1、RESEARCH MEMORANDUM EFFECT OF FREQUENCY OF SIDESLIPPING MOTION ON THE LATERAL STABILITY DERIVATrVES OF A TYPICAL DELTA-WING -PLANE By Jacob H. Lichtenstein and James L. Williams 1 NATIONAL .ADVISORY COMMITTEE FOR AERONAUTICS WASHINGTON September 12, 1957 Provided by IHSNot for ResaleNo reproduction
2、or networking permitted without license from IHS-,-,-NACA RM L57FO7 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS I RESEARCH MEMORANDUM 1 EFFECT OF FREQUENCY OF SIDESLIPPING MOTION ON THE LATERAL STABILITY DERIVATIVES OF A TYPICAL DELTA-WING AIRPLANE By Jacob H. Lichtenstein and James L. Williams An
3、 investigation has been made in the Langley stability tunnel at low speeds to determine the effect of frequency of sideslipping motion on the lateral stability derivatives of a 600 delta-wing airplane configuration. The results of the investigation have shown that, for either the wing alone, the win
4、g-fuselage combination, or the wing-fuselage-vertical- tail combination, changes in the frequency of oscillation generally had only minor effects on the stability derivatives at low angles of attack, with the exception of the yawing-moment derivatives of the wing-fuselage- vertical-tail configuratio
5、n which exhibited a considerable effect of fre- quency. At tbe high angles of attack the magnitude of all the stability derivatives measured underwent very large changes as a result of the oscillatory motion. It was also found that for the wing-alone configuration the leading- edge radius had a very
6、 pronounced bearing on the effects due to the oscil- latory: motion. Decreasing the leading-edge radius, for instance, con- siderably increased the magnitude of the effects due to changes in frequency. The use of the oscillatory stability derivatives in calculating the period and time to damp to one
7、-half amplitude, instead of the use of the steady-state derivatives, resulted in an increase in the indicated damping and stability for high angles of attack. It did, however, increase the time to damp somewhat at low angles. Provided by IHSNot for ResaleNo reproduction or networking permitted witho
8、ut license from IHS-,-,-2 INTRODUCTION Recent developments have shown that stability derivatives obtained from oscillation tests can be considerably different from those obtained by steady-flow tests for some angle-of-attack and Mach nuniber ranges (refs. 1, 2, and 3) and that these differences can
9、be quite important in the calculation of the stability and motions of an airplane (ref. 4). It was also found that the magnitude of these measured oscillatory derivatives depended to a large extent upon the frequency and amplitude of the oscil- latory motion (ref. 3) . A common and widely used oscil
10、lation technique is one wherein the model is simply oscillated about a fixed vertical (Z) axis relative to the model. These tests are comonly called oscillation-in-yaw tests, and yield a derivative that is a combination of two terms; for example, the damping term consists of the damping in yaw Cnr a
11、nd an acceleration- in-sideslip term Cni in the combination Cnr - Crib. However, in the equations used for calculating the airplane motion, these two derivatives are needed separately. Techniques have recently been developed at the Langley stability tunnel which will permit the measurement of the ya
12、w and sideslip terms independently. Oscillatory tests in pure yawing, as described in reference 6, involve a snaking motion in which there is no sideslip, and oscillatory tests in pure sideslip involve a side-to-side motion in which there is no rotation (ref. 3). Fresented in this paper is a low-spe
13、ed investigation of pure side- slipping motion on a 60 delta wing alone and in combination with a fuselage and vertical tail. The range of reduced frequencies of oscil- lation varied from 0.066 to 0.218 at a maximum amplitude of sideslip of +2O, and the angle of attack varied from 0 to 32O For compa
14、rison with the wing which had an NACA 65AO03 airfoil section, a flat-plate 60 delta wing also was tested in sideslipping motion. In addition to the sideslipping tests some results are reported for oscillation-in-yaw tests (e.g., Cnr - derivative) for both of the wings. Computations of the period and
15、 time to damp to one-half amplitude were made using the measured oscillation sideslip data. These computations were made for a typical delta-wing airplane. CnP SYMBOLS The data are presented in the form of standard NACA coefficients of forces and moments which are referred to the stability system of
16、 axes with the origin at the projection on the plane of symmetry of the quarter- chord point of the mean aerodynamic chord. The positive direction of Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-7 3 i i forces, moments, angular displacements, and
