and the spmmise displacement
33、of the tmilirg edge rela-tive to the leachqg edge of the chord line isl=c sin +(-3dCA dO-.HdCnA d o-.dCL(1Ao.Dihedral onqle,37,degreesFlauIuz Effect of dfhodrd on raka of ohmge of mIlfng-momen& yawfng-momen and crcs%wfnd form maftlafents wftb angle of yaw.d(dc)oand(%)oConsequently, the values ofa A
34、were determined from fibgure22 for the W with theArmy tip and have been plotted against fraction of wingsemispan in figure 23 for the three anglea of attack.Then, owing to the dihedral angle, the trding edge ofthe new chord of the rearward wing is higher than itsleading edge by an amounth=l sin IPro
35、vided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-158 REPORTNO. 548 NATIONALADVISORYCOMMTMEEFOR AERONAUTICSwhich may be writtenh=c sin + sin IThis value makes the angle of attack of c less than theace of at& of c so titNow for smallrmglesthe sineequalsthe
36、 angle in radians,SOthatAa= #r (all in mdwns)Likewise, on the for&rd” W the are of attack isincreased byAa=$rWksdsberger has shown (reference 12) that the rollingmoment due to an unsymmetrical span load distxi-0004 I I IAngle ofa#&”oAT/00.0m9 15()d dCz(+)1 IdA 0 y J+dCn 0 ( - 0.000024KUdr d+.A d d+
37、: %- -n ? 4 s .8 Lo-frocfionofsemispon,KFmoRE ZL-EflW of dihedral SFWI on rate of change wfth dfhedml angle of therate of age of rolffng moment wfth angle of yam.bution resulting from equal changes in angle of attackof opposite sign on the two halves of a rectanamwing may be expressed bywhere is a f
38、actor dependent on the aspect ratioand the slope of the lift curve for a wing of titsaspect ratio and aCis the change in angle of attack.Expressing this equation in coefficient form resultsin*r forSubstituting for a. its equal m,(7: the valueof 6, and for the value 0.127 from Wkmlsberger andAsano (r
39、eference 13) for a change in angle of attackover 93 percent of the span, -=0.1272X6.Then Werentiating with respect to +d dC() =0.000232d#Oand r,which is, within the limits of mmracy, equal to thevalue found from the experiments reported herein.CONCLUSIONS1. The rate of change of rolling moment with
40、angleof yaw was greatly affected by wing-tip shape.2. Agreement was obtained between cemputad andexperimental values of the rate of change of rollingmoment with angle of yaw due to dihedral of a rec-tangular wing.3. The dihedral effect was maintained to u higherangle of attack with dihedral of only
41、the outer one.fourth of each semispan than when the entire semi-span had dihedral.LANGLEYMEMORIALAERONAUTICALLABORATORY,NATIONALADVISORYCOMITYEEFORAERONAUTICS,LANGLEYFIELD,VA., Au 2?7,1936.REFERENCES1. Rhodq Richard V.: The Influence of Tip Shape on the WingLoad Distribution as Determined by Flight
42、Tests. T. R.No. 500, N. A. C. A., 1934.2. Beisel, It_ B.: Wing Tip Forms. Aircraft Teoh. Note No.106, Navy Dept., Bur. Comstr. and Repair, 1921.3. Irving, H. B., and Powell, C. H.: The Effeot of Rounding thoWiig Tips of an Aerofoil Having a High Value of MaxhnunLfft Coefficient. R.&M. No, 330, Briti
43、sh A. C. A., 1017.& Relf, E. F.: Effect of Shape of Wing Tips on the Lift, Dreg,and Centre of Pressure of an Aerofoil. R. & M. No. 162,Seotion I.(iv), British A. C. A., 1914.5. Parkin, J. H., Crane, H. C., and Galbraith, S. L.: Wing TipResearch. Part I.Effect of Outline and Washout ofCamber on the A
44、erodynamic Efficiency. Univ. TorontaEng. ,W. Bull. No. 2, pp. 78-110. Aero, Res, Paper No.4, Dec. 1920.6. Blenk, Herman: G6ttingen SLx-Component Measurementson Wfnge with Dihedral, Sweepback, and Warp. A. C. T.IL, Translation No. 2S0, Mat6riel Div., Army Air Corps,1929.7. Ralf, E. F., and Landells,
45、A.: Forew and Momenti on anAerofoil Having a Dihedral Angle. R. & M. No. 152,Section I (iii), Bntiih A. C. A., 1914.8. Hunsakor, J. C., and Doug D. W.: Esperbnenta on nDihedral Angle Wing. Smithsonian Miao. Collootons,vol. 62, no. 1916.9. Harrie, Thornaa A.: The 7- by 10-Foot Wind Tunrml of the10.11
46、.12.13.National Advisory Committee for Aeronautic.s. T. R. No.412, N. A. C. A., 1931.Williams, D. H.: Prwaure Dfatribution Over a Yawed Aero-foil. R.& M. No. 1203, British A. R. C., 1928.Zimmerman, C. H.: Characteridics of Clark Y Airfojls ofSmall Aspect Ratios. T. R. No. 431, N. A. C. A., 1032,Wiel
47、a&qger, C.: Themetiud Inv#lgation of the Effeot ofthe Ailerons on the Wingof an Airplane. T. M. No. 510,N. A. C. A., 1929.Wiaelaberger,C., andAaano,T.: Deterrnlnationof theAhForc and Momenta Produced by the Ailerons of anAirplane. T. M. No.488, N. A. C. A., 1928.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
