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RM H55H1O

RESEARCH MEMORANDUM

FLIGHT MEASUREMENTS OF THE DYNAMIC LATERAL

AND LONGITUDINAL STABILITY OF THE BELL X-5

RESEARCH AIRPLANE AT 58.7° SWEEPBACK

By Edward N. Videan

High-Speed Flight StationEdwards, Calif.

U!3FWRYCOPY

C LASWFIED DOCUMENT

This material contains information affecttns the National Defense of the United States within the memuneof the espiomge laws, TiUe 18, U.S.C., Sees. 793 and 794, the trm.smisslon or revelation of wluch m anymanner to an unauthorized person is prohibited by law

NATIONAL ADVISORY COMMITTEEFOR AERONAUTICS

WASHINGTONOctober 6, 1955

I

i .

AERONAUTICS

RESEARCH MEMORANDUM

FLIGHT MEASUREMENTS OF THE DYNAMIC LATERAL

AND LONGITUDINAL STABILITY OF THE BELL X-5

RESEARCH Anp- AT 58.70 SWEEp13ACK

By Edward N. Videan

SUMMARY

An investigation has been made of the dynamic stability of theBell X-5 research airplsme at 58.7° sweepback and at altitudes of40,000 feet and 25,000 feet over a Mach number range of 0.50 to 0.97.

The results of this investigation show that the longitudinal oscil-latory motions are well damped over the entire Mach number range exceptfor residual oscillations resulting principally from engine gyroscopiccoupling with the lateral oscillatory mode. The lateral oscillatory modeis moderately well damped except for nonlinear damping characteristicsabove a Mach number of 0.80. The damping is high for large amplitudesbut for sideslip angles of less than 2° the damping is poor. The air-plane is highly sensitive to small inadvertent control motions whichproduce apparently undamped small amplitude oscillations in the Machnumber range above M = 0.80.

By U. S. Military Specifications, the lateral oscillation is mar-ginal except in the nonlinear damping range where it is definitelyunsatisfactory.

The longitudinal and lateral frequency-response characteristics wereobtained ad some coupling effects were noted. Longitudinal frequency-response calculations were characterized by adjacently located doublepeaks in amplitude ratio. This behavior is satisfactorily explained bytheoretical calculations of frequency response involving engine woscopiccoupling to the lateral mode. Lateral frequency responses showed somedependence on the direction of the initial disturbance.

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2

INTRODUCTION

NACA RM H55K10

The Bell X-> research airplane was designed primarily for investiga- -ting the effects of wing sweep angle on transonic airplane characteristics.Accordingly, this airplane incorporates a wing which ~s ‘Weepback ‘ari-able in flight from 200 to 58.70. As part of the research program,flight measurements have been made with the X-5 airplane to determinethe longitudinal and lateral dynamic stability characteristics over aMach number range of 0.50 to 0.97 at an altitude of about 40,000 feetand with a wing sweep angle of 58.7°. Flight measurements have also

been made at 25,0CX)feet to determine altitude effects. This paper pre-sents the longitudinal and lateral dynamic characteristics in termsof P, T1/2 at altitudes of 40,000 feet and 25,000 feet. Some of the

longitudinal stability derivatives sre also presented for these altitudes.The longitudinal and lateral frequency responses are given for the testsat an altitude of

b wing

CL lift

C% = dCL/du

CLbe = dCL/dbe

40,000 feet.

SYMBOLS

span, ft

coefficient, L/qS

Cm pitching-momentof gravity

C% = d~lda

Cmb = dC~d6ee

coefficient about airplane center

.-

NACA RM H55H10 $CONFIDENTIAL

dCmcm~ = . .

7T‘%

I

3

c% rate of change of pitchingmoment with precessional

CNA normal-force coefficient

momentyawing

due to enginevelocity

gyroscopic

Cn~ rate of change of yawing moment due to engine gyroscopicmoment with precessional pitching velocity

c%= dC~d$

c~ = dCn/d~

cl/2 cycles for oscillation to damp to one-half amplitude

cl/lo cycles for oscillation to damp to one-tenth amplitude

c chord, ft

5 mean aerodynamic chord, ft

D d/dt, differential operator with resPect to the

l!3 acceleration due to gravity, ft/sec2

hp pressure altitude, ft

Iy moment of inertia about Y-body axis through center ofgravity, slug-ft2

IZ moment of inertia about Z-body axis through center ofgravity, slug-ft2

L lift, lb

M Mach number

m mass, slugs

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- CONFIDENTIAJA NACA RM H55KL0

normal acceleration, g units

period of oscillation, sec

dynamic pressure, +@12, lb/sqft

area of wing, sq ft

time for oscillation to damp to one-half amplitude, sec

time, sec

velocity, ft/sec

.* @, ft/secequivalent side velocity,

.

angle of attack, deg or radians

da/dt, radians/see

angle of sideslip, deg

double

single

amplitude of p in oscillatory mode

aileron position, deg

elevator position, deg

rudder position, deg

pitch angle, radians

or radians

pitching angular velocity, de/dt, radians/see

air density, slugs/cu ft

air density ratio

phase angle, deg

rolling angle, deg

rolling angular velocity, radians/see

double amplitude of qJ in oscillatory mode

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—

NACA RM H55H10 CONFIDENTIAL

* angle of yaw, radians

$ yawing angular velocity, d$/dt, rad$ans/sec

u) frequency, radians/see

AIRPLANE AND INSTRUMENTATION

A three-view drawing of the X-5 research airplane is shown infigure l(a), and a photograph is presented in figure l(b). Pertinentphysical characteristics are described in table I.

Standard NACA internal recording instruments were used to measureairspeed, altitude, normal acceleration, pitching, rolling, and yawingangular velocities, angle of attack, angle of sideslip, and controlsurface position. All recordings were synchronized by a common timer.

The angular velocities were measured by rate wos with accuraciesof 0.5 percent of instrument full scale. These instruments have thefollowing ranges and dynamic characteristics:

Angular velocity Range, Natural frequency, Dampingradians/see cps (approx.) (approx.)

Pitch *0.5 9.0 0.65 criticalYaw tl.o 13.5 0.65 criticalRoll *3.O 17.0 0.65 critical

The flow direction recorders were vane-type pickups mounted on the noseboom. The undamped natural frequency is about 8 cycles per second andthe dsmping ratio is approxhately 0.7.

Rudder, aileron, and elevator positions were measured by trans-mitters linked directly to the control surfaces. The frequency responseof the transmitter-recorder system has been measured and found to beflat to 20 cycles per second over the amplitude range of the controlmovements presented.

Airspeed was measured from a calibrated nose-boom installation.The accuracy of the airspeed calibration is tO.01 in Mach number.

