Flight measurements of stability and control derivatives of the x-15 research airplane to a mach number of 6.02 and an angle of attack of 25 deg

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FLIGHT OF STABILITY

MEASURE_TS

AND CONTROL DERIVATIVES OF

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THE X-15 RESEARCH AIRPLANE

A MACH NUMBER _02 AND

AN ANGLE OF ATTACK OF 25 °

OTS PRICE

by Roxanah B. Yancey -

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Flight Research Center

MICROFILM Edwards, Calif.

NATIONAl AERONAUTICSAND SPACEADMINISTRATION • WASHINGTON, D, C • NOVEMBER1964 • w" FLIGHT MEASUREMENTS OF STABILITY AND CONTROL DERIVATIVES OF THE X-15 RESEARCH AIRPLANE TO A MACH NUMBER OF 6.02 AND AN ANGLE OF ATTACK OF 25 ° By Roxanah B. Yancey Flight Research Center Edwards, Calif.

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION For sale by the Office of Technical Services, Departmer_t of Commerce, Washington, D.C. 20230 -- Price" $1 t25 FLIGHT MEASUREMENTS OF STABILITY AND CONTROL DERIVATIVES OF THE X-15 RESEARCH AIRPLANE TO A MACH NUMBER OF 6.02 AND AN ANGLE OF ATTACK OF 25 °* By Roxanah B. Yancey Flight Research Center SUMMARY Flight tests of the x-iS airplane provided data from which longitu- dinal, lateral, and directional stability and control derivatives were deter- mined over a Mach number range from 0.60 to 6.02 and over an angle-of-attack range from -2.7 ° to 25 ° . The data were obtained with the lower rudder on and off, speed brakes open and closed, and power on and off.

The longitudinal derivatives show the expected trends of increasing levels through the transonic region and diminishing levels as the Mach number increases in the supersonic region. A high level of longitudinal stability is indicated by the flight data.

When the lower rudder is on, the effective dihedral Cl_ has a positive trend with increasing Mach number and changes from a negative (favorable) value to a positive value at a Mach number of about 2.2. When the lower rudder is off, the favorable level of the effective dihedral and that of the directional cross- control derivative C/5 v improve considerably. However, with the lower rudder removed, the level of the directional-stability derivative Cn_ and the level of the directional control derivative Cn5 v decrease substantially.

When the speed brakes are open, a favorable increment is added to the values of both the directional-stability derivative Cn_ and the side-force coefficient Cy_. Little effect of speed-brake deployment is noted on the effective dihedral CI_. No specific power effects are apparent on the trend of either the longitu- dinal or the lateral-directional data.

The derivatives obtained from flight data compare fairly well with wind- tunnel predictions for corresponding configurational and flight conditions.

However, the flight data show a slightly higher longitudinal stability between a Mach number of 1. 3 and 2.0 at the lower angles of attack and also reveal a generally lower level in the directional parameters Cn_ and Cn8 v _°ver the Mach number range investigated than predicted by the wind-tunnel data__ INTRODUCTION During the expansion of the X-15 flight envelope, maneuvers have been performed to provide data from which to determine stability and control deriva- tives. The information obtained is used to update the X-15 simulator_ which is instrumental in flight planning and pilot indoctrination, and to verify the aerodynamic characteristics predicted in wind-tunnel studies.

The initial flight-determined derivative study (ref. i) was made with the interim Reaction Motors LRII rocket engines over a Mach number range from 0.6 to 3._I and for an angle-of-attack range from 0 ° to i_ °. With the more powerful YLR99 engine, the study has been extended to a Mach number of 6.02 and an angle of attack of 25 ° Data were obtained with the lower rudder on and off, speed brakes open and closed, and power on and off. This paper presents the results of both of the derivative studies and compares flight data with wind-tunnel predic- tions. The studies were made as part of a hypersonic flight program being con- ducted with the X-15 airplane by the National Aeronautics and Space Administra- tion, the U.S. Air Force_ and the U.S. Navy at the NASA Flight Research Center, Edwards_ Calif.

SYMBOLS The body system of axes is used.

normal acceleration at center of gravity_ g units a n transverse acceleration at center of gravity, g units at b wing span, ft Rolling moment CZ rolling-moment coefficient_ _Sb lateral-stability derivative, cz_ _C z aileron-effectiveness derivative, _-_, per deg variation of rolling-moment coefficient with rudder deflection_ _cz _ per deg Pitching moment pitching-moment coefficient, Cm qSc oscillatory damping-in-pitch derivative, Cmq + Cry. _) per radian _C m longitudinal-stability derivative, _--, per deg Cm_ Cm_ static margin, fraction of mean aerodynamic chord CN_ _C m stabilizer-effectiveness derivative, _Sh, per deg Cm$ h anW CN normal-force coefficient, 97 _C N normal-force-curve slope, _ , per deg CN_ Yawing moment yawing-moment coefficient, Cn _Sb r_Cn _Cnl, oscillatory damping-in-yaw derivative, Cnr - Cn_ ) per radian _C n directional-stability derivative, _B ' per deg Cn 0 variation of yawing-moment coefficient with aileron deflection, Cn5 a _Cn _5--_' per deg rudder-effectiveness derivative, Cn5 v atW Cy side-force coefficient, _7 _Cy side-force derivative, _ , per deg cy_ mean aerodynamic chord, ft acceleration due to gravity, ft/sec 2

