1、RESEARCH MEMORANDUM TBE STATIC AND DPNAMIC-ROTARP STABILITY DERJVATTVES AT SUBSONIC SPEEDS OF AN AJRPLAFE MODEL I WITH AN UNSWEPT WING AND A HIGH 0 -1 col cas Yh HORJZONTAL TAIL P: 2 QBY Dandld A. BueUf Verb D. Reed; and Armando E. Lopez d- 4 Ames Aeronautical Laboratory Moff ett Field, Calif. WlIRY
2、 copy hIATmNAL ADVISORY COMMITTEE cs . FOR AERONAUTICS WASHINGTON December 5, 1956 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.A 4 * NACA RM A56104 - - NATIONAL KESEARCH “ORANDUM AT SUBSOMC SPEZXIS OF Aw AIRPLANE MDDEL By Donald A. Buell, Verlin
3、 D. Reed, and Amando E. Lopez Measurements were made in a wind tunnel of the atatic and dynamic- rotary stability derivatives of a model having an unawept whg OS low aspect ratio and a high horizontal tail. The tests were conducted at Mach numbers from 0.25 to 0.94 at Reynolds numbers of 0.75 to 8.0
4、0 mlllion. The angle-of-attack range wae -8O to 24O. The components of the model were tested in various combinations and the contributions of these comgonents to the measured aerivatives are dtacussed. The stick-ffxed oscilhtory reaponse of a representative air- plane w8s calculated for fEt at altit
5、udes from se pv2se 2 Cn yawing-moment coefficient, yawing moment $V?5b r i; Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 NACA RM A56104 ( ) referred to body axe8 The stability system of axes used for the presentation of the data, together with a
6、n indication of the positive direction of forces, moments, and angles, is presented in f“.gure 1. The various stability derivatives are defined as follows: MODEL The complete model consisted of 811 wept wing of aspect ratio 2.44, a horizontal tail mounted In a high position OR a vertical tall, and a
7、 body with a circular cross section modified by the addition of a canopy and protuberances afmulating side inlets. Figure 2 is a three-view drawing of the model shouing Bome of the important dimensions. A photo- graph of the model mounted on the oscillation apparatus in the wind tunnel is shorn in f
8、igure 3. Additional geometric and dimensional model data are given in table I. Construction detaile of the model are of interest because of the unique problems presented in dynamic testing. Although the weight of the model did not have a direct bearing on the accurscy of the measured aerodynamic dat
9、a, it was desirable to keep the weight as low as practi- i cable because in this way other design and vibration problems in the model support and oscillation mechanism were minimized. Structural rigfdity in the model waB also felt t0 be desirable to minlmize flutter and aeroelastic distortion; howev
10、er, no quantitative measurements were made to evaluate their paeaible effects. “ The model was built of magnesium alloy in five major parts: the wing, the vertical tail, the horizontal tail, the body shell, and the cage, which enclosed the oscillation mechanism or the strain-gage balance, and to whi
11、ch the other parts were attached. The wing, vertical Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM A56104 3 A t nunfber of cycles for the lateral amplitude oscillations to damp to half Mach number Reynolds number wing area time to damp to h
12、alf amplitude velocity equivalent airspeed, ft/sec Ve fel wing span wing mean aerodynamic chord angle of horizontal-tail incidence, deg tail length rolling velocity pitching velocity yawing velocity time angle of attack, radians except where noted angle of sideslip, radians except where noted effect
13、lve angle of downwash at the horizontal tail, deg angle of pitch, deg air density angle of bank, deg angle of yaw, deg circular frequency of oscillation, radi that is, the sidewash at the tail was expected to produce negative C% .i Provided by IHSNot for ResaleNo reproduction or networking permitted
14、 without license from IHS-,-,-14 HACA RM A56104 increments in Cnp, and the test results established that the Cnp of the cmplete model was much more negaixLve than would result from a simple n addition of the body-wing values and the body-tail dues. 4 The effects cS wing dihedral and Reynolds number
15、OII Cnp are shown in figure 20. Generally, a change in wing dihedral f ram -loo to Oo resulted in substantial positive increases Fn Cnp, particularly at the higher cos CL for the complete model is evident fn figure 25 above loo angle of attack at Mach numbers of 0.80 and higher. This large change, p
16、resumably assoclated with an asymmetric loss of wing lift, did not materialize at the lower Reynolds number, however (see fig. 20(c). - The effects of dihedral on Czr - Czi were irregular over the angle- of-attack we, and were Largest at the higher Mach numbers, being aimilar to Cnp in thls respect.