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6 CONFIDENTIAL NACA RM H55H10

TESTS

The data were obtained from the transient oscillation of the air-plane in response to rudder pulses, elevator pulses, and aileron pulses.The rudder pulse magnitudes were 50 to 12°, the elevator pulse magni-tudes were 4° to ~, and the aileron pulse magnitudes were 20° to 28°.The time duration of all pulses was 0.3 second to 1.0 second. At alltimes the pilot attempted to have the pulse terminate with the controlsurface in its initial position and to hold the control surface fixedfor the duration of the maneuver. Generally all other controls werealso held constant throughout the maneuver. The pulses and resultingtransient oscillations at pressure altitudes of 40,000 feet and at Machnumbers below 0.93 were obtained for initial 1 g trfi flight conditionsTo obtain data at speeds greater than M = 0.93 it was necessary todive the airplane at angles up to 10°. However, these dive angles weresufficiently small so that the change in altitude wo~d have ne@igibleeffect on the oscillation. A smaller number of pulses were mad: a~25,000 feet to investigate altitude effects. Figure 2 presents theaverage normal-force coefficient CNA as a function of Mach number

all pulses at both 25,000 feet and 40,000 feet.

RESULTS AND DISCUSSION

Longitudinal Stability

for

Figure 3 presents representative time histories of the X-5 airplanetransient-longitudinalresponse to an elevator pulse at 40,000 feet.These time histories were chosen to cover the important parts of theMach number range of the flight test measurements. Figure 3 shows thatthe longitudinal motions immediately following the elevator pulse dampquickly over the entire Mach number range. However, the time historiesalso show that the longitudinal oscillations induce a lateral-directionalmode of oscillation which in turn affects the initial transient-longitudinal oscillation. This coupling will be discussed later inconjunction with lateral stability and frequency response.

Figure 4 presents the variations with Mach number of the period,time to damp to one-half amplitude, and cycles to damp to one-tenthamplitude for the longitudinal response of the ?irplane to an elevatorpulse. These measurements were obtained from 0 over the first partof the transient oscillation immediately following the cessation ofcontrol movements. This portion of the curve was chosen for making themeasurements in an attempt to minimize the effects of cross couplingwith the lateral mode. It is impossible to exclude these effectsentirely because, as the time histories show (fig. 3), the lateral-directional mode is disturbed almost as soon as the longitudinal mode

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NACA RM ~5H10 commmw

is disturbed. This condition makes the measurement of

larly difficult and casts some doubt on the validity of

7

T1/2 particu-

the measurementsof both period and time to damp to one-half amplitude, but it is consid-ered to be the best approximation to the true uncoupled longitudinalperiod and damping. The data at 40,000 feet (fig. 4) show that theperiod varies smoothly with Mach number, decreasing gradually from about2.o seconds at M = 0.>6 to about 1.5 seconds at M = 0.92. Above thisspeed the period drops more sharply, reaching 1.1 seconds at M = 0.97.The data at 25,000 feet show that the period decreases by about 20 percentto 26 percent of the value at 40,000 feet. The approximate theoreticalchange with altitude is 29 percent, based upon the approximation thatthe ratio of the periods at the two altitudes is equal to the square rootof the inverse ratio of dynamic pressure.

The damping at 40,000 feet changes only slightly with Mach number,the time to damp to one-half amplitude varying from near 1.0 secondat M = 0.55 to near 0.5 second at M = 0.97. This results in a vari-ation with Mach number of the number of cycles to damp to one-tenthamplitude as shown in figure 4. At 25,000 feet T1/2 ‘d cl/lo ‘howonly small differences from the data at 40,000 feet.

Fi@mre 5 presents the variation of the longitudinal stabilityderivatives ‘C;

altitudes. Theseby the relations:

andC+Cm~ %with Mach number

derivatives were calculated from

81YC@ + C% -

(

pvs 0.693-—~svE2 c%=

)

.—T1/2

for the two test

the period and damping

.

The lift-curve slope used in the computation ofc% + c%

was obtained

from flight measurements as presented in reference 1. Reference 2 showsthat above M = 0.6 and below the pitch-up boundary (ref. 3) theX-5 airplane possesses two static stability regions and a transitionalregion which are dependent upon Mach number and CNA. These regions

(low lift - decreased stability, transitional stability, moderate lift -increased stability) are marked in figure 2. It may be seen that most ofthe pulse maneuvers performed at 40,000 feet are in or near the transi-tional region, whereas the maneuvers performed at 25,000 feet are in aregion of constant though decreased stability. Values of C% (fig. 5))

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8 CONFIDENTIAL NACA RM H55H1O

calculated from the data at 40,000 feet are, therefore> more subject toscatter than the data at 25,000 feet. Figure 5 shows that the agreementof & calculations for the two altitudes is not.perfect. It appears

that closest agreement is obtained between M = 0.8 and M = 0.9 wherethe average CNA at the two altitudes is on the same side of the transi-

tional region of stability (fig. 2).

The values of ~ + C%, also presented in figure 5, show some

scatter which is common to this method of obtaining the derivative. Thescatter is possibly aggravated by the aforementioned effects of couplingon the determination of T1/2. However, the difference between the data

at 40,000 feet and 25,000 feet is larger than the average scatter.

Lateral Stability

During the early flights at 58.7° sweepback, the pilots complainedand records showed that the airplane oscillated almost continuously inthe lateral-directionalmode at small amplitudes, particularly at Machnumbers above 0.80. An investigationwas made to determine if this poorlateral dynamic behavior was affected by the magnitude of the disturbanceand if the motions resulting from large disturbances were stable.

Accordingly, rudder pulses of large amplitude were performed at40,000 feet over the Mach number range from 0.52 to 0.96 and rudderpulses of varying amplitude were performed at Mach numbers between 0.8and 0.9. Throughout each pulse of the latter group the stick was heldfixed by a mechanical stop to prevent inadvertent stick movements.

Figure 6 presents typical time histories at 40,000 feet of thetransient response of the X-5 airplane to rudder pulses over the Machnumber range tested. In the measurement of damping from such timehistories it was noted that T1/2 at large amplitude depended somewhat

on the direction of the initial disturbance. Also, though good dampingas measured by T1/2 was usually present at large amplitudes, it was

observed that the damping would decrease with decreasing amplituderesulting in near zero damping at small amplitudes (fig. 7). To showthe nonlinear effect, the damping was measured as shown by the hypo-thetical curve in figure 8. The “large smplitude” range and “smallamplitude” range were separated at about IBI = 2°. The period anddamping for these two portions of the oscillations are shown in figure 9.The characteristics of the residual oscillation are presented in fig-ure 10. Figure 9 shows that the period varies smoothly with Mach number,ranging from 2.8 seconds at M = 0.52 to about 1.3 seconds at M =0.96.The damping measured over the large amplitude portion of the oscillationalso shows a smooth and fairly consistent variation up to M = 0.75.

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NACA RM H55H1O CONFIDENTIAL 9

For higher Mach numbers, despite scatter, there is a noticeable separationbetween values of T1/2 for large amplitude and small amplitude. This

behavior appears to continue to the highest Mach numbers tested. Thecycles to dsmp to one-half amplitude show a similar trend. In general,the damping of large amplitude lateral motion is good throughout theMach number range.

The damping measured for small amplitudes (fig. 9), however, showsappreciably large variations with Mach number. The low amplitude dampingbegins to vary noticeably from the large amplitude damping at a Machnumber of about 0.83 and reaches a maxtium T1/2 value about double the

large amplitude T1/2 at M ==0.86 to M=O.88. Above M=O.93 the

low amplitude damping increases rapidly and again generally approachesthe large amplitude damping. The cycles required to damp generallyfollow a variation similar to the time required to damp. This variationbetween small amplitude and large smplitude dsmping thus defines a regionof nonlinear damping extending from about M s 0.80 to the test limit.However, the pilots report that the airplane apparently regains much ofits damping in the small amplitude range above M = 0.93.

