NASA NACA-RM-A55G19-1955 A study of conical camber for triangular and sweptback wings《三角形和后掠型机翼的锥形弯度研究》.pdf

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1、Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-MCA RMA55CEL9 A STUDY OF CONICAL CAMBE FOR TRIANGIIIAR AND -c!K WINGS By John W. Boy-d, Eugene Migotsky, and Benton E. Wetzel November 18, 1955 Figure l(b): The ordinate of figure l(b) is incorrect. The

2、 numerical values of d!z m 0 - dx mod %d as read from the figure should be multiplied by a factor 0f 25. NACA - Langley Field, Va. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-u NACA RM Am19 Z a RATIONALADVISCRYCFCRAEKONACS ASTUDYOFCONICAGCAKEEEFC

3、RTRIANGULAR AND SWEPTBACK WlNGs By John W. Boyd, Eugene Migotsky, and Benton E. Wetzel . A theoretical and experimental study has been made to determinelthe effectiveness of camber in reducLng the drag due to lift resulting f3om pressure forces acting on low-aspect-ratio triangular and sweptback win

4、gs. *- The wings investigated were derived by lifting-surface theory for sonic and supersonic speeds, and the theoretical surface shapes were modified to provide airplane surfaces which could be manufactured without undue difficulty. Design charts are included which aid in the selection of camber fo

5、r various sweepback angles and Mach numbers. Experimental data obtained for certain wings desfgned from these charts are presented as a measure of the adequacy of the theory. The experimental results for the triang hence, the change in skin-friction drag with a change in lift coefficient is negli- g

6、ible. This*component must, therefore, be removed in wind-tunnel tests in order that proper estFmates of the drag-due-to-lift chxacteristics can be made for full-scale aircraft. The other cmponent of the drag due to lift, that due to pressure forces, may be estimated by thin-airfoil theory. Linear th

7、eory, however, predicts very large suction pressures at the leading edges of planar wings which give.ri8e.to.a force Fn the. thrust direction. Since these pressures cannot be fully developed in a real.fluid, a question arises as to how much of the leading-edge thrust can be obtained. Previous experi

8、mental investigations (refs. 1, 2, and 3) . have indicated that at transonic and supersonic speeds it is difficult to develop a significant portion of this leading-edge thrust for plane trian- gular wings-of small thibess (3 to 5 percent.thick). A theoretical study by Jones in reference 4 indicated

9、that one way to attain an equivalent leading-edge thrust would be to-camber the wing leading e-dge. In this manner the suction pressures would be distributed over a relatively large area of the wing rather than concentrated at the airfoil leading edge. Thus, the magnitude of i in percent chord, and

10、z is the perpendicular distance from the chord, in percent chord. For dimensions referring to the body the origin is at the nose of the body. a angle of attack of wing root chord, de; ad angle of attack at desiw.1if-t coefficient, deg B m rl slope of leading edge of superposed uniformly loaded secto

11、r 5 (see sketch (a) Q A angle of sweepback of wing leading edge, deg Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-ESACA RM A55G19 9 angle of sweepback of a rayfromthe wing apex Subscripts a solution for summatFon of srrperposed sectors C theoretic

12、al cambered surface modified cambered surface U constant-load solution for entire wing a quantities associated with an;z,)-; cash-l-)c =$ (1 - A2)log*-$+A2 _ .- (13) 04) Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM A35GlP ll ! Design Chart

13、s for Modified Cambered Surfaces ng - It will be noted that the cambered surface defined )%ss may then be writ! for 05A5 0.8 dz 0 dx =o mod (md = ($)c + OS8 for 0.85A51.0 A=o.s n 05) Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 NACA RM A55C19 a

14、nd 0 z x mod =o The slope of the trace at A = 0.8 in the region 0.2 E (Jl _ a2m2) and the leading-edge suction term CDs9 which results from the singularity in the angle-of-attack loading, is given by (ref. 4) CD, = - JyyCL - CLd2 Provided by IHSNot for ResaleNo reproduction or networking permitted w

15、ithout license from IHS-,-,-NACA RM A55G19 For a design Mach number of unity, the preceding integrals can be evalu- ated anslytkall.y. For supersonic speeds, however, the expression for the slope of the cambered surface is unwieldy snd the integrals involving We). in addition to being cumbersome, ha

16、ve singularities at the leading edge. Therefore, the integrals were separated into two parts, one of which contained the singularity and another which was bounded throughout the interval of integration. The sdngularpartwas evaluated analytically, and the integrals with bounded functions were determi

