NASA
Technical
Paper
1538
Simulator
Study
of
Stall Characteristics
Fighter
Airplane
Longitudinal
Luat
T.
Kemper
DECEMBER
Nguyen,
S.
Kibler,
1979
With
Static
Marilyn
Phillip
Stall/Postof a
E.
W.
Relaxed
Stability
Ogburn,
Brown,
William
and
P.
Perry
Gilbert,
L. Deal
NASA
Technical
Simulator
Stall
Paper
Study
T.
Kemper
S.
Langley
Research
Hampton,
Marilyn
Kibler,
Phillip
Center
Virginia
BJt A
National
With
Static
Nguyen,
Aeronautics
and Space Administration
Scientific and Technical
Information
Branch
Stall/Postof
Airplane
Longitudinal
1979
of
Characteristics
Fighter
Luat
1538
E.
W.
a
Relaxed
Stability
Ogburn,
Brown,
William
and
P.
Perry
Gilbert,
L. Deal
TABLE
OF
CONTENTS
1
°°°°°•°°°
oo.oooo_OO°°°•
SUMMARY
.........
1
•°°o°o°O°°°
•••oo°°°°°°•°
INTRODUCTION
......
2
°°o°O•°°°°
°°°°°o°°o•°°•
SYMBOLS
.........
7
.....
DESCRIPTION
OF
AIRPLANE
°•
...................
8
°
°
o
o
°
°
°
°
°
°
o
°
°
°
°
•
°
°
°
8
DESCRIPTION
OF
Coc
kpit
Visual
and
SIMULATOR
.......
Associated
Equipment
Display
Computer
9
...............
................
9
..........
Program
°
..........
.................
9
•
EVALUAT
Wind
PROCEDURES
I ON
-Up
Bank-to-Bank
Turn
•
Tracking
.............
...............
Tracking
Task
.................
o
°
•
....
i0
•
..............
Performance
°
I0
Task
of
•
......
Tracking
Task
Evaluation
•
i0
•
ACM
....
°
°
°
°
°
•
°
•
°
°
°
•
°
°
°
°
•
I0
.
.
.
"
"
"
°
°
°
•
•
•
•
°
............
ii
CHARACTERISTICS
DISCUSSION
OF
STABILITY
Longitudinal
AND
CONTROL
Characteristics
Lateral-Directional
DISCUSSION
OF
...... °
Characteristics
.NG
•
o
12
............
HIGH-ANGLE-OF-ATTACK
INERTIA-COUPLI
°
............
KINEMATIC-
PHENOMENA
AND
13
........
............
16
DEPARTUREBasic
AND
SPIN-RESISTANCE
Control
System
Control-System
Effect
SIMULATION
Aft
16
.............
18
.........................
Modifications
of
RESULTS
Center
of
24
....................
Gravity
............
25
DEEP-STALL
SIMULATION
RESULTS
25
............
°
Description
of
Methods
of
Problem
Recovery
•
°
°
.....
•
........
•
°
°
°
.
•
°
°
.......
27
•
°
.................
29
.
TRACKING
Results
RESULTS
of
Basic
Results
of
.......
Control
Control
°
System
Systems
B
°
•
o
(Control
and
C
•
•
°
System
°
•
.
•
A)
°
•
°
°
•
•
•
°
29
3O
.........
•
°
.
°
•
•
............
32
o
INTERPRETATION
OF
RESULTS
.
o
•
°
o
°
.................
32
°
SUMMARY
OF
RESULTS
o
°
°
•
o
°
•
°
°
...............
34
APPENDIX
A
-
DESCRIPTION
OF
CONTROL
SYSTEM
.............
36
APPENDIX
B
-
DESCRIPTION
APPENDIX
C
-
SPECIAL
OF
EQUATIONS
AND
DATA
EMPLOYED
IN
SIMULATION
41
.
EFFECTS
...................
iii
°
°
REFERENCES................................
42
TABLES ..................................
43
FIGURES..................................
94
iv
SUMMARY
A real-time piloted simulation has been conducted to evaluate the highangle-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 conducted on the Langley differential
maneuvering simulator,
and
the evaluation involved representative
low-speed combat maneuvering.
Results of the investigation
showed that the airplane with the basic control system was resistantto
the classical
yaw departure; however, it was susceptible to pitch departures induced by inertia
coupling
during
rapid,
largeamplitude
which
rolls
could
system
at
be
low
flown
modifications
ceptibility
means
to
for
the
airspeed.
The
into
and
from
were
developed
airplane
which
which
inertia-coupling
recovering
from
also
it
was
greatly
departure
the
deep
exhibited
difficult
a
to
decreased
and
deep-stall
the
which
trim
recover.
Control-
airplane
provided
a
sus-
reliable
stall.
INTRODUCTION
Rapid
advances
possible
the
aircraft.
ciple
to
In
of
low
even
sonic
operates
bility
are
at
Obviously,
factory
tem
pilot
to
The
have
use
of
angles
of
which
and
2)
inherent
trol
on
positive
attack
system
in
some
of
characteristics
the
low-speed
pitch
result
impose
that
F-16.
at
The
(DMS)
study
and
wind-tunnel
of
design
these
used
in
severe
the
the
higher
of
subscale
static
of
system
throughout
on
the
attained.
of
present
their
on
the
of
on
on
the
conducted
was
stability
areas
conducted
and
configuration
results
at
high
flight
maneuver-
differential
the
at
the
problem
fighter
Langley
based
models
a
systhe
investigation
investigation
effects
attack
of
maximum
earlier
satis-
envelope.
problems
design
An
to
flight
control
sub-
control
appears
the
demanding
low
insta-
provide
the
airplane
air-
which
at
to
Fundamentally,
the
an
pitch
high-angle-of-attack
data
and
F-16,
control
that
designed
regimes.
margin
levels
characteristics
of
i) ;
the
on
the
prin-
is
configurations-
The
aerodynamic
is
fighter
the
flight
fighter
are
and
conducted
(ref.
negative
to
future
potential
was
known
RSS
made
to
airframe
certain
requirements
concept.
angles
turned
basic
of
have
concepts
in
of
some
desired
problems
been
much
stability
high
tests
use
such
resistance
RSS
well
years
(CCV)
the
characteristics.
can
some
the
greatly
static
order
identified
with
for
stability
departure/spin
evaluate
simulator
rely
control
however,
ability
(ref.
and
are
makes
levels
considered
artificial
RSS,
control
to
designs
which
involving
recent
has
stability
which
moderate
CCV
in
pitch
concept
designs
being
provide
(RSS)
this
very
now
stability
must
of
in
vehicle
attention
static
development
Advanced
also
technology
configured
stability
negative
under
speeds.
avionic
control
considerable
benefits
currently
nominally
of
static
or
performance
plane
aircraft
particular,
relaxed
have
The
in
application
maneuvering
of
the
conbased
a
NASA
number
Langley
of
and Ames Research Centers.
The objectives
of the study were (i) to determine
the controllability
and departure resistance of the subject configuration
during
lg and accelerated stalls;
(2) to determine the departure susceptibility
of the
configuration
during demanding air-combat maneuvers; (3) to identify
high-angleof-attack problems inherent to the RSS design and assess their impact on maneuverability;
and (4) to develop and evaluate control schemes to circumvent or
alleviate
these shortcomings.
SYMBOLS
All aerodynamic data and flight
motions are referenced to the body system
of axes shown in figure i.
The units for physical quantities
used herein are
presented in the International
System of Units (SI) and U.S. Customary Units.
The measurements and calculations
were made in U.S. Customary Units.
Conversion
factors for the two systems are given in reference 3.
an
normal acceleration,
(ig : 9.8 m/sec 2)
ay
lateral
b
wing span, m (ft)
CL
lift
C_
rolling-moment
positive
acceleration,
coefficient,
Aerodynamic
along negative
positive
Z body axis,
along positive
Aerodynamic
lift
Y body axis,
force
9s
coefficient
rolling
about
X
body
axis,
moment
_Sb
total
rolling-moment
pitching-moment
Aerodynamic
coefficient
coefficient
pitching
w
about
Y
body
axis,
moment
--
qSc
Cm,t
total
pitching-moment
Cn
yawing-moment
Aerodynamic
coefficient
coefficient
yawing
about
Z
body
axis,
moment
_Sb
Cn,t
total
CX
X-axis
yawing-moment
force
Aerodynamic
CX,t
total
X-axis
coefficient
coefficient
X-axis
force
along
force
coefficient
positive
X
body
axis,
g units
g units
Y-axis
Cy
force
coefficient
Aerodynamic
Cy,t
total
Cz
Z-axis
Y-axis
Y-axis
force
force
total
wing
mean
along
force
aerodynamic
chord,
lateral
Flong
pilot
longitudinal
stick
Fped
pilot
pedal
positive
GARI
ARI
g
acceleration
gcom
pilot-commanded
He
engine
h
altitude,
IXz
stick
due
angular
m
moments
product
body
axis,
(ft)
positive
force,
for
right
positive
for
gravity,
roll,
for
right
yaw,
m/sec
2
aft
N
(ft/sec
acceleration,
momentum,
N
(ib)
force,
N
(ib)
(ib)
g
kg-m2/sec
2)
units
(slug-ft2/sec)
(ft)
of
of
2
to
normal
inertia
inertia
(slug-ft
Mach
Mic
pitching
moment
m
airplane
mass,
P1
Z
m
force,
force,
M
P
positive
gain
kg-m
Ni c
axis,
coefficient
pilot
z
body
force
Flat
Ix,Iy,I
Y
coefficient
Z-axis
Z-axis
positive
force
coefficient
Aerodynamic
Cz,t
along
about
with
X,
respect
Y,
and
to
X
Z
body
and
Z
axes,
body
kg-m
2
(slug-ft
axes,
2)
number
yawing
period,
engine
moment
due
kg
due
to
inertia
coupling,
(I Z
-
IX)Pr
, N-m
(ft-lb)
(slugs)
to
inertia
coupling,
(I x
-
Iy)pq,
N-m
(ft-lb)
sec
power
command
based
command
to
on
throttle
position,
percent
power
P2
engine
power
P3
engine
power,
percent
of
engine,
maximum
percent
power
of
maximum
power
of
maximum
2)
P
airplane
Pcom
pilot-commanded
(Pcom)max
roll
rate
roll
maximum
X
about
rate,
commandable
stability-axis
Ps
static
q
airplane
pitch
rate
airplane
pitch
acceleration
component
of
qa
roll
rate,
N/m
2
rate,
deg/sec
or
rad/sec
deg/sec
deg/sec
(ib/ft
or
rad/sec
2)
about
airplane
axis,
deg/sec
roll
Pstab
pressure,
body
Y
body
axis,
about
pitch
Y
deg/sec
body
acceleration
or
axis,
rad/sec
deg/sec
2
due
to
aerodynamic
due
to
inertia
or
rad/sec
moments,
or
< Iy]
qicl
m,t'
component
deg/sec2
of
rad/sec2
airplane
pitch
acceleration
coupling,
%
Iz
q
free-stream
R
range,
m
Ig_)pr,
dynamic
rf
filtered
rstab
stability-axis
rate
yaw
about
rad/sec
N/m
distance
Z
yaw-rate
acceleration
component
of
component
2
2
(lb/ft
2)
between
subject
deg/sec
or
and
target
airplanes,
S
wing
s
Laplace
T
total
Tidle
idle
Iy)
area,
signal,
about
rad/sec
2
deg/sec
Z
airplane
rad/sec
deg/sec
rate,
body
yaw
or
rad/sec
axis,
acceleration
deg/sec2
deg/sec
2
or
due
to
aerodynamic
due
to
inertia
moments,
rad/sec2
airplane
qp,
yaw
deg/sec
m 2
2
acceleration
or
rad/sec
2
(ft 2)
variable,
i/sec
instantaneous
thrust,
axis,
or
of
I X IZ
-
body
yaw
(qSb_ C
<-_--y] n,t'
4
or
pressure,
straight-line
yaw
ricl
2
(ft)
r
ra
deg/sec
N
engine
(Ib)
thrust,
N
(lb)
coupling,
2
maximum
thrust,
N
(ib)
Tmax
military
thrust,
N
(ib)
Tmil
time,
t
time
sec
to
damp
to
one-half
amplitude,
sec
tl/2
components
UyVrW
of
m/sec
V
airplane
velocity
along
X,
y,
and
Z
body
axes,
(ft/sec)
airplane
resultant
velocity,
airplane
acceleration
m/sec
along
Z
(ft/sec)
body
axis,
m/sec2
(ft/sec2)
w
component
of
w
due
to
aerodynamic
force,
Q_mSlCz,t
'
_a
m/sec
2
(ft/sec2)
component
of
w
due
to
pitch
rate,
component
of
w
due
to
kinematic
airplane
body
qu,
m/sec2
(ft/sec2)
Wacl
coupling,
-pv,
m/sec2
(ft/sec2)
Wac2
axes
(see
fig.
i)
X,Y,Z
center-of-gravity
location,
fraction
Xcg
of
location
reference
for
aerodynamic
data
center-of-gravity
Xcg,ref
angle
of
attack,
filtered
deg
angle-of-attack
signal,
deg
@f
indicate
angle
d
angle
of
of
sideslip,
attack,
deg
deg
aileron
deflection,
positive
for
left
roll,
aileron
deflection
commanded
by
control
maximum
aileron
deg
6a
system,
deg
_a,c
deflection,
deg
6a,max
differential
horizontal-tail
deflection,
differential
horizontal-tail
deflection
positive
for
left
roll,
by
control
deg
6d
5d,c
control,
horizontal
_h,C
system
deg
horizontal
@h
commanded
stabilator
deflection,
positive
for
deflection
commanded
by
airplane
nose-down
deg
stabilator
control
system,
deg
@lef
leading-edge
6r
rudder
flap
deflection,
6sb
speed-brake
@tef
trailing-edge
C
tracking
rudder
flap
error,
horizontal
1
component
e,_,_
Euler
TT
engine-thrust
angles,
aircraft
p_bb
2V
CZ
Cm
36r
3
q
CXq
_
Cn_,dyn
CZq
axis
and
factor
sec
deg/sec
3c
r_bb
2V
=
_
_
3c
6a
Cnp
_@a
Cn_
Iz
--Cz
I X
3C n
pb
2-V
3
Cn r
3
_C n
sin
_
Cn_
-
a
_6 a
Cn6
r
_6 r
3Cy
q_
2V
Cyp
rb
2--_
3C n
-
_
_
3Cy
pb
2V
CYr
_
rb
2--_
Subscripts:
ds
deep
lef
increment
of
variable
produced
flaps;
for
example,
ACm,le
by
6
stall
retraction
of
leading-edge
by
f
full
retraction
indicates
flaps
of
increment
from
25 °
z
-
C_
3C n
q_
2V
=
z
_
_
3C Z
q_
2V
body
deg
deg
velocity,
-
3Cx
X
down,
deg
constant,
3C n
_
edge
airplane
z
Cn_
off),
trailing
3C m
_r
_,
for
C z
_
3C_
deg
deg
evaluation
Zr
down,
deg
effectiveness
angular
3c
_
edge
deg
total
C
p
(angle
of
time
3c_
-
leading
yaw,
positive
between
stabilator
lateral
left
deflection,
R
for
deg
angle
vector
for
deflection,
deflection,
range
positive
positive
pilot-commanded
r,com
C z
deflection,
to
leading-edge
in
0°
Cm
produced
o
initial
value
sb
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°
6i=j
Abbreviations
._ACM
:
air-combat
maneuvering
ARI
aileron-rudder
interconnect
CAS
commandaugmentation
CCV
control
DL
deflection
DMS
Langley differential
IAS
indicated
LCDP
lateral
RL
rate
RSS
relaxed
rms
root mean square
SAS
stability
SM
static
configured
limit,
vehicle
deg
airspeed,
control
limit,
system
maneuvering simulator
knots
divergence
parameter
deg/sec
static
stability
augmentation
system
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 in
table I.
The airplane control system is described in detail
in appendix A.
The primary aerodynamic controls include symmetric deflection
of the horizontal
tail
(stabilator)
for pitch control,
deflection
of conventional wing-mounted
ailerons and differential
deflection
of the horizontal
stabilators
for roll
control,
and rudder deflection
for yaw control.
One special feature of the configuration
is the use of a normalacceleration-command longitudinal
control system which provides static stability,
normal-acceleration
limiting,
and angle-of-attack
limiting.
The airplane is balanced to minimize trim drag, with the effect that it has slightly
negative static longitudinal
stability
at low Mach numbers; the desired static
stability
is provided artificially
by the control system. Other features
include (i) wing leading-edge flaps which are automatically
deflected as a function of angle of attack and Mach number; (2) a roll-rate
commandsystem in the
roll axis; (3) an aileron-rudder
interconnect
and a stability-axis
yaw damper
in the yaw axis; and (4) a force-sensing
(minimum displacement) side-stick
controller
and force-sensing
rudder pedals.
The airplane engine characteristics
used in the present study are described in appendix B, and the buffet characteristics
are described in appendix C.
Most of the simulated flights
were made at a center-of-gravity
location
0.35_ although locations as far aft as 0.39_ were also investigated.
All
results shown in this report are for the 0.35_ center-of-gravity
location
unless otherwise stated.
of
DESCRIPTIONOF SIMULATOR
The Langley differential
maneuvering simulator
(DMS) is a fixed-base simulator which has the capability
of simultaneously simulating two airplanes as
they maneuver with respect to one another and of providing a wide-angle visual
display for each pilot.
A sketch of the general arrangement of the DMShardware
and control console is shown in figure 3. Two 12.2-m (40-ft) diameter projection spheres each enclose a cockpit, an airplane-image projection
system, and a
sky-Earth-Sun projection
system. A control console located between the spheres
is used for interfacing
the hardware and the computer, and it displays critical
parameters for monitoring hardware operation.
Each pilot is provided a projected image of his opponent's airplane, with the relative
range and attitude
of the target shown by a television
system which is controlled
by the computer
program.
Cockpit and Associated
Equipment
A photograph of one of the cockpits and the target visual display is shown
in figure 4. A cockpit is provided with an instrument display and a computerdriven gunsight representative
of current fighter aircraft
equipment.
However,
this study used a fixed gunsight for tracking.
Each cockpit is located to
position the pilot's
eyes near the center of the sphere so that he has a field
of view representative
of that obtained in current fighter
airplanes.
For the
present study, a special modification
was made to one cockpit to incorporate the
side-stick
controller
as shown in figure 5. The controller
was placed in the
same 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)
other
than the regular seat armrest which provided more of an elbow rest than a support for the forearm.
The normal hydraulic control feel system was not employed
for this simulation since the side-stick
controller
and rudder pedals were force
sensitive,
with no deflection
required to activate the controls.
Although the
cockpits are not provided with attitude
motion, each cockpit incorporates
a
buffet system capable of providing programmable root-mean-square
(rms) buffet
accelerations
as high as 0.5g, with up to three primary structural
frequencies
simulated.
Visual
Display
The visual display in each sphere consists of a target image projected onto
a sky-Earth scene. The sky-Earth scene is generated by two point light sources
projecting
through two hemispherical transparencies,
one transparency of blue
sky and clouds and the other of terrain features;
the scene provides a welldefined horizon band for reference purposes.
No provision
is made to simulate
translational
motion with respect to the sky-Earth scene (such as altitude
variation);
however, spatial attitude
motions are simulated.
A flashing light
located in the cockpit behind the pilot is used as a cue when an altitude
of
less than 1524 m (5000 ft) is reached.
The
target-image
generation
system
uses
an
airplane
model
a
zoom
lens
to
F-16
size
airplane,
with
For
an
- (300
ft)
to
contrast
13
mounted
700
between
blackout
"anti-g"
cues
to
high
four-axis
000
can
the
sky-Earth
engine,
of
of
and
of
The
DMS
CYBER
lated
is
by
of
of
equations
d
(M
_
=
conducted
Mach
of
0.i
in
range
to
equations
of
Reynolds
to
a
and
in
history
results
records
maneuvers
test
current
fighter
test
pilot
also
flew
The
of
the
a
pilots
airplane
in
the
system
airplane
warning
4.
were
The
sec)
calcu-
numerical-
data
derived
data
from
were
the
as
from
not
force
included
-30 °
an
to
angle-
30 ° .
included
aerodynamic
func-
results
Effects
in
data
the
and
the
and
time-
B.
PROCEDURES
based
controls,
with
a
Control
(forced-oscillation)
U.S.
on
and
evaluations
familiar
a
were
aerodynamic
range
of
and
(1/32
data
sideslip
were
however,
inflat-
sound
Air
high-angle-of-attack
comments
tracking
were
the
pilot
performed
air-combat
Force
flight
the
various
by
two
NASA
maneuvers
test
tests
for
pilot
of
the
used
and
a
F-16
with
contractor
airplane
simulator.
evaluation
"open-loop"
were
airplanes;
involved
the
who
of
an
and
reference
simulation
dynamic
appendix
motions,
Most
of
artificial
in
evaluation
aeroelasticity
investigation
airplane
performed.
research
the
of
as
given
nonlinear
EVALUATION
The
well
facilities.
or
simulation
use
loads,
are
These
descriptions
given
as
m
range.
include
the
90
brightness
minimum
C),
fixed-interval
used
and
number,
are
the
form.
90 °
Complete
motion
with
wind-tunnel
-20 °
model.
of
static
10-to-i
hardware
sphere.
from
Program
equations
0.2)
DMS
digital
tabular
several
from
number,
mathematical
in
a
camera
the
range
at
appendix
facility
dynamics
motion
television
within
simulated
with
noise
DMS
real-time
The
and/or
low-speed
of-attack
a
The
technique.
of
tests
by
computer.
using
integration
tions
driven
175
a
normal-acceleration
Computer
Data
the
weapons
the
a
background
(see
simulation
and
projector
airplanes,
features
details
system
target
provide
accelerations
for
wind,
the
between
and
normal
Additional
to
system
ft)
target
gimbal
image
the
(45
garment
simulate
systems.
a
an
special-effects
at
able
m
the
Additional
of
in
provide
was
maneuvers
at
high
conducted
to
assess
angles
of
in
basic
attack,
two
phases.
stability
and
the
The
and
second
first
control
phase
phase
involved
characteristics
involved
tracking
of
a
simulated F-16 as a target airplane through a series of maneuvers representative
of those used in air combat in order to examine flying qualities
under these
conditions.
Maneuvers used in the first
phase included ig and accelerated
stalls,
with various control inputs applied at specific conditions.
Table II
lists the primary maneuvers used in this phase. In addition to documenting the
stability
and response to control characteristics
of the airplane and familiar E
izing the pilot with these characteristics,
this phase also provided an assessment of the departure and spin susceptibility
of the configuration.
Results
from the first
phase of the study were used to design the tracking task_ used in
the second phase. Several tasks were chosen for use during the second phase of
the study:
(i) a steady wind-up turn tracking task, (2) a bank-to-bank maneuvering 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 increasing
angle of attack in order to provide a tracking situation
in which the pilot could
evaluate the fine tracking capability
of the evaluation airplane at high angles
of 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 the
target and at the same heading as the target.
Upon initiation
of the run, the
target established a left-bank attitude
which varied between -40 ° and -i00 °
during the maneuver. Angle of attack was gradually increased up to a maximumof
about 3g normal acceleration.
The evaluation pilot attempted to track the target
as 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 airplane
through a series of bank-to-bank maneuvers (or horizontal
S's) at high angles
of attack.
These maneuvers enabled the pilot to evaluate his ability
to roll
the subject airplane rapidly,
to acquire the target,
and to stabilize
while at
high angle of attack.
ACMTracking
Task
The ACMtracking task was developed to be more representative
of the complex, 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, the
task covered a speed range of 0.25 to 0.6 Mach and required the tracking airplane to perform several large-amplitude
rolling
maneuvers at low-speed, highangle-of-attack
conditions.
Evaluation
of Performance
In evaluating the simulated airplane,
numerous runs were made in each of
the tasks.
Sufficient
flights
were made to ensure that the pilot's
"learning
i0
curve" was reasonably well established before drawing any conclusions on evaluation results.
Evaluation of performance was based on pilot comments, the
ability
of the pilot to execute the tasks assigned, and the analysis of time
histories
of airplane motions and tracking.
DISCUSSIONOF STABILITY AND CONTROL
CHARACTERISTICS
To provide a foundation for the analysis and interpretation
results which follow,
selected aerodynamic stability
and
tion
istics
of
this
the
simulated
airplane
configuration
presented
and
character-
discussed
in
section.
Longitudinal
The
these
aerodynamic
data
characteristics
dynamic
but
the
highly
A
level
swept
as
at
attack
approximately
longitudinal
attack
feedback
that
figure
nose-up
-4
to
i0
stabilator
these
extreme
percent.
that
deflection
(6 h
angles
of
attack,
the
of-attack/normal-acceleration
attempt
to
complete
in
limit
limiting
the
angle
of
system
attack
control
Two
other
important
points
regarding
figure
i0.