g

h

geometric altitude, ft moment of inertia relative to body X-axis, slug-ft 2

IX

moment o_ inertia relative to body Y-axis, slug-ft 2

iy

moment of inertia relative to body Z-axis, slug-ft 2

IZ

product of inertia, _(i Z - IXlsin 2c, slug-ft 2

IXZ

M Mach number

P period of longitudinal or lateral-directional oscillation, sec

rolling angular velocity, radians/sec or deg/sec

P

pitching angular velocity, radians/sec or deg/sec

q

1 2 free-stream dynamic pressure, _oV , ib/sq ft yawing angular velocity, radians/sec or deg/sec r S wing area, sq ft time required for transient oscillation to damp to half TI/2 amplitude, sec t time, sec true airspeed, ft/sec V W airplane weight, Ib airplane angle of attack, deg app_arent stability parameter _h airplane angle of sideslip, deg total aileron deflection (left aileron down positive), ga

(Sh - I'deg

horizontal-tail deflection (leading edge up positive), _h _hL + _hR), deg speed-brake deflection_ deg 5j vertical-tail deflection (trailing edge left positive), _v _Vu + 5v_), deg angle of inclination of principal X-axis of airplane relative to the body X-axis (positive when principal X-axis is below body axis at the nose), deg < ratio of actual damping to critical damping mass density of air, slugs/cu ft o roll attitude, deg Sub scr ipt s : L left lower vertical tail R right u upper vertical tail indicates the derivative of the quantity with respect to A dot over a symbol time. The symbol represents the absolute magnitude of a quantity.

A_PL_ TYie X-15 airplane (figs. i and 2) was designed as a research vehicle to investigate the hypersonic flight regime and is capable of speeds up to about 6,000 feet per second and altitudes greater than 350,000 feet. Tg_e cylindrical fuselage is composed mainly of integral propellant tanks, thus requiring fairings on each side of the fuselage to enclose the components of the various systems.

A research instrumentation compartment is located immediately to the rear of the cockpit, ahead of the liquid-oxygen tank. Physical characteristics of the air- plane are listed in detail in table I.

For the interim flight program (ref. !), the X-IT was equipped with two Reaction Motors LRII rocket engines, installed one above the other in the rear of the fuselage. For the flights to higher Mach numbers, the propulsion unit con- sists of one Reaction Motors YI_99 variable-thrust, liquid-rocket engine. The YLR99 engine was designed to develop a thrust of 50,000 pounds'at sea level, and the ratio of the area of the exhaust to the area of the throat is 9.8. The vari- ation with airplane weight of the moments of inertia of the airplane about the body reference axes for power-on and power-off conditions is shown in figure 3.

The center of gravity was approximately 20 percent of the mean aerodynamic chord.

The X-15 has a 5-percent-thick wing with an aspect ratio of 2.5, a i0 °

wedge-shapedvertical tail, and an all-movable horizontal surface. All aero-

dynamic control surfaces are positioned by irreversible hydraulic systems.

Landing flaps are also hydraulically actuated. The horizontal stabilizer pro-

vides longitudinal control when deflected symmetrically and lateral control when

deflected differentially. The outer portions of the upper and lower vertical

tails are all-moving surfaces affording directional control. Speedbrakes are

provided at the rear of the inboard sections of the upper and lower vertical

tails. Flights are madeboth with and without the lower rudder. Whenthe lower

rudder is on during filight_ however, it must be jettisoned before landing to

provide adequate ground clearance.

Two of the three X-15 airplanes are equipped with a stability augmentation

system (SAS) that provides damping through the aerodynamic-control surfaces to

increase three-axes stability. During the flights with the lower rudder on_ an

interconnect damper system (termed 'Tar") feeds yaw-rate signals into the roll-

control surfaces to provide additional roll damping. The gains and authority of

the pitch, roll, yaw, and yar damper systems are shown in table II. The sta-

bility augmentation system is discussed in detail in reference 2.

The Honeywell adaptive control system is installed in one of the X-I_

airplanes. This system automatically adapts itself to the changing control-

surface effectiveness and varying basic-airplane characteristics by providing

an essentially constant rate of response to control input.

INSTRUMENTATION

Standard NASAsensing and internal recording instruments_ synchronized at

O.l-second intervals by a common timer, were used to record pertinent data_ such

as normal and transverse accelerations_ angular velocities and accelerations 3

and control-surface deflections.

Airspeed and altitude for the flights with the YLR99engine were obtained

from measurementsmadeby ground-based tracking radar at Edwards, Calif., and at

Ely and Beatty, Nev.

