1、51 - SEARCH MEMORAN DUM WIND-TUNNEL MEASUREMENTS AT SUBSONIC SPEEDS OF THE STATIC AND DYNAMIC-ROTARY STABILITY DERIVATIVES OF A TR.IANGULAR-WING AIRPLANE MODEL HAVING A TRIANGULAR VERTICAL TAIL By Benjamin H. Beam, Verlin D. Reed 3 and Armando E. Lopez 9 Ames Aeronautical -w-A“ rxe - iifrRfTP 01: LI
2、BRAW f.-dI,*-(IC - -*v- cLAssIpIEDDocuMENT - This matcrfal con- wormtion meeting the tiod Defense of the united states within - * of the eapiomp laws, TMO 18, U.S.C., Secs. I83 and 764, tbe tranamisaion or revelatioo of which in p4p manner to 8x1 uuaubried penaon Is prohibited law. NATIONAL ADVISORY
3、 COMMITTEE FOR AERONAUTICS WASHINGTON April 25, 1955 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM 5528 . I .) NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS RESEARCH MEMORANDUM WIND-“NEL MEASUREMENTS AT SUBSONIC SPEEDS OF THE STATIC AND DYNAM
4、IC-ROTARY STABILITY DERIVATIVES OF A TRIANGULAR-WING AIRPLANEl MODEL HAVING A TRIANGULAR VERTICAL TAIL By Benjamin H. Beam, Verlin D. Reed, and Armando E. Lopez SUMMARY Oscillation tests were conducted in a wind tunnel to measure the dynamic-rotary stability derivatives of an airplane model at high
5、subsonic speeds. The model wing was approximately triangular with an aspect ratio of 2.2 and the vertical tail was triangular. The Mach number range was from 0.25 to 0.95 and the basic Reynolds number was l,5OO,OOO. The angle- of-attack range was from -8 to +18O at low speeds but was more restricted
6、 at high speeds because of model safety considerations. The oscillation frequency for the majority of the tests was approximately 8 cycles per second; however, some data are included for an oscillation frequency of approximately 4 cycles per second. approximately 2. The oscillation amplitude was Mea
7、surements included the damping in pitch, damping in yaw, damping in roll, the rolling moment due to yawing velocity, and the yawing moment due to rolling velocity. The static force and moment characteristics of the mgdel are also presented. Comparisons have been made between experi- mental values of
8、 the stability derivatives and values estimated by current semiempirical methods using the wind-tunnel static-force data. Generally fair agreement between estimation and experiment was obtained at low angles of attack for Mach numbers below 0.92. Some sizable differences were noted but these could b
9、e accounted for by simple modifi- cations to existing methods of computation. For Mach numbers of 0.94 and 0.95 the damping in pitch and damping in yaw were considerably lower than at a Mach number of 0.92, and for angles of attack above loo at high Mach numbers the rolling derivatives were violentl
10、y affected by flow irregu- larities on the wings. 1Corrected version supersedes original version which was found to P contain a computing error in the yawing-moment coefficients measured therefore, a trailing vortex system does not have to be considered and the effects of finite span will be greatly
11、 reduced. The damping in pitch given by equation (1) does not include Cm one of these is the blanketing effect of the body, and the other is a shortening of the tail height due to inclination of the model longitudinal axis. In addition, B Effects of fences.- In figure 21 it is shown that the additio
12、n of wing fences resulted in a more nearly linear variation of angle of attack for Mach numbers of 0.25 and 0.60 and near 10 angle of attack. Data were not taken at high Mach numbers in this range of angles of attack, but it appears from a study of the static-force data (figs. 5 and 14) that a chang
13、e similar to that shown in figs. 21( a) and (b) would be expected at higher Mach numbers. Czr-Cz. with B Effects of Reynolds number.- For the Reynolds numbers at which oscil- lation tests were conducted (l,5OO,OOO and 2,750,000) there were no large effects of Reynolds number on the lateral rotary de
14、rivatives (fig. 22). It will be recalled, however, from the discussion of Cn in this range that there was a change in the tail contribution to of Reynolds number, No effects of Reynolds number on the contribution of the wing were apparent in these data or in the longitudinal characteristics (figs. 6
15、 and 11). and figure 18 P CnP Effects of oscillation frequency.- The effects of frequency were found to be small from additional tests conducted at a frequency of approximately 4 cycles per second, roughly half the oscillation frequency at which most of the oscillation data were obtained. The combin
