NASA Technical Paper 1538

Simulator Study of Stall/Post-

Stall Characteristics of a

Fighter Airplane With Relaxed

Longitudinal Static Stability

Luat T. Nguyen, Marilyn E. Ogburn, William P. Gilbert,

Kemper S. Kibler, Phillip W. Brown, and Perry L. Deal

DECEMBER 1979

https://ntrs.nasa.gov/search.jsp?R=19800005879 2018-03-28T18:33:54+00:00Z

NASA Technical Paper 1538

Simulator Study of Stall/Post-

Stall Characteristics of a

Fighter Airplane With Relaxed

Longitudinal Static Stability

Luat T. Nguyen, Marilyn E. Ogburn, William P. Gilbert,

Kemper S. Kibler, Phillip W. Brown, and Perry L. Deal

Langley Research Center

Hampton, Virginia

BJt ANational Aeronautics

and Space Administration

Scientific and Technical

Information Branch

1979

TABLE OF CONTENTS

SUMMARY .........

INTRODUCTION ......

oo.oooo_OO°°°•

•••oo°°°°°°•°

°°°°°o°°o•°°•

°°°°°•°°°

•°°o°o°O°°°

°°o°O•°°°°

..... °•

SYMBOLS .........

DESCRIPTION OF AIRPLANE ...................

° ° o o ° ° ° ° ° ° o ° ° ° ° •

DESCRIPTION OF SIMULATOR ....... ° ° ° °

Coc and Associated Equipment ...............kpit ................

Visual Display .......... ..........

Computer Program .................

• • .... • • ° o ° •

PROCEDURES .............EVALUAT I ON ......

Wind Turn Tracking Task ...............-Up ....

Bank-to-Bank Tracking Task .................• • ° ° ° • • ° • ° ° ° •

ACM Tracking Task .............. . . .° ° ° ° ° °

Evaluation of Performance ............

CHARACTERISTICS " " "DISCUSSION OF STABILITY AND CONTROL ......

° ° • o ° ° ° • •

Longitudinal Characteristics ............ • • °

Lateral-Directional Characteristics ............

DISCUSSION OF HIGH-ANGLE-OF-ATTACK KINEMATIC- AND ........

INERTIA-COUPLI .NG PHENOMENA ............

DEPARTURE- AND SPIN-RESISTANCE SIMULATION RESULTS .............

Basic Control System .........................

Control-System Modifications ....................

Effect of Aft Center of Gravity ............

DEEP-STALL SIMULATION RESULTS ............° • ° ° ..... • ° ° ° . • ° °

Description of Problem ........ • ....... • °

Methods of Recovery .................

. ° ° • o • • ° ° • . • ° • ° ° • • • °

TRACKING RESULTS .......

Results of Basic Control System (Control System A) .........• ° . ° • •

Results of Control Systems B and C ............

o . o • ° o °

INTERPRETATION OF RESULTS .................

° o ° ° • o ° • ° °

SUMMARY OF RESULTS ...............

APPENDIX A - DESCRIPTION OF CONTROL SYSTEM .............

APPENDIX B - DESCRIPTION OF EQUATIONS AND DATA EMPLOYED IN SIMULATION

. ° °

APPENDIX C - SPECIAL EFFECTS ...................

1

1

2

7

8

8

9

9

9

i0

I0

i0

I0

ii

12

13

16

16

18

24

25

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27

29

29

3O

32

32

34

36

41

iii

REFERENCES................................ 42

TABLES .................................. 43

FIGURES.................................. 94

iv

SUMMARY

A real-time piloted simulation has been conducted to evaluate the high-angle-of-attack characteristics of a fighter configuration based on wind-tunneltesting of the F-16, with particular emphasis on the effects of various levelsof relaxed longitudinal static stability. The aerodynamic data used in thesimulation were based on low-speed wind-tunnel tests of subscale models. Thesimulation was conducted on the Langley differential maneuvering simulator, andthe evaluation involved representative low-speed combat maneuvering.

Results of the investigation showed that the airplane with the basic con-trol system was resistantto the classical yaw departure; however, it was sus-ceptible to pitch departures induced by inertia coupling during rapid, large-

amplitude rolls at low airspeed. The airplane also exhibited a deep-stall trim

which could be flown into and from which it was difficult to recover. Control-

system modifications were developed which greatly decreased the airplane sus-

ceptibility to the inertia-coupling departure and which provided a reliable

means for recovering from the deep stall.

INTRODUCTION

Rapid advances in aircraft avionic technology in recent years have made

possible the application of control configured vehicle (CCV) concepts to fighter

aircraft. In particular, considerable attention has been turned to the prin-

ciple of relaxed static stability (RSS) in which the basic airframe is designed

to have low or even negative static pitch stability in certain flight regimes.

The performance benefits of this concept are well known (ref. i) ; and an air-

plane currently under development which makes use of RSS is the F-16, which

nominally operates at very moderate levels of negative static margin at low sub-

sonic speeds. Advanced designs involving much higher levels of pitch insta-

bility are also now being considered for future fighter configurations-

Obviously, CCV designs rely greatly on the control system to provide satis-

factory stability and control characteristics. Fundamentally, the control sys-

tem must provide artificial stability such that the airplane appears to the

pilot to have positive static pitch stability throughout the flight envelope.

The use of RSS, however, can result in some demanding control problems at high

angles of attack which impose severe requirements on the design of the flight

control system in order that the desired characteristics of maximum maneuver-

ability and departure/spin resistance are attained. An earlier investigation

(ref. 2) identified some of the potential high-angle-of-attack problem areas

inherent with the RSS design concept. The present investigation was conducted

to evaluate some of these problems and their effects on the stability and con-

trol characteristics at high angles of attack of a fighter configuration based

on the F-16. The study was conducted on the Langley differential maneuvering

simulator (DMS) and used aerodynamic data based on the results of a number of

low-speed wind-tunnel tests of subscale models conducted at the NASA Langley

and Ames Research Centers. The objectives of the study were (i) to determinethe controllability and departure resistance of the subject configuration duringlg and accelerated stalls; (2) to determine the departure susceptibility of theconfiguration during demanding air-combat maneuvers; (3) to identify high-angle-of-attack problems inherent to the RSSdesign and assess their impact on maneu-verability; and (4) to develop and evaluate control schemes to circumvent oralleviate these shortcomings.

SYMBOLS

All aerodynamic data and flight motions are referenced to the body systemof axes shown in figure i. The units for physical quantities used herein arepresented in the International System of Units (SI) and U.S. Customary Units.The measurements and calculations were made in U.S. Customary Units. Conversionfactors for the two systems are given in reference 3.

an normal acceleration, positive along negative Z body axis, g units(ig : 9.8 m/sec 2)

ay

b

lateral acceleration, positive along positive Y body axis, g units

wing span, m (ft)

CL lift coefficient, Aerodynamic lift force9s

C_ rolling-moment coefficient about X body axis,

Aerodynamic rolling moment

_Sb

total rolling-moment coefficient

pitching-moment coefficient about

Aerodynamic pitching momentw --

qSc

Y body axis,

Cm,t total pitching-moment coefficient

C n yawing-moment coefficient about Z body axis,

Aerodynamic yawing moment

_Sb

Cn,t total yawing-moment coefficient

C X X-axis force coefficient along positive

Aerodynamic X-axis force

X body axis,

CX,ttotal X-axis force coefficient

Cy

Cy,t

Cz

Cz,t

Flat

Flong

Fped

GARI

g

gcom

He

h

Ix,Iy,I z

IXz

M

Mic

m

Ni c

P

P1

P2

P3

Y-axis force coefficient along positive Y body axis,

Aerodynamic Y-axis force

total Y-axis force coefficient

Z-axis force coefficient along positive Z body axis,

Aerodynamic Z-axis force

total Z-axis force coefficient

wing mean aerodynamic chord, m (ft)

pilot lateral stick force, positive for right roll, N (ib)

pilot longitudinal stick force, positive for aft force, N (ib)

pilot pedal force, positive for right yaw, N (ib)

ARI gain

acceleration due to gravity, m/sec 2 (ft/sec 2)

pilot-commanded normal acceleration, g units

engine angular momentum, kg-m2/sec (slug-ft2/sec)

altitude, m (ft)

moments of inertia about X, Y, and Z

product of inertia with respect to X and

kg-m 2 (slug-ft 2)

Mach number

pitching moment due to inertia coupling, (I Z - IX)Pr , N-m (ft-lb)

airplane mass, kg (slugs)

yawing moment due to inertia coupling, (I x - Iy)pq, N-m (ft-lb)

period, sec

engine power command based on throttle position, percent of maximum

power

engine power command to engine, percent of maximum power

engine power, percent of maximum power

body axes, kg-m 2 (slug-ft 2)

Z body axes,

P

Pcom

(Pcom)max

Pstab

Ps

q

qa

qicl

q

R

r

rf

rstab

r a

ricl

S

s

T

Tidle

airplane roll rate about

pilot-commanded roll rate, deg/sec

maximum commandable roll rate, deg/sec

stability-axis roll rate, deg/sec or rad/sec

static pressure, N/m 2 (ib/ft 2)

airplane pitch rate about Y

X body axis, deg/sec or rad/sec

body axis, deg/sec or rad/sec

airplane pitch acceleration about Y body axis, deg/sec 2 or rad/sec 2

component of airplane pitch acceleration due to aerodynamic moments,

or< Iy] m,t' deg/sec2 rad/sec2

component of airplane pitch acceleration due to inertia coupling,%

Ig_)pr, deg/sec 2 or rad/sec 2Iz

free-stream dynamic pressure, N/m 2 (lb/ft 2)

range, straight-line distance between subject and target airplanes,

m (ft)

yaw rate about Z body axis, deg/sec or rad/sec

filtered yaw-rate signal, deg/sec

stability-axis yaw rate, deg/sec or rad/sec

yaw acceleration about Z body axis, deg/sec 2 or rad/sec 2

component of airplane yaw acceleration due to aerodynamic moments,

(qSb_ C or<-_--y] n,t' deg/sec2 rad/sec2

component of airplane yaw acceleration due to inertia coupling,

I X - Iy)IZ qp, deg/sec 2 or rad/sec 2

wing area, m 2 (ft 2)

Laplace variable, i/sec

total instantaneous engine thrust, N (lb)

idle thrust, N (Ib)

4

Tmax

Tmil

t

tl/2

UyVrW

V

w

_a

Wacl

Wac2

X,Y,Z

Xcg

Xcg,ref

@f

6a

_a,c

6a,max

6d

5d,c

@h

_h,C

maximum thrust, N (ib)

military thrust, N (ib)

time, sec

time to damp to one-half amplitude, sec

components of airplane velocity along X, y, and Z body axes,

m/sec (ft/sec)

airplane resultant velocity, m/sec (ft/sec)

airplane acceleration along Z body axis, m/sec2 (ft/sec2)

component of w due to aerodynamic force, Q_mSlCz,t '

m/sec 2 (ft/sec2)

component of w due to pitch rate, qu, m/sec2 (ft/sec2)

component of w due to kinematic coupling, -pv, m/sec2 (ft/sec2)

airplane body axes (see fig. i)

center-of-gravity location, fraction of

reference center-of-gravity

location for aerodynamic data

angle of attack, deg

filtered angle-of-attack signal, deg

indicate d angle of attack, deg

angle of sideslip, deg

aileron deflection, positive for left roll, deg

aileron deflection commanded by control system, deg

maximum aileron deflection, deg

differential horizontal-tail deflection, positive for left roll, deg

differential horizontal-tail deflection commanded by control system

deg

horizontal stabilator deflection, positive for airplane nose-down

control, deg

horizontal stabilator deflection commanded by control system, deg

@lef

6r

r,com

6sb

@tef

C

1

e,_,_

T T

leading-edge flap deflection, positive for leading edge down, deg

rudder deflection, positive for left yaw, deg

pilot-commanded rudder deflection, deg

speed-brake deflection, deg

trailing-edge flap deflection, positive for trailing edge down, deg

tracking error, angle between evaluation airplane X body axis and

range vector R (angle off), deg

horizontal stabilator effectiveness factor

lateral component of _, deg

Euler angles, deg

engine-thrust time constant, sec

aircraft total angular velocity, deg/sec

3c_ 3c z 3c z 3c z

C z - C - C z = _ C_ -p _ p_bb Zr _ r_bb _ _ 6 a _@a

2V 2V

3C_ 3C m 3C n 3C n

CZ - Cm - q_ Cnp pb Cn r rb_r 36r q 3 2V 3 2-V 3 2--_

3C n I z _C n 3C n- - --Cz sin _ - -

Cn_ _ Cn_,dyn = Cn_ I X _ Cn_ a _6 a Cn6 r _6 r

3Cx 3C Z 3Cy 3Cy

CXq _ q_ CZq _ q_ Cyp _ pb CYr _ rb

2V 2V 2V 2--_

Subscripts:

ds deep stall

lef increment of variable produced by full retraction of leading-edge

flaps; for example, ACm,le f indicates increment in C m produced

by retraction of leading-edge flaps from 25 ° to 0°

6

o

sb

6i=j

initial value

increment in variable produced by deflection of speed brake

deflection of control surface i to value j; for example, AC%,6a=20o

indicates increment of C_ produced by deflection of ailerons to

6a : 20°

air-combat maneuvering

Abbreviations :

._ACM

ARI

CAS

CCV

DL

DMS

IAS

LCDP

RL

RSS

rms

SAS

SM

aileron-rudder interconnect

commandaugmentation system

control configured vehicle

deflection limit, deg

Langley differential maneuvering simulator

indicated airspeed, knots

lateral control divergence parameter

rate limit, deg/sec

relaxed static stability

root mean square

stability augmentation system

static margin

DESCRIPTIONOF AIRPLANE

A three-view sketch of the simulated configuration is shown in figure 2,and the mass and geometric characteristics used in the simulation are listed intable I. The airplane control system is described in detail in appendix A.The primary aerodynamic controls include symmetric deflection of the horizontaltail (stabilator) for pitch control, deflection of conventional wing-mountedailerons and differential deflection of the horizontal stabilators for rollcontrol, and rudder deflection for yaw control.

One special feature of the configuration is the use of a normal-acceleration-command longitudinal control system which provides static sta-bility, normal-acceleration limiting, and angle-of-attack limiting. The air-plane is balanced to minimize trim drag, with the effect that it has slightly

negative static longitudinal stability at low Mach numbers; the desired staticstability is provided artificially by the control system. Other featuresinclude (i) wing leading-edge flaps which are automatically deflected as a func-tion of angle of attack and Mach number; (2) a roll-rate commandsystem in theroll axis; (3) an aileron-rudder interconnect and a stability-axis yaw damperin the yaw axis; and (4) a force-sensing (minimum displacement) side-stick con-troller and force-sensing rudder pedals. The airplane engine characteristicsused in the present study are described in appendix B, and the buffet charac-teristics are described in appendix C.

Most of the simulated flights were made at a center-of-gravity location of0.35_ although locations as far aft as 0.39_ were also investigated. Allresults shown in this report are for the 0.35_ center-of-gravity locationunless otherwise stated.

DESCRIPTIONOF SIMULATOR

The Langley differential maneuvering simulator (DMS) is a fixed-base simu-lator which has the capability of simultaneously simulating two airplanes asthey maneuver with respect to one another and of providing a wide-angle visualdisplay for each pilot. A sketch of the general arrangement of the DMShardwareand control console is shown in figure 3. Two 12.2-m (40-ft) diameter projec-tion spheres each enclose a cockpit, an airplane-image projection system, and asky-Earth-Sun projection system. A control console located between the spheresis used for interfacing the hardware and the computer, and it displays criticalparameters for monitoring hardware operation. Each pilot is provided a pro-jected image of his opponent's airplane, with the relative range and attitudeof the target shown by a television system which is controlled by the computerprogram.

Cockpit and Associated Equipment

A photograph of one of the cockpits and the target visual display is shownin figure 4. A cockpit is provided with an instrument display and a computer-driven gunsight representative of current fighter aircraft equipment. However,this study used a fixed gunsight for tracking. Each cockpit is located toposition the pilot's eyes near the center of the sphere so that he has a fieldof view representative of that obtained in current fighter airplanes. For thepresent study, a special modification was made to one cockpit to incorporate theside-stick controller as shown in figure 5. The controller was placed in thesame general cockpit location as the controller in the F-16 airplane; however,no special armrest was provided (as is the case in the actual airplane) otherthan the regular seat armrest which provided more of an elbow rest than a sup-port for the forearm. The normal hydraulic control feel system was not employedfor this simulation since the side-stick controller and rudder pedals were forcesensitive, with no deflection required to activate the controls. Although thecockpits are not provided with attitude motion, each cockpit incorporates abuffet system capable of providing programmable root-mean-square (rms) buffetaccelerations as high as 0.5g, with up to three primary structural frequenciessimulated.

Visual Display

The visual display in each sphere consists of a target image projected ontoa sky-Earth scene. The sky-Earth scene is generated by two point light sourcesprojecting through two hemispherical transparencies, one transparency of bluesky and clouds and the other of terrain features; the scene provides a well-defined horizon band for reference purposes. No provision is made to simulatetranslational motion with respect to the sky-Earth scene (such as altitudevariation); however, spatial attitude motions are simulated. A flashing lightlocated in the cockpit behind the pilot is used as a cue when an altitude ofless than 1524 m (5000 ft) is reached. The target-image generation system uses

an airplane model mounted in a four-axis gimbal system and a television camera

with a zoom lens to provide an image to the target projector within the sphere.

For an F-16 size airplane, the system can provide a simulated range from 90 m

- (300 ft) to 13 700 m (45 000 ft) between airplanes, with a 10-to-i brightness

contrast between the target and the sky-Earth background at minimum range.

Additional special-effects features of the DMS hardware include simulation

of blackout at high normal accelerations (see appendix C), the use of an inflat-

able "anti-g" garment for simulation of normal-acceleration loads, and sound

cues to simulate wind, engine, and weapons noise as well as artificial warning

systems. Additional details of the DMS facility are given in reference 4.

Computer Program

The DMS is driven by a real-time digital simulation system and a Control

Data CYBER 175 computer. The dynamics of the evaluation airplane were calcu-

lated by using equations of motion with a fixed-interval (1/32 sec) numerical-

integration technique. The equations used nonlinear aerodynamic data as func-

tions of d and/or _ in tabular form. These data were derived from results

of low-speed (M = 0.i to 0.2) static and dynamic (forced-oscillation) force

tests conducted in several wind-tunnel facilities. The data included an angle-

of-attack range from -20 ° to 90 ° and a sideslip range from -30 ° to 30 ° . Effects

of Mach number, Reynolds number, or aeroelasticity were not included in the

mathematical model. Complete descriptions of the aerodynamic data and the

equations of motion are given in appendix B.

EVALUATION PROCEDURES

The results of the investigation were based on pilot comments and time-

history records of airplane motions, controls, and tracking for the various

maneuvers performed. Most of the evaluations were performed by two NASA

research test pilots who were familiar with the air-combat maneuvers used with

current fighter airplanes; however, a U.S. Air Force test pilot and a contractor

test pilot involved in high-angle-of-attack flight tests of the F-16 airplane

also flew the simulator.

The evaluation was conducted in two phases. The first phase involved

"open-loop" maneuvers to assess basic stability and control characteristics of

the airplane at high angles of attack, and the second phase involved tracking a

simulated F-16 as a target airplane through a series of maneuvers representativeof those used in air combat in order to examine flying qualities under theseconditions. Maneuvers used in the first phase included ig and acceleratedstalls, with various control inputs applied at specific conditions. Table IIlists the primary maneuvers used in this phase. In addition to documenting thestability and response to control characteristics of the airplane and familiar Eizing the pilot with these characteristics, this phase also provided an assess-ment of the departure and spin susceptibility of the configuration. Resultsfrom the first phase of the study were used to design the tracking task_ used inthe second phase. Several tasks were chosen for use during the second phase ofthe study: (i) a steady wind-up turn tracking task, (2) a bank-to-bank maneu-vering task, and (3) a complex, vigorous air-combat maneuvering (ACM) task.

Wind-Up Turn Tracking Task

A steady wind-up turn was flown, with the target airplane slowly increasingangle of attack in order to provide a tracking situation in which the pilot couldevaluate the fine tracking capability of the evaluation airplane at high anglesof attack. Initially, both airplanes were at an altitude of 9144 m (30 000 ft)and M : 0.6, with the subject airplane 457.2 m (1500 ft) directly behind thetarget and at the same heading as the target. Upon initiation of the run, thetarget established a left-bank attitude which varied between -40 ° and -i00 °during the maneuver. Angle of attack was gradually increased up to a maximumofabout 3g normal acceleration. The evaluation pilot attempted to track the targetas closely as possible while maintaining a range of less than 609.6 m (2000 ft).Time histories of the target motions are shown in figure 6.

Bank-to-Bank Tracking Task

As shown in figure 7, this task involved tracking the target airplanethrough a series of bank-to-bank maneuvers (or horizontal S's) at high anglesof attack. These maneuvers enabled the pilot to evaluate his ability to rollthe subject airplane rapidly, to acquire the target, and to stabilize while athigh angle of attack.

ACMTracking Task

The ACMtracking task was developed to be more representative of the com-plex, nonrepetitive maneuvers which may be encountered during air-to-air combat.The time histories of the target motions are shown in figure 8. In general, thetask covered a speed range of 0.25 to 0.6 Mach and required the tracking air-plane to perform several large-amplitude rolling maneuvers at low-speed, high-angle-of-attack conditions.

Evaluation of Performance

In evaluating the simulated airplane, numerous runs were made in each ofthe tasks. Sufficient flights were made to ensure that the pilot's "learning

i0

curve" was reasonably well established before drawing any conclusions on evalua-tion results. Evaluation of performance was based on pilot comments, theability of the pilot to execute the tasks assigned, and the analysis of timehistories of airplane motions and tracking.

DISCUSSIONOF STABILITY ANDCONTROLCHARACTERISTICS

To provide a foundation for the analysis and interpretation of the simula-tion results which follow, selected aerodynamic stability and control character-

istics of the simulated airplane configuration are presented and discussed in

this section.

Longitudinal Characteristics

The aerodynamic data are listed in table III, and the representation of

these characteristics in the simulation is discussed in appendix B. The aero-

dynamic characteristics of the configuration as noted during wind-tunnel flow-

visualization tests were such that the outer wing panels stalled near d = 20 ° ,

but the highly swept wing-body strake continued to produce lift at higher angles

of attack, as shown in figure 9. Maximum C L was obtained near d = 35 ° .

A notable characteristic of the configuration is that it exhibits a modest

level of static pitch instability at the nominal center-of-gravity position

(0.35_) at low speeds, as shown in figure i0. Static margin at low angles of

attack is approximately -4 percent. To provide satisfactory flying qualities,

the longitudinal control system is equipped (see appendix A) with angle-of-

attack feedback to provide artificial pitch stability. It is important to note

that figure i0 also indicates that the airplane will trim at _ = 66 ° with full

nose-up stabilator deflection (6 h = -250). To inhibit inadvertent excursions to

these extreme angles of attack, the pitch control system incorporates an angle-

of-attack/normal-acceleration limiting system which drives the stabilator in an

attempt to limit the angle of attack to below 25 ° . A further discussion of the

complete pitch control system is given in appendix A.

Two other important points regarding longitudinal stability should be noted

in figure i0. The first is the marked loss in nose-down stabilator effective-

ness due to stall of these surfaces for angles of attack greater than 25 ° . The

loss in nose-down control effectiveness is particularly critical because the

limiter system relies on the available nose-down control moment to prevent

from exceeding 25 ° . The other important characteristic shown in figure i0 is

the existence of a stable deep-stall trim point. Note that even with the stabi-

lators deflected for full nose-down control, the airplane exhibits a weak but

stable trim point at _ = 60 ° •

Another important aerodynamic characteristic exhibited by the simulated

airplane is the variation of C m with _ at high angles of attack, an example

of which is shown by wind-tunnel data for d = 25 ° in figure ii. As can be

seen, there is very little variation of pitching moment with sideslip for

_h = 0°" However, the data for nose-down stabilator deflections show a sharploss in stabilator effectiveness for sideslip magnitudes greater than about i0 °.

ii

Thus, if a departure involving large sideslip excursions should occur, theeffectiveness of the angle-of-attack limiter system to maintain _ at or below25° will be further degraded by the reduction in available nose-down controlmoment.