17、velocities are shown in figure 1. The coefficients and symbols used are defined as follows: I CD c2 Cn MX MZ My P v S b I C lift coefficient, - Lift SSW drag coefficient, - Drag SSW lateral-force coefficient, Lateral force q% rolling-moment coefficient, %/$, yawing-moment coefficient, ir, V velocity
18、 along the Y-axis, - aY at, j;, ir acceleration along the Y-axis, U angle of attack with respect to ft/sec NACA RM L37FO7 -, a;t ft/sec2 at wing chord plane, deg P angle of sideslip, tan 1 radians unless otherwise specified V B=,-T - radians/sec 0 angular velocity, 2d, ra,dians/sec Yf angle of yaw,
19、radians 7 mass unbalance about mounting point, slug-ft f frequency, cps t time, sec cob - reduced frequency parameter 2v 2 - b 2v sideslipping-acceleration parmeter referred to semispan of wing - rb 2v yawing-velocity parameter referred to semispan of wing - Pb 2v rolling-velocity parameter referred
20、 to semispan of wing r yawing velocity, h, radians/sec at yawing acceleration, fi, rdians/sec2 at2 P rolling angular velocity, radians/sec Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I NACA RM L57FO7 cnB = - zn a(I) oscillatory Provided by IHSNot
21、 for ResaleNo reproduction or networking permitted without license from IHS-,-,-MODELS AND APPARATUS Models I The model used in the majority of the tests of this investigation. is shown in figure 2 and pertinent geometric information is given in tables I and 11. The configuration is, in general, fai
22、rly typical of a delta-wing airplane; the wing had an aspect ratio of 2.31, a 60 swept- back leading edge, and an NACA 65A003 airfoil section. The fuselage was a body of revolution pointed at the nose and blunt at the rear to simulate a jet configuration. The vertical tail was triangular, of aspect
23、ratio 2.18, and had a leading-edge sweepback of 42.5 and an NACA 65-006 airfoil section. A photograph of the complete model mounted in the 6- by 6-foot test section of the Langley stability tunnel is shown in figure 3. The model had separable wing, fuselage, and tail surfaces in order to facilitate
24、testing of the model as a whole and as components. The components were made of balsa wood covered with a thin layer of fiber glass in order to minimize the mass and make the natural frequency of the model on its mounting as high as possible. An attempt was made to bal- ance the model in pitch, roll,
25、 and yaw in order to decrease the out-of- balance moments. S0m.e tests were made with another wing which had the same plan form as the basic wing but had a flat-plate airfoil section with a thickness ratio of 2.4 percent based on the chord and rounded leading edge with a radius of one-half the thick
26、ness. The trailing edge was beveled to give a 10 trailing-edge angle. Apparatus The apparatus used in this investigation for oscillation in side- slip is similar to that used in reference 3, except that the oscillatory motion of the apparatus was forced at a constant amplitude for these tests and th
27、e oscillatory motion was free to damp in the tests of reference 3. The oscillating portion of this apparatus (oscillating support strut) shown in figures 4(a) and (b) consisted of a 9-foot length of streamlined steel tubing which spanned the tunnel jet and extended through the walls of the 6- by 6-f
28、oot test section of the Langley stability tunnel. The ends of this streamlined strut were sup- ported by triangular-shaped swinging arms, which were pivoted and sup- ported by. rigid tunnel structural members. The oscillating .motion was imparted to the strut by the push rod which had one end pinned
29、 tothe strut and the other end mounted off center on the rotating flywheel (fig. 4(b). The location of the push-rod attachment at the flywheel could be changed so that the amplitude of the motion could be adjusted Provided by IHSNot for ResaleNo reproduction or networking permitted without license f
30、rom IHS-,-,-8 - NACA RM L57FO7 to give the desired sideslipping velocity for a given frequency. The off-center mass of the attachment was balanced by a lead weight mounted on the flywheel. The inertia of the flywheel was made large in order to reduce, as much as practical, the fluctuations in circul
31、ar velocity that occur during a cycle. The flywheel was driven by a 1-horsepower direct- current motor through a gear drive system with a reduction ratio of 6 to 1 (fig. 4(c) ) . The frequency of the oscillation was controlled by varying the voltage to the drive motor. A pure lateral oscillatory mot
32、ion cannot be obtained with such an apparatus; however, by using a swinging-arm radius of 45 inches, the streamwise motion of the model can be considered negligible (about 3/4 of 1 percent of free-stream velocity). A sketch depicting typical motion of the model is given in figure 5. Because of the e
33、ccentricity of the crank arm, the resulting motion is not a true sinusoidalmotion. The distortion varies from zero at the ends of the motion to a maximum at the center of the motion. The data-reduction system (ref. 6) was such that the error at the maximum distortion was less than 1 percent for the