Included as points in figure 9 are the results of the series ofrudder pulses in the Mach number range of”0.80 to O.w in which rudderdeflections of various amplitudes were made. As shown in the figure,points for large and small oscillatory amplitude as previously definedare fairly well grouped. The scatter existing in these two groups couldnot be identified with the size of the rudder pulse. Therefore it isconcluded that the magnitude of the rudder disturbance does not directlyaffect the dsmping to any extent, except as it affects the initial aMpli-tude of the oscillations.

Figure 10 presents the amplitude of the residual undamped oscil-lation of the lateral transient oscillation for the stick held fixedwith the mechanical stop as well as with simple manual restraint. Thesedata were obtained primarily at the end of the transient oscillations.However a few points, mostly those of the higher amplitude, are takenfrom undamped self-excited oscillations such as those of figure 7. Thesedata show that with the stick restrained by the mechanical stop theresidual oscillation amplitude reached a maximum of 0.3° as compared witha maximum residual amplitude in sideslip of about 2.5° when the stick isheld manually. From these tests it would appear that small aileron move-ments are the major cause of the residual lateral oscillation. Figure 7does not appear to bear out this conclusion since all controls are fixedwithin the limits of the recorder as noted in figure 7. However, asstated in the following pilots’ comments, smy small disturbances such asgusts may initiate these oscillations. It will be noticed that the ‘smplitude of the residual oscillation and the nonlinear damping character-istics follow the same variation with Mach number. Therefore, it would

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10

appear that outside thehigher damping at small

CONFIDENTIAL NACA RM H55H10

nonlinear damping range, below M s 0.80, theamplitude of oscillation keeps the small disturb-

ances from causing a continuous oscillation. .

Figure 11 presents the period and damping for the response to rudderpulses at 25,000 feet. It may be noted from the figure that the cyclesto damp to one-half amplitude show about the same variations as shown bythe large amplitude points at 40,000 feet. However, at the lower alti-tudes and lower CNA (fig. 2) the nonlinear damping effects have disap-

peared and the damping remains constant with amplitude over the wholeamplitude range.

The data shown in figures 9 to 11 are in substantial aaeement withthe pilots’ comments on the dynamic stability of the X-5 airplane. NACApilots who have flown the X-5 airplane feel that the Mach number rangeof 0.85 to 0.92 is dynamically less stable than at speeds above thisrange. The pilots agree that in the least stable region the airplane issubject to almost continuous lateral oscillations of low amplitude withzero damping, similar to the time history of figure 7. The pilots report -that gusts, changes in power setting, or small control motions initiatethese undamped oscillations.

Figures 12 smd 13 present the new Military Specifications fordynamic lateral stability (ref. 4) and the recently superseded U. S. AirForce criteria for dynamic lateral stability (ref. 5), respectively. Thenew Specifications (fig. 12) relate the reciprocal of the number of cyclesto damp to one-half amplitude to the ratio of roll angle to side velocity,

IPI_ .1$’1 57.3which is given by ,Ve,~ ~“

The value of Q was obtained by

integrating the roll velocity, whereas ~ was measured directly from aflow direction recorder. The points presented are calculated for thevarious damping regions of the transient oscillation previously mentioned.According to the new Specifications, some points fall into the satis-factory region and others into the unsatisfactory region. At the lowestMach number range the points fall in the satisfactory region but arenear the border of the unsatisfactory region. In the other speed rangesthe majority of points fall into the unsatisfactory region.

The superseded Air Force criteria (ref. 5) is presented in figure 13.A representative number of points over the Mach number range have beenplotted in this figore. The majority of points fall into the unsatis-factory region but are fairly close to the boundary between the unsatis-factory and satisfactory region.

It will be noticed thatlateral stability of the X-5

by both the old and new criteria the dynsmicairplane is predominantly unsatisfactory.

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In evaluating the airplane, the pilots feel that the lateral dynamicstability characteristics are unsatisfactory, but tolerable, except inthat portion of the speed range where the damping-becomes noticeablynonlinear. In this region the low damping at small amplitude coupledwith a large roll-to-sideslip ratio makes the behavior intolerable.

Coupling of Oscillatory Motions

As shown by the time-history plots (figs. 3, 6, and 7), there iscoupling between the lateral and longitudinal oscillatory modes. Ingeneral, coupling csm be caused by inertial couPling effects> aerodyn~iccoupling, or engine gyroscoPic effects. Although the relative magnitudeof each type of coupling has not been determined for the X-5 airplane,examination of the time histories would indicate that both ~oscopicand aerodynamic coupling are present in appreciable amounts.

Figures 3(b) and 3(c) show the coupling from longitudinal to lateraldirectional mode for an elevator pulse. Note that an up-elevator pulseproduces a right yawing motion, whereas a down-elevator pulse producesa left yaw. Since the aerodynamic coupling to the lateral mode from adisturbance in pitch is usually negligible, this coupling is believeddue to ~roscopic effects. The initial directions of coupled motion forthe two disturbsmce directions agree with those expected from the ~o-scopic precessional torque of the jet engine.

Figures 6(a) and 6(b) show the coupling from the lateral mode tothe longitudinal mode for rudder pulses. These the histories show thata right rudder pulse produces a small initial decrease in angle of attackand a left rudder pulse produces a large increase in angle of attack.Again gyroscopic coupling is hnplied; however, there are large initialamplitude and phase differences in the coupled oscillation for rightand left rudder pulses, suggesting the probability of both aerodynamicand gyroscopic coupling. Sideslips performed with the airplane haveshown no appreciable pitching moments caused by sideslip, indicating nostatic aerodynamic coupling.

In the X-5 airplane configuration the mass is concentrated to alarge extent in the fuselage and near the center of gravity. This phys-ical characteristic makes the moments of inertia about the Y- and Z-axesrelatively small as compared with a conventional jet-powered airplane ofcomparable weight (determinedexperimentally by the method of ref. 6,

Iy = 9,495 Slug-ftp, Iz = 10,110 slug-ft2). Therefore, engine gyro-

scopic torques are effective in producing disturbances in pitch smd yaw.It will also be noted by comparing figure 1+and figure 9 that the periodsof the longitudinal and lateral oscillations are almost equal. This con-dition will produce a near resonant state for the woscopic coupling

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12 CONFIDENTIAL

torque and resultant coupled oscillation.oscillation in either the longitudinal or

NACA RM H55H1O

In this case a poorly dampedlateral mode would produce a

forced resonant oscillation in the other mode. For example, an elevatorpulse in the directional nonlinear damping region would couple a disturb- -ante to the lateral mode, producing a small poorly dsmped oscillationwhich is coupled back to the longitudinal mode and appears there as anear resonant forced oscillation. For these reasons engine ~roscopiceffects are consideredof the X-5 airplane.

important in an analysis of the characteristics

Frequency Response

The trsmsient responses of the X-5 airplane have been snalyzed bymeans of the Fourier transform and the frequency response obtained.These calculations were made in order to present the dynamic character-istics of the airplane in a form that would be more usable to automaticcontrol system designers. The calculations were made on an IBM machinecalculator by a numerical integration procedure using the methods ofreference 7. The data selected for smalysis were from the same tran-sient responses previously discussed smd were analyzed about the airplanebody aXiS. In addition to the above transients, a.series of aileronpulses were made over the Mach number range for frequency responsg only.The airplane responses analyzed and presented in this paper are bj~e,

Reference 8 shows that the frequency-response characteristics areinvariant with control pulse shape and size only when the system islinear. It has been shown previously that the lateral mode of theX-5 airplane is nonlinear in damping over part of the amplitude rangeof the oscillation. The frequency-response curves therefore representthe airplane only for the range of rudder amplitudes used in thisinvestigation.

