1、NASA TN D-232 Ylii-6 TECHNICAL NOTE D- 232 EPERIMENTAL DETERMINATION OF THE EFFECTS Or“ FREQUENCY -AND ANPLITUDE OF OSCILLATION ON THE ROLL-STABILITY DERIVATIVES FOR A 60“ DELTA-WING AIRPLANE MODEL By Lewis R. Fisher Langley Research Center Langley Field, Va. NATIONAL AERONAUTICS AND SPACE ADMINISTR
2、ATION WASHINGTON March 1960 (1JB SA-TN-D-232 ) OF THE EFFECTS OF FREQUENCY AND APIPLXTUDE OF OSCILLATION ON THE BOLL-STBBILXTY DERIVATIVES FOR A 60 DECREE DELTA-WING Unclas AIRPLN DETERMINATION OF THE EFFECTS OF FREQUENCY AND AMPLITUDE OF 0SCIL;LATION ON THE ROLL-STABILITY DERIVATIVES FOR A 60 DELTA
3、-WING AIRPLANE MODEL* By Lewis R. Fisher A 60 delta-wing airplane model was oscillated in roll for several fr.eyueiicizs zxd zgdit.1-1.d of oscillation to determine the effects of the oscillatory motion on the roll-stability derivatives for the model. Ine derivatives were measured at a Reynolds numb
4、er of 1,600,000 for the wing alone, the wing-fuselage combination, and the complete model which included a triangular-plan-form vertical tail. -. M Both rolling and yawing moments due to rolling velocity exhibited large Trequency effects for angles of attack higher than 16O. variations in these deri
5、vatives weye measired for the lowest frequencies of oscillation; as the frequency increased, the derivatlves becaTe more nearly linear with angle of attack. Both velocity derivatives were con- siderably different at high angles of attack from the corresponding derivatives measured by the steady-stat
6、e rolling-flow technique. The largest Rolling and yawing moments due to rolling acceleration were measured and similarly found to be highly dependent on frequency at high angles of attack. reveal the significance of the acceleration derivatives, indicated that inclusion of the measured derivatives i
7、n the equations of motion length- ened the period of the lateral oscillation by 10 percent for a typical delta-wing airplane and increased the time to damp to one-half amplitude by 50 percent. Some period and time-to-damp computations, which were made to r) * Supersedes recently declassified NACA Re
8、search Memorandum L57L17 by Lewis R. Fisher, 1958. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 INTRODUCTION The results of several experimental investigations (refs. 1 to 3) have demonstrated that large-magnitude lateral-stability derivatives m
9、ay exist under oscillatory conditions for delta- and sweptback-plan-form wings and that at high angles of attack these oscillatory derivatives may be much different from those measured under steady-flow conditions. The stability derivatives which have been measured by oscillation tests are those whi
10、ch determine the directional stability, and those which determine the damping in yaw, Cn and Cn* . These derivatives have been measured individually by oscillating the models with a sideslipping motion (ref. 1) or a yawing motion (ref. 2) , and in combination by oscillating the models in yaw about t
11、heir vertical axes (ref. 3). and C c“P,m n;. ,m r,m P,m Because the sideslipping and yawing derivatives of certain configu- rations are affected to a large degree by the frequency and amplitude of an oscillatory motion, it would seem likely that the phenomena which produce these results would affect
12、 the roll-stability derivatives in a like manner. A preliminary investigation in this asea is reported in reference 4, for which an unswept-wing airplane model was oscillated in roll primarily at zero angle of attack. attack data in reference 4 gave an indication that differences do exist between th
13、e oscillatory and the steady-state rolling derivatives. Certain of the higher angle-of- In the present investigation, an airplane model with a 60 delta wing was oscillated in roll about its longitudinal stability axis for several frequencies and amplitudes of oscillation in order to measure the effe
14、cts of oscillatory motion on the roll-stability derivatives of the model. steady rolling flow, the resulting data being regarded as zero frequency data, The tests were made for the complete model, for the wing-fuselage combination, and for the wing alone at a Reynolds number of 1,600,000. For a basi
15、s of comparison, the model was also tested in SYMBOLS The data are referred to the stability system of axes (fig. 1) and are presented in the form of coefficients of the forces and moments about a point which is the projection of the quarter-chord location of the wing mea aerodynamic chord on the pl
16、ane of symmetry. The coeffi- cients and symbols used herein are defined as follows: Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-3 b CD CL Cl wing span, ft Drag qs drag coefficient, - Lift lift coefficient, - qs Rolling moment rolling-moment coeff
17、icient, qSb ac i Clr = - a(%) C2,S rolling-moment coefficient, qSb YlS qsc pit ching-moment coefficient , - Cm Cn Yawing moment yawing-moment coefficient, qsb Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 Cn, w yawing-moment coefficient, CY later
18、al-force coefficient, h KX KZ Kxz Lateral force L 8 2 2 i ,- mean aerodynamic chord, ft maximum diameter of fuselage, ft lateral force, lb frequency, cps altitude, ft radius of gyration about X-axis, nondimensionalized with respect to b (ref. j) radius of gyration about Z-axis, nondimensionalized wi
19、th respect to b (ref. 5) nondimensional product-of-inertia factor (ref. 5) . c Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-5 radius of gyration about X-axis, ft (ref. 5) radius of gyration about Z-axis, ft (ref. 5) product-of-inertia factor (ref.
