1、O_oo!ZNASA TM X-39/w -o_3g_ _ g/TECHNICAL MEMORANDUMX- :59DYNAMIC LONGITUDINAL ANDDIRECTIONAL STABILITY DEIKIVATIVES FOR A45 SWEPTBACK-WING AIRPLANE MODEL ATTRANSONIC SPEEDSBy Ralph P, Bielat and Harleth G. WHeyLangley Research CenterLangley Field, Va.iNATIONAL AERONAUTICSWASHINGTONAND SPACE ADMINIS
2、TRATIONAugust Z999Declassified August 19, 1960Provided by IHSNot for Resale-,-,-Provided by IHSNot for Resale-,-,-NATIONAL AERONAUTICS AND SPACE _ISTRATIONTECHNICAL M_4ORANDUM X-59DYNAMIC LONGITUDINAL ANDDIRECTIONAL STABILITY DERIVATIVES FOR A45 SWEPTBACKWING AIRPLANE MODEL ATTRANSONIC SPEEDSBy Ralp
3、h P. Bielat and Harleth G. WileySUMMARYAn investigation was made at transonic speeds to determine some ofthe dynamic stability derivatives of a 45 sweptback-wing airplane model.The model was sting mounted and was rigidly forced to perform a single-degree-of-freedom angular oscillation in pitch or ya
4、w of +-2 . The inves-tigation was made for angles of attack _ from -4 to 14 throughout mostof the transonic speed range for values of reduced-frequency parameterfrom 0.015 to 0.040 based on wing mean aerodynamic chord and from 0.04 to0.14 based on wing span.The results show that reduced frequency ha
5、d only a small effect onthe damping-in-pitch derivative and the oscillatory longitudinal stabilityderivative for all Mach numbers M and angles of attack with the exceptionof the values of damping coefficient near M = 1.05 and _ = 8 to 14.In this region, the damping coefficient changed rapidly with r
6、educed fre-quency and negative values of damping coefficient were measured at lowvalues of reduced frequency. This abrupt variation of pitch damping withreduced frequency was a characteristic of the complete model or wing-body-vertical-tail combination. The damping-in-pitch derivative varied consid-
7、erably with _ and M for the horizontal-tail-on and horizontal-tail-offconfigurations, and the damping was relatively high at angles of attackcorresponding to the onset of pitch-up for both configurations.The damping-in-yaw derivative was generally independent of reducedfrequency and M at a = -4 to 4
8、 . At a = 8 to 14, the dampingderivative increased with an increase in reduced frequency and a forthe configurations having the wing, whereas the damping derivative waseither independent of or decreased with increase in reduced frequency forthe configuration without the wing. The oscillatory directi
9、onal stabilityderivative for all configurations generally decreased with an increase inthe reduced-frequency parameter, and, in same instances, unstable valueswere measured for the model configuration with the horizontal tail removed.Provided by IHSNot for Resale-,-,-2INTRODUCTIONRecent design trend
10、s in airplanes and missiles have resulted inhigh-density configurations which have their massprimarily concentratedalong the fuselage. As a result, it was believed that someof the dynamicstability derivatives which were previously neglected are important andshould be included in the calculations of
11、the motions of the newer con-figurations. Several low-subsonlc investigations have been madeof thedynamic stability characteristics of triangular-, swept-, and unswept-wingmodels (for example, see refs. l, 2, and 3), and a limited amount ofexperimental data at supersonic speeds exists for these char
12、acteristics(for example, see refs. 4, 53 and 6). At transonic speeds, however,little experimental data exist.Several methods for investigating dynamic stability in wind tunnelsare available such as the free-decay method, self-excitation method, andrigidly forced to oscillate method, but each system
13、has its own limita-tions. It was believed, however, that the rigidly forced methodwouldbe the most suitable to use to investigate dynamic stability at transonicspeeds provided that the mechanismfor producing reciprocating motioncould be contained within the model and that the model could be sting-su