Presented in figure 14(a) are typical results of the investigationin the longitudinal mode, showing the frequency response of the pitchingvelocity for an elevator input ~/be as obtained by analyzing an elevator

pulse maneuver. This figure shows the amount of scatter obtained in thecalculated response points snd the fairing made in such cases. Fig-ures 14(b) to 14(d) present composites of these curves showing the Machnumber variation. The double peak found in these responses is ratherunusual and at first seems to indicate the presence of two modes ofoscillation with natural frequencies fairly close together. The simi-larity in magnitude of the natural frequencies of the longitudinal anddirectional modes plus the large mode coupling appears to offer a basisfor explanation of the shape of the longitudinal frequency-responsecurves. However, the time histories of pitching velocitY do not aPPear

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...

NACA RM H55H10 CONFIDENTIAL 13

to contain two frequency modes, nor is there any natural frequency inpitch or yaw closely corresponding to the lower frequency-response peak.In an effort to show the effects of engine ~oscopic coupling, testswere made performing elevator pulses at a given speed and altitude withthe engine idling and at maximum revolutions per minute. To achieve aslarge a difference in engine speed as possible, the tests were performedat 15,000 feet where the engine can be idled as low as 60 percent ofmaximum rpm. The tests consisted of a pulse made with the engine idlingat 60 percent of maximum rpm while the airplane speed was decreasingthrough M = 0.6. Another pulse at 100 percent rpm was made while theairplane speed was increasing through M = 0.6. The frequency-responsecalculations for these pulses are presented in figure 15. The frequency-response plot shows that the difference between the maximum and minimumin the double peak is slightly less for the low rpm than for the 100 per-cent case. This difference would tend to substantiate the fact thatthere is an engine woscopic moment acting on the airplane. However,considering the accuracy of the tests, the differences are too small forany definite conclusions to be drawn.

In a further attempt to determine the cause of the double peaklongitudinal frequency response, calculations of longitudinal frequencyresponse were made from theoretical trsmsfer functions derived fromsimplified equations of motion as shown in the appendix. Two sets ofcalculations were made, assuming first a two-degree-of-freedom systemand then a three-degree-of-freedomsystem. The two-degree-of-freedomsystem consisted of the classical longitudinal equations and asstiedconstant forward velocity. The three-degree-of-freedomsystem includedthe same two previous equations, modified to include a moment term dueto gyroscopic coupling from yawing velocity. The third degree of freedomwas assumed to be yaw about the Z-axis. This equation also included amoment term due to gyroscopic coupling from pitching velocity. Thetransfer function hl~e was obtained for both the two- and three-degree-

of-freedom cases and the frequency response was calculated by usinglongitudinal and simplified lateral derivatives which were obtained byassuming only a single degree of lateral freedom. These lateral deriv-atives were calculated from the flight data as described in the appendix.These theoretical frequency-responsecalculations were made for twoMach numbers, M = 0.70 and M = 0.87, at 40,000 feet and are presentedin figures 16(a) and 16(b). The responses are admittedly rough approxi-mations to the actual airplane frequency responses, since at leasttwo degrees of lateral freedom are neglected along with all inertialand aerodynamic coupling terms. However, it is evident that the dominantairplane response characteristics are demonstrated by the simplifiedthree-degree-of-freedomcalculations. Figure 16(b) shows that the fre-quency responses obtained from the transfer function of the three-degree-of-freedom system match in general shape and amp~itude the frequencyresponses obtained experimentally (fig. 14). The agreement of frequencylocation for the corresponding peaks in these figures is not too good.

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14

Results

system,

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of calculations of 6/be for the

neglecting coupling, are given in

NACA RM H55H1O

classical two-degree-of-freedom

figure 16(a). It is interestingto note. in com~arin~ the two-degee-of-freedom sy~t~ to the three-degree-~f-freed-m sy~tem, that tie frequency locations of all the peaksdiffer. The transfer functions were factored to determine the roots ofthe numerator and denominator. The classical two-degree-of-freedom systawas found to be of the form

6 (D + Y)

~= (D2+AD+B)

where the denominator has a pair of conjugate complex roots. The three-degree-of-freedom system transfer function was found to have the form

(D+71)~+AlD+Bb 1)q= )(D2 + A2D + B2)

D2 i-A5D + B5

with a real root and a pair of conJugate complex roots in the numeratorand two pairs of conjugate complex roots in the denominator. The complexroots indicate that this system has two natural frequencies. However,as shown by the values of the roots given in the appendix, the conjugatecomplex pair in the numerator is close to the value of one of the conju-gate complex pairs in the denominator and tends to cancel the effects ofthe latter.

Figures 17, 18, 19, and 20 present, respectively, the results ofthe experimental frequency-response calculations for rudder pulse PI% Y

~/5r, $/br, and i/8r. Since some differences were noted on the time

histories between the airplane response to right and left pulses, thefrequency-response characteristics are presented separately for rightand left pulses. Also presented in each figure is a plot showing theindividual calculated points for a specific type of response. Plotsof p/8r are presented in figures 17(a) to 17(c). It will be noticed

that the frequency-response variations with Mach number are not alwaysconsistent. It is not known whether this lack of consistency is due tononlinearity in some aerodynamic parameters or to scatter in the data.The composites for right and left rudder pulses show little differenceexcept that the left pulses have a smaller amplitude ratio peak at thelowest Mach numbers. The general remarks made about ~/br are true

also for $/br and @/Er (figs. 18 and 19). However, for the rolling

velocity response @/ir (fig. 19) the right

appear to increase somewhat over the left atThe pitching response to rudder disturbance

CONFIDENTIAL

pulse amplitude ratio peaks

$he highest Mach numbers.e/8y is presented in

I \\,...


figure 20. Although the differences in amplitude ratio are small forright and left pulses, the differences in phase angle are large. Thesedifferences were noted previously from an examination of time histories.

Aileron pulses in both directions were also made and responses wereanalyzed in frequency response form. The results for rolling velocityresponse $/ba are presented in figure 21. Again, large differencesare noted in the curves for right and l~ft pulse groups. An effort wasmade to obtain the frequency response $\ba but the results were not of

sufficient quality to present.

Because of the complicated nature of the transfer functions of thisairplane and the presence of some nonlinear derivatives, no attempt hasbeen made to determine the lateral stability derivatives, except somesimplified derivatives for the longitudinal frequency-response calcu-lation described in the appendix.