16、ation of changes in Mach number and oscillation frequency made available a range of reduced fre- quencies 0.26 at low speeds. wb/2V, from approximately 0.003 at the high Mach numbers to Experimental data for three representative Mach Provided by IHSNot for ResaleNo reproduction or networking permitt
17、ed without license from IHS-,-,-NACA RM A55A28 22 P numbers are shown in figure 18 for the sideslip derivatives and in figure 22 for the rvtary derivatives. It will be noted that in figure 22 the data on the cross derivatives have been presented as the combined derivative term cnp + ir-czS)* This fo
18、rm was considered justifiable because of the lack of apparent fre- quency effects in the range investigated, and resulted in considerable simplification in the test procedure. Effects of oscillation amplitude.- All the experimental data pre- sented in this report were taken for a peak oscillation am
19、plitude of approximately 2O. lation amplitudes from less than lo to approximately 3.5O to establish the effects of oscillation amplitude (see ref. 13). directed to the type of low-amplitude instability in pitch at high Mach numbers noted in reference 6 but no similar effects were found in the presen
20、t investigation. The range of the tests, however, included peak oscil- Particular attention was Dynamic-Stability Estimates. In order to provide more perspective in the evaluation of the dynamic stability of this particular configuration, the data in the foregoing figures have been applied to estima
21、tes of the dynamic motions for a repre- sentative airplane geometrically similar to the model. Values of the period and time to damp of the short-period longitudinal and the lateral- directional oscillations have been calculated. The longitudinal charac- teristics have then been compared with the Ai
22、r Force and Navy flying qualities requirements (ref. 25) defining the relation between the period and damping which is considered satisfactory from the standpoint of dyna- mic stability. These criteria of dynamic stability do not necessarily imply that unsafe or divergent motions will result if the
23、criteria are not satisfied, but are merely rough indications as to whether the airplane will be able to execute satisfactorily its expected maneuvers in this range. A wing area of 650 squale feet and an airplane weight of 23,000 pounds has been assumed in the calculations. Additional assumed mass an
24、d geomet- ric data are listed in table 11. The airplane was considered to be in level flight at the start of the motion with no movement of -the control surfaces during the oscillation. Dynamic longitudinal stability,- The method used in the estimation of the period and damping of the short-period l
25、ongitudinal oscillation is given in the appendix, and the results of the calculations are presented in figure 24. On the basis of figure 24 it appears that the dynamic sta- bility is satisfactory for level flight between the Mach numbers of 0.25 Provided by IHSNot for ResaleNo reproduction or networ
26、king permitted without license from IHS-,-,-. NACA RM A55A28 23 U- IC and 0.94. For Mach numbers between 0.92 and 0.94, the strongest cantri- buting factor in the increase in time to damp is the decrease in damping in pitch in this range (fig. 13). positive values of damping-in-pitch coefficient do
27、not result in similarly lightly damped or divergent motions in the stick-fixed, longitudinal oscillation because of the additional damping contributed by C . (See The extremely low negative or even Appendix A, eq. (A7) .) La A number of other aerodynamic derivatives enter into tke estimation of the
28、longitudinal oscillation (see appendix), but the effects of these additional terms can be shown to be small and in many cases entirely negli- gible. Variations in C and CL through a range of values from 0 to 4 (typical for this configuration) resulted in changes in period and time to damp of the ord
29、er of 1 to 2 percent. Cm I is the mass moment of inertia about the y axis; and Aa is an incremental change in angle of attack. The solution is of the form Aa,q = (const.)eAt 21 - - Withthe substitutions T = - K=- and by use of the opera- LY, - - pvs pv*ss. ;I U tor D = - the above equations become,
30、dt where h is a root of the characteristic rquation of the system, given by Ah2 + BA + C = 0 (A?) and tcRmmmB Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-t t . NACA RM A55A28 27 I Thus, -B f JB2 - 4AC 2A A,h, = For an oscillatory system, 4ACB2 an