Lateral-Directional Characteristics

Static lateral-directional stability.- The static lateral-directional sta-

bility characteristics of the basic airplane with scheduled leading-edge flap

deflections are presented in figure 12 in terms of the static directional sta-

bility derivative Cn_, the effective dihedral derivative CZ_, and the dynamic

directional stability parameter Cn_,dy n as functions of angle of attack. At

each angle of attack, Cn_ and C_ were computed by sloping Cn_ and C_

between _ : -+4° . The parameter Cn_,dy n has been used in past investigations

as an indication of the existence of directional divergence (nose slice) at high

angles of attack. Negative values of this parameter usually indicate the exis-

tence of a divergence. The data of figure 12 indicate that the configuration

was statically stable (both directionally and laterally) for angles of attack up

to about 28 ° . Above _ : 30 ° , Cn_ reached large unstable (negative) values,

which caused a sharp decrease in the value of Cn_,dy n at _ : 35 ° . Neverthe-

less, it is seen that this parameter remained positive up through _ : 40 ° , and

a directional divergence would therefore not be expected at high angles ofattack.

The lateral-directional aerodynamic control characteristics for the configu-

ration at _ : 0 ° are shown in figure 13 in terms of moment increments caused

by full control. The rudder effectiveness was high and essentially constant

over the operational range of angle of attack (_ < 25o). Roll-control effective-

ness of the ailerons and differential tails was good and well sustained up to the

angle-of-attack limit, whereas the adverse yaw produced by these surfaces above

= 20 ° was very small compared with moments produced by the rudder. Only

above _ : 40 ° do the adverse yawing moments become significant compared with

the available rudder moments. These data indicate that the configuration should

exhibitgood lateral-directional control characteristics up to the angle-of-

attack limit (_ : 25 ° ) if proper coordination of roll and yaw controls is used

to suppress the roll-control adverse yaw and to minimize sideslip.

The lateral control divergence parameter (LCDP) is often used to appraise

roll-control effectiveness at high angles of attack. This parameter is definedas

/Cn6a_

LCDP : Cn_ - CZ_C--_@a)

12

for ailerons only, or by

I_ + GARICn6r_LCDP= Cn$ - CZ_k 6a@a+ GARIC_6r]

where GARI is the ratio of rudder deflection to aileron deflection for an air-plane with an aileron-rudder interconnect (ARI). Positive values of this param-eter indicate normal roll response, and negative values indicate reversedresponse. When reversed response is encountered, a right roll-control input bythe pilot will cause the airplane to roll to the left. The variation of LCDPwith angle of attack for the subject airplane is presented in figure 14. Forthe airplane with the basic control system, the parameter becomes negative above

= 25° , which indicates reversed response if roll control alone was used inthis region. Addition of the ARI provided a large positive increment in LCDPabove _ : 15° such that the LCDPvalues remained positive up through d = 40° .This result indicates that the augmented airplane should exhibit normal responseto roll-command inputs throughout the operational angle-of-attack range.

Dynamic lateral-directional stability.- The classical dynamic lateral-

directional stability characteristics of the airplane were calculated on the

basis of three degree-of-freedom linearized lateral-directional equations and

the aerodynamic data of appendix B. The results of the calculations with the

SAS on and off are presented in figure 15 in terms of the damping parameter

i/tl/2 and the period P of oscillatory modes. Positive values of I/tl/2indicate damped or stable modes of motion. Data are shown for the classical

Dutch roll, spiral, and roll modes of motion as a function of angle of attack

for ig trim conditions. The data for the airplane without SAS show that all

three modes are stable for values of _ up to 30 ° . The stability of the Dutch

roll and roll modes tends to decrease with e, whereas the opposite is true for

the spiral mode. Stability characteristics of the airplane with the lateral-

directional SAS operative are also shown in figure 15. Figure 15 shows that the

roll and yaw SAS significantly enhanced the stability of both the Dutch roll and

roll modes in the normal flight envelope (_ _ 25o).

A detailed discussion of the lateral-directional control system is con-

tained in appendix A; the primary features of the roll/yaw SAS are (i) a roll-

rate-command augmentation system, (2) a stability-axis yaw damper, (3) an

aileron-rudder interconnect, and (4) an automatic spin-prevention system which

activates when _ exceeds 29 ° .

DISCUSSION OF HIGH-ANGLE-OF-ATTACK KINEMATIC- AND

INERTIA-COUPLING PHENOMENA

As an additional aid in analyzing the simulation results which follow,

several kinematic- and inertia-coupling phenomena which significantly influence

the high-angle-of-attack characteristics of the F-16 airplane are brieflyreviewed in this section.

13

Figure 16 illustrates the kinematic coupling between angle of attack andsideslip that occurs when an airplane is rolled about its X-axis at high anglesof attack. If the airplane is flying at angle of attack with the wings level(fig. 16(a)) and the pilot initiates a pure rolling motion about its X-axis(fig. 16(b)), all the initial angle of attack will have been converted intosideslip after 90° of roll. Because it is undesirable to generate large amountsof sideslip at high angles of attack from a roll-performance, as well as adeparture-susceptibility, viewpoint, most current fighters (including the F-16)are designed to roll more nearly about the velocity vector than the body axis.

)It is obvious that this conical rotational motion [indicated by Pstab elimi-

nates the coupling between _ and _. Resolving Pstab into the body-axis

system shows that this motion involves body-axis yaw rate as well as roll rate

and that these rates are related by the expression

r : p tan

If this equality is not satisfied during a roll, then sideslip will be generated

due to kinematic coupling, with _ varying as

-- p sin d - r cos

The control system of the F-16 incorporates an ARI and a stability-axis yaw

damper which attempt to make the airplane roll about its velocity vector

throughout its normal flight envelope. (See appendix A.)

In the case of rolling with an initial sideslip, it is seen from fig-

ure 16(b) that body-axis rolling will result in the initial _ being converted

into d after 90 ° of roll, with _ varying as

---q - p cos _ tan

The second term in this expression indicates that rolling with adverse sideslip

(p and _ having the same signs) tends to reduce _, whereas rolling with pro-

verse sideslip (p and _ having opposite signs) tends to increase _. This

latter effect can be important in CCV configurations requiring an angle-of-

attack limit in that substantial increases in _ can be generated due to

kinematic coupling if the airplane is rolled with proverse _ (using excessive

rudder, for example).

The second form of coupling that is important to the high-angle-of-attack

dynamics of the F-16 configuration is due to inertial effects. Figure 17(a)

illustrates the inertial pitching moment that is produced when the airplane is

rolled about its velocity vector at high angles of attack. The desirability of

this type of roll from a kinematic-coupling viewpoint was previously discussed;

unfortunately, the resulting nose-up pitching moment caused by inertia coupling

can be a problem for CCV configurations that employ relaxed static pitch sta-

14

bility. As an aid in visualizing this effect, the fuselage-heavy mass distri-bution of the airplane is represented as a dumbbell, with the mass concentratedat the two ends. If the airplane is flying at some angle of attack and rollsabout its velocity vector, the dumbbell will tend to pitch up to align itselfperpendicular to the rotation vector Pstab" This nose-up pitching moment dueto inertial coupling Mic can be expressed as

Mic : (I Z - Ix)Pr

Substituting P = Pstab cos _ and r = Pstab sin d,

Mic (i z IX ) 2 1 2= - Pstab cos _ sin _ = _(I Z - Ix)Pstab sin 2d

The preceding expression shows that the pitch inertia-coupling moment resultingfrom stability-axis rolling is always positive (nose up) for positive d andvaries as the square of the stability-axis roll rate Pstab"

For CCVconfigurations with relaxed static stability, the nose-up momentmust be opposed by the available nose-down control moment. If this controlmoment is less than the inertia-coupling moment, the horizontal tail can reacha travel limit, at which time the airplane will lose the stability contributionof the tail and the airplane will pitch up beyond the _ limiter boundary,which results in loss of control.

The inertia-coupling moment which results from the combination of roll andpitch rates is illustrated in figure 17(b). The airplane mass distribution isrepresented by the dumbbell, and the airplane is shown rolling to the right andpitching up. As can be seen, the dumbbell will tend to yaw nose left to alignitself perpendicular to the rotation vector _. The expression for the inertia-coupling moment is given by

Nic : (I x - Iy)pq

Consider the case q > 0 (nose-up pitch rate). Because I x < Iy, the precedingexpression shows that the yaw inertia-coupling moment will always be opposite insign to the roll rate. Recalling that to minimize adverse _ generation due tokinematic coupling, r must be equal to p tan _, it is obvious that this formof inertia coupling will inhibit stability-axis rolling that can lead to thebuildup of large amounts of adverse _ which, in turn, can result in loss ofcontrol at high angles of attack.

This section has briefly reviewed kinematic- and inertia-coupling phenomenathat, in various degrees, are important to the high d flight dynamics of allmodern fighter aircraft. In the section entitled "Departure- and Spin-ResistanceSimulation Results," it will be seen how these phenomena interact to signifi-cantly influence the characteristics of the subject configuration.

15

DEPARTURE-ANDSPIN-RESISTANCESIMULATIONRESULTS

Basic Control System

The first portion of the simulation investigation consisted of documentingthe normal stall-, departure-, and spin-resistance characteristics of the con-figuration equipped with the basic flight control system described in appen-dix A. For convenience, this system will be referred to as hontrol system A inthis report. Figure 18 shows time histories of a ig stall to the limit angleof attack (_ = 25o). Rudder doublets were applied at various angles of attackto evaluate lateral-directional stability at these conditions. The data showthat the motions were well dampedand that the airplane exhibited no tendencytoward directional divergence within its normal _ envelope, as predicted by

the Cn_,dyn criterion. In addition, application of lateral stick inputs at: 25° resulted in rapid roll response in the commandeddirection, as pre-

dicted by the LCDPvalues discussed previously.

Further evaluation of departure/spin resistance was performed by applyingcross controls in ig and accelerated conditions. Figure 19 shows time historiesof the motions resulting from cross-control application from ig trim at _ = 25° .The control traces show that although the pilot was holding full right stick andfull left pedal, the roll and yaw controls deflected in a coordinated sense,primarily due to the ARI and the _ fade-out of pilot rudder inputs. As aresult, the airplane rolled and yawed in the direction of the stick input. Notethat the roll and yaw rates were sufficiently high to produce a significant nose-up pitching moment (see qicl trace) caused by the inertia-coupling phenomenonpreviously discussed. This effect caused the airplane to pitch up so that theangle of attack continued to increase beyond 29° . At this point (t : 8.5 sec),the automatic departure-/spin-prevention system activated and applied roll andyaw controls to oppose the yaw rate. As a result, r decreased, which reducedthe inertia-coupling moment. Furthermore, the reduction in yaw rate increasedthe _/_ kinematic coupling since the airplane was now rolling more closelyabout its body axis; the result was a trade-off of angle of attack for sideslip,as evidenced by the rapid grmwth in adverse _ and Wac2 becoming sharply morenegative. The combination of increased kinematic coupling and reduced inertiacoupling reversed the growth of angle of attack and caused it to drop backbelow 29° . Cross controls were held for an additional 9 sec but resulted in noprolonged departure or loss of control. The angle of attack varied between 20°and 36° , and the maximumyaw rate obtained was 48°/sec.

The response to cross controls applied at the limit angle of attack in anaccelerated turn is shown in figure 20. As can be seen, the motions were verysimilar to the ig case, with inertia coupling causing a "pitch-out" departurein which _ increased to about 36o; however, there was no tendency for thedeparture to develop into a spin. These results indicated that (i) inertiacoupling could overpower the _ limiter system to cause _ to increase farabove the 25° limit and (2) the airframe's inherent lateral-directional sta-bility, combined with the effectiveness of the automatic spin-prevention system,minimized the possibility of a departure progressing into a spin entry.

16

It quickly became obvious that roll-pitch inertial coupling would be aprimary cause of departures on this configuration. The reason for its impor-

tance is illustrated in figure 21. Shown is the variation with roll rate of the

nose-up inertial-coupling moment caused by stability axis rolling; note that2

the moment varies with Pstab so that very significant moments can be produced

at high roll rates. Also shown are representations of the available nose-down

control moment for a specified _ at two values of dynamic pressure,

ql and q2 (ql < q2 )" The points of intersection with the coupling-moment

curve indicate the highest roll rates (PI* and p2*) at which there is suffi-

cient control moment to counter the nose-up coupling moment. If Pstab should

increase and be sustained above these values, then it is very likely that a

pitch-out departure will occur. Note that PI* < P2*' which indicates that the

susceptibility to this type of departure becomes more acute as dynamic pressure

decreases.

The foregoing observations are apparent in figure 22, which shows an

attempted 360 ° roll, starting from a ig trim condition at d : 25 °, using full

lateral stick input. Note that in addition to maximum roll-control deflections,

30 ° of coordinating rudder was also obtained due to the ARI. As a result, the

roll and yaw rates began to build up rapidly in the direction of stick input.

Initially, d dropped to about 20 ° due to kinematic coupling; however as p

and r increased, the inertia-coupling moment (see qicl trace) caused a

significant nose-up pitch rate to build up and _ began to increase. At this

point, q coupled with p to create a yaw coupling moment which opposed the

yaw rate (see ricl trace) and halted its growth (t _ 5 sect; on the other

hand, p was still increasing and thus resulted in the kinematic generation of

a large amount of adverse _ (t _ 6 sac). By this time, _ had increased to

above 30 ° , despite the angle-of-attack limiter system applying full nose-down

stabilator deflection (6 h : +25o). Comparison of qicl to qa shows that, at

this point, the nose-up coupling moment was much greater than the nose-down

aerodynamic moment produced by @h = +25o; as a result, a pitch-out departure

occurred as the airplane completed about 300 ° of the roll. During this period

of loss of control, which lasted about 5.5 sac, _ reached a maximum of 41 °

while _ oscillated between ±25 ° . However, there was no tendency for the yaw

rate to diverge into a spin entry (maximum r _ 33°/sac).

An attempted 360 ° roll from an accelerated turn at the limit _ is shown

in figure 23. In this case, the pilot banked the airplane to _ _ -60 ° and

rapidly applied maximum pitch command, which resulted in about 3.7g as

increased to the limiter value (_ = 25o). At V = 170 knots, the pilot applied

and held full right lateral stick input in attempting the roll. The time his-

tories show that the resulting motions are quite similar to those obtained at

ig in that the airplane experienced a pitch-out departure upon completing about

270 ° of A_. Again, despite the large excursions in _ and _ during the

loss-of-control period, the yaw rate did not build up and the airplane did not

enter a spin.

Because full 360 ° rolls are not very useful from a tactical viewpoint,

assessment was also made of the effects of rolling through smaller bank-angle

changes (A_ _ 180°). Figure 24 shows 70 ° bank-to-bank reversals using maximum

lateral stick inputs starting from ig trim at _ = 25 ° . As expected, the

17

angle-of-attack excursions due to inertia coupling were less than thatencountered in the full 360° roll; _ never exceeded 32° . Nevertheless, thestabilators were very near saturation (@h= +25o) during each reversal.Furthermore, large adverse sideslip excursions occurred (reaching -18° at onepoint), caused by kinematic coupling resulting from the high roll rates com-bined with insufficient yaw rate (Irl < IPl tan _).

These results, along with those obtained in the 360° rolls, strongly indi-cated that the airplane roll-rate capability at high angles of attack couldresult in (i) pitch-out departures due to insufficient nose-down pitch controland (2) large adverse sideslip excursions due to insufficient coordinating yawcontrol. In summary, the airplane equipped with control system A was found tobe susceptible to inertia-coupling departures during large-amplitude roll maneu-vers. There was no tendency, however, for the departures to progress into spinentries.

Control-System Modifications

Control system B.- It became evident that the most obvious means of alle-

viating the pitch-out departure problem (other than resizing the airplane con-

trol surfaces or further limiting its _ envelope) was to limit the airplane

roll-rate capability at high angles of attack. Therefore, an alternate flight

control system with a lower roll-rate-command limit was investigated. If a

pitch-out departure (defined as d exceeding 30 ° ) occurred, the maximum roll

rate was reduced. Three center-of-gravity locations were investigated:

(i) 0.35c, which is the nominal location and results in a static margin of

about a negative 4 percent at low _; (2) 0.41c which, although outside of the

operational center-of-gravity range of the airplane, was chosen to indicate how

severely roll performance would have to be compromised in this extreme case;

and (3) 0.29c, chosen to indicate the roll performance that the airplane would

have if it did not incorporate RSS (positive 2-percent static margin).

The results of the center-of-gravity study are summarized in figure 25.

As expected, the 0.29c (SM = 0.02) configuration did not have an inertia-

coupling pitch-out problem, and maximum roll rate was limited only by the

available roll control. To avoid coupled departures with the center of gravity

at 0.35_ (SM = -0.04), the roll rate above _ : 20 ° had to be restricted to

values below what the roll control is capable of providing. Comparison to the

results obtained at 0.29_ indicates that about a 30-percent penalty in maximum

roll rate is incurred at _ = 25 ° due to the desire to fly the airplane at a

static margin of -0.04. As the center of gravity is moved farther aft of 0.35_,

the roll-performance penalty rapidly becomes more severe, as indicated by the

data for SM : -0.i0. At this level of instability, the roll rate had to be

restricted above _ = 13 ° such that at d : 25 ° , the maximum allowable roll

rate was only about 30 percent of what the roll control is capable of providing.

Beyond their implications for the subject configuration, these results indicate

that future CCV designs incorporating high levels of static pitch instability

may face very substantial roll-performance penalties unless they are provided

with sufficient nose-down pitch control to prevent inertia-coupling pitch-out

departures.

18

Once an indication of the maximumsustainable roll rates was obtained, aroll-rate limiting scheme was implemented on the subject airplane. As previ-ously discussed, the basic control system includes a high-gain roll-rate-commandaugmentation system in which the pilot commandsa roll rate propor-

tional to lateral stick force, up to a maximum of 308°/sec. (See appendix A.)

Obviously, the most straightforward technique for limiting the airplane roll

rate is simply to limit the roll rate that the pilot commands. The difficulty

lies in determining which parameters to use to evaluate what the roll limit

should be at any particular instant. Three roll-rate-scheduling parameters

were investigated: angle of attack, dynamic pressure, and symmetric stabilator

deflection.

There were two reasons for considering angle of attack as a scheduling

parameter: (I) the nose-up inertia-coupling moment varies with sin 2_, and

(2) as shown in figure i0, the amount of nose-down control movement available

to counter the nose-up coupling moment decreases as angle of attack increases.

The same reasoning was used in choosing q; as illustrated in figure 21, the

nose-down control moment decreases with q, which results in lower rates of

roll that can be sustained before a pitch-out departure occurs. Symmetric

stabilator deflection was thought to be a proper scheduling parameter in that

it directly indicates the pitch control remaining to counter the inertia-

coupling moment. The three scheduling schemes were evaluated individually, and

it was found that two basic drawbacks are inherent (to varying degrees) with

each scheme, as illustrated in table IV.

The use of _ and q scheduling resulted in the greatest degradation in

initial roll response because they do not differentiate between large-amplitude

rolling maneuvers (A_ _ 360 ° ) where limiting is needed and smaller amplitude

rolls (A_ < 120 ° ) which are of sufficiently short duration to preclude pitch-

out due to inertia coupling. Scheduling versus stabilator deflection minimizes

loss in initial roll "response because it operates as a direct function of the

remaining restoring control moment. Unfortunately, this scheme also increases

the coupling between pitch and roll motions because roll rate is being influenced

by the primary pitch control. This increased cross-axes coupling can manifest

itself as oscillations about both the roll and pitch axes. It was found that

combining all three parameters (_, q, @h) resulted in the most satisfactory

compromise in terms of minimizing both initial roll-response degradation and

cross-axes coupling.

The control law developed to limit roll rate is shown in figure 26. (The

control system incorporating this modification will henceforth be referred to

as control system B.) Roll-rate limiting was achieved by reducing maximum com-

mandable roll rate (Pcom)max from the normal value of 308°/sec to as little

as 80°/sec, based on instantaneous values of q, _i' and _n,c. The_ varia-

tion with dynamic pressure was -0.0115°/sec/N/m 2 (-0.55°/sec/ib/ft z) for

< i0 500 N/m 2 (219.3 ib/ft2). (The value of i0 500 N/m 2 corresponds to an

indicated airspeed of 250 knots.) This was combined with a reduction of

4°/sec/deg of angle of attack for _ > 15 ° . Finally, nose-down symmetric

stabilator deflections in excess of 5 ° caused a reduction of commanded roll

rate of 4°/sec/deg.

19

The resulting limit on commandedroll rate is illustrated in figure 27,which shows (Pcom)max versus _ for ig trim flight conditions. With thestabilator deflected for trimmed flight, (Pcom)max is reduced from 280°/secat _ : 5° to 170°/sec at _ = 25o; these values would be representative ofthe (Pcom)max available at the initiation of a roll. Also shown are thevalues that represent the situation in which full control has been used tocounter the inertia-coupling moment with the stabilators deflected full nosedown (@h= +25o)" As shown in the figure, this case results in a decrease of80°/sec in (Pcom)max from the values obtained at trim 6h such that the max-imum commandable roll rate is only about 90°/sec at _ = 25° .

Control system B also incorporated a modification to the pitch axis toassure proper stabilator response during rolling maneuvers. This modificationis shown in figure 28 and involved creating an equivalent angle-of-attacksignal A_p based on roll-rate magnitude. The variation of h_p with IPlis plotted in figure 29; note that a 20°/sec deadband was included so that thesystem was inactive during low-rate, precision maneuvers when it was not needed.The pseudo angle-of-attack signal was fed to the _ limiter, which recognizedit as an increase in _ and therefore applied nose-down stabilator deflectionto oppose it. This system, therefore, assured that the pitch control wasdeflected in the proper direction to oppose the nose-up coupling moment gener-ated by rapid rolling at high angles of attack.

The effectiveness of control system B in preventing inertia-couplingpitch-out departures is illustrated in figure 30, which shows a 360° rollinitiated from Ig trim at _ = 25° using full lateral stick input. As previ-ously discussed, this maneuver, when performed with the basic control system(control system A), resulted in loss of control. (See fig. 22.) For controlsystem B, figure 30 shows that although the pilot applied maximum lateral stickinput, the resulting commandedroll rate was limited to only about 165°/sec (asopposed to 308°/sec for control system A) so that the maximum roll rate achievedwas 70°/sec. The resulting nose-up coupling moment was smaller, and there wassufficient aerodynamic nose-down control moment to essentially cancel it, as canbe seen by comparing the qicl and qa traces. As a result, _ neverexceeded 26° during the maneuver and the maximum _ generated was less than3° . Thus, in this particular situation at least, roll-rate limiting eliminatedthe two problems experienced with the basic airplane, that is, _ pitch-outsdue to excessive roll-pitch coupling and large _ excursions due to excessiveroll-yaw coupling. Examination of the control traces shows that significantlyless than maximumroll-control deflections were used. Even in the initiationof the roll when p is low and coupling is therefore not a problem, only -15 °of the available -21.5 ° of 6a was obtained. The net result is a slowerinitial roll response compared with that of the basic airplane (control sys-tem A); as discussed previously, this response degradation is due mainly to theuse of q and _ in the limiting scheme. One other point to note on thecontrol time histories is that only about 60 percent of the available rudder isused for coordination through most of the maneuver.

2O

A 360° roll initiated from an accelerated turn at the d limit is shownin figure 31. The results are very similar to the ig case in that the maneuverwas well controlled, with the airplane never approaching an out-of-controlcondition.

Time histories of the 70° bank-to-bank reversals initiated from ig trimat e = 25° are shown in figure 32. Again the roll-rate limiting scheme ofcontrol system B significantly improved the controllability of the airplane inthis maneuver. Angle of attack was maintained below 28° and sideslip excursmonsbelow 4° . These results should be contrasted with those obtained with the basicairplane (fig. 24), which encountered momentary departures with _ exceeding 32°and _ excursions above 15°.

