NASA NACA-RM-A53A30-1953 Lift drag and pitching moment of low-aspect-ratio wings at subsonic and supersonic speeds《在亚音速和超音速下 低展弦比的机翼升力 阻力和俯仰力矩》.pdf

1、/iLcopy/2 3RM A53A30i ESEARCH MEMORANDUM_LIFT, DRAG, AND PITCHING MOMENT OF, LOW-ASPECTRATIO.WINGS AT SUBSONIC AND SUPERSONIC SPEEDSBy Charles F. HallAmes Aeronautical LaboratoryMoffett Field, Calif.CLASSIFIED DOCUMENT_hiS material contains information affecting the National Defense Of the United St

2、ates within the meaninghe esptonage laws, Title 18, U.S.C., 8ecs. 798 and 794, the transmiss_on or revelatio_* o_ which in anymanner tO an unauthorized person is prohibited by law.NATIONAL ADVISORY COMMITTEEFOR AERONAUTICSWASHINGTONApril 14, 1953_ONFIDENTIALProvided by IHSNot for ResaleNo reproducti

3、on or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACARMA53A30 CONFIDENTIALNATIONAL ADVISORY COMMITTEE FOR AERONAUTICSRESEARCH MEMORANDUMLIFT, DRAG, AND PITCHING MOMENT OF LOW-ASPECT-RATIOWINGS AT

4、 SUBSONIC AND SUPERSONIC SPEEDSBy Charles F. HallSUMMARYResults are presented of a coordinated investigation to evaluate thelift_ drag_ and pitching-moment characteristics of thin, low-aspect-ratiowings in combination with a body. Wind-tunnel data were obtained in theMach number range from 0.25 to a

5、s high as 1.9.The investigation of a series of 3-percent-thick triangular wings of2, 3, and 4 aspect ratio showed that the lift-curve slope was predictedsatisfactorily by linearized theory except near a Mach number of unityand over portions of the supersonic speed range. As predicted by linear-ized

6、theory, the aerodynamic center moved aft with increasing Mach numberat subsonic speeds, the over-all travel increasing with aspect ratio.The data indicated that, in general_ it would be more accurate to calcu-late the drag due to lift at supersonic speeds, assuming that the netforce due to angle of

7、attack was normal to the wing chord than to useavailable theoretical methods which consider leading-edge thrust.The investigation of a series of 3-percent-thick wings having swept-back, unswept, and triangular plan forms of aspect ratios 2 and 3 showedthat, as predictd by theory, the lift-curve slop

8、e decreased with increas-ing sweepback, but with increasing Mach number the effects of plan formand aspect ratio on the lift-curve slope diminished and essentiallyvanished at the highest supersonic Mach number of the investigation. Theover-all travel of the aerodynamic center decreased with increasi

9、ng sweep.The investigation of a series of triangular wings of aspect ratio 2and thicknesses of 3, 5, and 8 percent showed that the wave drag was pro-portional to the thickness ratio squared. The drag due to lift decreasedwith increase in thickness ratio from 3 percent to 5 percent, the effectbeing m

10、ost pronounced at Mach numbers of 0.9 and below.A series of wings was investigated to determine the effects ofthickness distribution. The results showed that, in general, wings withsharp leading edges had a lower value of minimum drag at supersonicCONFIDENTIALProvided by IHSNot for ResaleNo reproduc

11、tion or networking permitted without license from IHS-,-,-2 CONFIDENTIAL NACARMA53A30speeds above those estimated for attachment of the bow wave, and a highervalue at subsonic speeds than wings with round leading edges. The effectsof airfoil section on the drag due to lift were small, however.The re

12、sults showedthat twisting and cambering a triangular wing ofaspect ratio 2 reduced the drag coefficient at a lift coefficient above0.i. Suchbenefits of camber and twist did not occur, however, if thecomponentof the free-stream Machnumberperpendicular to the leading edgeexceeded a value of approximat

13、ely 0.7.INTRODUCTIONIn selecting a wing for a high-speed interceptor airplane, thedesigner has the choice of a large variety of possible shapes. Since anintelligent selection requires a knowledge of the effects of the variousshape parameters on the aerodynamic characteristics of the wings, a pro-gra

14、m to provide information was formulated at the AmesLaboratory in thelatter part of 1950. The purpose of this program was twofold:i. To investigate at Machnumbers from 0.25 to 1.9 the effects oftype of plan form, aspect ratio, thickness, thickness distribu-tion, and wing camber and twist for wing-bod

15、y combinations.Such combinations would be selected to minimize the effects ofother differences generally present An a comparison of dataobtained from several facilities, such as body shape, body size,and Reynolds number.2. To provide data at supersonic speeds to fill the gap existingbetween tests ma