The
is
marked
due
loss
in
to
stall
system
of
lators
deflected
stable
trim
point
important
is
the
of
is
shown
seen,
_h =
loss
there
0°"
in
is
=
very
However,
stabilator
A
in
angles
is
available
qualities,
important
_
=
to
66 °
note
with
full
excursions
the
an
to
angle-
stabilator
in
discussion
stability
nose-down
of
of
attack
nose-down
greater
an
the
the
moment
that
airplane
in
even
noted
25 ° .
because
shown
Note
be
effectivethan
critical
control
point.
should
stabilator
particularly
control,
of
A.
characteristic
trim
is
further
longitudinal
important
to
prevent
figure
with
exhibits
a
The
the
i0
the
is
stabi-
weak
but
60 ° •
aerodynamic
of
characteristic
Cm
with
wind-tunnel
little
drives
modest
angle-of-
incorporates
25 ° .
angles
angles
inadvertent
which
20 ° ,
35 ° .
a
low
with
at
system
=
position
flying
trim
appendix
loss
for
nose-down
variation
by
in
deep-stall
full
_
the
other
stable
at
given
surfaces
on
The
for
airplane
which
a
the
below
effectiveness
relies
25 ° .
existence
Another
these
control
exceeding
the
of
nose-down
limiter
from
first
is
to
pitch
ness
system
control
=
exhibits
A)
inhibit
d
higher
d
at
It
will
To
pitch
it
margin
stability.
airplane
-250).
at
near
that
flow-
near
lift
appendix
aero-
wind-tunnel
satisfactory
(see
pitch
The
center-of-gravity
provide
the
=
is
of
B.
stalled
obtained
Static
equipped
artificial
during
produce
was
i0.
To
indicates
to
representation
appendix
panels
nominal
figure
is
noted
C L
the
the
in
configuration
at
in
and
wing
continued
the
system
provide
also
as
Maximum
shown
control
III,
discussed
outer
strake
9.
of
as
is
the
instability
speeds,
table
configuration
that
figure
pitch
low
is
the
such
characteristic
static
(0.35_)
in
in
simulation
wing-body
shown
notable
of
were
Characteristics
listed
the
of
tests
attack,
the
are
in
characteristics
visualization
of
are
of the simulacontrol
data
variation
the
data
for
effectiveness
_
for
of
exhibited
at
d
high
=
pitching
angles
25 °
in
moment
by
of
figure
with
the
simulated
attack,
ii.
an
As
sideslip
nose-down
stabilator
deflections
for
sideslip
magnitudes
greater
show
than
can
example
be
for
a sharp
about
i0 °.
ii
Thus, if a departure involving large sideslip excursions should occur, the
effectiveness
of the angle-of-attack
limiter
system to maintain
_ at or below
25° will be further degraded by the reduction in available
nose-down control
moment.
Lateral-Directional
Static
bility
lateral-directional
characteristics
deflections
bility
are
directional
each
of
between
as
_
an
angles
of
tence
was
Cn_,
a
about
which
caused
less,
it
a
is
a directional
attack.
The
ration
by
_
:
0°
ness
of
the
=
20 °
the
:
very
40 °
available
to
The
the
(_
:
the
These
proper
control
effectiveness
divergence
at
/Cn6a_
LCDP
:
Cn_
-
produced
become
CZ_C--_@a)
indicate
high
yaw
of
parameter
angles
and
35 ° .
to
by
for
the
the
and
configucaused
constant
effectiveup
surfaces
rudder.
Only
compared
to
yaw
the
to
above
with
configuration
up
and
of
sustained
these
the
minimize
attack.
40 ° ,
angles
significant
roll
:
increments
well
up
Neverthe-
_
high
by
that
(LCDP)
of
:
Roll-control
characteristics
and
attack
values,
essentially
25o).
produced
moments
data
at
and
of
through
moment
good
yaw
coordination
adverse
<
moments
control
roll-control
lateral
roll-control
as
12
with
yawing
high
(_
was
adverse
_
high
exis-
configuration
angles
at
of
at
the
(negative)
up
C_
slice)
characteristics
terms
attack
tails
the
compared
if
in
was
of
n
expected
control
13
for
Cn_,dy
be
the
unstable
positive
not
differential
moments.
25 ° )
of
and
indicate
that
laterally)
remained
angle
adverse
indicate
At
investigations
(nose
usually
large
effectiveness
of
whereas
small
do
12
value
past
dynamic
attack.
Cn_
in
sta-
the
of
sloping
used
parameter
and
figure
lateral-directional
limit
suppress
and
rudder
exhibitgood
attack
rudder
limit,
was
_
in
been
and
angle
divergence
reached
the
of
flap
directional
CZ_,
by
sta-
leading-edge
static
functions
has
this
aerodynamic
range
ailerons
n
therefore
shown
The
operational
angle-of-attack
above
in
the
computed
figure
Cn_
would
are
control.
of
parameter
lateral-directional
full
the
this
of
directional
of
30 ° ,
decrease
that
of
lateral-directional
scheduled
derivative
as
directionally
:
divergence
at
over
_
sharp
seen
Cn_,dy
data
(both
Above
n
were
values
The
terms
dihedral
C_
existence
Negative
stable
28 ° .
and
static
with
in
Cn_,dy
parameter
the
divergence.
statically
to
The
of
12
effective
Cn_
attack.
of
the
The
airplane
figure
parameter
-+4° .
indication
basic
in
attack,
:
the
presented
stability
angle
stability.-
of
derivative
Characteristics
should
angle-of-
controls
is
used
sideslip.
is
often
This
used
parameter
to
appraise
is
defined
the
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 airplane with an aileron-rudder
interconnect
(ARI). Positive values of this parameter indicate normal roll response, and negative values indicate reversed
response.
When reversed response is encountered, a right roll-control
input by
the pilot will cause the airplane to roll to the left.
The variation
of LCDP
with angle of attack for the subject airplane is presented in figure 14. For
the airplane with the basic control system, the parameter becomes negative above
= 25° , which indicates reversed response if roll control alone was used in
this region.
Addition of the ARI provided a large positive
increment in LCDP
above _ : 15° such that the LCDPvalues remained positive
up through d = 40° .
This result indicates that the augmented airplane should exhibit
normal response
to roll-command inputs throughout the operational
angle-of-attack
range.
Dynamic
lateral-directional
directional
basis
stability
of
three
the
aerodynamic
SAS
on
and
i/tl/2
indicate
Dutch
for
off
roll,
three
are
and
are
roll
modes
yaw
roll
modes
in
values
to
A;
augmentation
aileron-rudder
activates
when
DISCUSSION
_
the
primary
and
29 ° .
OF
with
shown
in
the
(_
As
an
additional
kinematic-
aid
and
the
high-angle-of-attack
reviewed
in
this
section.
in
e,
whereas
of
the
_
features
(2)
(4)
a
an
of
15.
analyzing
characteristics
of
with
both
attack
that
opposite
Figure
of
is
the
15
the
all
the
Dutch
true
for
lateral-
shows
that
the
Dutch
roll
and
25o).
control
the
roll/yaw
stability-axis
automatic
system
SAS
yaw
are
damper,
spin-prevention
HIGH-ANGLE-OF-ATTACK
inertia-coupling
of
show
stability
the
stability
parameter
angle
SAS
airplane
figure
the
values
of
I/tl/2
for
the
classical
of
The
and
with
damping
without
30 ° .
the
equations
function
to
on
calculations
the
lateral-directional
INERTIA-COUPLING
several
a
lateral-
calculated
Positive
are
shown
as
up
the
of
airplane
envelope
system,
interconnect,
_
exceeds
of
enhanced
of
the
terms
motion
the
also
dynamic
were
of
modes.
Data
for
decrease
flight
discussion
in
characteristics
are
normal
results
15
of
data
significantly
appendix
rate-command
for
operative
detailed
in
modes
The
tends
the
figure
classical
airplane
lateral-directional
The
of
oscillatory
modes
of
motion.
Stability
SAS
B.
in
roll
stable
SAS
and
A
and
mode.
directional
tained
presented
period
P
or
stable
the
linearized
appendix
conditions.
spiral
roll
of
spiral,
trim
modes
roll
the
data
The
of
degree-of-freedom
and
the
damped
ig
stability.-
characteristics
KINEMATIC-
is
con-
(i)
a
(3)
an
system
roll-
which
AND
PHENOMENA
the
simulation
phenomena
of
the
results
which
F-16
which
significantly
airplane
are
follow,
influence
briefly
13
Figure 16 illustrates
the kinematic coupling between angle of attack and
sideslip that occurs when an airplane is rolled about its X-axis at high angles
of 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 into
sideslip after 90° of roll.
Because it is undesirable to generate large amounts
of sideslip at high angles of attack from a roll-performance,
as well as a
departure-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
nates
the
system
and
that
coupling
shows
that
these
If
this
this
rates
:
p
control
damper
its
In
ure
the
16(b)
into
sin
(p
second
and
verse
90 °
effect
limit
kinematic
for
The
dynamics
14
a
into
rate
as
the
elimi-
body-axis
well
as
roll
rate
expression
in
with
_
_
_
ARI
and
about
a
will
be
generated
in
varying
as
velocity
yaw
vector
A.)
sideslip,
result
stability-axis
its
appendix
indicates
signs)
tends
having
important
it
the
that
to
opposite
in
substantial
the
an
initial
will
expression
and
if
sideslip
is
seen
initial
_
from
being
figconverted
tan
same
be
then
roll
(See
an
with
the
that
roll,
as
airplane
envelope.
roll,
cos
a
varying
incorporates
rolling
this
can
in
during
the
CCV
airplane
rolling
reduce
_,
signs)
is
in
rolled
with
whereas
tends
configurations
increases
second
form
of
the
F-16
configuration
the
inertial
about
be
F-16
make
flight
p
(p
of
its
from
the
problem
coupling
vector
a
resulting
for
CCV
that
is
is
pitching
velocity
roll
unfortunately,
can
the
_
of
type
Pstab
yaw
)
Pstab
to
can
with
be
sideslip
rolling
with
increase
requiring
_
adverse
_.
an
generated
proverse
_
pro-
This
angle-ofdue
(using
to
excessive
example).
illustrates
rolled
Resolving
by
cos
the
of
coupling
rudder,
this
-
sideslip
attack
r
rolling
having
latter
-
to
of
term
_
[indicated
body-axis
by
with
body-axis
---q
The
d
of
case
after
_.
satisfied
normal
that
d
not
attempt
throughout
and
motion
involves
related
coupling,
system
which
_
motion
are
is
kinematic
-- p
The
rotational
tan
equality
to
conical
between
that
r
due
this
due
moment
at
high
important
to
that
nose-up
configurations
is
angles
kinematic-coupling
to
inertial
of
that
moment
employ
high-angle-of-attack
effects.
produced
viewpoint
pitching
the
attack.
was
caused
relaxed
Figure
when
The
the
is
desirability
previously
by
17(a)
airplane
discussed;
inertia
static
of
pitch
coupling
sta-
bility.
As an aid in visualizing
this effect,
the fuselage-heavy mass distribution of the airplane is represented as a dumbbell, with the mass concentrated
at the two ends. If the airplane is flying at some angle of attack and rolls
about its velocity
vector, the dumbbell will tend to pitch up to align itself
perpendicular
to the rotation vector
Pstab" This nose-up pitching moment due
to inertial
coupling
Mic can be expressed as
Mic :
Substituting
(I Z - Ix)Pr
P = Pstab cos _
and r = Pstab sin d,
Mic = (i z - IX ) Pstab
2
1 Z - Ix)Pstab
2
cos _ sin _ = _(I
sin 2d
The preceding expression shows that the pitch inertia-coupling
moment resulting
from stability-axis
rolling
is always positive
(nose up) for positive
d and
varies as the square of the stability-axis
roll rate Pstab"
For CCV configurations
with relaxed static stability,
the nose-up moment
must be opposed by the available nose-down control moment. If this control
moment is less than the inertia-coupling
moment, the horizontal
tail can reach
a travel limit,
at which time the airplane will lose the stability
contribution
of 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 and
pitch rates is illustrated
in figure 17(b).
The airplane mass distribution
is
represented by the dumbbell, and the airplane is shown rolling
to the right and
pitching up. As can be seen, the dumbbell will tend to yaw nose left to align
itself
perpendicular
to the rotation vector
_. The expression for the inertiacoupling moment is given by
Nic :
(I x - Iy)pq
Consider the case q > 0 (nose-up pitch rate).
Because I x < Iy, the preceding
expression shows that the yaw inertia-coupling
moment will always be opposite in
sign to the roll rate.
Recalling that to minimize adverse _ generation due to
kinematic coupling,
r must be equal to p tan _, it is obvious that this form
of inertia
coupling will inhibit
stability-axis
rolling
that can lead to the
buildup of large amounts of adverse _ which, in turn, can result in loss of
control at high angles of attack.
This section has briefly
reviewed kinematic- and inertia-coupling
phenomena
that, in various degrees, are important to the high d flight
dynamics of all
modern fighter
aircraft.
In the section entitled
"Departure- and Spin-Resistance
Simulation Results,"
it will be seen how these phenomena interact
to significantly influence the characteristics
of the subject configuration.
15
DEPARTURE-ANDSPIN-RESISTANCESIMULATIONRESULTS
Basic Control
System
The first
portion of the simulation investigation
consisted of documenting
the normal stall-,
departure-,
and spin-resistance
characteristics
of the configuration
equipped with the basic flight
control system described in appendix A. For convenience, this system will be referred to as hontrol system A in
this report.
Figure 18 shows time histories
of a ig stall to the limit angle
of attack (_ = 25o).
Rudder doublets were applied at various angles of attack
to evaluate lateral-directional
stability
at these conditions.
The data show
that the motions were well damped and that the airplane exhibited no tendency
toward 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 predicted by the LCDPvalues discussed previously.
Further evaluation of departure/spin
resistance was performed by applying
cross controls in ig and accelerated conditions.
Figure 19 shows time histories
of 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 and
full 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 a
result,
the airplane rolled and yawed in the direction
of the stick input.
Note
that the roll and yaw rates were sufficiently
high to produce a significant
noseup pitching moment (see qicl
trace) caused by the inertia-coupling
phenomenon
previously discussed.
This effect caused the airplane to pitch up so that the
angle of attack continued to increase beyond 29° . At this point (t : 8.5 sec),
the automatic departure-/spin-prevention
system activated and applied roll and
yaw controls to oppose the yaw rate.
As a result,
r decreased, which reduced
the inertia-coupling
moment. Furthermore, the reduction in yaw rate increased
the _/_ kinematic coupling since the airplane was now rolling
more closely
about 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 more
negative.
The combination of increased kinematic coupling and reduced inertia
coupling reversed the growth of angle of attack and caused it to drop back
below 29° . Cross controls were held for an additional
9 sec but resulted in no
prolonged 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 an
accelerated turn is shown in figure 20. As can be seen, the motions were very
similar to the ig case, with inertia
coupling causing a "pitch-out"
departure
in which _ increased to about 36o; however, there was no tendency for the
departure to develop into a spin.
These results indicated that (i) inertia
coupling could overpower the _ limiter
system to cause _ to increase far
above the 25° limit and (2) the airframe's
inherent lateral-directional
stability,
combined with the effectiveness
of the automatic spin-prevention
system,
minimized the possibility
of a departure progressing into a spin entry.
16
It
primary
tance
quickly became obvious that roll-pitch
cause of departures on this configuration.
is
illustrated
nose-up
the
high
varies
roll
control
ql
figure
inertial-coupling
moment
at
in
and
(ql
indicate
cient
control
increase
a
<
to
departure
susceptibility
to
this
type
that
departure
p2*)
it
<
P2*'
PI*
becomes
produced
nose-down
coupling-moment
which
is
there
If
very
is
suffi-
Pstab
likely
which
more
be
pressure,
moment.
then
the
that
can
the
at
of
note
available
dynamic
coupling
values,
the
imporrate
rolling;
with
and
nose-up
Note
of
of
its
roll
moments
intersection
these
occur.
axis
of
values
would be a
for
with
significant
(PI*
the
above
will
of
reason
variation
stability
two
rates
counter
sustained
at
points
roll
the
very
coupling
The
representations
_
The
highest
is
by
that
are
specified
moment
be
so
shown
q2 )"
the
and
pitch-out
Also
Shown
caused
2
Pstab
with
for
q2
curve
moment
rates.
moment
21.
inertial
should
that
indicates
acute
as
a
that
dynamic
the
pressure
decreases.
The
foregoing
attempted
360 °
lateral
30 °
stick
of
roll
observations
roll,
input.
yaw
Initially,
d
that
rudder
rates
to
dropped
to
a
in
was
began
apparent
from
Note
coordinating
and
are
starting
due
and
r
increased,
significant
nose-up
the
inertia-coupling
pitch
rate
to
build
point,
with
yaw
q
rate
hand,
a
coupled
(see
ricl
was
still
p
large
above
amount
this
the
aerodynamic
as
loss
of
_
rate
in
An
attempted
figure
applied
increased
and
to
held
tories
ig
in
270 °
that
of
the
A_.
enter
a
° .
360 °
roll
from
this
case,
Again,
an
(_
stick
despite
the
25o).
input
in
at
V
=
p
of
increased
full
to
nose-down
shows
the
that,
at
nose-down
pitch-out
departure
During
a
the
other
generation
qa
this
maximum
period
of
tendency
the
in
170
attempting
quite
not
as
the
had
than
for
limit
airplane
the
in
up
_
about
41 °
the
roll.
yaw
as
The
applied
time
his-
obtained
at
completing
_
the
shown
and
pilot
those
and
and
is
-60 °
3.7g
upon
_
_
_
the
to
departure
build
to
knots,
similar
excursions
did
_
no
the
input.
opposed
on
to
was
result,
33°/sac).
pitch-out
large
rate
stick
which
reached
resulted
At
are
a
the
_
the
which
=
a
of
kinematic
a
full
trace)
caused
a
increase.
At
this
roll.
turn
banked
motions
yaw
the
accelerated
experienced
period,
result,
of
_
As
applying
a
an
using
deflections,
sect;
qicl
there
r
5
greater
sac,
However,
command,
resulting
as
300 °
5.5
pilot
value
airplane
+25o;
(maximum
the
pitch
lateral
the
loss-of-control
±25
entry
right
=
about
spin
system
much
to
time,
of
was
about
lasted
limiter
that
@h
a
maximum
the
full
show
by
between
In
moment
_
the
this
Comparison
25 °,
however
moment
(t
in
By
ARI.
qicl
began
coupling
resulted
shows
:
coupling;
growth
sac).
d
direction
(see
_
limiter
+25o).
completed
which
into
23.
:
produced
oscillated
diverge
6
which
at
the
the
kinematic
yaw
22,
roll-control
to
in
its
thus
_
coupling
airplane
control,
to
rapidly
nose-up
the
a
angle-of-attack
(6 h
moment
occurred
while
the
and
(t
due
to
halted
_
maximum
moment
up
and
create
and
increasing
deflection
point,
to
adverse
30 ° , despite
stabilator
of
of
p
trace)
to
rapidly
20 °
figure
condition
obtained
up
about
in
trim
addition
also
build
ig
about
during
airplane
the
did
not
spin.
Because
assessment
full
was
changes
(A_
lateral
stick
_
360 °
also
rolls
made
of
180°).
Figure
inputs
starting
are
the
not
very
effects
24
shows
from
ig
useful
of
70 °
trim
from
rolling
a
through
bank-to-bank
at
_
tactical
=
smaller
reversals
25 ° .
viewpoint,
As
bank-angle
using
expected,
maximum
the
17
angle-of-attack
excursions due to inertia
coupling were less than that
encountered in the full 360° roll;
_ never exceeded 32° . Nevertheless,
the
stabilators
were very near saturation
(@h= +25o) during each reversal.
Furthermore, large adverse sideslip excursions occurred (reaching -18 ° at one
point),
caused by kinematic coupling resulting
from the high roll rates combined with insufficient
yaw rate (Irl < IPl tan _).
These results,
along with those obtained in the 360° rolls,
strongly indicated that the airplane roll-rate
capability
at high angles of attack could
result in (i) pitch-out
departures due to insufficient
nose-down pitch control
and (2) large adverse sideslip excursions due to insufficient
coordinating
yaw
control.
In summary, the airplane equipped with control system A was found to
be susceptible to inertia-coupling
departures during large-amplitude
roll maneuvers.
There was no tendency, however, for the departures to progress into spin
entries.
Control-System
Control
viating
system
the
trol
surfaces
roll-rate
or
system
pitch-out
was
(i)
0.35c,
roll
(3)
if
results
roll
(SM
below
results
is
for
SM
restricted
rate
may
with
:
only
their
future
face
very
sufficient
departures.
18
at
about
At
=
30
implications
CCV
_
=
designs
substantial
nose-down
13 °
due
percent
for
_
of
that
at
of
the
what
the
of
gravity
control
to
more
the
:
roll
fly
control
levels
penalties
to
prevent
the
as
is
rate
in
aft
had
allowable
capable
static
pitch
unless
they
inertia-coupling
to
at
0.35_,
by
the
to
be
providing.
indicate
instability
are
a
of
roll
of
results
the
maximum
airplane
these
of
gravity
to
indicated
maximum
configuration,
high
the
restricted
farther
roll
25.
of
penalty
the
25 ° , the
by
center
be
moved
would
figure
Comparison
severe,
instability,
d
to
30-percent
is
how
case;
inertia-
only
the
providing.
desire
the
indicate
airplane
an
limited
had
of
in
have
with
20 °
a
to
roll-performance
pitch
:
about
subject
incorporating
was
of
becomes
level
such
rate
departures
of
margin).
summarized
not
margin
extreme
the
a
roll
outside
to
this
static
did
capable
center
rapidly
this
that
roll
that
chosen
performance
above
is
25 °
the
penalty
_
rate
static
in
2-percent
coupled
control
As
-0.i0.
maximum
avoid
maximum
although
was
are
flight
If
investigated:
a
compromised
study
con-
alternate
were
in
alle-
airplane
investigated.
which,
configuration
indicates
-0.04.
above
was
Beyond
that
incurred
roll-performance
roll
the
the
airplane,
be
(positive
0.02)
roll
roll
0.29_
of
the
to
the
and
the
at
margin
=
To
the
of
limit
an
of
airplane
occurred,
results
0.41c
center-of-gravity
(SM
problem,
what
(2)
to
was
30 ° )
means
the
Therefore,
locations
have
RSS
was
limit
and
_;
indicate
the
-0.04),
attack.
obvious
resizing
envelope)
location
low
most
than
exceeding
range
control.
=
_
of
d
would
0.29c
obtained
rate
data
as
at
to
of
the
0.35_
static
angles
the
roll-rate-command
incorporate
pitch-out
values
the
percent
not
available
roll
4
chosen
did
its
nominal
performance
expected,
coupling
at
the
it
that
(other
center-of-gravity
is
0.29c,
The
As
high
lower
center-of-gravity
severely
have
a
Three
negative
evident
problem
(defined
which
operational
became
limiting
at
with
reduced.
a
and
further
departure
rate
It
departure
capability
control
about
B.-
pitch-out
Modifications
provided
pitch-out
Once an indication
of the maximumsustainable roll rates was obtained, a
roll-rate
limiting
scheme was implemented on the subject airplane.
As previously discussed, the basic control system includes a high-gain roll-ratecommandaugmentation system in which the pilot commandsa roll rate proportional
to
lateral
Obviously,
the
stick
most
rate
is
simply
lies
in
determining
should
be
were
to
at
force,
limit
the
which
any
up
to
straightforward
roll
rate
to
instant.
angle
of
maximum
of
the
use
(See
limiting
pilot
to
Three
attack,
308°/sec.
for
that
parameters
particular
investigated:
a
technique
the
commands.
evaluate
appendix
The
what
the
pressure,
roll
difficulty
roll
roll-rate-scheduling
dynamic
A.)
airplane
limit
parameters
and
symmetric
stabilator
deflection.
There
were
parameter:
(2)
(I)
as
shown
in
counter
the
The
same
reasoning
control
roll
can
it
found
as
The
of
use
initial
roll
rolling
out
due
loss
by
the
as
combining
pitch
terms
of
control
system
roll
80°/sec,
tion
<
with
i0
indicated
rate
based
N/m
2
pressure
4°/sec/deg
of
stabilator
deflections
rate
of
angle
of
of
250
in
excess
that
and
degrees)
with
and
the
rate
q,
for
_
of
scheme
rate
was
>
15 ° .
5°
caused
axes.
It
in
most
combined
by
found
N/m
with
reduction
that
be
308°/sec
26.
nose-down
of
to
maximum
to
as
The_
z)
com-
little
varia-
for
corresponds
a
(The
referred
_n,c.
