Aircraft handling qualities data

1.
Report
No.
2.
NASA
4. Title
and
3.
No.
Recipient's
5._Report
l)ecemoer
tIANI)LING
K.
Performing
tleff!cy
QUALITIES
and
Organization
Systems
Wayne
Name
Technology,
ttawthmme,
F.
and
Jewell
Sponsoring
Agency
National
Performing
Organization
Code
8.
Performing
Organization
Report
Name
and
Work
Supplementary
16.
Abstract
11.
Contract
for
10
for
each
information
14.
representative
by
qualities,
derivatives,
(of
functions
parameters
and
have
are
the
envelopes
been
systems
Data
presented
inputs,
computed
the
C-5A,
aerodynamic
are
control
power
NT-a3A,
inertia,
augmentation
airplanes.
for
including
B-747,
No.
4-1729
Type
of
Report
and
Period
Covered
Report
Sponsoring
Agency
Code
and
F-104A,
F-4C,
functions,
control
this report}
tabulated
HL-10,
for
handling
10
The
Distribution
Statement
Unclassified-
stability
20.
Unlimited
Security
Classif.
(of
this
21.
page)
by the
National
Technical
Information
No.
of
Pages
343
Unclassified
sale
airplanes
Jetstar,
systems
Unclassified
' For
different
andXB-70A.
18.
transfer
given
deriv-
selected
configuration.
X-15,
documented
are
dimensional
several
are
derivatives,
is
sources
and
and
approach
Author(s))
airplanes,
Classif.
Flight
conditions
CV-880M,
weight
stability
contemporary
airplane.
documented
(Suggested
on
and
transfer
flight
Security
A(ln_inistration
characteristics,
qualities
19.
Grant
Notes
ativcs,
llandling
or
Contractor
Space
Available
Words
1004-1
No.
20546
control
Key
Unit
Address
Address
m_(t
I).C.
15.
Report
10.
No.
90250
Aeronautics
Washington,
1972
Technical
Inc.
Califon_ia
Date
6.
NAS
17.
No.
DATA
13.
12.
Catalog
CR-2144
Author(s)
Robert
9.
Accession
Subtitle
AII_CHAFT
7.
Government
Service,
Springfield,
Virginia
22151
22.
Price*
$6.00
TABIZ
I.
ii.
III.
IV.
v.
VI.
VII.
viii.
D{.
INTRODUCTION
I
•
•
•
F- IO_A
.
.
.
F-4C
•
•
•
•
.
.
61
x-15
•
•
•
•
.
.
Io8
HL-IO
•
•
•
•
•
•
137
JETSTAR
•
.
.
1 66
CONVAIR 880M .
•
•
•
193
•
.
.
210
•
.
.
2_3
•
•
•
273
•
.
LOCKHEED
C-_A
....
XI.
XB-70A
•
APPENDIX
A.
APPENDIX
•
NT-33A
747
APPENDIX
COI_TERTS
.
BOEING
x.
OF
B.
C.
•
•
•
•
•
•
•
•
32
•
•
AXIS SYSTEMS,
AND DERIVATIVE
TRANSFORMATION
DERIVATIVES
TO
EQUATIONS
•
SYMBOLS,
COMPUTER
MNEMONICS,
DEFINITIONS
....
OF STABILITY
AXIS
BODY AXIS
......
OF MOTION
AND
TRANSFER
iii
....
FUNCTIONS
.
.
.
A-I
B-I
•
C-I
SECTION
I
INTRODUCTION
The
gators
purpose
with
craft.
the
aircraft's
For
following
The
insofar
those
data
required
are
response
to
control
augmentor
aircraft
the
b.
Mach/altitude
3-
Control
system
4.
Stability
5-
Tabulations
derivatives
6-
Dimensional,
7-
Dimensional
8.
Transfer
9"
Selected_andling
notation,
An
contemporary
transfer
analytical
air-
functions
relating
description
of
information
was
available,
the
presentation:
computations
(e.g.,
fuel
are
load_
made
flaps,
combinations
description
description
and/or
plots of non-dimensional
for trimmed
flight
mass,
and
stability
functions
flight
condition
stability
parameters
derivatives
for
control
qualities
three
and
index
inputs
parameters
has
is presented
been
to make
nomenclature,
appendices.
definitions
of
B gives
derivatives.
Appendix
C includes
used
herein.
this
Appendix
Appendix
functions
in
Table
report
definitions,
derivatives.
transfer
obtain
investi-
given.
which
augmentation
cross
symbols,
in
qualities
sources
intention
as
for
Configtu_ations
gear, etc.)
arrangement
number
and
handling
representative
to
complete
a.
Data
also
contents
General
several
inputs.
is
for which
2.
described
and
on
Flight
conditions
including:
10.
is to provide
data
summarizes
7.
document
usable
stability
those
page
this
readily
Included
aircraft's
A
of
axis
the
completely
etc.
A covers
nondimensional
the
I-1.
system
aircraft
The
axis
and
self-consistent
system
systems,
dimensional
transformations
equations
used
is
symbols
stability
for
of motion
the
and
the
X
I
g
o
i
i
<_
o_
_ _
_
_
_o_
o_ _ _o _ _
_
aa
_''_'"
.
_.
.
_
The
and
aircraft
uses.
were
In
considered
each
computed
case_
for
of
interest.
for
up
and
of
all
trimmed
Also,
wind
depending
by
stability
Where
motion
Handling
tion
with
are
given.
transfer
A
substantial
mnemonics
The
small
are
be
used
in
are
used
in
of those
shown,
and
the
While
qualities
complete
'_oest" data
accessible
for
would
to
some
the
for
also
given
are
of this
report
printout
over
definitions
the
is
of
given
HAS-on
was
picked
flight
Also,
the
axis
body
with
in the
the
in the
axis
system
"
system
or
is
'body"
of
systems
functions.
on
the
functions
body
equations
and
handling
quantities.
axis.
All
position.
acceleraThrust
characteristics.
form
of
computer
MIL-F-8785.
represent
majority
Although
A
are
functions
printout.
A.
report
The
in Appendix
results,
control
in Appendix
years.
based
clarification
motion
response
are
transfer
pilot's
along
test
effect
axis
plots
are
"rigid,
of
transfer
transfer
cruise)
words
in this
the
flight
(Further
defined
given
versions
with
engine
are
parameters
present
for
the
is presented
significant
stick-free
cover
the
along
parameters
coefficients
or
speeds,
configuration,
Descriptions
given
4)
developed
F.R.L.
a
any
qualities
past
are
by
sizes,
coefficients
data_
given
include
this
in conjunction
handling
given
used
fraction
values
portion
handling
always
The
plot.
A.)
has
the
(a z and
do not
case
stability
the
are
system
parameters
functions
approach
indicated
Appendix
systems
are
moment
data
with
a bobweight)
functions
is
to
nominal
and
a body-fixed
in
this
of
qualities
selected
flexible
aero
aligned
given
handling
coefficients.
each
for
functions
qualities
transfer
on
control
(as
Transfer
force
a power
range
(generally
aerodynamic
This
augmentation
a longitudinal
qualities
The
is
were
For
data 3 estimated
system
used
which
a wide
and
configuration
aerodynamic
"stability"
systems
functions
cases,
"flight"
span
conditions.
availability.
a body-fixed
and
of
of
and
indicated
axis
flight
tunnel
upon
"flexible,"
for
nominal
in most
a tabulation
on rigid
A
away
report
conditions
non-dimensional
presented.
with
transfer
flight
regimes
in this
a
presented
only
general
to
only
SAS-off
and
yield
here
could
SAS-on
parameters.
coverage
be
of
desirable,
author.
aircraft,
This
and
each
the
aircraft
major
is why
also
criterion
only
why,
including
3
used
isolated
as those
only
people
was
the
"latest"
that
and
the
data
be
flight
conditions
are
more
intimately
familiar
with each particular aircraft will recognize, the data presented may represent an early estimate in the design process and perhaps the "nominal configuration" is one which never left the drawing board. The data have been reviewed
and, although not all those presented indicate unquestionable trends, those
data known to be based on only early "guesstimates" or showing unreasonable
trends have been deleted.
In somecases data were estimated by the author.
As to how well the data can be expected to match the flying aircraft,
it is
assumedthat those for whomthis document is intended knowwell the difficulties
of obtaining derivatives
from flight
to insure reliable translation,
from their source documents.
test data.
interpretation,
The manufacturers of the aircraft
Every attempt has been made
and transcription
of the data
described herein can not be held account-
able for the information presented, nor would they be bound to concur in any
conclusions with respect to their aircraft which might be derived from its use.
4
-33A
ACXSXOmm
"The NT-33A
variable
stability
airplane
(Serial
No. 51-4120)
is an extensively
modified
T-33 jet trainer.
The elevator,
aileron
and rudder
controls
in the front cockpit
are disconnected
from their respective
control
surfaces
and have been connected
to separate
servomechanisms
that make up an 'artificial
feel'
system.
In addition,
the elevator,
aileron
and rudder
control
surfaces
have been connected
to individual
servos
which can be
driven
by a number
of different
inputs.
These
servos
receive
their
electrical
inputs
from the artificial
commands,
position
or force),
attitude
and
feel system
(pilot's
rate gyros,
accelero-
meters,
dynamic
pressure,
_ vane and _ probe.
through
a response-feedback
system,
allows
the
derivatives
to be augmented
to the extent
that
This arrangement,
normal
T-33
the handling
qualities
of many existing
airplanes,
future
airplanes
or hypothetical
research
configurations,
can be simulated.
The original
T-33 nose section
has been replaced
with the larger
nose of an
F-94 to provide
the volume
required
for the electronic
components
of the response-feedback
system
and the recording
equipment."*
Transfer
thrust
trol
functions
although
crossfeed
and
Aerodynamic
longitudinal
andMach
the
NT-33A
feedback
data,
data
number
are
for
given
also
has
only
other
the
primary
control
surfaces
surfaces
and
and
engine
a range
of
con-
combinations.
for
the
the
high
derivatives
for
most
lift
from
part,
was
taken
configuration
NACA-RM-7116.
6
from
was
AFFDL-TR-70-71.
obtained
from
LAL
However,
1 27
0
.r-I
4_
.r-I
0
or-I
0
I1)
m
(1)
0
r-4
CD
I::"
0
•_
0
.r_
P-I
0
,.-I
•r_
_/_
t-.-.1
q_
bid
.,rl
,-4
I
I
0
0
0
0
0
0
q
0
Ca
I
o
O
.r_
4_
E_
,
_d
o
c)
©
4_
I
¢-
i
f-!
!
@
r/l
.r-I
-,-4
I:I
O
,'d
O
0
.,,-I
.4,}
d
o
Q
0
o
(\J
4_
c_
i
(_
4_
q_
i
O
Ckl
-P
0
¢..}
f2_
•,-I
,-I
q_
b4]
_lC4
_
_)
cq
b.O
4 4
cH
I
,,--,i
,-,8_8oo
_
_
t_
CO
0
_
_
0.1
tk.l
r"-t
C}
-P
b[
[- 4
II
tl
p_
._
0
CL,
0
_£r
-J
II
II
\D
,--I
_
_
0
0
c_
_.
_
kC_
C'_
0
0
[_
C_d
0
0
_
O
0
0
0
Od
II
II
II
r4
0
%
42
II
0
bD
_h
'_d
_
q_
r4
Ill
0
E_
,rl
#
4_
_
• Od
_--7
4-_
c+d
_:
f
,,,4
.r-4
[::
O
I-I
_
H
H
Lr'_
>
r-I
_
_
@
II
II
htg
N
_
N
N
.JO
__o
4._
d_
°"
t_
qJ
O
!
I-'4
b
I
N
II
I!
II
.--i
8
NT-33A
PITCH
AXIS
Variable
Variable
Feel
Stability
Input
Input
I
FST(Ib)
_..026
ROLL
AXIS
s z +.89s
_]ST(in) ----]
+ 22.5
_.3
-I0
Variable
Feel
Input
Be(rod)
Variable
Stability
Input
FLAT (ib)
I
sT
YAW
_._
OST _,n
I0
_a(rad)
AXIS
Variable
Variable
Feel
Input
Stability
Input
I
FpED(Ib)_
78
Feel
to
system
I_PED(in) = I _._
2.34
parameter
values
the "Front
Seat
Engage"
Figure
11-3.
NT-33A
9
shown
mode
Control
_.
correspond
(normal
System
NT-33)
8r(rad)
TABLE
Power_oach
11-I
Non-Dimensional
h
=
sea
level
VTo
=
228
ft/sec
oo
=
2.2 °
Longitudinal
Stability
=
Derivatives
139 kt
Lateral-Directional
( Stability
Axis )
cL
=
.813
cy0 = -.72/r
cD
=
.139
Cn_
=
CLm
=
5.22/rad
C_0
=
--.127/rad
CD_
=
.94/rad
C_p
=
-.O7/rad
%
=
--.401/rad
C_p
=
-.045/rad
-mo/raa
C_r
=
.20/rad
Cnr
=
--.16/rad
--.O09/rad
Cmq :
:
.049/rad
CL5e
=
.34/rad
Cn5 a
=
Cm6e
=
-.89/rad
C_5 a
=
.14/rad
CYSr
=
.17/rad
Cnsr
=
-.O73/rad
C_5 r
=
-.OO2/rad
10
'
14
w
12
B
10
n
....
------
SL
20,000
ft
40,O00ft
Clo
(deg)
8
D
6
D
4-
\
Z-
0o
11
NT-33A
13700 Ib
.263
Rigid
0
LO
rrJ
O
oJ
0
0
I
,:_
_Q
Od
I
-0
I
I
I
1.0
0
(%1
0
-O.
_C)
0
o.
, 0
F-r'-
z_
(..)
.4-W_-
W.--
f..) 0_
x
O0
O0
O0
I.LJ w.
j.-
_Jc_o
o.
000J_
!
,
:l
II
(.)
I
I
I
I
I
0
o_
0
--
LO
o_
-0
0
12
-
LO
0
0
m
6CL a
(red
NT-33A
13700 Ib
!
I
-I )
4
4-
Rigid
!
!
!
SL
.....
20,O00ft
-------- 40,000 ft
2-
0
0
I
.4
I
.2
I
.6
I
.8
.6
.8
Mach
1.2
CDa
(rad "l)
I
I
.8
l
I
I
l
%
.4
0
0
.2
,4
Mach
13
0
0
Mach
.2
I
.4
I
(_
I
.6
.8
I
I
/
(rad -i)
-.8
.....
--"--
-1.2
0
0
SL
20,O00ft
40,O00ft
NT-33A
13700 Ib
.263_
Rigid
Mach
• .2
.4
.6
_
.8
Cm&
Cmd,
-4
Cmq
(rod")
-8
-12
_Cmq
-16
14
NT-33A
13700 Ib
.263 F.,"
1.0
CL
Rigid
M
"21
0
|
2
_
_
3
6
.4 Mach
8
4
i
.6
-I.0
SL
20,O00ft
40,O00ft
.....
------.3CD M
I
0
0
.2
.4
.6
.8
.6
.8
Mach
Moch
0
.2
.4
0
Crn M
-.2
-.4
15
.4
CL8 e
(rod "l )
NT-33A
.2
Rigid
O0
I
.2
I
.4
I
.6
I
.8
.6
I
.8
I
Mach
Moch
0o
.2
I
.4
I
-.4
Cm_ e
(rod -j )
-.8
-I.2'
1 _;
Mach
0
0
.2
.4
.6
.8
I
I
I
1
Cy_
(rad-i)
-.4
--
SL
NT-33A
.....
20,O00ft
13700
-------
40,O00ft
Stability
Rigid
.2
Cn/_
(rad -i )
0
I
I
.2
.4
I
Mach
f.®." /
-.2
17
.6
I
.8
Ib
Axes
Mach
0
0
.2
I
.4
t
.....
--- "-"-
SL
20,O00ft
40,000
.6
l
.8
-.2
-.4
c.tp
(rod "I)
m6
Boa
ft
NT-S3A
137001b
Stability
Rigid
.O4
0
Cnp
(rod "l)
-.04
-,08
_4r
_,f
Axis
•
-------
SL
20,000
ft
40,O00ft
NT-33A
13700 Ib
Stability
Axis
Rigid
.3-
C._r_
Cn r
.2
(rad "l)
--
\',,
\.
%%%
_
" """
C._r
0
I
I
I
I
.2
.4
.6
.8
Mach
'.1
Cn
t9
r
.2O
.16
C}s a
(rad "l )
.12
0
0
'
SL
.....