Classical spin-susceptibility testing was conducted by applying cross-"controls in ig and accelerated conditions. An example is shown in figure 33,in which cross controls were applied from an accelerated turn at the limit _.As obtained with the basic control system, the inertia coupling resulting fromthe generated roll and yaw rates caused _ to overshoot above the 25° limit;however, _ never exceeded 30° , _ was maintained below ii °, and the maximumyaw rate encountered was only about 28°/sec. Recovery was obtained immediatelyafter the controls were neutralized.

The results to this point indicated that the control modifications incor-porated in control system B significantly enhanced the departure resistance ofthe subject airplane in high d maneuvers, during which lateral stick alone orcross controls were used. This improvement resulted primarily from the factthat the pilot was constrained to commandless roll- and yaw-control deflectionsthrough lateral stick deflections due to the roll-rate limiting scheme employed.However, it was still possible for the pilot to augment rudder deflection byapplying pedal inputs in the direction of the lateral stick input. Therefore,an assessment was made to examine how the additional rudder might affect thedeparture-resistance characteristics of the configuration.

Figure 34 shows time histories of a 360° roll initiated from lg trim at: 25° with maximumcoordinated stick and pedal inputs. As previously dis-

cussed, performance of this maneuver with lateral stick alone resulted in a

well-controlled roll, with little fear of encountering a pitch-out departure.

(See fig. 30.) However, application of coordinating pedals resulted in quite a

different situation, as shown in figure 34. Examination of the control traces

indicates that the primary difference in the control inputs was obtaining sus-

tained full (-30 ° ) rudder deflection; the roll-control deflections, on the

other hand, were about the same as obtained in the earlier stick-only maneuver.

The combination of very large rudder deflections and reduced aileron and

differential-tail deflection resulted in overcoordination of roll, to the point

that some 8 ° of proverse _ was generated. This large amount of proverse

sideslip was detrimental for two reasons: (i) it acted through dihedral effect

to augment the roll rate, which in turn coupled with the higher yaw rate caused

by the larger 6 r to substantially increase the nose-up inertia-coupling

moment (see qicl); and (2) it kinematically coupled with the high roll rate

to cause an increase in angle of attack (_ _ -p_, see Wac2)- The result was

21

a rapid pitch-out departure despite the application of full nose-down stabilatorby the control system; angle of attack reached a maximumof 70° , whereas side-slip oscillated ±30° during the departure. Use of full coordinated inputs toperform 360° rolls at other ig and accelerated flight conditions resulted insimilar loss of control situations.

In summary, control system B was found to significantly enhance the depar-ture resistance of the subject airplane as long as coordinating pedal inputswere not used during large-amplitude roll maneuvers. Use of large amounts ofcoordinating pedal in these maneuvers often resulted in severe pitch-out depar-tures. It should be pointed out that there should be no need for the pilot toapply coordinating rudder inputs since this is automatically done for him by theARI. However, it is felt that during air combat there would be a strong ten-dency by the pilot to use rudder pedals in an attempt to obtain maximumrollperformance, particularly in view of the fact that the roll-rate limiting schemeof control system B resulted in noticeable degradation in the initial rollresponse of the airplane.

Control system C.- Based on the foregoing results, an attempt was made to

correct the two primary deficiencies of the airplane equipped with control sys-

tem B, that is, (i) susceptibility to pitch-out departures when coordinating

pedal inputs are used, and (2) initial roll-response degradation. To accomplish

this objective, two modifications to control system B were developed and are

shown in figure 35. For convenience, the control system incorporating these

additional features will be referred to as control system C. Alleviation of

the pitch-out departure problem due to excessive use of coordinating rudder

pedals was accomplished by using a scheduled gain in the pilot rudder command

path which faded out pilot inputs between roll-rate magnitudes of 20°/sec and

40°/sec. Elimination of pilot rudder inputs at high roll rates (IPl _ 40°/sec)

was designed to eliminate any aggravation of the inertia-coupling pitch-out

problem. At low roll rates <IPl _ 20°/sec), however, the system allowed the

pilot full use of the rudders (_i _ 20o) and therefore did not detract from his

ability to perform smaller amplitude, precision maneuvers such as tracking cor-

rections. The second deficiency of control system B, degraded initial roll

response, was corrected by adding a scheduled gain to the roll-rate limiting

path such that the limiting did not become fully effective until the roll-rate

magnitude exceeded 50°/sec; furthermore, all limiting was eliminated for

IPl _ 30°/sec- This scheme, therefore, imposed limiting only at the higher

roll rates where it was needed to prevent inertia-coupling departures; at the

lower roll rates, however, the pilot was allowed full roll capability so as to

obtain maximum initial roll response from the airplane.

The effectiveness of control system C in resolving the critical roll-

response problem is illustrated in figure 36, which shows a full lateral stick,

360 ° roll initiated from ig flight at _ : 25 ° . These time histories should be

compared with those obtained in the same maneuver with control systems A and B

(figs. 22 and 30). Note that with control system C, maximum roll- and yaw-

control deflections were obtained during initiation of the roll; in fact, in

this phase of the maneuver, the control motions with control system C were Very

similar to those obtained with the basic control system without roll-rate limit-

ing (control system A). As previously discussed, only about 75 percent of the

maximum roll control was available to initiate the maneuver when control

22

system B was used. In examining the response obtained with control system C, itis seen that as the roll rate increased to values where inertia coupling becamea factor, roll-rate limiting was imposed and the roll- and yaw-control deflec-tions were reduced to essentially the levels obtained with control system B; apitch-out departure was avoided.

A quantitative comparison of roll response obtained in this maneuver withall three control systems is shown in table V. The figure of merit that wasused was time to bank to 90° and 180° . The data for At_:90o indicate that 'control system B suffered a 15-percent degradation in response when comparedwith control system A, whereas there was no degradation with control system C.For 180° of roll, control system C was only 3 percent slower than A, as comparedwith 13 percent slower for control system B. In summary, control system C wassuccessful in combining the desirable features of control system A (high initial9oll response) and control system B (high resistance to inertia-couplingdeparture) without incurring the deficiencies of either system.

The ability of control system C to prevent pitch-out departures due toexcessive pilot coordinating rudder is illustrated in figure 37. Shown aretime histories of a 360° roll from ig trim at _ = 25° using full coordinatedstick and pedal inputs. It is seen that fade-out of the pilot rudder commandsabove IPl : 50o caused the resulting airplane motions to be essentially iden-tical to those obtained using lateral stick alone. The maximumangle of attackreached was 25° , and the airplane was not near a departure condition at anypoint in the maneuver. These results should be contrasted with those obtainedwith control system B, where a rapid pitch-out departure to _ : 70° wasencountered (fig. 34).

Further evaluation of departure/spin susceptibility was accomplished byapplying maximumcross controls at Ig and accelerated flight conditions. Anexample is shown in "figure 38, in which the controls were applied from ig trimat _ = 25° . The time histories show that although full prospin controls wereheld for 14 sec, _ did not exceed 26° and yaw rate was maintained below35°/sec.

Figure 39 shows cross controls applied from ig trim at d = i0 °, followedimmediately by rapid full aft stick application. The inertia-coupling moment,combined with the full nose-up pilot command, resulted in _ increasing to 28° .Nevertheless, there was sufficient aerodynamic control moment to preventfurther d excursions such that although the prospin inputs were held for over12 sec, angle of attack never exceeded the 25° limit.

A further evaluation of the resistance of control system C to inertia-coupling-induced departures is shown in figure 40. The initial conditions forthe maneuver were ig trim flight at M : 0.6 and h° = 9144 m. From thisstarting point, full lateral stick input was applied, followed in_nediately byfull nose-up pitch command. The large angular rates resulting from theseinputs would be expected to maximize inertia-coupling effects. The data showthat very high rates, particularly in roll, were generated; however, the limit-ing features of the control system effectively limited these rates to valuesthat could be handled by the available aerodynamic control moments. As a

23

result, the maximum _ excursion was only 27° , despite the fact that the con-trols were held for approximately ii sec.

Effect of Aft Center of Gravity

It should be noted that all the maneuvers discussed up to this point wereconducted with the airplane center of gravity at its nominal'location of 0.35_.As previously discussed, more aft center-of-gravity locations should aggravatethe inertia-coupling departure problem because less nose-down aerodynamic con-trol moments would be available. Therefore, a brief investigation was con-ducted to see what effect more aft center-of-gravity locations might have onthe departure-prevention ability of the control system developed for a centerof gravity of 0.35_. For this evaluation, center-of-gravity locations of0.375c and 0.39_ were evaluated. Figure 41 shows a maximum lateral stick, 360°roll from ig trim at _ : 25° with a center of gravity of 0.375_. The datashow that more nose-down stabilator was required to trim at this condition dueto the increased static instability caused by the rearward center-of-gravityshift. Comparison of the time histories of this maneuver with those obtainedwith a center of gravity of 0.35_ (fig. 36) verifies the loss in nose-downaerodynamic pitching moment at 0.375_. This loss is reflected in the @htrace which shows that the stabilators were at the full nose-down positionthrough most of the maneuver; nevertheless, angle of attack increased to 27°(as compared with the 25° obtained with a center of gravity of 0.35_). Althougha departure did not occur in this case, the fact that the pitch control remainedsaturated for such an extended period of time and was still unable to holdbelow the limit value indicates that control was very marginal in this situa-tion. A more severe coupling maneuver would, therefore, be expected to resultin a departure. An example of loss of control is shown in figure 42, whichshows the high coupling maneuver previously discussed, in which the pilotapplied full roll and pitch inputs from ig trim flight at M : 0.6. As previ-ously discussed, this maneuver performed with the center of gravity at 0.35_did not result in loss of control. However, figure 42 indicates that with thecenter of gravity at 0.375_, the available nose-down control was overpowered bythe inertia-coupling moment, and a rapid pitch-out to _ : 76° ensued. Follow-ing the departure, the airplane entered the deep-stall trim condition previouslydiscussed; the deep-stall problem is addressed in more detail in the sectionentitled "Deep-Stall Simulation Results."

These results indicated that rearward center-of-gravity movement beyond0.375_ would require further limiting of roll rate in order to obtain an accept-able level of departure resistance. These indications were verified when con-trol system C was flown with the center of gravity at 0.39_. An example isshown in figure 43, which presents time histories of an attempted 360° rollusing full lateral stick input starting from ig trim at _ : 25° . It is seenthat the aerodynamic nose-down control was easily overpowered by the inertia-coupling moment and resulted in a sharp pitch-out departure to _ : 84° andentry again into the deep-stall trim condition. Attempts at other roll maneu-vers that were accomplished without incident with the center of gravity at 0.35cresulted in a similar loss of control.

24

It was found that the airplane equipped with control system C that wasflown with the center of gravity at 0.39_ was at least as prone to departuresas the basic airplane was at 0.35_. It thus became clear that the roll-ratelimit would have to be reduced significantly at a center of gravity of 0.39_ toreestablish a level of departure resistance comparable to that obtained at0.35_. However, as indicated in figure 25, this level of roll performance maynot be adequate from a tactical viewpoint. In summary, control system C wasfound to provide a high level of departure resistance for the airplane with thecenter of gravity at its nominal location. Large-amplitude maneuvers at Ig'andaccelerated flight conditions involving gross application of adverse controls

did not result in loss of control. However, rearward center-of-gravity shifts

deteriorated departure resistance to the point that it was marginal at 0.375_.

Operation at center-of-gravity locations aft of 0.375c would require further

reductions in maximum allowable roll rate.

DEEP-STALL SIMULATION RESULTS

Description of Problem

As discussed in the section entitled "Discussion of Stability and Control

Characteristics," the 0.35_ pitching-moment data for the subject configuration

exhibit stable deep-stall trim points in the vicinity of _ = 60 ° , even with

the stabilators deflected full nose down. The trim point, however, is com-

paratively weak, and an investigation therefore was conducted to see if it was

possible to fly into a stabilized deep-stall trim point. The departures

described in the previous section for aft center-of-gravity locations (figs. 42

and 43) all resulted in the airplane flying into this deep-stall trim condition.

The results of the present study indicated that entry into the deep stall

was possible during rolling maneuvers at high angles of attack or from very low

airspeed conditions at high angles of attack. One such low airspeed maneuver

was to put the airplane into a steep-attitude, decelerating climb, with Q

reaching a maximum of about 70 ° , with the intention of reaching very low air-

speeds at the top of the climb and allowing the airplane to fall through at

essentially zero g. The resulting kinematic generation of a large angle-of-

attack excursion could not be effectively opposed by the _ limiter system due

to lack of control effectiveness at low dynamic pressure. An example of such a

maneuver is shown in figure 44.

The data of figure 44 show that, at the top of the maneuver, the airspeed

and normal acceleration decreased to M = 0.2 and 0.1g, respectively. As the

airplane fell through, the angle of attack increased to 70 ° , despite the appli-

cation of full nose-down pitch control by the d limiter system. After several

cycles of oscillation, the airplane stabilized into the deep stall trim point

with _ _ 58 ° , _ _ 0°, r _ 0, G _ 6 ° , and a n _ ig. Note that, at this

point, the pilot had absolutely no control over the airplane. In pitch, the

limiter caused the stabilators to remain at the full nose-down position, inde-

pendent of pilot inputs. In roll and yaw, the automatic spin-prevention system

took control away from the pilot, and the system was commanding control deflec-

tions to oppose any yaw rate. For a fighter having a fuselage-heavy mass

25

loading, the most effective spin-recovery controls are obtained when therudders are applied to oppose yaw rate and the ailerons are applied in thedirection of the yaw rate. It should be recognized that these systems did suc-cessfully prevent any yaw-rate buildup and therefore eliminated the danger ofthe motions progressing into a spin; nevertheless, this was of little conse-quence to the pilot since he was locked in the deep-stall condition, with noway of recovering by using his normal controls.

It is important to note that all the maneuvers discussed to this pointwere conducted with an aerodynamic model which did not include aerodynamicasymmetries; that is, the aerodynamic coefficients Cy, C_, and Cn were zerofor _ = 0° and neutral lateral-directional controls. In the normal angle-of-attack flight envelope of current fighter aircraft, this modeling assumptionhas been found to be generally valid in that wind-tunnel measured asymmetriesare normally insignificantly small. However, experience has shown that, inmany configurations, these asymmetries can reach significant magnitudes atpost-stall _. Figure 45 shows Cy, C_, and Cn asymmetries measured duringwind-tunnel tests on the subject configuration. The data confirm that withinthe normal _ flight envelope, these asymmetries are small enough to beignored. However, they rapidly increase in magnitude for _ > 30° . Of par-ticular significance is the fact that the yawing-moment asymmetry reaches itsmaximumvalue in the _ region of the deep-stall trim point. In order toassess the importance of this characteristic, the deep-stall investigation wasconducted with two aerodynamic models, one that included the wind-tunnel mea-sured asymmetries of figure 45 and one that omitted them.

Figure 46 shows time histories of a deep-stall entry with the asymmetriesincluded. Comparison with the results obtained without asymmetries (fig. 44)indicates little difference in the initial phase of the entry. However, oncethe airplane began to settle into the trim point, figure 44 shows that thenose-left yawing-moment asymmetry caused the yaw rate to build up to about-20°/sec, despite the application of significant amounts of opposing aileronand rudder deflections by the spin-prevention system. The airplane also assumeda left wing low (_ _ -16 ° ) and nose low attitude (0 _ -23o). Note that thenose-up inertia-coupling moment resulting from the nonzero roll and the yawrates caused the airplane to trim at an angle of attack roughly 4° higher thanthat obtained without the asymmetries. Another important indication from theseresults is that the asymmetries would probably have driven the airplane into aspin without the action of the automatic spin-prevention feature of the controlsystem.

With regard to the ease of experiencing the deep-stall trim, it was foundthat the first _ peak during the entry was critically important in that anovershoot to values of _ too much above the trim point resulted in the genera-tion during the downswing of sufficient nose-down pitch rate to drive the air-plane nose down over the Cm > 0 hump and result in recovery. Generally, theairplane did not consistently drop into the deep-stall trim point if the initialpeak in _ was greater than 75° . Control of the initial _ excursion wasdifficult, and the pilots were therefore not able to obtain the deep-stall trimon every attempt.

26

stick in phase with the airplane motions, with the hope that sufficient angularmomentumwould be created during a downswing cycle to drive the airplane overthe positive Cm hump and back down within the normal _ envelope of theairplane.

A recovery attempt using this technique is shown in figure 50. Startingfrom a stabilized trim at _ _ 62° , the pilot activated the pitch rocker systemand rapidly applied full aft stick at t : 71.3 sec. In response, the stabi-lators moved from the full nose-down position commandedby the _ limi[er tofull nose up. The resulting nose-up moment caused _ to increase to 75° , atwhich point the pilot reversed his controls and applied full forward stick toobtain @h: +25o- This action generated a large nose-down moment, indicatedby the qa trace at t : 74, and _ decreased rapidly. As expected, qabecame positive (t : 75 sec) for a brief time as _ traversed the hump in theCm curve; however, there was sufficient momentumto cause the airplane to con-tinue to pitch downward until a recovery was obtained at t : 78 sec. Itshould be noted that in this particular case, the pilot very accurately kepthis inputs in phase with the motions and therefore obtained a recovery within1 cycle of the oscillation. However, it was found that in situations where thepilot was somewhat out of phase with the oscillation, recoveries were delayedsignificantly so that as many as three to four pumping cycles were required forrecovery.

Further assessment of the deep-stall and recovery characteristics wereobtained by moving the center of gravity aft to 0.375_. Figure 51 shows anentry and recovery attempt using the speed brakes and flaps; aerodynamic asym-metries were not modeled in this case. As can be seen, trim was achieved at

= 60° with r = 0, _ = -13° , and G : 0. At t : 67.5, the speed brakeswere deployed and the flaps reconfigured, and a rapid recovery was obtained in4.5 sec. A quite different result was obtained with asymmetry modeling; anexample is shown in figure 52. The data indicate that the airplane tri_ed ata mean angle of attack of about 65°, with the asymmetries causing a yaw rate of-16°/sec. At t = 65 sec, recovery was attempted using the speed brake andflaps. As can be seen, the resulting nose-down pitching-moment incrementcaused _ to decrease by about 4o; however, it was not sufficient to effectrecovery and the airplane established another trim condition with _ _ 63° andr = -20°/sec.

Generally, it was found that recovery to normal flight conditions couldnot be attained with this technique unless the pilot made the speed-brake andflap change early in the entry while there were still large oscillations in themotion and unless the inputs were made during a downswing in _ so that theyreinforced the downward motion. Obviously this is very difficult to do, and inthe majority of cases, recovery was not obtained. The primary reason for thedifference in the results obtained with and without asymmetry modeling was theexistence of the yaw rate with modeling. Apparently, the additional nose-upinertia-coupling moment caused by the angular rate was sufficient to negate therelatively small amount of nose-down moment generated by the speed-brake andflap changes.

28

Methods of Recovery

Once it was determined that the airplane could be flown into the deep-stall trim point, techniques were developed to recover from it. As previouslydiscussed, the primary controls could not be used because the pilot had nocontrol over them in this situation. Consequently, other schemes for obtainingthe needed nose-down pitching momentwere investigated in the wind tunnel, andtwo potentially useful concepts were identified. The first method involvedreconfiguring the flaps by retracting the leading-edge flaps and deploying _hetrailing-edge flaps (61ef = 0°, 6te f : 20o), whereas the second involvedspeed-brake extension to maximumdeflection (@sb= 60o)" The locations of thesesurfaces are shown in figure 2. Note that the speed brakes are located on theupper and lower surfaces of the aft fuselage shelf next to the stabilators, andtheir deployment therefore would be expected to provide a nose-down moment in i

, the deep-stall region.

Figure 47 compares the resulting pitching moments with those for the normalconfiguration (61ef : 25o' 6tef : 0°' @sb: 0°); note that all data are forthe full nose-down stabilator deflection that would be maintained by thelimiter system. The data show that reconfiguring the flaps provides an incre-ment of about -0.018 in Cm in the angle-of-attack range of interest (55° to60o), whereas speed-brake deployment results in about -0.025. Note that neitherscheme clearly eliminates the trim point with the center of gravity at 0.35_,and therefore they would not be expected to be always effective, particularlyfor center-of-gravity locations aft of 0.35_. However, as shown in figure 47,combining the two schemes results in a pitching-moment-coefficient increment ofabout -0.05, which eliminates the deep-stall trim point.

Figures 48 and 49 show time histories of recovery attempts using the combi-nation of speed-brake deployment and flap reconfiguration. The results obtainedwithout asymmetry modeling are shown in figure 48. The recovery attempt wasinitiated at t : 78 sec, with the airplane stabilized in the deep-stall trim,and, as can be seen, a rapid, positive recovery was obtained within 4 sec. Theresults with asymmetry modeling are shown in figure 49. Although a positiverecovery was also attained, the recovery was not as rapid, taking some 8 sec tooccur. The reason for the slower recovery was the existence of the yaw ratewhich created an additional nose-up moment due to inertia coupling that had tobe overcome by the nose-down recovery moment.

One additional recovery technique that was investigated consisted ofreconfiguring the pitch control law to reestablish pilot control over the stabi-lators in the deep-stall region. The reconfiguration involved deactivating allfeedbacks, including the d limiter system, so that the only signal thatremained was the pilot stick command. With this system (henceforth to bereferred to as the pitch rocker), the deflection of pitch control was directlyproportional to pilot inputs. The reason for doing this can be seen by review-ing the pitching-moment data for maximum stabilator deflections shown in fig-ure I0. The data show that at the deep-stall trim point (_ _ 60°), a largepitching-moment increment results in going from full nose-down to full nose-upcontrol deflection (ACm _ 0.i). Thus, a possibility exists to use this avail-able control moment to initiate and build up a pitch oscillation by moving the

27

The effectiveness of the "pitch-rocking" technique in providing recover-ies with the center of gravity at 0.375c is illustrated in figure 53. In thisparticular case, pitch rocking was initiated early in the entry (t = 52 sec)while the motions were still quite oscillatory; in addition, the pilot did avery good job of phasing his inputs in that the initial aft stick applicationswere made just as the airplane was beginning a nose-up cycle. As a result,was driven up to 84° and sufficient momentumwas generated in the followingdownswing to reestablish normal flight. The recovery was obtained within 8 secafter the pilot initiated recovery action. Figure 54 illustrates the results,that were obtained when the pilot did not optimally phase hi_;rocking inputswith the ai,rplane motions. In this case, recovery was not obtained until thepilot had completed five rocking cycles, and the time interval between initia-tion of recovery action and actual attainment of recovery was some 30 sec.These results emphasize the criticality of proper pilot usage of the pitch-rocking technique; nevertheless, this technique was found to%e effective inproviding deep-stall recovery for all the conditions (center-of-gravity locationand asymmetry modeling) investigated in this study.

TRACKINGRESULTS

Following completion of the departure, deep-stall, and spin-susceptibilityinvestigation, the tracking evaluation phase of the study was conducted to deter-mine how these characteristics and the control-system changes affected theability to track a target airplane through maneuvers representative of air com-bat. The evaluation was conducted at the nominal 0.35_ center-of-gravity loca-tion and included an assessment of the three control-system configurationsstudied in the first phase.

Results of Basic Control System (Control System A)

Time histories of the airplane motions during the wind-up turn trackingtask are shown in figure 55; included are the range between the two air-planes R, the total angular tracking error g, and the lateral componentof g I. The data indicate that the pilot had little difficulty in trackingthe target airplane through the task. Note that the design of the lateral-directional control system allowed him to track using only the stick, and no

pedal inputs were required. The airplane motions were well damped and, as

expected, none of the inertia-coupling problems previously discussed were

encountered in this task due to the absence of any large-amplitude rolling

maneuvering.

Figure 56 illustrates the performance of the airplane with the basic con-

trol system (control system A) in the bank-toT_9nk tracking _ask. As indicated

by the pilot-input time histories, this was a much more demanding task than the

wind-up turn in that a combination of bank-to-bank reversals-followed by rapid

pull-ups to high _ was required to maintain tracking. The very dynamic

nature of the task requiring rapid and accurate control in all three axes

simultaneously tended to accentuate any handling-quality deficiencies. Note

29

that the pilot used very large lateral stick inputs to make the reversals, andthe inertia-coupling moments resulting from the high roll and yaw ratesrequired large countering nose-down stabilator deflections. Maximum _ andexcursions were 30° and i0 °, respectively. The £ and _ data show that thepilot had difficulty in maintaining tracking during the reversals; however, oncethe reversal was completed, he was able to reacquire the target within about 5to i0 sec. It should be pointed out that the pilot was aware of the potentialpitch-out tendency if too much coordinating rudder was used, and he thereforeflew the task essentially without pedal inputs. Furthermore, by using_only thestick, the amplitude of the bank-angle changes that were required (IA_I _ 180 ° )

was insufficient to cause a departure due to inertia coupling. As a result, no

departures were observed during any of the runs made on this task.