14、pported in order to minimize support interference.A mechanical system for measuring dynamic stability derivatives ofmodels has been designed and constructed for the Langley 8-foot transonicpressure tunnel. In this system, the model was mechanically forced tooscillate in a single degree of freedom at
15、 known angular frequency andamplitude while measurementswere madeof the momentrequired to sustainthe motion. The system allows for a wide range of rigidly controlledfrequency and amplitude and is adaptable to almost any model configurationfor tests in either pitch or yaw. A somewhatsimilar system to
16、 thatdescribed herein for measuring dynamic stability derivatives has beendesigned for the Langley transonic blowdowntunnel. The results of testsand a description of the mechanismare reported in reference 7.The present investigation was madein the Langley 8-foot transonicpressure tunnel on a 45 swep
17、tback-wing airplane model. The model wassting mounted and was rigidly forced to perform a single-degree-of-freedomangular oscillation in pitch or yaw of 2 . The tests were madeforangles of attack from -4 to 14 throughout most of the Machnumber rangefrom 0.70 to 1.15 for values of reduced-frequency p
18、arameter from 0.015 to0.040 based on wing meanaerodynamic chord and from 0.04 to 0.14 based onwing span. The Reynolds number, based on wing meanaerodynamic chord,varied from 0.99 lO6 to 1.19 x lO6.IIProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS3SYMB ST
19、he data presented are referred to the body system of axes, and allmoments are referred to the intersection of the oscillation axes whichare located at the quarter chord of the wing mean aerodynamic chord. Thecoefficients and symbols used herein are defined as follows:bCyCZeIyIzJ=4JKyKzMMyMzqRVY,Zwin
20、g span, ftsystem damping about Y-axis, ft-lb/radian/secsystem damping about Z-axim, ft-lb/radlan/secwing mean aerodynamic chord, ftbase of natural system of logarithmsmoment of inertia about Y-axis, slug-ft 2moment of inertia about Z-axis, slug-ft 2system spring constant about Y-axis, ft-lb/radiansy
21、stem spring constant about Z-axis, ft-lb/radianMach numberapplied moment about Y-axis, ft-lbapplied moment about Z-axis, ft-lbangular velocity in pitch, radians/secReynolds number based onangular velocity in yaw, radians/secwing area, sq fttime, secfree-stream velocity, ft/seclateral and vertical bo
22、dy axes, respectivelyProvided by IHSNot for Resale-,-,-4angle of attack of wing chord plane with respect to free-stream direction, deg or radlansangle of sideslip measured to plane of sy_netry and in plane ofrelative wind, deg or radlansphase angle between applied moment and angular displacement,rad
23、iansP mass density of air, slugs/cu ftinstantaneous displacement angle, radians4 otoamplitude of displacement angle, radiansangular frequency of oscillation, radians/secC m pitching-moment coefficient, Pitching momentV2S8CmCmq - 8(2q_)8CmCmq = 8(di2_8Cm2V !C n yawing-moment coefficient,Yawing moment
24、ipV2Sb8CnCnr - _(rb_Provided by IHSNot for Resale-,-,-58Cn4v2/8CnCn_ =_C nSubscripts :6O data obtained by oscillation testsaero aerodynamic characteristicsA dot above a symbol denotes differentiation with respect to time.APPARA_7SFor tests, the model configuration was mechanically driven insinusoida
25、l motion at a constant amplitude of _o at frequencies varyingfrom 6 to approximately 18.9 cycles per second while measurements weremade of the moment required to drive the model.The mechanism developed for these tests consisted of a model supportor carrier which was pivoted about an axis normal to t
26、he stream at theupstream end of the sting support (fig. 1). The support and attachedmodel were forced to perform a constant-amplitude, essentially sinusoidalmotion about the oscillation axis by a mechanical Scotch yoke and crankarrangement (figs. 2 and 3). The crank was connected by a long driveshaf
27、t and magnetic clutch to a 5-horsepower electric motor mounted inthe downstream end of the sting. The drive-motor speed was set at variousconstant values to provide a range of oscillating frequencies. A canti-lever spring was mounted between the fixed sting and the oscillating modelsupport (fig. 2).
