1、, “NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS TECHNICAL NOTE No. 1669 INVESTIGATION AT LOW SPEEDS OF THE EFFECT OF ASPECT RATIO AND SWEEP ON STATIC AND YAWING STABIUTY DERIVATIVES OF UNTAPERED WINGS By Alex Goodman and Jack D. Brewer Langley Aeronautical LaboratoryLangley Field, Va. Washington Augu
2、st 1948UUS1NESS SCIENCE at high lIft coefficients, the values of the rolling moment due to yawIng decreased and in some instances became negative near maximum lift. The rate of change of rolling moment due to yawing with lift coefficient usually Increased with both sweep and aspect ratio for the low
3、 lift-coefficient range. In general, the data at low and moderate lift coeffi-cients were in fair agreement with a simple sweep theory. INTRODUCTION Estimation of the dynamic flight characteristics of airplanes requires a Imowledge of the component forces and moments resulting from the orientation o
4、f the airplane with respect to the air stream and from the rate of angular motion of the airplaneabout each of its three axes. The forces and moments resulting from the orientation of the airplane usually are expressed as the static stability derivatives, which are readily determined in conventional
5、 wind-tunnel tests. The forces and moments related to the angular motions (rotary derivatives) have generally been estimated from theory because of the lack of a convenient experi-mental technique.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 NAC
6、A TN No. 1669 The recent application of the rollingflow and curvedflow principle of the Langley stability tunnel has made equally possible the determination of both rotary and. static stability derivatives. Preliminary tests made in the Langley stability tunnel to investigate characteristics of swep
7、t wings indicated that, although the rotary stability derivatives of unswept wings of moderate or high aspect ratio can be predicted quite accurately. from the available theory, the use of sweep - and, perhaps, low aspect ratio - introduces effects which arenot readily amenable to theoretical treatm
8、ent. For this reason a systematic research program has been established for the purpose of determining the effects of various geometric variables on both rotary and. static stability characteristics. The present investigation, which represents a part of the general program, Is concerned. with the de
9、termination of the effects .of independent variations of the aspect ratio and the sweep angle on the static and. yawing stability characteristics of a series of untaperedwings. dI.IS)j The data are presented in the form of standard NACA coefficients of forces and moinents,which are referred. in all
10、cases to the stability axes, with the origin at the quarter-chord. point of the mean aerodynamic chord of the models tested. The positive directions of the forces, moments, and angular displacements are shown in figure 1. The coefficients and symbols used herein are defined as follows: - CL lift coe
11、fficient (L/qS) CD drag coefficient (-X/qS) CD1 induced-drag coefficient Cy lateral-force coefficient (Y/qs) C1 rolling-moment coefficient (Lt/q.Sb) Cm pitching-moment coefficient (M/qs)C yawing-moment coefficient (N/qSb) L lift X longitudinal force Y lateral force L ro1ling moment about X-axis Prov
12、ided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN No. 166? M pitching mnent about Y-axis N yawing moment about 1-axis q. dynamic pressure (.v2) p mass density of air V free-stream velocity S wing area b span of wing, measured perpendicular to plane
13、 of syirmietry c chord of wing, measured parallel to plane of syimnetry y distance measured perpendicular to plane of syimnetry - c mean aerodynamic chord - C dy chord noraal to leading edge x distance of quarter-chord point of any chordwise section from leading edge of root section measured paralle
14、l to plane of symmetry x distance from leading edge of root chord. to quarter chord Z ifb/2 mean aerodynamic chord (- J cx dY) A aspect ratio (b2/s) angle of attack, measured in plane of symmetry A angle of sweep, degrees angle of yaw, degrees lateral flight-path curvature (for constant sideslip, ra
15、tio of semispan to radius of curvature) r yawing angular velocity, radians per second I L . . Ci . Clr=-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-i11AOA Ti No. 166 Cr1, = - C;=1 =211 =2VAPPARATUS ARD TPSTS !Phe test of the rOOiit inetiMOfl AOe
16、OfidiiOd. in bhe 6- by 6-foot curved.-flow test section Of the LnglOy stability tunnel In thl Ot1n Od. flight i 1miltd. O5dtei-y by dIiOtin the aII In a. Ifr.rOd. th .bij.t a fid Odi The thOdOl tstd Oos1tOd Of a ri Of iitad. wig, all of which had. NACA 001 airfoil section in plne normal to the leadi