Operational limitations did not permit the use of standard NASAfree-

floating vanes mounted on the nose boomto measure angles of attack and sideslip

at Machnumbers beyond 3.4. The sensorswere replaced by a gimbal-mounted, null

pressure-seeking spherical _ and _ sensor mounted on the nose of the X-15

(fig. 4). It should be noted that the sensor, or "ball nose," senses the side-

slip angle oriented with respect to the stability system of axes; whereas_ the

angle-of-sideslip vane on the nose boomoriented its reading to the body system

of axes. No attempt was madeto correct the angle-of-sideslip indications of

the ball nose to the body-axes system, inasmuch as the errors in the angle-of-

attack range of the flight data were considered to be within the experimental

accuracy of the data. For the few data points at an angle of attack of 2_°j the

error in angle of sideslip is on the order of i0 percent.

The average ranges and dynamic characteristics for the sensing and recording instruments were: Undamped natural Function Range Damping ratio frequency_ cps -20 ° to 40 ° 12 0.64 ±20 ° .64 12.5 .64 -3g to 8g 31 an .64 18.5 ±Ig at bt8 .62 P a±4 radians/sec d18 .62 c±6 radians/sec 2 12 .62 ±0.5 radian/sec q 12 .62 ±i radian/sec 2 .62 r 12 ±0.5 radian/sec 2- 12 .62 ±i radian/sec 2 aFor X-15-3, ±2 radians/sec.

bFor X-15-3, 13 cps.

CFor X-15-3, ±3 radians/sec2.

dFor X-15-3, 13 cps.

Recordings are generally accurate within ±2 percent of the full-scale reading.

FLIGHT-TEST DATA The derivative characteristics presented in this paper were determined from time histories of pitch_ yaw, and roll pulses, random oscillations_ and sideslip maneuvers. Most of these maneuvers were performed with either the stability augmentation system or the adaptive control system functioning. Although two dampers were off on several of the maneuvers analyzed, all three dampers were disengaged on only one of the maneuvers. X-IT missions and performance charac- teristics made it difficult to obtain the type of controlled response at the higher Mach numbers that would lend itself to analysis of both static and dynamic derivatives by use of simplified mathematical expressions. Thus, an analog- matching method (ref. i) was used to supplement the simple methods of analysis.

A time history of a pitch pulse, representative of those obtained at the higher Mach numbers, is shown in figure 5. Typical time histories of roll and yaw pulses are shown in figures 6 and 7. The roll control was difficult to hold fixed in the lateral-directional maneuvers; therefore, most of the roll- and yaw- pulse maneuvers had some roll-control input during their transient oscillations.

A limited number of sideslip maneuvers were also analyzed to determine static lateral-directional derivatives. A time history of a typical sideslip maneuver is shown in figure 8.

Some random pitch, roll, and yaw oscillations yielded useful data. Fig- ures 9 and i0 are representative time histories of such oscillations.

The maneuvers analyzed covered the following overall ranges of flight con- ditions: Mach numbers from 0.60 to 6.02; altitudes from 22,400 feet to 131_400 feet; dynamic pressures from 78.5 ib/sq ft to 1,583 ib/sq ft; and angles of attack from -2.7 ° to 25 ° . Although the ball-nose readings of angle of attack and angle of sideslip are in error at low subsonic speeds, because of flow effects around the nose of the airplane, all the data presented herein were at low angles of attack where errors are negligible. Figure ii shows the area in which flight measurements of derivatives were made.

ANALYSIS AND PRESENTATION OF DATA The mathematical and analog-matching techniques used to obtain the longitu- dinal and lateral-directional stability and control derivatives of the X-15 airplane at the higher Mach numbers and angles of attack are the same as those used in the study of reference i. The nature of much of the data precluded the use of simplified mathematical expressions; thus, the analog-matching technique was used to obtain the desired derivatives as well as to verify the results obtained with the simple equations. The results were in good agreement when both methods were used to analyze a particular maneuver which was amenable to the application of the simple equations. Figures 12 and 13 show analog matches of a pitch osciilation and a rudder-induced lateral-directional osciilation_ respec- tively. When the derivatives were obtained by using simplified mathematical expressions_ the necessary basic data (periods_ time-to-damp to half amplitude_ damping ratios, and amplitude ratios) were obtained from time histories similar to that shown in figure _ for the longitudinal mode and to those shown in fig- ures 6 or 7 for the lateral-directional mode. These basic data are presented in tables Ill to V. The period is considered accurate within 0.05 second for the low damping ratios (_ < 0.3).

Often_ the augmentation systems could not be completely deactivated because of safety-of-flight restrictions; therefore, the desired controls-fixed condition for many of the pulse maneuvers and osci!iationskcould not be attained. In such instances, an empirical correction to the basic data was applied to account for the effects of the augmentation system (ref. i).

Cm_ / \ The longitudinal derivatives CN_ _ C_ C-_ 3 _Cmq + Cm_)_ and Cm5 h are plotted as functions of Mach number and compared with wind-tunnel predictions in figures 14, 15, 16, 17_ and 18_ respectively. The variation of the lateral- directional derivatives Cn_ , Cl_ , eye, (Cnr- end), Cnsv, CZSv, Cn5 a,

and CZ8 a with Machnumber and a comparison with wind-tunnel results are pre-

sented in figures 19 to 25. The wind-tunnel data were obtained from the sources

listed in references 3 to 16.