20,000
ft
40,O00ft
I
.2
I
.4
NT-33A
13700 Ib
Stability
Rigid
I
.6
I
.8
.6
.8
Axis
Mach
.01
Mach
.2
.4.
0
Cn8 o
(rod -j )
-.01
-.02
¢
So is sum of both right and left
aileron deflections
2O
Cy_ r
(rod "l )
I
.?_
O0
I
.4
I
.6
I
8
.6
I
.8
I
Mach
Mach
0
.2
I
0
.4
I
-.04
Cn8
r
(rad"I)
-.08
,
------ _m
*==
NT-33A
13700 Ib
Stability
Axis
Rigid
SL
?_O,O00ft
40,O00ft
.04
C,_sr
(rad "l )
.02
I _
0
0
i
.2
.4
Mach
21
I
I
.6
.8
_e
<1
,0
r,,l
I'-
o
•
o_
p
• _
_
¢'_
¢_J
+,PI
i_
_
•
_r+
..4
_
-_ "
_
_
I<'I
0j
•
.4
1%1
_"41"
,_
•
<_
.
•
C._
0
o
1%1
0
o
P_I
II
Io
0
ell
3
_
. _
o
eg
_
I_
_+ o
, r.-
_
_; "
17
_o
o
_
,-I
__ ' _
_"
_
+
o _o t+_
o
_%j
o_
(_;
_l"
o
0_
_- _+ _ o
_• _ • P". .•
o
+ ,
_• ®•
j
o
;
+
t
II
I<"X
I
GO
22
0
_
o
o
o
_
0
o
•
•
O
•
I
0
•
0
I"
*
O
,Ti
_
I"
o"
I"
"
T
•
N
l,O
;
=
I
_,
o•
•
I
rJ_
H
_.
•4"
,,..4
I_.
cO
N
I_.
,0
u_
03
bl_
LIJ
0
N
0
4
_
o
•
0
i
o
I"
o
0
•
I=I
0
0
_
o
•
I
"
_
I_
0
o
u
I"
0
I"
0
_
_0
I"
•
_
_.i
_
_
",I"
IJ"
o
0
I
"
C)
o
ooo
.i.)
I
It)
I_•
0
•
,-4
o
I
I
0
0
0
i
"
I
H
I
-ff'l
0
_
•
I
I
I
_
I
_
oo o
I
_
"
"
[/]
A
-,-I
_I"
I_
._t
_
0
_I
_
0
_
I
I
lJu
i",4
U
0
L(_
0
I
._u
I_
--
¢_1
0
I
"
w
g
o
0
0
•
_
I
0
,,1"
_0
I_-
n,_
r'm
_
0
_0
•
,_D
*
0
•
I
I
#q
v
......
_
•
_
_r
g)
0
0
I
o
,0
N
..J
_
-1"
r'J
•
-.1O
O
•
I
ur_
,-_
•
I
O
O
_
"-_
•
•
0_
•
I
,o
O
O
•
0
0
I'
I
u'_
'd"
"-_
0
0
O_
0
I
uJ
0
$
•
•
!
_0
._
-tO
_
N
•
_0
r¢l
,-4
,4)
od
c_
_
_
r_I
•
0
0
0
co
0
•
_
C_
(o
0
0
|
l
_
0
"
0
I
l
I"
23
I*
.,t
_
_
_
"
0'
h-
"-'
"
a
N
0
0
I
C_
•
0
'
O
Om
,4
N
_o
er,
OO¢_
•
,,
•
,0..0
e¢_
_oe
I
I
fel
0
.-,_ N
f¢, C_ 0
•
•
I
I
I
v
O
_.
u_
<D _ rr_
or.
_1"
OO
•
e(O
_o
00000_
i_
i°N_
)N
_
I
°,-_
I
ww
O'.4"
O
. O
eft/
Pr'i
e O- u_
O0"OO
._r .-4
•
I
.N
f_-
co
_JO0
_T__.
i
•
f,.
oo
00
.,--,i
_0 N f_
OO
_phi
._o
I
I
I
ee
I
_0
.o-.I"
'4"
•
•
I
e rrl
..-4c)
I_ _'$
•
•
ou
I"
•
I
u
njf,_
•
I
0
OOU_
•
fMf_
,.4P_
1
•
I
w_
_o_
•
_ule_
!
• ",lr 0
I
f.r. _r" ¢0
e ...4 _0
•
e_-I
,
e,_
IN
..I-,-4
I
•
I
•
!
I
r_
oe
O
_0_
_)
.--, lir_ u'_
"
"'.1"0
i
I
I
•
I
I
I
_-_o
_0_
_ODO_
eO_
eJe_
I
_- • •
I
v
Z
24
e..-,
v
O
IDur_
O
_O
f..
•
•
e_.a
oO
•
0.
I
II
v
_D
_O
r_- i_-
o
f_" N
_
_0
_O
OO_
OO
,4"
_,
OO
O
O
OO_'_
• ,
!
._
I
v
"
|
ra-
O
(Du%
OO
OO
N
,._ 4Om-,_
00
•
00.-*
•
o_
.,too
,
CI_ .N
•
!
_w
.0
!
UJ (N _"
_0
•
I
I
,.T
I
r.J _
_4
{_
. 0D
.
I'I _n
.-:r
I
I
II
1.1%
!
OO
OO.y
L)
•
• !
ueot
I
u,%
_0U%
•
!
•
!
H
E4
----
._
I
I
0
I
erl kr% .0- .-.i
-P
(,9
LrA
.I"
v) r-•
_o_
oo._,r.2
.Oe,J
•
_'
_
.0,4"
(D i'-
•
o.o_
H
CH
O9
•r-I
r.9
•
•
I
I
u,._"
I
re% ,,T
our
_
0
•
•
• I
I
_o_
oo
0
•
I
I
I
_o
uJ
-_ ,o u.
".T
0
co
r-.(%1
•
!
I
-,T '_
"
°
I
,_er_N
UJ 0"4"
p-_p_
•
0
°r_,
°
I
I
I
|
0",
eel c0
_r_
r_.o
Oo
oo
O
_% ('4
(DO_T
(DO
•
•
•
I
,,-.4
I
,.r> p%
I"
,.-IN
p.
Z_
Z
2_
Z
I"
D
O
o
o
_
_
I
.-,
÷
v
I_
0
ur_
0
•
0
P_
(%1
_
•
_
_
F.d
0
0
I•
o
t'_
•
0
0
m
_.I
Q
0
co
N
uJ
x
÷
,,-4
p,,
o
m
_
O
O
I
N
•
*
_t
I_'
o_
(%I
eel
•
I_
_
_0
L¢_
i
I
I
'-4
-J
,m
o
cN
0I_
i*
26
f_.
II
*
,-_
•
¢_1
O
r--
,,1"
c0
_0
r--
r_
_
O
(_
•
I
O
O
u'_
co
_
I-I
E_
_Ir
LI_
I
I
I'-•
I
_
I
,-4
•
O
¢)
•
I
I
_
u_
_0
_I
I
I
_
O
_
,,
I
I
..-4
•
,_)
_I_
,,I"
O
",I"
"-_
el
•
"-I"
O
I
Q0
L_
O"
00
,._
.-4
O
0
_
_
O0
_e
o•
co
•
(7'
H
O
I--I
I_0 _-_
O
C_
0
O
c_
•
J
0
C_
,0
0
_
•
'-'4
C'q
I
".0
O
-_I
0
,,I"
_
•
0
_
00
•
I
_
#
o
_
r
I
!
0
÷
oO
_--
I.--I
H
H
,--1
o
cq
*
•
_
_
_
o
•
o
0
0
_
_
0
,--4
O
-I"
o
o
o
r_
I
Co
O
c_
M
0
o
_
•
0
t'_
0
0
I-4
_
_
_
I
I
I
I
I
I
I
I
I
I
I
I
+
I
i.-1
N
0
•
÷
o
I
27
I
I
.
*
v
o
eo
r_
o_n
,_',D
O
e'% '4,0
P"
• P.- O
er_ .%
•-._O ,_D e4
•
N
•
e,.._
¢00"
O0,
0
O
0"_0
"_0
C,
•
•
o,,-i
"
•
• 00
ec}
•
!
P..
c)
o_r_
e.,4 P,-
erl
aO
00,'-4
Nrr_o
O
ON
,0
oO4
•
el1_
I
I
,-_0_
r_ O, f,_
• 00'
U_
",,tOO
•
t_40
era4
0
•
u%
,O
eq _',
O,
0_'_
,0_
•4"0
•
el%J
I
_._
0
•D
Ou_
NU_
N
er_ ,O
O
0,=4
P"
,4" O
,0
0_
,.._ ,d"
,_)
0_0_
,00,0
•-* 0
"'40
,
,,-.4
_0
,0,0
.,.., e-4
.-4 ,
0,...4
•
I
i°
0
_0
O0
,.4 ,.4
_nwD_
I_0
,-J ,_ ,0 ,.-4
00"0
•
•
• _.J ,-4
WD
_0_
,,
_0_
_0
,0_
(,q
•
Mlo,e
•
I
,_
I_
¢_
• ,-.4
_/"
,('1
r.-
I
¢;.i
o,_r
,,,,.If,,,
,0
• eW p,¢%10',0
•
I
u
U,_U
I
!
t,_
=ju
,"l CM 0
h0
,,..4
•
ee%;
,,,--4
0
•
r_l r-.
e(,_
_0
N
• ,....4
_
•
.-e
t
!
H
"
0
"0
ee._
_o_.
•
_O_U_
_0
f_
W_ ¢13 _
e,,-4
_r_ _"_ 0
_.
O_
'4" •
J_
I
!
_0
_OQ_
•
,.,4_
f%l ,...4
•
ep,.
0"_"
0_0_
eo_
•O
•
•
I!
I
_N
._
_
_w_wv
_v
_Z
5
28
,I
o_
O
0"%U'_ ,n
N_
'4",O
o_o_
_ID
+0
o4 ,-+ _)
r-e (,n (_t
I
_P 0
..-I
e
I
I
I
I
_
0
I
I
!
4,
4"
o°
r-.
o41--.
t.%tP.....4
O
ON
O0
"O
•
, o
_o_
,N
•
•
I
I
I
I
a) u,_
oO
, ,.-4
r-- O
o40_
--4
I
I
÷
o
o_
_o
0
,0,0
"0
0
O0
N
'0 _
•
,
I
I
CO
L_ m'J I_
_o_
_O_O
• o
_O_
•
,O,,,
I
I
i"
I
T
4-
B
o
•
o
u%m-
cO
,0_,0
oo
_o_
..-+(_ 0-% •
oo(oo
_
•
• wI"
.0+-_
_o_
I
+
I
OO_
I
I
o_._
• O
I
I
I'
N
-,t
o
c,_ u,%
O0
ic,_
I
_ , ,-+
• u'%
,
4" ..-1 .--.
I
,...+ 0
I
i°
c_
,,t
+
4._
oo_
_0_
4"-4
•
<_
H
I
,0
.;i-f_. ,
N
._
•
_
_O_
,O
• o
,,o_
.,-#
•
•
•
_0_
I
C)
I
I
I
I
!
+
_o
N
tON
_j
_
0_ u% .o
e4_o
N
.-+ 00_
I
I
I
I
÷
_o
¢J_
O0
•
0
,04
('4
I"
ON_@
"
_o
, O _0,0
I
•
I
o_g
I
I
,O,_,
I,
_2_
_ww
z_
0
_.) ,o4
I
I
_o
_O
-1" -4" N
7
Z
I
÷
CO
O
u_
_
O
-J
u _,
_t
•
cO
e_
N
_
_
I
I
•
O
_
--
-_
t_
--
_
I__
_
u_
O
_
**,I
_
*
a0
_I
_
u_
_t
,0
-,
--
U'_
O"
_
_
_
41
--_
I
v"
I_-
p..
O
u_
I_
0
_r_
•
o
_
O
0
_
P_
I
I
um
*
o
r_ *
O
..t•
O
_0
0_
I
I
c_
•
_
O
+
_
_
•
0_
_O
O
O
O
O
_
_
_ •
co
_
o
•
•
4
(]Q
_O
O
_1
_
_
®
a0
_
•
_
r_
0
o
p
0_
e_I
_
_
_
_1
•
_
O
_l
!
v
_0
r_
I-I
+
<_
0
_
E_
u_
o
r'_
.0
_. _
-,t"
_
O
O
-
I_
•
•
I
"_
*
0_
I
-.1"
,_
t_-
O
O"
O
*
_
O
-
_
o
_
o
o
_
t'--
...0
o
_
•
,-,I
_0
•
O
_
_
•
H
*
+
@
!
÷
A
I
I
.-_
J
0
L+r',
•
I
,_
L_
I
•
c_
,.,.,+
_
•
0
('%1
P'--
,'_
u",
+
•
0
_
.-4
_,+
I%J
I
t'%l
,_
_
l_
•
+
LU
_-
_
_
_
--
3O
<++._
_,
<'%1
,-,+ ,
r,,.,l
Or,
"_
I
_j
._
NT-33A
Hall,
DATA
SOURCES
G. Warren,
and Ronald
W. Huber,
System
Description
Performance
Data for the USAF/CAL
Variable
Stability
Airplane,
Air Force Flight' D_nsmics
Laboratory
Rept.
AFFDL
Tests
TR-70-71,
Aug.
1970
of a I/5 Scale Wind
Lockheed
Aerodynamics
Cleary,
of
Joseph
a Model
Results,
Statler,
W., and
Pursuit
C.,
et
Tunnel
Model of the TP-80C
Trainer,
Laboratory
Rept. No. LAL 127, Jan.
Lyle J.
Airplane
NACA-RM-7116,
Irving
and
T-33
No.
al,
Gray, High Speed
and Correlation
.Jan. 21,
The
23,
1948
Wind-Tunnel
Tests
with Flight-Test
1948
Development
and
Evaluation
of
the
CAL/Air
Force Dyuamic
Wind Tunnel
Testing
System_
Part l-Description
and Dynamic
Tests Of an F-80 Model,
A_'_'DL-TR-66-153,
Feb.
Flight
1967
Manual_
USAF
Series
T-33A
Aircraft,
31
T.
O.
IT-33A-I.
SECTION
F-IO4A
32
III
F- 104A
The
fighter
a full
F-IO4A
is a
powered
by
span
boundary
and
are
without
fully
The
is
edge
flap.
system.
while
A bobweight
is used
source
with
be
at
the
of
data
the
shown
yaw
LR
have
by
superiority
here.
wing
has
a blowing-type
and
yaw
Pitch
is a
longitudinal
The
conventional
roll_
control
in the
pilot's
was
flaps
Pitch_
is not
air
afterburner.
is provided
stabilizer.
irreversible
supersonic
edge
Control
effect
to
engine
Trailing
their
assumed
primary
lightweight_
turbojet
all-movable
however
boost.
position
from
an
place_
single
control
and
incorporated_
trols
a
leading
layer
rudder
single
BACKGROD'AID
ailerons
dampers
and
roll
cable-actuated
feel
system.
are
conrudder
Its
location.
10794.
Drag
information
was
obtained
LR-12873.
The
based
loading
on
nominal
actual
at
flight
configuration
weight
manual
and
used
balance
approach
here
is the
data.
speeds.
33
The
combat
PA
loading
configuration
for
the
F-]O4A
is a typical
o
.H
o
c)
,-t
\,-
.,-4
OJ
p_
o
o
•r-I
o
._
o
0
,r--I
%
ry_
o
4_
!o
rl
I
I
I
8
o
8
o
o
d
q
41
q
_1
i/]
o
o
r_)
I
o
°r--I
,--t
o
I
f---4
H
H
u/
-e-I
(1)
-rq
b_
.r-I
,-t
o
.,-I
-r-t
O
o
-,-I
ii
_3
.H
ii1
-r-t
.rt
o
._I
4_
._I
.r-I
0
,rl
Od
4_
c)
_-_
l_q
4_
0
111
0
o
"d
O
b.0
_
r-I
¢
:d
c_
4.>
¢+_
I
",
o
_
oJ
oJ
-p
4->
r_
rH
i
i
b.O b_
_
,--I
_h
cO
II
I1
,-I
o
o
_
_
o
_,
ksD
_
_o
_-_
0
P,
I'--I
U
II
II
rl
o o
_
4._
r--I
O
H
II
r.D
34
03
f_
Cb
4_
_
II
_
_
0
I-4
H
II
H
II
0
ID
wu
_0
r-i
c_
©
Z
m
o
I
&
!