The performance of the basic airplane in the ACM task is illustrated in

figure 57. As previously discussed, this task required two rapid, large-

amplitude (IA_I _ 180 ° ) rolls at the limit _ and low airspeeds and therefore

exposed the airplane to potential inertia-coupling departure situations. The

data show that in this particular run, a near-departure condition occurred

during the first roll maneuver in that full nose-down stabilator was held for

over 1 sec to oppose the nose-up coupling moment; maximum _ reached 29 ° . No

further near-loss-of-control situations occurred during the remainder of the

run. Note that, again, the pilot did not use pedal inputs; this factor cer-

tainly accounted, to some extent, for the fact that no pitch-out departures

were encountered.

Results of Control Systems B and C

Effects on tracking capability resulting from the control-system modifica-

tions incorporated in control systems B and C were assessed by flying the air-

plane equipped with these systems against the three tracking tasks. The results

were compared with those obtained with the basic control system (control

system A) to determine whether the roll-rate limiting schemes used to enhance

departure resistance had significantly degraded the tactical effectiveness of

the airplane.

The results obtained for control systems B and C in the wind-up turn task

are essentially identical to those obtained with the basic control system.

This was an expected result since this task did not require any rapid, large-

amplitude roll maneuvers.

Figure 58 illustrates the performance of the airplane equipped with con-

trol system B in the bank-to-bank tracking task. This figure should be compared

with figure 56, which shows the basic airplane flying against the same task.

Although the pilot generally applied similar amplitude lateral stick inputs in

both cases, the resulting roll- and yaw-control deflections were significantly

less in control system B due to the rate limiting scheme previously discussed.

As a result, the roll and yaw rates were lower, and the reduced inertia-

coupling moments are reflected in the decreased use of large nose-down stabi-

lator deflections. Comparison of _ traces also shows the reduction in side_

slip excursions seen earlier during the departure susceptibility evaluation.

The pilots commented that they noticed a definite degradation in initial roll

3O

response in going from control system A to control system B. They indicatedthat this was mildly bothersome since they felt that they had to hold largelateral stick forces longer in order to obtain the same net roll response. One

small positive aspect of the slower roll response noted by the pilots was that

it reduced the tendency to overcontrol during tracking. This characteristic

can be seen by comparing the lateral input traces, which show that the inputs

were somewhat less oscillatory with control system B than with A. Overall, the

pilots stated that the reduced roll-response characteristic of control system B

did not significantly affect their ability to track the target through this '

task. Comparison of the _ and _ traces tends to confirm this observation.

An example of tracking performance in the bank-to-bank task for the air-

plane equipped with control system C is shown in figure 59. The time histories

show that the pilot accurately tracked the target through all the reversals

except the final one. The pilots commented that the initial roll response

obtained with this system was noticeably better than that of control system B

and was only very slightly slower than that of the basic airplane. Moreover,

the improved sideslip control (much smaller sideslip excursions) resulting from

the proper limiting of roll rate resulted in much improved bank-angle control;

the pilot was able to make the roll reversals rapidly and cleanly with a minimum

of oscillations. Comparison of the time histories of lateral stick input in

figures 59 and 56 indicates a markedly smoother, less oscillatory trace with

control system C than with control system A. Overall, the pilots stated that

they could track slightly better and with less workload with control system C

than with either A or B.

When the airplane equipped with control systems B and C was flown in the

ACM task, the comparative results were essentially the same as those obtained

in the bank-to-bank task. Representative runs are shown in figures 60 and 61

for control systems B and C, respectively. Again, the pilots noted the degraded

roll response of B but commented that it did not significantly affect their

tracking ability. Again, they mildly preferred C over the other two control

systems due to the characteristics previously discussed.

In summary, the tracking evaluation phase of the study determined that the

roll-rate limiting scheme that was used to prevent pitch-out departures resulted

in no significant degradation in tracking capability. On the contrary, the

control system using roll-rate limiting but also incorporating features to

minimize initial roll-response loss (control system C) was found to provide

slightly improved tracking while reducing pilot workload. It should be reempha-

sized that the evaluation was conducted at the nominal center-of-gravity loca-

tion of 0.35_. As previously discussed, operation at center-of-gravity loca-

tions farther aft, particularly aft of 0.375_, will require further limiting of

roll rate to minimize susceptibility to pitch-out departures; the resulting

roll-performance degradation would be expected to degrade tracking ability

significantly more than previously indicated. With regard to deep-stall trim,

it should be pointed out that no deep-stall entries occurred during any of the

tracking runs. This was not an unexpected result in view of the fact that no

pitch-out departures were encountered, and the tracking tasks did not entail

extreme low-speed zero g maneuvers.

31

INTERPRETATIONOF RESULTS

The fidelity of the simulation in representing the actual F-16 airplanewas evaluated by comparing simulation results with actual airplane flight testdata and by having pilots with F-16 experience fly the simulator. Throughoutthe present study, close coordination was maintained with the flight testing Ofthe full-scale airplane to ensure correlation between simulation and flight andto expedite development of airplane modifications for testin@ in flight whenproblems were encountered. As a result, the major characteristics an@resultsderived from this investigation have also been encountered in flight. Flighttest results have confirmed that the airplane can experience pitch departuresduring rolling maneuvers and/or low-airspeed maneuvers at high angles ofattack. Flight results have also shown that the airplane can enter the deep-stall trim condition from the flight conditions described herein. Moreover,the various control-system modifications and deep-stall recovery methodsstudied in the present simulation have been flight tested and were found to beas effective as the simulation predicted.

It should be recognized, however, that the present study was limited inscope, and these limitations should be kept in mind when applying the resultsand conclusions of this study. A primary limitation is that the aerodynamicdata were measured at low values of Mach number and did not incorporate anycompressibility effect; consequently, the results can only be considered validfor Mach numbers less than about 0.6. It should also be kept in mind that onlythe clean configuration was investigated and that it is likely that certainstore configurations (particularly asymmetrical stores) can degrade thedeparture/spin resistance of the airplane.

SUMMARYOF RESULTS

A piloted simulator investigation has been conducted to evaluate the high-angle-of-attack characteristics of an F-16-based fighter configuration incor-porating relaxed longitudinal static stability. The following major resultswere derived from this study:

1. The airplane with the basic control system was found to be resistantto the classical yaw or nose slice departure; however, it was susceptible topitch departures caused by having insufficient nose-down control to counter the

inertia-coupling moment generated during rapid, large-amplitude roll maneuvers.

In addition, the airplane was susceptible to pitch departures when flown to

very low airspeeds at high angles of attack.

2. Pitch-out departures produced by inertial coupling were prevented by

limiting the maximum roll rates at the lower speeds and higher angle-of-attack

flight conditions.

3. A modified control system incorporating roll-rate limiting and other

departure-prevention features made the airplane extremely departure resistant

without significantly degrading roll performance. However, the airplane could

still be flown to angles of attack above the angle-of-attack limit at very low

airspeeds.

32

4. Although the airplane with the nominal center-of-gravity location couldbe made more departure resistant without sacrificing maneuverability, itappeared that center-of-gravity locations significantly farther aft wouldrequire more drastic roll-performance penalties that could compromise tacticaleffectiveness.

5. The simulated airplane could be flown into a deep-stall trim condition,from which recovery was not possible with the basic control system using theprimary pilot controls. The roll-rate limiting control concept developed inthis study could not prevent very low airspeed entries into the deep stall.

6. It was not possible to define reasonable control laws (short of limitingminimum airspeed) whichcould prevent departure and entry into the deep stallat very low airspeeds. Changes to the airframe to increase high-angle-of-attack10ngitudinal stability and/or control would probably be necessary to eliminatethese problems.

7. Reconfiguring the wing leading- and trailing-edge flaps and deployingthe speed brakes generated a sufficient nose-down moment increment to recoverthe airplane from the deep-stall trim point, provided that the rotation rate

_was very small. However, steady yaw rates as low as 15°/sec could negate theeffectiveness of this recovery technique, particularly at the more aft center-of-gravity locations.

8. It was possible for the pilot to oscillate the airplane out of the deep-stall trim point by applying maximumpitch-control inputs in phase with theairplane motions. The effectiveness of this technique was found to be a directfunction of proper input timing by the pilot; with correct pilot action, thistechnique successfully recovered the airplane, even at the aft center-of-gravitylocations investigated. Use of this procedure, however, required a modificationto the control system to enable reestablishment of pilot control over thestabilators above the limit angle of attack.

Langley Research CenterNational Aeronautics and Space AdministrationHampton, VA 23665September 20, 1979

33

APPENDIXA

DESCRIPTIONOF CONTROLSYSTEM

Longitudinal

A block diagram of the longitudinal control system used in the .simulationis presented in figure 62. The implementation was a fly-by-wire, commandaug-mentation system (CAS) whereby the pilot commandednormal acceleration througha minimum deflection, force-sensing side-stick controller. Washed-out pitchrate and filtered normal acceleration were fed back to give the desiredresponse. A forward-loop integration was used in an attempt to make thesteady-state acceleration response match the commandedacceleration. The!air -plane had slightly negative static longitudinal stability at low Mach number;the desired static stability was provided artificially by the control system b_means of angle-of-attack feedback.

The longitudinal control system also incorporated an angle-of-attacklimiting system which functioned by using an _ feedback to modify the pilot-commandednormal acceleration. The angle-of-attack feedback reduced the com-manded normal-acceleration limit by 0.322g/deg between _ = 15 ° and 20.4 ° and

by 1.322g/deg above _ : 20.4 ° . This feature resulted in an angle-of-attack

limit in ig flight of approximately 25 ° . The maximum allowable positive com-

manded normal acceleration is shown in figure 63. The stabilator actuator was

modeled as a first-order lag of 0.0495 sec, with a rate limit of 60°/sec. The

surface deflection limit was ±25 ° .

Leading-edge flap deflection was scheduled with angle of attack and q/Psaccording to the following relationship:

61e f = 1.382S+7.25

S+7.25_ - 9.05 i+ 1.45

Ps

The flap actuator was modeled as a first-order lag of 0.136 sec, with a rate

limit of 25°/sec. Maximum flap deflection was 25 ° .

Lateral

The lateral control system is shown by the block diagram given in fig-

ure 64. The system incorporated a roll-rate command feature whereby the pilot

commanded roll rates up to a maximum 308°/sec through the force-sensing control

stick. Above _ : 29 ° , an automatic departure-/spin-prevention system is acti-

vated which uses a yaw-rate feedback to drive the roll-control surfaces to

oppose any yaw-rate buildup. In this mode, the roll-rate CAS is disengaged so

that the pilot has no control over the airplane laterally.

34

APPENDIXA

The roll-control system uses both aileron and differential-tail deflectionsat a ratio of 4° of @a per 1° of @d" The surface actuators were modeled as0.0495-sec first-order lags, with rate limits of 60°/sec for the differentialtail and 80°/sec for the ailerons. The surface deflection limits were ±5.38°and ±21.5 ° for the differential tail and ailerons, respectively.

Directional

A block diagram of the directional control system used in the simulationis presented in figure 65. The pilot rudder input was computed directly frompedal force and was limited to ±30° . Furthermore, this commandsignal wasreduced to zero between 20° and 30° angle of attack in an attempt to preventdepartures resulting from excessive pilot rudder usage at high angles of attack.,Yawstability augmentation consisted of feedbacks of r - p_ (mrstab) and ay.The stability-axis yaw damper provided increased lateral-directional damping inaddition to reducing sideslip during high _ rolling maneuvers. The lateralacceleration feedback had little effect at the low-speed flight conditions ofthe present investigation. The directional control system also incorporated anaileron-rudder interconnect (ARI) for improved coordination and roll perfor-mance. At low speeds, the ARI gain was scheduled as a linear function of angleof attack with a slope of 0.075/deg. As in the roll axis, above _ = 29° , adeparture-/spin-prevention mode is activated which drives the rudder at a gainof 0.75 deg/deg/sec to oppose any yaw-rate buildup. The rudder actuator wasmodeled as a 0.0495-sec first-order lag with a rate limit of 120°/sec. Thetotal rudder travel was limited to ±30° .

35

APPENDIXB

DESCRIPTIONOF EQUATIONSANDDATAEMPLOYEDIN SIMULATION

Equations of Motion

The equations used to describe the motions of the airplanes were nonlinear,six-degree-of-freedom, rigid-body equations referenced to a body-fixed Axissystem shown in figure 1 and are given as follows:

Forces:

: rv - qw - g sin 0 + q__SCx,t +m m

% : pw - ru + g cos 0 sin _ + qS_--Cy,t

6 : qu - pv + g cos G cos % + qS--_--Cz,t

Moments:

Iy - I Z

I x

I z - I X

Iy

qr + IXZ (r + pq) + _ C ZIX IX ,t

D B

qScIXZ(r 2 _ p2) + __

pr + Iy Iy Cm, t - Her

I X - Iy IX----_Z(p- qr) + qS__bb- IZ Pq + IZ I Z Cn,t

+ Heq

where the total aerodynamic coefficients CX, t, CZ, t, Cm, t, Cy, t, Cn, t,

are defined in the next section. Euler angles were computed by usingand CZ, t

quaternions to allow continuity of attitude motions. Auxiliary equations

included

_ = tan -I (uw-]

V : Qu 2 + v 2 + w 2

36

APPENDIXB

an =qu - pv + g cos Q cos _ -

g

-pw + ru - g cos Q sin _ +

ay = g

Aerodynamic Data

The aerodynamic data used in the simulation were derived from low-speed

static and dynamic (force oscillation) wind-tunnel tests conducted with subscale

models of the F-16 in wind-tunnel facilities at the NASA Ames and Langley

Research Centers. The static aerodynamics were input in tabular form as func-

tions of both angle of attack and sideslip over the ranges -20 ° _ _ _ 90 °

and -30 ° _ _ _ 30 ° . The dynamic data were input in tabular form for _ = 0°

over the same _ range. Total coefficient equations were used to sum the

various aerodynamic contributions to a given force or moment coefficient as

follows.

For the X-axis force coefficient:

where

CX,tCX(_,_,6 h) + ACx,lef( 1

+ _[CXq(_) + ACXq,lef

25 / ,sb

(_)(i 6 le f_7 -jj

ACx,Ie f : CX,lef(_,_) - CX(d,_,@ h = 0 °)

For the Z-axis force coefficient:

where

/CZ, t : Cz(_,8,6h) + ACz,lefkl

+ _q[c Z (_) + hCZq2V [ q ,lef

+ ACz,sb(_) \ 60/

ACz,lef : CZ,lef (_' _) - CZ(_' _'6h : 0°)

37

APPENDIXB

For the pitching-moment coefficient:

where

Cm,t : Cm(d,8,@h)_@h(@h)

( sq+ ACm, sb (_) \-_--]

+ Cz,t(Xcg,ref - Xcg) + ACm,lef<l

[C ( 61ef_]_q (_) + ACmq (_) 1+ _ mq , lef 25 /J

+ ACm(_) + ACm,ds(_,@ h)

ACm,le f = Cm, lef(_,8 ) - Cm(d,8,@ h = 0°)

For the Y-axis force coefficient:

where

Cy, t = Cy(d,8 ) + ACy,lef(1 61ef-]25 /

+ACy

+ ACY,@r:30 o + --2V Yr

+ ICyp (_) + ACyp,lef (_) (1

+ ACy (1,@a=20 ° ,6a=20O,lef

(_) + ACYr,lef (_) (i

61e_f)]2s ]P)

ACy,le f : Cy,lef(_,8) - Cy(d,8)

ACy, @a:20o : CY,@a:20o(_ 8) - Cy(_,8)

ACy,@a=20O,lef: cy (a, 8)

'@a=20°,lef

F- Ic (_, 8) -

Y,@a:20 oL

ACy (_,B) - Cy (_,8),@r:30 o : CY,@r:30o

38

APPENDIXB

For the yawing-moment coefficient:

Cn, t = Cn(_,_,6h) + ACn,lef(l @lef) - Cy,t(Xcg,ref

+ IACn,6a=20o + ACn,@a=20O,lef( 1

+ ACn, + (_) + ACnr (_) 1@r=30 o _ _ nr ,lef

+ ICnp (_) + ACnp,lef(_)(l 61ef-_]p] +ACn_(_)__II

where

ACn,le f = Cn,lef(d,_) - Cn(_,_,@ h = 0 O)

Xcg)b

r

= C n (_,_) - Cn(_,_,@ h : 0 O)ACn, @a:20 o ,6a:20o

: C nACn,6a:2OO,lef ,6a=20O,lef (_'_) - Cn,lef(d,_)

-[Cn,6a:20o(C_,[{)- Cn(Ct,[_,6h : 0°) -]

= Cn,6r=30o(_,_) - Cn(_,8,6 h = 0O)ACn,6r=300

For the rolling-moment coefficient:

c = c_,t 61ef )_(_,_,@h ) + hCt,le f 1 25

+ + ACt, (1 25Ct,@a:20o @a:20O,lef

(@r) b (E c (_) + (_)(i+ hCt,@r:30o. _ + _ t r ACtr,le f

E c ( 61ef_ P]+ (_) + (_) i _g _ + Ac t (_)Btp ACtp,le f 8

r

39

where

APPENDIX B

hCZ, le f : CZ,lef(d,_) - CZ(_,_,@ h : 0 °)

AC_,@a:20o : C_,@a:20o(_,_) - C_(_,8,@ h = 0 °)

ACl,@a=20O,lef = CZ,6a=20O,lef (_,@) - CZ,lef(_,@)

-[CZ,6a:20 o(_,8) -C_(d,_,@h : 0°)]

- cl( ,B,6h °°)AC_,@r:30o : C_,@r:30o

The aerodynamic coefficients contained in the preceding coefficient equa-

tions are presented in table III as functions of the indicated independent

variables. The aerodynamic moment coefficients are referenced to a center-of-

gravity location of 0.35_ and were corrected to the desired flight center-of-

gravity position in the coefficient equations.

Engine Simulation

The F-16 is powered by an afterburning turbofan jet engine. The thrust

response to throttle inputs was computed by using the mathematical model indi-

cated in figure 66(a). The throttle command gearing is shown in figure 66(b).

The response was modeled with a first-order lag which varied as shown in fig-

ure 66(c). Presented in table VI are thrust values for idle, military, and

maximum thrust levels. Engine gyroscopic effects were simulated by represent-

ing the engine angular momentum at a fixed value of 216.9 kg-m2/sec

(160 slug-ft2/sec).

4O

APPENDIXC

SPECIAL EFFECTS

Buffet Characteristics

Aerodynamic buffeting of the airframe at high angles of attack was simu-lated by shaking the cockpit with a hydraulic mechanism. The buffet intensgtyand frequency content were controlled by the computer, with the buffet ampli-tude varying with angle of attack, as shown in figure 67. Buffet onsetoccurred near _ = 15 ° , and the level of buffet increased fairly linearly

thereafter with increasing angle of attack. The frequency content was con-

trolled to represent the relative buffet amplitude contributions of the three

_ primary structural modes of the airframe.

Simulation of Blackout

Pilot blackout or "grayout" under sustained high values of normal accelera-

tion was simulated by decreasing the brightness of the projected scene and the

cockpit instruments as a function of the cumulative time spent at high load

factors. At the same time, dimming of the target image was delayed relative to

the scene in order to partially simulate tunnel vision for steady tracking

maneuvers. This simulation of blackout provided a cue, in addition to the

inflatable anti-g suit, of the extent of operation at high normal acceleration,

and it penalized the pilot who flew at unrealistically high values of normal

acceleration. The blackout representation assumed that a pilot will experience

grayout if exposed to greater than 5g normal acceleration and will tend to

recover when returning to below this level. The algorithm used a direct rela-

tion between the logarithm of the load factor a n and the logarithm of the

time to blackout; the simulation used 300 sec to blackout at 5g and i0 sec to

blackout at 9g, with simulated tunnel vision during the interim period.

41

REFERENCES

1. Impact of Active Control Technology on Airplane Design. AGARD-CP-157,Oct. 1974.

2. Gilbert, William P.; Nguyen, Luat T.; and Van Gunst, Roger W.: SimulatorStudy of the Effectiveness of an Automatic Control System Designed toImprove the High-Angle-of-Attack Characteristics of a Fighter Airplane.NASATN D-8176, 1976.

,q

3. Mechtly, E. A.: The International System of Units - Physical Constants and

Conversion Factors (Second Revision). NASA SP-7012, 1973.

4. Ashworth, B. R.; and Kahlbaum, William M., Jr.: Description and Performance

of the Langley Differential Maneuvering Simulator. NASA TN D-7304, 1973.

42

TABLE I.- MASSANDDIMENSIONALCHARACTERISTICSUSEDIN SIMULATION

Weight, N (ib) ........................ 91 188 (20 500)

Moments of inertia, kg-m2 (slug-ft2) :IX ............................. 12 875 (9496)Iy ............................. 75 674 (55 814)IZ ............................. 85 552 (63 I00)IXz ............................... 1331 (982)

Wing dimensions:Span, m (ft) .......................... 9.144 (30)Area, m2 (ft 2) ....................... 27.87 (300)Mean aerodynamic chord, m (ft) ................. 3.45 (11.32)

Reference center-of-gravity location ................. 0.35_

Surface deflection limits:Horizontal tail -

Symmetric (@h), deg ........................ ±25Differential (6d), per surface, deg ................ ±5.375

Ailerons (flaperons), deg ...................... ±21.5Rudder, deg ............................. ±30Leading-edge flap, deg .................. . .... 25Speed brake, deg .......................... 60

43

TABLEII.- DEPARTURE-/SPIN-SUSCEPTIBILITYMANEUVERS

Initial condition

ig trim; _ = 10°;h = 9144 m

ig trim; _ = i0°;h = 9144 m

lg trim; _ = i0°;h = 9144 m

ig trim; M = 0.6;h = 9144 m

Maximumg deceleratingturn; h = 9144 m

Maximumg deceleratingturn; h = 9144 m

Maximumg deceleratingturn; h = 9144 m

ig trim; _ = 25o;h = 9144 m

lg trim; _ = 25o;h = 9144 m

lg trim; _ = 25o;

h = 9144 m

Ig trim; _ = 25o;

h = 9144 m

Steep-aCtitude,

decelerating climb;

h = 9144 m

Maneuver

360 ° roll

360 ° roll

Response to cross

controls

Inertia coupling

360 ° roll at

170 knots IAS

360 ° roll at

170 knots IAS

Response to cross

controls at

170 knots IAS

360 ° roll

360 ° roll

Response to cross

controls

70 ° bank-to-bank

reversals

Deep-stall entry

Zilot input

Maximum lateral stick

Maximum coordinated lateral

stick and pedal

Maximum opposite stick and

pedal, followed by abrupt

full aft stick

Maximum lateral stick,

followed by abrupt full

aft stick

Maximum lateral stick

Maximum coordinated lateral

stick and pedal

Maximum opposite lateral

stick and pedal

Maximum lateral stick

Maximum coordinated lateral

stick and pedal

Maximum opposite lateral

stick and pedal

Maximum lateral stick

Stick neutral or full

forward

44

TABLEIII.- AERODYNAMICDATAUSEDIN SIMULATION

CX(<_,_,@h = -25°)

t_

R[TA

ALPHA

-PO.O

-]_.0

-10,0

0.0

+5.0

,fo.n

*}5,0

*PO.O

,30.0

+35.0

*_0,0

,45•0

*KO,O

*_5.0

*_0,0

$70.0

*RO,O

*qO.O

-.1R680

-.17160

-. !_750-.lq_ln..1787n-.tlSln-.143P0-.OqO?O-.113_0-.0_160

-.nn7qoL_nl_no

.o_560.nq3?o.07400

.09510

.11110

.0q15o

.!o7_0

.I_630

.1_060

.t4710

.l_56n

.i_o6n

.Y_nin

.I_010

.i_9_n

.1_600

-25.0

-.1RqgO-.17_bO-. lRO_qO-.16_70-.17690-.1P'_PO-, 16_S0

-oOq_50-.1 l;_90-.05_70

.-.06P60-,01080-.0];30

..03qRO, e_330.07B60.09750.11_40.ll_PO,10i00

.14q10

.11370

.16_.70

.14_70•17110•16030•164g0

.15_#+0

.171_.0°16150.17430.15(_90.17_80.15960,1710n.16150.15730.16510.167_0

-?0:. 0 -15.0* 4.0 * 6.0

-,19o40 .._ Rqc)O-, 19ftPO -,'19000

-,179_0 -,1RPTO-.')8760 -.1R6RO-.t6qPO -,r171RO-. 17;_90 -.17110-.1_760 -.13170

-,14P_O -.14100-,I0430 -, I0C)30-,111_0 --,11100-°06n30 -.06400

-.06_00 -. 06F,40-.OOqqO -,01010-.01 n_,O -. n0_,._0

,03_PO '. n4OPO.05360 .05;_70.07460 .07450.093q0 ,09130

,!IOPO .]0670,IIP50 .I1360

.09750 , I07110

• 14070- ,t37q0,11 qRO ,127@0.16640 .16ml70

..