DISCUSSION

The derivatives obtained from flight data are discussed in the following

sections_ and flight-determined characteristics and wind-tunnel predictions are

compared. Desired flight data in specific Machnumber and angle-of-attack

regions were not always obtainable; thus, there are gap_ in the derivative presen-

tations over the Mach number range. Trends in the data are generally apparen%

however. Although the flight-determined derivatives ar_ presented at various

angles of attack within an angle-of-attack range, the wind-tunnel data are given

only for the average angle of attack of the flight-test range. Comparison of the

flight-determined and the wind-tunnel derivatives showsthe correlation between

the data. No attempt was madeto correlate the flight-determined derivatives

with the results of theoretical studies; this comparison may be found in

reference 17.

Longitudinal Derivatives

In the flight data presented in figures 14 to 18, the longitudinal stability

and control derivatives showthe usual trends of increasing levels of lift-curve

slope_ static stability_ damping, and control effectiveness through the transonic

region and diminishing levels of these characteristics as Mach number increases

in the supersonic region. Although a distinction between power-on and power-off

conditions is made in the flight data, power effects do not appear to be signifi-

cant. No distinction has been madebetween lower-rudder-on and lower-rudder-off

data because the rudder has little effect on the longitudinal characteristics.

The effect of speed brakes is shown only for Cm_ _ inasmuch as the other longi-

tudinal derivatives are not significantly influenced by speed-brake deployment.

Insufficient longitudinal data were obtained with the speed brakes open to

enable any conclusions to be madeon the effects of the brakes.

The peak value of the stability derivative Cm_(fig. 15) occurs at a

slightly higher Mach number than the control-effectiveness derivative Cm8 h

(fig. 18) and at low supersonic speeds decreases more slowly than Cm$ h with

increasing Mach number. These trends result in a general decrease in the

Cm_ h

apparent stability parameter _Sh, obtained from Cm _ , as speed increases from

subsonic Mach numbers to M _ 2.5, followed by someindication of an increase in

apparent stability at higher speeds. An appreciable level of longitudinal

Cm_

stability is indicated by the static margin obtained from -- (fig. 16)

CN_ particularly for low supersonic speeds. The damping derivative Cmq (fig. 17), which is moderately high in the transonic region, decreases rapidly between Mach numbers of i and 2 and remains at a relatively constant level above M= 2.0.

In general, the longitudinal flight and wind-tunnel data are in fairly good agreement, with the flight data indicating that the predicted levels of stability have been realized. At angles of attack up to 6 °, the flight-determined static- stability derivative C_ is slightly higher than anticipated between M = 1.3 and M = 2.0 (fig. 15). In the lower range of stabilizer positions, the values of Cm_ h obtained from flight data are slightly lower than those predicted by wind-tunnel tests (fig. 15) Although the damping derivative Cmq more difficult to obtain than the static derivatives_ because of inadvertent control inputs, the flight-determined values of this derivative are in good agreement with wind-tunnel data.

Lateral-Directional Derivatives Fairly good consistency is shown in the variation of the flight-determined lateral-directional stability and control derivatives with Mach number (figs. 19 to 25). Both power-on and power-off data are presented, but no specific power effect is noted.

In the low-angle-of-attack region_ the static directional-stability derivative Cn_ (fig. 19(a)) peaks at about M = 1.3 then diminishes rapidly until M _ 2._ Above M _ 2.5 the rate of decrease is much lower. At Mach numbers below approximately 2, the value of Cn_ decreases substantially as the angle of attack increases. At high Mach numbers the increase in effectiveness of the lower vertical tail with increasing angle of attack_ as a result of the high intensity of the bow and wing compression shocks, more than offsets the decrease in effectiveness of the upper vertical tail_ which is in the expansion field. The result is that Cn_ increases with increasing angle of attack (ref. 17).

When the lower rudder is removed_ the anticipated decrease _n the value of Cn_ is evident (fig. 19(b)), with as much as a 50-percent drop noted for Mach numbers above 3.0 at low angles of attack. The negligible values of Cn_ between M = 3.0 and 3.5 at moderate angles of attack indicate that the vertical tail with the lower rudder off barely compensates for wing-fuselage instability in this flight range.

In general, there is a favorable increment in Cn_ when the speed brakes are open. This increment decreases as angle of attack increases.

With the lower rudder on, there is a positive trend in the flight data for the effective dihedral derivative CZ_ in all angle-of-attack areas as the Mach i0

number increases (fig. 20(a)). The values of this derivative change from favor-

able (negative) to adverse near M = 2.2 and change little with increase in

Mach number above M = 3.0. This positive trend is caused by the asymmetry in

effectiveness between the upper and lower vertical tails resulting from bow and

wing shock expansion and compression fields (ref. 17). The adverse dihedral

effect at higher Machnumbers is relieved when the lower rudder is removed, as

shown in figure 20(b) where the values of CZ_ determined from flight maneuvers

with the lower rudder off are favorable for the Mach number and angle-of-attack

range studied. There seemsto be little effect of speed-brake deployment on

CZ_ at low angles of. attack; however, CZ_ is generally more adverse with

speed brakes open at the higher angles of attack.