H
_o
._
I
!q-
>°
II
rJ)._
iu
C-_
35
F-104A
PITCH
AXIS
8SsAs(rad)
G
57.3
FST(Ib)
8s(rad)
i
-20
3.2
32.2
-I0
8s(deg)
0
I0
Oz
B
F
B
az assumed
to be at pilot location
/in)
AXIS
ROLL
8aSAs(rad)
F LAT
--I
ST (Ib)
--i
I
I
2.7
_!
i
2,,4
5"_ _
8a (rod)
YAW AXIS
SpED(in)
7.35
57.3
FpED(Ib)
KDIR_
_ 8r(rad)
2.0
K°["/'Ib/in_
1.0
o,
0
I
I
.4
.8
Figure
111-3.
Mac h
F-IO4A
36
I
I
I
1.2
1.6
2.0
Control
System
Power
Approach
Non-Dimensional
Stability
h
=
sea
level
VTo
=
287
ft/sec
_o
=
2"3°
_s
=
--7.1°
Longitudinal
=
Derivatives
170 kt
Lateral-Directional
(Stability
CL
=
.735
Cyp
%
=
.263
CL=
=
3.44/tad
CDa
=
.45/rad
Cm_ = -.6_/ra_
Cma
=
Axis )
--I.6/rad
Cmq = ->.8/ra_
=
-1.17/rad
cn6 =
.5o/r_
C2p
=
--.175/tad
C_p
=
--.285/tad
Cnp
=
--.14/rad
C_r
=
.26_/rad
Cn r
=
--.7_/rad
Cg_s
=
.68/tad
Cnsa
=
Cm_s
=
--1.4g/rad
C£5a
=
37
.O0_2/rad
.039/rad
Cy_r =
.2OS/ra_
C_Sr
:
.045/rad
C_ r
=
--.16/rad
CY_d
=
• 0325/rad
CnSd
=
--.025/tad
Cg5 d
=
-.O044/rad
I
I
I
I
I
I
1
0
0
00_
G)
88
m_
o.
jO
_LLO
_0
O0
I
LL_D
I
0
--
I
I
_
I
OJ
--0
Q
I
_
q
I
0_1
0
0
0
0
000
Oooo
_000
_J
O0
Od
0
0
c_
O_
.l(
_o.
_J
O0
_D
/
_o.
q
!
to
!
_GO
!
--LD
I
0
!
I
0
0
I
0
I
I
0
0
u
f.j
Q
o
L
40
0
0
IE
q
C_J
.D
0q.
ooo_
I
N
I
0
0
I
JE
o
0
J::
o
co
O0
E)
q,..
q--
q_-"
"-00
ooo8
ooo
0
'Ill
I
'ili,
0
I
0
0
0
o.
o.
0
0
0J
I
!
_1"
I
I
i
I=ll
E
E
"o
L_
L.
41
E
r.j
"0
O
,,..
I
I
O0
i
0,1
!
-
I
I
I
N
--c_l
N.
I
I
0
0
I"
42
I
Iv)
I
_
I
--_
I
0
,--:
I
I"
_o
q
m
oJ
_
cl)
I
OO
OO
o o
__{D
0r)i_ ii
-)
II
I
i
!
II
i
OJ -I
_o.
o(cJ
_E
-- 0D
0D--
(.i{)
--
m'-o
o o
-_
_
u___,T
0J --
_I
I
oJ
00
I
,
O
O
I
O
O
I
i
I
m
u)
(w_
_I
i/1
!
"T3
O
_J
L)
43
L
Oa
i
O
I..
-...
I
o
q -®
B
Od
_o_
o
_-
j÷
|
,, __E.
--®
m
i
_m
I
m
|
I
t'
_/
, --
,t
i
/,
N
0
i
,
o._
u
O
I
i
--
o.
I
o.
m
u
O
8o(.
o
o_
II
1o
N
N.
O
O
I
,I
1
O
o.
O
1
q
I
1
_.
I
_.
N
T
'"o
O
O
I
I
I
!
I"
!
O
O
L
V
44
q
N
°_
3'(
I
_--.-__
_o--
®
T_
_..-
O0
,._
I
t,u
0
q-rU
#
/I
•
I
000
0000
0000
____
'I II,
I
I
o
I
I
I
,
I
I
I
I
I"
I°
I
0
I
!
¢j
45
a')
0
I
_
I
o
_
I
Q.-L-O
_.)
_
I
I
0
0
o
!
0lb.
I
I
I
o.
q
o
._ILO
i
I
I
!
J
|
i
#
/
,¢.
_C_J
Od
--o
I
I
to
=E
u¢O
<_
.Q
i
>,
,,ore
_oo.-"_.'2
-:_,oo,
LL __U')
I
_'i_
I
I
I
•"-:
o
0
I
0
I
!
lb.
_
(..)
I
0
!
I
m
g
|
w0
0
0
lb.
46
o
I,.
I
I
(30
I
o.
I
i
I
i
!
I
Q
T
F
c_
tC_
t-
I
Q
t--
.C_o_0
I,.
4--
t-
O0
O0
CD
D
0
.Q
Qo
_I if)if)
¢/)re)if)
_
I
II
/
!
I !
II
qcD
I,
_
_'_
_gr_
I
/
#
0
--o
e'U
.£:
u
o
o_
x
c_
m
I
_O
o
I
_.
o
t,_
C.)
i
0
I
I
_0
0
0
o.
O.
o.....
0
!
O
I.
47
o.
oJ
_m.
_0
oJ
_o.
r(J
0
=S
--aO
_J
I
I
OJ
--_
I
I
I
l
0
0
,
,"
O.
o.
,.. -;>"
r_
0
,.-
c_o "o
c
0
48
_<
0
0
0
÷
÷
d
C,
P,-,
•
0
0
O,
r_
O,
.,IC)
e
•
C,
0
_
•
d
_
"
•
0
q_
I-I
u_
I-I
OX
o
.-.,
0
,dO
cO
o
_
ol
0
o
o
-_
?
?
?
•_
o
o
o
I
I
I
I
I
I
o
lu
q_
H
H
O'x
•,-.I
_
C,
u',
I
"
"
"
•
_
H
IC_
r-,.o
e_
,_.-_
00
,,t_
0_
,_
O_
_'_
I_
_
t__,-4
_
_l
°
0
,-a
IJ
0
°
"
0
°
0
O"
,_1
'
,-a
O"
,0
"
o:
0
0
0
0
?
?
0
0
0
?
?
?
o
,
I
0
0
-_
!
,
ut_
u,,,,
LL..
"t"
I
_
_
fD
0
:>
:>
::_
_:
49
,
_
O_
G
G
0
p...
uh
_,
!
C
,I
I
LF
•
I
I"
I'.-
I
I
I
•
,t
I
•
c
l
•
I•
•
0
"
I
l"
I"
0
I"
I"
_
I'-
_
_._
O0
0
•
•4"
.-4
O TM
•
O
•
I
O
•
l
O
C)
"
0
"
•
O
_
I
0
e
0
•
I
f"
,_"
0
0
0
•
I
I
I'
P_
""
,lJ
I_
_
"
_
e
_"-_
_
0
_
•
i
-
I'_i
Oe
"0
,
cq
_
I'IJ"
_-_
0
0
I
'
0
_
T
fll
N
t._
--
o
o
•
I
•
o
0
o
•
"
-I'_
I
o
o
,
I
o
o
0
"
I
•
_
I
t"
•
_
I_-
I_I
O_
4)
Im
CO
-_
_
_-
_
m
o
m
_
CO
O
O
O
O
'
O
O
•
"
o
7
_
•
•
I
o
I
•
"
7
'
I
I'
l_
IAJ
.-_
0
CO
"
",t
o
O
•
-_
-,I"
_
gJ
I
o
0
,0
"
o
"
I_-
-
_
_
_
P'-
O
'_ "'
|
,_D
u
"
"
O
+
(D
o
u" O0
..4
,-4
`0OO
• 0
4"
*_0"
_.- c, 1
4)
_o _ .
• f_- ,0
`00
cO
OH
*
I•
T
• t'4
,0000
.-'_0
*
*
. i',-¢X)
I
*
*u'_
I
+
-Z
._S_
0
0`,
_o
4.
,_
*f_4.
OOO'4
•
e,,I
_
o
o
_
f*-- _7
_0_
_000
,,-,4 ¢_1 0
OOtkl
*
,
I
!
_
I
1
4-
o
`0
4.o
Or,
* ,.-_ oo
eOOt_
j,
*0
I*
o_o
,.-4
7
• _J
* (;"
!
O"
I
v"
_
u,% •0",,-.4
u,% o_ co i--
•
,....4
_0
oo
*_'0
o
t_.
,
.T 0
_o
oo
I
0
?
_
I
ooo
,-_
I
I
I
b-
o
,1"_ o
[--!
r.)
,o
*4"0,,0
4",-,
o
`0
,_u,%
_o_
0,4-,-4,0
C_--_
*0
I
u_
0`0o i'xl `0
-.-* o
o
_o_
I
•
_
eel
,,I3
I
I
H
0
•
`0
oo
-7,
_
*-40
.4- _
`0
`0
I
r,-O
II
•
i•
•0"I
4.
_ _
H
_o
r-(xJ .-_ u-%
0,40,
_oo
_,o
_
`0
_o
t--
._,o
.e4_
0-0<9O
u% -4" 43
e4*_
I
•0
e_
• ,-4 ,..*
i
I
4.
H
pll
q-_
O
_
_
m
, 4. 00 t-- i_-
oo_ oo
,
_o_o
• _0 ,0
•
,--,* 0 0 CO
-,tO
•,'-_
I
*
I
I%JO
•
`0
•¢_1
I
P.,-o
•
,,._
!
!
÷
*
!
•
m-_e4
• q" ..r •
co ._
.4
f_l
I
*OOi
,---I
m- _
_
rn
I
•O
`0
t--
•,-_
I
I
r.0_ co _-_ _
,-4
u3_l
04
I
'4"
•
*
0",,1",;.,'
r'-- 0 _
.,--*4"
4.
•
•
|
r_l
• Un `0
e4
• -,t
I
r.-- cu
U'_
I
,..._ ¢xl
A_w
u_ ,'-J
A.
°W<_WW
Z
51
,-i
._ o _ _, "_.
.._
0
0
,4-
?
-_ _._ _
OCs
4"
-o_
L," •
-'4"
I
!
I
I I."
"-¢G
OC_C
C_C_
_-_0
I
e4w
f'--O
e_
ado
_
,
..4"
I
I
•
I
I
I
.4 .-_
I
o
1:o
•
ku<t
,,I •
_
• CJ
, _'1
Go
o
cr_ .4-
,IF,
:-4
• e'_
•
I"
•
I
I
v
4_
r_
4I
I
4"
LU an_
_o_
00_
O0
.-e
CC
,L-_
e4 ut% (7.
._,
N
I_"
u%
• ,4" •
moo
""i"
•
I
w_
o
4"
II
_o
_o_
_w_
o_
u%
I
,I-
'4".00
• 4
.
000_
,7
I
#
o
u_o
tU
H
_t 00
_gG_
O_
o"
r_
_'% r'% u-_ 0
o_
,.-i
4_uI
•
_
,,0 ,_C O"
.to
._
• I
I
I
r_
u
u_
OO
r,lL_
_u o
co o
R
_o-
um
l_ ....
_,_ _0
.
c2 ._
._
•
I
u
,-4
u_
_.-
0
i'd
I
I
I
•
•
_ID 0
_o_o
00"_
•
T
I
I
(9
?
m-O"
.U"
•
I
..
•
I
I
t
•
I
•
•
I
I
•
°
I
4
u.J o
_
-_ -r -r
O_
"_
.,T _rl ',T
_,'_
i
""
_J
_
I
Lu
uJ
\I--If
_
<_'_.
',,4 __
52
.%1 b'_ .
_o_
o
I
w o o- u'%
IN
,4
_o
t-- o ,._
,
-30
O0
u%
I
I
o
0
aO 0 u',
• • I
I
I
I
o
O
br_ co
mJr4
O
I'41"40
•
e,_ .-_ e,,ie,l
¢_ O
O 00
•
• ,_4
I
*
_000
°O
.-,t"
• l'4
I
•
rn,_0
e40
,-'_
O_'X*
• O
I
•
,_
oo
*
._
•
,_
•
e_
I
+
S
_o
4-I."%
_
,1"4"
_O_
O
O
_
,.-*(xJ O
•,I"O
O *%J
_o_
O hn o_ O
O.-_O
•
OO
.U"%
,,I" •
O_
I
i
I
• O
I
I
I
I
÷
,4
,4"a_
i,_....e
,o
,o .--.i
aD
OOO'I
o
.O
.O u'% '_
t-.- (..) c.)
.-4
•
I
O_"
• 0
.._
i
I
I
l
I
oo
o
,O ,O .-'
_'
O',4"
:xJ 0_ _n t-..
O c00_
L*'%
.-4
O
_OOO.
• O
!
|
OO,_D
I
I
I
!
I
O"
.4",4"-.1".0
ca I_- ,_ t'-
o
,0
_o
_O
_
_-- 0
_o
O
O
t-- O
C) (_
.
• (DO
',_
|
*
,
I
0" ,_'
I
H
w
O
u,%
t'.-
u'_o
_,,o
00.4
•
H
*
.
_o,
00
O
,,0 r4
_
"0"
I
.,.-4
,0
t-.i
_-
O
O
,'40
--'_
I
•
I
•
I
I
•
I
•
;_
o
.-.
a_
(x) cO
.-'I--40
_O_
.-_ O e4
•
•
,
*u%
|
!
.OOC
.-_O
•
•
*Q'
I
!
[*4
M
rJ
_
_
O
÷
J
_;.
o_
O-.tU_
•-4
*
._)
_o_.
,-4
_o
In
._
.OOO_
?.?,_
'N
I
I
t_
O
•
•
u_
,O
. a0 _r,
:W t'- _"_ e4
*_0
•
I
-e
,0 a0 u'% ,O
r,.-,a" ,.-Is%
• ,..4 .o
,-.,
_0_
4" C'4m*
C'4 ..-e_I"
o'_ _
exl
u-*
..-4
I
!
I
*
!
r,(D _. m.. a0
0" I-- _", a_
£%10
O O
_0
_.Jt_
._
O
U'_
e.4 o
0
4"
o,
,
I
.,-_I
I
...e
C3v_
#- u.
,_,%_
:D
z
_:)'_
7
53
Z
• .._ U-%
I
I
•
I
_e
4"
•
?
u] (x'_
_CZ
um _
COl::)
OO
"4"
.oe
_,
f'-
I
40"
_
(%!
_
U% _
C,
I
,I
I
I
0
I',.c.
•
•
I
• _,
.(
oo
I
I
,,9
I
_,_'
I"- Q
• c2
"4-
I -_"
I.I-C_ .L.,
,..-,
N l.I
eoo_
GOC
C, CJ*_
I
_
•
I
!
,L_
t"
I
LL, I'M _
•-, c('l4"
I
I_- oUm
I
<'_
•
•
I
-u'_
_b
._ _
I
o
I
_w
•,.t
_D
,o
I
o
LIJI"_i_..-.,
00
(f,O
0
r-I
i5 °
,'f,l
_• I
I
,,0_
H
I
..4r
I
4"
H
L0_
bfl
[/3
H
_
._
CQ
uu
e*
L_
._
•
,---¢
•
I
I
I
I
f
LU
I"11i',i
l.u I:o
_gN_
oo
_
4
U
"P_
0_
o,
I
I
I
0
T
bJ (.J nl l'_-
_g2;
.o i'--.
(_o
_i_ oa
.-i L] r,j
00
r,,l
•
I
O"
•
•
i
cu
iJJ_
._r c." co
? o r..lu'_.o_
,.& ,]
o_i
._ o l-.i ._,.
• • I
t
u_
pr_oo
,0 IP.
_"
"
uJ (:_ ,,o
LP {_Jco
'JJ 4" O
cq _
.-i ..-4
• I
w_
I
•
I
..L
_.?
•
I
I
,,t
b-
_-u 4"
,.-.¢
r_
_, .-'
o
_o.T I
I
54
i
o
o
Lr
,
o
I
I
D_
G
r_
r_
Io
O"
i'_
r_l
o
'
.-_
t_
C
_rq
0
N
.-4
Io
_
_
I
0
0
0
rQ
I
1
!
H
E-I
v
-.t
I
uJ
g.
H
0
I%t
_
¢'_
T"-
!
