1、 , NATIONAL. ADViSORY COMMITTEE i?Oft AERbNAUTICS . REPORT 1130 - By JOHN D. BIRD,. LEWIS R. FISHER, and SADIE k HUBBARD - , 1: 1953 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARY KAFB, NM I llllll I Ill IIn Ill Ill11 lllll Ill Ill 0143
2、077 REPORT 1130 SOME EFFECTS OF FREQUENCY ON THE CONTRIBUTION OF A VERTICAL TAIL TO THE FREE AERODYNAMIC DAMPING OF A MODEL OSCILLATING IN YAW By JOHN D. BIRD, LEWIS R. FISHER, and SADIE M. HUBBARD Langley Aeronautical Laboratory Langley Field, Va. I Provided by IHSNot for ResaleNo reproduction or n
3、etworking permitted without license from IHS-,-,-National Advisory Committee for Aeronautics Headquurters, 1724 F Street NW., Washington 25, D. C. Created by act of Congress approved March 3, 1915, for the supervision and direction of the scientiik study of the problems of flight (U. S. Code, title
4、50, sec. 151). 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., Massachusetts Institute of Technology, Chuirman DETLEV W. BRO
5、NK, PH. D., President, Rockefeller Institute for Medical Research, Vice Chairman HON. JOSEPH P. ADAMS, member, Civil Aeronautics Board. ALLEN V. ASTIN, PH. D., Director, National Bureau of Standards. LEONARD CARMICHAEL, PR. D., Secretary, Smithsonian Institu- tion. LAURENCE C. CRAIGIE, Lieutenant Ge
6、neral, United States Air Force, Deputy Chief of Staff (Development). JAMES H. DOOLITTLE, SC. D., Vice President, Shell Oil Co. LLOYD HARRISON, Rear Admiral, United States Navy, Deputy and Assistant Chief of the Bureau of Aeronautics. R. M. HAZEN, B. S., Director of Engineering, Allison Division, Gen
7、eral Motors Corp. WILLIAM LITTLEWOOD, M. E., Vice President-Engineering, American Airlines, 111. HON. ROBERT B. MURRAY, JR., Under Secretary of Commerce for Transportation. RALPH A. OFSTIE, Vice Admiral, United States Navy, Deputy Chief of Naval Operations (Air). DONALD L. PUTT, Lieutenant General,
8、United States Air Force, Commander, Air Research and Development Command. ARTHUR E. RAYMOND, SC. D., Vice President-Engineering, Douglas Aircraft Co., Inc. FRANCIS W. REICHELDERFER, SC. D., Chief, United States Weather Bureau. THEODORE P. WRIGHT, SC. D., Vice President for Research, Cornell Universi
9、ty. HUGH L. DRYDEN, PH. D., Director JOHK F. VICTORY, LL. D., Ezecutive Secrefary JOHN W. CROWLEY, JR., B. S., Associate Director for Research E. H. CHAMBERLIN, Ezecutiue O however, only a small amount of experimental substantiation of the results is available for the low-frequency range of oscillat
10、ion. As a result, a program has been undertaken in the Langley sta- bility tunnel to det,ermine the effects of such variables a,s frequency and amplitude of moGon on the cont,ribution of the various airplane components to t.he stability derivatives of prese.nt-day airplane configurations. The work r
11、eported herein covers that phase of the invcstiga.tion which considers frequency effects on the directional damping and stability of a model undergoing a freely damped oscillatory yawing motion. The effects of vertical-tail aspect ratio ancl com- pressibility as predicted by the theoretical treatmen
12、t.s are discussed in relation to the experimental stability charac- teristics obtained by the free-oscillation and by the curved- flow procedures. SYMBOLS The data are referred to the system of stability axes and are presented in the form of standard NACA coefficients of forces and moments about the
13、 quarter-chord point of the mean aerodynamic chord of the normal wing location of the 1 model tested. (See fig. 1.) The coefficients and symbols 1 used herein are defined as follows: j CL lift coeEicient, LIqS, CD drag coeficient, D/q .333 .213 . 028 i .312 , . 203 I . 22 I .30 .0293 3. 40 29 27 032
14、1 13. 80 3.21 1 06 / .030 1 007 .023 i -. 058 Fuselage alone : 75 . . . 74 . 0119 ; 34. 36 ; 13. 77 38 .044 I :OlS .026 -.015 I Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-EFFECTS OF FREQUENCY ON TAIL CONTRIBUTION TO DAMPING IN YAW 5 successive c
15、ycles were measured and plotted to a logarithmic to one-half amplitude by the slope of the amplitude envelope scale against time. Inasmuch as the damping is of a loga- rithmic nature, the resulting plot is a straightline from which at the largest angles of yaw in order to minimize the error in deter
16、mining t,he damping derivatives. This source is may be read the time for the motion to damp to one-half believed to have resulted in no more than a 5-percent amplitude (fG-(Np-N+N,)-(N-N)=O (1) where- N;l and N$ refer to the mechanical friction of the system ,and the flexure-pivot spring constant, r
17、espectively. The solution of equation (1) can be written as l)=c-yL4 sin 2nftfB cos 2?rjt) (2) where Various unsteady-lift theories were employed to calculate the contributions of the vertical tail to the directional stability and damping of the model for comparison with the experimental results. Th