With the lower rudder on, the values of the side-force derivative Cy_

(fig. 21(a)) increase to the transonic region, then gradually decrease with

rising Machnumber. With the lower rudder removed (fig. 21(b)), the values of

the side-force derivative are appreciably lower in all Mach number and angle-of-

attack ranges investigated. At the low angles of attack, speed-brake deployment

raises_ in general, the level of Cy_.

The flight-determined value s of the damping-in-yaw derivative (Cnr - C_)

for the lower-rudder-on configuration peak in the transonic region, then showa

gradual decline with increasing Mach number (fig. 22). Within the accuracy of

the data, there seemsto be little angle-of-attack effect. The scatter in the

SAS-ondata is probably due to the large SAScorrections for damping-in-yaw

derivatives, which give rise to considerable uncertainty in the flight data

(ref. i). Too little damping-in-yaw data have been obtained with the lower rudder off to be considered in this paper.

The flight control derivatives are characterized by peak magnitudes in the transonic range and decreasing levels with increasing Mach number (figs. 23 to 25). The data for lower-rudder-on and lower-rudder-off configurations of the airplane are presented separately for values of Cn5 v and CZ5 v but are com- bined for CZ8 a and Cnsa, since there is no discernible difference in the data for the latter two derivatives with the two tail configurations.

The value of the flight-determined directional-control derivative Cnsv, similar to Cn_ , decreases considerably _hen the lower rudder ls removed (fig. 23(b)). Moreover_ Cn5 v shows no significant angle-of-attack effect with the lower rudder on (fig. 23(a)), but decreases appreciably with increase in angle of attack when the lower rudder is removed.

When the lower rudder is on, CZ5 v changes from positive to negative as Mach _number increases in the supersonic range (fig. 24(a)). This sign reversal occurs at a lower Mach number at the higher angles of attack than at the lower angles of attack. When the lower rudder is off (fig. 2k(b)), CZ5 v remains ii

positive throughout the Machnumber and angle-of-attack ranges studied. With the

lower rudder on, C/_v becomesmore negative with increasing angle of attack.

With the lower rudder off, C/_v becomesless positive with increasing angle of

attack.

Somescatter is noted in both the Cn$ a and CZ_ a flight data (fig. 25),

particularly at the high angles of attack; this scatter is partly the result of

differences in angle of attack within the 12° to 24° range. For Mach numbers

greater than 4, the flight values of both Cn$ a and C/8a are generally higher

at the larger angles of attack than at the smaller values.

In general, the flight data for Cn_ (fig. 19) confirm the wind-tunnel

prediclions, although there is a somewhatlower level in the flight values of

Cn_ with the lower rudder on at low angles of attack and at supersonic Mach

numbers. Also, a smaller increment in the flight-determined values of Cn_

resulting from speed-brake deployment at moderate and large angles of attack is

apparent_ and the flight data show an appreciable scatter in the Cn_ increment

as a result of speed-brake deflection. The flight-determined dihedral deriv-

atives are also generally in accord with the wind-tunnel measurements. The

variation with Mach number of the side-force derivatives determined from flight

data showsgood correlation with wind-tunnel data at all angles of attack when

the lower rudder is on and at low angles of attack when the lower rudder is off.

The scarcity of flight data at the higher angles of attack for the lower-rudder-

off configuration precludes any valid comparison. The values of the damping

derivative _Cnr- Cn_ _ determined in flight agree, in general, with the wind-

\

tunnel predictions, although the flight data showconsiderable scatter when the

stability augmentation system is engaged. Whenthe lower rudder is on, values

of Cn8 v obtained from flight data are slightly lower than predicted by wind-

tunnel tests. This lower trend appears to coincide with the aforementioned

lower level of the flight-determined stability derivative. Lower levels in the

flight-determined derivatives are also apparent for Cn_ a and C/5a in the

hypersonic region. Except as noted, all flight-determined control parameters

showfairly good agreement with the wind-tunnel results.

CONCLUSIONS

Flight tests of the X-15 airplane to determine stability and control deriv-

atives to a Machnumber of 6.02 and an angle of attack of 25° with speed brakes

open and closed, lower rudder on and off, and power on and off indicate the

following:

i. The longitudinal stability and control derivatives showedthe usual

trends of increasing levels through the transonic region and diminishing levels

as Mach number increased in the supersonic region. A relatively high level of

c_ longitudinal stability was indicated by the static-margin parameter CN_

( +

particularly for low supersonic speeds. The damping derivative Cmq decreased rapidly between Nach numbers of 1 and 2, then remained fairly constant for higher Mach numbers, 2. With the lower rudder 0n_ the values of the lateral-directional deriv- atives_ except CZ_, in the low and moderate angle-of-attack ranges increased to the transonic region and then declined with rising Mach number. At the higher Mach numbers_ the directional-stability derivative Cn_ increased with increasing angle of attack. The effective dihedral derivative CZ_ had a positive trend as the Mach number increased and changed from favorable to adverse near a Mach number of 2.2.