17、ng edge ?he nOdO1 cofiguiations are idOntlf led. b the f011Owing ddigrlations: Win ApOct iO Seepbaak (deg) _ I 2 I5 L ; _1 0 5 2.61 : 6 J L _ _ 66 ( o 8 5.16 9 J - _The wing plan forms and. other pertinent model data are preeented. in figure 2. The models weie rigidly mounted on a single strut at th
18、e Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN No. 1669 7 quarter-chord point of the mean aerodynamic chord. (See fig. 3 . ) me forces and. moments were measured by means of electrical strain gages mounted on the strut. All the tests were
19、made at a dynamic pressure of 21-.9 pounds per square foot, which corresponds to a Mach number of 0.13 . The sweep angles, the aspect ratios, the Reynolds numbers, and the values of corresponding to the four air-stream curvatures used are presented in table I The first Reynolds number given is, as i
20、s customary, based on the mean aerodynamic chord and the free -stream velocity. Some evidence is available to indicate that a Reynolds number based on the chord and velocity normal to the leading edge is of greater siiificance than the conventional Reynolds number with regard to separation phenomena
21、. (See reference i.) For this reason the second Reynolds number has been included in the table. The aerodynamic characteristics of the wings were determined in both straight and yawing flow. In the straight-flow tests six-component iaeasuements were obtained for each wing through an angle -of -attac
22、k range from approximately zero lift up to and beyond maximum lift at angles of yaw of 00 and 70. The yawing-flow tests were made for zero yaw angle and at four different wall curvatures corresponding to the values of shown in table I. Each model was tested in yawing flow through an angl-of -attack
23、range from approximately zero lift up to and beyond maximum lift.CORRECTIONS The following corrections for jet-boundary effects were applied to the data:= EDiT = 573wCL CD = S2 whereboundary-correction factor obtained from reference 2 C tunnel cross-sectional area 01T uncorrected tunnel rolling-mome
24、nt coefficient K correction factor from reference 3 modified for application to present testsProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 NACA TN No. 1669 The lateral-force coefficient has been corrected for the buoyancy effect of the static-pre
25、ssure gradient associated, with curved flow, according to the following equation: Ar i vrb = where v is the volume of the model. An approximate angle-of-attack correction for deflections resulting from the aerodynamic loads has been applied to the data of the present investigation. The values of C h
26、ave been corrected for the tare associated with the induced load reu1ting from. the presence of the strut with the wing at zero angle of attack. The same correction was applied throughout the angle-of-attack range. No other tare corrections have been applied to the data. No corrections have been app
27、lied for the effects of blocking or for any effects of turbulence or static-pressure gradient on the boundary -layer flow. RESULTS AND DISCUSSION Presentation of Data The static stability characteristics of the present series of wings are given in figures 14 to 9 . Results of the tests made through
28、the angle-of-attack range for 50 yaw are not presented because they were used only for determining the lateral stability derivatives presented in figures 8 and 9 . The basic yawing-flow data for a part of the present series of wings are presented in figure 10. The yawing stability charac-teristics a
29、re presented in figures 11 to lii. Characteristics in Straight Flow Lift.- In general,the maximum lift coefficient obtained for the wings tested increased with sweep for constant aspect ratio (fig. Ii-). Since the tests were made at low Reynolds numbers (see table I), very little significance can be
30、 attributed to this result. Past experience has shown that the maximum lift coefficient for an unswept wing decreases as the scale of the test decreases. Comparison of results from large-scale tests of tapered wings made in the Armies -O- by 80-foot wind tunnel with low-scale test results indicates
31、that, while such a decrease can be quite large for unswept wings, it may be relatively small for highly swept wings.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN No. 1669 7 An application of simple sweep theory given in reference 14. indica
