REG NACA-TR-968-1950 Investigation at low speeds of the effect of aspect ratio and sweep on rolling stability derivatives of untapered wings.pdf

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2、r networking permitted without license from IHS-,-,-TECN LIBRARY KAFB, NM REPORT 968 INVESTIGATION AT LOW SPEEDS OF THE EFFECT OF ASPECT RATIO AND SWEEP ON ROLLING STABILITY DERIVATIVES OF UNTAPERED WINGS By ALEX GOODMAN and LEWIS R. FISHER Langley Aeronautical Laboratory Langley Field, Va. I Ir-. _

3、 ._._ - .-.- Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-National Advisory Committee for Aeronautics Headquarters, 17.24 F Street NW., Washington 26, D. C. Created by act of Congress approved March 3, 1915, for the supervision and direction of th

4、e scientific study of the problems of flight (U. S. Code, title 50, sec. 15). Its membership was increased from 12 to 15 by act approved March 2,1929, and to 17 by act approved May 25, 1948. The members are appointed by the President, and serve as such without compensation. JEROME C. HUNSAKER, SC. D

5、 Massachusetts Institute of Technology, Chairman ALEXANDER WETMORE, SC. D., Secretary, Smithsonian Institution, T7ice Chairman DETLEV W. BRONK, PH. D., President, Johns Hopkins Univer- sity. JOHN H. CASSADY, Vice Admiral, United States Navy, Deput,y Chief of Naval Operations. EDWARD U. CONDON, PH.

6、 D., Director, National Bureau of Standards. HON. THOMAS W. S. DAVIS, Assistant Secretary of Commerce. JAMES H. DOOLITTLE, SC. D., Vice President, Shell Union Oil ” Corp. R. M. HAZEN, B. S., Director of Engineering, Allison Division, General Motors Corp. WILLIAM LITTLEWOOD, M. E., Vice President, En

7、gineering, American Airlines, Inc. THEODORE C. LONNQUEST, Rear Admiral, United States Navy, Deputy and Assistant Chief of the Bureau of Aeronautics. DONALD L. PUTT, Major General, United States Air Force Director of Research and Development, Office of the Chief of Staff, MatBriel. ARTHUR E. RAYMOND,

8、 SC. D., Vice President, Engineering, Douglas Aircraft Co., Inc. FRANCIS W. REICHELDERFER, SC. D., Chief, United States Weather Bureau. HON. DELOS W. RENTZEL, Administrator of Civil Aeronautics, Department of Commerce. GORDON P. SAVILLE, Major General, United States Air Force, Deputy Chief of Staff-

9、Development. WILLIAM WEBSTER, M. S., Chairman, Research and Develop- ment Board, Department of Defense. THEODORE P. WRIGHT, SC. D., Vice President for Research, Cornell University. HUGH L. DRYDEN, PH. D , Director JOHN F. VICTORY, LL. D., Executive Secretary JOHN W. CROWLEY, JR., B. S., Associate Di

10、rector for Research E. H. CHAMBERLIN, Executive Oficer HENRY J. E. REID, D. Eng., Director, Langley Aeronautical Laboratory, Langley Field, Va. SMITH J. DEFRANCE, B. S., Director, Ames Aeronautical Laboratory, Moffett Field, Calif. EDWARD R. SHARP, SC. D., Director, Lewis Flight Propulsion Laborator

11、y, Cleveland Airport, Cleveland, Ohio TECHNICAL COMMITTEES AEROPYNAMICS OPERATING PROBLEMS POWER PLANTS FOR AIRCRAFT INDUSTRY CONSULTING AIRCRAFT CONSTRUCTION Coordination of Research Needs of Military and Civil Aviation Preparation of Research Programs Allocation of Problems Prevention of Duplicati

12、on Consideration of Inventions L NGLEY AERONAUTICAL LABORATORY, LEWIS FLIGHT PROPULSION LABORATORY, AMES AERONAUTICAL LABORATORY, Langley Field, Va. Cleveland Airport, Cleveland, Ohio Moffett Field, Calif. Conduct, under unified control, jor all agencies, of scientific research on the fundamental pr

13、oblems of JEight OFFICE OB AERONAUTICAL INTELLIGENCE, Washington, D. C. 11 Collection, classification, compilation, and dissemination of scientijic and technical information on aeronautics Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REPORT 968 IN

14、VESTIGATION AT LOW SPEEDS OF THE EFFECT OF ASPECT RATIO AND SWEEP ON ROLLING STABILITY DERIVATIVES OF UNTAPERED WINGS By ALEX GOODMAN and LEWIS R. FISHER SUMMARY A low-scale wind-tunnel investigation was conducted in rolling flow to determine the e$ects of aspect ratio and sweep (when varied indepen