3. When the lower rudder was removed 3 the value of the static directional- stability derivative Cn_ dropped as much as 50 percent above a Mach number of 3.0 at low angles of attack. At moderate angles of attack the value of Cn_ approached zero near a Mach number of 3.5. A decided decrease in the levels of the side-force derivative Cy_ and the rudder-effectiveness derivative Cn5 v also occurred with the removal of the lower rudder. However_ when the lower rudder was removed, the values of the effective dihedral CZ_ remained favorable (negative) and the values of the cross-control derivative CZ5 v remained posi- tive for the Mach number and angle-of-attack ranges investigated.

4. Opening the speed brakes produced favorable increments in the values of both Cn_ and Cy_; however, the Cn_ increment decreased as the angle of attack increased. On the whole_ little effect of speed-brake deployment on the effective dihedral derivative CZ_ was apparent at low angles of attack, but the derivative appeared to be somewhat more adverse with speed brakes open at the higher angles of attack.

5. Although both power-on and power-off conditions were investigated_ there appears to be no specific power effect on the trend of any of the principal de- rivatives.

6. The flight-determined derivatives are_ with a few exceptions, in agree- ment with the wind-tunnel predictions. The static longitudinal-stability derivative Cm_ determined from flight data is slightly higher than predicted by wind-tunnel tests at low angles of attack in the Mach number range from 1.3 to 2.0. The flight-determined directional-stability derivative Cn_ and the vertical-tail-effectiveness derivative Cn8 v show slightly lower values at low angles of attack and at supersonic Mach numbers than do the wind-tunnel data at the same conditions. A trend to values lower than predicted is also evident in the hypersonic regions for the flight-determined roll-control derivative UZ8 _.

Flight Research Center_ National Aeronautics and Space Administration_ Edwards_ Calif._ July 13, 1964.

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3. Anon: Revised Basic Aerodynamic Characteristics of the X-15 Research Air- plane. Rep. NA-59-1203, (Contract AF 33(600)-31693), North American Aviation, Inc., Aug. 7, 1959.

4. Hassell, James L., Jr., and Hewes, Donald E.: Investigation of the Subsonic Stability and Control Characteristics of the i/7-Scale Model of the North American X-15 Airplane With and Without Fuselage Forebody Strakes. NASA TMX-210, 1960.

5- Lopez, Armando E., and Tiniing, Bruce E.: The Static and Dynamic-Rotary Stability Derivatives at Subsonic Speeds of a Model of the X-15 Research Airplane. NASA RMA58F09, 1958.

6. Driver, Cornelius: Effect of Forebody Strakes on the Aerodynamic Character- istics in Pitch and Sideslip of a Hypersonic Airplane Configuration at Mach Numbers of 1.41, 2.01, and 6.86. NASA TMX-II6, 1959.

7. Tunnell, Phillips J., and Latham, Eldon A.: The Static and Dynamic-Rotary Stability Derivatives of a Model of the X-15 Research Airplane at Mach Numbers From 1.55 to 3.50. NASA MEMO 12-23-58A, 1959.

8. Franklin, Arthur E., and Lust, Robert M.: Investigation of the Aerodynamic Characteristics of a O.067-Scale Model of the X-15 Airplane (Configu- ration 3) at Mach Numbers of 2.29, 2.98, and 4.65. NASA TMX-38, 1959.

9. Anon: A Third Series of Supersonic Force Tests on the Full-Span Model X-15 for North American Aviation, Inc. WTR 228, M.I.T. Naval Supersonic Lab., Nov. 1958.

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ii. Dunning, Robert W.: The Control Characteristics of Two Preliminary Models of the X-15 Research Airplane at Mach Numbers of 2.98 and 4.01. NASA TMX-212, 1960.

12. Penland, Jim A., and Fetterman, David E., Jr.: Static Longitudinal, Directional, and Lateral Stability and Control Data at a Mach Number of 6.83 of the Final Configuration of the X-15 Research Airplane. NASA TMX-236, 1960.

13. Paulson, John W., and Hassell, James L., Jr.: Low-Speed Measurements o£ Oscillatory Lateral Stability Derivatives of a i/7-Scale Model of the North American X-15 Airplane. NASA TMX-144, 1959.

14. McKinney_ Royce L._ and Lancaster_ Julia A.: Investigation of the Aero- dynamic Characteristics of a 0.02-Scale Model of the X-15 Airplane at Mach Numbers of 2.96, 3.96, and 4.65 at High Angles of Attack. NASA TMX-$20, 1963.

15. Nelson_ Duane A.: Test of a 0.02-Scale Model of the North American Aviation X-15 in the 21-1nch Hypersonic Wind Tunnel. WT 21-32, Jet Prop. Lab., C.I.T., Mar. 3_ 1961.

16. Nelson_ Duane A.: Test of a O.02-Scale Model of the North American Aviation X-15. WT 21-63, Jet Prop. Lab., C.I.T., Mar. 21, 1962.

