1、NATIONAL ADVISORY COMMITTEE TECHNICAL NOTE 1977 8 NQV 4 1949 . SUMMARY OF THE THEORETICAL LIFT, DAMPING-IN-ROLL, AND CENTER-OF-PRESSURE CHARACTERISTICS OF VARIOUS WING PLAN FORMS AT SUPERSONIC SPEEDS By Robert 0. Piland Langley Aeronautical Laboratory Langley Air Force Base, Va. Washington October 1
2、94 9 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-W ! NATIONAL ADVISORY COMMITTEE FOR AWONAUTICS . l SUMARY OF THE: THMlRETICAL LIFT, DAMPING-IN-ROIL, AND CENTW-OF-RESSURE CHARACTERISTICS OF VICXJS WING PLAN FORMS AT SUPERSONIC SPEEDS By Robert 0.
3、 Piland SUMMARY The informition for the determination of the theoretical lift, damping-in-roll, and center-of-pressure characteristics for a group of plan forms at supersonic speeds has been collected. This information is presented in three forma: first, equations; second, figures presenting general
4、ized curves in which the quantities plotted are combinations of the geometric and aerodynamic parameters; and third, figures presenting curves for representative groups of specific configurations showing variation of the derivatives with Mach number. From this group several observationa have been ma
5、de as to the effect of taper ratio, angle of sweep, and aspect ratio on the values of the derivatives. IN!I!E?OMJCTION The linearized theory for supersonic flow has been used by various investigators to develop expreasions for the stability derivatives. The information is scattered, however, through
6、 a number of reports, not all of which use the same notation. derivatives are therefore collected herein for future comparison with experimental work and to aid designers by presenting the informtion in convenient form. A few of the more important In order to make the paper more useful for purposes
7、of comparison and design work, calculations were made for related groups of specific configurations. The results of these calculations are presented as plots of lift-curve slope, damping in roll, and center of pressure against Mach number. in the form of generalized figures in which the quantities p
8、lotted are combinations of the geometric and aerodynamic prameters. In addition, all available informtion is presented Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I 2 NACA TN 1977 SYMBOLS x, Y, P v M x S A h ht D mt recta coordinates (fig. 1) ear
9、 velocity about x-axis (fig. 1) flight speed stream Mach number speed of sound Mach angle angle of attack (fig. 1) density of air local chord root chord tip chord mean aerodynamic chord taper ratio (ct/cr) wing area aspect ratio (b2/S) angle of weep of leading edge angle of sweep of trailing edge co
10、tangent A cotangent Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 1977 3 U IV complete elliptic integral of second kFnd with modulus k WPm) complete elliptic integral of first kind with modulus k L lift 2 rolling moment M pitching moment ab
11、out apex (+) lift coefficient I cL c2 ( plotted against Mach number, are shown in figures 14(a), 14(b), and 14(c). Equations (14) to (16) are applicable for a range of Mach numbers for which the Mach line from the apex lies ahead of the leading edge (l3m $ + i) were obtained from an unpublished anal
12、ysis by Mr. Sidney M. Harmon of the Langley Stability Research Division and are as follows: 21 Limiting condition: P + - m Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-14 NACA TN 1977 P4m4( - 4p4m4 + 8P%n2)c0s- The variation of PCLU and -pCz, with
13、 b for various values of PA is shown in figure 9. No equation is available for the case in which the Mach line from the apex cuts the side edge of the wing; consequently the points obtained from equations (19) and (20) have been faired to the curves obtained from equations (21) and (22). regions are
14、 indicated by dashed lines. These No equations were available Xcp for wept untapered wings. curves of CL and -Czp, varying for Cr U with Mach number, for the swept untapered wings shown in figure 3(e) are presented in figures 15(a), l5(b), and 15(c). Swept Tapered Wings Equatiorm for and C2 for ewep
15、t tapered wings obtained from reference 12 and from the previously mentioned unpublished analysis follow (no equation is given for, supersonic leading edge): P for the case of a wing with a c2P . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA T