15、dently) on the rolling stability deriva- tives for a series of untapered wings. The rolling-jlow equip- ment of the Langley stability tunnel was used for the tests. The results of the tests indicate that, when the aspect ratio is held constant, an increase in the sweepback angle causes a signSo”?dy)

16、 lift coefficient (L/qS) drag coefficient (-X/qS) lateral-force coefficient (Y/qS) rolling-moment coefhcient (L/qSb) yawing-moment coefficient (N/qSb) lift longitudinal force lateral force normal force rolling moment pitching moment yawing moment dynamic pressure (*pV”) mass density of air free-stre

17、am velocity wing area span of wing, measured perpendicular to plane of symmetry chord of wing, measured parallel to plane of s3-netr.y Y distance measured perpendicular to plane of symmetry 2 distance of quarter-chord point of any chord- wise section from leading edge of root chord measured parallel

18、 to plane of symmetry c!a5034-51 1 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 a: d X A x Q A pb/W P c =SL L- bar Q =? A=45O. FIGURE 3.-Wings mounted in the 6.foot-diitmeter rolling-flow test section of the Langley stability tunnel. TABLE I.-TE

19、ST CONDITIONS AND CONFIGURATIONS Aspect Reynolds ratio, number- Wing whereas, no abrupt change was noted for the unswept wing except at maximum lift. The abrupt changes in damping in roll occur at approxi- mately the lift coefficients at which the drag increment CD-g begins to increase. (See fig. 4

20、b).) Changes in the damping in roll (as well as in other rotary and static derivatives) might be expected because an mcrease in the CL” increment CD-;z should correspond to the beginning of 0 4 8 12 16 20 24 28 32 36 40 Angle of attack, or, deq (b) A=2.61. FIGURE 4.-Continued. Provided by IHSNot fo

21、r ResaleNo reproduction or networking permitted without license from IHS-,-,-EFFECT OF ASPECT RATIO AND SWEEP ON ROLLING STABILITY DERIVATIVES OF TJNTAPERED WINGS 5 flow separation from some point on the wing surface. ; Appreciably sharper breaks in the curves of CD-g were obtained for the sweptback

22、 wings having an aspect ratio of 5.16. (See fig. 4 (c).) The breaks occur at lift coefficients of about 0.3 and 0.5 for the wings with 60 and 45O sweep- back, respectively, which are in fair agreement with the lift coefficients at which breaks occur in the damping-in-roll curves (fig. 5). An increas

23、e in Reynolds number, which would delay CL2 separation .and consequently cause the increases in CD-YA to occur at higher lift coefficients, probably would also extend the linear portions of the curves of damping in roll and of the other rotary derivatives. The experimental values of CIP for CL=0 det

24、ermined from these tests are compared with the theoretical values obtained from the approximate theory of reference 3 and by an appli- cation of the theory of Weissinger as presented in reference 4. (See fig. 6.) The variation of CzP for CL=0 as given by reference 3 is C,_+4) cos A A+4 cos n (%A=0 .

25、6 0 4 8 I2 I6 20 24 28 32 36 40 Any/e of attack, DZ, dey (c) A=6.16. FIGURE 4.-Concluded. where (C2,), for CL=0 is obtained from the best available theory or experimental data. A section-lift-curve slope of 5.67 per radian was used for both the Weissinger and approxi- mate theory computations. In ge

26、neral, the experimental data compare about equally well with either of the theories. Both theories indicate a decreased effect of sweep as the aspect ratio is reduced, although the variations indicated by reference 4 appear to be somewhat more reliable than those indicated by reference 3, particular

27、ly at low aspect ratios. Full-span leading-edge spoilers tested on two unswept wings (wings 1 and 4) had little effect on Clp over a greater part of the lift range. (See fig. 7.) At high lift coefficients, a definite reversal in the sign of CIP was obtained slightly before maximum lift was reached.

28、A reversal in the sign of Clp for the wings without spoilers could not be established because near maximum lift the model vibrated so severely that accurate measurements could not be made. -2 0 2 4 .6 .8 LO I.2 64 Lift coefficienf, c, (a) A=1.34. (b) A=2.61. (c) A=S.lfi. FIGURE li.-Variation of CZ.

29、with lift coefficient. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 REPORT 968-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS -Theory of reference 3 -Theory of reference 4 . I Angle of sweep, A, deq (a) A=1.34. (b) A=2.61. (c) A=5.16. FIGURE 6.-Var

30、iation of Cb for zero lift with sweep angle. LATERAL FORCE DUE TO ROLLING The derivative Cyp varies linearly with lift coefficient in most cases for only a limited range of lift coefficients. (See fig. 8.) The slopes CyP/CL through zero lift are compared in figure 10 with values obtained by the appr

31、oximate t,heory of reference 3. Both theory and experiment indicate an increase in slope with sweep for constant aspect ratio. The agreement between theory and experiment is poor, however, at the lower aspect ratios. The theory of reference 3 does not account for the values of CyP/CL obtained at zer