I
v
_
O
O
N
O
,,-.I
_C_
,.--I
,--4
I
I
O"
C
•4t
,'_
_
,.t-
u'_
o
_
_
I
I
I
I•
•
I_
¢_
G
I.,L
55
CO
,"4
U_
--
_
h"
N
--
0"
0
4
"--8
0
;--
CO
_
o
o
_
3
I
÷
I
"_
n_
oO
_0
0
0
_
_
0
0 •
0
0
o
0
3
_
_0
°3. j
I
I
n l
0
,_"
Q
P-
I
_"
N
I_-
,0
3
_
_
•
I
_
I
h
0
,0
d
u_
o
,-.
_
_.
.-I
N
¢_0
N"
I
__
0
_
,-4
I
56
0
0
_o
_a0
_... O
O
t_.-
_0
ao _-_ 0
.-e
OCY_O
•
•
*o
a00
e.-_
eO
•
_0_0
i°
I"
i°
+
0
_--q_
o0aD
*O
U'_O
,-40
0.-_
•
, er_
I
I
0
o_
,-., ID,
O'
,0
if-
oO
t_ O"
e_J
_0
I*
I
I
÷
0
0
0_0
.-4
*0
0_-4
OC_
•
I
I
.'-40
J_
_
O
e_
_0
I
I
÷
.4"
0
o
_
."4
_
O
_1" .4- r,.I
*o
•
t_u _,
t-- u',
0
co_O_.
_00 _
O'*O
,-'O
I
_0_
e_O
_0
*
!
I
I
o
o_
a0._
,.no
eO
_
®_o
o
_-oo
!
e_
0
I
•
_0_
,,I"0
*
•-e
• r_
I
I
I"
C_
_o
o
_
_0_
_.
_0
0"0
_0
-00
eO
•
_eee_
I
I
o
l
÷
o',
•,'l- ao ._
_0
O
_,
o0 o,
._
_o_
,,too
•
,,I"0
i0u_
u", O
•
t
i°
÷
0
jo
a0_O
0_0
0
0_
,0
ee_
I
I
jO
_.o.o _.
_
!
el%l
I
_0
oN_
._
I
I
•,:r o
•
O
O_
•
!
a_
_o_
,0_
*O
*N
I
I
I
!
I
o
w
Z
ZZ
57
Z
I
O
",t
÷
0
0
u'_ (I)
_o
O_NO0
0_0
0
•
•
O" -:r
CP.-_
.0
o0@@
0o,_
,_
l
.,f
,4" ¢_1 (xl
I
I
I
NO0
_0_
NO
e_
•
I
l
÷
Q,.
0
_.'nO
._
,
I_',r.,r,NI
0
,_)
•
0.--_
01',_
_o_
O_
wDO
,0
cOO
._
_0_
._
NI"@
I
,0,_0
_0_
!
I
I
I
.IF
o
_o_
0
u_100
..i .-I 0"0"
°0
;_0
00,_
00_
,0
I
o
0
IN. o,
00"0
..-.i,
!
0_,
,.-4
I
"0
oo
,h-
•
•
I
I
I
, Lira I_
er_ •
•
•-4 (_w i,g
I
.wD,O
I
NOe._
I
0
o
NWD(_
_0_
_
w0
•
0,0
• o
.-i 0
"_ 0
_.-I
•
I
I
i
•
(_ _
!
o
I
I
•
I
I
o-oo
0¢0
leo_
_0_
• 0
o0_
0".
•._ _
•
•
,ONe;
I
I
_o°
erlc}
. r,,I _t
O0
tn
I
lu_
I
_l"
_..
,_
r_
f,_ f, rl
• I
I
_3
0
I
°
I
,0 _ N r-
,00
e,,-_
I
I
!
I
.-_o
0
.0
;-.
°
•
,o o
I
I
!
I
•
I
(_.-i
i_.
0
o
!
.I.
I
rxl ,_D
•
•
I
I
o
_no
• ,?,
,I.
-_
b_K_
O_
°_
i'_irm
• I
!
_i" o
I
_r
ell
ON
_
_0 ('_ ,0 P,.-4
.000
0_
ii_
;',.O'
_J_
,gr:,
"i.
_
0
00
O-a
.(X;
.
I
I
I"
F.i_ .,l"(.J w0
r,_ ,,_ ,0 r'• 00_0
•
t{% 0
•
•
• I
I
_i
I
I
o
o_
,0,0"
I
.,._-
,l) ,-_ e,l
•
,-a_
!
!
g
w
O_
I.)
_N_
w
Z
58
_
,0
_N
ZZ
,,-a
I
I
P"
0
oom
_0___
•
o
._,
_
•
•
_
o
,_
,
_-
0,
-
-
e
,o
m
o_
r-
o
o0
.
.t
._
,
o
_,
•
_,
_,
I
,4
0
o
o,
•
o
_-
O"
_
•
N
_.
n,l
•
,-_
•
O,
0
•
,O
o
,,.4-
O"
0
•
t_
m
_
u_
o
,O
•
,o
U'_
,4"
-,1"
0
,0
•
u'_
0'_
,0
•
I_
0]
,0
_
0
o
_
_
_
0
e_
o
_.
_-
O
_
_
0
o
0
_q
I',-
0
I
_
o
_1
,-_
_
,_-
o
,.- o, _
.o 0, _
O
I_-
,,I-
N
.-_
" _
0"
..'_
o
3H
H
CH
O
D3
O3
_-
_
o
.
_.
0
Pq
I_
I'_
_
r-
_
_
O
.,- _
O_
o
0
_
_
_
_
_
_..
o
o
i_
,,,I_
I_,
O
O
I
_
_
I
n,i
NoD
r'-
r_-
_I
_
•
.
•
h.
I
_o
fM
I
ILl
UJ
U')
rf
_
v
%
0_.
j
O.
59
_
_
I
O
F- 104A
Stabi? [ty and Control
and
No. LR 10794,
12 Dec.
DATA
SOURCES
Handling
1955
Qualities_
Andrews,
William
H., and Herman
A.
bility
and Control
Derivatives
Low Aspect-Ratio
A!or.
'1959
Performance
t F-IO4D,
Flight
Manualt
F-IO4A
15 Dec. 1961
Unswept
Lockheed
and
Wing
Technica ! Manual t Flight
Controls
Aircraft,
T. O. 1F-104A-2-8,
and
a Tee-Tail,
No.
USAF
LR-12873,
Series
t USAF Series
15 Mar.
1960
6O
Lockheed
Rediess,
Flight-Determined
of a Supersonic
Airplane
Rept.
F-IO4B
F-IO4A,
NASA
Aircraft,
F-IO4A
Stawith a
Memo
I May
Rept.
2-2-59H,
1958
T.
and
O.
IF-IO4A-I,
F-I04C
SECTION
F-4C
61
IV
F-_C BAC_DROUND
The
F-4C
all-weather
is
an Air
air-to-air
ailerons
in
provides
longitudinal
is
Landing
speed
edge
(BLC).
flaps
deflection
in
layer
and
whose
Lateral
spoilers
through
by
fighter
combat.
stability
reduced
Boundary
on
control
a swept
control.
span
conjunction
control
is
is achieved
by
A
swept
edge
is automatically
and
inboard
plain
layer
control
boundary
induced
and
combination.
flaps
blowing-type
stabilator
stability
fin-rudder
leading
with
wing.
mission
Directional
a conventional
full
primary
when
full
flap
occurs.
Features
F-4B,
with
accomplished
is
tactical
missile
combination
control
trailing
Force
distinguishing
the
USAF
F-4C
from
its
with
flaps
Navy
counterpart,
the
are:
Data
•
Lack of drooped
higher
landing
•
Dual flight
controls
resulting
control
system
inertia.
•
Wing bumps
to house larger
in a slight
drag increase.
included
Special
here
emphasis
its
relative
been
addqd
ailerons
speeds.
was
obtained
is placed
complexity
to help
on the
when
illustrate
in
main
this
system.
resulting
MAC
control
other
Report
No.
system
because
aircraft.
Also,
in
increased
wheels
from
longitudinal
to
resulting
slightly
gear
primarily
compared
down
care
Figure
has
9842.
IV-4
been
taken
of
has
to
0
retain
e.g.,
s_m%
qB
The
roll
SAS
functions
and
of
the
PBF
(see
Stability
system
Fig.
is
it is
not
nomenclaure
used
by
the
manufacturer,
IV-5).
Augmentation
described
since
control
block
included
faded
out
diagrams
in lateral
with
the
position.
62
are
shown
directional
lateral
control
in Fig.
SAS
stick
IV-7.
on
The
transfer
out
of
neutral
_p
:d
q-i
O
O
,--I
@
O
(9
O
m
o
o
o
.,q
tl
o
.p
,m
(9
oO
i-.-]
[..,
<.9
-i
(i;,
rs]
q_
rH
qd
O
.rd
4g
.r_
O
C}
d_
®
I
I
b4)
r--I
0
0
o
I
0
Od
>
H
(b
.r4
68
E
,-I
r_
H
.,-I
0
4--
q.- r--
_1"
o .o
II
II
II
.Q
IU
64
F-4C
PITCH
AXIS
_SsAs (rad)
Feel System
I
_
18sT(in)_
.0569qePsF
FST(Ib__
_-_.0369s
+ .OI57qBPBF
2 +.208s
-*
Gearing
,:_1
_--
/
Actuator
8s(rad)
_
I _'-_I- _ -I°_'+'1
See Fig
and
for feel system
details
Bobweight
az ts---__)
ROLL
of
JtB= 39.3 ft
AXIS
8OsAs (rad)
Feel Spring
Gearing
/
_;T,,_ -I 2"961 =1_ i-_
Sa(rad)
Spoiler
-__
AR!
CLEAN
C38r
{-.46
= _-.69
8sp( ra d )
Gain
O ,/
PA
SAS OFF
SAS
ARI
__r
ON
I___--
<_rAm(rod)
_-:1_
YAW AXIS
8rARl(rad)
Feel Spring
.._j_'_
Gearing
3rsAs (rad)
\
\
/
Rudder
Flexure
/
SPED(i n) .___.J__
_"_°_'_- I _ I
_I _
I- _ - l""txl _--
K mR
G air
V<235KIAS
36.61b/in
-11.5deg/in
V>220KIAS
8.51b/in
-6.5deg/in
Figure
IV-3.
F-hC
65
Control
System
8r(rad)
See Fig
ID
C
O
°_
C
t_
.J_
C
E o
O
S_
t_
.c
_o __
..Q
¢)
_
"t_
C
O'_
O
Er0
c)
_O
0,;
v
t_
C
O
°_
,.i,.,.
O
D_
"-
LL
"_
{I)
,,i,.-.
._
c
,-4
©
.Q
O
O
.I
rn
C_
•-_
O
°--
_L
'NI--
w
I-4
ID
•-_
O
.t-
I--
o
"X-
66
.,.-4
.6
qB
-4C
q
/
I
4
O0
_----
35,00Oft
389:)4
....
55,00Oft
.289
I
8
I
12
I
1.6
1
2.0
L
1.2
1
1.6
I
2.0
Ib
Mach
J.I
m
1.0PBF
(ft z)
8
I
0
I
.4
I
.8
Mach
60k
40k
Viscous
h
"l//f/[_
(ft)
Viscous
20k
SLo"
Domper
b=_
I
.4
Damper Off
3.03 Ib/in/sec
I
On Stop
I
.8
I
1.2
I
1.6
I
2.0
Mach
Figure IV-5.
F-4C Feel System
6?
}arameters
Stop
N
I
I
I
!
,
_o.
i
-
I
00
rH
o
0
I_ :
©
N
//,,,/
..c
0
//7
:E
i °
_0.
/
I
000
H
oOOq
LO
-r-I
['!ll=
=111
l
o
I
_
I
_
I
_.
I
O4
X
I,I.
68
0
0
F-4C
PITCH
SAS
E} (rad/sec)
_1
.15s
_SsAs(rad)
-
ROLL
I
s+l
SAS
PG(rad/sec)
_I
P6 = P (Roll
rate
-.265
gyro
I
assumed
_--- 8asAs(rad)
aligned
with FRL)
Note." Roll GAS faded out with lateral control
out of neutral
YAW SAS
_I ,s
rG (radlsec)
_1
ay'
_rsAs (rad)
S+'5
(ftlsecz)
I
.0168
rG = r cos(-I.5
I--
°) +p sin (-I.5 °)
I
ay = ay + 9.9 _"-.391b
Yaw
rate
lateral
Figure
gyro
inclined
accelerometer
IV- 7.
F-4C
1.5° below
at
ES. 198.0and
Stability
69
FRL
and
W.L.23.0
Augmentation
TABLE
IV- I
F-_C
Power
A_roach
Non-Dimensional
8tability
h
=
sea
level
VTo
=
230
ft/sec
%
=
11.7°
_s
=
-9 .1°
Longitudinal
=
136
=
.915
CD
=
.242
CL_
:
CD_
=
Cm_
-
Cm&
-
Cmq
=
CL5 s
=
kt
Lateral-Directional
(Stability
CL
Derivatives
Axis )
Cy6
:
--.655/rad
Cnl3
:
.199/rad
2.8/rad
C26
=
-.156/rad
.555/rad
C£p
=
--.272/rad
.098/rad
Cnp
=
-.013/rad
.95/rad
C_r
=
.20_/rad
-2.0/rad
Cnr
=
-.320/rad
.24/rad
CYSa
=
--.0359/rad]
C-mss
=
--.322/tad
CD5 s
=
--.14/rad
Cnsa
=
--.O041/rad
I
= .o 7/r aj
CYSr
=
.124/rad
Cnsr
=
--.072/rad
C_5 r
=
--.O009/rad
70
Spoiler
Effects
Included
/
cM
_J
I
.Q
0
_1" IU
_J
/
I
d mm
r¢_ t%l
GO
-M"
0000
0000
0000
#
I
i
%
!
i
I
li!l!
Ii_Ii
"
k
I
I
I
I
I
I
/
/
oJ
/
/
)
I
0
(D
_D
L
-- oJ
1
I .... 1 ....._[
0,J
m
0
I
I
_
I
I
I
e,J
0
m
oJ
I
I
cO
I
I
og®
71
I
0
I
I
I
i
_1
I
0
0
?2
o
-
I
t_
I
oa
I
('U
,¢
0
I
_,. _0
¢1
/
-o
tim
73
I
_
ed
o
0
¢.)
o
IIII
0
0
I
I
_.
o
,-.
_T
I
c
_
I
I
0
a
o"
E_
"/4
_"
"U
E
E
o
T
o.
0J
!
|
I
l
_i:
e,l
0
N
N
-c,l
I
I
1
I
I
oJ
_.
rO
0J
--
0
I
I
OJ
--
I
0
J
I
•
0
-=
z
E
0
0
75
I
N
J"
I
I_
I'
.Q
U__U_
4__4--'4--
00o
O0
0°oq
I!'
I1' I
_J
I
I
I
0
I"
•J
_
E
U
o
7G
!
|"
I
0_
o._i
®
q_
1
m
o_
x
m'-T_ ._
, _
cO
0
0.__
(9
|
4-"
4.--
Oo
oO
II'
I
0
I
I
1
I
I
0
o
I
<..)
v
77
0
,..
(M
OJ
o.
OJ
GO
0
o._
O0 --
I
0
0
s"_
I
I
l
rO
CO
,_-
,.
Q.
(,_
I
OJ
,
q
I _
q
---
_
Q
0
0
78
,
0
_
q
!
o
i..
I
1
cO
q
!
!
K
._.
i,-
"_
0
I
1
I
I
i°
i °
|"
I
I ..10
o
79
Od
o
I
I
I
I
1
I
o
I
oT
¢0
U
>'
0
_..
q
q
q
I
q
O--
2
0
o
I
q
--
1
o
o.
/
_
0
I
o
.-.o.
_
I
"o
_
o
I-
8O
c
0
I
q
'
--
Od
®
0
OJ
..C
0
0
i
/
!
!
I
,!
II
0
\
%
%
-%_.
N
I
0
I
o
o.
5.
I
0
81
'-
c
rNI
_
•
Lr_
C
_
O"¸
"1"
2,_n°,
O'
¢_/
_
,£
_'_
_
_
_
u',
,-"
_
•
_r,
o"
n
a
i_
r-
O"
°
°
O
O,_
_
,_
I_-
_
r,-
o"
q
r-
o
O
,.0
•
__, _
•
•
_
"
¢_
!
v
o
• _
_
40
tH
i
_'_
o
o
_0
O
O
H
".0
*
,,,3
o
o_
¢_
0
_
_,
C'_
• _, o-
4,0
0_
_
_
_
o
o
_
I_
o
C_
_
,:
•
.._
°
I
0
o _
cO
,.1"
,.o
¢_
I"
O
•
.,0
r._
e,J
¢_
f'-n'l
•
CO
C_J
_
Pt_
_r_
÷
_: o
_
O
,.o
o_
r_l
_
,,: o.
