1、RESEARCH MEMORANDUM I PRELLmNARY MEASUREMENTS OF THE AERODYNAMIC YAWING DERIVATIVES OF A TRiANG-ULAR, A bWEPT, AND AN UnSWEPT WING PERFORMING PURE YAWIVG OSCILLATIONS, WITH A DESCRXTLON OF THE INSTR-UMENTATION EMPLOYED “ - .“_ “ “ “ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WASHINGTON April 2, 195
2、6 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-D YAWING DERJXATWES OF A TRIAI!IGurS;, A SWEPT, AND AN uNSTfim WING PERFORmG PURE YAWING OSCILLATIONS, WITH A DESCRIFCION OF THE INSTRUNEXTATION EBPLOYED sy 14. J. Quei jo, Herman S. Fletcher, C. G. M
3、arple, and F. M. Hughes A preliminary investigation has been =de to determine the effect of notion periodicity on %he aerodyrdc derivatives due to yawing velocity and yawing acceleration for a 60 delta wing, a 45 sweptback wing, and 211 unswept wing. Results were obtained from steady-state .yawing-f
4、low tests en-d fron tests of the models qerfo-ming pure sinusoidal yawing ascillations. Tle oscillation tests were made at one value of the reduced-frequence paraneter, hence this fact should be kept in dnd in considering the following ststenents. The results showed that at low angles of attack ther
5、e was good agreement, between steady-state and oscillatory values os the aer0Qnani.c deriva- tives due to yawing velocity for all three winss. At high angles of attack large differences occurred between steady-state and oscillatory values of the derivatives due to yawing velocity for all three wings
6、. The derivatives due to yawing acceleration varied approximately Linearly with angle of sttack 1r1 the low angle-of-attack range. At angles of attack near and zbove mzxim lift, these derivatives showed no linear dependence on mgle f attack an2 a%tained large numerical values. A description of the d
7、esign and “ction of the instrumentation used in the investigation is included in the aspendix. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 INTRODUCTION a. The advent of high-speed airplanes of high relative density has focused attention or, cer
8、tain problems associated witn the dynamic sta- bility of aircraft which, because of previous unimsortance, have here- tofore beerr neglected. An;ong the problems ere the effect of periodicity of the airplme motion on the stability derivatives, a-d the possibility that acceleration derivatives (xbich
9、 generally have been neglected when making dyndc stability calculations) may be important for certain air- plme configurations. Some information on both problems already has been obtained exper- imentally. References 1 through 3, for exaxple, show comparisons between damping-i:n-yaw derivatives obta
10、ined from steady-state tests performed by use of the Langley stability tunnel curved-flow technique and from tests in which -the models were oscillated about their vertical axes. The farmer technique permits measurenents of the derivatives due to yawing velocity, for example the yawing monent due to
11、 yawing velocity C . The lattez technique pernits measurement of a conibination of ming derivatives (Cnr, - Cng,J. A comparison of results from the two tech- niques for the sane model under identicel conditions indicates the approximate magnitude of the sideslip acceleration derivative Such comparat
12、ive tests have indicated that for certain configurations the iierivatives associate8 wlth acceleration in sideslip can be quite large at high angles of attack. Direct measurement of the si6eslip acceleration derivatives (reference 4) have, of course, substantiated the resul-;s of the conparative tes
13、ts. nr cni,uo # There is little experimental data avaihble on the effect of mtiom periodicity on aero-c derivatives associated with linear or angular velocity. Recent tests on a series of wings performing lateral plunging oscillations across the jet of a tunnel (ref. 4) have permitted evelua- tior?
14、of tile derivatives associated with sideslip velocity during a sinus- oihl sideslipooscillation. These results indicated that for a 60 delta and a 45 sweptback wing et high angles of attack the sideslip derivetives extracted from lateral oscillation tests were much different fron the cierivatives ob
15、tained by the usual steady-state wind-tur-ne1 procedures. As e. continuatioc of the program to determine effects of motion periodici4;y on the various stability derivatives, the present investiga- tion wes made to deternine the derivatives zssociated with yawing veloc- ity and yawing acceleration by
16、 use of an apparatus which similated a pure yawing oscillation. Dete elso were obtained from steady-state yawing tests by use of tne Langley stability tunnel curved-flow technique for comparison with the oscillation data. * - Provided by IHSNot for ResaleNo reproduction or networking permitted witho
17、ut license from IHS-,-,-SrnOLS 3 The =ar at Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-5 The subscript (u when used with a derivative (for exaqple, Cz, I indicates that the derivat-ive was obtained from an oscillation test. APPARATiS Oscillztion
18、 Tests The tests of the presert investigation were concfi 2 7 The Ciste-n-ce between the model mounting point and the center of the drive flywheel is y = - cos Ir - R cos 2zft 2 hence the velocity of the model tmard tne drive flywheel is The model sideslip velocity is or Substitution of equations (2
19、) and (4) into equation (1) yields . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-a 2Rz2cos 2aft which, for the nechanism sketched in figme 2, is the relatiomhip between V and f for a pure yawing oscilla.tion. This variation is rather complex sinc
20、e V is to some exten-i; depen6ent on angular position of the Plywheels as indicated by the first term within the bracket. The effect of this term can be niniciized by mking 2 large relative to R which is, of course, a restriction on the magnitude of the yaw angle. In the present investigation R was