2
and
figure
reducing
and
Finally,
a
in
henceforth
500
manifest
satisfactory
(-0.55°/sec/ib/ft
i0
influenced
can
was
the
increases
being
degradation
shown
of
of
also
is
coupling
_i'
2
of
minimizes
function
roll
value
of
pitch-
deflection
direct
achieved
normal
amplitude
preclude
this
is
will
value
This
to
the
in
large-amplitude
smaller
roll-response
-0.0115°/sec/N/m
(The
a
pitch
was
values
and
duration
resulted
roll
degradation
between
as
modification
knots.)
attack
greatest
stabilator
initial
limit
from
was
in
inertia-
individually,
the
cross-axes
@h)
limiting
ib/ft2).
of
Symmetric
the
varying
because
roll
q,
instantaneous
(219.3
airspeed
the
this
(Pcom)max
on
dynamic
500
increased
Roll-rate
the
rates
parameter
(to
needed
operates
This
to
21,
lower
counter
Unfortunately,
both
developed
B.)
it
(_,
incorporating
system
mandable
as
law
is
versus
motions
minimizing
in
and
increases.
figure
evaluated
in
short
roll
both
2_,
available
attack
in
differentiate
limiting
because
about
parameters
coupling.
not
moment.
three
sin
occurs.
to
resulted
do
sufficiently
and
of
scheduling
were
scheduling
IV.
where
control.
oscillations
proper
inherent
Scheduling
pitch
angle
results
remaining
schemes
table
of
control
in
control
360 ° )
are
a
a
movement
illustrated
departure
are
they
"response
between
cross-axes
control
_
which
be
scheduling
coupling.
compromise
The
q
because
roll
all
in
and
restoring
itself
as
scheduling
(A_
primary
to
drawbacks
as
pitch-out
control
basic
inertia
coupling
which
three
_
initial
remaining
the
pitch
illustrated
120 ° )
q,
with
as
with
control
as
a
attack
varies
nose-down
q;
two
response
<
to
in
thought
the
of
decreases
before
of
moment
moment
decreases
was
angle
choosing
The
maneuvers
(A_
amount
in
sustained
that
scheme,
the
used
moment
be
considering
coupling
was
moment.
was
rolls
i0,
indicates
coupling
each
inertia-coupling
deflection
directly
it
for
nose-up
nose-up
nose-down
stabilator
reasons
the
figure
to
that
two
reduction
to
an
of
symmetric
commanded
roll
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 the
stabilator
deflected for trimmed flight,
(Pcom)max is reduced from 280°/sec
at _ : 5° to 170°/sec at _ = 25o; these values would be representative
of
the
(Pcom)max available at the initiation
of a roll.
Also shown are the
values that represent the situation
in which full control has been used to
counter the inertia-coupling
moment with the stabilators
deflected full nose
down (@h= +25o)" As shown in the figure,
this case results in a decrease of
80°/sec in
(Pcom)max from the values obtained at trim
6h such that the maximum commandable roll rate is only about 90°/sec at _ = 25° .
Control system B also incorporated a modification
to the pitch axis to
assure proper stabilator
response during rolling
maneuvers. This modification
is shown in figure 28 and involved creating an equivalent angle-of-attack
signal
A_p based on roll-rate
magnitude.
The variation
of h_p with
IPl
is plotted in figure 29; note that a 20°/sec deadband was included so that the
system was inactive
during low-rate, precision maneuvers when it was not needed.
The pseudo angle-of-attack
signal was fed to the _ limiter,
which recognized
it as an increase in _ and therefore applied nose-down stabilator
deflection
to oppose it.
This system, therefore,
assured that the pitch control was
deflected in the proper direction
to oppose the nose-up coupling moment generated by rapid rolling
at high angles of attack.
The effectiveness
of control system B in preventing inertia-coupling
pitch-out
departures is illustrated
in figure 30, which shows a 360° roll
initiated
from Ig trim at _ = 25° using full lateral
stick input.
As previously discussed, this maneuver, when performed with the basic control system
(control system A), resulted in loss of control.
(See fig. 22.) For control
system B, figure 30 shows that although the pilot applied maximum lateral
stick
input, the resulting
commandedroll rate was limited
to only about 165°/sec (as
opposed to 308°/sec for control system A) so that the maximum roll rate achieved
was 70°/sec.
The resulting
nose-up coupling moment was smaller, and there was
sufficient
aerodynamic nose-down control moment to essentially
cancel it, as can
be seen by comparing the qicl
and qa traces.
As a result,
_ never
exceeded 26° during the maneuver and the maximum _ generated was less than
3° . Thus, in this particular
situation
at least, roll-rate
limiting
eliminated
the two problems experienced with the basic airplane,
that is,
_ pitch-outs
due to excessive roll-pitch
coupling and large
_ excursions due to excessive
roll-yaw coupling.
Examination of the control traces shows that significantly
less than maximumroll-control
deflections
were used. Even in the initiation
of 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 slower
initial
roll response compared with that of the basic airplane
(control system A); as discussed previously,
this response degradation is due mainly to the
use of q and _ in the limiting
scheme. One other point to note on the
control time histories
is that only about 60 percent of the available
rudder is
used for coordination
through most of the maneuver.
2O
A 360° roll initiated
from an accelerated turn at the d limit is shown
in figure 31. The results are very similar to the ig case in that the maneuver
was well controlled,
with the airplane never approaching an out-of-control
condition.
Time histories
of the 70° bank-to-bank reversals initiated
from ig trim
at e = 25° are shown in figure 32. Again the roll-rate
limiting
scheme of
control system B significantly
improved the controllability
of the airplane in
this maneuver. Angle of attack was maintained below 28° and sideslip
excursmons
below 4° . These results should be contrasted with those obtained with the basic
airplane
(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
from
the generated roll and yaw rates caused _ to overshoot above the 25° limit;
however, _ never exceeded 30° , _ was maintained below ii °, and the maximum
yaw rate encountered was only about 28°/sec.
Recovery was obtained immediately
after the controls were neutralized.
The results to this point indicated that the control modifications
incorporated in control system B significantly
enhanced the departure resistance of
the subject airplane in high d maneuvers, during which lateral
stick alone or
cross controls were used. This improvement resulted primarily
from the fact
that the pilot was constrained to commandless rolland yaw-control deflections
through lateral
stick deflections
due to the roll-rate
limiting
scheme employed.
However, it was still
possible for the pilot to augment rudder deflection
by
applying pedal inputs in the direction
of the lateral
stick input.
Therefore,
an assessment was made to examine how the additional
rudder might affect the
departure-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 discussed, performance of this maneuver with lateral
stick alone resulted
in
a
well-controlled
(See
fig.
different
that
tained
full
other
hand,
the
were
some
augment
by
the
moment
to
cause
of
larger
(see
an
the
very
proverse
roll
6r
qicl);
increase
rate,
to
in
same
large
detrimental
the
in
figure
as
34.
in
_
was
generated.
for
two
reasons:
(2)
angle
it
the
in
turn
control
in
it
coupled
_
-p_,
was
obtaining
amount
through
the
higher
nose-up
of
the
maneuver.
and
to
the
point
proverse
dihedral
effect
yaw
caused
rate
inertia-coupling
with
see
roll,
a
sus-
on
aileron
of
quite
traces
stick-only
reduced
acted
coupled
(_
control
large
with
the
kinematically
attack
earlier
and
This
in
the
deflections,
the
(i)
departure.
resulted
inputs
overcoordination
increase
of
pitch-out
of
roll-control
deflections
in
a
pedals
Examination
obtained
resulted
which
encountering
coordinating
the
rudder
substantially
and
of
of
deflection;
deflection
8°
fear
difference
rudder
about
of
was
to
shown
primary
differential-tail
sideslip
little
application
as
(-30 ° )
combination
that
with
However,
situation,
indicates
The
roll,
30.)
the
Wac2)-
high
The
roll
result
rate
was
21
a rapid pitch-out
departure despite the application
of full nose-down stabilator
by the control system; angle of attack reached a maximumof 70° , whereas sideslip oscillated
±30° during the departure.
Use of full coordinated inputs to
perform 360° rolls
at other ig and accelerated flight
conditions resulted in
similar loss of control situations.
In summary, control system B was found to significantly
enhance the departure resistance of the subject airplane as long as coordinating
pedal inputs
were not used during large-amplitude
roll maneuvers. Use of large amounts of
coordinating pedal in these maneuvers often resulted in severe pitch-out
departures.
It should be pointed out that there should be no need for the pilot to
apply coordinating
rudder inputs since this is automatically
done for him by the
ARI. However, it is felt that during air combat there would be a strong tendency by the pilot
to use rudder pedals in an attempt to obtain maximumroll
performance, particularly
in view of the fact that the roll-rate
limiting
scheme
of control system B resulted in noticeable degradation in the initial
roll
response of the airplane.
Control
correct
tem
system
the
B,
two
that
inputs
this
objective,
shown
in
the
At
ability
to
response,
was
that
magnitude
maximum
The
compared
control
this
and
to
(control
maximum
roll
of
to
the
roll
control
ig
in
that
in
were
obtained
maneuver,
system
A).
was
the
with
As
figure
the
during
control
the
basic
in
36,
:
the
as
from
initial
only
his
tracking
cor-
roll
limiting
the
roll-rate
eliminated
for
at
the
higher
departures;
resolving
at
capability
so
critical
roll-
the
which
shows
These
C,
initiation
the
as
the
to
only
about
maneuver
in
system
without
A
and
roll;
stick,
should
systems
roll-
control
system
lateral
histories
control
of
the
full
maximum
with
control
a
time
with
system
initiate
allowed
detract
until
roll
40°/sec)
airplane.
25 ° .
motions
_
roll-rate
was
full
discussed,
to
the
limiting
maneuver
control
previously
available
_
same
with
to
and
pitch-out
such
degraded
command
(IPl
not
B,
of
20°/sec
system
did
limiting
the
C
at
the
effective
allowed
from
flight
Note
obtained
was
rudder
of
rates
inertia-coupling
system
illustrated
fully
prevent
response
obtained
control
gain
become
pilot
30).
those
scheduled
imposed
needed
those
the
a
not
roll
are
these
rudder
inertia-coupling
system
therefore,
scheme,
from
deflections
phase
similar
22
with
22
control
accomplish
Alleviation
pilot
maneuvers
all
was
high
therefore
furthermore,
of
is
of
the
sys-
and
coordinating
magnitudes
however,
and
50°/sec;
initial
initiated
20o)
To
C.
to
control
incorporating
of
in
made
coordinating
developed
system
the
precision
adding
however,
problem
roll
(figs.
by
at
of
20°/sec),
_
amplitude,
deficiency
effectiveness
response
inputs
were
use
gain
did
it
rates,
_
(_i
with
when
system
roll-rate
aggravation
<IPl
B
control
limiting
This
where
roll
obtain
ing
the
control
between
was
degradation.
excessive
rudder
any
corrected
30°/sec-
lower
pilot
equipped
system
as
attempt
departures
scheduled
inputs
rudders
second
to
to
a
airplane
control
the
using
smaller
the
an
roll-response
to
due
results,
pitch-out
initial
referred
rates
the
exceeded
rates
360 °
roll
of
The
such
of
perform
path
_
by
eliminate
low
use
rections.
IPl
be
pilot
Elimination
full
(2)
problem
out
to
of
convenience,
will
faded
problem.
roll
For
accomplished
designed
pilot
and
departure
which
40°/sec.
was
35.
foregoing
to
modifications
features
was
path
the
deficiencies
used,
figure
on
susceptibility
two
pitch-out
pedals
(i)
are
additional
Based
primary
is,
pedal
C.-
and
in
were
roll-rate
75
when
percent
control
B
yaw-
fact,
C
be
Very
limit-
of
the
system B was used. In examining the response obtained with control system C, it
is seen that as the roll rate increased to values where inertia
coupling became
a factor,
roll-rate
limiting
was imposed and the rolland yaw-control deflections were reduced to essentially
the levels obtained with control system B; a
pitch-out
departure was avoided.
A quantitative
comparison of roll response obtained in this maneuver with
all three control systems is shown in table V. The figure of merit that was
used 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 compared
with 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 compared
with 13 percent slower for control system B. In summary, control system C was
successful in combining the desirable features of control system A (high initial
9oll response) and control system B (high resistance to inertia-coupling
departure) without incurring
the deficiencies
of either system.
The ability
of control system C to prevent pitch-out
departures due to
excessive pilot coordinating
rudder is illustrated
in figure 37. Shown are
time histories
of a 360° roll from ig trim at _ = 25° using full coordinated
stick and pedal inputs.
It is seen that fade-out of the pilot rudder commands
above IPl : 50o caused the resulting
airplane motions to be essentially
identical to those obtained using lateral
stick alone.
The maximumangle of attack
reached was 25° , and the airplane was not near a departure condition at any
point in the maneuver. These results should be contrasted with those obtained
with control system B, where a rapid pitch-out
departure to _ : 70° was
encountered (fig. 34).
Further evaluation of departure/spin
susceptibility
was accomplished
applying maximumcross controls at Ig and accelerated flight
conditions.
example is shown in "figure 38, in which the controls were applied from ig
at _ = 25° . The time histories
show that although full prospin controls
held for 14 sec, _ did not exceed 26° and yaw rate was maintained below
35°/sec.
by
An
trim
were
Figure 39 shows cross controls applied from ig trim at d = i0 °, followed
immediately 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 prevent
further
d excursions such that although the prospin inputs were held for over
12 sec, angle of attack never exceeded the 25° limit.
A further evaluation of the resistance of control system C to inertiacoupling-induced
departures is shown in figure 40. The initial
conditions for
the maneuver were ig trim flight
at M : 0.6 and h° = 9144 m. From this
starting point, full lateral
stick input was applied, followed in_nediately by
full nose-up pitch command. The large angular rates resulting
from these
inputs would be expected to maximize inertia-coupling
effects.
The data show
that very high rates, particularly
in roll,
were generated; however, the limiting features of the control system effectively
limited these rates to values
that could be handled by the available aerodynamic control moments. As a
23
result,
the maximum _ excursion
trols were held for approximately
Effect
was only 27° , despite
ii sec.
the fact
that the con-
of Aft Center of Gravity
It should be noted that all the maneuvers discussed up to this point were
conducted with the airplane center of gravity at its nominal'location
of 0.35_.
As previously
discussed, more aft center-of-gravity
locations
should aggravate
the inertia-coupling
departure problem because less nose-down aerodynamic control moments would be available.
Therefore, a brief investigation
was conducted to see what effect more aft center-of-gravity
locations might have on
the departure-prevention
ability
of the control system developed for a center
of gravity of 0.35_.
For this evaluation,
center-of-gravity
locations of
0.375c 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 data
show that more nose-down stabilator
was required to trim at this condition due
to the increased static instability
caused by the rearward center-of-gravity
shift.
Comparison of the time histories
of this maneuver with those obtained
with a center of gravity of 0.35_ (fig. 36) verifies
the loss in nose-down
aerodynamic pitching moment at 0.375_. This loss is reflected
in the @h
trace which shows that the stabilators
were at the full nose-down position
through 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_).
Although
a departure did not occur in this case, the fact that the pitch control remained
saturated for such an extended period of time and was still
unable to hold
below the limit value indicates that control was very marginal in this situation.
A more severe coupling maneuver would, therefore,
be expected to result
in a departure.
An example of loss of control is shown in figure 42, which
shows the high coupling maneuver previously
discussed, in which the pilot
applied full roll and pitch inputs from ig trim flight
at M : 0.6. As previously 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 the
center of gravity at 0.375_, the available nose-down control was overpowered by
the inertia-coupling
moment, and a rapid pitch-out
to _ : 76° ensued. Following the departure,
the airplane entered the deep-stall
trim condition previously
discussed; the deep-stall
problem is addressed in more detail in the section
entitled
"Deep-Stall Simulation Results."
These results indicated that rearward center-of-gravity
movement beyond
0.375_ would require further
limiting
of roll rate in order to obtain an acceptable level of departure resistance.
These indications
were verified
when control system C was flown with the center of gravity at 0.39_. An example is
shown in figure 43, which presents time histories
of an attempted 360° roll
using full lateral
stick input starting
from ig trim at _ : 25° . It is seen
that the aerodynamic nose-down control was easily overpowered by the inertiacoupling moment and resulted in a sharp pitch-out
departure to _ : 84° and
entry again into the deep-stall
trim condition.
Attempts at other roll maneuvers that were accomplished without incident with the center of gravity at 0.35c
resulted in a similar
loss of control.
24
It was found that the airplane equipped with control system C that was
flown with the center of gravity at 0.39_ was at least as prone to departures
as the basic airplane was at 0.35_.
It thus became clear that the roll-rate
limit would have to be reduced significantly
at a center of gravity of 0.39_ to
reestablish
a level of departure resistance comparable to that obtained at
0.35_.
However, as indicated in figure 25, this level of roll performance may
not be adequate from a tactical
viewpoint.
In summary, control system C was
found to provide a high level of departure resistance for the airplane with the
center of gravity at its nominal location.
Large-amplitude maneuvers at Ig'and
accelerated flight
conditions
involving
gross
application
of
adverse
controls
did
not
result
in
deteriorated
loss
of
departure
Operation
at
reductions
control.
resistance
to
center-of-gravity
in
However,
maximum
the
point
locations
allowable
roll
discussed
in
exhibit
the
stable
possible
described
nose
43)
was
possible
all
The
the
to
resulted
of
put
the
a
speeds
at
attack
the
top
of
maneuver
The
full
of
oscillation,
_
58 ° ,
limiter
caused
pendent
of
oppose
_
the
that,
to
angle
pitch
0 °,
from
r
_
any
yaw
0,
by
the
or
to
the
was
deep
_
with
low
Q
low
air-
through
large
at
angle-of-
limiter
An
stall
very
maneuver
very
fall
a
42
condition.
from
climb,
reaching
of
it
(figs.
airspeed
pressure.
G
roll
For
the
=
top
0.2
_
the
system
example
of
at
and
yaw,
and
the
a
an
fighter
the
_
the
the
ig.
due
such
a
automatic
system
was
Note
that,
several
trim
at
In
point
this
pitch,
position,
the
inde-
spin-prevention
fuselage-heavy
the
appli-
After
stall
commanding
a
the
system.
deep
nose-down
the
airspeed
As
70 ° , despite
airplane.
full
having
the
respectively.
limiter
into
over
maneuver,
to
d
and
control
remain
the
0.1g,
increased
by
6° ,
of
and
stabilized
no
pilot,
rate.
at
M
control
to
In
the
into
low
airplane
opposed
attack
airplane
stabilators
away
of
absolutely
inputs.
such
generation
dynamic
if
trim
attack
of
the
effectively
show
the
had
pilot
control
to
_
pilot
allowing
decreased
the
nose-down
entry
intention
see
departures
deep-stall
of
One
with
com-
locations
this
angles
even
is
to
The
decelerating
the
60 ° ,
conducted
that
high
attack.
low
=
however,
point.
into
kinematic
at
_
Control
configuration
44.
44
through,
of
the
and
be
figure
figure
cycles
tions
not
in
cation
took
resulting
effectiveness
of
fell
_
climb
of
point,
was
trim
steep-attitude,
The
acceleration
airplane
a
0.375_.
further
and
subject
center-of-gravity
at
70 ° , with
the
could
shown
data
normal
into
at
require
Stability
the
trim
indicated
of
of
for
vicinity
The
aft
study
angles
of
control
is
present
about
the
flying
at
g.
excursion
for
maneuvers
of
in
airplane
high
data
therefore
rolling
airplane
maximum
zero
lack
point,
the
the
marginal
would
"Discussion
deep-stall
section
was
Problem
down.
investigation
stabilized
in
during
essentially
with
a
conditions
reaching
and
an
previous
results
airspeed
was
and
into
in
and
to
points
full
fly
of
entitled
trim
it
0.375c
shifts
RESULTS
pitching-moment
deflected
weak,
to
section
0.35_
of
SIMULATION
deep-stall
stabilators
paratively
the
the
that
aft
Description
As
center-of-gravity
rate.
DEEP-STALL
Characteristics,"
rearward
system
control
deflecmass
25
loading, the most effective
spin-recovery controls are obtained when the
rudders are applied to oppose yaw rate and the ailerons are applied in the
direction
of the yaw rate.
It should be recognized that these systems did successfully prevent any yaw-rate buildup and therefore eliminated the danger of
the motions progressing into a spin; nevertheless,
this was of little
consequence to the pilot since he was locked in the deep-stall
condition,
with no
way of recovering by using his normal controls.
It is important to note that all the maneuvers discussed to this point
were conducted with an aerodynamic model which did not include aerodynamic
asymmetries; that is, the aerodynamic coefficients
Cy, C_, and Cn were zero
for _ = 0° and neutral lateral-directional
controls.
In the normal angle-ofattack flight
envelope of current fighter aircraft,
this modeling assumption
has been found to be generally valid in that wind-tunnel measured asymmetries
are normally insignificantly
small.
However, experience has shown that, in
many configurations,
these asymmetries can reach significant
magnitudes at
post-stall
_. Figure 45 shows Cy, C_, and Cn asymmetries measured during
wind-tunnel tests on the subject configuration.
The data confirm that within
the normal _ flight
envelope, these asymmetries are small enough to be
ignored.
However, they rapidly increase in magnitude for _ > 30° . Of particular
significance
is the fact that the yawing-moment asymmetry reaches its
maximumvalue in the _ region of the deep-stall
trim point.
In order to
assess the importance of this characteristic,
the deep-stall
investigation
was
conducted with two aerodynamic models, one that included the wind-tunnel measured asymmetries of figure 45 and one that omitted them.
Figure 46 shows time histories
of a deep-stall
entry with the asymmetries
included.
Comparison with the results obtained without asymmetries (fig. 44)
indicates little
difference
in the initial
phase of the entry.
However, once
the airplane began to settle into the trim point, figure 44 shows that the
nose-left
yawing-moment asymmetry caused the yaw rate to build up to about
-20°/sec, despite the application
of significant
amounts of opposing aileron
and rudder deflections
by the spin-prevention
system. The airplane also assumed
a left wing low (_ _ -16 ° ) and nose low attitude
(0 _ -23o).
Note that the
nose-up inertia-coupling
moment resulting
from the nonzero roll and the yaw
rates caused the airplane to trim at an angle of attack roughly 4° higher than
that obtained without the asymmetries.
Another important indication
from these
results is that the asymmetries would probably have driven the airplane into a
spin without the action of the automatic spin-prevention
feature of the control
system.
With regard to the ease of experiencing the deep-stall
trim, it was found
that the first
_ peak during the entry was critically
important in that an
overshoot to values of _ too much above the trim point resulted in the generation during the downswing of sufficient
nose-down pitch rate to drive the airplane nose down over the Cm > 0 hump and result in recovery.
Generally,
the
airplane did not consistently
drop into the deep-stall
trim point if the initial
peak in _ was greater than 75° . Control of the initial
_ excursion was
difficult,
and the pilots were therefore not able to obtain the deep-stall
trim
on every attempt.
26
stick in phase with the airplane motions, with the hope that sufficient
angular
momentumwould be created during a downswing cycle to drive the airplane over
the positive
Cm hump and back down within the normal _ envelope of the
airplane.
A recovery attempt using this technique is shown in figure 50. Starting
from a stabilized
trim at _ _ 62° , the pilot activated the pitch rocker system
and rapidly applied full aft stick at t : 71.3 sec. In response, the stabilators moved from the full nose-down position commandedby the _ limi[er
to
full nose up. The resulting
nose-up moment caused _ to increase to 75° , at
which point the pilot reversed his controls and applied full forward stick to
obtain
@h: +25o- This action generated a large nose-down moment, indicated
by the qa trace at t : 74, and _ decreased rapidly.
As expected,
qa
became positive
(t : 75 sec) for a brief time as _ traversed the hump in the
Cm curve; however, there was sufficient
momentumto cause the airplane to continue to pitch downward until a recovery was obtained at t : 78 sec. It
should be noted that in this particular
case, the pilot very accurately kept
his inputs in phase with the motions and therefore obtained a recovery within
1 cycle of the oscillation.
However, it was found that in situations
where the
pilot was somewhat out of phase with the oscillation,
recoveries were delayed
significantly
so that as many as three to four pumping cycles were required for
recovery.
Further assessment of the deep-stall
and recovery characteristics
were
obtained by moving the center of gravity aft to 0.375_.
Figure 51 shows an
entry and recovery attempt using the speed brakes and flaps; aerodynamic asymmetries 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 brakes
were deployed and the flaps reconfigured,
and a rapid recovery was obtained in
4.5 sec. A quite different
result was obtained with asymmetry modeling; an
example is shown in figure 52. The data indicate that the airplane tri_ed
at
a 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 and
flaps.
As can be seen, the resulting
nose-down pitching-moment increment
caused _ to decrease by about 4o; however, it was not sufficient
to effect
recovery and the airplane established another trim condition with
_ _ 63° and
r = -20°/sec.
Generally, it was found that recovery to normal flight
conditions
could
not be attained with this technique unless the pilot made the speed-brake and
flap change early in the entry while there were still
large oscillations
in the
motion and unless the inputs were made during a downswing in _ so that they
reinforced
the downward motion.
Obviously this is very difficult
to do, and in
the majority of cases, recovery was not obtained.
The primary reason for the
difference
in the results obtained with and without asymmetry modeling was the
existence of the yaw rate with modeling.
Apparently,
the additional
nose-up
inertia-coupling
moment caused by the angular rate was sufficient
to negate the
relatively
small amount of nose-down moment generated by the speed-brake and
flap changes.
28
Methods of Recovery
Once it was determined that the airplane could be flown into the deepstall trim point, techniques were developed to recover from it.
As previously
discussed, the primary controls could not be used because the pilot had no
control over them in this situation.
Consequently, other schemes for obtaining
the needed nose-down pitching moment were investigated
in the wind tunnel, and
two potentially
useful concepts were identified.