17. Walker_ Harold J._ and Wolowicz_ Chester H.: Stability and Control Deriva- tive Characteristics of the X-15 Airplane. NASA TMX-714, 1962.

TABLE I. PHYSICAL CHARACTERISTICS OF THE X-15 AIRPLANE Wing: Airfoil section ................... _ . NACA 66005 (modified) Total area (includes 94.98 sq ft covered by 2OO fuselage), sq ft .........................

22.36 Span, ft ...............................

Mean aerodMnamic chord, ft ...................... 10.27 Root chord,i ft .......................... 14.91 2.98 Tip chord, _t .............................

0.20 Taper ratio\ ..............................

Aspect rati0' ........................... 2.50 Sweep at 25-percent chord line, deg .................. 29.64 Incidence, deg ............................

Aerodynamic twist, deg ........................

Flap - Type ................................ Plain 8.30 Area (each), sq ft .........................

Span (each), ft ......................... 4"50 2.61 Inboard chord, ft ..........................

I.O8 Outboard chord, ft .........................

0.22 Ratio flap chord to wing chord ...................

Ratio total flap area to wing area ................. 0.08 Ratio flap span to wing semispan ................... 0.40 Trailing-edge angle, deg ...................... 5.67 Horizontal tail: Airfoil section ............. ......... NACA 66005 (modified) Total area (includes 63.29 sq ft covered by fuselage), sq ft ........................ 115"34 18.o8 Span, ft ...............................

Mean aerodynamic chord, ft ...................... 7.05 10.22 Root chord, ft ..........................

Tip chord, ft ............................. 2.11 Taper ratio .............................. 0.21 Aspect ratio ............................. 2.$3 Dihedral, deg ............................. -15 Ratio horizontal-tail area to wing area ................ 0.58 Movable-surface area, sq ft ...................... 51-77 Deflection - Lateral differential (pilot authority), deg ............ ±15 Lateral differential (autopilot authority), deg .......... ±30 Control system ....... Irreversible hydraulic boost with artificial feel TABLE I.- PHYSICAL CHARACTERISTICS OF THE X-i5 AIRPLANE (Concluded) Upper vertical tail: i0 ° single wedge Airfoil section .......................

40.91 Total area, sq ft ...........................

4.58 Span, ft ..............................

8.95 Mean aerodynamic ehord_ ft ......................

10.21 Root chord, ft ............................

7.56 Tip chordj ft .............................

0.74 Taper ratio ..............................

o.5i Aspect ratio .............................

23.41 Sweep at 25-percent chord line, deg .................

0.20 Ratio vertical-tail area to wing area .................

26.45 Movable-surface area, sq ft ......................

±7.50 Deflection_ deg ............................

Sweepback of hinge line_ deg .....................

....... Irreversible hydraulic boost with artificial feel Control system Lower vertical tail: Airfoil section ....................... i0 ° single wedge Total area, sq ft ........................... 34.41 Span, ft ............................... 3"83 Mean aerodynamic chord, ft ...................... 9.17 10.21 Root chord_ ft ............................

Taper ratio .............................. 0.78 Aspect ratio ............................. 0.43 Sweep at 25-percent chord line, deg .................. 23 .41 Ratio vertical-tail area to wing area ............... 0.17 Movable-surface area, sq ft ...................... 19.95 Deflection, deg ............................ ±7.50 ....... Irreversible hydraulic boost with artificial feel Control system Fuselage: Length, ft ................ , ............. 50.75 Maximum width, ft ........................... 7.33 Maximum depth, ft ........................... 4.67 Maximum depth over canopy, ft ..................... 4.97 Side area (total), sq ft ....................... 215.66 10.91 Fineness ratio ............................

Speed brake (typical for each of four): Area, sq ft ............................ 5.57 ! .67 Span_ ft ...............................

Chord, ft ............................. 3.33 20 +i Center-of-gravity location, percent mean aerodynamic chord .......

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544.5 66,800 Open 8,0,0 2.58 6.4 3.27 8.57 2.26 8.60 .029 Off Open 8,6,0 2.68 7.4 483.0 71,150 Off Open 8,0,0 3.62 7.18 2.05 5.35 .042 571.5 68,400 2.74 5.0 Off 4.16 .17 1.60 1.39 .126 2.84 1.8 Open 4,4,4 545.8 69,398 Off Open 4,4,4 3.92 .15 1.68 1.40 .131 514.3 72,457 2.97 1.7 On Closed 8,6,8 2.17 3.93 "2.60 1.36 .206 2 -99 2.0 466.0 77,054 Off open 8,6,8 3.70 8.00 2.50 II. 30 .025 473.0 76,775 3.O4 7.4 Off 3.87 .13 1.68 1.85 •099 501.3 74,938 Open 4,4,4 3.11 1.7 Off Open 8,0,0 3.86 7,80 2.00 ......