21、12 inches and 2 was 156 inches, hence the mgnitude of the term within the bracket varied fron 0.83 to 1.15. An average value of 1.00 was used tkroughout the investigation so Via% tle relationship between V md f was given by v = sf2 Tne pwing and rolling monenks acting or? the models ooo Anngle-of -a
22、ttack range 0 to 32 0 to 32O 0 to i6: 0 to 320 o to 32 o to 16O . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 COKRECTIONS Jet boundary correctims to angle of ztteck enti Zrag coefficierrt, deterrined by the nethoC of reference 6 ma based on th
23、e data obtained from tie steady-yawing-flow tests at rb/2V = C, have been applied to both the steaAc3-stz;te and oscillatory results. Eo corrections were applied -bo the oscillatory derivatives because they were felt to be smll (ref. 7). The resonance efrects discussed in reference 8 beccme imFortax
24、?t, for the s-equency considere5 herein, only at Mhch numbers near unity, and thus require no consideration for the present investi- gation. The data have not been corrected for blockage, turbulence, or support interference although the latter my have a sizeable magritude at the higher angles of att
25、zck. The equations of motion for a model performing a force2 sinusoidal yawing oscillztion are about the z axis, an6 =bout the x ais, where B an6 D are tie mxinm in-phase yawing md rolling moments respectively, and C and E the corresponding out-of-phase xtioments supplied by the strain gage. The yaw
26、 mgle of the model in the present tests was giver? by equation (2), wnich for small yaw angles can be written as $ = - - sin 2rrft 2R 2 from which ii = - - cos 2xft 4flm 2 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Substituting equations (8) and
27、 (9) into equations (6) and (7) an hence the coefficients were readily obtained from the followin: eqmtions : wind on - win6 o2f 1 n2f2RpSb2 i Cnr = As is shown in the appendix, the instrumentation used in this investi- gstion yielded readings on a voltmeter 8, or El directly proportional to the ysw
28、ing and rolling moments, hence the aerodynamic moments B, C, D, and E could be obtained readily and used with equations (12) to obtain the desired aerodynamic derivatives. RESULTS AID DISCUSSION The results of this investigation are presented in figures 5, 6, and 7 as cwves of the various paraneters
29、 plotted against angle of ettack. Iiecent investigations of derivetives measured on oscillating models have shown a large dependence of some serivatives on reduced frequency, particularly at Ngh angles of attack (refs. 4 and 9) , hence the results of the present oscillatory tests, made at one value
30、of reduced frequency, would probably be modified by frequency changes. Static Longituzlinal Characteristics The static longitudinal characteristics of the three models are presented in figure 5 as curves of k, CD, and C, plotted against Provided by IHSNot for ResaleNo reproduction or networking perm
31、itted without license from IHS-,-,-angle of attack. These an. increased negztively approximately linearly with angle of attack Tor all three wings. At angles of attack near and above mexilmun lift however, Cz;. for the unswept and 45O swept- back wing showed a rapid positive increase. - Prelininary
32、tests have been made to determize effects 05 motion periodicity on the aerodynanic derivatives due to yawing velocity and acceleration for a 6o0 delta wing, a 45 sweptback wing, and zn m-swept Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-wing. The
33、 oscillation tests were made at oce value of %he reduced- frequence parmeter, cub/2V = 0.23. Tests of nodels. on other oscillating system have sho-m- a large ciependence of sone derivatives on the reduced frequency, particulzrly at high mgles of attack, kence this fact should be kept in mind in cons
34、idericg the Tollowing statexerbs: 1. At lox angles of aztack there was good agreement between steady- state ax5 oscilla%ory values of tie aerodynmic derivatives due to yawing velocity for 211 three xitxs . 2. At, high angles of attack large differences occurred between steady-state =ti oscillatory v
35、dues of tne derivatives due to yawing velocity. 3. The deriv, by using resolver. In this case is the the obtained in a manner similar to that used in sine rzther than cosine component of the equation obtained is Provided by IHSNot for ResaleNo reproduction or networking permitted without license fro
36、m IHS-,-,-Equations (AS) ard (Ag) can 5e nondimensionalizea to obtain the 6esired derivatives and 2? distortion in Yne vsltage powering the strein gage. The loutput of the wire strain gage is gut into a two-stage amgli- fier in order to obtein sufficient iriput into the p2ase-sensitive klf- wave dem
37、o6ulakor with the low loads obtained on the balmce in the present investigation. The deaoduhtor output is read 012 a damped direct- current xicroameter . lossible Xrrors Associated with Reduction of Data Referring to equations (A5) ar-d (A7), it is seen that tne elec- kical multiplying and ictegrati
38、ng processes elimimke tie signals not i- ?base wiCj the reference voltsge, E. Consider %he lollowing unwmted xoments which the belence senses: Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-(a) Aerodyllamic noments due to hmonics of basic model moti
39、oc due to linkage .- Harmonics such as cos %, cos 3ccrt, etc., being of dif- ferent frequency frm -E?! reTerence voltage, are elidnated. (b) A TOP view. Figure 2.- Schematic draw5.ng of mechanism for simulating pure yawing oscillation. . I 1 “. I Provided by IHSNot for ResaleNo reproduction or netwo
40、rking permitted without license from IHS-,-,-I * 1 I Rsrolvar (b) View looking upstream., Figure 2. - Concluded. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-(a) Driving flywheel. Fielrc 3.- Apparatus Gsed in obtaining pure yawing oscillatlon. b L
41、 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I P I 2-87046 (b) Model support strut and unswegt wing. Figum 3. - Continued. . “_ Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-F (c) Top view of .rallcwing flywheel. Figme 3. - Continued. 1 2-87 162 I k Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