20、 5) rolling moment, ft-lb rolling moment in phase with velocity of oscillation, ft-lb rolling moment out of phase with velocity of oscillation, pitching moment, ft-lb yawing moment, ft-lb . yawing moment in phase with velocity of oscillation, ft-lb yawing moment out of phase with velocity cf oscilla
21、tion, mass of airplane, slugs period of oscillation, sec ft-lb ft-lb dynamic pressure, pV2, lb/sq ft 2 yawing velocity, dJc radians/sec wing area, sq ft time for oscillatory motion to damp to half-amplitude, sec time, sec dt Provided by IHSNot for ResaleNo reproduction or networking permitted withou
22、t license from IHS-,-,-6 v V x,y,z free - stream vel0 ci ty , ft / se c lateral component of velocity, ft/sec system of stability axes (fig. 1) U angle of attack, deg B angle of sideslip, radians except when otherwise indicated 7 angle of flight path, deg (ref. 5) angle of attack of principal longit
23、udinal axis of inertia, deg (ref. 5) P relative density factor, m/pSb P mass density of air, slugs/cu ft PI angle of roll, deg or radians PI0 amplitude of oscillation, deg or radians $ angle of yaw, radians L 8 2 2 w = 2fif The symbol CI) following the subscript of a derivative denotes the is the os
24、cillatory value c2P,CI) oscillatory derivative; for example, 2P of c APPARATUS Oscillation Equipment The tests were conducted in the 6-foot-diameter rolling-flow test section of the Langley stability tunnel. in figure 2 and mounted externally on the tunnel test section was used to oscillate the mode
25、ls. A connecting rod pinned to an eccentric center on the flywheel passed through a hole in the tunnel wall and transmitted a31 essentially sinusoidal motion to the model support sting by means of a crank asm attached to the sting. This equipment is shown in figures 2 and 3. The roll axis of the sti
26、ng was alined at all times with the wind stream. A motor-driven flywheel shown Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-L 8 2 2 The apparatus was driven by a 1-horsepower direct-current motor through a geared speed reducer. by controlling the
27、voltage supplied to the motor and the amplitude of oscillation was varied by adjusting the throw of the eccentric on the flywheel . The frequency of oscillation was varied Model The model tested had a triangular wing with a 60 apex angle, an aspect ratio of 2.31, and NACA 65AO03 sections parallel to
28、 the plane of symmetry. The fuselage was a body of revolution which had a sharp nose and a truncated afterbody with the wing mounted at the midfuselage height. The fuselage contained a two-component wire strain-gage balance to which the model was mounted at the quarter-chord point of the wing mean a
29、ero- dynamic chord. The model was also equipped with the triangular-plan- form vertical tail shown in figures 4 and 5. The entire model was con- structed of balsa wood to minimize inertia moments during oscillation and was covered with a thin layer of fiberglass-reinforced plastic to provide strengt
30、h. Additional geometric characteristics of the model are presented in table I. Recording of Data The model was mounted to the support sting by means of a resistance- type wire strain-gage balance which measured rolling and yawing moments. The strain-gage signals, during oscillation, were modified by
31、 a sine- cosine resolver driven by the oscillating mechanisru 50 t1ia.t the maswed signals of the strain gages were proportional to the in-phase and out- of-phase components of the strain-gage moments. These signals were read visually on a highly damped direct-current galvanometer and the aerodynami
32、c coefficients were obtained by multiplying the meter readings by the appro- priate constants, one of which was the system calibration constant. This data recording system is described in detail in reference 2. Steady Rolling-Flow Equipment In order to measure the steady rolling derivatives, the mod
33、el was supported by the same strain-gage balance and support sting as were used for the oscillation tests with the angle of roll fixed at zero. The air flow over the model, however, was forced to roll by a rotor placed in the airstream ahead of the model. This is the standard rolling-flow test proce
34、dure employed in the Langley stability tunnel and is described in reference 6. For these tests, the resolver in the data recording equipment was bypassed and the total strain-gage output signals were read directly from the galvanometer. Provided by IHSNot for ResaleNo reproduction or networking perm