°13500 .14410.16QQO .16550.16050 ,16040

.16KO0 . "167_0

.I_460 .16710

.17PRO .1.74_0• 15680 .16_10• 16_60 °16770

.16670 .15P50

.17300 .17.';160,15690 ,16PO0.171_0 ,173n0.15590 .15_00.15630 ,15R60

.16080 .'166R0

.166_0 .16_60

;10,0 - 8,0 - 6.n - 6,0 - 2,0+ R,O *10.0 +15.n *_0,0 *25,0 ,30,0

-.15690-.1R960-.IPI60

-.18480

-.17060-.1_90n-.13970-.11200

-.110P0-.06530

-.06500-.00760-.00830

0_770.OqO_O-.

0R6700R670

.1t010

.111q0

._i_o

-.191_0 -.187_O-.18A30 -.lP_O

-,18410 -.18r',_O-•16930 -.17n_0

-.16980 -.17_I0

-.14150 -.14_00

-.13720 -,1P_oO-.i1150 -.11_0

-,t0_0 -ilO_O-.06610 -.06_0-.06490 -.06_10-,00700 -,007_0-.00800 -.01070

.05030 .0_0

,08880 ,O@PSO,OlPiO ,070PO,IIPIO ,IilAo,10750 ,I0410

.13330 .13000

-.18600 -.18600-.18380 -.17870 -.17710-.18530 -.18770-.18170 -.1_900-,17390--.17350 -.17720-.16950 -.16300 -,t-53_0-,1_250 -.1#370-,t_580 -.12t_0 -,11330-.11240 -.11300-.10tS0 --_00570 -.0_790-.06750 -.06900-.05960 -.0_580 -.05050-•00900 -°01160-.01050 -.011_0 -.00850

_05530 ,0_380i03960---,0-3660 .... -14i_J6LiO -.....,09410 ,09480 ..........07030 ,07130 ,069T0

,11290 .11230 --.10760 .lOqflO .t0660

,16220 ,1_430 ....

.t3500 .13230

.16020 .14250

.¢_600 .14600

.15740 .15850

.16110 .15670

.16370 .16710

.1_970 .15730

.171_0 .1712017250 .17300

.17780 .17690

.17240 .17610

.16640 .16620

.1721_ - .16880

.15730 .15950

.17200 °16860

.15210 .15210

.15580 .15720

.1676n .16600°17110 .1_770

,l_?mO ,15700 .t6230.13_0 .12560 ,11950 .1t370.16nlo .16820 .17260,t4_aO .13430 .14300 ,129g0

.16_40 ,16390 .16740,15_00 ,15_10. .1-53g0 ..... ,l_'lO.

.16_0 •16440 .16560.15_0 .1_570 .16350 .13620.176_0 .17_90 °17620.17PPO .13_70 .16680 ,16420,17n40 .17100 .17190

.-,16710 .... °1_620- ._1860 ..... _._600- -.1TRIO .17150 .17380.14740 .15670 .15570 .i_450

.15q_O ,15850 .15660

.141nO o16100 .1_670 .15380

.16R_O .16670 .16690°.15_10 .11930 .156.9_L_ .16P-._O-

TABLE III.- Continued

c @,B,6h: -10o)

BETA

ALPHA-PO.O

-{S•O

;io,o

0•0

5°0

*PO•O

_p_'.O

_30•0

_0•0

*4S•O

*,o,o

*_5.0

*60'0

_70,0

+RO,O

*QO.O

0•0 * P.O + 4.0 * 6•0 * RoO +lO•O

..]OlAO-.1147_

-.OA9_O-.04830

-.01IRO-.017_0

oO:6fiO

e97-_0.._gaTo

.1_0

.1_740

.14070

•lo_o

•107g0.179K0

.179A0

• -.[_710

.14RAO

........ _s_n.T_7_o

.lP110

.1_870.... .17470

-.13_10-•17460-•17450

-,10660-•1o950-•07060-•08PSO-•0_090-,061t0-•01060-•01780

•O_P80,03q90

•08000.,t0_]0

•17750•1_?0•t4740.14i80•IP_tO

•16400.•11_40•17_30,14170,18100,14R60

.,1.6_0•14100

•15490.13670,14_30.13_nO

• o13_60.11740

•130! 0.116.10.llq_O

,1_410

-.14190-•1P470-•1P350-•t1_70-•_o_o-•1OR60-•07_60-•OAT_O-o.O_3PO-,060_0-,OOq60-•01670

•03670

•08a70.I0970

,17580

,13380,14660•144_0•lP_70

•1_4_O-•lPqqO•18040°13650,17710•1_170,16530-,14_0•15470,l?SlO

,13610

.13_0°13200

,11850o1_630°11360.119_0.1_140

-•i3_6o-•1_?0-•1POLO-•llRPO-,10710-•10770-.07710

-•05440-,0_950-•OlOPO-.o1_60

•039_0•041_0

•o9340,I01_0• 1 ?4qO

• 1 _430

.14K40

.14A70•14370

,13770,t7870

°17100

.!5_oo

.1A_O0

.14860

._5600,13_60.13700

._15_0.13870

.11080,_27n0

.1_50

._]o

-.1_740 -.13_00-.17570 -,128?0-.11760 -,11760-.ltTAO -,11840-.10610 -,10680-o10630 -,10_0-.00360 -,08640

-eOp4?o -,081PO-.0_780 -,05890

-_0_770 -,056t0-.0t470 -,0t480-.0t410 -,01330

.041PO .04170,04140 ,04120.0q830 ,10060.t0080 ..,0(;t830--..13260 .13470

.1_100 ,tSORO

.146_0 ,14860

.14470 °14390

,ISO00 ,161_0

,16t50 ,15030.1_230 ,15810.174_0 ,16750.15970 ,16220,170_0 ,16590.16080 ,16130._A970 .15&9.0

.I_610 .15700

.1_38N ,15440

.14670 ,14720

.14050 ,14310

,1_850 ,12890.13230 ,13100.11610 .i1870

'I_81.0 .12680

e11580 ,I1480.19040 ,I1770.1_650 ,12560_1_0_o ,lzsTo

- 6•_ - 4,0*ls,n .,_0,0

-,l?_RO -,12490-.12_aO -•13270

-,t1_00 -,11770--,1Pt_0-,12_30-,10_=0 -,10830-,107_0 -,10760-,OA_O -,08870-,07_70 -,07220-,O_OVO -,06060-,OF_=_O -,0_i50-.Ol:_O -.01610

-,00_0 -,00870,04naO .0¢130,03QOO .03670• 10_0 ,10340,0_40 ...... ,08870• 13_O0 ,13490

• 12=t0 ,12300• t4_KO ,14530• 14_aO .14400

•,lkKK0 .t6600_t_=O0- -.t3900,17==0 ,t7890,t_=00 ,14510,I7=KO ,17620• t51_0 ,14270

,t5o70 .16710,_4a.10 ol&780-• 15_a0 ,15110• 14_0 ,14050,14_0 ,14650,13nn0 ,12150

,13_60 .13510,11790 ,13800• 13760 ,13120

,I_I_0 ,12920• ]14_0 .I1940,lla_0 ,11550,12_70 ,12360.1_I_0 ,12060

.... 2,,0• 2_,0 +30•0

-,12P?O-.17590 -,12700

-.11840-.17530---,1_240-.10940-.10740 -,10260-,08890-,06820 -•06310-,06130-.04g?O.--.o_r,,s/_O-.-,01770-,01060 -,OIP70

,04060,03_80 ,0_680•10330

-. ,08000.. ._7350--.13250.I_470 ,i1940

.14_90

.14480 ,13480,16630

.,1_5¢0-- -,t-t_0.18010• 13060 ,17270,17980

.14740 .13970

,16670_.14_70- .1_820--..15150.13930 .13290,14620,13310 ,13390,13720,13850. ,13#10.°13530

,1281_ ,12780.11770,11800 .12200.12480.12330 ,12790

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0£90I • O[_[l" O_LOI • O_Ot" OS_II • U_SLt" UUg[L"OEBIL • 0S6I[" OLLd[" O[[ZI • U60_t" U(gLL"

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0£6_I" OBSlI" ObSII • O_o[[" O0_ZI" 0_0_[ • O0_t"09L£I • 02£_l • O_u_I" 0_£I' OO[_I • OL_ _•

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OL_UI' 09[[[ • O[9EI" Ought" 0_8_I" 06_h[" U_oS_ •0[[9l• 066SI • O_bSi • OI6EI • O_EE[" OLUlL •

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019_0 •- 06000 • - 0[I60 •- OVk60"- 09060 •" 08600_" 0_Lb0"-06200 • - 00160 °- O_UO0 •- 0E060"- 096_0'" O_OoO •"

09IOI'- 0£_0l'- O£EOI'- O_uO[ +" O_LOO •" 0_900_" OdLoO'-O_4bO'" 04960"" OO_bO'" 09960 •- 0_960"" O_ObO •"

O0_bO'" 06900"" 04_0['" O?uO['- O_ObO •" OLgO0 _" 0_96U'-O_O0 •- ObSbO'" Ou_bO'" 0090I'" u_O['- UgbOL'"

0•0_* 0'_2" 0"0_* U'_I+ O'OI÷ 0•_ ÷ 0•9 ÷0•2 - O't = u•9 . 0•8 - O•Ol" O'h["

(o0 = qg'_'_)) xo

08_0 •Oub40 •

00040 °O4_LO •O4UOt °OLssO °09gll •

0_0[ •O_SLL •099[L •

09_[t •O_t"

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coTABLE III.- Continued

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ALPHA-PO.O

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ALPHA

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-.14140 -,?_n_O -.08360 -.07670 -o13310

-.33_30 -,26_10 -._0050 -.29240

-.31240 -.31_0 -.30340 ".31820 -.30330

-.42350 -.42_0 -°43210 -,41100

-.41750 -.460_0 -.47370 -.45750 -.41540

-.58_10 -.56170 -.58590 -.57730

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TABLE III.- Continued

ohb_

BETA

ALPHA-PO,O

-15.0

-iO.O

- 5°0

0o0

+ 5.0

,10.0

,is.n

*PO.O

+PSon

*30.0

'35,n

+40,0

+_5.0

*KO°O

,65.0

+_0.0

+70.0

*AO.O

+_0.0

Cm(G,B,6 h = 0 O)

-_0.0 -P_.o -PO#O0.0 + P.O * 4.0

.OqTAO .071qO .06_10 .043o0.01_70 .OONtO .00_30 ._00_0

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.0_4_0 .01_70 .01q40 -.NO_QO

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.eO_4PO -.0_90 -.036_0 -.04_60

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.O_SO0 .OOgO0 -..05PO0 -.n6100-.OR3_O -.0_170 -,Oq?lO -.I_A?O

...00100 -.05_00 -.06000 -.Qq_no

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-_OAPkO -,ORO80 -,I_i?0 -._01o._Og100 -.01800 -,06500 -,0_00-.073A0 -.0_10 -.10530 -.10_00

+,

-.1_00 -,14_00 -.17300 -._7_00..

-.I_1_0 -.14_60 -.14_70 -.15_10-.3R300 ..3qRo0 -.RR_O0 .-._RTO0

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-_6_300 -o6300_ -.61600 -,_1600..618a0 -.61630 -,60_0 -.A0730

-i_.o -10.0 - 8.0 - 6.n - 4.0 - ?.0+ 6.0 + R.o ,10.0 +l_.n +20.0 ,25.0

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.00220

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-.34440

..47880

-.63810

bo

TABLE III.- Continued

8ETA

ALPHA

-70.n

-]5.n

-10.0

- 5.0

0.0

+10.0

÷15.0

¢70.n

+75.0

+30.0

+35.0

+40.0

**5,0

+g0.0

÷_5.0

_AO.O

+70.0

eRO.O

+gO.O

-90.0

rnTnno

-.171qn

-.0_4q0

T?]12o0

-.117oo

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-.1_0_0-.oq7no

1.1_48o

-.00700

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-=10_0q

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-.A0010

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-25.0

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l,Oq_SO

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--,18_20

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1.12530

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Cm(_,8,@ h : i0 °)

-15.0

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--.15Q00

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-._97q0

-10.0 - 8.0 - 6.n - 4.0 - 2.0

+ P.O +10.0 +l_.n *?0.0 *_5.0 ,30.0

-.07780

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-1_700

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-.28440

-.48770

-.47870

-.59090

- 61090

-.09640 -.O0_O -.08550 -.OR150

-.07430 -.02_g0 -.00400 .00340 ,02680

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TABLE III.- Continued

t_

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ALPHA

-]0.0

0.0

$ 9.0

*i0.0

*15.0

*PO.O

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*30'0

$3S.0

¢40.0

$45.0

+_0.0

+_5.0

+_0.0

+?0.0

+80.0

+00.0

Cm(_,8,6 h = 25 ° )

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-.10600

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Oh

TABLE III. - Continued

Cm, lef (_' _)

BETA

ALPHA

-_0.0

-I_.0

-]-0. n

0.0

,** 5.0

*iO.O

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¢_0.0

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-20.0

O,t)

-.OKO_O

-_lnl_n.0_510

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-sOmOAN

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• 2.N

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-._2170

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-.nl_40

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-.0_080

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LO

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TABLE IV.- LEVELS OF ROLL-RESPONSE DEGRADATION

AND CROSS-AXES COUPLING FOR VARIOUS

ROLL-RATE LIMITING TECHNIQUES

Scheduling

parameter

6h

Initial

roll-response

degradation

High

Moderate

Low

Cross-axes

coupling

Low

Moderate

High

TABLE V.- COMPARISON OF ROLL RESPONSE TO

FULL LATERAL STICK INPUT

Control

system

A

B

C

a, max '

degAt_:90o

-21.5

-16.1

-21.5

2.6

3

2.6

At@:180o

3.8

4.3

3.9

92

TABLE VI.- THRUST vALUES uSED IN sIMULATION

m 3 0480

(a) SI units

ThruSt values at an altitude, m, of -

9 1446 096

12 19215 240

Tidle 7 5625 916

0.2 2 824 1 890 3 069 4 492 6 783iii i 535 3 358 5 026267 -l 334 i 557 4 048 6 049

.4 -3 158 -i 099 2 669 4 893

.6 -4 537 -5 782 -890 3 i14

.8 -12 010 -8 451 -i 521-6 227 -2 647

-16 013

i. 0 Tmil 6 227

17 970 i0 987 6 939

0.2 56 401 40 699 28 080 II 56512 632

.4 56 089 41 420 29 401 19 082 7 384663 14 456

.6 56 223 43 764 31 536 20 728 8 58527 133 16 902

8 55 ill 45 263 34 472 23 i0 275• 43 804 35 806 l

51 9531.0

Tmax iI 565

32 573 19 727 12 610

0.2 95 276 69 834 49 929 22 24074 993 54 488 36 269 14 30041 300 25 354 17 570

.4 i00 970 84 112 61 204 30 51B49 440 22 494

.6 107 820 9B 742 71 057 38 44059 977

.8 115 959 81 398128 485 103 723

1.0

(b) U.S- customary Uni%S

• values at an altitude, ft, of -

__y oooom 0

I 1 360

1 i loo

1 130

910

600

-200

00' 12 680 9 150 1 560

0.2 2 610 9 312 i 660

3 950

_o

¥

w

Z

\

\

\

\

\

\\

\

\

×

Figure i.- Body system of axes.

T5.Ol

L15.09

Figure 2.- Three-view sketch of airplane configuration.

All dimensions given in meters.

95

<oO_

Figure 3.- General arrangement of Langley differential maneuvering

simulator (DMS) facility.

................................................. L-73d6831

Figure 4.- View of cockpit and visual display within one sphere of DMS.

97

GO

Figure 5.- View of side-stick installation in simulator cockpit.

M

an,

g units

deg

deg _too

-200 L_l

deg

2001

lO0

0

-100

-200

\\

I \\

__fl I /'1SO00 !=_,__ _

h, 10000 ---_ .... =--_= ....i

O0 5 I0 15 20 25 30 35 _0 _5 50 55 60 65 70 75 80 85 80 95 itl_8.Time, sec

Figure 6.- Time histories of target motions in wind-up turn task.

99

M

.3

.6

.3

0

g

q

2 /0

deg

_0

2O

0

i00

-lO0

L --_-_

_ _-_ b--- _ -_- ._._ _ ___ _ ._---- _ _ _ .__/

lO0

(o,0

deg _Ioo

/k

f

i00

_' 0

aeg _loo

f7 f _._

i0000

h, sooo

mo

o S 10 1S 20

Figure 7.- Time histories

2S 30 35 u_o qS

Time, sec

of target motions in

SO 55 60 65 70

bank-to-bank task.

i00

Id

deg

L%

m

\\L

\

'\

-9

-_-000

0

histor-'es_ of target motions in ACM task.Time8.-Figure

CL

2.0

1.6

1.2

.8

.4

I i l I l I i !

5 I0 15 20 25 30 35 40

_, deg

Figure 9.- Untrimmed lift characteristics of simulated

configuration. _ : 0 °.

102

.4

6h

0 0°

[] +25 °

<_ -25°

Cm

-.6 i i i 6 i l i !

0 20 40 60 80

c_, deg

Figure i0.- Variation of pitching moment with _ for various stabilator

deflections. Center of gravity at 0.35_.

103

24

.20

.16

.12

, O8

.04

m 0

-.04

-. 08

-.12

_-.16

-.20

_.24

-.28

-30

[_]_6 h +I0°(Sh +25°

I I j ! i I I I I I I

_25 420 -15 -lO -5 0 5 lO 15 20 25 30

B

Figure ii.- Variation of pitching moment with sideslip for

various stabilator deflections. _ : 25 °"

104

.016

.012

.008

Cn{3' CIB' .004

CnB,dyn J

per deg 0

-. 004

- .008

-.012

-.016_ I

0 5I0 15 20 25 30 35 40

c_, deg

Figure 12.- Variation of lateral-directional stability characteristics

of basic configuration with angle of attack for scheduled leading-

edge flap deflections. 6h = 0°"

105

.06

_Cn

.05

.04

.03

-.02

(_ = -- 0

6_ = _5°

•06 -

ACl

.o_

aa = -20°004

.03

.02

.Ol

0 5 lO 15 20 25 30 35 40 45 50 55 60

_, deg

Figure 13.- Variation of lateral-directional control derivatives

with angle of attack. _ : 0 °.

106

LCDP,

per degree

.020 -

.016

.012

•008 -

•0040 1

-.004

-. 008

Augmented

Normal

response

_-_Reve.rsed

response

Basic

0 5 l0 15 20 25 30 35 40

c_, deg

Figure 14.- Variation of lateral control divergence parameter (LCDP)

with angle of attack for simulated configuration.

107

i

ti12

sec-I

1.5

1.0

.5

0I I I I I I

5 I0 15 20 25 30

a, deg

SAS onSAS off

P11

sec

5

4

3

2

I

0

I I I I I I

5 i0 15 20 25 30

a, deg

(a) Dutch roll mode.

Figure 15.- Variation of airplane dynamic lateral-directional stability

with angle of attack for airplane with and without SAS. h : 9144 m

(30 000 ft); velocity for ig; level flight.

108

1

6

4

2

0 5 10 15 20 25 30

a, dog(b) Roll mode.

SAS onSAS off

1

t1/2

sec -1

.4-

.3-

.2 -

.1 -

0

()

5 I0 15 20 25

el,deg

I

30

(c) Spiral mode.

Figure 15.- Concluded.

109

P

V

(a) _ = o°.

X

V

(b) _ : 90 °.

Figure 16.- Illustration of kinematic coupling between

angle of attack and sideslip.

ii0

P

P stab _i

(a) Pitching moment created by roll and yaw rates.

x.

(b) Yawing moment created by roll and pitch rates.

Figure 17.- illustration of inertia-coupling phenomena.

iii

_0

EZ, 20

deg o

10

13, 0

_eg - 1o

80

_o

P' odeg/sec

-q@

-[30

d

C

/%

J

M/

_,_\] ,_. v

A A

qO

r, 0

deg/sec -_-o

/" _-x

\ /

,f

qO

q' 0

deg/sec -_o

100

O

deg -10o

_00

200

Pcom, 0

deg/sec-200

-LIO0

(

i00

Flat' o

N-I00

0 S 10 15 20 25 30 35 _0 u,5 50 55 60 65 70 75 80 85

Time, sec

9O 95

Figure 18.- Time histories of ig stall to limit angle of attack.

Control system A; h o = 9144 m.

112

.6

_, i000

deg -loo

_, t°°°

deg -too_

6a ' 300

deg -30

5d, i°o

deg - 10

6r, 300

deg -30

6h, 200

deg -20

g units

_00°Yped, .

N -_oo0 5 10 15 20 25 30 35 q0 q5 50 55 60 65 70 75 80 85 90 95

Time, sec

Figure 18.- Concluded.

\\\

\\

\\

113

Q:,

deg

deg

_0

2O

0

3O

2O

10

0

-]0

\ /f _\

/_'J \ /'_,.j

f

_/

p,

deg/sec

120

8o i

_0

@/

j_.. /\/ \

/ \/

r_

deg/sec

q_

deg/sec

deg

80

40

0

-40

. r- _L_._

200

tO0

0

-100

-200

/ / /

_/ /--- /

/ // // g

qO0

Pcom, 200

deg/sec o / /'°°o I /

0 2 L_ 6 8 10 12 1u, 18 18 20 22 2q 28 28

Time, sec

Figure 19.- Response to full cross-control input at d : 25 ° .

Control system A; h o : 9144 m.

114

an,

g units o

M.6

.3

0

I

ioow, Ol

deg _1oo

Op

deg

loo

o

-tO0J

i

6a,

deg -3o::\

6d,

deg

lO

o

-10

f

Y

6r,

deg

30

0

-301\/ \ I/ "\

5h,

deg

u,o

2o

o

-20

\.___ /

/ L

gcom •

g units': II IL

o

o

Fped, _u,ooN

-8000 2 6 8

I/10 12 1_ 16 18 20 22 2_ 26 28

Time, sec

Figure 19.- Continued.

ll5

t_0 i

Cl, @ i

deg/sec2 __ t

_--- V7 J---A

Cticl,

deg/sec 2

B@

40 ....

-_@

_j

/\

40

qa, 0

deg/sec 2-4o

80

4O

i', 0

deg/sec2 4oiFf "_

40

i.icl, o

deg/sec 2 -40

-80 I

q@

/'a, 0

deg/sec2-_o ---

f_

--I

40

w' 0

m/sec 2 -4@

F\

VCacl_

rfl/SeC 2 0 .I-,/ \ _'

4O

--,_Wac°' 0 ---_ _ _ / -- _" _-/

-80

Wa, o[_[5._I I ___J I 1 I I I I LJ I I I I Im/sec_ qol I i I I I I I I I I I I I I TT59-TTI I I I I I I0 2 q 6 8 10 12 14 18 18 20 22 24 28 2B

Time, sec

Figure 19.- Concluded.