28、 Springs of different stiffnesses provided a range ofresonant frequencies within the range of operating frequencies. Thecantilever springs were equipped with calibrated strain gages to providea signal proportional to model displacement. A stiff strain-gage beam,located between the model and the pivo
29、t axis, gave a signal proportionalto the moment applied to oscillate the model and, because of its location,was uninfluenced by any friction or mechanical play in the system.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS6Signals from the moment and disp
30、lacement strain gages were passedthrough coupled electrical slne-coslne resolvers (fig. l) which weremounted in the sting fairing forward of the drive motor. The tworesolvers were geared to the drive shaft and rotated at the fundamentaldrive frequency. A 30-pole-slgnal generator was also attached to
31、 thedrive shaft to indicate oscillation frequency.A new sting, which supported the oscillating model and contained thedrive shaft, motor, clutch, resolvers, and frequency-slgnal generator,was constructed for the tests. The sting was equipped with longitudinalstiffeners to provide a sting resonant fr
32、equency above the maximum oscll-lating frequency of the model so that model motion would not excite stingmotion. In addition, the sting was rigidly braced to the tunnel walls,floor, and ceiling by preloaded stay cables to restrict any sting motionthat might be present (fig. 1). The cables were attac
33、hed at the stingpivot center to allow an angle-of-attack travel from -4 to 14o.The oscillating model support and balance assembly was arranged sothat the pivot axis could be turned 90 In reference to the model plane ofsymmetry. Tests could, therefore, be made wlth the model oscillating inpitch or ya
34、w.In operation of the system, calibrated outputs of the moment anddisplacement strain gages were passed through coupled electrical sine-cosine resolvers which rotated at the frequency of oscillation (fig. 1).The resolvers transformed the moment and amplitude functions intoorthogonal components which
35、 were read on suitably dsm_ped direct-currentmicroa_mneters. From these components, the resultant applied moment anddisplacement and the phase angle between them were found, and with theknown oscillation frequency the aerodynamic damping and oscillatorystability moments were computed. The instrument
36、ation and the blockdiagram of the electronic circuits used to measure the model displace-ment and applied moment were similar to that described in reference 7-The mechanism used in the present tests was designed to providemaximum stiffness of all drive linkages so that the model responded onlyto the
37、 essentially sinusoidal forcing input of the crank and Scotch yoke.The drive shaft was very stiff with the result that twist or wlnd upbetween the resolvers and the model was negligible and did not appre-ciably change over a range of operating frequencies. The resolvers,therefore, could be carefully
38、 oriented with the model so that one second it, therefore,passed a signal proportional only to model velocity and, thus, registeredon the corresponding meter the moment required to overcome the damping.Because of the rigid sinusoidal input of the Scotch yoke and thecontrolled phase relationship betw
39、een the model and resolver axes, therelatively small damping moments on the model system were highly ampli-fied and, thus, resulted in a high accuracy of measurement. Testscould, therefore, be made at speeds other than those at system reso-nance with considerable accuracy.The static pitching and yaw
40、ing moments were measured with the dis-placement beam removed and the drive shaft and model locked at a displace-ment of 0.MODELTwo-view drawings showing the physical characteristics of the modelused in this investigation are presented in figure 4. Lightweightmaterials were used in the construction
41、of the model; and the center ofgravity of the model, although not coincident, was near the axis ofrotation to reduce the moment-of-inertia effects insofar as possible.The model had an aluminum wingwith 45 sweepback at the quarter chord,an aspect ratio of 4.0, a taper ratio of 0.2, and an NACA 65A005
42、 airfoilsection parallel to the plane of symmetry. The wing was mounted on thefuselage center line with an angle of incidence of 0 and had no twist ordihedral. Thehorizontal tail was made of aluminum and had 45 sweepbackat the quarter chord, an aspect ratio of 3.5, a taper ratio of 0.4, andan NACA 6
43、5A005 airfoil section parallel to the plane of symmetry. Thehorizontal tail was mounted on the fuselage center line with an angle ofincidence of 0. The vertical tail was made of aluminum and had 45sweepback at the quarter chord, an aspect ratio of 1.23, a taper ratioof 0.4, and an NACA 65A005 airfoi
44、l section parallel to the stream. Thefuselage, which was made of magnesium, had an ogive nose and a cylindricalafterbody and had a fineness ratio of 9.84. Fuselage coordinates aregiven in figure 4. The axes of pitch and yaw rotation passed through theintersection of the fuselage longitudinal center
45、line and the quarterchord of the wing mean aerodynamic chord. A photograph showing the modeland the method of supporting it in the wind tunnel is presented in figure 5.TESTSThe tests were conducted in the Langley 8-foot transonic pressuretunnel, which is rectangular in cross section. The upper and l
46、ower wallsProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS8of the test section are slotted to permit continuous operation throughthe transonic speed range. The tests were made through a Mach numberrange from 0.70 to 1.15. All data presented from this tunn
47、el areessentially free of wall-reflected disturbances. The tests were performedat approximately one-half atmospheric stagnation pressure and at a dew-point temperature such that the air flow was free of condensation shocks.For the present tests, the Reynolds number, based on wing mean aerodynamiccho
48、rd, varied from 0.99 x 106 to 1.19 X 106 (fig. 6).Measurements were made of the damping-in-pitch parameter Cm +q,_ Cm_,_ _2the oscillatory longitudinal stability derivative Cn_,c 0 - (_I Cmq,_ thedamping-in-yaw parameter Cnr,_ - Cn_,_ cos _, and the oscillatory direc-cos _ + _b_2 Ctional stability d
49、erivative Cn_,_ _j n_,_ at angles of attackfrom -4 to 14 throughout most of the Mach number range. The reduced-frequency parameter in pitch a_/2V varied from 0.015 to 0.040, thereduced-frequency parameter in yaw _b/2V varied from 0.04 to 0.14, andthe maximum amplitude of pitch and yaw oscillation was 2 for the tests.Measurements of the static pitching moment and yawing moment were made atangles of attack f
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