653.5 74,450 3.40 4.5 Off 3.03 .... ].00 1.37 .234 467.5 80,850 Closed 8,6,8 3.40 7.3 Off Open 8,6,8 3.75 9.79 1.78 4.75 .041 506.0 79,350 3._1 2.6 Off ........ 3.40 1.20 .298 Closed 8,6,8 3.46 9.8 439.0 83,050 Off Closed 0,4,8 2.26 .... 3.30 5.20 .215 280.0 92,250 3.9o 7.7 Off .... 8.46 2.70 -6.50 -. 046 Open 8,8,0 3.54 8.7 449.5 84,400 3.25 .16 2.50 1.78 .153 Off Closed 4,4,h 717-1 73,648 3.61 6.8 Off 2.46 4.17 4.20 2.47 .184 Closed 8,6,8 260.0 97,325 3.70 ]2.5 2.82 5.89 2.60 -32.30 -.009 Off Open 6,6,0 302.2 96,350 3.84 8.1 Off 2.34 5- 71 3.60 3.70 .107 Closed 8,6,8 3.84 8.2 342.0 93,525 Off Closed 8,6,8 1.99 3.05 6.00 4.35 .150 226.0 104,200 3.99 ll ._ 4.25 .20 2.00 2.63 .084 .08 2.6 Off Closed 4,4,4 796-3 76,618 Off 2.76 5.25 3.60 4.50 .109 4.14 9.7 330.0 97,675 Closed 8,6,8 Off ........ 5.00 ..........

Closed 8,6,8 4.31 12.8 238.8 106,650 Off Open 8,6,8 2.85 5.69 2.60 2.15 .132 h.32 8.0 321.0 99,000 Off 3.45 .18 2.10 1.43 .160 892.8 76,741 Closed 4,4,4 4.33 2.9 2.43 5.56 4.20 9.50 .049 Off Closed 8,6,8 4.36 to.5 318.0 100,450 Off 2.05 5-18 3. OO 7.30 .045 4.40 2.2 Closed 0,4,4 359.0 97, 400 Off ........ 2.30 1.67 .i02 Closed 4,4,6 4.43 2.0 558.5 86,0oo Off Closed 4,4,8 1.95 .... 4.40 4.38 .ii0 4.48 12._ 256.0 106,800 1.96 .... 5.00 6.15 .089 Off Closed 8,6,8 4.76 lO.8 281.2 107,625 4.67 5.05 2.49 -4.25 - .063 Off 203.2 115,35o Open A,A,F 4.87 25.1 2.02 .... 2.80 1.24 .242 Off Closed 8,6,8 5.1o .7 396.0 lO2,875 2.29 .... 2.80 2.18 .140 Off Closed 8,6,8 5.18 .6 498.0 99,900 Off 3.62 8.72 1.72 _ .....

973.0 96,250 Open 8,0,0 5.47 3 .i Off Open 8,0,0 3.o5 7.84 2.00 ......

478.0 101,550 5.55 2.7 Off 1.89 5.33 3.20 o_ .....

485.0 100,725 Closed 8,0,0 5.59 1.7 Off Closed 8,0,0 1.81 5- 45 3.40 _ .....

5.62 i .6 482.0 101,400 pitch, roll, and yaw, respectively.

aNumbers for SAS gain settings are damper-gain knob positions for II. The letters A and F denote adaptive Damper gains corresponding to various knob settings are shown in table control and fixed gain, respectively.

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m_ -2 Ixz 12 14 16 18 20 22 24 26 28 30 32 34x103 W, Ib Figure 3.- Variation of inertia characteristics of the X-15 airplane with airplane weight (data supplied by manufacturer).

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84x103/ 3.6 _-M h, ft J M 76L :3.2 _v, deg I ._-_u .I r_ P, .2[ rodions/0 rodions/0 sec sec2 / -.21- -.I .2 ,, I_, .8 r P_ rodions/0 I- radions/0 sec _' _.,i>__ ,,,-_-_=-.t f sec2 _ 8_ -.2 .I, -.I I /_, deg 0 I 2 3 4 5 6 tl sec Figure 6.- Time history of lateral-directional response characteristics induced by an aileron _nput. Power off; SAS gain settings of 8, 6, 8 for pitch_ roll_ and yaw_ respectively.

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-._ .O5 /% r, r, radians/ 0 radians/ sec 2 SeC -.05 -,I at,g -4 -40 I 2 3 4 5 6 7 8 t, sec Figure 8.- Time history of a sideslip maneuver. Power on; SAS gain settings of O, 4, 8 for pitch, roll, and yaw, respectively.

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radians/ 0 I J sec 2 -.2 .I q| radians/ 0 sec J -.I a, deg 4 _/__/_ an, g 0 I 2 3 4 5 6 t, sec Figure 9.- Time history of random longitudinal oscillations. Power off; SAS gain settings of O, 4_ 8 for pitch_ roll_ and yawj respectively.

121xlO 3 5.0 h, ft 117 t M 4.81 113L 4.6 So, deg _v, deg 0

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M 55O Flight Analog q, 450 ....._. _- _ ib/sq ft -I0 8 h, deg 2O I -2O I0 -I0 a, deg 4 /_ _ "_ an, g 0 I 2 3 4 5 6 7 8 9 t, sec Figure 12.- Analog match of a pitch pulse. Power on; SAS gain settings of O, 4, 8 for pitch, roll, and yaw, respectively.

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