116

deg

20

0

deg

2°!_10

0-- I-10

i /z \/ /-",._,.._ -

p,

deg/sec

qO

0

-8[

-12_

r\.,

\

qO

r, 0

deg'/sec. -_to

qo

q' 0

deg/sec -_o

I

deg

2o01 IlO0

-iO0

-200

I ],//

i

qO0

200

Pcom, 0

deg/see

-200

-qOO

J

] _ II l

I i

I00

i 'Flat, o V;N -100 ,

0 2 q 6 8

/' I/ , /10 12 1u, 18 18 20 22 2q 26 28 30 32. _u,

Time, sec

Figure 20.- Response to cross controls applied in accelerated

turn at limit angle of attack. Control system A;

h o = 9144 m.

117

an,

g units

,9

M .6

.3

0

o

_' -tO0

deg -2oo

O)

deg-tOO

30

5a' 0

deg -30

1O.

5d' 0

deg - 1o

30.

6r' 0

deg =so

Li0

2O

5h' 0deg

-20

lO

gcom, 8

g units o.

0

FP ed' -_ooN

-8000

/\r

2

/

I

_J

f

1 t \j

\/,_z" x

/

f/

/.,.

JI</I' 1

6 8 10 t2 I_ 16 18 2D 22 2q 26 28 30 32 3q

Time, sec

Figure 20.- Continued.

118

^11 t /:deg/sec2 -_0

/ticl, _o ! ! /-" \

deg/sec' o I i / "-" --''t-_S.

j --J %.q&' 0 \, \

deg/sec__L_O "- ..- _ ,

F_

deg/seC _u_OJ

ricl' 0 _"- f J Fdeg/sec2k_o _ "-_

m/sec2-__o

/- -_ // \,Wacl, Li° / \ / \,

mlsec 2 0 " _J _'---J' \_j_

-L}O

Wae2, o. -,. . " % -m/see 2 -qO.

O. ' ' ' £-J-4-_1

m/sec2 o: 2 Lt 6 8 10 12 l_ tb t_ 20 22 2

Time, see

Figure 20.- Concluded.

119

70

Nose-up inertial-coupling momentAvailable nose- downcontrol moment

60q2 = 3556 Nlm 2

50

Pitching-momentmagnitude,

kN-m

40

30ql = 1778N/m 2

20

! I

,o I i' I

I iI , I , I I I

•m ,1_

0 20 40 Pl 60 I)2 80 100

Pstab, degI sec

Figure 21.- Comparison of inertial-coupling moment for increasing

roll rate with available pitch control moment at two values

of dynamic pressure. _ = 25 ° .

120

_p

deg

6O

qO

20--

deg

3O

20

10

0

-10

-20

-30

/,

/\,\

/ /

P*

deg/sec

120

80

_0

0

-YO

-80

f

/ \k)

F

40 _ _ /

r' 0 Kdeg/sec -qo-f t\/

qO

q' 0

deg/sec -40-

deg

200

tO0

o

-tO0

-200

Rn,

g units

qoo

Peom, 200

deg/sec 0

2oFU4+-¢1_,, ,-444-¢K_

]Ylat,N

o

1oo[<deg -1oo

@, 0 _-

deg -too -

6a' 0 _ / -Ideg -30 _

_°1 I 2_

deg -ao

/ / \/" _

,,'- \ / 6 h, _ ,/ d I r

I / 1"/ deg O_2o _- f "_

} o

'°°o//tt_ / [ '_,_.'°°o[I I 1/ 140 2 q 6 8 10 12 lq 16 18 UO N 0 2 q 6 8 10 12 lq 16 18 uO

Time, sec Time, see

Figure 22.- A 360 ° roll attempt using full lateral stick input applied

from ig flight at _ = 25 ° . Control system A; h o = 9144 m.

121

qo

el, o

deg/sec_-qo

8O

_licl, 40

deg/sec _ 0

-qo

\ f \i ,J--..

- /

qO

qa, 0

deg/sect_4 o

4o

o

deg/_-_c'_40

IX_ F__

i"/k]

qO

i'iel, 0 _.a._,_,._lw_c t -40 "" "

_f

rio

ra, 0 s_'" \ /\ it ..,i

@' o -_-- \, \s Jm/see* -40 _/

qO

wa_o, o _.__-_ I/"_ _\ /\__' - _ \/ I

*" °ofm/sec2-q 0 2 q 6 8 10 12 lq 16 18 20

Time, see

Figure 22.- Concluded.

122

C[,

deg

60

qO

2

I I

I

' 11i'lll' I 4 I

30

20

10

B,

deg o

-10

-20

-30

/liI

/ /I / titt"III\ i

tt0

P,0

deg/sec-tJ0

-80

-120

120

80 '

t

I

I III,Y

I

'fII

l,8O

1",

deg/sec 0

-40

1_'L[IlillT_

8O

qOq,

deg/sec 0

-q0

,I, t_+t_',, , ,2001

$, i0_

deg-loo

-2001 ll! _ ,

I I

I -+

!

I

Pcom, 200 Ideg/sec 0 1/

-200 I

1°o,[ -1 /1![I_,_,, _l IL r 1N -1o_ I I' II I0 2 q 6 8 10 12' lq 16 18 20 22 2q 26 28 30

Time, sec

Figure 23.- A 360 ° roll attempt using full lateral

stick input applied in an accelerated turn at

limit 2. Control system A; h o = 9144 m.

123

an,

g units2

0

/

M

,9

,3

0 ¸

0

W, -lO0

deg _oo

x _J

I

100

_' 0 -----

deg -i00

3O

5a' 0\

deg -3o

IO

6d' 0 \

deg -_o

3o

5r' o "_- /_ /

dog I_ ILlr_

\

_0

deg o - --_..._,_ / \

-20

10

gcom, 5 /

g units O. J/-

-5

F,ped, L_O_N O. 2 L_ 6 8 10 12 tLt 16 18 20. 22 2LI 28 28 30

Time, .sec

Figure 23.- Concluded.

124

deg

EtO

2O

0

j-- --,_ ....

deg

20

]0

0

-10

-20\

120

80.

qO.

p)

deg/sec O.

-qO

-80

-120

./

1 _ ,

deg/sec

8O

f /

qO /"-" / \ / \ / \/_ \ \0 / \ / / \ // /

_-,. / \_ / "-. / \ / \\,f

/-

q)

deg/sec

_o llilllIllllll Illlllllillillllllilllllll III

tO0 _-_ /--..., _\ / \, / _. ,¢' 0 / "" t: t

X .j X / "/ I" \\deg -10o -,i / \ / \/ ---* '--'--'

EtO0

200

Pcom, odeg/sec

-200

-EtO0.

\ . 1 t \

Flat,N ,o:, j].... -t

-100 .......0 2 LI 6 8 10 12 let 16 18 20 22 2Et 26 28 30. 32 3q 36

Time, sec

Et2 EtEti

Et6

Figure 24.- Bank-to-bank reversals using maximum lateral

inputs applied from ig flight at _ : 25 ° . Control

system A; h o : 9144 m.

stick

125

an,

g units0

M.6

,3

0

deg

100

0

-100

fl -.. f _. f

deg

i00

0

-I00

p

6a,

deg

3O

-30L____J

(-- -- ____

Lf

6d,

deg

10

o \_j10

/ \ //

\ /

\/ "\

6r,

deg

30

0

-30 1

/

\I\_

/

6h,

deg

N0

2O

0

-20

_f

//

/

/

\-/

/

\/ J

/V

// ,:t / I / \

- / v- i/J

10

gcom, 5

g units0

Fped ' _00

N 00 2 Li 6 8. 10 12 1F! 16 18 20 22 24 26 28 30 32 3u_ 36 38 L_0_ u_2 u,u, _6

Time, sec

Figure 24.- Continued.

126

'°[L _ ',deg/sec2 __o I I" V \]

+o / \ /\_iei.,_°_ -,, ,,_ "' \ /

-q0

,__

,4

/

/-.

'4'

G) \

/\ t--\ /'., / ,-,'\j ,,.. ,....

i-, o /-_- /- x,--,,., v,/ h

deg/sec2_tio I I I I _//

i%

\\_/ x_

+,. Oo t -m/see '::'-_t 2 I llllTllVIO. 2 14 6 8 10 12 lq 16 18 20 22 . 26 28 30 32 3q 36 38 qO q2 qq q6

Time, .sec

Figure 24.- Concluded.

127

Maximum

roll

ratet

deg I sec

200 -

180 -

160 -

140 -

120 -

100 -

80

60

40

20

\

\\\

Roll-control limited

'""--'-'_ Pitch-out limited

,. SM =0.02

_'_t_, _m =-0. 04

II

SM =-0. I0

I I I I i

0 .5 I0 1.5 20 2.5

a, deg

Figure 25.- Variation of maximum roll rate with _ for

various levels of static margin, ig flight;

360 ° roll; h o = 9144 m.

128

+<b-

I

+

-- (Pcom) max

8h ,cl

E,]Figure 26.- Roll-rate limiting scheme used in control system B.

50UD

320

280

240

200

( Pcom) max, 160

deg/ sec120

8O

4O

0I I I I I

5 10 15 20 25

a, deg

Control system A

Control system B; 5h : trim

Control system B; 5h : +25°

Figure 27.- Variation of maximum commandable roll rate

with _ for ig trim.

130

Ipl

0.67

s+ 0.67

38.4

(toa

Z_ap

limiter)

Figure 28.- Pitch-axis modification used in control system B.

Aap, deg

2 -

I

0 I0

I

20 30 40 50 60

I p I, deg/ sec

Figure 29.- Variation of A_p with roll-rate

magnitude for control system B.

131

an, 21111111_1ol I I I Iq-I I I I I I I I I I I

g units

$

.6

M

o

deg

p_

deg/sec

r_

deg/sec

qO

2O

o

I0

0

-Io

8Of_

--- \_0 /"

/ \0 11 ____

io0_J" _ k_

Ol _J--_

deg _lOOi

too

O, 0 ---"--.

deg _tOO

3O

6a,0 \ /_

deg -3o

10

A,,.5d' 0 \ .--,----"ee' - 10

_0

q' 0

deg/sec -Lm

f

30

6r" 0 \ i-deg -30 ,-_I"I-

200A

1O0 ///

_' 0 ///

deg /

-loo /-200

2001 IPcom,ol I/I I I I I_

deg/sec

1N 0 2 q 6 8 I0 12 lq 16

Time, sec

qo

6h, 20 _ / \/

deg 0 "

-20

10

gcom, s

g unitso

Fped, _00°N 0 2 _ 6 8 io t2 {_ t6

Time, sec

Figure 30.- A 360 ° roll initiated from lg trim at _ : 25 ° using maximum

lateral stick input. Control system B; h o : 9144 m.

132

deg/sec2-_o I

/lid, 40

deg/sec2 -40

deg/sec'-40

40

÷a, o

deg/sec: -40

40

w, 0

m/sec2 -40

4O

wacl, o

m/sec2 -4o 1

J

__JWac2, o

m/sec 2 -qO

m/see2 -400 2 4 6 8 IO 12 14 16

Time, sec

Figure 30.- Concluded.

133

deg

deg

_o

2o

o

lO

o

-10

f,/

/

//

120

8O

qO

P,

deg/sec o

-_0

-8o

-120

/ \\

/ \

r, 0 ,_._L / ""_

deg/sec -qo

q_

deg/sec

qo

200

loo /¢, /

deg 0 \ / , / --- --

- 1O0 /i-200

200 --'-_

Pcom, 0 / -_

deg/sec-20o \/v

too

Flat' 0 [ /

N- oo \/o 2 '4 6 8 10 12 lq :1.8 18 20 22 2q

Time, sec

Figure 31.- A 360 ° roll initiated from accelerated

turn at limit d using full lateral stick

input. Control system B; ho : 9144 m.

134

an,

g unitsI

o t ----

M_ ].3

O- [

_JJ_

deg

loo _ t -Jdeg _ioo 1

deg -3o

6 d, 0 " -, _ -/

deg - 1o

_o_ l j-_-_5r' 0 ""_

deg -3o [ \ JF_-

6h, 20 _-/

deg o - I / /

-2o - I /

lO /gcom, 5 -

g units 0 / [

'_o_'_°°I ill 1 tN °o 2 '4 6 8 10. 12 1_4 16 18 20 22 2'4

Time, .sec

Figure 31.- Continued.

135

qo

4, @

deg/sec2 qO

I

8O

_ticl, _o

deg/sec' @j

qO

qa,0

deg/sec2_4 0

:'40

r, 0

deg/seC -qo_ffl

qO

ricl, oJ _/ 2

ueg/sec _L_O

qO

ra, 0

deg/sec2u 0

k

qO

W,0

ITI/SeC 2 -qO

/\

Wac 1 , _,

m/sec 2 \.140

0

qO

Wac2' 0

m/see2 -qO

Wa_, 110 2 14 6 8 10 12 lq 18 18 20 22 2q

Time, see

Figure 31.- Concluded.

136

4O(_, 2O

deg o

10

/S, 01

aeg -Io

8O

'40

P' 0deg/sec

-40

-80

/

i

/\

/

/xJ

'4O

r, 0

deg/sec _LiO

i- ..-4 ..-4\/ _\ / \ /_\ , \

/ \"\_ \ / / \ 1/ \

\

x_+

f_/

'40

q' 0

deg/sec _u,O

_ooI¢' 0

deg _ioo

1 \ / "\ / /\ / t \ /

I

\ i/

I

'4OO

2OO

Pcom, 0deg/sec

-200

-qO0

' < / J \ J _ i\\ i _f \_ i \..._ / \ /

'°°- , C--Flat, oN

-ioo ) - --0 2 4 6 S 10 12 1'4 16

l-- t /__F_ L__J

18 20 22 2'4 26 28 30 32 3 u, 36

Time, sec

Figure 32.- Bank-to-bank reversals using full lateral stick inputs

initiated from ig trim at d : 25 ° . Control system B;

h o = 9144 m.

38 '40,

137

an,

g units ____ _._+-_+....__f _j_f-_j

.6M

.3

deg

1o0

o

-i0o

ioo

(9, O_

deg _ioo

3o

6a' 0\

deg -3o\ \._J

I0

6d' 0 \_deg -lOi

30

6r' 0

deg -3o _ _\ i j J

t/_o

6h ' 20

deg o

-20

f_/

/ \\ /i\ /

J K/

\ .-\ / " //'\Ik/ J \ \/

/j

1o

gcom, 5

g units o

Fped ' _o_[N0 2 q 8 8 i0 12 lq 18 18 _0 22 2q 28 28 30 32 3q 38 38 qo

Time, sec

Figure 32.- Continued.

138

6EI

"p_pnI_uoD -'Z[ _an6T£

I I o_

__ _ 0_- :oa@/ui

_'_--/-- O_

0t7- _ODll/lll1 0 'Ill

f

/ -_ f" _J

0tl

f o , IaT_

0t7

t ¸ JJ- rJ _J

iOh

I,m \ \\ \ \ \ \/,'I"_

I

I

<z

08-

0t_- pas/_ap

0

O_

"/ I_ , \../'\ / \ /" --._/

11 ¢ 1

- o ,ia!b

Oh

50

deg

20

/3, I0

deg 0

-i0

80

YO

P,0

deg/sec-50

-80i

50

r, 0

deg/sec -YO

50

q' 0

deg/sec -_0 -

/-

_/

I

/j/-\ /.f \

_1_f\ / \ f._.4-./ "._

\ /1\

.I i "x _ //_ _ \

k_

200

I00

qb,0

deg i

-too

-2001

/ /./

/ //f ,/

/ /' /

/

500

Pcom, 200

deg/sec 0

-200 _'v b

f

/ "" \ J \l

tOO

Flat' o

N //////-100 v v v

0 2 Y 6 8 10 12 lY 16 18 20 22 25 26 28 30 32 35Time, sec

Figure 33.- Response to full cross controls applied in accelerated

turn at limit _. Control system B; h o = 9144 m.

140

an,

g units

/2 /0

M

.g

3 I0

_, o _11 I I I I_F--LII I t_---4_ I II I I I I I _ [deg -too I I I I I I I_ I I'_ I I 1_ I I t t i

looI I0, 0 - ---+--- _ -. _._7 _ J

deg _t oo I

30

5a, 0 .A ,-,_[ \ ^',

deg -30 I .....

d

10

6d, o -_ t, _.[__deg -lo

,,zJ

3O

6r' 0 "

deg -30

/_ _\_ _ I_

I

u_o

6h, 20

deg o

-20

/ ",-,_

gcom •

g units

loI5 ¸

0

//

0

Fped, -_ooN

-8000 2 q 6 8

I /i0 12 lq 16 18 20 22 2q 26 28 30 32 3q

Time, sec

Figure 33.- Continued.

141

_0

el, o

de'g/_c2 -40

qO

/ticl, o

deg/sec2 _um

/',.1

f_ .)\

_0

qa, 0

deg/sec240

4o

r, 0

deg/sec* 40_v

\ F_

40

{'ict, o

deg/sec2 40

40

ra, 0

deg/sec2_4 o

40 _,

w, o " -__ ,m/see 2 _40

80

Wacl, 40 /_ /

m/see 2 0 _ j "

-u_o

x,

\/r--

40

_rac2' 0 _. _ _ -m/sec _ -_o

_r a, o_ I I I I I I_IA._I I I I I I Im/sec_-4ol I I I I I I _ I I I I 1 I 1 I I I I I I I I I I I 1 I I0 2 q 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34

Time, sec

Figure 33.- Concluded.

142

[_,

deg

deg

8O

60

qo

2o

o

_o II

i°o- -_ \

-io

-2o

-3o

//

i

I/

\\

!

/

/\v

i

an,

g units

M

2 IIIAIII

O.

P,

deg/sec

120

80

_o /0

-qO

-80

I,I/ \v

i \ f_

L

io:.0, -- l

deg -too \ // _._

deg -3o i -

qO "/f _"d

r, 0

deg/sec -_0

f IO6d' 0

deg -lo

q' o J/

deg/sec _o_oI _/,\ /_. ,--.1; 5r, o ,\ \,

deg -3o \ / _"

200

i00

$,

deg o

-i00

-200

./

J

,/

l/

\ /

Pcom,20_J_--t4 tdeg/sec

_oofl IYlat, 0 i :

N -1oo I_0 2 L1 6 8 i0 12 lq 18 18 20

Time, sec

L_O" @--i_ ' F---_

5h ' 20 / -_

deg 0 / f -

-20

gc°m"li L Ig units

/ [FP ed' _oo. /N o

0 2 q 8 8 I0 12 ILl iS 18 20

Time, sec

Figure 34.- A 360 ° roll attempt applied in ig flight at d = 25 °

using full coordinated stick and pedal inputs. Control

system B; h o = 9144 m.

143

4O

q' 0

deg/sec2-qO I

\

60

_ticl, _o

deg/sec 2 o

-qo ]

/

qo

qa, 0

deg/sec2 -_0

\-.../

rio

i_, 0

deg/seC -_0

-80

\ r" _x4

40

i'icl, o

deg/sec2 -40

_0

÷a, o -"_- it...

deg/sec2 40 _ _--'-_--, / '--/

80

_r, 40 / \m/sec' 0 - -----" - -_

' v l/\j \/-40

ffacl, o _ / -... r

m/sec 2 -4o

Wac2, 0 _1 \i/ \/ / \/m/sec i -40 4

_ra, oH__+___l I I

m/sec=-4ol I I I I I I I I I I I I I I I I I I I I0 2 q 8 8 i0 12 lq 18 18 20

Time, sec

Figure 34.- Concluded.

144

Fped

Commandgradient

ii

-F-30

_/_._ 489.

Scheduledgain

0 . 0

I ScheduledgainII

IIIi

201p140

lpl--]

-III

I _ 6r,co mI

III

j m

(a) Yaw-axis modification.

Figure 35.- Modifications to yaw and roll axes incorporated in going from

control system B to C (modifications enclosed in dashed lines).

Oh

+

ai+

I

6h'c

+

I

II

I

+ iI

II

I

I

Scheduled gain

I

0

30 Ip1.50

(b) Roll-axis modification.

Figure 35.- Concluded.

an,

g units

M

2 I

.6!

0

deg

tO0

oeg _too

B, 0 "-.._j-

deg -io

1O0 [__...

deg _too

80 1-x/

P' _o /J \deg/sec o J "b---___

3O

a_6a' 0 \ j._./"-+'_'_ee -30 _

deg/sec

_0

q' 0

deg/sec -_o

(_,

deg

200!

tO0

0

-tO0

-200

/

./

/,/V

I

/

10

ue_ -i0

30

6r' 0 / _'--+_b_

deg -3o \ / _

cto

,....._ -'_

6h, 20 /"" i\deg 0 "_

-20 [

_00

Pcom, 200

deg/see 0

i0

gcom, 5g units

0

Flat,N 0 2 q 6 8 10 12 tq

Time, sec

Fped, _000N 0 2 q 8 8 10 12 lq

Time, sec

Figure 36.- A 360 ° roll initiated from ig trim flight at _ = 25 ° using

full lateral stick. Control system C; h o = 9144 m.

147

_0

ct, o

deg/sec_ __

deg/sec 2

_0

qa, 0 ---. /deg/sec2-_o "_

r, 0

deg/sec 2__01

rio

i'icl' o

deg/sec2 -_o

i'a, ol

deg/sec 2- _ o !

qO

w' 0

m/sec 2 __o

qO

Wacl, 0

m/sec2 __

j/L

_0

W at2, 0

m/sec 2 -btO

m/sec2 -_°o 2 q 6 8 Io 12 lq

Time, sec

Figure 36.- Concluded.

148

an )

g units

M

2 I

,3o I

CI,

deg o

io

B, o /" \

deg -Io

P' _io \deg/sec 0 \

deg/sec

q' o _--

deg/sec -_0 - 1

,oo1IC. -deg _1oo

ioo I /deg _too

6a, 0 fJ

deg -30 _-_ <

'°II 6d' 0 --_

deg -Io _'_

(51"' 0

deg -30 i f _ 1

deg

200

100

0

-tOO

-200

//

/

../ i/

/

('_I I

<'°°'/_IPcom, 200 --..._._

deg/sec 0

Flat, t°°ol-I1 I I/ I. I 1 tN 0 2 q 6 8 10 12 lq

Time, sec

_° J,\6 h, 20 .t"_

deg 0 < /

-20

,o i /gcom, 5

g units o-

_oo_

Fped'N _'°°o_- ]

o 2

Figure 37." A 360 ° roll initiated from ig flight at

using full coordinated stick and pedal.

h = 9144 m.o

6 [9 i0 12 lq

Time, sec

= 25 °

Control system C;

149

it, o

deg/sec2 -_o

deg/sec 2 o

_0

qa, Q

deg/sec2 _o

qO

r, 0 \- _ _______- _--

deg/sec2 _o,

_0

ricl' 0

deg/sec2 -_0

fJ

_0 ¸

ra, 0

deg/sec_ _o

w, _'010 i

1TI/Sec 2 -El0

Wacl, o/ 2m/SeC _qO

_0

ffac2, o

m/sec 2 _ _0

m/see2-_ 0 2 _ 8 8 i0 12 iN

Time, sec

Figure 37.- Concluded.

150

u_o

_' 20

deg o

I

lO

0 /'_'- '--

deg - 1o

12_0

8OP,

deg/sec qo

rt

deg/sec

q' 0

deg/sec -qo

f

/o /

j*f

Jf--_ f

_._.-- _._ .._._.I"--"_----- _'-"__ ....

L

deg

2OO

LO0

0

-lO0

-200

J/

/ /1 // / /

//

/'/ / /I'

'_00

Pcom, 200

deg/see 0

oltLLILL 110 " 2 u, 6 8 133 L2 Lq 16 18 20 99 2.q

Time, sec

Figure 38.- Response to full cross controls applied

in ig trim flight at _ : 25 ° . Control system C;

h o = 9144 m.

151

q

an ' 2

g units0

.6

M.3

i00

_' 0

aeg __oo

100

deg _ 100

3O

6a' 0

deg -30

kO

6d' 0

deg -lo

30

6 r, 0

deg -3a

_0

6h, 20

deg 0

-20

10

gcom,

g units o

0

FP ed' -_00

N-800

0

J

__J

\ /

J

J/

/

2. q 6 8 10 12 kq 16 18 20 22 2q

Time, sec

Figure 38.- Continued.