CONCLUDING REMARKS

An investigation of the dynamic stability of the X-5 research air-plane at 58.70 sweepback at altitudes of 40,000 feet and 25,000 feet overa Mach number range of 0.50 to 0.97 shows the following: The longitu-dinal motions are well damped over the entire Mach number range testedexcept for residual oscillations resulting principally from engine gyro-scopic coupling with the lateral oscillatory mode. This engine ~oscopiccoupling results in motion in both the longitudinal and lateral oscilla-tory modes for either a longitudinal or lateral disturbance. The lateraloscillatory mode exhibits moderately good damping except for nonlineardamping characteristics above a Mach number of 0.80 where the motion iswell damped at large amplitudes and poorly damped for double amplitudesideslip angles smaller than 2°. Small inadvertent aileron controlmotions often produce apparently undsmped small amplitude oscillationsin the Mach number range above 0.80.

By the current military aircraft dynamic stability requirements,the lateral oscillation is unsatisfactory over most of the Mach numberrange. The pilots concur with this finding and report the airplane tobe particularly intolerable in the range with nonlinear dampingcharacteristics.

The longitudinal frequency response 6/be has a large and unusual

double peak near the short period natural frequency. Theoretical calcu-lations have shown that engine ~oscopic coupling effects are princi-pally responsible for the shape of the 6/6e frequency-response curves.

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...


Lateral frequency-response calculations show some differences for rightand left rudder or aileron pulse disturbances, particularly the longi-tudinal response to a rudder pulse O/br and the lateral response to

an aileron pulse $/ha.

High-Speed Flight Sta,tion,National Advisory Committee for Aeronautics,

Edwards, Calif., August 3, 1955.

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NACA RM H55H10

DERIVATION OF

DESCRIBING

The form of the

17-CONFIDENTIAL

APPENDIX

A SIMPLIFIED THEORETICAL TRANSFER FUNCTION

THE ENGINE GYROSCOPIC COUPLING EFFECTS

equations of the two-degree-of-freedom system andits transfer function will not be presented in this paper since it isgenerally well lmown and may be found in reference 6. All the derivativesand airplane constants used in the calculations are contained in thederivatives smd constants listed for the three-degree-of-freedomsystem(table II).

The equations of motion assumed for the three-degree-of-freedomsystem are:

‘:D(8 - a) = C~a + cL~ebe (1)

(2)

(3)

These equations assume that the stability axes coincide with the airplaneprincipal axes of inertia and that there are two-degrees-of-longitudinalfreedom and one-degree-of-lateralfreedom. In formulating these equa-

tions it was assumed that the rotating engine mass produced ~oscopicmoment proportional to the precessional angular velocity where

R = axial moment of inertia, slug-ft2

G = spin of engine mass,

A = precessional angular

Q = moment, ft-lb

radians/see

velocity, radians/see

The coupling derivatives C ●mjr and %6 were

M = pitching moment

CONFIDENTIAL

obtained as follows: Let

1

18

then

CONFIDENTIAL NACA RM H55H10

letting

M= Q = RGA

dCm RGCm$ = ~(i) = —

qsE

where

The yawing-moment

RGthat cn~ = ~“

derivative Cnb is obtained in a similar manner so

The derivativeCw

corresponds to the usual deriv-

ative Cnp. In assuming a single-degree-of-lateralfreedom -~ = ~

and -Cnp = Cn$. For this simplified case

This relationship was used to calculate CnV. The other lateral deriv-

ative Cn~ was fo~d to have a very small effect and was estimated.

The other derivatives in table II were obtained from figures and refer-ences presented in this paper. In solving the equation, let

mV—=klqs

Iy—=k2qsc

lZ—-.kjqSb

CONFIDENTIAL

NACA RM H55H1O

Divide both sides of equation (1) by kl, equation (2) by k2~ and equa-

tion (3) by k3. By solving these equations ~fie is obtained as

6 Q3 +A$2 + A5D + A4

~=4D + A5D3 + A6D2 + A7D + A8

‘here

Al

A2

A3

A4

A5

A6

A7

A8

.

.

.

=

.

.

[

c%k1k2

cm.cLa 8e

-klk2

—

+

[

cLa

k1k2 1c?c%

k2k=j e

[%aCnVcLbe 1 1+CnVCLac~e k1k2k3

[

c + cm. CL‘6 a c<

k2-2+Tkl _

CL cm.aek1k2

cn.cL Cn Cm.cn c.%c +(J( )$a$ $6a-— _

+ k2k3 m~ m& - klk2k3 k3 k2k3 - ~

CLU(wc CmG - k2CW - c~cn~) c~cma

k1k2k3 + k2k3

c CL Cm.n~ue

‘lk2k3

“m

‘m LaW‘kk

23

-..

20 - CONFIDENTIAL NACA RM H55H1O

The frequency response was obtained from this transfer function by substi-tuting into the transfer function the proper values of the constants andD = iw.

Substituting the aerodynamic coefficients at M = 0.87 into thetransfer functions and factoring yields the following expressions: TWOdegrees of freedom

-15.082D + 1.510

D2 + 2.8520D + 19.3572

Three degrees of freedom

15.082D3 - 8.817D2 - 195.082D - 19.451

Db + 3.337D3 + 35.567D2 + 47.009D + 249.446

or

15.082(D+ 0.0999)(D2 + 0.483D + 12.886)

(D2+ 2.56D+ 21.8)(D2+ 0.80D+ 11.3)

CONFIDENTIAL

.-


REFERENCES

1. Bellman, Donald R.:Research Airplaneto 1.03. NACA RM

Lift and Drag Characteristics of the Bell X-5at 590 Sweepback for Mach Numbers From 0.60L53A09C, 1953.

2. Finch, Thomas W.: Flight Determination of the Longitudinal Stabilityand Control Characteristics of the Bell X-5 Research Airplane at~8.~0 Sweepback. NACARM H55C07, 1955.

3. Finch, Thomas W., and Walker, Joseph A.: Flight Determination ofthe Static Longitudinal Stability Boundaries of the Bell X-5Research Airplane With 59° Sweepback. NACA RM L53A09b, 1953.

h. Anon.: Military Specification - Flying QualitiesMIL-F-8785 (ASG), 1 September 1954.

5. Anon.: Flying Qualities of Piloted Airplane. U.Specification No. 1815-B, June 1, 1948.

6. Turner, Howard L.: Measurement of the Moments ofAirplane by a Simplified Method. NACA TN 2201,

of Piloted Airplanes.

S. Air Force

Inertia of an1950.

7. Schumacher, Lloyd E.: Methods for Analyzing Transient Flight Datato Obtain Aircraft Frequency Response. AF, Air Materiel Command,Wright-PattersonA.F.B. (Flight Test Div. Memo. Rep.)ser. MCRFT-2268, Jan. 1950.

8. Triplett, William C., and tiith, G. Allan: Longitudinal Frequency-Response Characteristics of a 350 Swept-Wing Airplane as DeterminedFrom Flight Measurements, Including a Method for the Evaluation ofTransfer Functions. NACARMA51G27, 1951.

CONFIDENTIAL

22

PHYSICAL

Airplane:Weight,lb:Full fuel . . .Less fuel . . .

