1、SECURITY INFORMATION RESEARCH MEMORANDUM LONGITUDINAL FREQUENCY-RESPONSE AND STABILITY CRARllCTERISTICS OF THE DOUGLAS D-558-II AIRPLANE As DETERMINED FROM TRANSIENT RESPONSE TO A MACH NUMBER OF 0.96 By Euclid C. Bolleman NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WASHINGTON September 18, 1952 mNFf
2、DENTlAL Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N . NACA RM L52E02 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS - - - - “ “ -. LONGITUDINAL FmQUENCY-RESPONSE AN3 STABILITY CHARACTERkTICS OF THE D0U;LAS D-558-11 RESPONSE TO A MACH NUMBER OF 0.9
3、6 By EucLid e. Holleman The longitudinal frequency-response characteristics and the sta- bility derivatives of the Douglas D-38-11 airplane were computed from transient-flight data. over a Mach number rasge of 0.60 to 0.96 and at altitude ranges of 21,000 to 25,000 feet, 28,000 to 33,000 feet, and a
4、t 37,500 and 43,000 feet. The results are presente3 as amplitude ratio and phase angle plotted against frequency, and a5 stability derivatives plotted against Mach number. The response amplitrrde of the system varied little with Mach number for the Mach number range of these tests; however, the reso
5、nant frequency increased with Mach number, The airplane transfer-function coefficients showed some variation with Mach number and some altitude effects. The longitudinal-stability derivatives agreed favorably with wind- tunnel results. The elevator control effectiveness varied little with Mach numbe
6、r at the lower Mach numbers but a loss in effectiveness was indicated at the higher test Mach numbers. The static stabflity of the airplane increased with Mach number for the Mach number range tested. The rate of change of drplane normal-force coefficient with angle of attack increased with Mach num
7、ber to a Mach number of 0.83. The damping derivative increased with Mach number to a Mach number of about 0.83 and a decrease was indicated to the higher test Mach numbers. INTRODUCTION + An investigation is currently being conducted by the National Advisory Committee for Aeronautics to determine th
8、e dynamic response Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 L. NACA RM L52E02 characteristics of research airplanes through the transonic speed range. As a part of this investigation, some results on the dynamic longitudinal response charact
9、eristics of the Douglas D-558-11 research airplane have L been obtained. These data are somewhat complete below a Mach number of 0.85 for two altitude ranges. Some data e presented for higher test Mach numbers and altitudes because of the general interest in data of this type. c Of the several metho
10、ds of obtaining the frequency response of free- flight dynamical systems, the pulse-disturbance technique was used because a minimum of flight time and instrumentation is required. Also, no special device is necessary to actuate the input control. By a Fourier analysis of the airplane response to an
11、 elevator- pulse, the frequency response of the airplane has been obtained. These results have been reduced to airplane stability derivatives. These tests were conducted over a Mach number range of 0.60 to 0.96 at altitudes ranging from 21,000 to 43,000 feet. For purposes of analysis the data have b
12、een divided into three altitude ranges: 21,000 to 25,000 feet, 28,000 to 33,000 feet, and at 37,500 and 43,000 feet. SYMBOLS a 6 it airplane normal-force coefficient angle of attack, deg elevator position, deg or radians stabilizer position, deg (positive when airplane nose down) pitching velocity,
13、radians/sec forward velocity, ft/sec mean aerodynamic chord, ft mass of the airplane, slugs wing area, sq ft normal acceleratiori, g units acceleration due to. gravity, ft/sec 2 . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM L5E02 - 3 . ai
14、r density, slugs/cu ft time, sec time to reach steady state, sec airplane weight, lb - pressure altitude, ft Mach number moment of inertia about Y-axis, slug-ft2 exciting frequency, radians/sec undamped natural frequency of the airplane, radians/sec phase angle between q and 6, deg disturbance funct
15、ion parameters of the transfer function differential operator, d/dt, per sec damping ratio, percent damping rate of change of lift coefficient with angle of attack, per deg rate of change of lift coefficient with elevator deflec- tion, per deg rate of change of airplane normal-force coefficient with
16、 angle of attack, per deg rate of change of pitching-moment coefficient with angle of attack, per deg rate of change of pitching-moment coefficient with elevator deflection, per deg rate of change of pitching-mment coefficient with pitching velocity, per radian rate of change of pitching-moment coef
17、ficient with angular velocity of angle of attack, per radian - Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 I NACA RM 5202 cmq + cm however, the stabilizer is the only trimming device on the airplane so that for some runs the stabilizer position
18、 was slightly different. The elevator pulse was of the order of 5O for about 1-second duration. An attempt was made to return the elevator control to its original position for trim. The resulting airplane response was a normal acceleration of approximately *1g or pitching velocity of kO.2 radian per
19、 second and was recorded until the airplane oscillation subsided to some steady-state condition. An average of about 7 seconds of flight time was required for one air- plane transient response from which an entire frequency response was obtained. METHOD OF ANALYSIS The method of analysis is broken d