32、tes that C may be expressed by the following relation: () (+2)cos (c) A A+2cosA The variation of Cj with sweep angle determined, from these tests is compared in figure 5 with the values of C obtained from the afore-mentioned relation and by the theory of Weissinger (reference 5) . A section lift-cur
33、ve slope of 0.105 was used for the Weissinger computations because it was considered appropriate for the conditions of the present tests . In general, the two theoretical methods yield approximately the same results, although the Weissinger method is in better a at high lift coefficients, the values
34、 of Clr decrease and, in some instances, become negative near maximum lift.Comparisons of the experimental and theoretical values of the slope Clr/CL, taken at low lift coefficients, are presented in figure 13. The trends resulting from sweep and aspect ratio appear to be properly predicted by the t
35、heory, although the magnitude of the effect of sweep Is considerably underestimated. In general,the slope Clr/CL increases with both sweep and. aspect ratio. Lateral force due to yawing.- In figure l, the variation of the experimental and theoretical values (reference I) of Cyr with lift coefficient
36、 is presented. This derivative is probably of very little significance.CONCLUSIONS The results of low-scale tests made in both straight and yawing flow on a series of untapered wings to determine the effects of aspect ratio and sweep (when varied independently) on the static and yawing derivatives (
37、for zero sideslip) indicate the following conclusions: 1. In general, the effects of sweep on the static stability charac-teristics, namely, lift-curve slope, drag, and the effective-dihedral parameter, became smaller as the aspect ratio decreased. 2. For constant sweep angle, the magnitude of the d
38、amping in yaw decreased with an increase in aspec.t ratio for the low lift-coefficient range. At some moderate lift coefficient, this derivative changed sign (became positive) for Ii.5 and 600 swept wings.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,
39、-,-10 NACA TN No. 1669 3 . For unswept wings, the experimental data Indicate that the rolling moment due to yawing is very nearlyproportional to the lift coefficient until maximum lift is attained. For the sweptback wings, linear variations were obtained over only a halted lift range; at high lift c
40、oefficients, the values of the rolling moment due to yawing decreased and, in some instances, became negative near maximum lift The rate of change of rolling moment due to yawing with lift coefficient usually increased with both sweep and aspect ratio for the low lift-coefficient range. Ii. In gener
41、al, the data at low and moderate lift coefficients were in fair agreement with a simple sweep theory. Langley Aeronautical Laboratory National Advisory Committee for AeronauticsLangley Field, Va., March 29, 191i-8Provided by IHSNot for ResaleNo reproduction or networking permitted without license fr
42、om IHS-,-,-NACA TN No. 1669 11 REFERENCES 1. Jones, Robert T.: Effects of Sweepback on Boundary Layer and Separation. NACA TN No. li-1-02, 197. 2.Silverstein, Abe, and White, Jas A. Wind-Tunnel Interference with Particular Reference to Off-Center Positions of the Wing and to the Downwash at the Tail
43、. NACA Rep. No, 517, 1937. 3.Swanson, Robert S.: Jet-Boundary Corrections to a Yawed Mod-el in a Closed Rectangular Wind Tunnel. NACA ARR, Feb. 191I3. 1 Toll, Thomas A., and Queijo, M. J.: Approximate Relations and Charts for Low-Speed Stability Derivatives of Swept Wings. NACA TN No. 1581, 191#8. 5
44、.Weissinger, J.: The Lift D1stributionof Swept-Back Wings. NACA TM No. 1120, 197. 6.Mutterperl, William: The Calculation of Span Load Distributions on Swept-Back Wings. NACA TN No. 83I4, l9Ll, 7. Zimmerman, C. II.: Characteristics of Clark Y Airfoils of Small Aspect Ratios. NACA Rep. No. 1431, 1932.
45、 8. Shortal, Joseph A., and Maggin, Bernard: Effect of Sweepback and Aspect Ratio on Longitudinal Stability Characteristids of Wings at Low Speeds. NACA TN No. 1093, l9+6.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 NACA TN No. 1669 o - H o -rn
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48、 CJ If H CJN- 0 .0 a)a) Cl) 0)0 . -Cl) I H4 V Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-x RELATIVENACA TN No. 1669 13 1 z ys4 of e iei b At34 iZguie /OC/27L/m,fc/.02 1 N0Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN No. 1669 27 Wit7q 0 0 0 0 0 .04 0 N 0 00 0 0 .02 0 0 000.00.02 00 co_!L 06 04 / c/erc/ (ugh/-pc/h curc/cre) (c)4cJ4=2.6/ hqure /c. Conrned.(
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