Power plant:

NACA RM H55H1OCONFIDENTIAL

TABLEI

CHARACTERISTICSOF BELLX-5AIRPLANEAT A SWQEPANGLE OF 5~.7’O

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10,006

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7,894

Axiai-flowturbojetengine. . . . . . . . . . .Center-of-gravityposition,percentM.A.C.:Full fuel. . . . . . . . . . . . . . . . . . . .Less fuel. . . . . . . . . . . . . . . . . . . .

Momentsof inertiafor 58.70sweep (cleanconfigurate:

body sXiS), ShJg-ft2:Abo;tAboutAbout

OverallOverall

Wing:AirfoilRoot

TiP .

. . . . . . . . . . . . . J35-A-17

. . . . . . . . . . . . . . 45.0

. . . . . . . . . . . . . . 45.5on full fuel,

X-45 .-. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5,165Y-axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9,495Z-axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10,110height,ft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2length,ft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.6

section (perpendicularto 38.02-percent-chordline):. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ‘CA 64(lO)AO1l. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .NACA64(08)ACQ8.28

.,Sweep angleatO.25chord, deg . . . . . . . . . . . . . . . . . . . . . . , . .Area, sqft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Span,ft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Span betweenequivalenttips,ft . . . . . . . . . . . . . . . . . . . . . . . .Aspect ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Taper ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Mean aerodynamicchord,ft . . . . . . . . . . . . . . . . ., . . . . . . . . .Locationof leadingedge of mean aerodynamicchord,fuselagestation . . . . . .Incidencerootchord, deg . . . . . . . . . . . . . . . . . . . . . . . . . . . .Dihedral,deg. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Geometrictwist,deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Wing flaps (split):Area, sqft. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Span,paralleltohinge centerline, ft.... . . . . . . . . . . . . . . . .Chord,parallelto line of symmetryat 20° sweepback,in.:Root . . . . . . . . . . . . . . . . . . . . . . . . .TiP. . . . . . . . , . . . . . . . . . . . . . . . . .

Travel,deg. . . . . . . . . . . . . . . . . . . . . . .Slats (leadingedge divided):Area, sqft. . . . . . . . . . . . . . . . . . . . . . .Span,parallelto leadingedge, ft . . . . . . . . . . .Chord,perpendicularto leadingedge, in.:Root . . . . . . . . . . . . . . . . . . . . . . . . .TiP. . . . . . . . . . . . . . . . . . . . . . . . . .

Travel,percentwing chord:Forward. . . . . . . . . . . . . . . . . . . . . . . .Down . . . . . . . . . . . . . . . . . . . . . . . . .

Aileron (45percent internal-sealpressurebalance):Area (eachaileronbehindhinge line), sq ft . . . . . .Span parallelto hinge centerline, ft . . . . . . . . .!l?ravel,deg.. . . . . . . . . . . . . . . . . . . . . .Chord,percentwingchord . . . . . . . . . . . . . . . .Momentarea rearwardof hinge line (total),in.3 . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

58.7183.7

20.119.32.200.4119.95101.2

000

15.96.53

50.819.260

14.610.3

11.16.6

10

5

3.625.15t1519.74,380


PHYSICAL

TABLE I.- Concluded

CHARACTERISTICS OF BELL X-5 AIRPLANE

Horizontal tail:

AT A SWEEP ANGLE OF 58.7°

Airfoil section (parallel to fuselage center line)Area, sqft . . . . . . . . . . . . . . . . . ● “Span, ft. . . . . . . . . ● . . ● . ● . ● ● . . ●

Aspect ratio.. . . . . . . . . . . . . . . . . .Taper ratio . . . . . . . . . . . . . . . . . . .Sweep angle at 0.25-percent chord, deg . . . . . .Mean aerod.mamic chord, in. . . . . . . . . . . .

.

.

.

.

.

.

.

. .

. .

. .

. .

. .

. .

. .

NACA 65AO06......

Position o> 0.25 mean aerodynamic chord, fuselage stationStabilizer travel, (power a~tuated), deg:Leadingedgeup . . . . . . . . . . . . . . . . . . . 0Leadingedgedown . . . . . . . . . . . . . . . . . . 0

.

.

.

.

.

.

.

.

.

Elevator-(20~8 percent overhang balance, 31.5 Percent sPan):Area rearward of hinge line, sq ft . . . . . . . .Travel from stabilizer, deg:m......””””””””””” ““””””Down. . . . . . . . . . . . . . . . . . . . ● .

Chord, percent horizontal tail chord . . . . . . . .

Moment area rearward of hinge line (total), in.3 . .

Vertical tail:Airfoil section (parallel to rear fuselage center

line) . . . . . . . . . . . . . . . . . . . . . .Area, (above rear fuselage center line), sq ft . . .Span, perpendicular to rear fuselage center line, ftAspect ratio. . . . . . . . . . . . . . . . . . . ●

Sweep angle of leading edge, deg . . . . . . . . . .Fin:Area, sqft . . . . . . . . . . . . . . . . . . .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

. .

. .

. .

. .

. .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

31.59.56

2.90.371

4542.8355.6

4.57.5

6.9

252030

4,200

NACA 65A006....

.

Rudder”(23.1 percent overhang balance, 26.3 Percent sPan):Area rearward of hinge line, sq ft . . .Span, ft. . . . . . . . . . . . . . . .Travel, deg . . . . . . . . . . . . . .Chord, percent horizontal tail chord . .Moment area rearward of hinge line, in.3

.

.

.

.

.

.

.

.

.

.

. .

. .

. .

. .

. .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

25.86.171.4746.6

24.8

4.74.43+3522.73,585

24 CONFIDENTIAL NACA RM H55H10

TABLE 11

PARAMETERS USED IN ESTIMATING AIRPLANE FREQUENCY RESPONSE

[ 1hp = 40,000 feet

M 0.70 0.87

v, fps 680 845

q, lb/sq ft 133 199

s, Sq ft 183.7 183.7

E, ft 9.95 9.95

b, ft 20.1 20.1

C%, radian-l- 2.80 2.865

C%, radian-l -1.976 -1.848

c radian-1WJ -.4870 -.4854

~%, (radians/see)‘1 -.0070 -.0070

c%? radian-l -.3438 -.3780

cm~ + ~%, (radians/see)-l -.0592 -.0597

c~b, (radians/see)‘1 -.0522 -.0527

C~, (radians/see)‘1 -.0556 -.0372

Cn6, (radian/see)‘1 .0278 -.0187

-1Cn$’

radian -.2350 -.1862

cn~r,(radians/see)-l -.0100 -.037 ~

...

FNACA RM H55H1O CONFIDENTIAL

t. 404. l“ —q

—-—-.— -

In uw

Stotion“o”

*

t-y240.6” —

-F_O“ Dihedrol

25

(a) Three-view drawing.

Figure l.- Bell X-> research airplane at 58.70 sweepback.

...

I

26 CONFIDENTIAL NACA RM H5’5H1O

(b) Photograph. L-87906

Figure 1.- Concluded.

CONFIDENTIAL

NACA RM H55H1-0 CONFIDENTIAL 27

CNA

7

.6

.5

g

7.-

.’2

(

Q 40,000 feet

3 ❑ 25,000 feet ‘

—

Pitch-up boundary—>

~%)

Increased stabi lit y

o0 Transitional region

~on

$

R

Decreased stability

.L .6 .7 .8 .9

M

Figure 2.- Average CNA during pulse maneuver.