20、own into three distinct phases: determination of the frequency response; calculation of the transfer- function coefficients; determination of the stability derivatives. Determination of the Frequency Response Time histories of the airplane pitching-velocity response to a pulse of the elevator provid
21、e the working data (figs. 2 and 3). These data were tabalated every 0.05 second which kept the accuracy of the method within 1 percent (ref. 2) and were transformed from the time plane to the frequency plene by a solution of the Fourier htegrals, -I Provided by IHSNot for ResaleNo reproduction or ne
22、tworking permitted without license from IHS-,-,-NACA RM L52E02 6(u) = 8(t)etdt as was done in references 2 and 3. These integrals were evaluated in two pmts - the transient and the steady state. The transient integrals were evaluated by numerical integration (Simpsons one-third-rule inte- gration).
23、For this analysis, Integrations were made at frequencies of 45, 60, 90, 120, 180, 225, 300, and 360 degrees per second. Once the complete Fourier integrals Rq, I, RE, and 18 are evaluated, they may be combined to give the freqLency response et# in terms of amplitude ratio 13 = and phase angle Calcul
24、ation of the Transfer-Function Coefficients For this aaalysis it is assumed that a two-degree-of-freedom system adequately describes the airplane longitudinally. Equations of motion for such a system me, as reported in reference 2, The transfer-function equation of the system as obtained by solving
25、the equations of motion simultaneously is Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 NACA RM 5202 D2q + 2hDq + w2q = COS + ClDS (7) where the transfer-function coefficients Co, C1, 2 therefore, errors at the higher frequencies give rise to err
26、ors in the transfer- function coefficients wkich subsequently appear in the stability deriva5ives. Determination of the Stability Derivatives The stability derivatives for the airplane nzay be calculated from equations (8) to (ll). A measure of the elevator control effectiveness is obtained from equ
27、ation (8) as b il Equation (U) may be solved to give a measure of the static sta- ity of the airplane as pitching moment due to angle of attack as Celculations show the term CLC% less than 1 percent of the term Cl$. - so that the equation may be simplified to pV2E Provided by IHSNot for ResaleNo rep
28、roduction or networking permitted without license from IHS-,-,-10 - NACA RM 5202 +SF Calculations also show the term - CQmq to be small compared m to - 21y(urn)2 so that it may be omitted. The simplified equation is pV2E I Equation (10) gives a measure of the damping characteristics of the airplane.
29、 Solving for the damping derivative gives The airplane normal-force-coefficient slope was obtained by plotting the airplane normal-force coefficient against the angle of attack measured during the subsidence of the airplane oscillation. RESULTS AND DISCUSSION 1 Presented as figures 2(a) and 2(b) are
30、 two representative time his- tories of the airplane response to an elevator pulse. The recorded quantities of pitching velocity and elevator position were analyzed to give the longitudinal frequency response of the system and the longitudi- nal stability derivatives. Figure 3 shows the trim airplan
31、e normal-force coefficient at an airplane weight of 11,000 pounds (x = 63 lb/sq ft) as a function of Mach number with the mean normal-fo.rce Coefficient during each test run shown as the test points. The test points for the two altitude ranges of 21,000 to 25,000 feet and 28,000 to 33,000 feet are s
32、hown by the flagged and unflagged circles, respectively. The squaxe and diamond indicate the points at altitudes of 37,500 and 43,000 feet. All tests at the lower Mach numbers were made with jet power only; how- ever, the higher-speed rum necessitated the use of both rocket and jet power. These runs
33、 were made at a higher altitude and at a heavier air- plane weight and consequently higher CN. S Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM L5Z02 Frequency Response c The frequency response of the system for the different test condi- tio
34、ns of Mach number and altitude is presented in figures 4 to 6 as amplitude ratio and phase angle as a function of exciting frequency. During each run the stabilizer position was constant; however, the sta- bilizer position varied slightly for some of the test runs as is noted in each figure. Figures
35、 4(a) to 4(f) present the frequency response of the system for an altitude ran;e of 21,000 to 25,000 feet. These results are pre- sented as amplitude ratio q/6 and phase angle # as a function of frequency cu with the calculated points indicated as circles and squares. Lines are faired and the result
36、s are compared for the different Mach 1312111- bers in figure 4(g). Figures 5(a) to 5(g) present res+ts obtained at an altitude range of 28,000 to 33,000 feet with the runs compared in fig- ure 5(h). Figures 6(a) and 6(b) present the frequency response at alti- tudes of 43,000 and 37,500 feet. These
37、 tests ax for a Mach number of 0.90 and 0.93 and the runs are compared in figure 6(c). For the llmited range of these tests little change in amplitude ratio with Mach number is shown; however, a change of about 1 in amplitude ratio from the higher- altitude data to the low-altitude results is shown.