35、itted without license from IHS-,-,-8 TESTS Both the oscillation and the rolling-flow tests were made at a dynamic pressure of 24.9 pounds per square foot which corresponds to a free-stream velocity of 145 feet per second (under standard conditions), a Reynolds number of approximately 1,600,000 based
36、 on the wing mean aerodynamic chord, and a Mach number of 0.13. The oscillation tests were made at frequencies of oscillation of 0.5, 1, 2, and 4 cycles per second, amplitudes of oscillation of *5O, +loo, and +2O0, and angles of attack from Oo to 320. correspond to a range of the reduced-frequency p
37、arameter from k = 0.033 to 2 k = 0.264. For certain combinations of the highest frequencies and ampli- L 8 2 The oscillation frequencies tudes, the yawing moments due to the inertia of the model exceeded the maximum design moment of the strain-gage balance and, for this reason, tests for these condi
38、tions were not run. For all conditions of frequency, amplitude, and angle of attack both a wind-off and a wind-on run were made. In order to establish the magnitude of the damping of the wing due to its rotation in still air, some tests were made in which the wing was enclosed in a plywood box. The
39、box, which was mounted to the sting below the model support, was forced to rotate with the sting so that the volume of air immediately surrounding the wing was forced to oscillate with it. The still-air moments measured in this manner were found to be negligible 4. and were not considered further. 1
40、 The steady rolling-flow tests were conducted for the same model con- figuration and angles of attack as for the oscillation tests. The rotary helix angles of the air flow by the model during these tests corresponded to values of pb/2V of 0.059, 0.033, 0.010, -0.021, -0.039, and -0.065. mDUCTION OF
41、DATA Subtracting the wind-off data from the wind-on data in order to eliminate the effects of model inertia on the derivatives and then multi- plying the results by the strain-gage balance calibration factors gives the in-phase moments Mxs, and MZs in foot-pounds and the out-of - 1 phase moments Mxs
42、2 and zy and three amplitudes of oscillation. The corresponding steaQ rolling-flow values of C are also presented in figure 7. Figure 8 is a similar fig- IP c”p* derivative Figures 9 and 10 rolling acceleration In the ation C tives are, of course, %a* ure for the presentation of the oscillatory valu
43、es of the yawing moment due to rolling velocity C together with the steady rolling-flow %,a present, respectively, the rolling moment due to and the yawing moment due to rolling acceler- czr; ,a steady rolling-flow case, the acceleration deriva- zero. The oscillatory rolling derivatives are cross-pl
44、otted directly as functions of reduced frequency in figures 11 to 14 for three of the higher angles of attack. In these figures, the corresponding steady rolling-flow derivatives are shown as zero frequency values. DISCUSSION The Damping in Roll The oscillatory damping in roll of the wing alone (fig
45、. 7(a) is shown to be largely dependent upon the frequency of oscillation for Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 angles of attack higher than 160. The values of C which become $P ,m most positive are those measured for the lowest freq
46、uency of oscillation. With higher frequencies, the curves become more nearly linear with angle of attack. The derivative remains negative for all angles of attack for only the two highest frequencies, but even for these frequencies a con- siderable reduction in the damping (where positive damping is
47、 indicated by negative values of C angle of attack. produced generally small effects on the damping-in-roll results. also fig. ll(a).) L ) takes place between the two extremes in 2P,(JJ A change in the amplitude of oscillation from 50 to 200 I (See A notable difference exists between the oscillatory
48、 and the steady- L L r state damping at high angles of attack. The steady-flow results indicate an increase in the damping as the angle of attack becomes large in con- trastwith the trends taken by the oscillation data. Similar differences between oscillatory and steady-state values of damping in ya
49、w for a simi- lar wing were observed in the investigation of reference 2. The addition of the fuselage (figs. 7(b) and ll(b) and of the fuse- lage and tail (figs. 7(c) and ll(c) served to modify the large positive values of C angles of attack. configurations are in the same direction as for the wing alone but are not as large. Certain effects of