CONFIDENTIAL

. .

CONFIDENTIAL NACA RN H55H1O

up5

8.,deg o

5-

Up5

8e,deg o 7“ -

5 v

10

a, deg

8, rodionskec

up1“

0 / uJ / \/ -

I \ I

2-

15-

10

5

Right 2.-7

b, deg o ./

A? _ — .

2 w

Right “

~, rodionskec O —\ ,’ L //- \ ,-- ,

,1

1.Right

+,mdianskec O — /---= . / {

k) 2 4 6 8 10 12

Figure 3.- Time history of

Time, t, sec

(a) M = 0.70. -

airplane transient oscillation in response toelevator pulse at 40,000 feet.

CONFIDENTIAL

.-

CONFIDENTIALNACA RN H55H1O

8.,deg

a, deg

9,

up5

0\ (

5

up5

0 > f

5d

10

8

6— / ~ ~ --- — \

4 \/

2‘

radkmskec

up.1

0 ‘ L Y

.1-

.2 v

Right ‘

t$, radianslsec O - /I

n . — .

b 2 4 6 8’1’10 12

Time, t, sec

(b) M=o.85.

Figure 3.- Continued.

CONFIDENTIAL

--

30 NACA RM H’35H1O

up5

8., deg o ‘\ /

5-

10.up

8e, deg 5 h

o-

.up

27

.16, radianslsec

o d I P I \\,/ \_ r ./ I - –

I i

20

15 f \

10 - w— \ — / \ —

5 -

Right2

~, deg o ~ \. P w —

2

Right.1

nJ,rudianskec O < r \ r / - A /-x

.1

I

Time, t, sec

(c) M = 0.96.


COIJFIDENTIAL

.-

NACA RM H55H1O 31

2

P, sec

(

T1/2

El

12

0❑ 25;000

feetfeet

El El

2

2

%10

r“5 .

I 1

I .7 .8 (M

Figure h. - Period and damping for the longitudinal response of theX-5 airplane to an elevator pulse.

C01iFIDE2JTIAL

32

Cme+Cma.

CONFIDENTIAL NACA RM H55H1O

-.2

>

0 401000 feet

❑ 25,000 feet

per deglsec

-.

Ic! i, &_o- .. . h

u

“- ‘nD F

A,, .-. .“

(3

L_?5

l---ho d! 10

00D.3Q 0.;

13 0+1

ElEl El

El

.7 -. .8

!3

I

Figure 5.- Variation of the longitudinal stability derivatives Cma

and cm; +C %with Mach number.

CONFIDENTIAL

-..

I

F

H55H1O CONFIDENTIAL 33

up5-

8., deg o ‘ ---- -’ 1

5

Rlgttt

8 ~ , deg

Right

Right

~, rodionskec

5

0 =-’\ /- “

5

I

0 / \)

/--- \

,1 i ‘‘u

2

Rlghtl”O

j, radionskec o/

“, \ .

1.0

a, deg

up

d, radionskec

n, 9

5

0.—.

\&”

% 2’4 6 8 10 12

Time, t, sec

(a) M = 0.70.

Figure 6.- Time histories of transient oscillations in response to a

rudder pulse at 40,000 feet.

CONFIDENTIAL


8., deg

8r, deg

up 5

0 -

5

Right20

i10 1

0 .

Io-

Right

p, deg

Right

~, rudianskec

Right

& radianslsec

a, deg

10

9/ \J

/’ —————

8 4

up.1

9,radians/sec O ‘ & a — — —

.1

(b)

Figure

Time, t, sec

M = 0.67.

6.- Continued.

CONFIDENTIAL

NACA RM H55H10 CONFIDENTIAL 35

up5

/o

5

Right

o 7 /’- ‘/

5

10 1

Righ

~, radionskc

t

Right

& rodionslsec

a, deg

.1

0 u -K 7- -’== ~

.1

.2

1. I

0 — — — =1-==- — —

I

2

w 9

1,5“

1.0 / 7\ J’

, ~ ---- ———.——

.562 4 6 8 10 12

Time, t, sec –

(c) M=o.89.


CONFIDEIJTTA1,

--

NACA RM H55H1O

2+, deg

B, deg

up5

I8., deg o ---,

5

10Right

5 A

o /\L _

5

+ rodionskec

a, deg

Right 2

I [ \

o

I

up

rodionskec

I

I

Time, t, sec

(d) M = 0.89.


CONFIDENTIAL

-.

NACA RM H55H10

l..

8Q, deg

8r, deg

up5

/

o

5

Right5

0 -r ‘

5 “

10

Right4

2

o

2

Right “11

+, mdianskc O ‘ I 7 / \ \ / \ /’- / /L /-

.1 / ~ / “ ‘v

Right 1

~, rodionslsec O \ / I .- / \ /- \ n

/ “

/ 1’ ~

I

1.5 1

1.0/ 6 P -/ - /- ./ - ../ \_/

.5

0 2 4 6 8 10 12

Time, t, sec

(e) M = 0.94.


CONFIDENTIAL

..


.

.

8., deg

~, deg

up 3 /

o

5

Right

Right

~, radians/see

.1

0 ~ —

.1 \/ kp“ ‘ “ “7

5

4 A

a, deg \

3 \r L ‘ — \

2

up1-

6, rodlonsAec O A [ \ ~ ~ ~ _ —

.1 / “ “

1.5

10 L > ~ .

50 2 4 6 8 10

Time, t, sec

(f) M = 0.96.


CONFIDENTIAL

...

NACA RM H55H1O CONFIDENTIAL

up5

So, deg o -

5

5Right

8r, deg o 1> /

5

Right.2

r.1 r

i A?.$,rodianskec O

“b/t—~ I 1~

.1

,21

up.1

6, radlonskec O ‘~

/ \ I/- . — — .

.1-

n, 9

1.5 A

1.0— ---- ~ / ---- — . / \

.50 2 4 6 8 10

Time, t, sec

(g) M = 0.96.


CCNFIDENTI-AL

40 - CONFIDENTIAL NACA RM H55H1O

LN

CONFIDENTIAL

i’

H55H10 CONFIDENTIAL

f)

it

.—zE0

NJ

~

x)

to

*

N

0

t“

Ml‘d+-Pcd

.:dGw-i

CONFIDENTIAL

.

I


o<>

0

0

0

I.b

!I

J o

I

d- (

0-

IQ

aJ

!/

cd

I

&

cL- + u

CONFIDENTIAL

.-

I

NACA RM H’55H1O

00

(

o

o

c

7..

0*

CONFIDENTIAL

ii

.. --

44 NACA RJlH55H10

P,

T

4

sec 2

0E

6

4

/2, sec 2

G 1/2

@

o

0 Right pulse

❑ Left pulse

4

2

8

‘5 .6

fib

II

-B-40 El

M

Figure 11.- Period and damping for the lateral response of the X-5 air-to a rudder pulse input at 25,000 feet.plane

,- ...

NACA RM H55H10 45

‘/c 1/2

6

G.

4

i.

