1、AERODYNAMIC DAMPING AND OSCILLATORY STABILITY IN PITCH FOR A MODEL OF A TYPICAL SUBSONIC JET-TRANSPORT AIRPLANE fl?+-Q /:$y mean angle of attack, degrees rl phase angle between T and 0, degrees 0 maximum angular displacement in pitch of model with respect to sting, radians 0 angular velocity, 2713,
2、radians/sec Cm pitching-moment coefficient, Pitching moment s,= per radian - aCm Cmq - per radian aCm Cm, = 5 per radian a, Cmq + Cmh Cm, - k2Cq damping-in-pitch parameter, per radian oscillatory-longitudinal-stability parameter, per radian A dot over a quantity denotes the first derivative with res
3、pect to time. 3 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-APPARATUS Model Design dimensions are presented in figure 1 for the test model, which is considered representative of current subsonic jet-transport airplanes. The model has a low swept
4、wing with a chord extension inboard of the engine pylons. The chord extension has a leading-edge sweep of 41.50. The wing, outboard of the extension, has a leading-edge sweep of 37.50. The four jet-engine nacelles are mounted on slab pylons beneath the wing and full-scale airflow is simulated throug
5、h the nacelles. Photographs of various views of the model are presented in figure 2. Y _I .0559 (.1834) .4985 .IO90 Sting and balance center line Fuselage modification necessary for sting clearance Figure 1.- Dimensions of test model. (Linear dimensions given first in meters and parenthetically in f
6、eet.) 4 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-L-64-7920 L-64-7929 Figure 2.- Photographs of test model. L-64-7930 5 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-“1 I Some of the geometric
7、 properties of the wing. horizontal tail. and vertical tail are as follows: Wing: Area. meters2 . ft2 Span. meters . ft Mean aerodynamic chord. meters . ft Aspect ratio . Taper ratio Geometric dihedral. deg . Horizontal tail: Area. meters2 . ft2 Span. meters . ft Mean aerodynamic chord. meters . ft
8、Root chord. meters . ft Aspect ratio Taper ratio Geometric dihedral, deg . 0.1413 1.5209 0.9970 3.2710 0.1536 0.5039 7.035 0.33 7 0.0321 0.3455 0.3304 1.0840 0.101 5 0.3330 0.13 59 0.4459 3.43 0.41 7 Vertical tail: Area. meters2 . 0.0196 ft2 0.2110 meters 0.1125 ft 0.3691 Aspect ratio . 1.80 Taper r
9、atio . 0.31 Mean aerodynamic chord. The airfoil coordinates for the wing and horizontal tail are given in table I . The model has no movable control surfaces . 6 1 . -_- . -=1111.1.111 1111111111111111111 11111 1111 111 II 1111.11111111 I II II I1111 I I Provided by IHSNot for ResaleNo reproduction
10、or networking permitted without license from IHS-,-,-The model is made principally of magnesium except for a fiber glass forward portion of the fuselage and an aluminum wing. The sting extends into the model through the bottom of the fuselage at an angle of loo with respect to the horizontal referen
11、ce line of the model in order to retain the geometry of the vertical and horizontal tail configurations. The model was tested in an aerodynamically smooth condition except for three- dimensional roughness which was applied to the model to assure that a turbulent bound- ary layer existed. The roughne
12、ss consisted of 0.25-centimeter-wide (l/IO-in. -wide) strips of No. 150 carborundum grains near the leading edge of the wing, horizontal and vertical tail surfaces, and engine nacelles; and a strip of No. 220 carborundum grains was located 0.86 centimeter (0.34 in.) rearward from the nose. the rough
13、ness were computed prior to testing with the use of the method of reference 1 to insure a turbulent boundary layer aft of the applied roughness. The size and location of Oscillation-Balance Mechanism A view of the forward portion of the oscillation-balance mechanism which was used for these tests is
14、 presented in figure 3. Since the oscillation amplitude is small, the rotary motion of a variable-speed electric motor is used to provide essentially Fixed balance support r- Osci I lation balance T - Pivot axis i Model attachment surface Figure 3.- Forward portion of the oscillation-balance mechani
15、sm. L-65-7934 7 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-sinusoidal motion of constant amplitude to the balance through the crank and crosshead mechanism. Although constant amplitudes of 1/2O, lo, and 2 can be obtained by changing the crank, a
16、n amplitude of lo was used for this investigation. The oscillatory motion is about the pivot axis which was located at the model station corresponding to the proposed center of mass of the configuration tested (F/4). The strain-gage bridge which measures the torque required to oscillate the model is
17、 located between the model attachment surface and the pivot axis. This torque-bridge location eliminates the effects of pivot friction and the necessity to correct the data for the changing pivot friction associated with changing aerodynamic loads. Although the torque bridge is physically forward of