16、deat low Reynolds numberover a range of angleof attack in small wind tunnels and tests with rocket-poweredmodels madeat high Reynolds number, but generally at zero lift.Whenthe program at the AmesLaboratory was first formulated, it wasrealized that a considerable period of time would elapse before i

17、ts com-pletion because of the time required to construct and test the models.Futhermore, it was desired to maintain a certain amount of fluidity inthe program so that parts might be added to the program as it progressed.Because of the time involved, it was decided to expedite publication ofthe resul

18、ts by reporting the data obtained for each wing-body combinationimmediately after testing. These reports (refs. I to 17) were brief andno analysis of the data was attempted. The purpose of the present reportis therefore to compareand to analyze these data. The data will also beused to ascertain the

19、adequacy of existing theoretical solutions in pre-dicting the lift_ drag_ and pitching-moment characteristics of low-aspect-ratio wing and body combinations.CONFIDENTIALProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACARMA53A30 CONFIDENTIALThe larg

20、e amount of data obtained during this program prevents apresentation in graphical form of all the results. However_ for theinterested reader_ all the data are presented in tables I through XIX.SYMBOLSAbCDCDminCLCLdesCLopt%c_aspect ratiowing span_ in.drag coefficient_ dragqSminimum drag coefficientli

21、ft coefficient, liftqSdesign lift coefficientlift coefficient at maximum lift-drag ratiopitching-moment coefficient_ pitching momentqS_(The pitching moment is referred to the quarter point of thewing mean aerodynamic chord.)local wing chord, in.mean aerodynamic chord of wing_fb/ecedy_ob/ec dy in.sec

22、tion lift coefficient, section liftqcc rdCL,/d_dc/d_dz/dxroot chord, in.rate of change of lift coefficient with angle of attack atzero lift, per degrate of change of downwash angle with angle of attackslope of the theoretical lifting surface, with respect to ahorizontal planeCONFIDENTIALProvided by

23、IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Fa(m)LL/D(L/D)=xMmmonapqRrr otl/cuwCONFIDENTIAL NACA RM A53A30force on wing due to angle of attack, ibj_ = m2_cosh-1 x - mBy cosh-Z x + ruby -=I +=7lift, iblift-drag ratiomaximum lift-drag ratiolength of body inclu

24、ding portion removed to accommodate sting_in.free-streamMach numbercotangent of sweepback angle of leading edge of uniformlyloaded wing surface or sectorcot Aarbitrary positive integerpressure difference between upper and lower surface of sector,lb/sq ftfree-stream dynamic pressure, lb/sq ftReynolds

25、 number based on the mean aerodynamic chord of the wingradius of body, in.maximum radius of body, in.wing area, sq ft(The area is formed by extending the leading and trailingedges to the plane of symmetry.)spanwise distance from wing plane of symmetry to edge of wing,in.ratio of maximum wing thickne

26、ss to wing chordperturbation velocity in the x direction, ft/secperturbation velocity in the z direction, ft/secCONFIDENTIALProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-rNACA RN A53A30 CONF IDENTIAL 5X, y, ZeACartesian coordinates in streamwise, s

27、panwise, and verticaldirections, respectively(The origin is at the wing apex for dimensions referring towing and at nose of body for dimensions referring to body.)angle of attack of body axis, degJ I1-M langle between the resultant force vector and the normal tothe wing chord, degangle of sweepback

28、of wing leading edge, degSubscriptsauconstant-load solution for superimposed sectorconstant-load solution for entire wing surfaceSELECTION OF MODELSThe geometric parameters which determine the aerodynamic character-istics of a wing are many and, in order to keep a research program withinreasonable l

29、imits, it is necessary to select carefully the range of var-iables to be investigated. As a guide in planning the present program,which was directed primarily to the investigation of wings for high-speed fighters, a study of current design trends and anticipated devel-opments for such airplanes was

30、made. In the following paragraphs, adiscussion of the various factors influencing the selection of the modelswill be given.WingsAspect ratio.- For the unswept wings at supersonic speeds and, toa lesser extent, for sweptback wings at Mach numbers above that at whichthe component of the free-stream Ma

31、ch number perpendicular to the leadingedge becomes sonic, the flow field over most of the wing is essentiallytwo-dimensional. In the region enclosed by the tip Mach cone, the effectsof tip shape are predominant. Variation of aspect ratio for such wingsmerely alters the extent of the wing subjected t

32、o the two-dimensionalflow, and it is possible to estimate with sufficient accuracy the effectsCONFIDENTIALProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 CONFIDENTIAL NACARMA53A30of aspect ratio from two-dimensional data when tip effects are known.