2

0 .2

JMach number

o 0.50 to 0.75

❑ .75 to .85

0 .85 to .93

A .93 to .97

“lagged symbols denote low amplitucl

a

Refe~ence 4

SatisfactoryUnsatisfactory

o 6

.6

Ill3 deg/ft per sec

‘e

.8

Figure 12.- Comparison of the dynamic lateral stability of the X-5 air-plane with Military Specifications, reference 4.

NACA RM H55H1O

12

10

e

T 1/2,sec 6

4

2

0

Mach number

o m to 075

75 to -85

?H5to .93

A .93 to .97

Flogged synlmls denote low amplitude

Reference 5

Unsatisfactory

f@$

I

Figure 13.- Comparison of theplane with superseded

2 3 4

P, sec

lateral dynamic stability of the X-5 air-Air Force criteria, reference 5.

CONFIDENTIAL

..

1.

NACA RM H55H1O

14&e

we

CONFIDENTIAL

‘“r40 \

\

o YP

-40\

-800 2

it

1“c)

12

47

W,mdlanslsec

(a) Sample calculation showing calculated frequency response points.M = 0.69; hp = 40,000 feet.

Figure 14.- Longitudinal frequency response as calculated from

longitudinal transient responses.

CONFIDENTIAL

,- ...

-CONFIDENTIAL NACA RM H55H1O

me

‘e/se

5

/

4.E

M

3 “% \\

2 /

/

I \

o

80

0

-40 Y‘

- ----80

-I2002 4 6 8 10 12

W, rod ianslsec

(b)


CONFIDENTIAL

NACA FM H55H1O

(

LI

/

I

J-M.69

\

120

30-

40

.:

0

-40

-80

-1200

,! .’””.- ‘,.

.,

h\K, /

-----

4 6 8 10

u, mdlanskec

. .

(c)

Figure 14. - Continued.

CONFIDENTIAL

.-

I


@e

I2(

8(

-4(

-8(

2

\ M

.96

\

8 10 Iu, radians\sec

(d)

2

Figure 14. - Concluded.

CONFIDENTIAL

...

NACA RM H55H1O 51

I3—

6

5

4

I

–100 percent

\\

I20

80

60 percent maximum rpm

40 I

o/

-40

-80

- I2002 4 6 8 10 12

Figure 15.- Longitudinalmaximum rpm at

W, radianslsec

frequency response with engine idling and at15,000 feet and Mach number of 0.6.

CONFIDENTIAL

.

52 CONFIDENTIAL

I

NACA RM H55H1O

e/2e

%e

6

5

4M

.70

3/

2 r

I -

0

I20

80 ‘1

40

0

-40

-80

-1200

\

\

----

4 6 8 Dw, radianslsec

(a) Two degree-of-freedom system.

Figure 16.- Longitudinal frequency response calculated from theoreticaltransfer function. hp = 40,000 feet.

COIJFIDENTIAL


6

5 n

4

@@ 3 -

2 I

I

o

‘%e

U, radianslsec

(b) Three-degree-of-freedom system.


CONFIDENTIAL

.-

CONFIDENTIAL NACA M H55H1O

100

@-wo

@@/sr-100

-200

-3000 2 4 6

)0

TIDunDU-

1

10

(a) Sample calculation showing calculated frequency responseat M = 0.75; hp = 40,000 feet.

Figure 17.- Iateral frequency response j3/5r as calculated

lateral transient responses.

CONFIDENTIAL

points

from

2

NACA RM H55H1O

5

4

F

CONKEDENTIAL 55

M

n

100M

.8

.83

% ar.IOO-

,6

-200 —

-30002 4 6 8 10

U,

(b) Frequency response for

rudianskec

right rudder pulses.


CONFIDENTIAL

-CONFIDENTIAL NACA RM H55H1O

.

8970

0

@@8r - 100

-200 — —

-3000 2 4 6 8 10 12U, radi ansAec

(c) Frequency response for left rudder pulses.


CONFIDENTIAL

.- .-

NACA RM H55H1O

6

4

$/8,

2

0

- CONFIDENTIAL

0+

+

(a) Sample calculation showing calculated frequency response points

57

—at M = 0.75; hp = 40,000 feet.

Figure 18.- Lateral frequency response ~/%- as calculated fromlateral transient responses.


lj#8~

6

4

2

0

-1oo

-140

-180

W@

-220

-260

-30Q

I M I

2 4

—

I

q radiansAec

(b) Frequency response of right rudder pulses.

Figure 18. - Continued.

CONFIDENTIAL

. .-

NACA FWlH55H1O CONFIDENTIAL 59●

jf/8r

w

6

4

2

-10(

-14(

-18(

@l@r-22(

-26(

- 30(

0’ I I I 1

M

$.7

1 1 ,4 6 8 10

q radianskec

(c) Frequency response of left rudder pulses.

—


CONFIDENTIAL

NACA RM H55H1O

200❑

n

I00

0 “

,=A-Iuu o 2 4 6 8 10

W, radians/see

(a) Sample calculation showing calculated frequency response pointsat M = 0.73; ~ = 40,000 feet.

Figure 19.- Lateral frequency response $/~r as calculated fromlateral transient responses.

CONFIDENTIAL

12

NACA RJlH55H1O

8C

6C

+/8, 4C

2C

c

%#.@r

20(

10(

(

-10(

.—

\

-20q3 2 4

(b) Frequency

F:

\

I

I

I8 I

response for right rudder pulses.

gure 19.- Continued.

CONFII)ENTIAL

M

) 12

61

62 NACA RM H55H1O

6C

4C

2C

c

20C

IOc

c

-Ioc

%

38

.66

M II

4 6 8

w, radianskec

(c) Frequency response for left rudder pulses.

) I

Figure 19. - cOnCIU&d.

NACA RM H55H1O

I

63

T)))

II

Q--’[

I

+

m (

(

f o

0

m

u):<u)

6.—-u0

* ;.

N

oI

N—

o

*

N

0

m

(n(d

I

o(u

cONFIDENTIAL

..


Eh

/

/

(D0

Q- m N

CONFIDENTIAL

.-


-0

w

.$

CONFIDENTIAL

.

66

1.-. .-

NACA RM H55H1O

10

8 ‘/

6 “ no

0(J

4 0’h

!.,2 )

m

o

w, radian slsec

(a) Sample calculation showing calculated frequency

at M = 0.88; hp = 40)000 feet.response points

o

-400

-80

- I20

-160

-20002 4 6 8 10 I

Figure 21.- Lateral frequency response $/ba as calculated from

lateral transient responses.

CONFIDENTIAL

...

NACA RM H55H1O CONFIDENTIAL

4/%

10

8

6

4

2

0

40

M

-40

-80

.87

-120 ‘

-16‘o 2 4 6 8 10 12

w, radianskc

(b) Frequency response for right aileron pulses.


CONFIDENTIAL

67

...

I

CONFIDENTIAL NACA RM H5’jHIO

M I

40

0

%)0-40

-80

r

k-1202 4 6 8 10 I

(C) Frequency response for left aileron pulses.

Figure 21. - concluded.

CONFIDENTIALNACA - Langley Field, va.

.

.$-U<zE0.5

l..

. .

RESEARCH MEMORANDUM - NASA · 2013. 6. 27. · RM H55H1O RESEARCH MEMORANDUM ... period of oscillation,sec dynamicpressure, +@12, lb/sqft area of wing, sq ft time for oscillationto

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