NASA-TN-D-209-1960 The rolling moment due to sideslip of swept wings at subsonic and transonic speeds《在亚音速和跨音速下 掠翼侧滑产生的滚动力矩》.pdf

1、NASA TN D-20: TECHNICAL NOTE D-209 THE ROLLING MOMENT DUE TO SIDESLIP OF SWEPT WINGS AT SUBSONIC AND TRANSONIC SPEEDS By Edward C. Polhamus and William C. Sleemm, Jr. Langley Research Center Langley Field, Va. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON February 1960 (IASA-TN-D-2G9) IBE

2、 SCLLJILG ECEEhT DUE IO N89-7G727 5iCESLlE GE ELEF3 lILGS AI 5TEZCEIC AND lbAbSCbIC SjEkEDE (EASA. Larsley besearch Center) 85 F Unclas 00/05 0197741 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-B b m NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

3、TECHNICAL NOTE D-209 THE ROLLING MOMENT DUE TO SIDESLIP OF SWEPT WINGS AT SUBSONIC AND TRANSONIC SPEEDS1 By Edward C. Polhamus and William C. Sleeman, Jr. SUMMARY An analysis has been made of results obtained in a systematic research program concerned with the effects of wing sweep, aspect ratio, ta

4、per ratio, and dihedral on the rolling moment due to sideslip of wing- fuselage configurations up to Mach numbers of about 0.95. Other test results are presented to show trends of rolling moment due to sideslip with Mach number for a few wings in the transonic and supersonic speed range. In viex of

5、the need for reliable procedures for estimating rolling rnomeiit due to sideslip at high subsonic speeds, new methods have been derived and design charts are presented for estimating the effects of compressibility and wing geometry. msted and experinental results indicated that the effects of wing a

6、spect ratio, taper ratio, sweep, and dihedral on the rolling moment due to side- slip of wing-fuselage configurations for sideslip angles up to fjo could be estimated with reasonable accuracy up to the force-break Mach number zt low lift coefficients. The overall agreement between esti- INTRODUCTION

7、 A systematic research program has been conducted in the Langley high-speed 7- by 10-foot tunnel to study effects of wing geometry on the aerodynamic characteristics of wing-body combinations at high sub- sonic speeds. This program included effects of sweepback, aspect ratio, taper ratio, and geomet

8、ric dihedral on the lateral aerodynamic character- istics for Mach numbers up to about 0.95. In order to expedite publica- tion of these data, each series was published separately (refs. 1 to 6) xith only a limited analysis of the data. Hodever, these limited analyses indicated, as does reference 7,

9、 the need for more reliable methods of lsupersedes declassified NACA Research Memorandum L54L01 by Edward C. Polhamus and William C. Sleeman, Jr., 1955. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 * predicting the rolling mornenti due to sidesl

10、ip which, for wings of current pose of this paper therefore is to summarize and analyze the results for the rolling moment due to sideslip of the aforementioned general research program and to develop new methods of estimating the derivative. tion, experimental data from other sources will be utiliz

11、ed where needed. interest, may be the most important of the lateral derivatives. The pur- -c In addi- COEFFICIENTS AND SYMBOLS The stability system of axes (axes yaw but do not pitch with model) was used and moments are referred to the quarter-chord point of the mean aerodynamic chord. CL Cl “2 9 v

12、P S b U P r A M R A h lift coefficient, Lift/qS rolling-moment coefficient , Rolling moment/qSb section lift coefficient dynamic pressure, pVq2, lb/sq ft free -stream velocity , ft / s e c mass density of air, slugs/cu ft wing area, sq ft wing span, ft angle of attack, radians (except where noted) a

13、ngle of sideslip, radians (except where noted) dihedral angle, deg; also circulation strength (appendix B) angle of sweepback of quarter-chord line, deg (except where noted) Mach number Reynolds number wing aspect ratio , b2/S wing taper ratio, Tip chord/Root chord 5 C t n Provided by IHSNot for Res

14、aleNo reproduction or networking permitted without license from IHS-,-,-3 rolling moment due to sideslip, - Mh Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 Kf fuseme effect (fig. 7) aspect-ratio effect at zero sweep (fig. 8) (cip4* dihedral effe

15、ct (ref. 10 or 11) CZPr compressibility correction to dihedral effect (fig. 12) Sr effect of fuselage on transverse flow (eq. (5) ) pr El All the design charts presented in this paper concerned with effects of wing sweep are given as a function of the half-chord sweep angle to minimize effects of ta