The first method involved
reconfiguring
the flaps by retracting
the leading-edge flaps and deploying _he
trailing-edge
flaps (61ef = 0°,
6te f : 20o), whereas the second involved
speed-brake extension to maximumdeflection
(@sb= 60o)" The locations of these
surfaces are shown in figure 2. Note that the speed brakes are located on the
upper and lower surfaces of the aft fuselage shelf next to the stabilators,
and
their deployment therefore would be expected to provide a nose-down moment in
, the deep-stall
region.
Figure 47 compares the resulting
pitching moments with those for the normal
configuration
(61ef : 25o' 6tef : 0°'
@sb: 0°); note that all data are for
the full nose-down stabilator
deflection
that would be maintained by the
limiter
system. The data show that reconfiguring
the flaps provides an increment of about -0.018 in Cm in the angle-of-attack
range of interest
(55° to
60o), whereas speed-brake deployment results in about -0.025.
Note that neither
scheme clearly eliminates
the trim point with the center of gravity at 0.35_,
and therefore they would not be expected to be always effective,
particularly
for 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 of
about -0.05, which eliminates the deep-stall
trim point.
Figures 48 and 49 show time histories
of recovery attempts using the combination of speed-brake deployment and flap reconfiguration.
The results obtained
without asymmetry modeling are shown in figure 48. The recovery attempt was
initiated
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. The
results with asymmetry modeling are shown in figure 49. Although a positive
recovery was also attained,
the recovery was not as rapid, taking some 8 sec to
occur.
The reason for the slower recovery was the existence of the yaw rate
which created an additional
nose-up moment due to inertia
coupling that had to
be overcome by the nose-down recovery moment.
One additional
recovery technique that was investigated
consisted of
reconfiguring
the pitch control law to reestablish
pilot
control over the stabilators in the deep-stall
region.
The reconfiguration
involved deactivating
all
feedbacks, including the d limiter
system, so that the only signal that
remained was the pilot stick command. With this system (henceforth to be
referred to as the pitch rocker),
the deflection
of pitch control was directly
proportional
to pilot inputs.
The reason for doing this can be seen by reviewing the pitching-moment data for maximum stabilator
deflections
shown in figure I0.
The data show that at the deep-stall
trim point (_ _ 60°), a large
pitching-moment increment results in going from full nose-down to full nose-up
control deflection
(ACm _ 0.i).
Thus, a possibility
exists to use this available control moment to initiate
and build up a pitch oscillation
by moving the
27
i
The effectiveness
of the "pitch-rocking"
technique in providing recoveries with the center of gravity at 0.375c is illustrated
in figure 53. In this
particular
case, pitch rocking was initiated
early in the entry (t = 52 sec)
while the motions were still
quite oscillatory;
in addition,
the pilot did a
very good job of phasing his inputs in that the initial
aft stick applications
were 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 following
downswing to reestablish
normal flight.
The recovery was obtained within 8 sec
after the pilot
initiated
recovery action.
Figure 54 illustrates
the results,
that were obtained when the pilot did not optimally phase hi_;rocking
inputs
with the ai,rplane motions.
In this case, recovery was not obtained until the
pilot had completed five rocking cycles, and the time interval
between initiation of recovery action and actual attainment of recovery was some 30 sec.
These results emphasize the criticality
of proper pilot usage of the pitchrocking technique; nevertheless,
this technique was found to%e effective
in
providing deep-stall
recovery for all the conditions
(center-of-gravity
location
and asymmetry modeling) investigated
in this study.
TRACKINGRESULTS
Following completion of the departure, deep-stall,
and spin-susceptibility
investigation,
the tracking evaluation phase of the study was conducted to determine how these characteristics
and the control-system
changes affected the
ability
to track a target airplane through maneuvers representative
of air combat.
The evaluation was conducted at the nominal 0.35_ center-of-gravity
location and included an assessment of the three control-system
configurations
studied in the first
phase.
Results
of Basic Control
System (Control
System A)
Time histories
of the airplane motions during the wind-up turn tracking
task are shown in figure 55; included are the range between the two airplanes R, the total angular tracking error
g, and the lateral
component
of g I.
The data indicate that the pilot had little
difficulty
in tracking
the target airplane through the task.
Note that the design of the lateraldirectional
control
system
allowed
him
to
track
using
only
the
stick,
and
no
pedal
inputs
expected,
were
none
encountered
required.
of
the
The
airplane
inertia-coupling
in
this
task
Figure
56
illustrates
system
(control
due
to
motions
problems
the
absence
were
well
previously
of
any
damped
and,
discussed
as
were
large-amplitude
rolling
maneuvering.
trol
by
the
wind-up
pull-ups
nature
system
pilot-input
turn
to
of
simultaneously
the
the
in
that
high
_
performance
A)
time
histories,
a
combination
task
tended
was
requiring
to
in
required
rapid
accentuate
the
the
airplane
bank-toT_9nk
this
of
to
of
was
tracking
a much
bank-to-bank
maintain
and
any
accurate
with
more
the
basic
_ask.
demanding
As
tracking.
control
handling-quality
The
in
than
by
very
all
indicated
task
reversals-followed
con-
dynamic
three
deficiencies.
the
rapid
axes
Note
29
that the pilot used very large lateral
stick inputs to make the reversals,
and
the inertia-coupling
moments resulting
from the high roll and yaw rates
required large countering nose-down stabilator
deflections.
Maximum _ and
excursions were 30° and i0 °, respectively.
The £ and _ data show that the
pilot had difficulty
in maintaining tracking during the reversals;
however, once
the reversal was completed, he was able to reacquire the target within about 5
to i0 sec. It should be pointed out that the pilot was aware of the potential
pitch-out
tendency if too much coordinating
rudder was used, and he therefore
flew the task essentially
without pedal inputs.
Furthermore, by using_only the
stick, the amplitude of the bank-angle changes that were required
(IA_I
_ 180 ° )
was
insufficient
departures
The
57.
As
amplitude
the
show
during
1
_
that
the
sec
to
basic
rolls
to
this
the
Note
that,
at
to
Effects
on
incorporated
plane
equipped
in
the
were
compared
system
A)
airplane.
are
essentially
The
pilot
was
58
system
B
with
figure
less
As
in
a
coupling
lator
slip
The
3O
the
control
result,
the
use
the
fact
Control
and
the
since
B
the
assessed
three
systems
this
with
task
this
tracking
did
No
the
factor
cer-
modifica-
flying
system
the
tactical
and
C
not
29 ° .
of
in
the
tasks.
schemes
the
for
departures
by
control
B
obtained
reached
control-system
limiting
degraded
held
C
from
basic
occurred
pitch-out
and
The
remainder
inputs;
no
therefore
was
_
the
were
the
roll-rate
control
condition
that
C
and
stabilator
pedal
in
situations.
maximum
no
large-
airspeeds
during
Systems
B
with
those
the
shows
B
roll
and
are
due
yaw
reflected
Comparison
seen
commented
basic
roll-
system
earlier
that
airplane
and
to
the
air-
The
results
(control
used
to
enhance
effectiveness
the
basic
wind-up
require
any
of
turn
control
This
flying
task
system.
rapid,
the
large-
rate
limiting
lower,
in
the
_
noticed
decreased
traces
the
use
also
departure
a
scheme
and
definite
the
of
shows
the
task.
inputs
in
discussed.
inertia-
nose-down
reduction
susceptibility
degradation
compared
significantly
previously
reduced
the
con-
be
same
stick
were
large
with
should
lateral
deflections
were
of
equipped
figure
against
amplitude
yaw-control
rates
airplane
task.
similar
during
they
of
tracking
applied
resulting
moments
performance
the
generally
the
excursions
not
bank-to-bank
which
deflections.
pilots
result
illustrates
in
pilot
cases,
moment;
significantly
to
low
result,
illustrated
rapid,
departure
occurred
for
is
two
nose-down
did
the
for
and
a
task.
task
near-departure
against
obtained
had
ACM
As
this
required
resulting
systems
obtained
56,
the
full
on
maneuvers.
Figure
Although
a
that
systems
whether
expected
roll
trol
both
those
the
_
run,
capability
identical
an
amplitude
of
control
determine
results
limit
coupling.
made
task
coupling
extent,
these
resistance
the
This
in
with
to
departure
tracking
with
in
situations
some
inertia
runs
inertia-coupling
Results
tions
the
nose-up
again,
accounted,
encountered.
to
the
this
potential
maneuver
oppose
of
airplane
particular
roll
due
any
discussed,
180 ° )
in
first
departure
near-loss-of-control
run.
tainly
were
of
airplane
the
further
a
during
previously
(IA_I
exposed
over
cause
observed
performance
figure
data
to
were
stabiin
side_
evaluation.
in
initial
roll
response in going from control system A to control system B. They indicated
that this was mildly bothersome since they felt that they had to hold large
lateral
stick forces longer in order to obtain the same net roll response.
small
it
positive
reduced
can
be
were
the
seen
did
An
that
the
example
of
show
that
except
the
the
obtained
with
and
was
the
improved
the
proper
the
accurately
this
only
was
able
to
59
control
and
56
system
C
than
with
could
than
with
either
When
the
airplane
task,
the
comparative
in
the
for
track
roll
due
In
the
initial
slightly
sized
of
tions
the
0.35_.
farther
rate
to
aft,
roll-performance
it
should
tracking
pitch-out
extreme
be
while
was
than
This
departures
low-speed
from
control;
with
a
minimum
input
in
trace
pilots
with
stated
control
reducing
aft
would
out
that
was
not
g
no
an
of
be
that
system
C
the
C)
workload.
60
and
the
61
degraded
their
two
control
determined
the
to
It
to
to
provide
should
be
reempha-
degrade
the
to
occurred
tracking
view
loca-
further
tracking
regard
in
loca-
center-of-gravity
require
entries
the
features
found
limiting
ability
deep-stall
tasks
the
did
of
resulting
during
of
the
resulted
contrary,
departures;
With
that
departures
center-of-gravity
at
will
the
was
nominal
result
and
the
affect
other
study
On
system
expected
unexpected
in
obtained
noted
incorporating
pitch-out
deep-stall
flown
those
figures
pitch-out
also
indicated.
encountered,
the
the
prevent
0.375_,
to
in
pilots
over
operation
of
was
as
significantly
pilot
at
C
same
capability.
conducted
previously
were
zero
Moreover,
stick
and
shown
C
(control
susceptibility
pointed
B
discussed.
but
discussed,
degradation
runs.
tracking
loss
particularly
more
to
B
the
not
phase
used
limiting
previously
minimize
significantly
was
in
tracking
did
preferred
evaluation
that
evaluation
are
previously
roll-rate
As
system
resulting
with
the
Again,
it
mildly
roll-response
improved
that
tracking
using
response
control
oscillatory
systems
runs
that
they
degradation
system
reversals
cleanly
the
air-
histories
bank-angle
workload
essentially
respectively.
commented
scheme
significant
minimize
C,
characteristics
the
control
were
Representative
and
but
limiting
control
roll
to
the
lateral
Overall,
less
the
time
airplane.
and
of
less
A.
with
with
results
Again,
summary,
roll-rate
no
B
rapidly
histories
system
for
excursions)
improved
B
'
observation.
roll
of
basic
much
smoother,
and
equipped
task.
of
time
system
this
B.
B
ability.
systems
tion
or
systems
response
tracking
in
A
the
sideslip
in
markedly
better
of
that
the
through
The
all
inputs
control
task
59.
One
that
Overall,
this
initial
than
reversals
the
control
slightly
bank-to-bank
control
a
that
confirm
the
the
A.
target
through
that
smaller
roll
that
with
figure
target
resulted
of
indicates
they
ACM
the
Comparison
characteristic
of
the
was
show
bank-to-bank
better
than
(much
rate
make
the
pilots
This
than
to
in
commented
slower
roll
the
shown
noticeably
control
of
oscillations.
figures
was
slightly
limiting
is
track
tends
in
C
pilots
system
very
traces
tracked
The
sideslip
pilot
system
B
the
characteristic
to
performance
control
one.
_
which
system
ability
and
by
tracking.
roll-response
_
noted
traces,
control
their
tracking
pilot
final
input
with
reduced
the
with
response
during
lateral
affect
of
roll
overcontrol
oscillatory
equipped
slower
the
less
Comparison
plane
to
significantly
task.
the
comparing
stated
not
of
tendency
by
somewhat
pilots
of
aspect
any
fact
not
trim,
of
that
the
no
entail
maneuvers.
31
INTERPRETATION
OF RESULTS
The fidelity
of the simulation in representing
the actual F-16 airplane
was evaluated by comparing simulation results with actual airplane flight
test
data and by having pilots with F-16 experience fly the simulator.
Throughout
the present study, close coordination
was maintained with the flight
testing Of
the full-scale
airplane to ensure correlation
between simulation and flight
and
to expedite development of airplane modifications
for testin@ in flight
when
problems were encountered.
As a result,
the major characteristics
an@results
derived from this investigation
have also been encountered in flight.
Flight
test results have confirmed that the airplane can experience pitch departures
during rolling
maneuvers and/or low-airspeed maneuvers at high angles of
attack.
Flight results have also shown that the airplane can enter the deepstall trim condition from the flight
conditions described herein.
Moreover,
the various control-system
modifications
and deep-stall
recovery methods
studied in the present simulation have been flight
tested and were found to be
as effective
as the simulation predicted.
It should be recognized, however, that the present study was limited in
scope, and these limitations
should be kept in mind when applying the results
and conclusions of this study.
A primary limitation
is that the aerodynamic
data were measured at low values of Mach number and did not incorporate any
compressibility
effect;
consequently, the results can only be considered valid
for Mach numbers less than about 0.6.
It should also be kept in mind that only
the clean configuration
was investigated
and that it is likely
that certain
store configurations
(particularly
asymmetrical stores) can degrade the
departure/spin
resistance of the airplane.
SUMMARY
OF RESULTS
A piloted
simulator investigation
has been conducted to evaluate the highangle-of-attack
characteristics
of an F-16-based fighter
configuration
incorporating relaxed longitudinal
static stability.
The following major results
were derived from this study:
1. The airplane with the basic control system was found to be resistant
to the classical
yaw or nose slice departure; however, it was susceptible to
pitch departures caused by having insufficient
nose-down control
to
counter
inertia-coupling
In
addition,
very
low
the
2.
at
Pitch-out
the
high
roll
during
rapid,
susceptible
angles
of
by
at
pitch
roll
departures
when
the
maneuvers.
flown
to
attack.
produced
rates
to
large-amplitude
the
inertial
lower
coupling
speeds
and
were
higher
prevented
by
angle-of-attack
conditions.
3.
without
A
modified
control
be
flown
system
features
significantly
airspeeds.
32
was
departures
maximum
departure-prevention
still
generated
airplane
airspeeds
limiting
flight
moment
to
degrading
angles
of
incorporating
made
roll
attack
the
airplane
performance.
above
the
roll-rate
limiting
extremely
departure
However,
angle-of-attack
the
and
other
resistant
airplane
limit
at
could
very
low
4. Although the airplane with the nominal center-of-gravity
location could
be made more departure resistant
without sacrificing
maneuverability,
it
appeared that center-of-gravity
locations
significantly
farther aft would
require more drastic roll-performance
penalties that could compromise tactical
effectiveness.
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 the
primary pilot controls.
The roll-rate
limiting
control concept developed in
this study could not prevent very low airspeed entries into the deep stall.
6. It was not possible to define reasonable control laws (short of limiting
minimum airspeed) whichcould
prevent departure and entry into the deep stall
at very low airspeeds.
Changes to the airframe to increase high-angle-of-attack
10ngitudinal
stability
and/or control would probably be necessary to eliminate
these problems.
7. Reconfiguring the wing leading- and trailing-edge
flaps and deploying
the speed brakes generated a sufficient
nose-down moment increment to recover
the 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 the
effectiveness
of this recovery technique, particularly
at the more aft center-ofgravity locations.
8. It was possible for the pilot to oscillate
the airplane out of the deepstall trim point by applying maximumpitch-control
inputs in phase with the
airplane motions.
The effectiveness
of this technique was found to be a direct
function of proper input timing by the pilot;
with correct pilot action, this
technique successfully
recovered the airplane,
even at the aft center-of-gravity
locations investigated.
Use of this procedure, however, required a modification
to the control system to enable reestablishment
of pilot control over the
stabilators
above the limit angle of attack.
Langley Research Center
National Aeronautics and Space Administration
Hampton, VA 23665
September 20, 1979
33
APPENDIXA
DESCRIPTIONOF CONTROLSYSTEM
Longitudinal
A block diagram of the longitudinal
control system used in the .simulation
is presented in figure 62. The implementation was a fly-by-wire,
commandaugmentation system (CAS) whereby the pilot commandednormal acceleration
through
a minimum deflection,
force-sensing
side-stick
controller.
Washed-out pitch
rate and filtered
normal acceleration
were fed back to give the desired
response.
A forward-loop
integration
was used in an attempt to make the
steady-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-attack
limiting
system which functioned by using an _ feedback to modify the pilotcommandednormal acceleration.
The angle-of-attack
feedback reduced the commanded normal-acceleration
limit by 0.322g/deg between _ = 15 ° and 20.4 ° and
by
1.322g/deg
limit
in
manded
above
ig
_
flight
normal
of
:
20.4
acceleration
modeled
as
a
surface
deflection
is
first-order
limit
Leading-edge
according
to
the
° .
The
flap
limit
lag
of
was
±25 ° .
in
=
1.38
-
sec,
9.05
63.
with
The
a
angle-of-attack
positive
stabilator
rate
with
i+
an
allowable
limit
angle
of
of
com-
actuator
was
60°/sec.
attack
The
and
q/Ps
1.45
Ps
modeled
Maximum
in
maximum
scheduled
S+7.25
was
25°/sec.
_
resulted
The
figure
0.0495
flap
deflection
was
following
relationship:
actuator
of
feature
25 ° .
shown
2S+7.25
61e f
This
approximately
as
flap
a
first-order
deflection
lag
was
of
0.136
sec,
with
a
rate
25 ° .
Lateral
The
ure
lateral
64.
The
commanded
vated
oppose
that
34
system
roll
stick.
Above
which
any
the
control
_
yaw-rate
pilot
has
is
incorporated
rates
uses
system
up
to
:
29 ° , an
a
yaw-rate
buildup.
no
control
a
a
shown
block
command
308°/sec
automatic
diagram
feature
through
the
given
to
this
the
drive
mode,
the
the
airplane
whereby
system
roll-control
roll-rate
laterally.
in
fig-
the
pilot
force-sensing
departure-/spin-prevention
feedback
over
the
roll-rate
maximum
In
by
control
is
surfaces
CAS
is
disengaged
acti-
to
so
APPENDIXA
The roll-control
system uses both aileron and differential-tail
deflections
at a ratio of 4° of @a per 1° of @d" The surface actuators were modeled as
0.0495-sec first-order
lags, with rate limits of 60°/sec for the differential
tail 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 simulation
is presented in figure 65. The pilot rudder input was computed directly
from
pedal force and was limited to ±30° . Furthermore, this commandsignal was
reduced to zero between 20° and 30° angle of attack in an attempt to prevent
departures resulting
from excessive pilot rudder usage at high angles of attack.
,Yaw stability
augmentation consisted of feedbacks of r - p_ (mrstab)
and ay.
The stability-axis
yaw damper provided increased lateral-directional
damping in
addition to reducing sideslip during high _ rolling
maneuvers. The lateral
acceleration
feedback had little
effect at the low-speed flight
conditions of
the present investigation.
The directional
control system also incorporated an
aileron-rudder
interconnect
(ARI) for improved coordination
and roll performance. At low speeds, the ARI gain was scheduled as a linear function of angle
of attack with a slope of 0.075/deg.
As in the roll axis, above _ = 29° , a
departure-/spin-prevention
mode is activated which drives the rudder at a gain
of 0.75 deg/deg/sec to oppose any yaw-rate buildup.
The rudder actuator was
modeled as a 0.0495-sec first-order
lag with a rate limit of 120°/sec.
The
total rudder travel was limited to ±30° .
35
APPENDIXB
DESCRIPTIONOF EQUATIONSANDDATAEMPLOYED
IN 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 Axis
system shown in figure 1 and are given as follows:
Forces:
: rv - qw - g sin 0 + q__S
m Cx,t + m
% : pw - ru + g cos 0 sin _ + qS
_--Cy,t
6 : qu - pv + g cos G cos % + --_--Cz,t
qS
Moments:
Iy
-
IZ
qr
+
Ix
IXZ
IX
(r
+
pq)
+
_
C Z
IX
D
I z
-
IX
Iy
IX
-
where
and
the
CZ,
total
are
t
quaternions
to
IZ
pr
+
IXZ(r
Iy
Pq
+
IX----_Z(pIZ
Iy
aerodynamic
defined
allow
36
=
tan
V
:
Qu 2
-I
+
the
continuity
(uw-]
v 2
_
p2)
qr)
+
+
coefficients
in
included
_
2
+
w 2
next
of
,t
B
qSc
__
Iy
Cm,
qS__bb
I Z
Cn,t
CX,
t,
-
t
+
CZ,
section.
Euler
attitude
motions.
Her
Heq
t,
Cm,
angles
t,
were
Auxiliary
Cy,
t,
computed
equations
Cn,
t,
by
using
APPENDIXB
qu
-
pv
+
g
cos
an =
-pw
ay
Q
cos
_
-
g
+
ru
-
g
cos
=
Q
sin
_
+
g
Aerodynamic
The
aerodynamic
static
and
models
of
the
Research
data
dynamic
(force
F-16
in
Centers.
tions
of
and
-30
over
the
various
both
°
_
_
_
same
of
30 ° .
_
the
simulation
were
wind-tunnel
facilities
at
the
NASA
aerodynamics
were
input
attack
and
over
the
The
sideslip
dynamic
data
Total
were
input
coefficient
contributions
to
a
derived
tests
static
range.
aerodynamic
in
oscillation)
wind-tunnel
The
angle
used
Data
in
given
in
force
Ames
tabular
were
or
low-speed
moment
with
and
tabular
ranges
equations
from
conducted
-20 °
form
_
form
used
subscale
Langley
_
as
_
for
to
sum
coefficient
func-
90 °
_
=
0°
the
as
follows.
For
the
X-axis
force
coefficient:
CX(_,_,6
CX,t
h)
+
ACx,lef(
1
25
/
-jj
(_)(i
+
_[CXq(_)
+
,sb
6 le f_7
ACXq,lef
where
ACx,Ie
For
the
Z-axis
f
:
force
CX,lef(_,_)
-
CX(d,_,@
h
=
0 °)
coefficient:
/
CZ,
t
:
Cz(_,8,6h)
+
+
_q[c Z
(_)
2V [
q
+
ACz,lefkl
+
ACz,sb(_)
\ 60/
hCZq
, lef
where
ACz,lef
:
CZ,lef
(_' _)
-
CZ(_'
_'6h
:
0°)
37
APPENDIXB
For the pitching-moment
coefficient:
Cm,t : Cm(d,8,@h)_@h(@h)+
Cz,t(Xcg,ref
-
Xcg)
+
ACm,lef<l
( sq
+
ACm,
sb (_) \-_--]
+
ACm(_)
+
[C
__q
mq
+
ACm,ds(_,@
(_)
+
ACmq
, lef
(_) ( 1
h)
where
ACm,le
For
the
Y-axis
Cy,
f
=
Cm,
force
t
=
lef(_,8
)
-
Cm(d,8,@
h
=
0 °)
coefficient:
Cy(d,8
+
ACy
)
+
ACy,lef(1
,@a=20
+
ACY,@r:30
+
ICyp
°
+
ACy
o
(_)
+
61ef-]
25
/
(1
,6a=20O,lef
+
-2V
ACyp,lef
Yr
(_)
(_) (1
61e_f)]
ACy,
f
:
Cy,lef(_,8)
@a:20o
:
-
CY,@a:20o(_
(a, 8)
F
Ic
L
38
Cy(_,8)
'@a=20°,lef
-
,@r:30
-
: cy
ACy,@a=20O,lef
ACy
Cy(d,8)
8)
o
:
CY,@r:30o
(_, 8)
Y,@a:20
ACYr,lef
2s ]P)
where
ACy,le
+
-
o
(_,B) - Cy (_,8)
(_) (i
61ef_]
25
/J
APPENDIXB
For the yawing-moment coefficient:
Cn, t = Cn(_,_,6h)
+ ACn,lef(l
@lef) - Cy,t(Xcg,ref
Xcg)b
+ IACn,6a=20o + ACn,@a=20O,lef( 1
r
+
ACn,
@r=30
+
I Cnp
(_)
o
+
+
_
_
nr
(_)
ACnp,lef(_)(l
+
ACnr
61ef-_]p]
ACn_(_)__
II
(_)
,lef
1
+
where
ACn,le
f
=
Cn,lef(d,_)
=
ACn,
@a:20
-
C n
o
Cn(_,_,@
(_,_)
-
h
=
0 O)
Cn(_,_,@
h
:
ACn,6a:2OO,lef
Cn
,6a=20O,lef
(_'_)
-
-[Cn,6a:20o(C_,[{)-
ACn,
For
the
6r=300
=
rolling-moment
c
=
:
0 O)
,6a:20o
Cn,lef(d,_)
Cn(Ct,[_,6h
Cn,6r=30o(_,_)
-
Cn(_,8,6
h
=
:
0°) -]
0 O)
coefficient:
c
_,t
+
_(_,_,@h
)
Ct,@a:20o
+
hCt,le
+
f
ACt,
1
61ef
25
)
@a:20O,lef
(1
25
+
ACtr,le
r
+
hCt,@r:30o.