31、d the roots are complex conjugates. The logarithmic decrement of the oscillation becomes - - and the time to damp to one-half amplitude becomes 2A Tl,2 = (F) In 2 = 1.386 ij A The period of the oscillation is derived from the imaginary part of the root as . c Provided by IHSNot for ResaleNo reproduc
32、tion or networking permitted without license from IHS-,-,-28 NACA RM A55A28 - REFERENCES 1. Toll, Thomas A, and eijo, M. J.: Approximate Relations and Charts for Low-Speed Stability Derivatives of Swept Wings. 1948. NACA TN 1581, 2. Sacks, Alvin H.: Aerodynamic Forces, Moments, and Stability Deriva-
33、 tives for Slender Bodiesof General Cross Section. NACA TN 3283, 1954 3. Bird, John D., and Jaquet, Byron M.: A Study of the Use of Experi- / /- mental Stability Derivatives in the Calculation of the Lateral Disturbed Motions of a Swept-Wing Airplane and Comparison With Flight Results. NACA Rep. 103
34、1, 1951. 4. Wiggins, James W.: Wind-Tunnel Investigation at High Subsonic Speeds to Determine the Rolling Derivatives of Two Wing-Fuselage Combina- tions Having Triangular Wings, Including a Semiempirical Method of 1 Estimating the Rolling Derivatives. / NACA RM L53L18a, 1954. 5. Tobak, Murray: Damp
35、ing in Pitch of Low-Aspect-Ratio Wings at Sub- sonic and Supersonic Speeds. NACA RM A52L04a, 1953. 6. Beam, Benjamin H.: The Effects of Oscillation Amplitude and Frequency on the Experimental Damping in Pitch of a Triangular Wing Having an Aspect Ratio of 4. NACA RM A52G07, 1952. / Triplett, William
36、 C., and Brown, Stuart C.: Lateral and Directional Dynamic-Response Characteristics of a 35 Swept-Wing Airplane as Determined from Flight Measurements. NACA RM A52117, 1952. r 7* 8. Donegan, James J., and Pearson, Henry A.: Matrix Method of Determin- ing the Longitudinal-Stability Coefficients and F
37、requency Response of an Aircraft from Transient Flight Data. NACA Rep. 1070, 1952. /9. Donegan, James J., Robinson, Samuel W., Jr., and Gates, Ordway B. Jr.: Determination of Lateral-Stability Derivatives and Transfer-Function Coefficients From Frequency-Response Data for Lateral Motions. NACA TN 30
38、83, 1954. 10. DAiutolo, Charles T.: Low-Amplitude Damping-in-Pitch Characteristics of Tailless Delta-Wing-Body Combinations at Mach Numbers from 0.80 to 1.35 as Obtained With Rocket-Powered Models. NACA F34 L54D29, 1954 Milliken, W. F., Jr.: Dynamic Stability and Control Research. Cornell f ll. Aero
39、nautical Laboratory Rep. CAL-39, Buffalo, 1951. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.- . NACA RM A55A28 29 12. Campbell, John P. and McKinney, Marion 0.: Summary of Methods for Calculating Dynamic Lateral Stability and Response and for Es
40、timat- ing Lateral Stability Derivatives. NACA Rep. 1098, 1952. 13. Beam, Benjamin H.: A Wind-Tunnel Test Technique for Measuring the Dynamic Rotary Stability Derivatives Including the Cross Derivatives at High Mach Numbers. NACA TN 3347, 1955. 14. Glauert, H.: The Elements of Aerofoil and Airscrew
41、Theory. The University Press, Cambridge, England, 1926, ch . XIV. 15. Herriot, John G.: Blockage Corrections for Three-Dimensional-Flow Closed-Throat Wind Tunnels With Consideration of the Effect of Compressibility. NACA Rep. 995, 1950. (Formerly NACA RM A7B28) 16. Runyan, Harry L., Woolston, Donald
42、 S., and Rainey, A. Gerald: A Theoretical and Experimental Study of Wind-Tunnel-Wall Effects on Oscillating Air Forces for Two Dimensional Subsonic Compressible h Flow. NACA RM L52117a, 1953. /l7. Wiggins, James W.: Wind-Tunnel Investigation at High Subsonic Speeds c of the Static Longitudinal and S
43、tatic Lateral Stability Character- . istics of a Wing-Fuselage Combination Having a Triangular Wing of Aspect Ratio 2.31 and an NACA 65003 Airfoil. NACA RM L53GO9a, - 1953 18. Smith, Donald W., and Heitmeyer, John C.: Lift, Drag, and Pitching Moment of Low-Aspect-Ratio Wings at Subsonic and Superson
44、ic Speeds - Plane Triangular Wing of Aspect Ratio 2 with NACA 0003-63 Section. NACA RM A5OK21, 1951. 19. Wyss, John A., and Herrera, Raymond: Effects of Angle of Attack and Airfoil Profile on the Txo-Dimensional Flutter Derivatives for Airfoils Oscillating in Pitch at High Subsonic Speeds. NACA RM A
45、54H12, 1954. /20. Tobak, Murray, Reese, David E., Jr., and Beam, Benjamin H.: Experimental Damping in Pitch of 45 Triangular Wings. NACA RM 5026, 1950. 21. Lehrian, Doris E.: Calculation of Stability Derivatives for Oscillating Wings. British ARC 15,695 - 0.1043, S. & C. 2750, 1953. Kemp, William B., Jr., and Becht, Robert E.: Damping-in-Pitch Characteristics at High Subsonic and Transonic Speeds of Four 35O Sweptback Wings. NACA RM L53G29a, 1953. /22. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