17、 In both derfvatives, Reynolds number effects varied with angle of attack in a nonuniform mer and were largest at the highest Mach number. Damping-tn-yaw derivative Cnr - Cni.- The data of figures 19 and 25 show that the damping in yaw of the camplete model was maintained at a high level for mes of
18、sttack up to atoLeast uO. There was some increase in damping at angles of attack above 6 with a subsequent loss at still higher angles, where the damping of the body-wing cornbination became less. The body appeared to be the major factor in the loss of damping at high angles of attack. It should be
19、stated here that the measurements made with the body alone were sufficient only to establish the values of khe damping in pw and the rolling moment due to yawing velocity reerred to body axes. To obtain the body-alone dqping referred to stability axes, as is presented In figure 19, it wa8 necessary
20、to assume that the moments due to the bodys rolling about its longitudinal axis were zero. Such an assumption may have _ i w Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM A56104 15 a created errors in the values of body-alone damping at the
21、 Larger angles of attack, but the data are presented, nevertheless, in the belief that the correct trend is indicated. i, As shown in figure 19, the addition of the horizontal tail increased the effectiveness of the vertical tail in providing damping in yaw, except at a Mach number of 0.94. The cont
22、ribution of the tail to damping Increased considerably with angle of attack for the wing-off case, but with the wing on there was much less increase. Eddently, the nature of the wing inter- ference on the tail -in; and on the tail restoring moments was quite different; that is, this interference on
23、Cnr - C$ was favorable at nega- tive angles of attack and unfavorable at high positive angles of attack, whereas the interference effect on CnB (fig. 14) was always f awrable . At Oo angle of attack there was an increase in damping with increasing Mach number up to about 0.85, as illustrated 3n figu
24、re 21, but above this Mach number there was a loss of damp- contributed by the tail. The latter effect was caused wholly by the horizontal tail, Which had an unfavorable interference effect on the damping of the vertical tail at high it was necessary to use dmqing deriva- tives measured at a Reynold
25、s number of 0.75 million in estlmsting the longitudinal dymmicstability for the higher Mach numbers. This procedure gave someat misleaaing results at a Mach number of 0.94, because a lar e Reynolds number effect was present I the data for an angle of attack (4 ) corresponding to an altitude of“k,000
26、 feet. Figure U(g) shows that at the lower Reynolds number the damping of the model decreased rapidly at angles of attack above 2 (corresponding to 20,000 feet). It is evident that the calculated stability characteristics of the airplane at the higher altitudes and at a Mach number of 0.94 would hav
27、e been better if the higher Reynolds number data had been used. - Dynamic lateral stability.- The period and damping of the short-period lateral-directional osciU+tions have been calcqlated by the method of reference 13. Derfvatives encountered in the calculations included Cyr and Cy , wMch were not
28、 measwed . the equations of reference 13 in phce of Cnr and Cz , with no consideration being glven to the terms separately. This is believed to be the most accurate way to take ELccoUnt of the possible effects of sideslipping accel- eration in the absence of independent measurements of all derivativ
29、es. P B P r Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM A56104 1.7 t J c The results of the calculations ase presented In figure 23. Although the period and time to damp were considered eufficient indications of the acceptability of the l
30、ongitudinal responae, they provide only part of the information necessary to evaluate the lateraL-directional stability. The damping parameter IJc, st= represents damp- In the same senae as was considered Fn longituainal motions, since It is merely the ratfo of the period P to the time requfred to d
31、amp to half amplitude, T, /2. However, the minim value desirable is no longer fixed, but varfes with the roll- excitation parameter Irpl/ Vel * Thie parameter, repreeentFng the tendency of the airplane to roll when disturbed in sideslip, was calculated by the method outlined in the Appenafx of refer
32、ence 14. The boundaries in fig-ure 23 Indicate mfnirmlm acceptable values 8s defked in reference 12. Boundary A represents a minimum for an afrplane with no artificial etability augmentation, and boundary 3 ie a min9mum for an airplane which normally employs an artificial stabilhing device but with
33、the device Fnoperative. The uppermost boundary is the minimum for a tactical mission and is therefore the value which must be attained at the design conditions, by aa artiffcial devlce if necessary. The calculated values in figure 23 fall well below the mfnimum required for 8 tactical mission, but t