(@r)
_
+
E c tp
ACtp,le
(_) +
+
_b
f
(E
c t r (_)
(_) ( i
61ef_
_g
_
P]
f (_)(i
+ Ac t
8
(_)B
39
APPENDIX
B
where
hCZ,
le f
:
CZ,lef(d,_)
AC_,@a:20o
:
-
CZ(_,_,@
C_,@a:20o(_,_)
ACl,@a=20O,lef
=
-
The
tions
:
aerodynamic
are
variables.
The
in
table
aerodynamic
gravity
location
of
0.35_
gravity
position
in
the
o(_,8)
The
F-16
is
to
as
moment
and
cated
in
figure
The
response
ure
66(c).
by
inputs
66(a).
was
modeled
Presented
an
table
maximum
thrust
levels.
Engine
ing
engine
angular
momentum
(160
4O
the
slug-ft2/sec).
in
functions
to
:
0°)]
preceding
the
coefficient
indicated
are
referenced
the
desired
equa-
independent
to
a
flight
center-ofcenter-of-
equations.
Simulation
afterburning
computed
a
the
of
corrected
throttle
with
in
0 °)
CZ,lef(_,@)
coefficients
were
was
The
-
=
-C_(d,_,@h
contained
III
coefficient
powered
throttle
h
- cl( ,B,6h °°)
Engine
response
0 °)
(_,@)
C_,@r:30o
coefficients
presented
:
C_(_,8,@
CZ,6a=20O,lef
-[CZ,6a:20
AC_,@r:30o
h
turbofan
by
command
are
at
a
lag
thrust
gyroscopic
fixed
jet
the
is
which
values
effects
value
engine.
shown
varied
for
were
of
The
mathematical
gearing
first-order
VI
using
in
as
idle,
kg-m2/sec
indi-
figure
shown
military,
simulated
216.9
thrust
model
by
66(b).
in
figand
represent-
APPENDIXC
SPECIAL EFFECTS
Buffet
Characteristics
Aerodynamic buffeting
of the airframe at high angles of attack was simulated by shaking the cockpit with a hydraulic mechanism. The buffet intensgty
and frequency content were controlled
by the computer, with the buffet amplitude varying with angle of attack, as shown in figure 67. Buffet onset
occurred near _ = 15 ° , and the level
of
buffet
increased
fairly
linearly
thereafter
with
trolled
to
_ primary
increasing
represent
structural
angle
the
of
relative
modes
of
the
attack.
buffet
Pilot
blackout
was
cockpit
by
instruments
factors.
At
the
the
in
order
scene
maneuvers.
it
suit,
the
if
when
tion
between
time
to
to
the
9g,
to
flew
with
the
than
of
of
simulation
simulated
5g
this
the
load
used
tunnel
image
a
operation
con-
the
three
was
cue,
in
high
unrealistically
normal
The
factor
vision
a
acceleration
level.
300
that
sec
an
and
blackout
during
the
relative
of
will
normal
tend
a
direct
logarithm
interim
the
experience
will
5g
to
acceleration,
values
at
the
load
to
normal
pilot
and
tracking
addition
used
the
accelera-
high
delayed
and
algorithm
to
at
steady
high
assumed
normal
scene
spent
for
at
of
projected
vision
provided
at
values
the
time
target
tunnel
representation
below
high
of
cumulative
blackout
extent
logarithm
the
the
of
who
greater
returning
of
the
blackout
exposed
blackout;
at
of
pilot
was
of
Blackout
brightness
simulate
of
content
contributions
sustained
the
dimming
partially
of
under
function
simulation
The
recover
a
time,
to
anti-g
grayout
blackout
same
penalized
acceleration.
"grayout"
decreasing
as
This
inflatable
and
or
simulated
frequency
airframe.
Simulation
tion
The
amplitude
and
of
i0
to
relathe
sec
to
period.
41
REFERENCES
1. Impact of Active
Oct. 1974.
Control
Technology on Airplane
Design.
AGARD-CP-157,
2. Gilbert,
William P.; Nguyen, Luat T.; and Van Gunst, Roger W. : Simulator
Study of the Effectiveness
of an Automatic Control System Designed to
Improve the High-Angle-of-Attack
Characteristics
of a Fighter Airplane.
NASATN D-8176, 1976.
,q
3.
Mechtly,
E.
Conversion
4.
Ashworth,
of
42
the
A.:
The
Factors
B.
R.;
Langley
and
International
(Second
Kahlbaum,
Differential
System
of
Revision).
William
Maneuvering
Units
NASA
M.,
-
SP-7012,
Jr.:
Simulator.
Physical
Constants
and
1973.
Description
NASA
and
TN
Performance
D-7304,
1973.
TABLE I.Weight, N (ib)
MASSANDDIMENSIONALCHARACTERISTICS
USEDIN SIMULATION
........................
91 188 (20 500)
Moments of inertia,
kg-m2 (slug-ft2)
IX .............................
Iy .............................
IZ .............................
IX z ...............................
Wing dimensions:
Span, m (ft)
..........................
Area, m2 (ft 2) .......................
Mean aerodynamic chord, m (ft)
Reference center-of-gravity
:
12 875 (9496)
75 674 (55 814)
85 552 (63 I00)
1331 (982)
9.144 (30)
27.87 (300)
3.45 (11.32)
.................
location
.................
Surface deflection
limits:
Horizontal tail Symmetric (@h), deg ........................
Differential
(6d), per surface, deg ................
Ailerons (flaperons),
deg ......................
Rudder, deg .............................
Leading-edge flap, deg ..................
Speed brake, deg ..........................
0.35_
. ....
±25
±5.375
±21.5
±30
25
60
43
TABLEII.-
Initial
DEPARTURE-/SPIN-SUSCEPTIBILITY
MANEUVERS
condition
Maneuver
ig trim;
_ = 10°;
h = 9144 m
ig trim;
_ = i0°;
h = 9144 m
lg trim;
_ = i0°;
h = 9144 m
Zilot
360 °
roll
Maximum
lateral
360 °
roll
Maximum
coordinated
stick
Response
to
cross
controls
and
Maximum
Inertia
coupling
Maximumg decelerating
turn;
h = 9144 m
Maximumg decelerating
turn;
h = 9144 m
Maximumg decelerating
turn;
h = 9144 m
roll
170
360 °
roll
170
Ig
=
trim;
h
=
_
9144
9144
=
25o;
m
_
=
25o;
44
=
9144
to
by
and
abrupt
stick,
abrupt
full
stick
Maximum
lateral
stick
Maximum
coordinated
stick
and
Maximum
opposite
stick
and
lateral
pedal
lateral
pedal
IAS
360 °
roll
Maximum
lateral
360 °
roll
Maximum
coordinated
to
cross
and
Maximum
stick
and
Maximum
lateral
pedal
opposite
stick
bank-to-bank
Deep-stall
climb;
m
cross
at
knots
Response
by
stick
lateral
stick
70 °
stick
lateral
pedal
lateral
stick
reversals
Steep-aCtitude,
h
IAS
controls
m
decelerating
at
controls
lg trim;
_ = 25o;
h = 9144 m
pedal
IAS
knots
Response
ig trim;
_ = 25o;
h = 9144 m
h
at
knots
170
lg trim;
aft
followed
360 °
lateral
followed
Maximum
aft
stick
opposite
pedal,
full
ig trim;
M = 0.6;
h = 9144 m
input
entry
Stick
neutral
forward
or
full
TABLEIII.-
AERODYNAMIC
DATAUSEDIN SIMULATION
CX(<_,_,@
h = -25°)
R[TA
-25.0
ALPHA
-PO.O
-.1R680
-]_.0
-10,0
0.0
+5.0
,fo.n
*}5,0
*PO.O
,30.0
+35.0
.!o7_0
*_0,0
.I_630
.1_060
,45•0
*KO,O
.t4710
*_5.0
.l_56n
*_0,0
.i_o6n
.Y_nin
$70.0
.I_010
*RO,O
.i_9_n
*qO.O
.1_600
t_
- 6.n
+15.n
- 6,0
*_0,0
-.15690
-.1R960
-.IPI60
-.191_0
-.18A30
-.187_O
-.lP_O
-.18480
-,18410
-•16930
-.16980
-.14150
-.13720
-.i1150
-,t0_0
-.06610
-.06490
-,00700
-.00800
.05030
-.18r',_O
-.17n_0
-.17_I0
-.14_00
-,1P_oO
-.11_0
-ilO_O
-.06_0
-.06_10
-,007_0
-.01070
.0_0
-.18600
-.18380
-.18530
-.18170
-.17350
-.16950
-,1_250
-,t_580
-.11240
-.10tS0
-.06750
-.05960
-•00900
-.01050
,08880
,OlPiO
,IIPIO
,10750
,O@PSO
,070PO
,IilAo
,I0410
_05530
,0_380
i03960---,0-3660
,09410
,09480
.07030
,07130
,11290
.11230
.10760
.lOqflO
.13330
.13230
.14250
.14600
.15850
.15670
.16710
.15730
.17120
.17300
.17690
.17610
.16620
.16880
.15950
°16860
.15210
.15720
.16600
.1_770
.13000
,16220
,1_430
,15700
.12560
.16820
.13430
,16390
,15_10.
.t6230
,11950
.17260
.14300
.16740
.1-53g0
•16440
.1_570
.17_90
.13_70
.17100
°1_620.17150
.15670
.16560
.16350
°17620
.16680
.17190
._1860
.17380
.15570
,15850
o16100
.16670
.11930
.15660
.1_670
.16690
.156.9_L_
-,1RPTO
-.1R6RO
-,r171RO
-.17110
-.13170
-,14P_O
-,I0430
-,111_0
-°06n30
-.14100
-, I0C)30
--,11100
-.06400
-.06_00
-.OOqqO
-.01 n_,O
-. 06F,40
-,01010
-. n 0_,._
0
..03qRO
, e_330
.07B60
.09750
.11_40
.ll_PO
,10i00
,03_PO
.05360
.07460
.093q0
'. n4OPO
.05;_70
.07450
,09130
,!IOPO
,IIP50
.09750
.]0670
.I1360
, I07110
.1t010
.111q0
.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
• 14070,11 qRO
.16640
°13500
.16QQO
.16050
,t37q0
,127@0
.16ml70
..
.14410
.16550
,16040
.16KO0
.I_460
. "167_0
.16710
.17PRO
• 15680
• 16_60
.1.74_0
.16_10
°16770
.16670
.17300
,15690
.171_0
.15590
.15630
.15P50
.17.';160
,16PO0
,173n0
.15_00
,15R60
.16080
.166_0
.'166R0
.16_60
.t3500
.16020
.¢_600
.15740
.16110
.16370
.1_970
.171_0
17250
.17780
.17240
.16640
.1721_
.15730
.17200
.15210
.15580
.1676n
°17110
.-.06P60
-,01080
-.0];30
.0q15o
- 8,0
*10.0
-,179_0
-.')8760
-.t6qPO
-. 17;_90
-.1_760
-.nn7qo
L_nl_no
.11110
;10,0
+ R,O
.._ Rqc)O
-,'19000
-. !_750
-.lq_ln
..1787n
-.tlSln
-.143P0
-.OqO?O
-.113_0
-.0_160
.o_560
.nq3?o
.07400
.09510
-15.0
* 6.0
-,19o40
-, 19ftPO
-.1RqgO
-.17_bO
-. lRO_qO
-.16_70
-.17690
-.1P'_PO
-, 16_S0
-oOq_50
-.1 l;_90
-.05_70
-.17160
-?0:. 0
* 4.0
-.17060
-.1_90n
-.13970
-.11200
-.110P0
-.06530
-.06500
-.00760
-.00830
0_770
.OqO_O-.
0R670
0R670
._i_o
-
,l_?mO
.13_0
.16nlo
,t4_aO
.16_40
,15_00
.16_0
.15_0
.176_0
.17PPO
,17n40
.-,16710 ....
.1TRIO
.14740
.15q_O
.141nO
.16R_O
°.15_10
- 2,0
*25,0
,30,0
-.18600
-.17870
-.17710
-.18770
-.1_900-,17390-.17720
-.16300
-,t-53_0
-.1#370
-.12t_0
-,11330
-.11300
--_00570
-.0_790
-.06900
-.0_580
-.05050
-°01160
-.011_0
-.00850
.... -14i_J6LiO -.....
.........
,069T0
-.t0660
....
.1t370
,129g0
..... ,l_'lO.
.13620
,16420
..... _._600.i_450
.15380
.16P-._O-
-
TABLE
III.-
Continued
c @,B,6h: -10o)
BETA
0•0
*
ALPHA
-PO.O
-{S•O
;io,o
..]OlAO
-.1147_
-.OA9_O
-.04830
0•0
5°0
-.01IRO
-.017_0
oO:6fiO
e97-_0
.._gaTo
*PO•O
.1_0
_p_'.O
.1_740
.14070
_30•0
•lo_o
_0•0
.179A0
*4S•O
*,o,o
-.[_710
*_5.0
.14RAO
*60'0
_70,0
........ _s_n
.T_7_o
+RO,O
*QO.O
.lP110
.1_870
.... .17470
•
+ 4.0
-.13_10
-•17460
-•17450
-.14190
-•1P470
-•1P350
-•t1_70
-,10660
-•1o950
-•07060
-•08PSO
-•0_090
-,061t0
-•01060
-•01780
•O_P80
,03q90
-•_o_o
•08000
.,t0_]0
•17750
•1_?0
•t4740
.14i80
•IP_tO
•08a70
.I0970
,17580
,13380
,14660
•144_0
•lP_70
•16400.
•11_40
•17_30
,14170
,18100
,14R60
.,1.6_0
•14100
•107g0
.179K0
•
P.O
•15490
.13670
,14_30
.13_nO
o13_60
.11740
• 130! 0
.116.10
.llq_O
,1_410
-•1OR60
-•07_60
-•OAT_O
-o.O_3PO
-,060_0
-,OOq60
-•01670
•03670
•1_4_O•lPqqO
•18040
°13650
,17710
•1_170
,16530,14_0
•15470
,l?SlO
,13610
.13_0
°13200
,11850
o1_630
°11360
.119_0
.1_140
*
6•0
-•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
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VNdTV
TABLE
IV.-
AND
LEVELS
OF
ROLL-RESPONSE
CROSS-AXES
COUPLING
ROLL-RATE
LIMITING
DEGRADATION
FOR
VARIOUS
TECHNIQUES
Initial
Scheduling
Cross-axes
roll-response
parameter
coupling
degradation
Low
High
Moderate
6h
TABLE
Low
V.-
COMPARISON
FULL
92
Moderate
LATERAL
Control
a, max
system
deg
'
High
OF
ROLL
STICK
RESPONSE
TO
INPUT
At_:90o
At@:180o
A
-21.5
2.6
3.8
B
-16.1
3
4.3
C
-21.5
2.6
3.9
TABLE
VI.-
THRUST
vALUES
(a)
ThruSt
SI
uSED
IN
sIMULATION
units
values
at
an
altitude,
m,
of
-
15
12
9
6
m
3
240
192
144
096
048
0
Tidle
0.2
2
824
267
.4
.6
-4
537
.8
-12
010
-16
013
1
890
iii
-3
158
-8
-6
451
227
3i
-l
069
535
334
-5
782
-2
647
i. 0
43
i
-i
492
358
557
099
-i
521
5
916
5
4
2
026
048
669
-890
7
562
6
6
4
783
049
893
3
Tmil
i14
0.2
.4
56
56
401
089
40
41
699
420
28
29
080
401
.6
56
223
43
764
31
536
8
55
ill
45
43
34
35
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806
•
51
263
804
17
970
19
082
663
728
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20
27
23
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II
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565
14
456
16
902
6
227
6
939
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8
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12
610
95
276
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54
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17
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440
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115
128
959
485
81
398
103
723
59
1.0
(b)
U.S-
•
__y
m
customary
values
at
Uni%S
an
altitude,
ft,
of
-
oooo
0
1
130
910
600
I
1
1
i loo
360
-200
'
12
0.2
2
00
680
9
150
1
560
610
9
312
i
660
3
950
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\
\
\
\
¥
\
\
\
\
\
w
×
Z
Figure
i.-
Body
system
of
axes.
T
L
5.Ol
15.09
Figure
2.-
Three-view
sketch
of airplane
configuration.
All
dimensions
given
in meters.
95
<o
O_
Figure
3.-
General
arrangement
simulator
of
Langley
(DMS)
differential
facility.
maneuvering
.................................................
Figure
4.-
View
of
cockpit
and
visual
L-73d6831
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
2001
\
\
lO0
0
deg
-100
I
\\
-200
!=_,__
1SO00
h,
10000
---_
__fl I
_
/'
....
=--_=
....
i
O0
5
I0
15
20
25
30
35
_0
_5
50
55
Time,
Figure
6.-
Time
histories
of
target
60
65
70
75
80
85
80
95
itl_8.
sec
motions
in
wind-up
turn
task.
99
.3
.6
M
.3
0
q
2
g
/
0
_0
2O
deg
0
i00
L
_
--_-_
_-_ b--- _
-_-
._._
_
___
_
._----
_ _
_
.__/
-lO0
lO0
(o,
f
/
0
k
deg
_ Ioo
i00
f
_'
7
f
_._
0
aeg
_ loo
i0000
h,
sooo
m
o
o
S
10
1S
2S
20
30
35
u_o
Time,
Figure
i00
7.-
Time
histories
of
target
motions
qS
SO
55
60
65
sec
in
bank-to-bank
task.
70
Id
deg
-9
-_-000
0
m
histor-'es_
L
%
Figure
\\
L
\
'\
8.-
Time
of
target
motions
in
ACM
task.
2.0
1.6
1.2
CL
.8
.4
I
i
5
I0
l
15
I
20
_,
Figure
9.-
Untrimmed
lift
configuration.
102
l
I
i
25
30
35
deg
characteristics
_
:
of
0 °.
simulated
!
40
6h
0
0°
[]
+25 °
<_
-25°
.4
C
m
-.6
i
i
0
i
6
20
i
l
40
i
60
!
80
c_, deg
Figure
i0.-
Variation
of
deflections.
pitching
moment
Center
of
with
gravity
_
for
at
various
stabilator
0.35_.
103
24
.20
.16
.12
, O8
.04
m
0
-.04
-. 08
(S
h
h
[_]_6
-.12
_-.16
-.20
_.24
-.28
-30
I
_25
Figure
I
j
!
420
-15
-lO
ii.-
Variation
various
104
i
-5
of
stabilator
0
B
pitching
I
I
I
I
I
I
5
lO
15
20
25
30
moment
deflections.
with
_
:
sideslip
25 °"
for
+25°
+I0°
.016
.012
.008
Cn{3' CIB'
CnB,dyn
per
.004
J
deg
0
-. 004
- .008
-.012
-.016
_
0
I
I0
5
15
20
25
30
35
40
c_, deg
Figure
of
edge
12.basic
flap
Variation
configuration
deflections.
of
lateral-directional
with
angle
of
6h
=
attack
stability
characteristics
for
scheduled
leading-
0°"
105
.06
.05
.04
(_
=
--
0
.03
_C n
6_ = _5°
-.02
•06 -
.o_
aa = -20°
004
ACl
.03
.02
.Ol
0
5
lO
15
20
25
30
35
_,
Figure
13.-
Variation
with
106
of
of
attack.
45
50
deg
lateral-directional
angle
40
control
_
:
0 °.
derivatives
55
60
.020 Augmented
.016
.012
LCDP,
per
•008 -
degree
Normal
response
•0040 1
_-_Reve.rsed
response
Basic
-.004
-. 008
0
5
l0
15
20
25
30
35
40
c_, deg
Figure
14.with
Variation
angle
of
of
lateral
attack
control
for
simulated
divergence
parameter
(LCDP)
configuration.
107
1.5
SAS on
SAS off
1.0
i
ti12
sec-I
.5
0
I
I
I
I
I
I
5
I0
15
20
25
30
a, deg
5
4
P
3
11
sec
2
I
0
I
I
I
I
I
5
i0
15
20
25
I
30
a, deg
(a)
Figure
with
(30
108
15.-
Variation
angle
000
ft);
of
attack
velocity
of
Dutch
roll
airplane
for
for
dynamic
airplane
ig;
mode.
level
lateral-directional
with
and
flight.
without
SAS.
stability
h
:
9144
m
6
SAS on
SAS off
4
1
2
10
5
0
15
20
25
30
a, dog
(b)
Roll
mode.
.41
t1/2
()
.3.2
-
.1
-
sec -1
I
0
5
I0 15
el,deg
(c)
Figure
Spiral
15.-
20
25
30
mode.
Concluded.
109
P
V
(a)
_ = o°.
(b)
_
X
V
Figure
16.-
Illustration
angle
ii0
of
of
attack
:
90 °.
kinematic
and
coupling
sideslip.
between
P
P stab
(a)
_i
Pitching
moment
created
by
roll
and
yaw
rates.
x.
(b)
Figure
Yawing
17.-
moment
created
illustration
of
by
roll
and
inertia-coupling
pitch
rates.
phenomena.
iii
_0
EZ,
20
deg
o
10
13,
0
_eg
- 1o
/%
_,_\] ,_. v
J
d
80
A
_o
P'
deg/sec
C
o
A
M/
-q@
-[30
qO
r,
deg/sec
/"
0
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-_-o
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q'
deg/sec
0
-_o
100
O
deg
-10o
_00
200
Pcom,
deg/sec
0
(
-200
-LIO0
i00
Flat'
N
o
-I00
0
Figure
S
18.-
10
Time
15
20
histories
Control
112
25
30
35
of
system
_0
ig
A;
u,5 50
55
Time,
sec
stall
ho
to
=
60
65
limit
9144
70
angle
m.
75
of
80
85
attack.
9O
95
.6
_,
i000
deg
-loo
_,
t°°
°
deg
6a
-too_
'
300
deg
-30
5d,
i°
o
deg
- 10
6r,
deg
300
-30
6h,
200
deg
-20
g units
Yped,
_00
.°
N
-_oo
0
5
10
15
20
25
Figure
30
35
18.-
q0
q5
50
Time,
55
sec
60
65
70
75
80
85
90
95
Concluded.
113
\
\
\
\\
\
\
_0
Q:,
f
2O
deg
0
3O
2O
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10
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deg
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120
/
8o i
p,
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deg/sec
/
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80
40
r_
deg/sec
0
. r-
_L_._
-40
q_
deg/sec
200
tO0
/
/
_/
0
deg
/
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-100
/
/
//
/
/
g
-200
qO0
Pcom,
deg/sec
200
o
/
/
'°°o I
0
2
/
L_
6
8
10
12
1u,
Time,
Figure
19.-
Response
Control
114
to
full
system
18
18
cross-control
A;
ho
20
22
2q
28
28
sec
:
input
9144
m.
at
d
:
25 ° .
an,
g units
o
.6
M
.3
I
0
ioo
Ol
w,
deg
_1oo
loo
o
Op
deg
J
-tO0
i
6a,
deg
:\
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lO
6d,
o
deg
f
Y
-10
30
6r,
0
deg
1
\/
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\
I/
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o
deg
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gcom
g units
•
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L
II
o
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o
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N
IL
_u,oo
-800
0
2
6
Figure
8
10
19.-
12 1_
Time,
16 18
sec
20
22
2_
26
28
Continued.
ll5
t_0
Cl,
i
@
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i
deg/sec2 __
V7
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40
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deg/sec
2
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40
qa,
0
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80
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0
deg/sec2
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"_
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40
i.icl,
o
deg/sec
2 -40
I
-80
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0
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deg/sec2-_o
f_
---
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40
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m/sec
0
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2 -4@
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0
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qol0 I 2i I qI I 6I I 8I
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I
I
I
I
I
I
TT59-TTI
I 24
I I 28I I 2B
I
10 12 14
18 18 20
22
Time,
Figure
116
19.-
sec
Concluded.
20
deg
0
2°!_
10
/
i\ /
z
/-",._,.._
-
deg
0--
I
-10
r
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0
deg/sec
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0
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0
I
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deg/sec
2o01
lO0
I
I
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deg
-iO0
i
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]
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200
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_
II
l
0
J
deg/see
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i
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I00
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N
-100
i '
o
V;
,
0
2
q
6
8
10
12
1u,
18
Time,
Figure
20.-
turn
h o
at
=
9144
Response
limit
to
angle
cross
of
attack.
18
/'
20
22
/
2q
26
I
28
30
32.
_u,
sec
controls
applied
Control
in
system
accelerated
A;
m.
117
an,
/
g units
I
,9
M
.6
.3
0
o
_'
-tO0
deg
-2oo
O)
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deg
-tOO
30
5a'
deg
0
/\r
f
-30
1O.
5d'
0
deg
- 1o
1t
\j
30.
0
6r'
deg
/,_z"
\/
=so
x
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5h'
deg
f
0
/
/.,.
-20
lO
8
gcom,
g units
o.