I--
I_
O
o
_-
I
OJ
I
÷
D'0
F--I
•
co
_r_
cM
c_
o
•-_
_r_
r,J
•
_-_
_
_
0
WD
•
_
rq
I
I
I
+
r/l
O
I-.4
O
_
ff'_
+
I'M
J
0
0
°
l%
O"
0_
0_
nJ
0_
_
I"--
(_
o
,
(%1
i°
÷
I
_
_
>_
u
_
_
u
I
I
I
I
_I
_J
_I
82
_
I._
_
I•
_
ur,
C"
!
I
¢2
r
0t
•
C_
I
I
t_
I•
I
it,
I
.,_
v
•
I*
I
_xl
,,t
I
0
I
(
I
I
•
I
I
I
t
_,
cu
43
I
I
"_
_
I
I_
o_
•
!
I
I"
0
*-_
0
.
O
I"
0
r-}
*
I
t'I'
I"
I
•
I
•
-.1"
I
O
I"
0
O
I
I
I
I"
t_I_
r4
0
0n
I
0
e_
I
0
O
I°
_
P-
I"
0
t_
I°
I"
-,I
_0
,_
tol
o0 _
__
O
I'
I*
_
._
_
O
_
I*
I*
0, _
O
I"
_
o
O
I"
_
N
,.t
I
I"
_
I
0
I'
I
",I"
.-_
o
o_
._ ,._
F
0
_
_
_- o
C_
_
0
.-_
¢¢",
C_
_I_
0
I
I
r-i_
i_
_,
I
I
I"
I"
+
_._
ur_
o
.
rc_
..-.
0
_,
_- _
_
_:)
0
0
0
CO
,.I-
_
0
I
o
H
._
_
_
0
I
I'
I'
",I"
I
0
i.
I'
0_
I
0
H
o
-_
o
•
0
o
0
•
I
I
• o
_
I
o
0
I
o
_
I
I
I
0- _
!
,-4
o
_
I
I
e_
_T
it,
o
_
o
"
!
*
I
"
I
I'
0
I
0
I
rJ
o
I
r_
N
_
co
I
_
_
_
-_
$,
o
o
o
o
I
I
I
_
•
I
I
$
_
o
o
I
o
I
r--
I
I
o
_
I"
,.I
I
'
I
_
I
I"
*
I
I
_
_
_
•
_
_
_
o
_
b-
-1"
N
o
.n
o•
I
I
I
I
I
I
I
I"
_
•
I
83
_o
I
I"
I
I
I
o
'
I
i
I'
•
I
?
CD
•-_
I_ O
b'% •
_'r-4
C_/ ,0 oD
C) C_
CC_
o
N_DO
CO _
O' C,
I
t
O
•
(D
_o
0
I
I
C,
_u
_,
N
• ,,_ c_
,O0oq
"C_
N_
_
(D
_000
e4 _
I
I
t_
O
00,-4
,o
•
.o_
•
•
T_
_fl
4"00
cOO
0_)1"
",00
• c0 0_ 0 ,
0
o_ tx, 0
.o
e_,e
OO_
O_-
aDoOO
I
I
÷
v
_o
0,4",04"
_
•
O_N_
_0 _00_
NN
o
_0
0_N
I
•
O0_D
c0 o
eO
,e
,4"000
040
7'
•
,_'-
!
I'
÷
SN
--_ N
_-
c_ N
.N_
0'OOO
CO
N_'_
oo
e_o
e_
•-400
7"
!
0
H
P_
I
÷
O_
co_
,no
N
eO
_"
O_o
o¢-)
,N_O
OO,,
N
e_
I
.o,_
O_OO
I
•
I
o
H
•
I
I
o
_o0n
•
•
O
_
N,0_
oo
•
I
I
O'm'O
",00"
OO
O_
O
C_
I
,NO
_?'O
•
N
" ,-_
I
I
ee'O
oZ..
•
el'.I
!
I
o
_o
040
OO
_OOO_
.NN
I
_.,
-,0
I
!
O
0"
_o_o
OO
'_0_
_ee
_O_
"
, e4 ,:_ ,,T u_
N O
.-_ O
,
@00
O
,-_ r,2
,4"
!
I
!
!
_v
O_O
OO-'
I
_N
_N_
_N
O_NN
_wuJ
Z
84
w
Z
v
Z
P_
t./
•,,1 c
UJ
.-+
I_,- r_
P--It
,,0 CO:,
C:
"
<1"
I
iP.
If, _+
_+
•
IN
0
•
O
C¢
•
+-<
I
I
T
_+
•
T
I
•
I
_-
_t
l_r
0
•
I
O
I
.--i
•
0 0
O(D
._- ,
o
+--_
ur_
_- o
xe
0O
• IM
"'7
.oo
;_. r¸_•
_
o
°
I"
•
I
O0
,l',d
OO
o,
II
N_
o
I
UJ
0_
O_
0
_
I
°
I
'_+r_+
waDO
_0_
o
Eq
•
•
+_N
I
•
•
I
I"
-,,I"
I t'+xt
I
, _
uJO
0_
0_
_o_
I'_ INI
E-!
i_,l ,-i
aa
I
•
I
O0
•
I
[
_
I
• I_
rlg
_
o
I
u.l
< o•
_-) o,
!
<_I +.0
o,_
I_
"_"
I
o
U_• m•
,h _
cl# ,,_"
O
.._1 ,.-.I
l_ CO _
t_O
,(..+
*
I
O
4"
I
T
o
A_
r2_
_
I"
II
I?
LIJ o<¢_
egO'
-_
l_j ,--+
gr_
,-4 o
.4
•4
I
Io
,-+
+-+ _,
I.LI
°,
it
I"
I
• u_
o
CJ
.r-I
.¢e,
I
"o+T_
•
I
I .-+
W 00 i_- Pq
_c,,d
1-1
_
I
I
00.-_
•
•0
•
II
<_'+ i?,
I'_ o'.
¢"d
o
,,#
•
I;
•
!
co
oe
I
¢¢',0
0 I+_ _
r¢_ i_ ¢..
o
_qc"
OL"
o.
LL_ 0
q
,-,
ff_C)
O0 +-_
+'Xl
o
e,1 0 •
o(.._
,co
u_o_
I_
o
•
•
i._
N
ie
r_
•
O,O
"
,.,.i ,-i
I
I
n
+am.
p..4
O, ,_o3us
Og
"
O0
''_"
•
i
I
_0
_o_
0_
_0_
,
I
I
I
T
0_
oi..
•
I
•
l
I
•
I
I
_N
0
O0_QO
Z
85
I"
I"
,j
G)
co
c_
u'x0O
•
.¢
I_
_f_
•
•
''4-
04
0
I
•
_,,_
r,'l
_,,_
:_
_r
,_
<_
e_O
I
I
I
I
t_
C) ,-._ _ 0
_ • t,.; _
c_J ,.O ,.1 if.
c9 r I', r•
!
v
er-_
_o
,4
•
I_,0
.
_oo,
O0,,t
•
I
v
c.
I_-
_
•
,,t
e._ O
r.._
p-
,-..i
I
•
.
•
umo,o
,ON
I
o
o
O O rr'.
•
0fxJ
I
"d
t_
0
:_
,D
.OC_
_._
t_o
o
_
*O'.0
*_,e_
,,00
_0_
u",
-..
I
I
oo
o-
_O
. q, ,._ l.m
,o0_o
_o
00_
,_
I
|
!
I
I
!
0o_
o
,/J ul
• I_l
,,lr
•
<r oo
I
I
i
|
*o
•
,,t" I_
<r
e_l p- O,
_'
0 00_
f_O
,c_l
0_ O
r_
_
I
o
I
0
N
m_
I
I
I
I
÷
g
o,1.,1"0,
0
*_
,4"0
_A
86
•
"
• D- 0,
0
O,_JCO
-0
-./ 0 0
-_
I
•
•
I
•
o,_
+
,4r or; u_
,-4 O- _)
I
I
÷
÷
_'_
_o
?o..
_~
_0
._4-
rc_
",I"O0
f-4
0
"0
f
+
0
-.t
MD
t
I
°
I
!
-0
N
......
.f,/ m
I
c.,-
¢.J
'
0
+
_°g,
o
Sg
-.r
I
÷
I
I
÷
_
I•
l
IM
8?
c
I
_._ _n _,0 (%_t_
.-_
u-,
w
p-t
•
_
_;_
(%1
¢'_Jp.,_ £1"_,
'_
•
I
I
I
v
b*,
u',. _4
N
L_ ,_3 ,_.
u", ,O O,
I,C',
/
II
I
era
o
t_rs _x'.
_1
•
,.-t
._@_°S_
I
_._o_
I
I
00_
_
o'%_
I
C_
I
II
v
0
u",O
_
*
_0_o
~_o_
00_
_e
_
I
lel '
_
I
÷
o
_o
_o
o
I
LU E', _t fxl
co ao .._
°
0", ,,-a _" .-n
!
'
I
I
I"-- f_
0_
,._0
I
u._
iu,
ON
r
_d_
•
•
°
_
•
C_
• .-4 t%l
o_
'r_co
"_," 0
I
I
I
0
o_o
0
0
m
_
•
o
¢_J r_ -..4 o, -,T
.4-,...4t_
• •
_
•
I
.
•
!
.4r _.rM
•
LUO
('_
•
I
I
.,-a .-_ t'.,I
I
<
!
O_
,
_
,.
!
I
I
,,t
,,O
/
-JO
O_
ee
_0
_"
m_
t--
rq
•.
c-._ ,,-q
oU'_
_.
_0_
•
J
i°
u_
zo_
,.o
_
_._
v
Z
88
I
*c_
.O_O-t_
,rr_
C,
_oo_" ._
I
.4"
•
.._
I
,4-_
_
.5.-,_.
, •
• ,4
•
_I"
I
_oo.._
•
_Cl 0
•
I
._o_o,,-4_I-•
,_*r_
•
I
I
"4"
,o
,_
,_ ....
•
_,
I
•
I
4"
-,t_
•
I
_
I"
_00_
I"
__
N
_
O_o
11)
o
,--t
"o
•
I
o
II
[..._
I
00_0,
I-I
•
I
•
II
O,
I
|
*
_.._
•
I
*11
_N_
•
"
I
I
0
,e
!
I
,,1"
I ,4"
N
O,JO
0
o_
I
_-.Ic_
_N_
_^_NN
•
I
•
"'4"
,IA
•
I
I
I
_N_
Z
89
c
_C_•
• h- _._ _ 0__• C
•
, • ,,? •
I
L_
O_
"_Oe4Lf',C_Q
"
_
.o_._ngo..
Q
N
I
OO_OO'O_
_0
4
•
_0
• ..._ o
erl
• t,j ,.,_
•
•
.u-%
.r,4
i,-._.-_
....
I
_2
o
o, lf_ P-- o
_r',,-_
• wD
.--_o
-_-
,-_ o
O,O_
..-_o
N_NN
"e
_O_O
,N
I
"O
-4)
_oo.Z_
_N
_
t,%
r_)
°
.r-.,_.-4
I
oo
•
U%
.N
e,._'4"
o ,.,-i
,,OO_
_
_,OO
OO_
!
÷
e
8o
O_'_
[-4
_o
NOO,O_
•
_O
•
_OO°
_
_
•
I
co
03
C3 .4"
._r (%1
..lr
(..) g_ _t)
•
•
O
.
,,-4
e_
,I
_N
"N
I
•
_
_°
(%J
o
U
O
_o_o;
Q_
•
l,,eO0
e,_
•
•
,,-.4
_,
.
U_
een
I
o
.-,I-
_
I
I
'
o
N
.Jo
L,_a0
_O_O"
9_-,
O
•
_
_o._
_o °
_p.
I
_0
_
•
Z_o.
I
_O_O_
._
_
8_
N_
U_
_
DmDDDD
Z
9O
NOO_
_
_o'_
_'O
__
o
_O_O_C_
,"_nC
O°
0
O"
"OO
t_4 "_
I
I
• -4
I
•
,--4 C,,it'_
,t"n
!
I
OO_t_OOO.4
{t, _
¢oo_
I
05
•
_.o ° -_•o O_ °
*
_1.
•
0n 04
OO.G
,O
_O
O
m-
O_ O
OO
• c_l 04
0"
, .-_ .-_ ._
O
._oo
.-_O
_~o
.-_O
¢%1
,N
I
-_- _._ 6"% O
*_OO
.-4
l
•
O
.-_e4
4-u%
0"
•
_0_0
?_
•
_O*,OO
_
_0
•-_ O
,.-_
N
.-_OO
O
0"
4"
_
0
.-_ t'4
'_00"
O
*_1
•
.-4'.:I"
*,-4
o
o
,...,
_..
_
,0
,o
_0
_
I
|"
•
,4"
O-I"("4OO
_-e_
_o_o
O
".TU
I
•
!
°
"--*N
_O_O
r_
_
_
_._ _
o
o_o_0o
*o',
I
I
•
!
!
O
.u
o
[D
uu
• r,% t'- u
a00
.-_ O
v
•
OD
(._
c- u
(X) t_
u% _u
O4
•
e(._
040
I
,.-_e.l
*'_,_
*t_
I
I
I
>
H
O(DO
oo_°_
•
.0
I
• (j
* .-4 ._ e4
o.I _ o
• ._ O
42 "-4
o
*_OO_
o
_
_oC
S_ZOo
_
*,'x3
I
.0 o
"4"
0%_
0
-o
"_OO_O
'
_
?_ec''_o
_o ._o
ec
e_ O
l
*--_txJ
•
*.-4
!
I
_.o _ o, o
_.
O_O_O
_
_O_
I
O_OO
*_
I
91
_O_
•
,04
o
u'c_
•4" ,4) .-4 L"
_.
r'-
_'_ 0'
0"
I
II
I
II
,/
+4"'4",4
•4-
,,t
O
{W O
00
C;_ b'%
•
•
•
•--I 0_,1,,..4
_
•
*('_.f'4+
J,,L_
,1_%
•
.e
e:'. ,_. N
co
,4-
•
u'_ (_
0,
..#
o
.#
_o. ,-._o'
"_"__ _. _ Z
• ..-..--.
*
•
elK,
00_'_
_
*¢'W
II
o
O
•
• .4)
C0_'_-_.,,,+
"-"O,,t"
* ,"
_J_
O0 _
000
O0
(D O
*
O
4
Io
Lf_ _
,
.,0
.--_ ,.._
0
,-_ ,-4 C_
{_'O'_-.f
•
4"
.-.*O
*U%
*04
v
_O
•
0
_0
t_- -,t
0_.
00,_
•.0
_.
_.O_
•
II
i°
o
w% o
_o
_@.
_
_
rn0"
I
II
v
o
-_" ¢'xt
•4"
*
O_
0, I-c0 I_-
,,t
,0
_
O _.-- N
e.4 c0 c0
_o_
!
O
51
0"_
H
4"
.-._
u_
.
•
I
•
,,-.4
,u'_
r_
°
_o .I
U_
ul
v_
_
0_
_-r_
,I'N
!
O
"%
w
•
II
o
I
r=,
_4
0
JO
.,,_ C0
I-'%0
I_" _1 .--I ",T
r:%u'%_".,,t
O O "..U °
"
•
.,4"
I
_O
_
_O_
_
_.
__.+
O _ er% _T
+4" "O
'
_" O ,"_ r"
...-4
._
xt
u.l l%J oD
.
0
00+-.4,--1.-+ +
I
Z_
92
•
"4"
!
od
c.-g'
CI_
•
.
I
•
.r_l
_-
,
Ix5 a0
_-
•
!
I!
,It
I
•
I
!
I!
T
_ ._ ._:
_=o =_ _t
_ ._-
1
T
,-4C,
.4"
I
,--dO
a_oD
_O0_C,
0-4"
•
Pq
I*
, ,-.4 ._
,0
_
_r
•_i
0o
,.-i •,.-I0
*(%1
I* I*
I
T
_.J cO 0 0 0
0 _'- OQ
0 -.-_ _::0 ,0
,._ t{'_
0"
*
,--_ -.t
_0_
_
_0_
_*_e
_..
_Z
t
,d
ID
,'d
I
==°°
0
_0_
_
_0_
o
0
•
!
**
I!