34、worst case and the average error over an entire cycle was considered to be negligible. The model was raised above the horizontal strut in order to reduce the interference of the strut on the model (fig. 3). The rolling and yawing moments were measured by a two-component strain gage located at the de
35、sired center of gravity of the model. The output from the strain gage was fed to a data-reduction system which permitted readings of the in-phase and out-of-phase portions of the total moment on a meter. This data-reduction system is described in detail in the appendix of refer- ence 6 and therefore
36、 will not be described herein. The apparatus used for the oscillation-in-yaw tests was the sane as that described in reference 5. The data-reduction equipment was the same as that used for the oscillation-in-sideslip tests. For the steady-state tests the conventional six-component mechanical balance
37、 system was used with the models mounted on a single strut support. J TESTS AND COIiRECTIONS Tests The tests were conducted in the 6- by 6-foot test section of the Langley stability tunnel at .a dynamic pressure of 24.9 pourids per square foot. This corresponds to a Mach number of 0.13 and a Reynold
38、s number of about 1.6 X LO 6 based upon the mean aerodynamic chord of the wing. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM L37FO7 Y 9 I 4 ,configurations, the NACA 65AO03 airfoil wing, the wing-fuselage combina- 1 tion, the wing-fuselage
39、-vertical-tail cambination. The angle-of-attack I ! in 2 increments). The basic model configurations were tested at one I amplitude of sideslipping oscillation, +20 for four frequencies (1, 1.63, 1 2.00, and 3.31 cycles per second) which corresponds to reduced frequency The oscillation-in-sideslip t
40、ests were made for three basic model range was varied from Oo to 32O (Oo to 160 in 4O increments and 1-60 to 32O 1 parameters of 0.066, 0.109, 0.132, and 0.218, respectively. 2v Same additional tests were made on a flat-plate wing. This wing was tested at the same. amplitude of oscillation (k2) and
41、angle-of-attack range (Oo to 32O) but at only two frequencies, 1 an3 3.31 cycles per second. F 11 :I frequencies as the oscillation-in-sideslip tests. The angle-of-attack I. range also was from Oo to 320. The oscillation-in-yaw tests were made only with the NACA 65AOO3 airfoil wing at an amplitude o
42、f oscillation of k2O and at the same four The static tests were made through the same angle-of-attack range (Oo to 320) at p = 00 for lift, drag, and pitching moment and at p = these correc- tions have been applied to the stew-state results. No boundary correc- tions were applied to the oscillation
43、derivatives because they were believed to be small (ref. 9). Blockage corrections determined by the methods presented in reference 10 have been applied to the dynamic pres- sure and drag. The dynamic data were corrected for the effects of a variation in angularity of the airstream as the model oscil
44、lated from side to side in the test section. A correction also was applied to the wind-off oscillation readings for the still-air aerodynamic effect on the model. This correctionwas obtained by first oscillating the model in free air ad then completely enclosing the model and strain gage in a wooden
45、 box. to shield. it from the air. (See fig. 6. ) The resonance effect discussed in reference 11 becomes important only for the fre- quencies considered at Mach numbers ne= unity and, therefore, requires no consideration for the present investigation. The data have not been L .I Provided by IHSNot fo
46、r ResaleNo reproduction or networking permitted without license from IHS-,-,-10 - NACA m 5707 corrected for turbulence or support-strut interference, although the latter may be sizeable at the higher angles of attack. REDUCTION OF DATA The equations of motion for a model performing a forced sinusoid
47、al oscillation in sideslip for the yawing moment is yZY = MY + M+ + A sin ut + B. COS ut and for the rolling moment is 4 Y$ = M + Mg + C sin ut + D COS ut where A and C are the maximum in-phase yawing and rolling moments, respec- tively, and B and D are the corresponding out-of-phase moments supplie
48、d by the strain gage. The terms 7z and 7x are used to represent any unbalance of the model about the .mounting point that may exist; yZ is proportional to the mass and the distance that the center of gravity of the mass is forward.or reward of the mounting point, and 7x is pro- portionalto the mass
49、and the distance of the mass center of gravity above or below the mounting point. These terms should be small since it was attempted to balance the model about the mounting point. The equations for the displacement, velocity, and acceleration along the Y-axis are given approximately by: y = yo sin cut f = you cos cut j; = -y whereas, for the pr