J
I</I'
1
0
FP ed'
N
-_oo
-800
0
2
6
8
10
t2
I_
16
18
Time,
Figure
118
20.-
2D
sec
Continued.
22
2q
26
28
30
32
3q
deg/sec2
-_0
/ticl,
_o
deg/sec'
^11
t
! !
o
/:
/-"
I i
\
/
"-"
--''t
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F_
q&'
0
j
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deg/sec__L_O
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,
J
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ricl'
0
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f J
"-_
F
m/sec2-__o
/- -_
Li°
Wacl,
mlsec
2
/
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Wae2,
m/see
o.
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.
"
%
-
2 -qO.
o:
2
£-J-4-_1
Lt
6
8
10
12
l_
tb
t_
Time,
Figure
20.-
20
22
2
see
Concluded.
119
Nose-up inertialcoupling moment
Available nose- down
control moment
70
60
q2 = 3556 Nlm 2
50
40
Pitchingmoment
magnitude,
30
kN-m
ql = 1778N/m 2
20
,o
0
20
!
I
I
i
'
I
I
I
,
40
Pl
•m
i
I
,
I
60
I)2
80
,1_
I
I
100
Pstab, degI sec
Figure
roll
of
120
21.rate
dynamic
Comparison
with
of
inertial-coupling
available
pressure.
pitch
_
=
25 ° .
control
moment
moment
for
at
two
increasing
values
6O
qO
_p
deg
20--
Rn,
3O
20
,\
/,
/\
10
oFU4+-¢1_,, ,-444-¢K_
g units
/
0
deg
2
/
o
-10
1oo[<
-20
-30
deg
-1oo
120
80
F
f
_0
deg/sec
\
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P*
0
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40 _
0
deg/sec
0 _-
deg
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6a'
deg
0
-30
k)
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r'
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K -f
t
_ /
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I
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0
deg/sec
-40deg
-ao
200
tO0
/
o
/
deg
,,'- \
-tO0
I
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/
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_
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6 h,
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deg
,/
_
d
I
_-
O_2o
r
f
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qoo
Peom,
200
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N
}
0
deg/sec
o
'°°o//tt_
Figure
0
2
q
22.from
/
6
A
ig
8
10
Time,
360 °
flight
[
16
12 lq
sec
roll
at
18
attempt
_
=
'_,_.'°°o[I I
UO
0
N
using
25 ° .
full
Control
2
lateral
system
q
1/
6
8
stick
A;
ho
10
Time,
input
=
9144
14
12 lq
see
16
18
uO
applied
m.
121
qo
el,
o
\
f
\i
,J--..
deg/sec_-qo
8O
_licl,
deg/sec
40
_
-
0
/
-qo
qO
qa,
0
deg/sect_4
o
IX_
F__
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deg/_-_c'_40
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0
a._,_,._lw
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o
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m/sec2-q
°of
0
2
q
6
_\
_
8
10
Time,
Figure
122
22.-
/\__
I
\/
12
see
Concluded.
lq
16
18
20
'i'll
11
l
60
C[,
I
qO
I
deg
'
2
I
I
4 I
30
/li/
I
20
10
B,
deg
o
-10
-20
titt"
III'f
l,
I
/I /
I
\
-30
120
80
'
t
tt0
I
i
I
I
P,
I
I
0
deg/sec
,Y
-tJ0
-80
I
-120
8O
1_'
L[I
lillT_
1",
deg/sec
0
-40
8O
q,
qO
deg/sec
,I, t_
+t_',
, , ,
0
-q0
2001
$,
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1 ll! _
deg
-loo
-200
Pcom,
deg/sec
200
0
-200
I
I
I
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I
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1°o
_l ,[
IL
rI
N -1o_
I
I' I -1
0
2
q
6
8
10
12'
lq
16
Time,
Figure
,
I
23.-
A
stick
input
limit
2.
360
°
applied
Control
roll
system
an
20
22
2q
1I
26
28
30
sec
attempt
in
/1![I
18
using
full
accelerated
A;
h o
lateral
turn
=
9144
at
m.
123
/
an,
2
g units
0
,9
M
,3
0 ¸
0
W,
deg
-lO0
x
_J
I
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100
_'
deg
0 -----i00
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5a'
deg
0
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IO
6d'
0
deg
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\
3o
r_
5r'
o
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dog
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deg
o
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/
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10
/
gcom,
5
g units
O.
J
/-
-5
F,ped,
N
L_O_
O.
2
L_
6
8
10
12
tLt
Time,
Figure
124
23.-
16
18
.sec
Concluded.
20.
22
2LI
28
28
30
EtO
j--
--,_
....
2O
deg
0
20
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0
deg
-10
\
-20
120
80.
qO.
p)
./
O.
deg/sec
-qO
-80
-120
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f
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0
deg/sec
\
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/
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/
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200
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\
-200
.
1
t
\
-EtO0.
Flat,
N
,o:, j]
....
-100
0
2
.......
LI
6
8
10
12
-t
let
16
18
20
22
2Et
Time,
Figure
24.-
Bank-to-bank
inputs
applied
system
A;
reversals
from
h o
:
9144
ig
flight
i
26
28
32
3q
36
Et2
EtEt Et6
sec
using
at
30.
_
maximum
:
25 ° .
lateral
stick
Control
m.
125
an,
g units
0
.6
M
,3
0
100
fl
-..
f
_.
f
0
deg
-100
i00
0
deg
p
-I00
3O
(--
--
____
6a,
Lf
deg
L____J
-30
10
6d,
deg
o
/
\_j
/
\
\
/
\/
/
"\
10
30
6r,
0
deg
-30
/
/
1
\I\_
N0
6h,
deg
2O
//
0
/
_f
\/
-20
\
/
/
t
/
/
/
,:
/
J
/
-
/
I / \ J
vi/
V
10
gcom,
g units
Fped '
N
5
0
_00
00
2
Li
6
8.
10
12
1F!
16
18
20
22
24
Time,
Figure
126
24.-
26
sec
Continued.
28
30
32
3u_
36
38
L_0_ u_2
u,u, _6
'°[L
_
',
/-.
'4'
,__
deg/sec2
__o
I I"
V
\]
,4
+o
_iei.,
_°_
-,,
,,_
/\
"'
/
/
\ /\
G
)
\
-q0
\ /'., //\ ,-, t-'\j
i-,
o
/-
/-_-
x,--,,.,
deg/sec2_tio
v,/
I I
I I
h
,,..
,....
/
_/
i%
\\_/
+,. Oo t
m/see
'::'-_t
O.
2
14
6
8
10
12
lq
16
18
20
22
Time,
Figure
24.-
26I
2.
llllTllVI
28
30
32
3q
36
x_
38
-
qO
q2
qq
q6
.sec
Concluded.
127
Roll-control
limited
Pitch-out
limited
200 '""--'-'_
180 \
160 -
Maximum
roll
rate t
deg I sec
140 -
\
\
\
120 -
,.
100 -
SM =0.02
80
_'_t_,
60
_m =-0. 04
II
40
SM =-0. I0
20
0
I
I
I
I
i
.5
I0
1.5
20
2.5
a, deg
Figure
25.-
various
360 °
128
Variation
levels
roll;
h o
of
of
=
maximum
static
9144
m.
margin,
roll
rate
ig
with
flight;
_
for
+<b+
-- ( Pcom) max
I
8h ,c
l
E,]
Figure
50
UD
26.-
Roll-rate
limiting
scheme
used
in
control
system
B.
320
Control
system A
280
240
200
( Pcom ) max, 160
Control
system B; 5h : trim
Control
system B; 5h : +25°
deg/ sec
120
8O
4O
I
0
Figure
27.-
5
I
10
15
a, deg
Variation
with
130
I
I
I
20
25
of
maximum
_
for
ig
commandable
trim.
roll
rate
0.67
s+ 0.67
Ipl
(toa
Z_ap
limiter)
38.4
Figure
28.-
Pitch-axis
modification
used
in
control
system
B.
Aap, deg
2 I
I
0
I0
20
30
40
50
60
I p I, deg/ sec
Figure
29.Variation
magnitude
for
of
A_p
control
with
system
roll-rate
B.
131
21111111_1
ol I I I Iq-I
an,
g units
I I I I I I I I I I
$
.6
M
o
_J"
qO
deg
2O
deg
io0
Ol
_
k_
_J--_
_lOOi
o
too
I0
O,
0
deg
0 ---"--.
_tOO
-Io
3O
6a,
8O
p_
f_
_0
deg/sec
/
0
--/"
\
deg
0
-3o
\
/_
\
11
____
10
0
A,,.5d'
r_
"ee'
deg/sec
_0
q'
deg/sec
.--,----
30
f
0
6r"
deg
-Lm
200
0
-30
\
i,-_I"I-
qo
A
1O0
_'
deg
\
- 10
///
0
//
/
-loo
20
0
6h,
deg
/
_ /
\
/
"
-20
/
-200
10
Pcom,
deg/sec
N
2001
gcom,
g units
I
ol I/I I I I I_
0
1
q
2
6
8
Time,
Figure
30.-
A
lateral
132
360
°
roll
stick
I0
12
lq
Fped,
N
16
s
o
_00
°
0
2
_
sec
initiated
input.
6
8
Time,
from
Control
lg
trim
system
at
_
B;
ho
:
25 °
:
9144
using
m.
io
t2
sec
maximum
{_
t6
deg/sec2-_o
/lid,
deg/sec2
deg/sec'
I
40
-40
-40
40
÷a,
deg/sec:
o
-40
40
w,
m/sec2
0
-40
4O
wacl,
m/sec2
Wac2,
m/sec
m/see2
J
o
-4o
1
__J
o
2 -qO
-400
2
4
6
8
Time,
Figure
30.-
IO
12
14
16
sec
Concluded.
133
_o
f
2o
deg
/
/
o
,/
/
lO
o
deg
-10
120
8O
/
/
qO
P,
deg/sec
\
\
\
o
-_0
-8o
-120
r,
,_._L
0
deg/sec
/
""_
-qo
qo
q_
deg/sec
200
loo
/
¢,
/
deg
0
/
\
, / --- --
- 1O0
-200
/i
200
Pcom,
--'-_
0
deg/sec-20o
/
-_
[
/
\/v
too
0
Flat'
N- oo
\/
o
Figure
31.-
turn
input.
134
at
'4
2
A
6
360 °
limit
Control
8
roll
d
10
initiated
using
system
lq
:1.8 18
sec
12
Time,
full
B;
ho
from
lateral
:
9144
20
22
2q
accelerated
stick
m.
an,
g units
M
I
o
t
----
_
]
.3
O-
[
_JJ_
deg
loo
deg
_ioo
deg
-3o
6 d,
0
deg
- 1o
5r'
6h,
20
-, _
-/
j-_-_
[
\ JF_-
_-/
o
-
I
-2o -
g units
-J
_o_
l
0
""_
-3o
gcom,
t
"
deg
deg
_
1
/
/
/
I
lO
/
50
'_o_'
_°o°°I
N
2
/
[
ill
'4
6
1
8
10.
12
Time,
Figure
31.-
1_4
16
18
20
t
22
2'4
.sec
Continued.
135
qo
4,
I
@
deg/sec2
qO
8O
_ticl,
_o
deg/sec'
@j
qO
qa,
0
deg/sec2_4
0
:'40
r,
0
_ffl
deg/seC
-qo
qO
ricl,
J
o
_/
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'
m/see2
0
-qO
Wa_,
0
2
14
6
8
10
12
Time,
Figure
136
31.-
lq
see
Concluded.
18
18
20
11
22
2q
4O
(_,
2O
deg
o
i
10
/S,
0
1
-Io
aeg
8O
'40
P'
deg/sec
/\
/
0
/
-40
/
xJ
-80
'4O
r,
i-
/
0
_\
/
"\_
/
..-4
\
/_\
\
..-4\
,
\
/
\
/
/
\
1
\
\
f_
/
x_+
_LiO
deg/sec
'40
0
q'
_u,O
deg/sec
_oo
I
¢'
0
deg
I
I
1
\
"\
/
\
/
/
/
t
\
/
\
i/
_ioo
'4OO
2OO
0
Pcom,
deg/sec
' <
\\ i
-200
_f
/
i
\_
\
J
\..._ /
J
_
\
i
/
-qO0
Flat,
N
'°°- ,
o
)
-ioo
0
2
4
6
S
10
12
-1'4
C-16
18
20
Time,
Figure
32.initiated
ho =
9144
Bank-to-bank
reversals
from
ig trim
at
d :
using
25 ° .
l-22
2'4
t /
__F_
26
28
30
L__J
32 3 u,
36
38
'40,
sec
full
lateral
Control
system
stick
B;
inputs
m.
137
an,
____
g units
_._+-_+....__f
_j_f-_j
.6
M
.3
1o0
o
deg
-i0o
ioo
O_
(9,
deg
_ ioo
3o
6a'
0
\
\
deg
\._J
-3o
I0
6d'
deg
0
-lOi
\_
30
6r'
t/
0
deg
-3o
_
_
\
i
j
J
_o
6h
f_
'
20
deg
/
/
\
\
o
/i\
\
/
J
.-\
k/
K/
/
"
/'\I
J
/
\/
\
/
j
-20
1o
gcom,
5
g units
o
Fped
N
'
_o_[
0
2
q
8
8
i0
12
lq
18
18
_0
Time,
Figure
138
32.-
Continued.
22
sec
2q
28
28
30
32
3q
38
38
qo
6EI
"p_pnI_uoD
-'Z[
_an6T£
I
I
o_
_
__
0_- :oa@/ui
_'_--/--
O_
1
0t7- _ODll/lll
0
'Ill
f
/
-_
f"
_J
0tl
o
f
, IaT_
0t7
t¸
JJ- rJ
_J
iOh
,m
\
08-
I
I
\\
\
\
\
0t_- pas/_ap
0
\/,'I"_<z
O_
I
11
"/
I_
, \..
/'\
/
\
/"
--._/
- o
Oh
¢
,ia!b
1
50
I
j/-\
/
deg
/.f
\
/-
20
/3,
I0
deg
0
/ \
"._
_1_f\
/
f._.4-.
\
/1\
-i0
80
YO
P,
.I i
"x
_
\
//_ _
k_
0
deg/sec
-50
-80i
50
r,
deg/sec
0
-YO
50
q'
0
deg/sec
-_0 -
_/
200
/
I00
/
qb,
0
deg
,/
/f
i
/
./
/
-too
/
/
-2001
/
'
/
500
Pcom,
200
f
/
deg/sec
""
\
J
\l
0
-200
_'v
b
tOO
Flat'
o
//////
N
-100
0
v v v
2
Y
6
8
10
12
lY
16
18
Time,
Figure
33.turn
140
Response
at
limit
to
full
_.
cross
Control
20
22
controls
system
25
26
28
30
32
35
in
accelerated
sec
applied
B;
h o
=
9144
m.
/
an,
2
g units
/
0
.g
M
30
_,
deg
I
o
_11
-too
I I I I_F--LII I t_---4_ I II
I I I I I I I_
I I'_
deg
[
I I t t i
looI
I
0
0,
I I I I I _
I I 1_
- ---+--- _
-. _._7
_
J
_t oo
I
30
0
5a,
.A
,-,
d
_[
-30
deg
\
^',
I
.....
10
,,z
J
6d,
deg
-lo
o
-_
t,
_.[__
3O
6r'
/_
"
0
_\_
_
I_
I
-30
deg
u_o
20
6h,
deg
o
/
",-,_
-20
gcom
g units
•
loI
/
5¸
/
0
I
0
Fped,
N
-_oo
/
-800
0
2
q
6
8
i0
12
lq
16
18
Time,
Figure
33.-
20
22
2q
26
28
30
32
3q
sec
Continued.
141
_0
el,
o
de'g/_c2
/',.1
-40
qO
f_
.)\
o
/ticl,
_um
deg/sec2
_0
qa,
\
0
F_
deg/sec240
4o
0
r,
_v
40
deg/sec*
40
o
{'ict,
40
deg/sec2
40
ra,
0
deg/sec2_4
o
40
w,
m/see
_,
o
"
-__
,
2 _40
80
Wacl,
/
40
_
m/see
2
0
_
j
/
x,
"
\/r--
-u_o
40
_rac2'
m/sec _ -_o0
_.
_
_
-
_r a,
o_
I I I I I I_IA._I
I I I I I I
m/sec_-4ol 0 I 2I I qI I 6I _ 8
I
I
I
I
1
I
1
I
I
I
I
I
I
I
I
I I 32
1 I 34
I
10 12 14 16 18 20 22 24 26 28 I 30
Time, sec
Figure
142
33.-
Concluded.
8O
60
[_,
\
\
qo
/
deg
/
2o
o
2
an,
_o
g units
II
M
i
I
i°o-
-_
\
O.
/
deg
!
/
-io
/
-2o
\v
-3o
i
120
0,
80
deg
P,
_o
deg/sec
0
/
i \
I/
-80
qO
"/f
\v
_"d
deg
L
6d'
deg
-_0
q'
o
deg/sec
_o
--
l
\
//
_._
f_
f
0
deg/sec
io:.
-too
I,
-qO
r,
IIIAIII
1;
J/
5r,
deg
-3o
i -
IO
0
-lo
,\
o
_o
I\
-3o
/
_/,\ _"/_. \,,--.
200
,/
i00
5h '
20
deg
L_O"
/
-_
./
$,
J
deg
\
o
-i00
/
f -
' F---_
l/
Pcom,
20_J_--t4
0
i
_oofl
-1oo
0
2
Figure
using
system
L1
6
g units
I_
FP ed'
N
34.-
A
full
B;
i0 12 lq
Time, sec
360 °
roll
18
18
attempt
coordinated
h o
=
9144
20
stick
applied
and
pedal
_oo. /
o
0
2
in
ig
I
/
:
I
8
gc°m"
li L
t
deg/sec
N
@--i_
-20
-200
Ylat,
/
0
q
flight
inputs.
8
[
8
I0
Time,
at
12 ILl
sec
d
=
iS
18 20
25 °
Control
m.
143
4O
q'
\
0
deg/sec2-qO
I
60
_ticl,
deg/sec
_o
2
/
o
-qo
]
qo
qa,
deg/sec2
0
-.../
\
-_0
rio
i_,
0
\
deg/seC
r"
_x4
-_0
-80
40
i'icl,
deg/sec2
o
-40
_0
÷a,
deg/sec2
o
-"_-
it...
40
_ _--'-_--,
/
'--/
80
_r,
m/sec'
40
0
/ \
- -----"
-40
ffacl,
o
m/sec
2 -4o
Wac2,
m/sec
0
i -40
_ra,
_ /
_1
-
-_
' v l/\j
\/
-...
\i/
\/
r
/
4
\/
oH__+___l
I
I
m/sec =-4ol0 I 2I I qI I 8I I 8I I i0
I I 12
I I lq
I I 18I I 18
I I 20I
Time,
Figure
144
34.-
sec
Concluded.
Scheduled
gain
Command
gradient
I Scheduledgain
I
ii
-30
Fped
-F
0
_/_._ 489.
. 0
I
I
I _ 6r,co m
I
Figure
35.control
Modifications
system
B
to
to
C
yaw
and
(modifications
201p140
I
i
Yaw-axis
lpl--]
axes
incorporated
enclosed
in
dashed
j
in
going
lines).
I
I
m
modification.
roll
I
I
I
(a)
-I
from
I
Oh
+
I
I
Scheduled gain
I
I
+
+
I
i
I
I
+
ai
0
30 Ip1.50
I
I
I
I
6h'c
(b)
Roll-axis
Figure
35.-
modification.
Concluded.
2
an,
I
g units
.6!
M
0
tO0
deg
B,
deg
oeg
0
_too
1O0 [__...
"-.._jdeg
-io
80
_too
3O
1-x
/
P'
deg/sec
_o
o
/J
\
a_6a'
J
"b---___
'_ee
0
j._./"-+'_
\
-30
_
10
deg/sec
ue_
-i0
_0
q'
deg/sec
0
30
-_o
6r'
/
0
deg
-3o
\
_'--+_b_
/ _
200!
tO0
(_,
cto
/
./
0
,....._
I
/
deg
/
-tO0
6h,
20
deg
0
,/
deg/see
200
0
Flat,
N
[
i0
_00
Pcom,
0
2
6
q
8
10
12
gcom,
g units
5
Fped,
_000
0
N
tq
0
2
q
36.full
A
360 °
lateral
roll
initiated
stick.
8
8
Time,
Time, sec
Figure
i\
-20
V
-200
-'_
/
""
"_
from
Control
ig
system
trim
flight
C;
ho
at
=
9144
_
=
10
12
lq
sec
25 °
using
m.
147
_0
ct,
o
deg/sec_
deg/sec
__
2
_0
qa,
deg/sec2-_o
0
---.
/
"_
r,
0
deg/sec
2__01
rio
i'icl'
o
deg/sec2
-_o
i'a,
deg/sec
ol
2- _ o !
qO
w'
m/sec
0
2 __o
qO
Wacl,
m/sec2
0
L
j/
__
_0
W at2,
m/sec
m/sec2
0
2 -btO
-_°o
2
q
6
Time,
Figure
148
36.-
8
Io
sec
Concluded.
12
lq
an
2
)
I
g units
M
,3
o
I
,oo
1IC.
deg
_1oo
deg
_too
-
CI,
deg
o
B,
o
deg
P'
deg/sec
I/
ioo
io
/"
\
- Io
_io
0
6a,
0
deg
-30
fJ
<
_-_
\
\
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0
deg
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--_
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o
deg/sec
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(51"'
_--
deg
1
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200
100
/
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0
if _
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1
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0
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</
,o
5
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i/
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0
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Flat,
N
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0
Figure
using
h
=
2
I
q
37."
A
I/
I.
I
6
8
10
Time,
sec
360 °
roll
full
coordinated
9144 m.
1
12
Fped'N
t
lq
_'°°o_- ]
o
2
6
[9
Time,
initiated
stick
from
and
ig
pedal.
flight
at
Control
=
system
i0
12
lq
sec
25 °
C;
o
149
it,
o
deg/sec2
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2
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Q
deg/sec2
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0
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0
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0
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o
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2
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o
ffac2,
m/sec 2 _ _ 0
m/see2-_
0
2
_
8
8
Time,
Figure
150
37.-
i0
sec
Concluded.
12
iN
u_o
_'
I
20
deg
o
lO
0
deg
/'_'-
'--
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12_0
8O
P,
f--_
J
f
j*
deg/sec
f
qo
/
o
f
/
rt
deg/sec
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0
deg/sec
_._.--
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_'-"__
L
-qo
2OO
/1
/
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/
0
/
/
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deg
....
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/
/
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/
/
I'
-200
'_00
Pcom,
200
deg/see
0
oltLLILL
0 " 2
u,
6
8
133 L2
Time,
Figure
38.-
in
ig
h o
=
trim
9144
Response
flight
to
full
at
_
:
Lq
16
18
20
11
99
2.q
sec
cross
controls
25 ° .
Control
applied
system
C;
m.
151
q
J
an '
2
g units
0
.6
M
.3
i00
_'
aeg
0
__oo
100
deg
_ 100
3O
6a'
0
deg
-30
__J
kO
6d'
deg
0
-lo
30
6 r,
0
deg
-3a
\
/
_0
6h,
J
20
/
/
deg
0
J
-20
10
gcom,
g units
o
0
FP ed'
-_00
N
-800
0
2.
q
6
8
10
12
kq
16
Time, sec
Figure
152
38.-
Continued.
18
20
22
2q
_J
qO
ct,
deg/sec_
o
-LiO
8O
Cticl,
deg/sec
/
_
/
_°
I
0
LiO
qa,
deg/sec
0
2_0
-80
b'
deg/sec_
_o
I
o'
f_
//
-u,O
u_O
ricl_,
deg/sec2
, i'a'
deg/sec_
o
_u,o
0
-_o
_0
f
m/see
F
_ _LtO
u_O!
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_
0
m/sec
2 -qO
m/sec2
-qo
j
I_,
o
m/sec2
0
l
2
IA--J
f_
ti
6
8
kO
k2.
kq
Time,
Figure
38.-
L "
L6
18
20
22_
u
sec
Concluded.
153
riO
deg
20
.._-
0
I0
/
0
deg
\
/\
-i0
120
80
/\f
_j
_0
\
0
-qO
qO
J
r,
deg/sec
0
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qO
q'
0
deg/sec
-_o
200
/'1
i00
/
,
/
p
0
/
/
/
/
deg
f
/
/
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z
/
f
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/
/
-200
qO0
Pcom,
200
deg/see
0
x° A
0
2
t
L_
6
8
10
12
Time,
Figure
ig
39.Response
to
trim
at
_ : i0 °,
stick
is4
application.
lq
16
18
20
22
sec
full
cross
controls
applied
followed
by rapid
full
aft
Control
system
C;
ho
:
9144
in
m.
q
an'
2
g units
0
•6 I
M
.3
0
i00
_'
0
aeg
_1oo
IooI
G,
0
.i
aeg
-I00
30
6a,
0
deg
-3o
6d',_
_,e_
100
- Io
30
6r'
0
deg
-3o
_O
6h,
20
/
deg
o
\
-20
10
5
gcom,
g units
0
-5
I_ped,
N
__o°o
-800
8
o
i0
Time,
Figure
39.-
12
lq
16
18
20
22
sec
Continued.