38、 The resonant fre- quency of the system increases with Mach number from about 2 to 4 radians per second. By assuming that a two-degree-of-freedom system adequately describes the airplane system longitudindly, the transfer-function coefficients Co, CI, 2(%, and (ca)2 were obtained for each of the res
39、ponses and are presented as functions of Mach number for the test altitude ranges in figure 7. The flagged circles indicate runs grouped at an altitude range of 21,000 to 25,000 feet. A possible fairing of these data is indicated by the dashed lines. The variation of the transfer-function coefficien
40、ts with Mach number for the altitude range of 28,000 to 33,000 feet is indi- cated by the circles. The test points at Mach numbers of 0.90 and 0.93 are at a higher test altitude and are indicated as the diamond and square. The disturbance parameters Co and C1 decrease gradually while the damping par
41、ameter 2!,% and the undamped natural frequency paam- eter (%)* increase wTth Mach number to a Mach number of 0.85. At a constant Mach number, the damping parameter, dtsturbmce pareter, and the undamped-natural-frequency parameter decrease with Fncreasing altitude. Longitudinal Stability Derivatives
42、By the method outlined, the sirplane transfer-function coefficients may be reduced to airplane stability derivatives. Plots of the Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 -L NACA RM L52E02 derivatives Cms, Cma, CN, and . Cm + Cq as functio
43、ns of Mach num- ber are presented as figure 8. Fairings are indicated for the altitude ranges of 21,000 to 25,000 feet and 28,000 to 33,000 feet. The two test points at the higher altitudes are shown by the diamond and square. 9 Elevator effectiveness.- The elevator control effectiveness CW is prese
44、nted for the test altitude ranges (fig. 8) and shows little change with Mach number up to a Mach number of about 0.85. A decrease in effec- tiveness is indicated to the higher test Mach numbers. The lower-altitude data show approximately 50 percent greater effectiveness than the higher- altitude res
45、ults. Static stability.- A measure of the airplane static stability was also obtained and is presented as a function of Mach number in figure 8. The static stability Cm, increases gradually from -0.01 at a Mach nu- ber of 0.61 to -0.017 at a Mach number of 0.85. At the higher Mach nu- bers it is ind
46、icated that the static stability increases more rapidly. The rate of change of airplane normal-force coefficient with angle of attack CN, is shown as a function of Mach number. This variation shows a gradual increase from 0 .O7 at a Mach number of 0.61 to 0.088 at a Mach number of 0.83 and has a val
47、ue of 0.071 at a Mach number of 0.96. Because of malfunctioning of the airplane angle-of-attack vane, data were not available over the dashed part of the curve. Damping derivative. - From the transfer-function coefficient 2 however, the difference in center- of-gravity location for the tests would i
48、ndlcate a difference of this order of magnitude. Also presented is a comparison between the rate of change of airplane normal-force coefficient with angle of attack % (presented as flight teets) and the rate of change of lift coefficient with angle of attack (indicated as wind-tunnel data). Reasonab
49、le agree- ment is obtained over the Mach nrmiber range with the flight data aligbtly higher at the middle Mach number range. a Damping derivative.- Presented also in figure 9 is a comparison of flight-test dampin; derivative C, + % and wind-tmel values of + C however, the flight data increase to 0.13 greater than