152

qO

ct, o

deg/sec_ -LiO

_J

Cticl,

deg/sec _

8O

_° I0

//

LiO

qa, 0

deg/sec 2_0

-80

_oIb' o'

deg/sec_ -u,O

f_

//

u_O

ricl_, o

deg/sec2 _u,o

, i'a' 0

deg/sec_ -_o

_0

m/see _ _LtO

f

Fu_O!

_'acl, 0

m/sec 2 -qO

f_j

_ I_, IA--J

m/sec2 -qo

o l L "

m/sec2 0 2 ti 6 8 kO k2. kq L6 18 20 22_ u

Time, sec

Figure 38.- Concluded.

153

deg

riO

20 .._-0

deg

I0

0

-i0

/ \ /\

120

80

_0

0

-qO

/\f _j

\

qO

r, 0

deg/sec -_o

J

qO

q' 0

deg/sec -_o

p

deg

200

i00

0

-i00

-200

/

/'1

//

/ // z

, / ff

/ //

/ /

qO0

Pcom, 200

deg/see 0

x° A t0 2 L_ 6 8 10 12 lq 16 18 20 22

Time, sec

Figure 39.- Response to full cross controls applied in

ig trim at _ : i0 °, followed by rapid full aft

stick application. Control system C; h o : 9144 m.

is4

q

an' 2

g units0

•6 IM

.3

0

i00

_' 0

aeg _1oo

IooIG, 0.i

aeg -I00

30

6a, 0

deg -3o

6d',_ 100

_,e_ -Io

30

6r' 0

deg -3o

_O

6h, 20

deg o

-20

10

5gcom,

g units 0

-5

I_ped, __o°o

N-800

o

\/

8 i0 12 lq 16 18 20 22

Time, sec

Figure 39.- Continued.

155

8O

• 1q, _iO .....

deg/sec 2 0 \_/"<_._'_" v_

8O

qicl, _0 / .1

deg/seC o /

-qo

\

qa, o ldeg/sec 2-qO

-80

\ l --- ]

qO

r, o

deg/seC -_io

/, I/-,

_ L/I

u,o

ricl' 0

deg/sec_ -_iO

u_o ,%

0

deg/sec_ -_o

v¢' 0 \

mlsec2 -LiO i

8O

Wacl, _0 / -"\m/sec 2 0

-qO

qO

Wac2' 0

ITl/Sec 2 -qO

_'a, °H--4--LI I I.J_4_-44-1 I _m/sec_-_ol I I I VI_I I I I I I I I I I I I I I I I ]0 2 Li 8 8 i0 12 lq 18 18 20 22

Time, sec

Figure 39.- Concluded.

156

yo

c(, 20

deg of/ "" _ L

M.6

.3

o

IO rB, o / _--_-_

deg -1o

_fp

deg

lOOl

o

-too

J _ _J

120 \ /-x

8o [P' _0

deg/sec J \o

-_o

80

deg/sec . j4 "x

q' 0 i " --- _/deg/sec -_o'

i_),

deg

2o0111 h III.

o Ill Ylll I/I II_,oo!/i)tll 11-2oo I I I I 1'1/ I I / I

tO0

@' 0

deg _ too

30

6a' 0

deg -3o

lO

6d' 0

deg - 1o

306r' Oi

deg -3o

_o

6h, 20

deg 0

-20

f-x

I

I

/ f,f

t{oo

Pcom, 200

deg/sec 0

lO

f"-. gcom, sf // "_" _ _ \ g units o

Flat,

NOo/ / Fped, _0

0 N0 2 u, 6 8 10 12 t u, 16 t8 20 0 2 ti 6 8 10 12 lq 16 18 20

Time, sec Time, sec

Figure 40.- Response to maximum inertia-coupling maneuver.

Control system C; h o : 9144 m.

157

8O

q, _0

deg/sec 2 0

8O

/licl, _o

deg/sec2 oI

/

qa,

deg/sec 2

80

rio

o i\-LiO

-8O

b

qO

0

deg/sec2__ 0

rf%_

i'icl, o

deg/sec 2-LtO

-80

_ f

8O

ra, qO

deg/sec 2 0

qO

0# 2

m/$ec _qo

\)< \ f_

Wacl,m/sec

120

80

_0

o)-utO

y "_' \\,

i

qO

Wac2, 0

m/sec I -_o

-80

Wa, ot-+q, I I I I I I I I I i_

m/sec_-<iol I I_ I FI I I I I I I I I0 2 ti 6 8 lO 12 lq 16 18 20

Time, sec

Figure 40.- Concluded.

158

qO

E3, 20 _-_

deg o

loB, Ol /

,,, deg -lo

80

P, u,O /

deg/sec 0 ._

r_,

deg/sec

qO

q' 0

deg/sec -_0

20O

100

d),0

deg-i00

-200

qO0

Pcom, 200

deg/sec 0

q00

3OO

Flat, 200N

100

00

a n ,

g units

M.6

0

\_J

Up

deg

100!

0

-I00

/J \

so I 1_4--b--LJ I I I I I I I Io _

__<v

//

f/

/

/

/

deg

6a,

deg

6d,

deg

6r,

deg

6h,

deg

100

0

-I00

30

0

-30

I0

0

-i0

\ /f

\ Jf

3O

=3o x, I/

qO

20 _ / \__ /

0 ,F

-20

10

gcom, sg units

0

2 q 6 8 i0 12 lq 18

Time, sec

Fped, _ooN °o 2 q 6 8 I0 12 lq 16

Time, sec

Figure 41.- A 360 ° roll from ig trim flight at _ = 25 ° using

full lateral stick input at a center-of-gravity location of

0.375_. Control system C; h o : 9144 m.

159

q0

ct, o

deg/sec2__@

j_-_ f,..,

deg/sec 2

Li0

deg/sec2 __@

_0

i', @

deg/sec2 _Li0

Li0

/'icl, o

deg/sec2 _Li@

Lio

i'a, @

deg/sec2 -_io

Li0

w, 0

m/sec 2 -Li@

Wacl,

IIl/$ec 2

qO

0

-qO

_J r

v

_0

Wac2' 01 2

m/see -Li0

v

m/sec 2 -LlO0 2 q 6 8 I0 12 I_ 16

Time, sec

Figure 41.- Concluded.

160

deg

60

Lt0

2

1/!1i ¸.

II

_t'! _ 1.1"

li I

deg

lo

o

-lo -

-20

-30

I III!II/1/

/, \_' ' I

I

I

P_

deg/sec

16o:1t20

[_ XI80

J

LtO

0 i

-_0

-80

i • I

r, I

1 ' _ f,\ /

, VlJ_

i

i

/\/ \ / \

\1/

I\'J I

i

8o ii

r, _i .r-[-deg/sec -_o II

Li I

i_-_

q' 0 I

deg/,ec-,oI IIIIIII/HIGH I_11

To°o!_/ h

o. o,l_ lll_' i]-loo I I/ /-2oo, II I[

_OOl tPcom, 200 /

deg/sec 0P\I/1\

I "I-IT It"II IIL

Flat,

N

3ooI

:°oil-100/ I

0 2 '{ 20 22 2lu, 26 ' 28 30 32

Ii

8 10 ll2 lY 16 18

Time, sec

I

Figure 42.- Response to maximum inertia-coupling

maneuver at a center-of-gravity location of

0.375_. Control system C; h o : 9144 m.

161

an,

g units

/

/

M.6

.3

0

100

_, 0

deg -loo

-200

_J

100

deg -1oo

f "----4.._

30

6 a, 0

deg -3o

I/\

I0

6d' 0

deg -10

3o

-- / \deg -30 - "

__/x. /

___2o F r--_ --I (

6 h , •

deg o --- v /-20

-q0

10

f 1

gcom, s 1

g units o

-S

l_ped, _0o

N O0 2 q 8 8 10 12 lq 16 18 20 22 2q 26 28 30 32

Time, sec

Figure 42.- Continued.

162

deg/sec 2

4a, 4_deg/seC /

Z

m/sec_ -qo

_racZ,

ITI / $ C C _

Time, scc

Figure 42.- Concluded.

163

deg

o _-t " - --

8,

deg

,o....... / _ ;o Y_%...F / i

- -<1---lo

_.o t/ j-30 L

80

qO

P,

deg/sec 0

-q0

-80

I _ _ I\ / \/ I

qo

r, o

deg/sec -qO

/

qo

q' 0

deg/sec -_o

0,

deg

qoo

Pcom, 200

deg/sec 0 / \- \

Flat,

N

qoo

300

200 --

tO0

o0 2 q 6 8 10 12 lq 16 18 20 22 2q 26

Time, sec

Figure 43.- A 360 ° roll attempt initiated in ig trim

flight at _ : 25 ° using full lateral stick

input at a center-of-gravity location of 0.39_.

Control system C; h o : 9144 m.

164

an,

g units

M

oI_ I I I I I I 1-11 1 IT-] I IT-I I I I

.6

L III00

deg -Ioo

-200

deg

I00

0

-i00

i __

6a,

deg

30

o \-30

/

6d,

deg

I0

0

"-tO

c_/,,

deg/

\N. J/

LiO

2O6h,

deg o

-20

JmJ

J

//

I/

,o Lgcom, s _.

g units o

Fped, L_O00N o 2 q 6 8 10 12 tq 16 1.8 20 22 2q 26

Time, sec

Figure 43.- Continued.

165

qO

j, o

deg/sec 2-_0

-80

\ /\/\J

qO

qicl, o

deg/sec2 -_0

qO

qa, 0

deg/sec 2 -qo

-8o

qO

r' 0

deg/sec2 -_iO

_0

tic1, oiaeg/sec_ _io]

^,/

LtO

ra, 0

deg/sec2 -qO

/\r

In/$ec 2

tlO

0

-qo

J

qO

Wacl' 0

m/sec 2 -q-O

//_ ¢,

_ / !c' /", . F,.

_ \

_,_... --.,j \

_0 ^ k

_kac2' 0 _+-_ -"\J /!\ !'_ rk'' \\/'\-_\lmi$8c2 -_0

m/sec2-q 0 2 L_ 6 8 I0 12 lq 16 18 20 22 2q 26

Time, sec

Figure 43.- Concluded.

166

80

60

L_Odeg

2Or.e. _I

l

_J

/ / \/'-.._. k_., \/ _t\i

_01 I AI _\ f\

P, o I ------.; I1\ ] V I vdeg/sec -_0 _ L/ V l_'

_0

r, 0 xJ _-

aeg/sec -_o

q' 0 _- -_ __I" .... /deg/se¢ -qo

i "" \x\ ----- -'-"

deg _ 1oo I

Pcom, 2°00 [deg/sec

Flat,

N

0_ ool [ / /.0 5 10 15 20 25 30 35 _0 _5 S0 55 60 65 70 75 80 85 90 95

Time, sec

Figure 44.- Deep-stall entry at a center-of-gravity location of 0.35_.

Asymmetries not modeled; ho = 9144 m.

167

an,

g units

q

0

M

.9

,6

.3

0

i00

W, 0

deg -too

-200

,,%

"--4-.--4--- __ --..- _ _ _ --

0_

deg

100

0

-100

tJ

If "-,-

63.,

deg

30

0

-30

10

6d' 0

deg -1.0

(_r,

deg

30

0

-30

"k j/'_ A A --

_0

6h, 20

deg o

-2o

J

S

gcom, 0 _"

g units _S

Fped ' _00 .

N Uo 5 10 15 20 25 30 35 u,o q5 50 55 60 65 70 75 80. 85 90 95

Time, sec

Figure 44.- Continued.

168

_0

q" 0

deg#ec2-_o

_0

qicl, o

deg/sec2-_{o

_Ol

qa, 6_

deg/sec2-_,o

_0

"r, 0

deg/see2 -qo

ricl: O.

deg/sec2-_o

qO

ra, 0

deg/scc2_Lio

RO

m/_':_:: 2 -qO

, _./" -'_ ...-" , _ "..-4 --

J_

_0.

Wacl: O. _/ -_-

m/sec 2 -'4o. [

_0.

_rac2' O.

m/_c _ -qO_

0 I I I IJ_I'--F-_ I I , . i i

m/secz 0 5 tO 15 20 25 30 35 u,O u_5 50 55 60 65 7[3 75 80 85 90 35

Time, .sec

Figure 44.- Concluded.

169

£00" _0"

]3 u3 'k3

¢

0 1700"-800"-ZO" I0"I I l I

09

OL

> - 06

C){-.

deg

80

60

qO

20

0

_J

2O

_o /, /\ r

\,.,e_ -lo

-3[

I

deg/sec -_0 _/

-80L

deg/se¢ _u,o

_0

deglsec -qO I

100. J-- ,...

m, 0 _-_" "\L I \ / _-',,ideg _ tOO I

_':<, °oil vv LV"""i L ILl L IIN -lo Ill0 S 10 15 20 25 30 35 _0 u_5 50 55 60 65 "70 75 80 85

Time, sec

Figure 46.- Deep-stall entry at a center-of-gravity location of 0.35c.

Asymmetries modeled; h ° : 9144 m.

171

q

g units - -_0

.3

2O0

100

W, /

0 _

deg-i00 -

-200

\ \

"'_-_ \\ \\ \ \

"1'4 \'

i00 ___

9, 0_._ j

deg -tOO

I

30

6a' 0

deg -30

6d,

deg

I0

0

-I0

(51",

deg

30

0

-30/k_/\

qO

6h ' 20.-

deg o

-20

5 I

gcom, 0

g units s i

Fped, _io_ _N o s to is 20 2s 30 35 qo qs 5o 5s 6o ss 20 vs 8o 8s

Time, sec

Figure 46.- Continued.

172

qo

q' o

deg/sec2 _io_'4- _ _ _I-" -" _'_-

_0

Clicl, o

deg/sec2 _u,o

LiO

qa, o

deg/sec2 _o__ ...,- ,_ '....,_Lf _ -'- ._,-,.

r' o!

deg/sec2 -_o

7icl, o

deg/sec_ -_o

LiO

i'a' o

deg/sec_ -_o

u,o

om/sec 2 -rio

LiO

Wacl' 0

m/sec t -qO

_o

_rac2' 0

m/see 2 -qO

m/sec 2-_Io s io 15 2o 2s 30 3s _o _s 5o s5 6o 8s 7o 75 8o 8s

Time, sec

Figure 46.- Concluded.

173

IX. 81ef =25°;6tef =O°;Sh =25°,8sb =0 °

0 81ef = 0°: 8tef = 20°;8h = 25°; 8sb = O°

E] 81ef = 25°; 8te f = O°;Sh = 25°; 8sb -----60°

<_ 81ef = 0°; 8tef = 20°; 8h = 25°; 8sb = 60°

0

Cm

-o ].

, I I I I I

10 20 30 40 50 60 70 80 90

a, deg

Figure 47.- Effect of flaps and speed brake on pitching-moment

variation with angle of attack at a center-of-gravity

location of 0.35_. 6 h : 25 ° .

174

deg

80

50

4O

2O

0

-20

f

J

_J

/%/

/

\ / \J - /_\ _"\

\

deg

20

10

0

-10

-20

-30

i/ .-Ii If,

k/

40

P, o

deg/sec -40

^ n \P A

/ ,/',: Vv /',"

tvd

40

r, 0

deg/sec -40

4O

q' 0

deg/sec -40

Pcom, 200

deg/sec o

Flat' _io°oN

60

6sb, 40

deg 20

oo 5

I10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 g5

Time, sec

Figure 48.- Deep-stall recovery using speed brake and flaps at a

center-of-gravity location of 0.35_. Asymmetries not modeled;

h o : 9144 m.

175

an,

g units

I f__ -_

.J÷t ,,f_f

M .5

.3

1oo

_y, o

deg -too

-200

/

0_

deg

ioo

o

-too

Ii III

6 a ,

deg

3O

o

-30

Io

6d' 0

deg -1o

6r,

deg

30

0

-30

IL

"---/ '-J \/^'v\''_" /

5h,

deg

_0

20

o

-20

-_o

/J

lO

5gcom,

g units 0 _ i

-s I

Fped ' _oo

N O0 5 tO 15 20 25 30 35 qO u,5 50 55 60 6S 70 75 80 8S _0. 9S

Time, sec

Figure 48.- Continued.

176

4Oq' O!F

v

4O

qicl, o

deg/sec_-4o

4O

qa, 0

deg/_c2_q 0

k

V

4O

÷,0

deg/_c240

ricl, 4:

deg/_c24o!

qO.

ra' O_

deg/_c_ _0

i

m/sec 2 -40

Wac2,

m/sec 2 -Lio

"1

40

Wa, 0 ---- ---_-_ _m/sec _ -qO _- -

O. 5 10 15 20 25 30 35 _0 45 50 55 60 85 70. 75 80 85 90 35

Time, scc

Figure 48.- Concluded.

177

deg

8@

60

LtO

20

0/

_f

>

/J

f \\

\

deg

20 I

lO

-lO

20

-3O

A

"// " J/,'IV1' _'

A

\hi \/_,

qO

oP,

deg/sec -_0

-80

\/ _ Vf_/\_

"x

r, 0

deg/sec -u_o/

qo

q' 0

deg/sec -_,0--_. / \j

/

\

100 [ /_ --_.

deg _ioo%/ -_f--

iDcorrI, 0 v vdeg/sec-2OO " T

Flat, ° U I V I VN -loo _

6o

6 sb, _o

deg 20

oO 5 10 15 20 25 30 35 q0 LIS SO 85 60 65 70 75 80 85

Time, sec

Figure 49.- Deep-stall recovery using speed brake and

flaps at a center-of-gravity location of 0.35_.

Asymmetries modeled; h o = 9144 m.

i

J

178

an,

g units

M

_p

deg

deg

6a,

deg

5d,

deg

6r,

deg

6h,

deg

gcom

g units

Fped,N

q

.6

.3

0

-J._-4__/

/

lOOI0

-100

-200

I \ \\

\ \

\

-100

__r_

O' _ ' ^' "_ _ -

-30

lo t I0 "

-'10

-3

2o / X0

-20

-u_o

o " l_ [,

_o_0 5 I0 15 20 25 30 35 40 u_5 SO 55 80 65 70 75 80 85

Time, sec

Figure 49.- Continued.

179

80

Cl, 40

deg/sec 2 0

-40

/\ ./,-, A iX /, 7,-, ,.^'-^ .slV

.#

4O

qicl, o

deg/sec2 -4o

qa, 0 -_

deg/sec2 -4o"" -v_v'-",/ l"" "

4O

r, o

deg/sec2 -40

4O

ricl' 0

deg/sec2 -40

4O

_'a, 0

deg/sec_ -4o

4O

m/see _ _q o \

4O

Wac2 ' 0

m/sec 2 -40

m/sec 2-4 0 5 I0 15 20 25 30. 35 qO 45 50 55 60 65 70 75 80 85

Time, sec

Figure 49.- Concluded.

180

deg

8O

60

_0

2O

0

/

/

1\/>, )\s,.l"; ." _

_Jff

/

fJ

\

2o _1lo /_ %!1

_l / / A/3, o _ t t/

deg -lo / / I t-2o i ts-30 I

[ _ A A

/_jt //_/"_j'_] /

deg/sec -_o L v , I

,I_/,

r\ it\

r_ _,

deg/sec -_0 I

_/--J

_0

j f --q' 0 "\J "-' _" " " Ldeg/sec -_io k j -

-C

100 /eft\ Ld_, O _ _ \, '

\ /_J _" .... i- _deg _1oo " t

J_

pcom,° ,v 1 Ideg/sec -2°°

Flat,

N- 2o vlJ "

0 S 10 15 20 25 30 35 L_O '45 50 85 80 BS 70 7S 80 _5

Time, sec

Figure 50.- Deep-stall recovery using pitch-rocking technique at a

center-of-gravity location of 0.35_. Asymmetries modeled;

h o : 9144 m.

181

an,

g units

M

.9

0

Jr-

deg

200

100

0

100

2O0

I I, \ \

\ \x

\ \ \x\ N "_

4

ioo

deg -too

30

6 a, 0

deg -3o

lo

6d,

deg

3o

5r, 0 /

_\_ /_" _J vr._ .........P r _ _ P/t /deg -30 ""

20 f 16h' 0 -"

l/-20

-qO

10

g units 0 "

5

Fped ' _o_N 0 5 lo 15 20 25 30 35 qo q5 So 5s 80 65 70 7S 80 85

Time, sec

Figure 50.- Continued.

182

q0

/t, o

deg/sec2 -_0

|

_0

_licl, o

deg/sec2 -_o -I

uiO

qa, 0

deg/sec2 _Lio

qO

"i', o Ldeg/sec2 -_io

_./_w _ =+_'-xt_ t_'- _ AJv

uiO

i'icl, o

deg/sec2 -qo

' _--,'T'...' -_

qo

i'a' 0

deg/sec_ -_ioy v-

T

'x.J _ .

40_

w, 0

m/$ec 2 -qO

j --.... v _ _ v -- ?

Wacl, 0

ITI/$ec 2 _ q 0

• _Olm/see 2 -qO

r

m/sec2 o 5 io 15 20 25 30 35

Time, sec

Figure 50.- Concluded.

183

_p

deg

8O

8O

_0

2O

0_

/-- c

ii

,\ . k_

deg

3O

2O

]0

0

-10

-20 --

-30

J

A

f_ ...............

II I1 A_"\II II I1!11 /

II IV\/ _I V .....

V

qO

P' 0

aeg/sec-'_o [

r _1

i \ v

qO

r, 0

deg/sec-q0 l

_0

deg/sec -qO

lO0

¢ ' 0 _--'-- J \

deg -i00

deg/sec

Flat ' lo__ _t+H ..... H _t-t-TqN

6OI

6 sb, qO

deg 20 --

00

_.[

lO 18 20 25 30 35 qO q8 50 SS 60 65 70 78 80 88

Time, sec

Figure 51.- Deep-stall recovery using speed brake and flaps at

a center-of-gravity location of 0.375_. Asymmetries not

modeled; h o = 9144 m.

184

an,

g units

4

2 /-0

J

M

.9

.3

o

fl

//

deg

2ool

loo

o

-I00

-200

/

Op

deg

too

o

io_

5d' 0

dog -io

6r,

deg

30

0

-30 I

\^,x/k, -_ ^

5h,

deg

40

20

0

-20

-40

//x

lOl5

gcom,

g units 0 _ _,

-5

Fped, _°°°N o 5 10 15 20 25 30 35 40 45 50 55 60 65 70 "75 80 85

: Time, sec

Figure 51.- Continued.

185

_0

Cl, o

deg/sec2 -_o

ti0

Clicl, 0

deg/sec2-_o

• YO

qa, 0

deg/see2__io II

t

i., 0

deg/sec2 -_o

J

_0

i'icl' o

deg/sec2-qo

_0

i'a' 0

deg/sec2 -_0

_0

m/sec 2 -u,o _j

_0

m/sec 2 -rio V

qo

Wac2, 0

m/$ec 2 -LtO,., j J } v _ J

m/sec 2 -u, OI .I I I I I I0 S i0 15 20 25 30 3S t{O q5 50 55 60 65 70 75 80 85

Time, sec

Figure 51.- Concluded.

186

deg

8O

6O

u,O

2O

0

Y

IfJ

, /,'_ // \ ,\j\,, kI

I

fL

deg

2O

10

0

-10

-20

-30

] f[_<\< iv _J\,'_'"

t

d

/ _P, o Cv -" - \/ / \,deg/sec -40

,,,/5

'° I <deg/sec -qO

q' 0 - -- ..... ---_ -._., _, ,-., d .." v

deg/sec -qO _

,°o ,I ++ +¢' 0 _ ( " _ _/- '_"_- _deg _1oo I

Pcom, ° I ' I" ] I] ] Ideg/sec -20°

-,o_1 iv vI!,_I_ I I

6 sb,

deg

6O

u,O

20

00 5 tO t5 20 25 30 35 u,O u,5 50 55 60 65 70 75 80 85

Time, sec

9O

Figure 52.- Deep-stall recovery attempt using speed brake

and flap at a center-of-gravity location of 0.375_.

Asymmetries modeled; h o : 9144 m.