I
!
|
I
Oh
i
r--_ I_J
•
I
I
•
*
|
_TrIAJ O
,--_ cO 0
_ o. _._.o
•
!
o
o_
f',-0
I
aO O_
I_r_ 0
0o
* ,0 ,,_r_
0"1 ".T
0
'
•
g"
/
I
,4"
_,
I
O_O"
•
I
_
I
|
I1_ IY1 0
a_
_
_rO .--I
I
_
•
o_o
•
!
|
93
,4"
(
_
!
f_-
v.
O
C
u'_c0
_.
I
um
_"
-1"
°
o,I
!
..j
o
co
_
•
oc_.O
•
•
*i_i
. ,=_ ._- pr_
I
o
°_
_e_
_0
_.0
O0
I
o
_
,.,no
_,0
_ ,g o.,4
•
•
I
r.D
÷
O
E_
<_0
,o .,,
_'.@
m,o
.c,'l
• ,.-_
::>
_"
,0
0_..)_
0
• o
u_
•
.S_-
go,0_o
,_
• ,..4 ..-,
I
•
I
._
i,-_
!
o
u_
_o
_ o.,_,_
._c.j
I
,tNI
e-4-
i¢_
I
0
o
_0_
I
0
I
.
I
r_
--IO
i_...."_
.4" r_
P'-
,'_, at, _1"
I
0
v_
cO
22_
Z_
r_
94
Z
c
_OON
_O,'CO
_OC
"
"0
"
I
I
_o
_
!
_o_
it, O0 0
o_
_lO
_,xJI#',U"
•
.-I
•
• _o
_0_o_0_
_o_o
_00.'0,
0
I
I
_0
0 I'M 0
I_- _.
1',.-,--40
.
•
COO
-N.'M
_0
_0_
,.0 0
i'_00
I
0_0
ul_ erl 00_
fxI
_'- r_ 0
_'
•
I1_0
.
.0
_00
_0_
,.-_ 0
I_I:0
0
•
°
I
_0
0_0
_00
_0
O.
I
I
©
0
_0_0
umr_
_0
0
rD
0
•
O, 0
•
•
I
I
_8_
I
"
I
°
8_
I
0
-U"
uu_
eO..-_O
,
,
H
_11"(._0
I
I
•
U
•
"
!
,o
_o
I_'O
7_oO_, _.
•
_0
J I'rl t_'1
0 '-'
m'_ 0
-.TOO
r"- O
,00
_'
_"
•
Oi,m
I
I
_0_
O0
_00_
°"
_
0
_
NOlO
_00
"_
I
!
_
....
,0
_0
"0_o
• _0
_o
I
•
IIII
Z
95
_0
_
I
°
I!
fIN
I is'.
IN_
ll_.,--_0"
_
_0 I_
I#'b
IN
_
°
.
•
I
¢io
_
•
I
I
2'_......
•
II
O
!_-
_
•
,-4
,I_
NOer,
O0
O0"N
,O1_
_N
_
ON
I
I
I0'
O
_o
000
_O_,
I
II
o
_0
I
_t_o
O
o
a
I
I
H
I
o_
4a
oo_
_>_
Z_
I
I
©
M
,I_
a_
,,,
__
g._o.
o
_-
O
_,_
$.
Oo
•
TM
_--o
I
8r._
"
I
I
!
•
,N-_-
eq
I
e_
o
o_
_
II
" _
_I_N_
° _
_o
,0
I
%
4.
"_" co
g
o
i.
I'
96
'
o
•
um
@J
e,J
•
i
•
I
•
I
I
I
-.,t
I
t
Lr_
,
_..
•
•
0Q.,
•
.-i
I"
I
I
I
_
-,:r
,o
u.J
,_7 P-- C,
O,r_lcf_,
02, G',
.
_
I_,
o
2,g_g"
.,-.,i,-i_-4
I
I
_u
G
0'. C.
•
i, ,-,
c0
._,-_
c_
.IN
I
•
or,
'
_O_,_
_'0_
,,
I
II
.-4
LU
"_'_g
O_
I
I
,
•
_-
U_
O
c_J
Or
I_1
_.•
LI_
oo-_,_ •
•
•
,
,.0
..t O
..i
N
,-.i
,'_0 ,'_-
_
(xl
I
I
I
,?
ru
-.t"
i.i_ .j- O
r,_
I
e,l
I
I
r'_ t'--
8_._.._.
¢,_ _._
,-I
O
O
C2,
•,,,1" -.0
I
'J_
r'CO
,
•
•
,--' r_
,I'XI
.O
(A_T
'_Xl
,imJ
l'x_ (._
-
,.-I _-
_-¢ ,-i
OIN
I
I
I
_00_
I
_0
c_
_0,,_I
O_
---IG,
@,
•
_
,_(.#
i
,
I
v_
I
O
_
-0
._
-.I"
,,--,
_
C--I
O,
•
I" ,r,/
•
N
I"
_"
t_
r,)
c,_
•
.-i
..4
¢_/
•
•
0
b"
c,l
0
_'o
"
•
I
t
"If',
",-_0
•
I
I
I
Lu
"1"
_
•
I
_-
co
_
0
t'd
_o
•
I"
I
97
I
_
F
I"
IN
,-#
o
u"
t_
"
0
co
.
c"
o
0
.
.,,1"
_
-.1"
,,0
co
.-_
c,n
_,
".t
0
,-4
"
_-
aO
0
0
t"*
io
f'.J
xo
!
!
|
o
I
I
I
I
0
I
1
,,o
•
t_
O
00
r-e,j
•
i°
o
r,..
,t.
o
i°
_
o
_
•
II
v
N
um
•
E-t
I-I
,._
t'_l
_o o
_
(M
,-I
----.
"_ _
rQ
0
I!
,o
cH
_
o_
=
,
o_ _;
o
r_
o
v
___
i°
--_
I
v
÷
_
_
o
LI_
_
"_
_
_,I
t_-
" _
_
o
_
I
_;_
_
_
_
_
0
I
"
l_-
!
o
r_
v_
t
(,_
_
o
o_ _
_. _
I
o
_, _.
,..J
_
LL.
<_
_i
a')
0
:..,,.
LL.
98
L,,L.
C;
_
OIl
r--
I.".
-.1_
0
_
,'_
t_h
I
I
•
,z" _
•
i_-
I
0
O"
¢C
0
..O
C'
,-4
,,_
0
•
I
._
_
I
.
0
_
rr_
/
t
_
I
_D.
CJ
I
I
•
I-P,
_
I
_
_,
•
_
o
•
_
o
.
I
I
um
....
_
I
o
I
_
_
_
I
I•
N
cO
0
,,.-¢
•
I"
7
T
,..4
T
O'
t'-
•
0
.r,
,Z_
?
0
I"
I'
CO
H
v"
._
H
o
o
o.
_
,.,, _
0.
o o•
..!1
,.-, b:.. "
o _
_• ._ ,-.,
,.-," ,,.
o _
1--
_ _
,,,
,-., _
o
o
,5
_
~
.._
.o
_ S'
..-," ,q
I
I°
I
'_
I
I
I
I"
+
_q
•0
o
O"
._
I
.-, ,.- ,_ _.
I
I
I
,-,4
,-- ,g
.,
I°
,,,
I
o
t'-
r_
_,
.-, _
•
_
I
I
ID
_d
to
,g
I
_,
I
t
,.,
o
I
I
I
I
I
r_)
o
.i-
i'_
r--
M
A
!
I
_1
_
I
,,. 0.
I
I
_
I
I
_
I
I
o
00 ,-. o
I
I
I
I
,-., 0.
,::,
•
•
I
0
,"
I
I
0
•
0
I
I
LL
99
_
I
_Xl
I
0
•
I
-.1"
0
_0
".0
I
N
C,
,.1
C
IZ_ r_
_
"OC
"4 rj
0
('m (p
.0
¢'q ,--_ _J c"
.
•
I_
I
I
I
!
0
0 _
_f
h_
_'_
0
*
¢'*;I _" N
'00
0
"-_
v
°G
I'M
•
I
I
I
I
O'
0
=
•
0
o
_
,O¢_N
_.
o
0
O,
u".
i_- 0-, u _,
*,.N
•
!
.i
r*_ ,_ _
_0_1
_,-# _t h'- I_
0
•0
.-d
I
!
_'_ ¢00
O_J"
_
•
!
0
--_
N
*0
r_
u-_
•
_0-o
*
I
* N
I
I
h_
0
r_
¢_
, O_ _
0oo
.-40
o_
o_
* ,...i
0.-_
•
I
0_
.00
O0
_N
I
•
oO
O' .--, _'lO
.
*
I
I
•(M
+
l_-
0
•._ i-JCO
_o
*00
-0
i•
I*
!
!
I
÷
N
o
•
I
i_
0
a_
0
_
*
O0
•
I
o
!
I
I
I
'.,T
_lJ tO
r,l
•
_o
0
_(_ m%
._c0
I
I
I
_0
@
_0
°
*'_"
* t'_ I'M
_0_
_0
• 0
IMEI
(%1 o
i._, .4
• .-_
..II
!
I
I
-..JO
0_
_g_9
o•_
cJ
,-.-_ ¢'4
*
I
m
_N
_zz_
g
z_
z
100
O- .-w
fx:
_
r_J cm r_ _
O-J
u u'
C
r*
c
•
e_
,--. _
c_oo
°
•
°
I
•
°
I
I
°
I
I
I
is¸
_
ur¸,,t _,
o, 0-
rg
_+
c,
,,.r, q
• 0
o
_
_
_ o..9 ._
t+_
I
"0
I
I
•
o,
c0t_
o
_._ t_
_S_L__
• o
oo
•
I'
•
_0
•
.(_J
°
T9
°
I
i+
' "+
I
O
0,
0
• 0
O0
.o_
.
• o
._
•
I
_._
I
•
N _, ,-+
I
O"
o
....+ ...< 0 _ ,,+
,0 ..-. ,D O'
+O
E_
O-"_
• o
_0_
N
+
o
_o
_o
_o_
o_
•
•
I
I
0
_D p+-
•
CO<_I
_
.
•
I
e,+ ..-_
I
-r
I
*¢'_N
.
I
•
.-+
ic_ Pm .-+
•
• .-.t
Lql_/
I
17,
,_t
•
I
II
o
_o
_o_
• u_
I
IC_
.
•
_o_
I
II
I
!
I
I
H
CH
I_
_
CO
+
0
_:
CO
u
u_
I
I
I
!
O
÷
o
o
m
m._
OO
0
+
• (3
•
•
I
_
•
C) .-_
r_l _
•
.,_
c0 t_
I
ao
pq
(M
•
o
_ ur_ _
+ pel ,.,-+ U',
0_0
'0
_¢_
--+ od
cP,
I
I
e_
O"
•
O
!
0
o
_o
_0_
co 4" f-+
rM 11"+1.i_
N_N_
_
o_
_O_
r--
en pr_
I
I
I
0
.-..i
,,._N
_
,.-i
I.-.+
u'_ co
i +..,i
_-
I'
I
°
r-- _m
+
•-'_ P-
O
_l
I
c_
7
101
•
I
"°
_
y_
C'
_'
,O
It".
I.ig
•
o_
,,C .., CY' C..,.
•
I
I
O"
I,t'L ,-I
,,.?
•
I
!
I'1"O" r(
_ C_ c(:
S"_ O ,"- O
,,IF-,
c_u',
ol.c,
0
r_l •
•
!
OD
I
I
Lcw
o,
(._
Ug IX_
,,t•
•-'wO
•
C..-w
•
(',._ ("_
I'M
c_
u'_ 0 .4" ,0 O"
r.. _ o_ (.d ,...,
•
.e,i
I
I
_CC
OO
O
u'_ ('h
.--_ 0 O0 _lPc, C_J _O _
_r_
OO
• .¢_.I
.r'-.,-w
or"_
,0-2
I"
.0
o
t,"_o
er_0.
I
O" o,,t_
_0
P", (F"
C_O
.OCO
(2) .,..,w.-,_._•
I
!
r_)
O
o_
_o_
wD ec, ..t r 4
.O
• r-- f.O. O1,,'_ • .
I"
÷
o
O_
wD O"
H
C01-.(_
,0
-_-
@
C) f_
•
•
-'-'•
I
I
I
I---t
r-
I
I
A
0
_D
(,q
o
_M u',
.O O
f._ r_
oq CO
f,'i
• --T .c'q
I'
I-4
_
-=1-
I
1
o
.-so
¢o _
c_
,0
c,4
_
0_
.o
rssO
• ¢'a ,--_
I
• o
0
' _
•
°_
I"
Z_
102
.0
,--,-.T o.
• .,.v "o
Z
c._
• ,OIp
.
I
o
I_, P- o" r '¢,
• IE,_
•
!
c_
,D
•
o
°o _,
0
..0 t_- ,
,-i ° °eq
n'_
°_0
,-4
• n_
•
i°
r.J _
I'_ I'M
_2
,r '_
i°
ID
I
0
o
CD
.r
_o
T
_,1- cj
v,
u_
r--t',.,.-i
•
°
•
,.-t cu
>
H
.-i _
.r q3 ,.¢_Tj
• .--ip.- ¢,m
.o
cJ
•
._,i
I
* ,o
• _.J ..-_
I
.o p.- _
o
Pn"1
• o° _
,
¢M,-I
.,-_
_0_0_
,i
,o,
103
2
f_ ,_1" t'_ r,J
C2 (_J _ c0
O _C c_ Cr
OC)
CO
•
b-Oq
"N
I
_r_
,$
•
!
i
o-"
,t,
-,I"0"
0"D"
O_
(:0
_
•
i
,4" o
,
OLf"
• Lr
•
O
..-4
,r_
eO_e
v
Q.
o
(o
,_- •
0
_r,
"'_ O'
0
C._ _
oo
e_
,.-IQ
_,-i
I
I"
I
o
_
U'. _
O,O
N
C0
'F-
I',-r,, O0
• OU'_
*..*
OO_.a
I"
co _r_
•
•
I
v,
_0
0
u'_o
_
0_
w_
_O_
C)
.
Itr_
OO_
,0"
_O
_
•
I
i°
!
ro
v,
0
Lr_
o
_O
0-,11
_O
e'_,O
u
o_
O0
.
O_O_O
o_
I
•
I
÷
0_
I
-/
o
-,1F
v'
U_U
"-_ O"
O_UOe
_0_0
H
_00_
0_
!
I
÷
8
.j
I
(..)
.-.4
00_ 0_
v
'0
ec_N
•
I
÷
rO
--I"
I
_0
_¢_0
_
0_
• o
|
_
_
I
,0
,-_ 0
I
,.0 -,1"
oo°_._
0
"_
"_
I
104
_0_
•
°
o
•
b,
•
•
_C
°
I
°
I
I
°
.,,I"
•
i
A
°
I
.
°
,-4
O_
I
I
•
v
v
if]
I'_
_G*u
¸,
¸
U"
,-.4
•
,
_r_¢'_ o.1
*
0
•
i_'h
urn
)<DC
O_
_',
•
•
cwO
c-]
•
I
I
i
I
•
l_
t
c,4
°LI'_
c,J
•
°
I
I*
c.j
0
t_
,_0
g"
grog"
_0_
c,a
•
•
•
.
I
C'.I
0
,
0
_
•-4
0
t]
0
L.'_
e,}
•
•
•
.-,
I
tl
I
b0
0
• u_
cW
•
._"
•
_{__
I
I
,,--,
.-,1"
I
I
_q
0
_-
0
,0
r_
r_
_
_'J
,_
•
,0
•
I
c_l
o4
I
I
'
a]_OOC_
_0_
"r¢_
-k'Ca
I
I
I
"U]
•
I
.OOm_O_L_
0
_
_'I
I
_.ta.
.<
105
I"
'
'
,-._
¢'xl
¢,el
>-
>-
>-
•
el.
C_J
u.
0
..t
•-_
r.r
q
0
I
v
u%
c,,_
cx.
.,-j
_.
o
c
v'
o
IC,
•
,,b
O
I_
o
0
,,I
o
o
o-
_
o
o
=
_.,
,L)
,_D
,0
•
@,
_
_
_,
_
.
o
o._,_
!
•
_
N
N
v
0
Lr_
N
i
o
o_
U_
r,-
,4"
(")
(7"
_o
co
oJ
0
N
rxi
O"
v
i=i
•
i_,
•
I/%
•
u_
0_
G_
_
_
N
I
I
I
0
'
,
.-i
,.I
p_
o
.
,_
÷
!
ro
--I-
0
_0
_r_
_D_
t_
_
_
_
_•
_
O_
4-
I
p.,
_.4
0
I
_•
_,_
i__
'-_
_
_
(_
i0
_-
_ •
_0•
G
G
MJ
B_
N
m
_.