155
8O
•
q,
1
_iO .....
deg/sec 2 0
\_/"<_._'_"
v_
8O
qicl,
_0
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o
/
\
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/
-qo
qa,
deg/sec
o
l
\
2-qO
l
---
]
-80
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/,
o
r,
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I
_
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0
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,%
0
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v¢'
0
\
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mlsec2
i
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m/sec
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2
/
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0
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0
ITl/Sec
2 -qO
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°H--4--LI
I I.J_4_-44-1
I _
m/sec_-_ol0 I 2I I Li
VI_I8 I 8I I i0
I I 12
I I lq
I I 18
I I 18
I I 20I I 22]
Time,
Figure
156
39.-
Concluded.
sec
.6
yo
c(,
M
20
f/
deg
o
B,
IO
o
deg
""
_
.3
L
o
lOOl
r
/ _--_-_
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o
deg
-1o
120
\
P'
_0
deg/sec
o
_
_J
tO0
/-x
0
@'
8o
J
-too
[
J
f-x
_ too
deg
\
30
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0
6a'
-3o
deg
80
lO
deg/sec
q'
. j4
0i
deg/sec
"x
"
---
-_o'
6d'
0
deg
- 1o
I
_
/
30
Oi
6r'
deg
2o0111
I
-3o
h III.
_o
i_),
deg
_,oo!/i)tll 11
Ill
o
Ylll I/I
-2oo
II
I I I I 1'1/
I I
6h,
20
deg
0
/ I
200
deg/sec
0
Flat,
N
0
0
f,
-20
lO
t{oo
Pcom,
f /
/
f"-.
"_"
_
_
\
/
/
2
u,
Figure
6
8
40.-
10
Time,
12 t u,
sec
Response
Control
16
t8
to
20
maximum
system
gcom,
g units
sf
o
Fped,
N
_0Oo
0
/
2
inertia-coupling
C;
ho
:
9144
ti
6
8
10
Time,
12 lq
sec
16
18
20
maneuver.
m.
157
8O
q,
_0
deg/sec 2
0
8O
/licl,
deg/sec2
_o
o
I
/
80
rio
o i\
qa,
deg/sec 2
b
-LiO
-8O
qO
0
rf%_
deg/sec2__ 0
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o
deg/sec 2-LtO
_
f
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ra,
qO
deg/sec 2 0
#
m/$ec
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2
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80
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m/sec
y "_' \\,
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o)
i
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qO
Wac2,
0
m/sec I -_o
-80
Wa,
ot-+q, I I I I I I I I I i_
m/sec_-<iol 0 I 2I_ ti
I FI12 I lqI I 16I I 18I I 20I
6
8
lO
Time,
Figure
158
40.-
sec
Concluded.
an ,
g units
.6
qO
E3,
deg
M
20 _-_
o
0
100!
B,
,,, deg
lo
Ol
-lo
\
/
Up
0
_J
deg
-I00
100
80
J
P,
u,O
deg/sec
0
r_,
so
o
deg/sec
\
0
/
deg
._
-I00
30
I 1_4--b--LJ I I I I I I I I
_
6a,
0
deg
__<
qO
q'
deg/sec
/
0
\
/f
\
Jf
-30
v
I0
6d,
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0
deg
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/
100
d),
3O
/
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0
f
deg
/
deg
/
=3o
/
-i00
-200
Pcom,
deg/sec
qO
qO0
6h,
200
deg
20
0
0
__
/
_ /
\
,F
-20
10
q00
3OO
Flat,
N
x, I/
/
200
gcom,
g units
s
Fped,
N
_oo
°o
0
100
0
0
2
q
6
8
i0
12
lq
18
2
q
6
Figure
41.-
full
0.375_.
A
lateral
360 °
roll
stick
Control
8
I0
12
lq
16
Time, sec
Time, sec
from
input
system
ig
at
C;
trim
a
ho
flight
at
center-of-gravity
:
9144
_
=
25 °
location
using
of
m.
159
q0
ct,
o
j_-_
f,..,
deg/sec2__@
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,
m/sec
0
2 -Li@
qO
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IIl/$ec
0
2
r
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v
-qO
_0
Wac2'
1
0
v
2
m/see
-Li0
m/sec
2 -LlO0
2
q
6
8
Time,
Figure
160
41.-
I0
sec
Concluded.
12
I_
16
!1i ¸.
60
1/
Lt0
deg
_t'!
li
I
2
_ 1.1"
I
I
lo
I III!
II/1/
o
deg
-lo
/, \
-
-20
_'
-30
16o:1
'
i
•
I
I
I
I
t20
[_
80
XI
r,
I
i
i
J
P_
deg/sec
LtO
0
1
i
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r,
8o
ii
_i
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q'
0
f,\
_
//
, VlJ_
-_0
deg/sec
'
/\
\
/
\
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I\'J
I
i
Li
I
i
_-_
I
deg/,ec-,o
I IIIIIII/HIGH
I_11
To°o!_/ h
o. -looo,l_I lll_'
i]/
I/
-2oo,
Pcom,
deg/sec
II
200
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0
I[
/
"II
IL
P\I/1\
I "I-IT It
t
I
3ooI
Flat,
N
:°oil
I
-100/
0
Figure
42.-
I
2
I
i
8
'{
Response
maneuver
at
0.375_.
Control
a
10
ll2
to
lY
16
Time,
maximum
18
20
sec
22
2lu, 26 ' 28
location
C;
32
inertia-coupling
center-of-gravity
system
30
ho
:
9144
of
m.
161
/
an,
/
g units
.6
M
.3
0
100
_,
deg
_J
0
-loo
-200
100
f
deg
"----4.._
-1oo
30
6 a,
deg
0
I/\
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I0
6d'
deg
0
-10
3o
deg
-30
-
--
"
/
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/
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6h ,
deg
2o
o ---
•
F r--_
(
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v
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10
1
f
gcom,
s
g units
o
1
-S
l_ped,
N
_0o
O0
2
q
8
8
10
12
lq
16
Time,
Figure
162
42.-
18
sec
Continued.
20
22
2q
26
28
30
32
deg/sec
2
4a,
4_
deg/seC
/
Z
m/sec_ -qo
_racZ,
ITI / $ C C _
Time, scc
Figure
42.-
Concluded.
163
deg
o
_-t
"
-
,o.......
8,
o
/
Y_%...F
deg
--
_ ;
i
/
-j -<1---
lo
_.o
t/
-30
L
80
qO
P,
I
0
deg/sec
_
_
I\
/
\/
I
-q0
-80
qo
r,
/
o
deg/sec
-qO
qo
q'
0
deg/sec
-_o
0,
deg
qoo
Pcom,
200
deg/sec
0
/
\-
\
qoo
300
Flat,
200 --
N
tO0
o
0
2
q
6
8
10
lq
12
Time,
Figure
flight
input
Control
164
43.-
A
at
at
360
_
a
°
:
roll
25 °
attempt
using
C;
h o
18
lateral
location
:
20
initiated
full
center-of-gravity
system
16
9144
22
2q
26
sec
m.
in
ig
stick
of
0.39_.
trim
an,
g units
oI_
I I I I I I 1-11 1 IT-] I IT-I I I I
.6
M
L
II
I00
deg
-Ioo
-200
I00
i
__
0
deg
-i00
30
6a,
deg
o
\
/
-30
I0
6d,
0
deg
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c_/,,
/
deg
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LiO
J
6h,
2O
//
J
mJ
deg
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o
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gcom,
g units
Fped,
N
,o
L
s
_.
o
L_O0
0
o
2
q
6
8
10
12
Figure
43.-
16
tq
Time,
1.8
20
22
2q
26
sec
Continued.
165
qO
j,
deg/sec
o
\/
\J
\ /
2-_0
-80
qO
qicl,
o
deg/sec2 -_0
qO
qa,
deg/sec
0
,/
2 -qo
^
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qO
0
r'
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0
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J
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mi$8c2
m/sec2-q
\
^
0
_+-_
-"\J
k
/!\
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rk''
0
2
L_
6
8
I0
12
Figure
43.-
16
lq
Time,
166
\\/'\-_\l
_,_... --.,j \
-_0
sec
Concluded.
18
20
22
2q
26
80
60
/
/
\/'-.._.
k_.,
\/
_t
\i
L_O
deg
_J
2O
r.e. _I
l
I
_01
A
I
P,
deg/sec
o
-_0
I
_\
------.;
_
f\
L/
I1\
V l_'
xJ
_-
] V
I
v
_0
0
r,
aeg/sec
-_o
0
q'
deg/se¢
_-
-qo
-_
i
deg
""
__I"
\x\
----- -'-"
_ 1oo
Pcom,
deg/sec
Flat,
N
/
....
I
2°00
[
_ ool
[
0
0
5
10
15
20
25
/
30
35
_0
_5
S0
Time,
Figure
44.-
Deep-stall
entry
Asymmetries
at
not
a
55
60
65
75
80
/.
85
90
95
sec
center-of-gravity
modeled;
70
ho
=
location
9144
of
0.35_.
m.
167
q
an,
g units
0
.9
,6
M
.3
0
i00
W,
,,%
0
-too
deg
"--4-.--4---
__
--..-
_
A
A
_
_
--
-200
100
If
0_
0
deg
J
"-,-
t
-100
30
63.,
0
deg
-30
10
6d'
0
deg
-1.0
30
(_r,
0
deg
"k
j/'_
--
-30
_0
6h,
20
deg
o
J
-2o
S
gcom,
0
g units
Fped
N
'
_"
_S
.
_00
Uo
5
10
15
20
25
30
35
u,o
q5
Time,
Figure
168
44.-
50
55
sec
Continued.
60
65
70
75
80.
85
90
95
_0
q"
0
deg#ec2-_o
_0
o
qicl,
deg/sec2-_{o
_Ol
6_
qa,
,
_./"
-'_
...-"
,
_
"..-4
--
deg/sec2-_,o
_0
"r,
0
deg/see2
-qo
ricl:
O.
deg/sec2-_o
qO
0
ra,
deg/scc2_Lio
RO
J_
m/_':_:: 2 -qO
_0.
Wacl:
m/sec
O.
_/
-_-
2 -'4o.
[
_0.
_rac2'
m/_c
O.
_ -qO_
0
m/secz
0
I I I IJ_I'--F-_
5
tO
15
20
I I
25
30
Figure
,
35
.
u,O u_5 50 55
Time,
.sec
44.-
i i
60
65
7[3
75
80
85
90
35
Concluded.
169
]3
£00" _0"
u3
'k3
0 1700"800"- ZO" I0"
I
I
l
I
¢
09
OL
>
- 06
C)
{-.
80
60
qO
deg
_J
20
0
I
2O
_o
,.,e_
/,
/\ r
\
-lo
-3[
deg/sec
-_0
_/
L
-80
deg/se¢ _u,o
_0
deglsec
I
-qO
J--
100.
m,
deg
0
_ tOO
,...
_-_"
"\L I
I
\ / _-',,i
_':<, °oil vv LV"""i
N
-lo
0
S
10
15
Ill
20
25
L ILl
30
35
_0
u_5
Time,
Figure
46.-
Deep-stall
entry
Asymmetries
at
a
50
55
60
h °
"70
75
80
85
sec
center-of-gravity
modeled;
L II
65
:
location
9144
of
0.35c.
m.
171
q
g units
0
- -_
.3
2O0
100
W,
\
/
0
"'_-_
_
deg
-i00
\
\\
\
\
-
"1'4
-200
i00
9,
___
0_._
deg
\
\
\'
I
j
-tOO
30
0
6a'
deg
-30
I0
6d,
0
deg
-I0
30
(51",
0
/k_/\
deg
-30
qO
6h
'
deg
20.o
-20
5
gcom,
g units
Fped,
N
I
0
s i
_io_
o
s
to
is
20
2s
30
35
qo
Time,
Figure
172
46.-
_
5o
qs
sec
Continued.
5s
6o
ss
20
vs
8o
8s
qo
q'
deg/sec2
o
_'4-
_ _ _I-" -" _'_-
_io
_0
Clicl,
o
deg/sec2
_u,o
LiO
qa,
deg/sec2
r'
deg/sec2
7icl,
deg/sec_
o
__
_o
...,-
,_
'....,_Lf
_ -'- ._,-,.
o!
-_o
o
-_o
LiO
i'a'
deg/sec_
o
-_o
u,o
m/sec
o
2 -rio
LiO
Wacl'
m/sec
0
t -qO
_o
_rac2'
m/see
0
2 -qO
m/sec 2-_Io
s
io 15 2o 2s 30
Figure
3s
46.-
_o _s 5o s5
Time, sec
6o 8s
7o 75 8o 8s
Concluded.
173
IX. 81ef =25°;6tef
0
=O°;Sh
81ef = 0°: 8tef = 20°;8h
=25°,8sb
= 25°; 8sb
E] 81ef = 25°; 8te f = O°;Sh = 25°; 8sb
=0 °
= O°
-----60°
<_ 81ef = 0°; 8tef = 20°; 8h = 25°; 8sb = 60°
0
C
m
-o ].
,
I
I
I
I
10
20
30
40
I
50
60
70
80
90
a, deg
Figure
47.-
variation
location
174
Effect
of
with
angle
of
0.35_.
flaps
and
of
6 h
attack
:
25 ° .
speed
at
brake
a
on
pitching-moment
center-of-gravity
80
/%
50
4O
deg
/
\
/
\J
-
/_\
_"
\
/
_J
2O
f
\
J
0
-20
20
10
f,
deg
.-Ii I
i/
0
-10
k/
-20
-30
40
P,
^
o
deg/sec
n
\P
t
A
vd
/ ,/',:
-40
Vv
/',"
40
0
r,
deg/sec
-40
4O
q'
0
deg/sec
-40
Pcom,
200
deg/sec
o
Flat'
N
_io°o
60
6sb,
40
deg
20
I
o
o
Figure
48.-
5
10
Deep-stall
center-of-gravity
ho
:
9144
15
20
25
30
35
40
recovery
location
45
50
Time,
using
of
0.35_.
55
sec
60
speed
65
70
brake
Asymmetries
75
and
80
85
flaps
not
90
g5
at
a
modeled;
m.
175
I
an,
f__
-_
f_
f
g units
.J÷t
M
,,
.5
/
.3
1oo
_y,
o
deg
-too
-200
ioo
deg
I
o
I
-too
I
i
0_
I
3O
6
a ,
o
deg
-30
Io
6d'
0
deg
-1o
6r,
deg
30
I
0
L
"--/ '-J \/^'v\''_"
/
-30
_0
/
20
5h,
J
o
deg
-20
-_o
lO
5
gcom,
0
g units
_ i
-s
Fped
N
'
I
_oo
O0
5
tO
15
20
25
30
35
qO
u,5
50
Time,
Figure
176
48.-
55
sec
Continued.
60
6S
70
75
80
8S
_0.
9S
F
4O
O!
q'
v
4O
o
qicl,
deg/sec_-4o
4O
qa,
k
0
deg/_c2_q
V
0
4O
÷,
0
deg/_c240
ricl,
4:
deg/_c24o!
qO.
i
ra'
deg/_c_
m/sec
O_
_0
2 -40
Wac2,
m/sec
"1
2 -Lio
40
Wa,
m/sec
0
_ -qO
O.
5
_10
----
15
20
25
---_-_
30
Figure
35
_0
48.-
_
45
50
55
Time,
scc
60
85
70.
75
80
85
90
35
Concluded.
177
8@
60
f
LtO
J
20
20
/
_f
>
0
i
\
/
deg
J
I
A
lO
deg
\\
"/
A
/
-lO
IV1'
" J/,'
_'
\hi
\/_,
20
-3O
qO
"x
o
P,
f_/\_
\/
-_0
deg/sec
_
V
-80
0
r,
/
-u_o
deg/sec
qo
q'
/
0
--_.
/
\j
\
-_,0
deg/sec
[
100
/_
--_.
%/
deg
0
iDcorrI,
deg/sec-2OO
Flat,
N
-_f--
_ioo
-loo
v
°U
_
I
v
"
T
V
I
V
15
20
6o
6 sb,
_o
deg
20
o
O
5
10
25
30
35
q0
LIS
Time,
Figure
flaps
49.at
Asymmetries
178
Deep-stall
a
recovery
center-of-gravity
modeled;
SO
85
using
location
ho
=
60
65
70
75
80
sec
9144
m.
speed
of
brake
0.35_.
and
85
q
an,
g units
M
-J.
.6
/
.3
_-4__/
0
I
lOOI
_p
\
\\
\
0
deg
\
-100
\
-200
deg
-100
__r_
6a,
deg
5d,
deg
O'
_ ' ^'
"_
_
-
-30
lo
t
0
-'10
I
"
6r,
deg
6h,
deg
-3
2o
/
X
0
-20
-u_o
gcom
g units
Fped,
N
o "
l_
[,
_o_
0
5
I0
15
20
25
30
35
40
u_5
Time,
Figure
49.-
SO
55
80
65
70
75
80
85
sec
Continued.
179
80
Cl,
deg/sec
40
2
/\
0
./,-,
A
iX
-,
/,
7,
,.^'-^ .sl V
.#
-40
4O
o
qicl,
deg/sec2
-4o
qa,
deg/sec2
0 -_
"" -v_v'-",/
l""
"
-4o
4O
o
r,
deg/sec2
-40
4O
ricl'
deg/sec2
0
-40
4O
_'a,
deg/sec_
0
-4o
4O
m/see _ _q o
\
4O
Wac2 '
m/sec
0
2 -40
m/sec 2-4
0
5
I0
15
20
25
30. 35
qO
45
Time,
Figure
180
49.-
50
sec
Concluded.
55
60
65
70
75
80
85
8O
60
1\/>, )\s,.l"; ." _
/
\
/
_0
deg
_J
2O
ff
/
f
0
J
2o
_1
lo
/_
%!1
/
/ A [
t/
]/_jt
_l
/3,
o
_
t
-lo
-2o
deg
/ i/
-30
tsI t
_ A A
,I_/,
//_/"_j'_
/
I
r\ it
deg/sec
-_o
L
r_
,
v
\
I
_,
_/--J
deg/sec
-_0
I
_0
q'
deg/sec
0
-_io
d_,
100
O
j
f
k j
_
/eft\
_
\,
_1oo
deg
"\J
"-'
"
--
L -C
"
-
/_J
\
_"
L
'
....
i- _
J_
t
"
pcom,
°
-2°°
_"
,v 1
deg/sec
I
- 2o vlJ "
Flat,
N
0
S
10
15
20
25
30
35
L_O '45
Time,
Figure
50.Deep-stall
center-of-gravity
ho
:
9144
50
85
80
BS
70
7S
80
_5
sec
recovery
using
pitch-rocking
location
of 0.35_.
Asymmetries
technique
modeled;
at
a
m.
181
an,
g units
.9
M
r-
J
0
200
I
100
I, \
\
0
\
deg
\
x
\
100
\
\
x\
N
2O0
"_
4
ioo
deg
-too
30
6 a,
0
deg
-3o
lo
6d,
deg
3o
5r,
0
/
_\_
-30
deg
20
0
6h'
-"
/_"
"" _J
vr._ .........
P r
_ _
f
P/t
/
1
l/
-20
-qO
10
g units
0
"
5
Fped
N
'
_o_
0
5
lo
15
20
25
30
35
qo
q5
Time,
Figure
182
50.-
So
sec
Continued.
5s
80
65
70
7S
80
85
|
q0
/t,
o
deg/sec2
-_0
_0
_licl,
o
deg/sec2
-I
-_o
uiO
qa,
0
deg/sec2
_Lio
qO
"i',
deg/sec2
o
-_io
L
_./_w
_
=+_'-xt_ t_'-
_
AJv
uiO
i'icl,
o
deg/sec2
'
_--,'T'...'
-_
-qo
qo
'x.J
0
i'a'
y
T
-_io
deg/sec_
_ .
v-
40_
w,
m/$ec
0
j
--....
v
_
_
v
--
?
2 -qO
Wacl,
0
ITI/$ec
2 _q0
r
•
m/see
m/sec2
_Ol
2 -qO
o
5
io
15
20
25
30
35
Time,
Figure
50.-
sec
Concluded.
183
8O
,\
8O
.
k_
_p
_0
deg
/
2O
--
c
i
i
0_
3O
2O
A
]0
0
II
J
f_
II
deg
II
I
-10
-20
...............
II
I1
I1!11 "\
IV\/
V
A_
/
_
.....
V
--
-30
r
qO
_1
0
P'
[
aeg/sec-'_o
i
\
v
qO
r,
0
deg/sec-q0
l
_0
deg/sec
-qO
lO0
¢ '
_--'--
0
deg
J
\
-i00
deg/sec
Flat '
N
lo__
_t+H
.....
H
_t-t-Tq
6O
I
6 sb,
qO
deg
20 --
_.[
0
0
lO
18
20
25
30
35
qO
q8
Time,
Figure
a
51.-
modeled;
184
Deep-stall
center-of-gravity
h o
=
9144
recovery
using
location
of
m.
50
SS
60
65
70
78
80
88
sec
speed
0.375_.
brake
and
Asymmetries
flaps
not
at
4
an,
g units
2
0
/-
J
.9
M
/
/
.3
fl
o
2ool
loo
/
o
deg
-I00
-200
too
Op
o
deg
io_
0
5d'
dog
-io
30
6r,
deg
0
\^,x/k,
-_ ^
I
-30
40
20
5h,
/
/x
0
deg
-20
-40
lOl
gcom,
g units
5
0
_
_,
-5
Fped,
N
_°°°
o
5
10
15
20
25
30
:
Figure
51.-
35
40 45 50
Time,
sec
55
60
65
70
"75 80
85
Continued.
185
_0
Cl,
o
deg/sec2
-_o
ti0
Clicl,
0
deg/sec2-_o
•
YO
qa,
0
deg/see2__io
t
II
i.,
J
0
-_o
deg/sec2
_0
o
i'icl'
deg/sec2-qo
_0
i'a'
deg/sec2
0
-_0
_0
m/sec
2 -u,o
_j
_0
m/sec
2 -rio
V
qo
Wac2,
0
,.,
m/$ec
2 -LtO
m/sec
2 -u, OI .I I I I I I
0
S
i0
15
20
25
Figure
186
30
3S
51.-
j
J
}
v
_
t{O q5 50
Time,
sec
Concluded.
J
55
60
65
70
75
80
85
8O
,
/,'_
/
/ \ ,\j\,, k fL
6O
I
u,O
I
deg
Y
2O
J
I
f
0
2O
]
10
t
iv _J\,'_'"
_<\<
0
deg
f[
d
-10
-20
-30
P,
deg/sec
o
-40
deg/sec
-qO
Cv
0
¢'
_
\/
'° I
q'
deg/sec
/
-
-"
-
,,,/5
/ \,
<
.....
--
---_
-qO
-._.,
_,
,-.,
d
.."
v
_
,°o ,I
deg
_1oo0
Pcom,
deg/sec
°
-20°
_
I
' I"
]
I
(
I]
" _
_/-
++
'_"_-
_
+
]
I
-,o_1 iv v I!,_I_
I
I
6O
u,O
6 sb,
deg
20
0
0
Figure
and
5
tO
t5
20
52.-
Deep-stall
flap
at
Asymmetries
a
25
30
35
u,O u,5
Time,
recovery
attempt
center-of-gravity
modeled;
h o
50
55
sec
60
using
location
:
9144
65
70
75
speed
of
80
85
9O
brake
0.375_.
m.
187
.9
M
.6
-'--_
.3
o
200
_
\
\
\
tO0
\
Up
\\
0
\
deg
\
-i00
\\
-200
lO0
_'
deg
o_
_1oo
30
0
6a'
deg
-30
IO
6d,
deg
o
I
-IO
30
6r'
deg
0
-3o
qo
5h'
20
deg
0
_--
J t
5
gcom,
g units
0
-I
L
I
Fped'N
u'°_
0
S
10
15
20
25
30
35
u_o.
'45
Time,
Figure
188
52.-
SO
sec
Continued.
55
60
65
?0
'75
80
85
90
_0
cl,
deg/sec2
o
/
v
-40
,
_,
\_/
t/
/
--i
I
_licl,
deg/sec2
0
-4o
ti0
(]a,
deg/sec2
0
A
-40
_0
i',
0
/
deg/sec2
-_0
_0
i'a,
deg/sec2
0
-4o
ti0
w,
0
i
m/sec
I
2 -40
_0
Gad'
m/$ec
i
0
v
_./-_
/_
_ ...._
v
_--'-,.
/--,.
,-"'-._
i
I
2 -40
40
_rac2'
mlsec
0
_ -40
_ra,
op-_l
I I I_L_I
I I
m/sec2-4ol 0 I SI I i0
I I 15
I I 20I I 25
I I 30
I I 35
I I 40
I I 45
I I 50
I I 55
I I 80
I I 65
I I 70
I I 75
I I 80
I I 85
I I _0I
Time,
Figure
52.-
sec
Concluded.