18、ese theories included the incom- pressible cases covered by Theodorsen (ref. 6) for two dimensions and by Jones (ref. 7), Reissner and Stevens (ref. B), a,nd Biot and Boehnlein (ref. 9) with various degrees of approximation for finite span. The two-dimensional work including the subsonic effects of
19、compressibility as given by Possio and Frazer and Skan is also employed. A short summary indicating procedures for obtaining the necessar.y de- rivatives from these theories is included here for completeness. N;-Nb+N+ m= - 2(1,-NY) The damping constant may be expressed in terms of the t.ime to da.mp
20、 to one-half amplitude as The directional stability and damping of the system may then be expressed in nondimensional form in a manner similar to that of reference 5 as TWO-DIMENSIONAL DERIVATIVES The work of Theodorsen on the derivation of the expres- sions for the unsteady lift and moment of a two
21、-dimensional surface undergoing sinusoidal oscillations in an incompres- sible fluid is given in reference 6. From this source, the moment per unit span about the airplane center of gravity of a vertical tail mounted on an airplane which is performing sideslipping oscillations can be shown to be N(p
22、)= -sqc, $+(u+;) m (5) A similar espression for an airplane performing yawing oscillations is (3) N(#)= -; pc13 ;-C?(k) (;-a) $+; ($+u) $1 (6) / An appendix to this report gives a discussion of the con- The terms Cn; and C,;, are necessarily in combination with Cnfl a.nd I?, respectively, because of
23、 the nature of the motion being considered. For the frequencies employed in these tests, the factor C.,k 3 0 2 should be small in comparison with C,e. In determining (h determined. The results of such an analysis would be as follows: +F ($-u) (8) The velocity terms contain only the F term of the The
24、odorsen function, whereas the acceleration terms contain the G term divided by k. The corresponding side-force derivatives are derived in the appendix. For the free-oscillation tests conducted for this report, the motion is such that the angle of sideslip is the negative of the angle of yaw. The dam
25、ping derivative measured therefore is the difference between the derivatives C, and C+, determined from equation (8). This fact was illustrated previously with respect to the reduction of the oscillation test data. In a like manner, the directional stability parameter measured can be shown to be a c
26、ombination of the Gas and C,; terms, specifically cn,-w,;k2 $ 0 Combinat,ion of the results of equations (8) to obtain the factors calculated for comparison with the oscillation tests gives (9) where B=-(u-i) k-(u+;) 2G+(u2-;) 2kF A=(u2+;) k2+(u+f) 2F+(u2-;) 2kG FINITE-SPAN DERIVATIVES The aerodynam
27、ic-span effect is considered in reference 7 for wings of aspect ratios of 6 and 3 by correcting the aero- dynamic inertia ancl the angle of attack of the infinite-span surface. An approximation employed in this analysis concerning motions of long wave length may make the results subject to question
28、for values of k near zero. The reference presents expressions for calculating the finite-span values of the Theodorsen function C(k). The use of these F and G circulation functions in equations (8) and (9) results in values of the various clerivat,ives considered for aspect ratios of 6 and 3. The ae
29、rodynamic-span effect is considered for wings of arbitrary aspect ratio in reference 8. The three-dimensional effect of the finite span may be obtained by adding a correc- tion term u to the basic Theodorsen two-dimensional func- tion. The finite-span function C(k)+a is employed in a rather lengthy
30、and tedious computation in order to deter- mine the components of the unsteady lift for each of five points along the span of the oscillating surface. The various stability derivatives may then be determined by a graphical integration of the in-phase and out-of-phase components. An approximation mad
31、e in this analysis is of such a nature as to make the method primarily suited to the higher aspect ratios. A practical lower limit of applicability is not known. A one-point approximation to the span effect for the cal- culation of the unsteady lift may be employed rather than the five-point procedu
32、re. Comparative calculations made for the present investigation have shown the one-point approximation to yield results for IOW aspect ratios which are essentially the same as those calculated by the longer procedure. Biot and Boehnlein (ref. 9) considered the aerodynamic- span effect on unsteady li
33、ft by an approach that yields a closed form for a one-point approximation to the span effect. The finite-span circulation functions used are ?= FSiG $=H+iJ For infinite aspect ratio r;=B= C(k) where C(k) is the two-dimensional Theodorsen function. The functions 7 and g may be calculated for the argu