.
..
_
g
106
=
=
I_-
z
F-4C
Bonine,
MAC
W. J.,
Report
B.
C.,
SOURCES
et al, Model F/RF-4B-C
9542, I0 Feb. 1964
Crawford,
W. N., and G.
Characteristics
for
Bridges,
DATA
Nadler,
the F-4
Calculated
Aerodynamic
Derivatives,
Static
and Dynamic
Control
Aircraft,
MAC Rept. F21_,
Longitudinal
Stability
and
System
16 Dec.
Performance
Characteristics
of the F-hB/C/D/J'
and RF-hB/C
Aircraft
plus
AN/ASA-32H
Automatic
Flight
Control
System,
MAC Rept F934,
19 Apr.
1963
Bridges,
B.
C.,
Calculated
Lateral-Directional
mance
Characteristics
of the F-4B/C/D/J
the AN/ASA-32H
Automatic
Flight
Control
3 May 1968
NATOPS
Flight
Manual_
I Nov. 1966
Navy
Model
F-4B
107
Stability
and RF-4B/C
System,
MAC
Aircraft,
NAVAIR
1966
and
the
Perfor-
Aircraft
plus
Rept. F935,
01-245
FDB-I,
SECTION
X-15
108
V
X- 15 BACKGROUND
The
at
X-]_
is
hypersonic
under
the
45_000
speeds
right
ft and
a powered
for
a single-place,
wing
a Mach
in
of
number
300_000
in two
configuration
with
pitch
by
and
and
feel.
rudder
provided
the
for
stick_
Only
the
each
given
not
loop_
SAS
for
have
The
and
loop
level
however_
are
this
been
flight
the
X-J5
the
and
recovered
flown
to
and
all
aloft
about
prior
the
three
performs
to vectoring
is capable
from
of the
ventral
and
of
conventional
and
is
a
stick
roll
the
an
of
altitude
off.
X-J5
The
axes.
basic
assume
by
the
In
addition
known
as
to
the
gain
settings
maximum
this
is definitely
show
on
actuated
bungee
roll
both
for
control_
stick
environments
been
made
their
consists
The
for
to
have
pilot.
considered
is
are
by
and
for
a side-located
stick
report
flights.
This
missions
this
actual
flight.
surfaces
pitch
however_
center
tail
is provided
for
surfaces_
with
first
is
at
the
flights.
here.
feedback
set
horizontal
in high-acceleration
the
in
aerodynamic
control
is used
X-15
shown
the
force
control;
used
three
for
through
Control
yaw
shown
manually
here
basic
with
aerodynamic
for
r -_5
conditions
made
the
pilots
all
realistic
intent
launch_
airplane
of
center
system
airplane
trimmed
of
the
control
control
an
the
Most
the
about
is
an altitude
technique,
be
flight
carried
glide
been
systems.
used
stick
there
is
a deceleration
yaw
All
pilot.
although
loops
at
After
for
of pitch
augmentation
feedback
used
are
the
center
have
is provided
conventional
control
of
side
SAS
A
can
airplane
for
here.
hydraulic
pedals
option
The
considered
control.
irreversible
pilot
altitudes
surfaces
roll
operational
designed
feet.
control
vertical
0.80.
by
configurations:
is
Aerodynamic
about
6 and
The
is launched
followed
of
airplane
altitudes.
and
of
this
to high
airplanes
a B-52
number
With
attaining
extreme
mission_
a landing.
Flights
of
a Mach
flight
excess
and
rocket-powered
general
effects.
109
the
YAR
speed
and
normal
each
are
all
for
altitude
rate
p -_$a
The
transfer
for
unrealistic
angular
loop.
SAS-on
airplane
of
roll
gains
for
functions
loop.
This
for
straight
this
may
airplane_
variation
®
\
\
do
0
_0
I
0
rl
0
0
rQb
0
a
\
®
q_
qJ
|
,--I
\
o
®
r_
E4
0
\
--
Od
I
4o
_J
c_
0
-p
_rj
I
I
I
l
0
0
0
0
0
0
0
0
q
o
o
(5
_
o
d
q
o
cO
_0
_v
_
cU
r
o
0
_
[._
0
(I,)
4_
_
_
(J
bD
I-_
i
hD
[1.)
,_
r--I
r_
bO
0
r,j
O_
qi_
L,r_
"D
_
II
©
II
H
II
%
II
"
F-H
110
0
_J
(D
I
(_
LD
,,
0
_J
I
Iu _'u_O
_u5
tC
bO
(,.9
.
:_-4.
L_
0
(_J
LL_
V
&
OJ
_J
b
4--
0
-
OJ
04
(_
--
II
II
II
o
d
III
X -15
PITCH
AXIS
8SSAS (rad)
8ST(in.)
I
FST(Ib)
_..
2.8
_"
8s(rad)
8s(deg)
-20
I
(TEU)
ROLL
-I0
0
I
I0
I
20
I
(TED)
AXIS
8aSAs(rad)
ST (Ib)
YAW
BLAT'in_
ST {
I
FLAT
r
I
1.55
8a(rad)
2.4
--I
57.5
AXIS
8VsAs (red)
BPED(inLI
FpEo(Ib)
2.3
By(rod)
12.2
Figure
V-3.
X-15
Control
112
System
X-15
PITCH
SAS
_(rad/sec)
ROLL-YAW-YAR
.75
SssAs(rad)
SAS
Roll
Gain
p (rad/sec)
BasAs(rad)
Yar Gain
Yaw
Gain
.3O
r (rad/sec)
BVSAs(rad)
Note:
Gains variable
in 10%
maximum
values which
(e.g. roll gains
.2_0, .25, .30,
Figure
V-4.
increments
are shown
of the
above.
selectable
are
.05,.I0,.15,
.35, .40, .45, and .50)
X-15
Stability
1 13
Augmentation
I
e_
!
!
X
I
C_J
oo
o
I-°
I-_.u_)
_
oo
_qq
88°°
[_
/
!IIi
/'
.t I
/"
I
/
j,/ll
I
¢_J
I
_
114
,_-°
1
_
o
0
uC,_l
D
_o.
o
Z
x
__
rood
Q
t
I
__
I
I
0
a
I
I
0,.I
0
0
0
(J
o
0
ooo
0oo
o o oo
_Io
O'_OJ
oo0
_0c0
I1!
ill
_o.
¢0
m
1
0
_
I
I
t13
Od
.J
115
I
-':
0
I
if)
0
I
o.
_'X,I
_o
Q
_o.
!
I
.Q
!
000
8008
eoooq
__o
O0
×_
/
(%1
--.6
/
/
/
/
/
//
¢%1
to
:E
0
/
/
/
./
/
/
/
/
/
l
#
/
OJ
.,,.;
-- (D
I
I
IF)
I
I
I
--
I
o
I
OJ
0
I:I0
0
0
116
I
117
D
,)
I
I
I
OJ
_I
o
0
I
1,0
I
I
04
..-=
2
l:3
¢.)
118
0
0
I
I
I
I
I"
I"
0
s:
C.)
q
_o.
(,D
-ud
.Q
O
,,i-
-,,6
i u')
x_
OJ
OJ
u
_o.
o._
(,D
N
m
..,.
--
I
I
I
GO
GO--
O
%
O
N
I
m_
.-T
.J
L)
I
T
,,v
119
O'
0
I
'"
I
"
I
I
T
_
I
I
I
I
I
0
I
120
"
I
0
i"
I
0
I"
I
0
I"
I
0
I"
I
!
-:
-'_
I
I
o. I
0
I
!
I11
_D
I
a_'_
T_
X_
I
0J
I
,<i_I_
_
®
0000
0000
t
,
co
4,,-
I
oooo.
i\!
'
I1111
Izili
0J
•
I/:
cO
0
0
0d-
I,D__
OO-"I
I
0
0
I
I
t_
!
_
i"
I"
o.
¢0
I
_.
I
I
_
I"
I
t
I
0
0
0
re}
0,I
--
i
c
o
o
121
v
o_.
0
I
I
0
0
_J
,--
I
O,
__
(Z)
U')
(
!
t
I
I
|
om
.Q
K
'_£
/
X_
®
0000
0000
0000
_.
I
I
if)
_
r..)
I /
_
I
0
0
0
\
I
_.
!
CO
i°
0
roo
122
I
N
I
_.
i
I
I
o.
N
I
O
q
o®
(.D
tO
|
!
D
[3
!
!
¢-
_D
tD
L_
'4-- O
.Q
o
m
ur)_D
4)
o _
._. -10
x __
._
N
oJ
rd-
O4
.N
._ "_
o
o.i-
OOOO
OOOO
co
Od
oooo.
(13
OJ
OJ
JO000
(_0 04 _t" E) (D
i
1!1!
',lli
0J
r"
tM
/
[3
i
o._
od
(.D
__ I_
CO
O
O
/)
od
- I
O
-
I
I
_
O
uf)
I
'_'-o
,
t_
(M
¢q
tM
G:)
¢0
\
I
O.
i_j
o
(.3
o
I
I
I
I
I
O
q
q
q
q
i-
123
O
,m.
I
I
I
l
O
co
_o
_1"
O
D
-
q
o
q
I
q
O
o
! oo I
El
iz') _0 >,
000
000
cO
_i
"-
_
.
o oqo
_odo
,
0
co
I
I
I
_.
,_.
N
o
0
o
0
I
I
I
-'_
_
_.
I
eO
I
"0
I"
JO
c
124
I
I
"0
I
_,"
I
q
I
I
re
oJ
q
q
I
-
q
o
o
Cs
0
u'
0
IP
0
o: ,.- o
0
c"
o
q.
,_
c
c•
_o £
C
¢0
•
I
°
C,
C_
c
I
4-
•
,._
.-i
c ¸
<1
C_
c_
1_
,-_
r%
£_
¢O
c_r'_
LF.
I"
O
(,m
rl_
_-_
cr]
a}
I
0
0
"_
a_
O
O
U_,
_q
_D
0
0_
,-_
r_
_
r,_
q)
•-_
0
c_
o
H
o
_
0
0
{I3
*
o
o
o
c,
o
o
_
_
0
C_
CJ
o
o
o
•
0
0
0
o
O
8
0
0
0
0
o
I_-
_-
I
0
$
c;
cO
C5
C)
a"
_-
O
'_
o
0
_t
¢0
"
V
_
o
¢0
•
I
Io
C_
,._
•
0
co
o
o
co
I
t
•
co
o
,-_
i_
o
o
o
o
co
o
r_
¢0
0
0
0
_m
crl
_
I'_
_ID
0
0
¢0
co
.-_
H
IN
_J
0
0
_
•
o
0
o
0_
q"
O_
¢xl
I
co
_
I
I
'
_
O'
0"O
m
Go
_1
I
r_
I
I
0
125
*.o
O
CO
N
o
o
o
o
I
I"
_
_
I"
_
_
I"
_
I°
_
_
I
ie
I
I
t
I
I
•
I
I
I
÷
o
0
t_-
I
I
gO
,._
I
_
,l_
I
I
0
0
I
I
_
I
I
O"
_
_D
0
r,3
O
I
I
I
0
_
0
I
I
I
•
f
•
I
_
0
O
I
_
,-4
c'4
_
I
0
•
I
I
I
!
I
I
I
•_
_
*
0
0
•
I
I
I'M
,.-i
"-3"
,#
¢0
I
+++:I"
_
0
0
I•
I"
I"
I_
i
I
+_+
0
_
0
I"
I
0
0•
'
_:O
0
l"
C._
0
gO
I"
PM
¢_1
0
0"
•
I
_
I
I"
+"+
+""
I
I+"
I
_
o
0
0 TM
P_
"_
_'_
I
+,..
_
•
I
0
0
0
0
0
_
l"
l
I"
I"
"i"
0
_
o ,+
• .
I
Pei
_,
h'.rM
.0
r_l
¢%1
•
I
I
_
o
o _ ..,:, +--,
. ,_ . - o.
I
o
.
_ ?-. ,-..l'
-_ _ +
I
P'-.
,
7+
I
I
._
"41
+'el
"T_
I
.23
•-'4
u +)
_.",
0
I+
0
I
0
0
•
•
,41
0
I"
126
0
0
0
I
P"I'
_
cc_ _
c_
C'O'_
,_
U_
• c
-'
_C
)
I
O
C7
•
I
r_
-..t o,
• ,_o
,--_re cJ 0
o-
,-<
t'-
..
)
_Jc
I'
I
•
I
I
rr_
o_
0.+
'JD
•
prl
, .¢
C_OC_
04_ 0_,
0
.a_
_-_
.-_
F-
U'm
" b_C.
o
I"
C_
_0 (_"
C'
C_
0 ¸
"
,J>
O0
OCO._
NOO
0
,'_
_o L)
!
t,_. F--
_000
_00
•
I+"
t_
[--I
c_
OrO_
,--4 i'_
o_.+
,_
0
_. O
-.0,---,
I
H
[-i
-_
o_
°
_eo
,t
_
O
.:1•
) ..10 ¢.,,_
.L) 0". I-- ,.-+
p-+ p-- ,p
L_
.OO
,+
O" e,J ,-_
• o
(-._
u",O
!
,
_ _J"+
_-.
_00
•
+
I
.+
)
(7.
• ¢'-.i 0_
L.m ¢D -t
_O
•
f,-
r_. _lh
I_
_---_00
r_l --<
.,:I
E-t
•
°
I
P
)
I
!
o
p:)
nr..,•L.) ,.--o ._+ _0
(..) (p
Cq_-T
o .-_ r_
+ ¢D pr_
4_+. _.
¢_
o
o
•"+ 0
o
c)
,,0
I
L,,l
I
•
I
o
P_
°°
f,..
. (x'_. ,,_- ,.L.
. a:_. or",
(Y' r_'. P_"I 0
,.,.,,a_-...
I
_A
•.?-_0 co gr.
• . f-j r_
•
.
e_l
o
•
7
•
•
@
•
,.--i
•
CO
I
I
sd_
"T"
o
N
.-'0
v'_00
0
•
. _. _._
r.i
g"
gh O
,0
00o
00
_:o
+_.
o
I
I
I
I
o
I
"_
127
2_
I
_
.1_
21:
,--+
,_,,0
o_
0
E_
v
c_
c
C
•
,_u• c
• LC
.-_oi_l--
,o_,
OI-
co
O, ,-w
co,-_
_ ,__'_
"_
OC'I
I
•
•
~q?,_
•
h'_ (D
C.. C
0-
I
,o
c)
r_
o
c,
.o
• o
i--.
u', c
I
t
c_
,,--_
I
e,j
°
I
U'_ ,--wp...--_
cMo
•
I
C)
,-I
•
f_
COI_N
._#..
_r_ bm wT_ (_
• ,tqO
•
I
._'_i,_
, cq h"_
...o _t,, LF, t_-
.o_
I
OO
WD
pr_
F-
G
OO
h-
i° ?
• o
,o
•
.-,
¢-J
00OJ
I
cO ,D u_
.Or,_
o,O
I
-
•
ON 0
(I) O
•
' •
F'- _'-I
_000
O" OC)
•
.t"-
I
0
co
_o ,..-_ 0
O"
0('4
N
.-4
O
O0
O" _
CI_
p_
{xJC _
.
'N
O' _,-i
_o_c_
_),-i
I
I
_r,O
_00
•
•
* ,
_.+ ._I
c)
..1 oO
o
,
,_r_
I
H
_g
0
p.- _
•
.-e
O0
. wD e,J
. ,_
-In
•-.wu
I
---WI
>
O
Fzl
0']
I
"J (D
._
_i"
oo
,
•
,{.u
I
I
v_
co
u'-w
,O_
I
ul
_D .--_ _
L) u
-,tm
r._0
I
!
• -4- -4 (Y'
C.)O
*
•
CO (_' -,t ,_"
•
I
• i'M
.¢J
• Uh P-- u_
aO _ CO t"
•
(DO
O
v
{D
o_
oc.)
o_r
t_, W& ,,O
, ,-w _.. (._ O
C._' 0
,-wo
_
C9, 0
.
•
.o,
I
I
I
I
!
o4
o
.JO
L,_co
0
,0
o
0
(',1
,0
• _t" 0
L_ ,,T
•
0 0
r'_
. ..-w
I
!
@
_o
_0
.o
0_
_
•"_
I
•
•
*-4
_
o_,
_D
!
u_
ZO0_
w_
u.