18、 the pivot axis, the electrical center of the bridge is located at the pivot axis so that all torques are measured with respect to the pivot axis. A mechanical spring, which is an integral part of the fixed balance support, is con- nected to the oscillation balance at the point of model attachment b
19、y means of a flexure plate. The mechanical spring and flexure plate were electron-beam welded in place after assembly of the oscillation-balance and fixed-balance support in order to minimize mechanical friction. A strain-gage bridge, fastened to the mechanical spring, provides a signal proportional
20、 to the model angular displacement with respect to the sting. Although the forced-oscillation balance may be oscillated through a frequency range from about 1 to 30 cycles per second, as noted in reference 2 the most accurate meas- urement of the damping coefficient is obtained at the frequency of v
21、elocity resonance. For these tests, the frequency of oscillation varied from 1.64 to 9.02 cycles per second. Wind Tunnel The tests reported herein were made in the Langley 8-foot transonic pressure tunnel. The test section of this single-return closed-circuit wind tunnel is about 2.2 meters square (
22、7.1 feet square) with upper and lower walls slotted to permit continu- ous operation throughout the transonic-speed range. Although test-section Mach numbers from near 0 to 1.30 can be obtained and kept constant by controlling the speed of the tunnel-fan drive motor, for these tests the aerodynamic
23、damping and oscillatory sta- bility in pitch were obtained at Mach numbers from 0.20 to 0.94. The Mach number dis- tribution is reasonably uniform throughout the test section with a maximum deviation from the average free-stream Mach number of about 0.010 at the higher Mach numbers. The sting-suppor
24、t system, when used in conjunction with the oscillation-balance mechanism used for these tests, is designed so as to keep the model near the center of the tunnel throughout a 250 angle-of-attack range. The angle-of-attack range for these tests was from about -60 to 180. 8 Provided by IHSNot for Resa
25、leNo reproduction or networking permitted without license from IHS-,-,-MEASUREMENTS AND REDUCTION OF DATA Strain-gage bridges are used to measure the torque required to oscillate the model and the angular displacement of the model with respect to the sting. The bridge outputs are passed through coup
26、led electrical sine-cosine resolvers which rotate with constant angular velocity at the frequency of the model oscillation. The resolvers resolve each signal into two components which are read on damped digital voltmeters. Details of the apparatus and procedure used in reducing the data are given in
27、 references 2 and 3. From the computed values of the maximum torque required to oscillate the model T, the maximum angular displacement in pitch of the model with respect to the sting 0, the phase angle q between T and 0, and the angular velocity of the forced oscillation w as explained in detail in
28、 reference 2, the viscous-damping coefficient for this single-degree-of-freedom system is computed as Also, the spring-inertia parameter is computed as where Ky is the torsional-spring coefficient of the system and IY is the moment-of- inertia coefficient of the system about the Y-axis of the body.
29、The damping-in-pitch parameter was computed as and the oscillatory-longitudinal-stability parameter was computed as T sin Inasmuch as the wind-off value of it is determined at the frequency of wind-off velocity resonance, because, as explained in reference 2, the wind-off value can be determined mos
30、t accurately at the frequency of velocity resonance, The wind-on and wind-off values of 4 are determined at the same frequency since these quantities are functions of frequency. is not a function of the oscillation frequency, T cos 9 Provided by IHSNot for ResaleNo reproduction or networking permitt
31、ed without license from IHS-,-,-TESTS The aerodynamic damping and oscillatory stability in pitch were obtained at Mach numbers from 0.20 to 0.94 at angles of attack from about -6O to 18O at Oo angle of side- slip. The Reynolds numbers, based on the mean aerodynamic chord of the wing, varied from abo
32、ut 0.6 X 106 to about 1.8 X lo6. Tests were made at an oscillation amplitude of 10 by using a forced-oscillation technique. The reduced-frequency parameter varied from 0.0026 to 0.0301. RESULTS AND DISCUSSION The variation of the damping-in-pitch parameter and oscillatory-longitudnal- stability para