189
100
80
f
/
\ /_\./\
u,O
deg
/
/
/"
/
\
30
i
2o
/
lo
o
deg
1
//
IIII
I
/
l
20
_/
1
/
-30
8O
_o
f
P,
---
/\
_ All
-80
LtO
P_
deg/sec
v
-qo
qO
A
k/-
-u,o
deg/sec
100
'
de°_
0
//_"
---
\
r,
\/k/.._,
-10o
P corn,
v
0
tool
°1 I I II//IV
I
Flat,
N
0
5
i0
I
V
15
20
25
30
35
Time,
Figure
53.-
technique
0.375_.
190
." i_ \/
Deep-stall
at
a
recovery
rio u_5
using
center-of-gravity
Asymmetries
modeled;
50
55
60
sec
pitch-rocking
location
h o
:
9144
of
m.
65
an, _
__
_+_
g units
M
,6
--_
jJ
o
I--_
deg
O,
deg
6a'
0
-10o
301
0
^
deg
-so
6d'
deg
lo
-10
6r,
deg
0
-30
i
I I
6h,
deg
O-J
1/
°
I
^
3o,II"
.........
_
_
_.,/'-,
A
'
-
v
L
]'
o
20
-L----
_0
I
]._=_
L_
gcom,
g units
Fped,
N
'
O
S
I0
Figure
15
20
53.-
25
'
30 35 LiO qS
Time,
sec
1
50
I ! i '
ba
68
Wb
Continued.
191
40
Cl,
deg/sec
'L.-_
o
vj
2 -40
-80
tt0
Clicl,
\i?,p
0
deg/sec2
-40
4O
deg/sec
2-40
8O
40
deg/Sec2
-4o
tto
ricl,
d/-eg-sec
0
....
2
6,
.......
r
v-
_
40
ra'
0
deg/seC
40
40:
/
m/sec
v
2 -t{O
4O
Wacl,
m/see2
0
-"
--'_---
_
--"--'/_/\/\V
-4o
V
40
Wac2,
m/seE
w&,
m/see2
o
_ " _', _"_',, ^ _ _ _A
v/
2 -40
0
-[{°0
5
10
15
20
25
30
Time,
Figure
192
,, _
53.-
35
40
see
Concluded.
45
50
55
GO
G5
IOO
80
60
deg
/
/
v
k.,
I
\/\
,-, _
,_
/
/
_o
2o
f
/
__j
d
v
\
h
L.
I-
i
o
30
2O
I0
B,
O
II /,j\,
deg
/^ I I
t/ Ill II
-IO
-20
-30
A
0
P'
....."--
F
--
,.
f
_
.,\
,,
,
I
A
I
I
(
I%/
v
-_0
-80
I
I
_
A'\ F
I
_0
r,
deg/sec
0
-_0
deg/sec
_L_O
_
deg
-too
Fiat,
o
too
_f
_ \_J J
__L
VIVI/II I IV_I/I
I I I I I t-I
0
5
Figure
at
-_'
ioo
N
A
_
54.a
10
15
20
25
Deep-stall
30
ho
=
9144
riO
q5
recovery
center-of-gravity
modeled;
35
location
50
Time,
using
of
55 60
sec
65
70
75
pitch-rocking
0.375c.
80
85
90
95
1UO
techniques
Asymmetries
m.
193
2E_
o/I
M
I I I I,
---q,
I
•3
0
_1
[
.......
I I I I I I I I_ L_.4_-dJ_L_4_J_4_4,_A
I I
I I I I I I I I I I I I I I I I FIN I
"
f
b _-_.
1
1_-q
F"
2OO
I00
qs
\
\
0
deg
-lOO
\\
_\
\
-200
tO0
0
G,
deg
_;oo
30
0
6a'
deg
v
30
lo
0
6d'
deg
-;o
6r,
deg
I/\l
2
dh,
deg
-20
-YO
10 .... l__
_com,
g units
o
5
5
'1
I '
I
'_°°Io
i_ i.l-t-H--F
-I_-I0
S
I0
!5
20
25
30
Figure
194
35
u,o
54.-
Y5
SO 55 60
Time,
sec
Continued.
65
"70 75
80
85
90
95
100
^
o .........
,ale1,
deg/seC
- .........
"1
v • -
/
-qo
_o
I
"
deg/seC-_io
"
_
J
-80
80
i,,
i
_o
_ "
_"
W _
-<io
I
L
i'icl,
,
o
deg/sec2 -_iO
deg/sec2
""1 V tc
l
v
"
....
__ _
/
_v u
17 "
_io
8o
_.,
<io
-qO
m/sec
Wac2'
1Ti/SCC
2 -qO
o
-,. ....
-..-_-v ......
--
I^../,
2 -q 0
_btq_
m/see2
o
s
IO
15
20
25
30
Figure
35
qo
54.-
q5
5o
Time,
55
sec
Concluded.
195
.9
M
.6
.3
0
qO
0,
20
0 _,.
deg
Lr
\f
/
f_jf
_
10
0
deg
-Io
qO
0
P'
deg/sec
-_0
qO
r,
0
deg/sec
-_0
qO
q'
Ov
deg/sec
-_,0
i00
¢'
0
deg
-loo
J
20o
Pcom,
0
deg/sec_200
I00
Flat'
N
o
A
-i00
qO0
FP ed'
N
o
-
-q@@
0
Figure
10
55.--
15
20
Performance
wind-up
196
25
30
35
qO
q5
of
airplane
turn
task.
50
Time,
55
60
sec
with
ho
=
65
70
control
9144
m.
75
80
system
85
30
A
in
95
100
6
/
an,
n£,
2
g units
/
t, ,,,
</
_._
_
_..z _
4
_
_ r
/
I
200
100
"L[.[I
V"
\
0
\
deg
-100
\
"F
-200
I00
@'
0
deg
-I00
6a'
3o I
0
deg
-30
30
_
6r'
deg
N
....
_
_L'x,
_-.-
_
_/'_
n,
_k_
[
200
_
o v-"_,
-'-'-_
_'_"
_'_
/
-200
range,
m
/'k,
-30
_oo
_long,
_
0
_oo ....
0
_ _
___
--
deg
deg
-20
0
5
10
15
20
25
30
Figure
35
q0
55.-
q5
50
Time,
55 60
sec
65
70
75
80
85
g0
gS
100
Concluded.
197
•:11
l_LII
M
deg
LILLI_J_L
:o_ lilllll}llll
-_SJ
I0
deg
-lo
I I I I ]-Wq-
/V
]
7
]
v
_f'11
FI
VLq/yVlViY-[
I_l//
I I/I
]T\/I_I
I/q
I
oolll/l J, /k J,,_
J,_tiJ
160
deg/sec
T_
.
_
V
^
80
IX
_U!/I illllVl,
V
' G I l/'l
IkV I
:7_f!,,kLL]_!_J,.,LA
!,J7_il
deg/sec
q, oLI,,I.L-'I,-,VLIX_I.,I,
k'-+,,,_,-,,-_
+J-I,kJq+t-<,o,,i:_<:_.o
[lllllll
[/'-I-'1
II
II II1111]
[to
II
LI
IAI
o1-11<_
Jr '/I_ivxi_,Jllm
deg
::: IIIIIIA,
/
,,
I_, !_lllllq
I /r
I I I _ IIIII.
L I I _1111111111111
71 J-]l_
nl k,-!,A[ I IAl
/
tI,K
I llllllSlllllklil
frillY,,/
_111
I_AII I/IV III/_l_'k/ll_lll
tlll_Vl I
_"
P¢om,
deg/sec
__oo_llll,iii _
Flat,
N
o,,u_,.,'!',J,d. /
_,_! ,'!, 7 !_!!! v! iff/4,,._.,,[_
::::i_'
'Ti'<'_'7
'''_''_'_''
7_"0i
It_1_?_
0
5
10
15
20
25
30
35
[t0
Time,
Figure
control
198
56.-
Performance
system
A
of
in
LIS
SO
55
60
65
70
sec
airplane
bank-to-bank
with
task.
q
•
ant
g units
"q/)
deg
0,
o
deg
6
r
-lo@
,
deg
I II
_
^
o-_'_'_V,
LA1-.\.^-^y
_(
__oi I
_
\
_,L&,4
_1 __
....
_---_
x....
_
_
_/
,A
_
V _
\
( _ ,A
d<kf
Fl°ng'
b
t4
..
i i
q i
-200
range,
_001 I I I I
Q_l--_rd-_[
I I L_L I
i I
I 1_ I I I I 1__14
i I i i I I_I-TI
i i i
i l/
m
deg
20
"h
0
'\G-
x
d_
<_r" _
"_ _-,
"_
deg
qo
i
0
5
10
15
Figure
20
25
56.-
30
-- +
38 qO q5
Time,
sec
50
55
60
65
"70
Concluded.
199
M
'°o 1
B_
deg
P,
IIIH I_LL/ALJ_IA_I
I LA/t
_1A,
LLLA /
:: / 7iii_rllTG
711-77_7G_IIx
% /
oKi
lim
IA_i.l A_LL^/]
r I I I/-r-I'+lAVll_Jt,
i_lM
r
r,ih_rt/tl,k
_.._°oI
IIIJlllA_li_.
_I?4.M_
_I I_LKI>K[
A_
deg/sec
I\1 ,(1
V
-_o
I I I
W
I
_/_7
IV/
II
VII
I I _/
v
v \/
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
, IIIII ^I,I I,I J_// IAII
kl_l
I I i I_1//I I_1 i/ill
I/ll_l
Ill I I
7 : ,llrl
_;7:7<;
_oo° . ,I l_I/IfT;_ll:It,Vl,,,,,_,.i
"_/l/ll'_-f_/ ,1_.
Flat,
N
-1OO
t
o
FP ed'
N
V
-_ioo
0
S
10
15
20
25
30
38
qO
Time,
Figure
57.control
200
Performance
system
q5
50
of
A
in
55
60
68
70
75
sec
ACM
airplane
task.
with
80
an,
2
_7
/" ' _ "_
o A
g units
\_-___
\
\
_
/_"
,f
J
h"l
-
-
200
tOO
*gl'p
0
deg
-tO0
-200
100
L_
_J
0,
J
i
r
deg
J
-tO0
r
6a,
deg
6 r ,
deg
_, .IJ I/l^
.k.
,r,
/,,
.,
.o ,_l.I i,A,J,.'11,,,
; _"
'AII
_'"
qo
I
5h,
deg
o
v'_
_ _v'"_ _
--
v_
"b_V
v
-
-20
I
200
u'O0!--
.,_
,/ "_'- "" ''\ '
r, A
I'v",/
0 _'_
h
_
v
-200
qO0
1
800
range,
m
u,oo
o
qo
2O
deg
_\
O_
'v \
.,ix '
\_j\./'-_..,v
qO
20
deg
r'-
o -:_
:....
\l ,.__\;i,
-
-2o
0
d
S
10
t5
Figure
20
-
25
30
57.-
35
qO qS 50
Time,
sec
__55
60
65
70
75
80
Concluded.
201
,,,, __-1-111_1
_
III
-Jq---f-__ ['VII-1[_IV//I_l"l_t[] I-IVl
p,
de
IIII
ol IAI,J,,II_,lIJl \l_u I/_ I_'_,_u l//I
J2 II
see
-
vv
V I I/A/l_/
I ,i,,,,,YI
] r I F_/I
uo
I
I J. Iol
"
I I I
cleg/sec
q. "°ol
L]_X_I
_,_/__1,_1
de_/sec-.oI_IVI
II II II II_1_1
I II I1I II IIIYl,I
iooI
,,
I
I DRI
/1_--kl
:°:ol-
Pcom,
oL_1/\],441
fll.JJI/IMil
I I
I,DI-QI
_II I/III
I ] 1 2.4-421
1 1
I_i/Ih,,
I/[
LolLlI,1/11111,
1
li'/
35
Time,
_{0 u_5 50
sec
'
Fped,
O
Figure
control
202
5
58.-
[O
15
20
2S
30
Performance
system
B
of
in
58
airplane
bank-to-bank
60
65
?0
with
task.
_,
deg
L
z"
.
?
-lOOE
o
++
deg
-30
deg
-30
_o!
deg
o
k,._.,
oh,20
/_ ^
-e° _
^
/"In
-
&_4,
,_,
I_
_j//_
-_
....
__'
,_
\f'
-_-^v
_v
1.
600
'400
%V_4 '
1
-200
range,
m
j
j'-^_
I_I
_ng,' 200
8o0
q0o
0_
/
__
_--_
'
/. i
dog2o-L/_,,
o .... /'
_'
4
_
l
60
qO
.....
L_
I
fL
20
deg
0
20
I,
I
-qO
5
10
1S
20
25
30
35
Time,
Figure
58.-
riO
qlS
50
55
60
65
/0
sec
Concluded.
203
.9
I
.6
M
I
I
T-
,3--
o
F_
--
deg
/f_7"'-
<J
J
lo
0
deg
L
v
J
/
f
-,'A]'
-10
160
80
P,
0
/,A
deg/sec
]V'_J
-8o
-160
40
O,
r,
deg/sec
4/
-40[
q'
0
deg/sec
-_0
_f
-
\/
/_,A_,
_'.
_A-/_,
/_
-
r
v
._--,
/"'_---_--_
'_'
'
_/v
J
'_
200
100
(_,
fx_
0
deg
/
\
f
_--_
_
:
_J \J
1 y
\
-100
_00
2OO
Pcom,
p_
o
deg/sec
-200
-_oo
ioO
Flat,
0
_p.pf^
N
/I
/,[I
/
_.
10o
HO0
Fped,
N
°I
-uool
o
Figure
control
204
5
59.-
lO
15
20
25
30
Performance
system
C
35
Time,
u_o u_5 5o
sec
of
in
airplane
bank-to-bank
55
60
6s
with
task.
7o
\
an
,
g units
_
_.
2
\ _ ^ <
0
/¢
/
deg
-10O
deg
-ioo
3o
da,
deg
0
-30
6r,
deg
o
-30
_
_,
J
I _
_.-_
u,
\,'
.^ A,p ,-.r',.
-20
-
V
f"
_
\l\i
]
v
l,_v
,
V"'
V'
A _,
/'_
'\
L. A ]
_
v/"-V'
.... _,_
6 h,
deg
\
,
-v
_I
' IJl
I
I_
'J
I
1
IJ
ik]" tl "'/I
X, t,
A
.....
.N\],
V
v,,-
V
qO0
Plong,
N
200
/_
o
,A_
;"
X,_/i_'X/V
_
/_-_,
?
½ _/_f
-2oo
range,
I
_o_
___
_
_.
q_'-J_
In
E,
6°1
deg
20
I
qo
f_
'v
.-_ /
O--_b'-J'r_
_-/_J
_"
_/k__,_
qO
20
/--
0
deg
-20
-qO
-60
0
5
I0
15
20
28
30
35
Time,
Figure
59.-
qo
q5
50
55
60
65
/0
sec
Concluded.
205
•3
-_
-
0
2o ....
deg
--
<
_
o
r_\
-
j
\
_
_\
/
/\
io
\J
deg
\
_J
-lo
160
P,
deg/sec
80
tl/t
0
'--
-_
_.
/
vV q
",,
-80
k
/
A
_/
YO
T,
0
deg/sec
-qo
_J
"\/
,.j
40
q'
deg/sec
o
-YO
_ZZ_l.
III li_-lqlll Jl /
/dl
II 111
LJ-ZIY
FIll
deg
400
200
P corn
0
deg/sec
ks
,./
-200
,,wI
200
IOO
Fiat,
N
0
t
!1 \/"
_,\,s\
\
k
V
-i00
-200
400
Fped,
N
L400
I
0
5
10
1S
20.
25
30
35
40
46
Time,
Figure
60.control
206
Performance
system
of
B
in
SO
5S
60
6S
sec
ACM
airplane
task.
with
70
7S
8o
an,
g units
.o!
lO
/if,
deg
-2001
I I I I I I I I I I I I i i _ _
°.,..
_eg-3
Oh,
range,
m
I_
Il-l?I_Y
I-
v-
:o 1/ 1tll .I1_
deg
l_1ong,
N
"
::ooflI/_1//I'lq_////_:_
qo
qO
deg
2
deg
Time,
Figure
60.-
sec
Concluded.
207
deg
deg
\ J
V-
-1o
160
r,
--
-_I
i
0
/
"_,
-v
V
\ jl
deg/sec
-qO ]
_
200
:
_
_oo
\
-
___
f
J
-zoo-2OOl
----
_"
I
/
-
/
---
7 -
_,
_oo I
20O
I
-_oo
Flat ,
0---
N
-ioo
FP ed'
N
. o
-uoo
I
Figure
....
"_ J
:[
_
-2oo,±LLL_ _
0
_
'
.
- .... t_ -
\
S
tO
61.control
2O8
;
_//_
I
15
20
25
30
38
qO q5 50
Time,
sec
Performance
system
of
C
in
ACM
55
airplane
task.
60
65
70
with
75
80
q _,EI
.
\
deg
6a,
ol I I I I _/ h
I_1 IAL I LI
I I 4/IA
h/I
IAIA
- v\_
'
7 N_I/I
_og__olfl-I
I-vi I ItrlYZ]_]
I I I l_h_,-,','_I_Yl
IV_,
,,'d
I1%1 I I I I I
Ifkllll_l
I
_,, 3oo_IIh,,,,_,L_IAL]LLIIIII_I.IIAIt,_,,,,,,.
6h,
deg
60O
'long,
QI I _r_
II--'l I P\ I
"
range,
ITI
I'L) j
V 11{_[_4V_ I_]I
I ]
]I4
I
] II//Ill4
\ 'I$'IIIt
_"
_°°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 I
deg
_I0
20
0
deg
IIILI
111/
L 1/t
20
_t0
60
5
15
10
20
25
30
35
_lO
Time,
Figure
61.-
_15
50
55
60
65
70
75
80
sec
Concluded.
209
O
negative
"g" limit
Pitch
_ schedule
gradient
See
figure
62(e)
Fl°ng
Qi
__
af
q
+
20.2
s + 20.2
DL =25; RL=60
6d, C
÷
20.2
s + 20.2
DL =25; RL =60
(a) Schematic
Figure
62.-
Simulated
basic
pitch
of
overall
control
system.
system
(control
system
A).
0
-2
Negative
"g" limit
-4
,
0
I
I
I
i
2
4
6
8
i
10
q, kNlm 2
(b)
Schedule
of
1.0
.8
.6
.4
.2
Pitch-rate
gain
negative
"g"
q.
I
I
I
I
I
4
8
12
16
2O
_,
Schedule
with
m
0
(c)
limit
of
kN/m 2
pitch-rate
gain
with
q.
1.0
.8
.6
.4
.2
D
Pitch-loop
gain
0
8
I
I
I
I
I
I
16
24
32
40
48
56
(],
(d)
Schedule
Figure
of
kN/m 2
pitch-loop
62.-
gain
with
q.
Continued.
211
III
10
8
Pitch
command, g
4
2
0
-2
-4
-80
,
-60
-40
-20
I,,
, I
,I
20
40
60
Flong,
(e)
Pitch
Figure
212
command
62.-
N
gradient.
Concluded.
80
I00
120
140
160
180
8
k
6
Incremental
commanded normal
acceleration
available, g units 4
2
I,
0
Figure
63.normal
Variation
acceleration
5
of
maximum
with
I
I
I0 15
a, deg
commandable
angle
of
20
25
30
incremental
attack.
213
Roll trim <
4__40
Roll
command
gradient
See figure
64(b)
Flat_
_.___.
20.2
s+20.2
_
+
(If >_29°
rt-x
[+
[
_
_
DL=21.5;RL=80
L222
_
6a,c
4s2 +64s+6400
s2+80s
+6400
I
(a)
Figure
64.-
Schematic
of
_6d,
Schematic
roll
axis
of
of
overall
basic
control
c
system.
system
(control
system
]
A).
50
Oh
Rudder
command
gradient
See figure
65(b)
÷ -i
afJ
3s + 15
_-_29 °
s_
÷
s+
÷
,
-
>
20.2
DL-_Oi
20.2_ =120l--4"
I
of > 29
ay
o.1.871.129_
_Ips
__i
Ps
(a)
Figure
65.-
Schematic
of
Schematic
yaw
axis
of
of
overall
basic
system.
control
system
(control
system
A).
_r
300
200
i00
Roll command,
deg/sec
/
•
J
-100
-200
-300
i
I
-60
I
-40
-20
0
2'0
'
40
60
Fla t, N
(b)
Roll
Figure
command
64.-
gradient.
Concluded.
215
[-j
0"_
Yaw
trim
Rudder
command
gradient
Fped ___
See figure
65(b)
s +6060
÷ "_--
o,I
s-TTg-3s+15
s + 20.2
+
DLT=3--_;
af> 29° r--_--]
(a)
Figure
65.-
Schematic
of
Schematic
yaw
axis
of
of
overall
basic
--12or
+ l
system.
control
system
(control
system
-_
A).
6r
-3O
-2O
-11
Rudder command,
deg
0
11
2O
3O
I
-400
0
-200
2OO
!
4OO
Fped, N
(b)
Rudder
Figure
command
65.-
gradient.
Concluded.
217
P1
1,
P2 = P1
P2 = 60
_T = 5.0
1
T T - f (P2
See figure
P2 = 40
- P3 )
=Tidl
Figure
218
- P3 )
See figure
1_3 = _
Logic
66.-
(P2
1
P3 = fP3
diagram
Simulated
- P3 )
66(c)
]_
1
dt
T = Tmil + (Tmax-Tmil)(P
e + (Tmii-Tidle)(P3/50)
(a)
TT
-- =f(P2
TT
66(c)
l
I
]" = 5.0
]
for
thrust
powerplant
dynamic
model.
characteristics.
3 - 50)/50
P2 = P1
loo
80
P1,
r 60
percent powe
4O
2O
Id
tmum
,
20
0
I
40
Percent
(b)
Power
variation
Figure
with
66.-
l,
80
,
60
I
100.
th rottle travel
throttle
position.
Continued.
219
_0
0
1.0
.8
i
.6
m
TT
i
sec
.4
.2
0
-100
-80
-60
-40
-20
0
20
40
60
( P2 - P3), percent power
(c)
Variation
of
inverse
of
thrust
Figure
time
66.-
constant
Concluded.
with
incremental
power
command.
8O
100
•12 -
• I0
• O8
rms
buffet
. O6
intensity,
g units
• O4
• 02
i0
0
15
I
I
]
I
20
25
30
35
a, deg
Figure
67.-
Variation
of
buffet
intensity
with
angle
of
attack.
4O
1. Report
No.
NASA
'"4.
Title
2. Government
Accession
No.
and Subtitle
SIMULATOR
OF
3.
Recipient's
5.
Report
A
STUDY
FIGHTER
STATIC
OF
STALL/POST-STALL
No.
AIRPLANE
WITH
RELAXED
LONGITUDINAL
Ogburn,
William
Date
December
CHARACTERISTICS
1979
6. Performing
Organization
Code
8. Performing
Organization
Report
STABILITY
7. Author(s)
Luat
T.
Kemper
Nguyen,
S.
Marilyn
Kibler,
E.
Phillip
W.
Brown,
and
P.
Gilbert,
Perry
L.
NASA
Langley
Hampton,
Deal
S_nsoring
Agency
Work
Addre_
Research
VA
Unit
No.
505-06-63-03
Center
11.
Contract
or Grant
13.
Type
Report
Name
of
and Period
Washington,
Covered
and Address
Aeronautics
DC
15. Supplementary
No.
23665
Technical
National
No.
L-12854
10.
9. PerformingOrganizationNameand
12.
Catalog
TP-1538
and
Space
Administration
14.
Sponsoring
Paper
Agency
Code
20546
Notes
16. Abstract
A
real-time
piloted
attack
characteristics
of
F-16,
the
on
ducted
on
involved
tion
inertia
airplane
which
it
which
greatly
departure
17.
coupling
Key Words
exhibited
was
difficult
decreased
and
(Sugg_ted
which
S_urity
the
provided
was
recover.
trim
and
the
Results
system
susceptible
to
could
means
stability
at
be
low
for
to
airspeed.
into
and
were
the
induced
The
from
developed
inertia-coupling
recovering
Distribution
con-
investiga-
departures
flown
the
the
resistant
modifications
to
were
was
evaluation
of
was
pitch
rolls
which
18.
static
simulator,
control
relaxed
simulation
simulation
susceptibility
reliable
the
of
The
Control-system
airplane
in
testing
levels
models.
large-amplitude
deep-stall
a
basic
high-angle-of-
wind-tunnel
various
used
maneuvering.
the
it
of
data
the
on
from
the
deep
stall.
Statement
Unclassified
-
Unlimited
stall
Departure
19.
to
effects
subscale
combat
with
rapid,
a
of
by Authoris))
Relaxed
longitudinal
High
angle
of
attack
Deep
during
the
evaluate
based
maneuvering
however,
to
aerodynamic
tests
airplane
departure;
also
on
The
low-speed
the
conducted
configuration
differential
representative
yaw
been
emphasis
wind-tunnel
Langley
that
has
fighter
stability.
low-speed
the
a
particular
static
showed
classical
by
of
with
longitudinal
based
simulation
prevention
Cla_if.(ofthisreport)
Unclassified
Subject
20.
SecurityClassif.(of
Unclassified
this
pege)
21.
No.
Category
08
of Pages
223
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NASA-Langley,
1979
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