17、ned mw-J.W. At Mach numbers dLfferent from the design Mach number, the camber loading is difficult to obtain by linear theory. Hence, iustead of com- puting the exact linear-theory drag, a method for approximately evaluating the linear-theory drag of the designed wings at off-design Mach numbers was

18、 developed. This method is based on the fact that the slopes of cam- bered surfaces designed for the Same lift coefficient but for different values of the parameter n, differ prFnrarily in magnitude; the spanwise distributions of slopes are very similar. The magnitudes of the slopes, however, are di

19、rectly proportional to the design lift coeffFcient (see eq. (l-l). Thus, by proper adjustment of the design lift coefficient, wings with essentially the ssme cambers were obtained for different values of design Mach number. Hence, the lift-drag polar of a wing designed for a Mach number, M, and lift

20、 coefficient, Cu, was assumed to be, at a Mach number M # M, the same as the polar for the equivalent wing designed for M* and C the corresponding Sketch (g) equivalent design lift coefficients at a Mach number of 1.0 for the swept- back wings as obtained from the above procedure were 0.225 and 0.29

21、2, respectively. APPARATUSANDMCDELS Test Fhcilities The experG.uental studies were conducted for the most part in the 6- by 6-foot supersonic vind tunnel, which i6.a.closed-circuit, vsriable- pressure-type wind tunnel with a Mach number range fm 0.6 to 0.9 and from 1.2 to 1.9. A detailed description

22、 of the wind tunnel and the char- acteristics of the air stream at supersonic speeds is available fn refer- ence 8. The low-speed (M = 0.22) characteristics of some of the models were obtained through additional tests in the 12-foot low-turbulence pressure wind tunnel, which is also a closed-circuit

23、, vsriable-pressure- type windtunnel. More detailed information concerning this tid tunnel can be obtained frcsn reference 9. In both wind tunnels the models were sting-mounted, and the forces andmoments measured 5th an internal, electrical, strain-gage-type balance. Provided by IHSNot for ResaleNo

24、reproduction or networking permitted without license from IHS-,-,-18 NiWA FM A55Gl9 Selection of Models r The present research program was-directed prFmarily to the investi- gation of the effects of conical camber on the drag characteristics of wings with sweptbackleading edges. For the.Ee+ent inves

25、tigation two wing plan forms were selected: (1) a trw wing of aspect ratio 2 and (2) a wing of aspect ratio 3 with 45O sweepback of the leading edge and taper ratio of 0.40. Sketches of the model plan forms are shown in figure 2. The wings were tested with both plane (uncambered) and coni- cally cam

26、bered mean surface shapes. Three uncs.m %d design lift Thickness Table for coefficient coordinates at M=l.O Triangular 0.577 0.250 0.2l5 3 percent III 5 percent 0 .225 .225 with modified Iv leading edge1 Sweptback *577 .330 .2g2 5 percent v 5 percent -577 -330 .2g2 with modtiied VI leading edge lSee

27、 figure 3. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM A55Clg 19 , Also included in the table is the equivalent design lift coefficient at a Mach number of 1.0 (see “Theoretical EeveloImen). Henceforth, the cambered wings till be identifi

28、ed by their equivalent design lift coeffi- cient at a Mach number of 1.0. In order to determine the effects of Reynolds nxsnber on the drag characteristics,tests were also made on a plane triangular wing which had RACA 0005-63 sections. The body used in conjunctfon tith the wings was that designed t

29、o have a minimumwave drag for a given volume (Sears-Haack). In order to acccm- modate the internal strain-gage balance, the body was cut off as shown in figure 2. The equation of the body is included in figure 2(a). For all models the ratio of the maximum cross-sectional area of the body to the plan

30、-form area of the wing was 0.0509. TESTS Am PRm- Range of Test Variables . The experimental portion of the investigation was extended over as tide a range of attitudes and from the pressure forces. It is evident, therefore, that the change-in hence the drag-due-to-lift characteristics include any va

31、riations resulting fram changes in the skin-friction drag coefficient with lift coefficient. Further, it was foundthatsome of the drag data presented ti reference 1 (for the wings cambered to approximate an ellip- tical span load distribution) were in error.9 Thus, the data in the present report sho

32、uld be used in lieu of the results of reference 1. The experimental data obtained in the present investigation are presented for the complete range of test variables in tables VIII through XV. For the purpose of analysis CepertinentdEttaarepresentedgraphically. Defect of Reynolds number.- Before eva