16、per ratio as shown in appendix A. Since the most commonly used sweep reference line is the quarter-chord, a chart has been prepared from which the half-chord sweep can be easily obtained from the quarter-chord sweep, aspect ratio, and taper ratio. For convenience in locating this chart, it has been

17、placed at the end of the figures (fig. 29). . I Effect of Sweep Angle Infinite aspect ratio.- In the analysis of effects of wing sweep on the rolling moment due to sideslip, determination of the expression for an infinite-aspect-ratio wing is of interest as a limiting case for wings of finite aspect

18、 ratio. sideslip for a wing of infinite aspect ratio can be assumed to arise entirely from lift increments associated with the difference in effective sweep angle on the leading and trailing wing panels in sideslip. leading wing is considered to have a lower effective sweep (A - p) and, consequently

19、, a higher lift slope; conversely, the trailing wing panel has a higher effective sweep (A + p) and a lower lift slope than at zero sideslip. The rolling moment due to sideslip for an infinite-aspect- ratio swept wing may be derived by replacing the sweep angle with effec- tive sweep angle (A f p) a

20、nd differentiating the expression for lift with respect to sideslip. The sweep effect on rolling moment due to The The total rolling moment can be expressed as c2 = (CI + (c1 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-7 where - then 2xa(cos A -

21、p sin A) (CdL = 2 - 23ta(cos A + p sin A) (“1 R - 2 Differentiating with respect to p gives Then Since the lift acts at the midsemispan and panel and negative for the right panel, y/b is positive for the left czp = aa(- -) sin A Provided by IHSNot for ResaleNo reproduction or networking permitted wi

22、thout license from IHS-,-,-8 + Subs t itut ing c2/ however, other factors must be con- sidered. The loss in lift, for example, on the trailing wing panel in sideslip occurs not only from the increased sweep (A + p) on this panel but also from the reduced geometric panel aspect ratio cos2A relative t

23、o the unyawed wing panel. Furthermore, because the increment of lift distribution resulting from sideslip is antisymmetrical, the aerodynamic induction effects would be similar to a wing having half the panel aspect ratio of the yawed panel. It is therefore assumed that the lift on the trailing pane

24、l of a swept wing in sideslip is the same as the lift (CL*) of a wing at zero sideslip whose aspect ratio and sweep are given by A cos2(A + p) A*=A+B Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-9 e Derivation of the rolling moment due to sideslip

25、 for the finite-aspect- ratio case is made in the same manner as for the infinite-aspect-ratio case with the aforementioned additional effects considered. The derivation of a very simple expression for the lift-curve slope of finite-aspect-ratio wings is described in appendix A which gives results t

26、hat are in excellent agreement with lifting-surface solutions. tion (AS) of appendix A is therefore used in the rolling-moment derivation for finite-aspect-ratio wings. Equa- At zero Mach number equation (A6) becomes C how- ever, experimental results with and without a fuselage consistently indi- ca

27、ted smaller values of rolling moment due to sideslip even when the wing was. raounted on the fuselage center line. Therefore, in addition to the well-known effect of wing height (refs. 7 and g), there appears to be an additional effect of the fuselage. A possible explanation of this addi- tional fus

28、elage effect is indicated in figure 7( a) which illustrates the possible reduction in effective sideslip angle over the wing caused by t,he presence of the fuselage. For the wing alone, each wing panel would be at an effective sideslip equal to the geometric sideslip angle as in the top portion of f

29、igure 7(a) whereas for the wing-fuselage configura- tion the fuselage would be expected to aline the flow field in the direc- tion to decrease the effective sideslip. An attempt to correct for this fuselage effect has been made by using eqerimental data from refer- ences 15, 16, and 17, and the resu

30、lts are presented in figure 7(b) as a function of the ratio of fuselage length ahead of the wing-tip half-chord to wing span. The relationship usedto derive Kf and a summary of per- tinent model geometry with appropriate references are also given in fig- ure 7(b). determination of Kf inasnuch as the

31、 only systematic investigation avail- able (ref. 17) indicated that the fuselage length had a fairly large effect on the rolling noment due to sideslip. Other parameters such as the ratio of fuselage dianieter to wing span should also be important; how- ever, the range of this parameter studied is t