34、ment k by methods given in reference 9, and equations (8). and (9) are again used to calculate the various stability deriva- tives. The factors A and B which appear in equations (9) must, however, be wz, + M, - d 1 The correspondence between the notation of Thcotlorsrn and that of Frazer and Skan is
35、 shoed in reference 12. The values of the Z and M funct,ions are tabulnt.ccl by Frnzna ant1 SBnn for Mach numbers 0, 0.5, and 0.7 nntl a significant range of reduced frequencies. Reissues has recently es- tended his work on oscillating wings of finite span t,o include, to the same degree of approxim
36、ation as for the incompressible cn.se, the subsonic eflect,s of compressibility. (SW ref. 13.) RESULTS AND DISCUSSION PRESENTATION OF RESULTS The experimental values of the longitudinal, directional, and yawing characteristics of the complete moclel, the model with wing removed, ancl the fuselage al
37、one as clet.ermined by force tests are given in figure 6. The espcriment.al valuce of the damping in yaw of the fuselage and tail nsscmll (designated FT) ancl the fuselage alone (clesignnt,ed fl obtained by t.he freely damped oscillation teclmiqur for several frequencies of oscillat.ion are shown in
38、 figures 7 nntl 8. The frequency a.ncl aspect-ratio effects on the damping in yaw contributed by the vertica.1 t,ail as calculated from the unsteady-lift theories discussecl previously are also shown in these figures. Figure 9 gives a comparison of the Irlntirr importance of C+ and Cn; on t.lic clam
39、ping in ynv of the model. Figures 10 to 12 are similar figures summarizing frequency and aspect-rat.io effects on directional stnl)ilitJ-. Figures 13 and 14 give the computed effects of coniprcssi- bility on the vertical-tail contribution to the clamping in -a nncl directional stability of the test
40、model. DISCUSSION The variation of the experimentally tletelmined damping in yaw of the test model with frequency is in rensonnbl good agreement for the range covered by the tests with t.he various approximate theoretical treatments which considel the effect of finite span. (See figs. 7 ancl 8.) The
41、 contribu- tion of the fuselage to the damping in yaw is small for the range of test frequencies. A two-dimensional approsimn- tion to the damping as is frequently employed for flutter work appears to be remarkably good for kO.l nnd for aspect 266367-54-Z ratios of 6 and greater (fig. 8). A large ef
42、fect of aspect ratio, however, is shown for aspect ratios below 6 for the entire frequency range and for all aspect ratios for frequencies less than k=O. 1. The two-dimensional result indicates a loss in clamping at. low frequencies much greater than the finite- span result and, in fact, shows a rev
43、ersal in sign of the damping at sufficient.ly low frequencies. A number of papers dealing with unsteady lift have noted this characteristic of the two-dimensional aerodynamic forces. (See refs. 1 to 3 and 14.) An examination of the values of the derivatives C, and C,!; ns computed from reference 6 f
44、or infinite aspect ratio nncl from reference 7 for aspect ratios of 3 and G (fig. 9) indicates that the derivative Cnb is critically depenclent on reduced frequency for the low range of reduced frequencies and infinite aspect ratio. The derivat,ive Cn, is only slightly dependent on the reduced frequ
45、ency for infinite aspect ratio nncl m-en lrss so for the lower aspect ratios. The dependence of C, on reduced frequency is responsible for the decrease in clamping shown for the infinite-aspect-ratio case as the frequent!- is reduced (figs. 7 and 8). The aspect-ratio-2 results shown in figures 7 and
46、 10 were obt.ained from the theory of Jones (ref. 7) for aspect ratio 3 11 use of a correction factor which was the ratio of the lifting-line-theory lift-curve slopes for aspect ratios of 2 and 3. This correction is only approximate and was made in order to place the results 011 a. comparable basis.
47、 The varia- tion of Cnr - !lnb wit.h reduced frequency, shown in figure 7, indicates 110 appreciable effect of frequency to zero frequency. In fact, the result of Jones for aspect ratio 3 reduces to a finite value nt, k=O given by Cnr-C,=-q )g (1.2a2-0.370a+0.515) - u) m which is not the case for th
48、e two-dimensional result that ilppronches infinity as k approaches zero. This result is not espectecl to be ver)- accurate close to k=O, however, because of the nature of t.he assumptions made in its derivation as mentioned previouslv. When the finite-spn.n effects are considered, it appears that th
49、ese eflects nre especially significant with regard to the clamping in yaw of this model for aspect ratios smaller than B. (See fig. 8.) The theory also indicates a significant tlecrense in the clamping at. low frequencies when the aspect rntio was increased from 20 to = . The experimental values of damping in yaw obtained by I free oscillation agree closely with the values of Cn, obtained by the standard curved-flow testing procedure used in the