33、luating the effectiveness of conical camber on the drag characteristics,it is necessary to determine any changes in tiscous forces with changes in lift coefficient and Reynolds number. Changes in viscous forces were believed to occur prima- rily as a result of a movement of the boundary-leyer transi

34、tion point. To establish the relative importance of the movement of the transition point on the drag characteristics, tests were conducted over a wide Reynolds number range with fixed and free transition. The results of these tests are shown in figure 5 for a 5-percent-thick plane wing for Mach numb

35、ers of 0.81, 0.90, and 1.30. These data demonstrate that, as Reynolds ntier was increased fraan 2.8KW to ll.3tiOs, the drag due to lift of the wing with free transitfon appeared to decrease rapidly (see fig- 5(a) 1. The results obtained tith fixed transition which simulated the fullyturbule.ntbounda

36、rylayer , characteristic of full-scale Reynolds numbers at transonic and supersonic speeds, showed a considerably smaller reduction in drag due to lift with increasing Reynolds number. Further- more, as can be seen in figure 5(b), with free transition the drag coef- ficient at zero lift increased wi

37、th increasing Reynolds nmber, while with fixed transition the drag coefficient at zero lift decreased with increasing Reynolds number. These transition strips must therefore be used on alI the wings for proper ccmparisons. That the high Reynolds number data of the plane wing are indicative of the dr

38、ag increment associated with the transition-strips is further substantiated by the results of the cambered wing (fig. 6) which shows essentially the s however, as can be seen in figure 8, reductfons in drag due to lift with resulting reductions in total drag at lift coefficients of 0.20 and above we

39、re also realized at supersonic speeds. Thus, despite the penalty in minimum drag due to camber at supersonic speeds, the maxinnun lift-drag ratio of the cambered wings, which occurs at a lift coefficient of approximately 0.2, is never lower than that of the plane wing for Mach numbers up to 1.90. As

40、 a means of further demonstrating the effectiveness of the design methods used to improve the drag-due-to-lift characteristics, the measured drag polars for the cambered wing are ccsqare d in figure 9 with those computedfromlinear theory. Experimental data for Wch numbers of 0.90, 1.30, 1.53, and 1.

41、90 are compared, respectively, with computed polar6 for Kach numbers of 1.0, 1.30, 1.53, and 1.90. Theoretical polars for the cambered wing are presented for the conditions of full leading-edge suc- tion and no leading-edge suction. For a Mach number of 1.0 there are shown two theoretical cambered-w

42、ing polsrs for the case of no leading-edge suction, the derivations of which are discussed in ?L!heoretical Develop- ment.“ In addition, the ideal drag polar for the plane wing with full leading-edge suction at M = 1.0 is shown. Experimentalvalues of CD0 for the plane wing were used in computing the

43、 theoretical polars for both the plane and the cambered wing. It is interesting to note that at a Mach number of tity where no wave drag exists the theoretical polar for the cambered wing closely approximates the theoretical polar for the plane wing, full leading-edge suction being assumed in both c

44、ases. This similarity of the two polar6 is a consequence of the fact that, in the design of the conically csmbered wing, the span load distribution resulting fram camber was very nearly equal to that due to angle of attack which for triangular wings is ellip- tical. Had the spanloading due to camber

45、 beenexactly the ssme as that due to angle of attackthetwo polars wouldhave been identical. The calculations for a Mach number of 1.0 show that the no-leading- edge-suction polar6 as well as the full-suction polar agree with the ideal-plane-wing polar at the design lift coefficient (O.U5) but depart

46、 as the lift coefficient is increased or decreased fram this value. The predicted values of the drag coefficient for no-leading-edge suction based on the solution of reference 7 are samewha.t less than those pre- dicted from the simple no-suction polar above or below the design lift coefficient. A c

47、omparison of the experimental data obtained at a Mach number of 0.90 with the theoretical polar for a Mach number of unity shows that conical camber is quite effective neax the design lift coefficient, the Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-

48、,-,-24 NACAHMA5XW increment in drag due to lift* being equal to the minimum drag due to lift increment possible for a wing of this aspect ratio. At lift coef- ficients less than the design value the eqerimental drag coefficients lie between the theoretical cambered wing polar for full leading-edge s

49、uction and those for no leading-edge suction. It is gratifying to note, however, that only a small penalty in the drag coefficient at zero lift was incurred from the camber, indicating that a significant smount of the leading-edge suction due to the pressure peak in the vicinity of the nose is still being achieve