33、For triangular wings_ however, the flow field over the entire wingsurface is affected by variation of aspect ratio. Hence, in this pro-gram, it was appropriate to investigate the effects of aspect ratio onwings of triangular plan form. Triangular wings of aspect ratios 2, 3,and 4 were investigated,

34、therefore, in combination with a body and areillustrated in sketch (a) for comparison. For this portion of the pro-A=2 A=3 A=4“-4 “4Sketch (a)gram, the thickness of the wings was 3 percent, a thickness structurallyfeasible and yet sufficiently small that thickness effects would notobscure the effect

35、s of aspect ratio.Type of plan form.- In the transonic speed range and at landing con-ditions, plan form is an important parameter, particularly in regard toits effect on the lift and pitching-moment characteristics. It wastherefore necessary to include a series of wings of varying plan form toinves

36、tigate these effects. Again the wings were 3 percent thick andwere investigated in combination with a body as shown in sketch (b).Aspectratio Triangular Sweptback UnsweptSketch (b)CONFIDENTIALProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-INACA RM A

37、53A30 CONFIDENTIAL 7The sweptback and unswept wings of aspect ratio 3 had the same taperratio in order to eliminate such effects from the comparison, and a valueof 0.4 was selected as representative of current design trends. A valueof unity was selected as the taper ratio for the unswept wing of asp

38、ectratio 2 since theoretical studies showed that such a wing had the highestlift-curve slope at a given aspect ratio at supersonic speeds.Thickness.- An investigation of the effects of wing thickness inthe present program is of greatest interest for wings of small aspectratio since, as the aspect ra

39、tio increases, such effects can be moreeasily estimated from the extensive theoretical and two-dimensionalexperimental results. Such results are more applicable for unsweptwings, however, whereas the effects of thickness on triangular wingsare not as well known. It was decided, therefore, to investi

40、gate theeffects of thickness using a wing with a triangular plan form of aspectratio 2. The models for this portion of the investigation are shownin sketch (c).tl/c = 0.03 t/c = 0.05 t/c = 0.087 7Sketch (c)Type of profile.- The criteria for selecting the type of profilewere that it should cause the

41、minimum wave drag and should be conduciveto a small value of drag due to lift. Available data indicated thatsmall wave drag at high supersonic speeds was generally associated withsharp leading edges and a small value of drag due to lift with roundedleading edges. Hence, wings having leading edges su

42、personic I over muchof the supersonic speed range of the tests and for which the wave dragmight be sizable were designed with sharp leading edges. A 3-percent-thick biconvex section was used. However, in order to ascertain thepenalty in wave drag due to round leading edges on such wings, the wingsiA

43、n edge is defined as subsonic or supersonic according to whether theedge lies behind or ahead of the free-streamMach cone from the mostforward point on the edge.CONFIDENTIALProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 CONFIDENTIAL NACARMA53A30sh

44、own in sketch (d) were also investigated with an elliptically shapedsection forward of the midchord. The coordinates for this latter sectionare given in table XX.A=2 A=2 A=3 A=4Sketch (d)Camber and twist.- In supersonic thin-airfoil theory for wings havingleading edges subsonic_ an infinite suction

45、associated with the lift onthe wing occurs along the leading edge which results in a force in the ,thrust direction and a reduction in the drag due to lift. In general_experimental data have indicated that the full amount of leading-edgethrust predicted theoretically is not realized with wings havin

46、g subsonicleading edges. A theoretical study by Jones in reference 18 showed_however_ that an effective leading-edge thrust could be obtained in thecase of a sweptback wing by cambering and twisting the wing. A theoret-ical study was made_ therefore, of various types of camber and twist fortriangula

47、r wings, using as a basis that required for a uniform load dis-tribution as given in reference 18.The shape of the surface for a uniform load distribution requiresa large twist at the root section. The study showed that because of thelarger root chord of the triangular wing in comparison to those of

48、 thesweptback wings treated in reference 18, the twist at the root resultedin a drag due to lift considerably greater than that indicated by theoryfor a plane wing. The large twist was associated with the last term inthe theoretical solution for the shape of the surface to produce a uni-form load di

49、stribution_ as given by= u G(mu)- 2 cosh- -i yI (Z)u 4_ muwhereas the camber near the leading edge which resulted in the effectiveleading-edge thrust was more closely associated with the first term.Since the above expression was obtained from a linearized-lifting-CONFIDENTIALProvided by IHSNot for ResaleNo reproduction or netwo