187

.9

M .6 -'--_

.3

o

Up

deg

200 _

tO0

0

-i00

-200

\

\\

\

\

\

\

\

\\

lO0

_' o_

deg _1oo

30

6a' 0

deg -30

6d,

deg

IO

o

-IO I30

6r' 0

deg -3o

qo

5h' 20

deg 0 _-- J t

5

gcom, 0 -I Lg units

I

Fped'N u'°_0 S 10 15 20 25 30 35 u_o. '45 SO 55 60 65 ?0 '75 80 85 90

Time, sec

Figure 52.- Continued.

188

_0

cl, o

deg/sec2 -40

I_licl, 0

deg/sec2 -4o

/ , _, \_/ t/ --iv /

ti0

(]a, 0

deg/sec2 -40

A

_0

i', 0

deg/sec2 -_0

_0

i'a, 0

deg/sec2 -4o

ti0w, 0

m/sec 2 -40

_0

Gad' 0

m/$ec 2 -40

/

i

I

i

_./-_ /_ ...._ _--'-,. /--,. ,-"'-._ iv _ v

I

40

_rac2' 0

mlsec _ -40

_ra, op-_l I I I_L_I I Im/sec2-4ol I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I0 S i0 15 20 25 30 35 40 45 50 55 80 65 70 75 80 85 _0

Time, sec

Figure 52.- Concluded.

189

100

80 f\ /_\./\ /

deg u,O // /"

/

\

30 i

2o / 1lo //

deg o IIII I /l

20 _ / 1 /-30

8O

_o fP, --- /\ _ All

-80

LtO

deg/sec -qo

P_ v

qO A

deg/sec -u,ok/-

100

' 0 //_"--- \ r,

\/k/.._, ." i_ \/de°_ -10o

P corn, 0 v

°1 I I I//IV I VFlat, tool I I I IN 0 5 i0 15 20 25 30 35 rio u_5 50 55 60 65

Time, sec

Figure 53.- Deep-stall recovery using pitch-rocking

technique at a center-of-gravity location of

0.375_. Asymmetries modeled; h o : 9144 m.

190

an, _ __ _+_g units

M ,6 --_jJ

o I--_

deg

O, 0

deg -10o

301 ^ i6a' 0

deg -so

lo 1/ I6d' O-- °

deg -10 J

I I^ L

v

3o,II"6r, 0 ......... _ _.,/'-, A ]'deg -30 _ ' -

6h,

dego

20 -L----

_0 I ]._=_ L_

gcom,

g units

Fped,N

' ' 1 I ! i '

O S I0 15 20 25 30 35 LiO qS 50 ba 68 WbTime, sec

Figure 53.- Continued.

191

40

Cl, o

deg/sec 2 -40

-80

'L.-_ vj

tt0

Clicl, 0

deg/sec2 -40

\i?,p

4O

deg/sec 2-40

8O

40

deg/Sec2 -4o

tto

ricl, 0 .... 6, r

d/-eg-sec 2 ....... v- _

40

ra' 0

deg/seC 40

40:

m/sec 2 -t{O

v

/

4O

Wacl, 0 -" --'_--- _ --"--'/_/\/\-

m/see2 -4oV V

40

Wac2, o _ " _', _"_',, ^ _ _ _A ,, _v/

m/seE 2 -40

w&, 0

m/see2 -[{°0 5 10 15 20 25 30 35 40 45 50 55 GO G5

Time, see

Figure 53.- Concluded.

192

deg

IOO

80

60

_o

2o

o

I-f

i

/ v \/\/ k., ,_ ,-, _ / / d

/ __j v h

I

\L.

B,

deg

30

2O

I0

O

-IO

-20

-30

II /,j\, /^ I It/ Ill II

A A IF ,. f .,\ ,, , I I ( I I _

P' 0 ....."-- -- _ I%/ A'\ F

-_0 v I-80

_0

r, 0 _ _ A --

deg/sec -_0 _' _f _ \_J J

deg/sec _L_O

ioo __L

deg -too

o VIVI/II I IV_I/IFiat, too I I I I I t-I

N 0 5 10 15 20 25 30 35 riO q5 50 55 60 65 70 75 80 85 90 95 1UOTime, sec

Figure 54.- Deep-stall recovery using pitch-rocking techniques

at a center-of-gravity location of 0.375c. Asymmetries

modeled; ho = 9144 m.

193

M

2OO

I00

qs0

deg-lOO

-200

tO0

G, 0

deg _;oo

30

6a' 0

deg 30

lo

6d' 0

deg -;o

6r,

deg

dh,

deg

_com,

g units

2E_ I I I I I I I I_ L_.4_-dJ_L_4_J_4_4,_A I Io/I I I I I, [ _1 I I I I I I I I I I I I I I I I FIN I

---q,

I "•3 ....... b _-_.

0

f

1_-q F"1

\ \

\\ _\ \

v

I/\l

2

-20

-YO

10 .... l__

5o

5

'1 I ' I'_°°Ioi_ i.l-t-H--F-I_-I-0 S I0 !5 20 25 30 35 u,o Y5 SO 55 60 65 "70 75 80 85 90 95 100

Time, sec

Figure 54.- Continued.

194

^

,ale1, o......... - ......... "1 v • -deg/seC -qo /

_o I

deg/seC-_io " " _ J

-80

80 i

i,, _o

_ " _" W _ ""1 V tc-<io I "

L ....i'icl, , o l v _ _ _ /deg/sec2 -_iO

deg/sec2 _io

8o

_., <io

-qO

m/sec 2 -qO

Wac2' o -,. .... -..-_-v ...... -- I^../, _v u 17 "

1Ti/SCC 2 -q 0

_btq_m/see2 o s IO 15 20 25 30 35 qo q5 5o 55

Time, sec

Figure 54.- Concluded.

195

.9

M .6

.3

0

qO

0, 20

deg 0 _,.

10

0

deg -Io

qO

P' 0

deg/sec -_0

qO

r, 0

deg/sec -_0

qO

q' Ov

deg/sec -_,0

i00

¢' 0

deg -loo

20o

Pcom, 0

deg/sec_200

I00

Flat' oN

-i00

qO0

FP ed' oN -

-q@@0

Figure

A

55.--

/Lr _

\f

f_jf

J

10 15 20 25 30 35 qO q5 50 55 60 65 70 75 80 85 30 95 100

Time, sec

Performance of airplane with control

wind-up turn task. h o = 9144 m.

system A in

196

an,

g units

6

2 n£,/

V" / </

/ t, ,,,_._ _ _..z _ 4 _ _ r

"L[.[I

deg

200

100

0

-100

-200

I

"F

\

\\

I00

@' 0

deg -I00

3o I6a' 0

deg -30

30

6r' 0

deg -30

_ _ .... _ _L'x, _-.- _ _/'_ /'k, n, _k_

_oo [_long, 200 _ _'_"

N o v-"_, -'-'-_ _'_/-200

range, _oo .... _ _ ___ --m 0

deg

deg -200 5 10 15 20 25 30 35 q0 q5 50 55 60 65 70 75 80 85 g0 gS 100

Time, sec

Figure 55.- Concluded.

197

M •:11l_LII LILLI_J_L

deg :o_ lilllll}llll -_SJI0

deg I I I I ]-Wq- /V 7 v VLq/yVlViY-[ ]T\/I_I-lo ] ] _f'11 FI I_l// I I/I I/q I

160 _ .oolll/l J, /k J,,_J,_tiJdeg/sec ^ V IX _U!/I illllVl, V

80 ' G I l/'l IkV I

T_

deg/sec

:7_f!,,kLL]_!_J,.,LA!,J7_ il

[to II LI IAIq, oLI,,I.L-'I,-,VLIX_I.,I,k'-+,,,_,-,,-_+J-I,kJq+t--<,o,,i:_<:_.o[lllllll [/'-I-'1I I II II1111]

deg o1-11<_Jr '/I_ivxi_,Jllm

::: IIIIIIA, / ,, I_, !_lllllqI /r I I I _ IIIII. L I I _111111111111171 J-]l_

P¢om, nl k,-!,A[ I IAl / tI,K I llllllSlllllklil frillY,,/deg/sec _111 I_AII I/IV III/_l_'k/ll_lll tlll_Vl I _"

__oo_llll,iii _

Flat,

No,,u_,.,'!',J,d. / _,_! ,'!, 7 !_!!! v! iff/4,,._.,,[_

::::i_''Ti'<'_'7'''_''_'_''7_"0iIt_1_?_

0 5 10 15 20 25 30 35 [t0 LIS SO 55 60 65 70

Time, sec

Figure 56.- Performance of airplane with

control system A in bank-to-bank task.

198

ant

g units

"q/)

deg

q •

0, o

deg -lo@

I II6 r , _ ^ _ _---_

deg o-_'_'_V, LA1-.\.^-^y _( \ _,L&,4 .... x.... _ _/__oi I _1 __ _,A _

V _

Fl°ng' d<kf ( _ ,A b t4 ..

-200

\

range, _001 I I I I I I L_L I I 1_ I I I I 1__14Q_l--_rd-_[ i I i I i i I I_I-TI i i i i i q i i l/

m

deg 20 "h '\G- d_ <_r" _ "_ _-,0 x "_

deg

qo i -- +0 5 10 15 20 25 30 38 qO q5 50 55 60 65 "70

Time, sec

Figure 56.- Concluded.

199

M

B_

deg

'°o 1 IIIH I_LL/ALJ_IA_II LA/t_1A,LLLA /

:: / 7iii_rllTG711-77_7G_IIx% / IA_i.l A_LL̂ /]

P, oKi lim r I I I/-r-I'+lAVll_Jt, i_lM r r,ih_rt/tl,k

_.._°oIIIIJlllA_li_._I?4.M__I I_LKI>K[A_deg/sec I\1 ,(1 I I I W _/_7 II VII v v \/ %

-_o V I IV/ I I _/ I I 71 I I

_1:_-,o_ I I I I I I _11"11I I I I I I rl I _11 71111

deg

_°oLdllll/I_IIIIL , IIII I,I I,I / IAIIkl_l I I i I_1//I I_1 i/ill I/ll_l I ^ J_/ Ill I I

_;7:7<;_oo° . ,I l_I/IfT;_ll:It,Vl,,,,,_,.i"_ /l/ll'_-f_/ ,1_.7 : ,llrlFlat,

N

-1OO V t

FP ed' o

N -_ioo -0 S 10 15 20 25 30 38 qO q5 50 55 60 68 70 75 80

Time, sec

Figure 57.- Performance of airplane with

control system A in ACM task.

200

an,

g units_7 h-2 /" ' _ "_ \ _ /_" "l

o A \_-___ \ ,f J - -

*gl'p

deg

200

tOO

0

-tO0

-200

0,

deg

100 L_ _J

-tO0

iJ

rJ

6a,

degr _, .IJ I/l.̂k.,r,/,,.,

6 r ,

deg.o ,_l.I i,A,J,.'11,,,; _"'AII_'"

5h,

deg

qo

o _ _v'"_ _

-20

I

v'_ -- v_ "b_V v -

u'O0!-- ,/ '200 "_'- "" ''\

0 _'_

-200

qO0 1

I.,_ r, A

I'v",/ h _ v

800

range, u,oom o

deg

qo

2O

O__ \ 'v \ .,ix ' \_j\./'-_..,v

deg

qO

20 r'- :....

o -:_ \l ,.__\;i,--2o d - __-

0 S 10 t5 20 25 30 35 qO qS 50 55 60 65 70 75 80Time, sec

Figure 57.- Concluded.

201

,,,, __-1-111_1 IIII III

_ -Jq---f-__ ['VII-1[_IV//I_l"l_t[] I-IVl

p, ol IAI,J,,II_,lIJl \l_u I/_ I_'_,_u l//Ide see - vv V I I/A/l_/ ] r I F_/I I "J2 II I ,i,,,,,YI

uo I J. Iol I I I

cleg/sec

q. "°olL]_X_I _,_/__1,_1de_/sec-.oI_IVIII II II II_1_1I II I1I II IIIYl,I

iooI I I DRI /1_--kl I I I,DI-QI I ] 1 2.4-421 1 1

,, _II I/III

:°:ol-Pcom, oL_1/\],441 fll.JJI/IMil I/[ I_i/Ih,,

LolLlI,1/11111, 1 li'/ '

Fped,

O 5 [O 15 20 2S 30 35 _{0 u_5 50 58 60 65 ?0

Time, sec

Figure 58.- Performance of airplane with

control system B in bank-to-bank task.

202

_, L z" . ?

deg -lOOE

o + +

deg -30

deg -30

_o!

oh,20 / _ _v^ ,_ \f'deg o k,._., ^ /"In &_4, I_ -_ _' -_-^v 1.

-e° _ _ - ,_, _j//_ ....

600

'400

I_I_ng,' 200 j'-^_%V_4 '

-200

j1

8o0 /range, q0o __

m 0 _ _---_

dog2o-L/_,,o.... /' _' 4 _

' i/.

deg

60

qO

20

0

20

-qO

..... L_ I

I5 10 1S 20 25 30

lfL

I,35 riO qlS 50 55

Time, sec

60 65 /0

Figure 58.- Concluded.

203

M

.9

.6

,3--

o

I I

T-

I

deg J

-- /f_7"'-F_

<J

deg

lo L0 v

-10

J / f -,'A]'

160

80

P,0

deg/sec

-8o

-160

/,A

]V'_J

40

r, O,

deg/sec -40[4/ _f - \/ _'. r v ._--,

q' 0 /_,A_, _A-/_, /_ /"'_---_--_ _/v J

deg/sec -_0 - '_' ' '_

(_,

deg

200

100

0

-100

fx_

/_--_ _J \J

\ f _ : 1 y \

_00

2OO

Pcom,o

deg/sec

-200

-_oo

p_

Flat,

N

ioO

0

10o

_p.pf^ /I /,[I/ _.

HO0

Fped,° I

N -uool

o 5 lO 15 20 25 30 35 u_o u_5 5o 55 60 6s 7o

Time, sec

Figure 59.- Performance of airplane with

control system C in bank-to-bank task.

204

an , _ _.

g units 2 \ _ ^ <

0

\

/ \ _ _, f" '\

deg -10O

/ ¢

deg -ioo

J L ]3o I _ _ . A _I I_ I

da, 0 _.-_ v/"-V' _ \l\i I ' IJl 'J 1deg -30 ]

6r, o .... _,_ u, \, v l,_v ik]" "'deg -30 ' tl /I IJ

6 h, .^ A,p ,-.r',. , , X, t, A .N\],

deg -20 - V V"' V' -v ..... V v,,- V

qO0

Plong, 200 /_ ;" _ /_-_,

N o ,A_ A _, /'_ X,_/i_'X/V ? ½ _/_f

-2oo I

range, _o_ ___ _ _. q_'-J_In

6°1 IE, qo f_ 'v

deg 20 .-_/ _"O--_b'-J'r_ _-/_J _/k__,_

deg

qO

20

0

-20

-qO

-60

0 5 I0 15 20 28 30 35 qo q5

Time, sec

/--

50 55 60 65 /0

Figure 59.- Concluded.

205

<•3 -_ -

0

deg2o .... -- _ -

o j \

r_\ _ _\ /

/\

deg

io

\J \

-lo _J

160

80P,

deg/sec 0

-80

tl/t

'-- -_ v V q ",, / Ak _/

YO

T, 0

deg/sec -qo _. / _J "\/,.j

40

q' o

deg/sec -YO

deg

_ZZ_l.III li_-lqlll Jl / /dl II 111

LJ-ZIYFIll400

200P corn

deg/sec 0

-200

ks

,./ ,,wI

Fiat,N

200

IOO

0

-i00

-200

t !1 \/" _,\,s\ \ k V

Fped,N

400

L400 I

0 5 10 1S 20. 25 30 35 40 46 SO

Time, sec5S 60 6S 70 7S

Figure 60.- Performance of airplane with

control system B in ACM task.

8o

206

an,g units

/if,

deg.o!lO

-2001 I I I I I I I I I I I I i i _ _

°.,..

_eg-3 " I_ Il-l?I_YI-

Oh,

deg

:o1/ 1tll .I1_v-l_1ong,

N ::ooflI/_1//I'lq_////_:_range, qo

m

deg

qO

2

deg

Time, sec

Figure 60.- Concluded.

207

deg \ J

deg -1o V - -- -_I

160 i

r, 0 / "_, -v V

\ jl

deg/sec -qO ] _ _" ----

200 _ : f ___

_oo J I

-zoo- - \ / / - --- 7 - _,-2OOl

_oo II20O

-_oo I I ....

Flat , 0--- _//_ ; "_ J :-

N -ioo _ [ _ '

-2oo,±LLL_ _ . - .... t_ -

FP ed' . o \

N -uoo

0 S tO 15 20 25 30 38 qO q5 50 55 60 65 70 75 80Time, sec

Figure 61.- Performance of airplane with

control system C in ACM task.

2O8

q _,EI . \

deg

6a, ol I I I I _/ h I_1 IAL I LI I I 4/IA h/I IAIA-v - - v- l_h \_ ' 7 N_I/I_og__olfl-II i I ItrlYZ]_] I I I _,-,','_I_YlIV_,,,'d

3o I1%1 I I I I I Ifkllll_l I_,, o_IIh,,,,_,L_IAL]LLIIIII_I.IIAIt,_,,,,,,.

6h,

deg

60O

'long, QI I _r_ II--'l I P\ I I'L) j V 11{_[_4V_ I_]I I ] ]I4 I

" \ 'I$'IIIt _"] II//Ill4range, _°°F-t-Gq_l I I I _ I 15-4_LI I I I I I Jr-tq--L I t_ I

ol I I I I]"PUI I I I I IT] I i I_H-tfi_[I I I I-FI I IITI

deg

deg

_I0

20

0

20

_t0

60

IIILI 111/L 1/t

5 10 15 20 25 30 35 _lO _15 50 55 60 65 70 75 80

Time, sec

Figure 61.- Concluded.

209

O

Fl°ng

negative"g" limit

Pitch _ schedule

gradient

See

figure62(e)

__ afQi

q + 20.2s + 20.2

DL =25; RL=60

6d, C

20.2

s + 20.2

DL =25; RL =60

÷

(a) Schematic of overall system.

Figure 62.- Simulated basic pitch control system (control system A).

0

Negative"g" limit

-2

-4, I I I i i

0 2 4 6 8 10

q, kNlm 2

(b) Schedule of negative "g" limit with q.

Pitch-rategain

1.0.8

.6

.4

.2 m

I I I I

0 4 8 12 16

_, kN/m 2

(c) Schedule of pitch-rate gain with q.

I

2O

Pitch-loopgain

1.0.8

.6

.4

.2

D

0 8

I I I I

16 24 32 40

(], kN/m 2

(d) Schedule of pitch-loop gain with q.

Figure 62.- Continued.

I I

48 56

211

III

Pitch

command, g

10

8

4

2

0

-2

-4-60 -40 -20-80

, I,, , I ,I

20 40 60

Flong, N

80 I00 120 140 160 180

(e) Pitch command gradient.

Figure 62.- Concluded.

212

8

Incrementalcommanded normal

accelerationavailable, g units

6

4

2

I, I

0 5 I0

k

15 20 25

a, deg

I

30

Figure 63.- Variation of maximum commandable incremental

normal acceleration with angle of attack.

213

Roll trim < 4__40

Flat_

Rollcommand

gradient

See figure64(b)

4s2 +64s+6400 Is2+80s +6400

+

20.2_.___. _ s+20.2

(If >_29° [+ _ _ DL=21.5;RL=80

[

rt-x L222_

6a,c ]

_6d, c

(a) Schematic of overall system.

Figure 64.- Schematic of roll axis of basic control system (control system A).

50

Oh

Ruddercommand

gradient

See figure ÷-i65(b)

afJ

ay

3s + 15s_

÷

Ps

o.1.871.129__Ips

__i

_-_29 ° ÷, - > 4" I

of >29

(a) Schematic of overall system.

20.2 l---

s+ 20.2

DL-_Oi _ =120_r

Figure 65.- Schematic of yaw axis of basic control system (control system A).

Roll command,deg/sec

300

200

i00

-100

-200

-300

/ •

J

i I I

-60 -40 -20 0

Fla t, N

2'0 '40 60

(b) Roll command gradient.

Figure 64.- Concluded.

215

[-j

0"_

Yawtrim

___ 60Fped s + 60

Ruddercommand

gradient

See figure ÷ "_--65(b)

o,I

3s+15s-TTg--

+

af>29° r--_--] + l

(a) Schematic of overall system.

s + 20.2 -_

DLT=-3--_; --12or

Figure 65.- Schematic of yaw axis of basic control system (control system A).

6 r

-3O

-2O

Rudder command,deg

-11

0

11

2O

3O

-400 -200 0I !

2OO 4OO

Fped, N

(b) Rudder command gradient.

Figure 65.- Concluded.

217

P2 = P1

1

TT - f (P2 - P3 )

See figure 66(c)

1,

_T = 5.0

P2 = 40

P1

P2 = 60 ]" = 5.0

] TT

-- =f(P2 - P3 ) P2 = P1TT

See figure 66(c)

l 1 11_3 = _ (P2 - P3 ) ]_

P3 = fP3 dt

I =Tidl e + (Tmii-Tidle)(P3/50) T = Tmil + (Tmax-Tmil)(P 3 - 50)/50

(a) Logic diagram for thrust dynamic model.

Figure 66.- Simulated powerplant characteristics.

218

loo80

P1, r 60percent powe

4O

2O

Id tmum

, I , l, I0 20 40 60 80 100.

Percent th rottle travel

(b) Power variation with throttle position.

Figure 66.- Continued.

219

_0

0

im

TT

i

sec

1.0

.8

.6

.4

.2

0-100 -80 -60 -40 -20 0 20 40 60

( P2 - P3), percent power

(c) Variation of inverse of thrust time constant with incremental power command.

Figure 66.- Concluded.

8O 100

•12 -

rmsbuffet

intensity,

g units

• I0

• O8

. O6

•O4

• 02

0

I I ] I

i0 15 20 25 30 35

a, deg

Figure 67.- Variation of buffet intensity with angle of attack.

4O

1. Report No. 2. Government Accession No.

NASA TP-1538

'"4. Title and Subtitle

SIMULATOR STUDY OF STALL/POST-STALL CHARACTERISTICS

OF A FIGHTER AIRPLANE WITH RELAXED LONGITUDINAL

STATIC STABILITY

7. Author(s)

Luat T. Nguyen, Marilyn E. Ogburn, William P. Gilbert,

Kemper S. Kibler, Phillip W. Brown, and Perry L. Deal

3. Recipient's Catalog No.

5. Report Date

December 1979

6. Performing Organization Code

8. Performing Organization Report No.

L-12854

10. Work Unit No.

505-06-63-03

11. Contract or Grant No.

13. Type of Report and Period Covered

Technical Paper

14. Sponsoring Agency Code

9. PerformingOrganizationNameand Addre_

NASA Langley Research Center

Hampton, VA 23665

12. S_nsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, DC 20546

15. Supplementary Notes

16. Abstract

A real-time piloted simulation has been conducted to evaluate the high-angle-of-

attack characteristics of a fighter configuration based on wind-tunnel testing

of the F-16, with particular emphasis on the effects of various levels of relaxed

longitudinal static stability. The aerodynamic data used in the simulation were

based on low-speed wind-tunnel tests of subscale models. The simulation was con-

ducted on the Langley differential maneuvering simulator, and the evaluation

involved representative low-speed combat maneuvering. Results of the investiga-

tion showed that the airplane with the basic control system was resistant to the

classical yaw departure; however, it was susceptible to pitch departures induced

by inertia coupling during rapid, large-amplitude rolls at low airspeed. The

airplane also exhibited a deep-stall trim which could be flown into and from

which it was difficult to recover. Control-system modifications were developed

which greatly decreased the airplane susceptibility to the inertia-coupling

departure and which provided a reliable means for recovering from the deep stall.

17. Key Words (Sugg_ted by Authoris))

Relaxed longitudinal static stability

High angle of attack

Deep stall

Departure prevention

18. Distribution Statement

Unclassified - Unlimited

Subject Category 08

19. S_urity Cla_if.(ofthisreport)

Unclassified

20. SecurityClassif.(of this pege)

Unclassified

21. No. of Pages

223

* For sale by the National Technical Information Service, Springfield, Virginia 22161NASA-Langley, 1979

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