34、he values are all above boundary B. It may be noted that there was a decrease in the stability as the altitude increased, particularly at the higher Mach numbers. Such a situation was due partially to aa increase in the relative density factor of the ab- plane, which is a factor relating 5nertia.l f
35、orces to aerodynamic forces. A second and important factor was the decrease Fn C, which accompanied P the Fncrease in angle of attack as altitude increased The dependence of the damping parameter on Cnp is demonstrated by the results of calculations for a Mach number of 0.9. For these calcu- lations
36、 the effect of the relative density factor was eli-ted by con= siderwg only a conetant altitude. It was here inaicatd that a decrease in kp of 0.1 would result in a loss in l/Cl,2 of about 0 .l5. By way of comparison, It may be noted. that the range of values of c”p which was encountered in the prep
37、aratfon of figure 23 was almoet 0.25. It is perhaps obvious that the effect of hp was Large for this particulaz model became of the Fnteraction of this derivative dth other factors in the equstLons of motion. An “bion of the equations indicated that a bge dihedral effect w of the moat importance in
38、this respect, and calculations verified that the effect of C, wotiLd have been negligible if czB had zero* P The damping-in=roll derivative, C2 , is the only other derlwtive 5nvolved to any -eat exbent Fn the dhanges of dynamic stability wfth altitude and Mach nmber that are indicated in figure 23.
39、The effect of increases a roll damping on the parameter l/, was fmorable and about P Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-one half a8 great a8 the effect of Cnp at a mch number of 0.90 and B 40,000 feet. However, at 20,000 feet C had pract
40、i- no effect, so that its importance is not simple to evaluate. The derivative Cnr - C$ I was almost constant in the range of fught conditions considered in fig- ure 23, so that thfs derivative had little to do with the changes in dJmamic stability shown. However, if Cnr - Cni hsd varied by an mount
41、 equal to Cnp it would have produced about one thfrd of the effect on l/Cl,z that was caused by Cnp. ZP I Figure 23 shows an increase of the roll-excitation parameter cp l/ve I with altitude. This was caused primarily by changes in the relative density factor. The only aeroaynamic derivatives which
42、cause eigntfTcant changes in fcp 1/1 Ve I are the static derimtves CzB and hB. Huwever, these did not vary enough $a the-range of flight conditions examined to cause much effect, Est-tes of Rotary Derivatives An estimation of the rotary derivatives of the model has been attempted, using s and for th
43、e tail using reference 13 and the static-force data. The reference did not actually consider terms, so they have been assumed equal to zero. The values, shown in figures 19 and 21, compared favorably with werlmental dues up to angles of attack of about loo, above which Large negative Increases were
44、measured (fig. 25) that were not predicted by theory. - Estimate of Cnr - C+.- The estate of -ping in yaw also was c and again assum3ng the fi term equal to zero. The exception to this pro- accomplished using reference l3 and static-force data for the most part cedure was the body estimate which was
45、 assumed to be: The estimate was fair (see figs . 19 and U) at small angles of attack but did not take account of the loss of dnslpbg with Fncreasbg angle of attack that was measured. The calculated wing contribution was amall in relation to the apparent experimental lncrement. It should be recalled
46、 that the measured damping in yaw about the stability axis for the body alone was an approximation since it was assumed that the body had no moments due to rolling about fts longitudinal axis. The contribution of the tail was underestMted at the lower Mach numbers, but the agreement wns improved at
47、the higher Mach numbers, largely because of the unexpected loss of the end-plate effect of the horizontal tail OIL the measured. values. The maximum disagreement between estimated and test dues of Cnr - Cn; for the complete model was of the same order of magnitude as was obtaFned with Czp. Better ag
48、reement was obtained at high Wch nzlnnbers C. because of the compensathg effects noted for the various model components. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-22 . NhCA RM A56104 Comparison of-theory and experiment by oscillatory-responee c
49、alculations.- The over-all agreement between the estimated and measured values of the rotary derivatives can be assessed from figure 24. This Y figure presents calculated values of the time to damp to half amplitude, since this is the only oscfllatory-response characteristic dfected eignif- icantly by the rotary derlvatives. The most s