16、N 1977 F: -I- CE! -+ 3 -3 15 +T Id W rl- n x VI1 VI1 x + W .r cu V x + rl 4 m W k g II 3 rl 8; x It d 3 a 3 m d d ,ml I .rl IW + + rl + n d W n ti + IVI n rl I d + 3 * + + rl I 1: 3 m rl (rl a rl I W 3 + rl + d n rl + n W a .VL n rl + d 3 I + I + Provided by IHSNot for ResaleNo reproduction or netwo
17、rking permitted without license from IHS-,-,-16 NACA TN 1977 I1 + + + rl + N14 I+ a Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 1977 17 The variation of Pcl_l and -Ezp with Pm for vazious values U of Curves of CL and figure 16 for the con
18、figurationa of figure 3(f). (for CL,) and (24) (for -C2 ) are applicable for the case in which the Mach line from ths apex lies ahead of the lead- edge and the Mach line from the trailing edge of the root chord lies behind the trailing edge. Violation of the latter condition will give values of the
19、derivative which have the significance of an upper limit (reference 12). These regions are indicated by the dashed parts of the curves. Equation (25) (for CL,) is applicable when the Mach line from the apex intersects the trailing edge (P + l+n ). The two prts of the curves obtained from the equatio
20、ns for have been faired together over the region where the Mach line from the tip crosses the side edge of the wing. PA for swept tapered wings of taper ratio 0.5 is shown in figure 10. -Czp plotted against Mach number are shown in Epuatiom (23) P 2 In CL Provided by IHSNot for ResaleNo reproduction
21、 or networking permitted without license from IHS-,-,-18 NACA TN 1977 REFWENCIS 1. Lagerstrom, P. A., and Graham, Martha E. : Low Aspect Ratio Rectangulm WFngs in Supersonic Flow. Aircraft Co., Inc., Dec. 1947. Rep. No. SM-l3llO, Douglas 2. Bonney, E. Arthur: Aerodynamic Characteristics of Rectazlgu
22、lar WFn;B at Supersonic Speede. Jour. Aero. Sci., vol. 14, no. 2, Feb. 1947, pp. 110-116. 3. Lageratrom, P. A., and Graham, Martha E.: Some Aerodynamic Formulaa in Linearized Supersonic Theory for Damping in Roll and Effect of Twist for Trapezoidal Wings. Rep. No. SM-13200, Douglas Aircraft Co., Inc
23、., March 12, 1948. 4. Harmon, Sidney M. : Stability Derivatives of Thin Rectangular Wings at Supersonic Speeds. NACA I“ 1706, 1948. Wing Diagonal8 ahead of Tip Mach Lines. 5. Tucker, Warren A., and Nelson, Robert L.: The Effect of Torsional Flexibility on the Rolling Characteristics at Supersonic Sp
24、eeb of Tapered UnrJwept Wings. NACA TN 189, 1949. 6. Brown, Clinton E. : Theoretical Lift and Drag of Thin Triangular Winga at Supersonic Speeds. NACA Rep. 839, 1946. 7. Ribner, Herbert S., and Malvestuto, Frank S., Jr.: Stability Derivatives of Triangular Wings at Superaonic Speeds. 1948. NACA TN 1
25、572, 8. Puckett, Allen E.: Supersonic Wave Drag of Thin Airfoils. Jour. Aero. Sci., vol. 13, no. 9, Sept. 1946, pp. 475-484. 9. Brown, Clinton E., and Adama, Mac C. : Damping in Pitch and Roll of NACA Rep. 892, 1948. Triangular Wings at Supersonic Speeds . 10. Malvestuto, Frank S., Jr., and Mazgolia
26、, Kenneth: Theoretical Stability Derivativea of Thin Sweptback WFngs Tapered to a Polnt with Sweptback or Sweptforward Trailing Edges for a Limited Range of Supersonic Speeds. NACA TN 1761, 1949. 11. Puckett, A. E., and Stewart, H. J.: Aerodynamic Performance of Delta Wings at Supersonic Speeds. no.
27、 10, Oct. 1947, pp. 567-578. Jour. Aero. Sci., Vol. 14, Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12. Malvestuto, Frank S., Jr., Margolis, Kenneth, and Ribner, Herbert S.: Theoretical Lift and Damping in Roll of Thin Sweptback Wings of Arbitrar
28、y Taper and Sweep at Supersonic Speeds. Edges and Supersonic Wailing Edges. Subsonic Leading NACA TN 1860, 1949. 13. Jones, Arthur L., and Alksne, Alberta: The Damping Due to Roll of Triangular, Trapezoidal Flow. NACA TN 1548, l9h. and Related Plan Forms in Supersonic Provided by IHSNot for ResaleNo
29、 reproduction or networking permitted without license from IHS-,-,-20 NACA TN 1977 3 i - m v A - rl v RE 3-Irlrlrl .Po ng 4 00000 00000 I f m N Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA !L“ 1977 I . A I I I. I. 21 Y Provided by IHSNot for
30、ResaleNo reproduction or networking permitted without license from IHS-,-,-22 NACA TN 1977 i 1 4 =e, Figure 2.-Various types of plan form for which equations are given- Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 1977 t I 2 X = 0.5. Figure 3.- Concluded. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