32、o sweep. These values are presumed to be caused by tip suction (analogous to leading-edge suction discussed in reference 5). For the wings considered, the effect of tip suction appears to be approximately independent of the sweep angle, be- cause the differences between the experimental and theo- re

33、tical curves are almost the same at all sweep angles, although the magnitude of the difference increases ap- preciably as the aspect ratio is reduced. The theory of low- aspect-ratio triangles presented in reference 5 indicates that the contribution of tip suction to the derivative CyP varies invers

34、ely as the aspect ratio. If the same relation- ship is assumed to apply to the present wings, an empirical expression for the effect of tip suction can be determined by plotting Cy,/CL for zero sweep against l/A. Such a plot, obtained from the present data and from unpublished data on a tapered wing

35、 is presented in figure 9. The data fall consistently below the curve indicated by reference 5 for low-aspect-ratio triangles but are in fair agreement with the following empirical expression: CY ( 1 c, bo=7i When this increment is added to the contribution caused by sweep, as given in reference 3,

36、 the following equation results : %- A+cos A 1 c-A+4 cos A tan +A (2) Results calculated from equation (2) are compared in figure 10 with the experimental results. The fact that good agreement is obtained is of little interest, since the same experimental results were used to evaluate the empirical

37、correction included in equation (2). The most important application of the tip-suction increment of CyP is in connec- tion with the derivative 4, as discussed in the section entitled “Yawing Moment Due to Rolling.” YAWING MOMENT DUE TO ROLLING For the unswept wings without spoilers, wings 4 and 7, t

38、he variation of CnP with lift coefficient was approximately linear up to maximum lift coefficient. The variation of CnP with lift coefficient for wing 1 (without spoiler) was linear for only the low-lift-coefficient range. (See fig. 11.) The sharp leading-edge wings, as simulated by attaching full-s

39、pan leading-edge spoilers to wings 1 and 4, yielded about the same values of C A=1.34. (b) A=O”; A=2.61. FIGURE 7.-Effect of leading-edge spoiler on the rolling derivatives of two unswept wings. which when added to equation (31) of reference 3 gives I The quantity (GJC ) L o was given as (CnP/CL)=O

40、in refer- ence 3, but the new symbol is used herein since this quantit,y does not include tip suction. (Equation (3) does not reduce to zero at A=O”.) Equation (4) has been used to construct the chart shown in figure 12. The symbol ( “%)l indicates that CL the chart applies only to that part of Cnp

41、contributed by the lift and induced-drag forces. Figure 13 shows a comparison of the experimental and calculated values of Cl I . I /T 0 c d O 0 I I =O / 0, -.- - I . I I I . 04 .4 .6 .a 0 2 .4 .6 .8 I I I I I I I I I I I 0 .2 .4 .6 .8 I.0 Lift coeffkient, CL (a) 4=1.34. (b) x4=2.61. (c) A=5.16. Frc

42、mm E-Variation of the experimental and czdculated values of C, D with lift coefficient for a series of swept wings. REFERENCES 1. MacLachlan, Robert, and Letko, William: Correlation of Two Experimental Methods of Determining the Rolling Characteristics of Unswept Wings. NACA TN 1309, 1947. 2. Goodma

43、n, Ales, and Brewer, Jack D.: Investigation at Low Speeds of the Effect of Aspect Ratio and Sweep on Static and Yawing Stability Derivatives of Untapered Wings. NACA TN 1669, 1948. 3. Toll, Thomas A., and Queijo, M. J.: Approximate Relations and Charts for Low-Speed Stability Derivatives of Swept Wi

44、ngs. NACA TN 1581, 1948. 4. Bird, John D. : Some Theoretical Low-Speed Span Loading Charac- teristics of Swept Wings in Roll and Sideslip. NACA Rep. 969, 1950. 5. Ribner, Herbert S. : The Stability Derivatives of Low-Aspect-Ratio Triangular Wings at Subsonic and Supersonic Speeds. NACA TN 1423, 1947

45、 6. Pearson, Henry A., and Jones, Robert T. : Theoretical Stability and Control Characteristics of Wings with Various Amounts of Taper and Twist. NACA Rep. 635, 1938. 7. Zimmerman, Charles H. : An Analysis of Lateral Stability in Power- Off Flight with Charts for Use in Design. NACA Rep. 589, 1937.

46、 I i,il i i I i i i I i i i i i i / / CL p 0 -.I .3 I I I I I P Ex- -1-1 2-,+ I -Es .2 .I -.I 0 .2 .4 .fi .R I.0 0 .? .4 .6 .8 f.0 (a) d=O; nose spoilers. (b) A=2.61; A=45O. (c) A=2.61; A=450. FIGURE 17.-Comparison of additional experimental and calculnted values of C, for several D swept wings. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-c ,_ - U”, ,- / : 7-a -j xx*-: I -. . : 73 -. - Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-