32、oo limited to evaluate adequately. correlation of figure 7, selection of this point was rather arbitrary and vas based only on the importance of the half-chord sweep and the fact that the load at the wing tip has the longest moment m. The most accurate correlation point undoubtedly would be a functi

33、on of wing plan fom and fuselage shape and probably would be located somewhat inboard of the tip; however, these refinements could not be determined from the linited data available. to fuselage effects and the correlation presented in figure 7 should be regarded as only an approximate indication of

34、these effects. The fuselage length was considered the main variable in the With regard to use of the wing-tip half-chord point in the Considerably more research is needed with regard Effect of Aspect Ratio In addition to the effect of aspect ratio on the sweep contribution to the rolling norzent due

35、 to sideslip, there is an additional aspect- ratio effect which occurs at zero sweep and is assumed to be relatively invariant with sweep angle. This increment, which is designated in this paper, has been treated theoretically by Weissinger (ref. 18) jclpCL)n Provided by IHSNot for ResaleNo reproduc

36、tion or networking permitted without license from IHS-,-,-14 for unswept wings .3 increased approximately linearly with 1/A and decreased somewhat with taper. Values of large number of wing plan forms and when combined with the sweep contri- bution (from fig. 6) showed fair agreement with experiment

37、. The lack of consistently good agreement between the aforementioned estimates and experimental results for wing alone suggested that greater accuracy might Weissingers results indicated that ., were determined from reference 18 for a f PCL )A be obtained by correlating a large amount of experimenta

38、l data to obtain The difference between experiment and theoretical L 8 1 2 (CZ).) Results (czp% of such i, (clpcL); ( was considered to be the aspect-ratio effect a correlation obtained from references 13, 19, 20, and 21 and presented in table I1 and in the upper part of figure 8 for 14 untapered wi

39、ngs of various aspect ratios and sweep angles appear to substantiate the line- arity of with 1/A and the assumption that sweep has little effect. The Dean line has been replotted for convenience in the lower part of figure 8 as a function of aspect ratio. Also presented is the mean line for zero tap

40、er which was obtained in a similar manner. Effect of Geometric Dihedral A large number of solutions pertaining to the effect of geometric dihedral on the rolling moment due to sideslip have been obtained by the Weissinger modified lifting-line method and are presented in design charts in terms of re

41、peated here. These solutions are, however, for the wing alone and a correction factor is needed to account for effects of the transverse flow over the yawed fuselage when applying these solutions to wing-fuselage configurations. rolling moment of wings without geometric dihedral is well known; howev

42、er an additional effect is introduced for wings having dihedral. This addi- tional effect is associated with the fact that the vertical position of a wing having dihedral varies along the span relative to the fuselage. A method is suggested in reference 9 by which estimates may be made for 3Subseque

43、nt to the original publication of the present paper, this method has been applied to swept wings by M. J. Queijo in NACA Report 1269 entitled “Theoretical Span Load Distributions and Rolling Moments for Sideslipping Wings of Arbitrary Plan Form in Incompressible Flow.“ in references 10 and 11 and th

44、erefore will not be CZPr Now, the effect of this fuselage flow field on the Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-a wing with dihedral by replacing it with a wing without dihedral at some effective height relative to the fuselage and evalua

45、ting the fuse- lage flow effect for this equivalent wing. The results of reference 9 show that the equivalent wing will have approximately the same rolling moment due to sideslip if its vertical position relative to the fuselage coincides with the wing with dihedral at the spanwise position equal to

46、 1.4D/b as illustrated in the following sketch: / . -I b l+-/- Actual wing .+-I Equivalent wing b The spanwise position of 1.4D/b with dihedral that intersect the vertical plane of symmetry at or near the midfuselage height. figurations, the reader is referred to figure 4 of reference 9. is consider

47、ed applicable only for wings For estimates regarding high- and low-wing con- Inasmuch as the aforementioned fuselage effect is relatively small when compared with the effect of the isolated wing, use of the simple expression for the effect of wing height given in referelice 7 should give satisfactor

48、y results. This expression for fuselages of circular cross section is where wing without dihedral or of an equivalent wing at a height corresponding to the height of the as mentioned previously. Therefore, for wings having dihedral zw i.s the height above the fuselage center line of an actual 1.4D/b spanwise station of a wing with dihedral and by substitution Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-16 where p and I7 are in degrees. Effect of Mach Number Very little theoretical work has been done with regard to the effects of compressib