33、meter with mean angle of attack is shown plotted in figure 4. The subsonic- transport configuration has positive aerodynamic damping in pitch ( a negative value of Cmq + Cmb) throughout the subsonic Mach number range except for angles of attack c CC,; mu per radian Cmm-kCni per radian 0.0254 k 00301
34、 Ndative bamping Positive damping I 0 4 8 12 16 20 Mean angle of attack, a, deg (a) M = 0.20; R = 0.6 X lo6. Cmu+Cm; per radian 40 20 0 -20 -40 -60 1 0 Cma-kFmi -1 per radian -2 -8 -4 -3 0.01375 k 0.0227 i; 0 4 8 12 16 Mean angle of attack, a,deg (b) M = 0.40; R = 1.2 X lo6. . I Figure 4.- Variation
35、 of damping-in-pitch parameter and oscillatory-longitudinal-stability parameter with mean angle of attack. 10 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-greater than about 15O at Mach numbers of 0.20 to 0.60. At these low Mach numbers, the dampi
36、ng decreases rapidly with angle of attack for values of CY greater than 8O and becomes negative for values of CY greater than 150. Because the sting entered the bottom of the model at an angle of 100 with respect to the model reference line (see fig. l), the sting may possibly alter the flow on the
37、tail surfaces at the higher angles of attack. The negative damping at the higher angles of attack and lower Mach numbers, therefore, may be caused by interference of the sting on the flow over the horizontal tail rather than by some sting-interference-free flow phenomenon such as wing stall. Additio
38、nal tests are required to evaluate this possibility. The negative values of the oscillatory-longitudinal-stability parameter CmCY - k2Cmi are indicative of generally stable trim conditions except at a Mach number of 0.60 at an angle of attack of 6O (fig. 4(c) and at Mach numbers of 0.90 and 0.94 nea
39、r an angle of attack of 9O (figs. 4(e) and 4(f). The sting entering the bottom of the model may have also influenced the oscillatory-longitudinal-stability parameter at the higher angles of attack. 40 20 Q c +c,; mq per radian -20 -4c -6 1 0 cmo-k%n4 -, per radian -2 -3 Mean angle of attack, a, deg
40、(c) M = 0.60; R = 1.6 X lo6. 000885 kS00187 40 20 0 c +c,; per radian -20 -40 -60 1 0 Cmm-k%; ., per radian -2 3 00078 S k 5 0.0160 -8 -4 04 8 12 16 20 Mean angle of attack, a, deg (d) M = 0.80; R = 1.8 X 10. Figure 4.- Continued. 11 Provided by IHSNot for ResaleNo reproduction or networking permitt
41、ed without license from IHS-,-,-c +cm; mq per rodion 0.0026 5 k 5 0.0143 Nqtive damping M Positive damping I, 1 0 -1 -2 -3 Mean angle of ottock, a, deg (e) M = 0.90; R = 1.7 X lo6. 40 0.0039 5 k 5 0.0128 20 0 -20 -40 -60 I 0 Cma-kFmi -1 per rodion -2 -a -4 0 4 8 12 16 20 -3 Mean angle of attack, a,
42、deg (f) M = 0.94; R = 1.6 x lo6. Figure 4.- Concluded. CONCLUDING REMARKS Measurements made to determine the aerodynamic damping and oscillatory sta- bility in pitch for a model of a typical subsonic jet-transport airplane indicate that aero- dynamic damping was positive throughout the Mach number a
43、nd angle-of-attack ranges except for negative damping at angles of attack greater than 15O at Mach numbers from 0.20 to 0.60. The sting, which entered the bottom of the model at an angle of 100 with respect to the model reference line, may have influenced the flow on the tail surfaces at the higher
44、angles of attack. Negative values of the oscillatory-longitudinal-stability parameter were present except at a Mach number of 0.60 at an angle of attack of 6O and at Mach numbers of 0.90 and 0.94 near an angle of attack of go. The sting entering the bottom of the model may also have influenced the o
45、scillatory-longitudinal-stability param- eter at the higher angles of attack. Langley Research Center, National Aeronautics and Space Administration, Langley Station, Hampton, Va., September 29, 1965. 12 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-
46、,-REFERENCES 1. Braslow, Albert L.; and Knox, Eugene C.: Simplified Method for Determination of Critical Height of Distributed Roughness Particles for Boundary-Layer Transition at Mach Numbers From 0 to 5. NACA TN 4363, 1958. 2. Braslow, Albert L.; Wiley, Harleth G.; and Lee, Cullen Q.: A Rigidly Fo
47、rced Oscilla- tion System for Measuring Dynamic-Stability Parameters in Transonic and Super- sonic Wind Tunnels. NASA TN D-1231, 1962. (Supersedes NACA RM L58A28.) 3. Bielat, Ralph P.; and Wiley, Harleth G.: Dynamic Longitudinal and Directional Sta- bility Derivatives for a 450 Sweptback-Wing Airpla
48、ne Model at Transonic Speeds. NASA TM X-39, 1959. 13 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TABLE I.- AIRFOIL COORDINATES Etations and ordinates have been nondimensionalized with respect to airfoil chordJ 0.0236 .0146 .0115 .0089 .0032 -.0051 -.0102 -.0159 -.0242 -.0319 -.0382 -.0433 -.0459 -.0459 -.0408 0 (a) Wing 0 .0050 .0083 .0125 .0249 .0500 .0748 .lo00 .1500 .ZOO0 .2500 .3000 .4000 .5000 .6000 .IO00 Lower surface Upper surface - Lower surface Upper surface Lower surface Upper surface id biion