Z_
Z
128
_
CO
wO 0
P" 0
{NO
P" 0
"
fe_ ..-¢
I
41"I
IN.,
I'-C re'
_
c1
u_
u_
o
c-
_
LC,
CO
7
I
o
0-
_
(,q,
,c
(.q
IT,
•
cn
,...i
O
t.-w
It
1_
eq
o
.--i
c_
I
0
o
c_
•
,,-4
E-4
X
I-.-
oo
.._
L_,
I_
,o
-P
cH
CH
,
_i-
I
O_
I.L
H
U3
-M
_1-
0
0
0
,J
(..)
g
uh
r.Lf_
6q
I
O
I---t
I_;
0
o
o
_D
co
CO
I-4
!
N
o
i_.
f'-J
I'-
!
M
•
I
,t
o
•-4
_
o
b
II
129
0
0
_
C_
_
I
.
•
_
_
*
,o
o
I
o
I
•
.-4
c,a
I
u_
l
•
l
0
_
0",
r_-
_
I_-
0
0
0
cO
_'_
r_
LI_
_
0
CI_
_
,
.-i
,
J
,
I_-
,--I
_-4
-_
,.3
,
,
c_
II.
,-#
I
.
I
I
I
I
i
_
o
i
o
I
Ill
I
o
I
.-,
•
I
o
--.
_
*
I
_
o
I
I
o
,_.
_
c.,,i
¢q
_
I
I
I
I
I
I
I
I
_-,
.o
0-
o
R
tr,
..t"
i%1
I
i'_
•
I
I
I
I
_
•
0
I
I
v
,o
o
CD
_
..0
•
0
0
0
c'.,I
I
1
*
0
I
--
I
_
-
I
0
Izl
C.
,"4
_
_"
_
0
_
I
I
.#
_
0 _
I
I
I
_-
--
_i"
0
_-
I
I
I
I
I
-#
c_
_t
,0
_"
(
I
|
'T
0
[
I
I
_
I
130
_
0_
,.-4
o
00
,0
C,
C.
•
C,
t+
,4g_"
_C
t _ C,
" _
+ l_m .@
_o_
I'q
I
t
I
I
•
I
I
o
Cb
0
o,0
_., ,43 i.r, c,
0
12:) '
"
,I'_
g_,_
o.? .o
1,1" p-. _,-I CD
00,.,..4
•
"OC,
CO0
0"_
+0
. ,<,.7,..g
g
I'q
,-I
I
I"
o
II"
"4
,0 t_-
OC>
C_ _'_ O_
elf,
+t_C
•
0
c
¢0 C
O,
•
I
|
_
v"
t_
oo
I1:
l")
o,
0,
4"
t,_ 04
i_
I_0
,
0
•
o-_0
•
_0
•
• ,,.1"
.!
I
0
_0_0
Or_
0_
0,1_
• I
;
o
•
•..t ,-_
•
_0
•
0
•
,U'_
I"
I
-.,¢
o°
0_
"4
0.0
o
O'
_
+S_ °"
*1._0
•
.5-0_
,oo
t,q
i°
II
I'
U"
CO C.3 .-_ U_
._
co o,
oe_.J
• t
0
o
•
*
o_
0_
I
I
v
,/
ro
oo
_00
_0_
_0_
_o_.
_'0_
b,_ 0
.m'_
e
I
III
T
X
_0
o
_m
m
o
_1_
eQ N
_o
o
_
_
_Z _.
•
e_
I
I
I
I
0
O, u,_ i_
.4D
_'4"
o_,. ,o_,,
*ON
I
I
,,-i
I
I
I
Z
13t
g
_
gg
e,-
0
it,
,
0
C
e t_
00,0_
.
0
C_,
C_
•
*or,
*O
•
.,,I
,
I
•
.--_
_
,D
0
°
*
I
,
,a
OC
¢,J
_01"-
0
,ore,
_
cC
_to
I
I
t_
¢0
I
O
0
O
•-_
-_
-t
C_
r_l
•
0
•
t-
-,t
0
*
0
p..
P.
•
*C'_
I
I
,i _
'
._
I
_r_
It"
O
J"
cO
OO
O,
t_l
0",
t_
I,_: _ ,.._
I"
O
¢I,
OO
_r,
O,_cO
O
00
,00
•
C_
.
..-,
O
._,dwO
•
trio
0
.,-*
I
I"
I
.
•
!
I
v
o
_0_0
OO
I'_ ,D
•DO
0
•
.
¢0
t,--
t,-_
.._
i_
_._o_
,g
4
r'--
_x_
_
,N
I
I
I
I
•
i
O
-2
O
tO
O0
0.-.,
m'_
0"
0
*0"
-_
U_
_>
E-i
0
I
I
I
I
1
•
C)
.
t._
C-,I
•
"4"
I
t'J
r'J
0,00
P'-
_ "_
_!"
I
I
I
O
_
oo
'.0
0
0
0
O
r_" rj, ,-_
_go_
•
* 0
C'_
t,#
o
P--
,--¢
.;gqg_'
,0
I
!
e_
0
O
.AO
I
0
*
X
!
I
I
I
0
O"
-.t
--JO
,0
aO
,0
_._
*cx;
,000"
•
o_
.
i°
I
•-,
tx¢
),-
>=
.Ira
Z
_21C_
Ua
_
tl_
_0
_L
-._
v
132
:-_-
_.L
:.=
0
r_
_
O0
,_
-.t"
t'./
C
c,_¢
¢'_ r,-. Cr
O_P
r_1 L_
..-I
.
C
•
,.?
l
I
C
_D
Card
0
_r
pr,
o5
_
_L.::., °
oc
0
C_ee,
•
_
•
.co
•
I%
•
I_0
•
,.-i
•,I
•
r<l
/
I
I
I
!
.-4
O0
•_r_
°_S_
'
0
_
/
I
•
I
0
eJ
c_
GO
¢r_
I'M
I
I
I
I"
i
0
•0
.r._
_0 o° _ ...,
C_L_
_D
<l'_a
0
_
I
I
I
I
_0
0
Or',:
•.C I_
_
,,,T
G_
I
I
0
I..i
•
•
C_
u'_
ba
C)
_
,D
_
o
rl
t
I
t
_°
_
_g
•4"
-4"
b_
.--.l
_
c,,j
p_
.
,.-.j
co
...-i
•
I
"4"
I
I
I
I
r.-
_0
_T
O0
,,-I
_
,--I
Pa
_0_
r_
._
oOCO
0
r_
-.,1-
.r-J
•
0
*
•
u_
cM
.,.._
I
I
I
u_
I
I'M
I/',
co
(,_
•
IP_
r.--
_0_
r-•
I
l
•
0_
i_i
I
I
t
/
/
-.I
O0
,_"
,0
_'_
O-
N.
P.-.
e¢'l
-4"
{.D
I"_
G:;
_o_
.-i
.
*
_0
I•
_
• r_
It
?
•
_o
I'M
.
"_
_1
I
i
u.J
°_
Iu
>-
F
_Z
133
_
>-
o
o
o °
•--4
CO
_0
I
I
•
,llm
II
I
I
¢M
0
0,
e_..D
q-0a_
o,_
i%1o
•
.0,_,
,f,r_
I
..--I
IN,--*
I
I
I
I
II
o
ea
oo
._
oo_
o_u%
• e-,l
I
oo"
•
• 0
,0
cO0
,00
•
,f_
I
•
I
I
I
I
I
I
!
0
_o
-0
I'M
0
_t
r,"l
•
o°
,-_ 0
,-d
o
aO .--_
•
•
_o
_o
III
i_-
00_
cO I'.-_
_
• 00
,#,
,
I
I
I
,U _.
I
F_
r_
!
o(_
•
I_.
•
I
u_ o,
I
I1!
_0 0
I
o_
I
!
I
,.LmlN
(::)0
,¢,'i .i-_I
._
0
O_O00
.-,
.=13
I I
.rim
I
÷
0
IZl
I
I
gg_
oo_
I
::>
I
_o
_.
r_
¢
¢0
0_1
o
g¢._.
I
oo,
I
0
•
LP, 0
._
I
I
Izl
0"
oo_
og
rj_
H
,-_ ,-..I i%1 r_
0 ,-'xl t_,, l'xl
L_ _ mm
O0
.r _
'--40
•
O0
rNl .-_
I
I
I
og
_t ,-_
•
I
I
I
I
I
I
I
o_
.oc0
*000_
°¢M
I
,oco
,"el
I
I
I
I
o,
"_
• cO_
•
,i_cxl
I
I
I,¢
I
t
I
I
I
i
!
I
I
I
÷
0
_o
_I0
3- ,o "M
0_ 0-4-o
u'-.
,u%_
1
I
!
>.::¥
_
c')
:_
GJ 'J.J
7
134
I
I
I
.--4
Q
_)
O
t_*
h"
¢N
0
ao
o
,o
..4
co
N
_
_J
O
I
II
II
II
II
0"
O
,-d
•
I'_
¢M
*
co
r..,
o%
•
4)
•
U_
*
_
*
{%1
,4"
•
v'
o"
o
II
•
_0
*
i_
O"
_
•0
.,I"
t.--
•
0_
•
_
0
0_
•
..4
.
O
t_
,41--'
o
0
0"
_.
o
_
_
-_
_
N
,-4
.
eM
*
_
a_
,0
o
O
o,
rtl
0_
r_
.-4
O
[--I
O
u'_
O
-,t
,,t"
O
_t"
I
I
*
_
t_a
I
I
0"
,'_
•
•
0_
_
_
0,
.-4
•
•
!
i
!
i
I
I
I
I
,4"
•
O
•
-O
El
Pq
r3
v
cO
_
cO
_
•
.-.
,..4
¢._
{_
o,_
0
I'.-
O"
,o
,0
0
o
_
,_t
¢'_
r_
0
.,T
n._
o
N
i:1
N
-J
u')
°
o
co
•
o
_
_
...4
..4
_
_
¢o
*
co
N
4-
0
aO
,-4
0
o
@
co
¢M
,o
07
0 •
I
IJu
3
1-
LU
_,0
_e
o
_
LU
'-4
•-,i
-
_
,'_
135
O,.
0,.
p_.
_
_
I
C_
0
{3
_.
(J
_
a{3
_--
I--
I'-
d.J
"I-
_'7
G.
Ci.
¢.
_
'_-
:i[
"t"
X-I 5 DATA
SOURCES
Revised
Basic Aerodynamic
Characteristics
of X-15
American
Aviation,
Inc. Report
No. NA-59-12033
Osborne,
Robert
S.,
Stability
and
Control
Research
August
Characteristics
of
Model
of the Final
Version
of the North American
X-15
(Configuration
3) at Transonic
Speeds,
NASA TMX-758,
Franklin,
Arthur
E.
Characteristics
tion 3) at Mach
November
1959.
Penland,
and
Final
April
Jim A.
Lateral
and
Robert
M.
Lust,
of a O.067-Scale
Numbers
of 2.29_
and David
Stability
Configuration
1960.
of
North
a O.0667-Scale
Research
Airplane
April
1963.
the
Aerodynamic
of the X-15 Airplane
_ConfigurAand 4.65, NASA TM X-38,
E. Fetterman,
Jr., Static
Longitudinal
t Directional,
and Control
Data at a Mach Number
of 6.83 of the
of the
Tunnell,
Phillips
J. and
Stabilit_
Derivatives
Numbers
from 1.55 to
Investigation
Model
2.98_
Airplane,
19_9.
X-15
Research
Airplane,
NASA
TMX-236,
Eldon A. Latham,
The Static
and D_mamic-Rotar_
of a Model
of the X-15 Research
Airplane
at Macb
3-50, NASA Memo 12-23-58A,
January
19_9.
Hopkins_
Edward
J., David E. Fetterman,
Jr. and Edwin J. Saltzman,
Comparison
of Full-Scale
Lift and Drag Characteristics
of the X-I} Airplane
With
Wind-Tunnel
Results
and Theory,
NASA TM X-71 33 March
1962.
Walker,
Harold
J. and Chester
H. Wolowicz,
Theoretical
Stability
Derivatives
for the X-15 Research
Airplane
at Supersonic
and H_personic
Speeds
Includin_
a Comparison
With Wind-Tunnel
Results,
NASA TMX-287,
August
1960.
Yancey,
Roxanah
B., Flight
Measurements
of Stability
and Control
Derivatives
of the X-I_ Research
Airplane
to a Mach Number
of 6.02 and an Angle
of
Attack
of 25 °, NASA TN D-2532,
November
1964.
Saltzman,
Drag
Edwin
J.
and
Darwin
Characteristics
Taylor,
Lawrence
Augmentation
W._ Jr.
System,
of
J. Garringer,
the
X-15
Summary
Airplane,
and George
B. Merrick,
NASA TN D-1157,
March
Tremant,
Robert
A., Operational
Flight
Control
System,
NASA
Experiences
TN D-1402,
136
NASA
X-_5
1962.
of Full-Scale
TN D-3343,
Air_lane
and Characteristics
December
1962.
Lift
March
and
1966.
Stability
of the
X-15
SECTION
HL-IO
137
VI
EL- I 0 BACKGROUND
The
HL-IO
airplane
one
of
a number
typically
launched
In numerous
glide
powered
of
and
1.8
is
is
Mach
Following
and
90,000
leading
edge
of
Mod
II configuration.
lifting
from
a B-52
flights
the
body
at
research
0.8Mach
HL-IO
has
vehicles.
and
been
4_,000
flown
in
The
feet.
excess
feet.
problems
the
of
involving
the
tip
The
fins
the
loss
of
was
modified.
roll-control
This
information
contained
is
by
here
effectiveness,
became
known
is for
as
the
Mod
control
by
the
II
HL-IO.
Pitch
and
conventional
using
combinations
The
The
are
stability
all
control
rudder.
combinations
about
roll
three
flight
A
of
obtained
subsonic
speed
specified
or
a transonic
brakes_
in
Fig.
augmentation
elevons
elevon
and
yaw
configuration
flaps,
and
tip
is
fin
a
selected
flaps.
These
VI-I.
system
consists
of
angular
rate
feedback
axes.
conditions
shown
correspond
138
to
actual
flight
test
points.
loops
_
o.
q4
.&.
0
%
_
E-I
v
£-_
•
_)
0
._I
o
ZJ
,-I
(D
m
,-I
ID
(.)
_
_
.,-I
0
[-_
_-®
.,-I
,-I
0
.,-I
ff'x
_
©
r_
0
N_
I
I
I
I
8
0
0
0
0
0
0
o.
o
o
o
d
o.
o
_I)
_
e4
0
.,-I
hO
.el
o
0
_1
(n
_ o%
i
i-
0
•
,-I _
4-_
0
eO .,-I
•,-4
0
.,.4
._,
.r-t
_
0
°
0
t_
•,-I.,-I
00
_
OJ
4_
Od
OJ
4_
!
C_J
!
eo,...t
.o
v
o
.,-I
0
0
_
_
_
_
e8
_
al
,'el
II
.la
_
II
II
II
II
i;
bO
_q
_q
M
_q
139
O_
0
0
0
--
...I
O_
-
_i
/I
Ix
4,n
©
11 --\
_,,.
/I
0
0
i
H
-r4
-o
C-_-'3
C2- -._
C:--_
o _. t'__ __. -il
II
C_.-_"I
_lI
U
0
._i
140
HL-IO
PITCH
AXIS
(_eSAS(rad)
Gearing
Feel Spring
_ST (in.)
I
FST (Ib)
G
-_)_
(_e (rad)
57.3
6.5
!
-2O
-I0
1
I
_e (deg)
0
I0
I
--
-2
G(deg/in)
-6
ROLL
AXIS
(_aSAS(rad)
Feel Spring
SST
I
ST
FLAT
(Ib)
YAW
I
(in.)
Gearing
2.7
_,_
_
_o(rad)
AXIS
8UsAs(rad)
FpED(Ib)
(Sr (rod)
22.2
Figure
Vl-3.
HL-IO
Control
141
System
HL-I0
PITCH
SAS
(rad/sec)
_eSA S
ROLL
SAS
p(rad/sec)
YAW
8aSAs
SAS
r (rad/sec)
Figure
=
VI-4.
HL-IO
J
s 7"._,3
.4s
Stability
t42
I
Augmentation
_
arsAs
0
n
o
U_
TI.D
, /
/
/
/
.-. /
OI
//
•41"
,I--
,¢--
/"
/
,¢--
0000
0000
oooo
jO000
,ll l
/
_.
J"
='_
/
I ! I,
®
II li
i
.,p
to
o
/
(
x
'%
L,,,p ,,2
,,_
I
n
I
I
--GO
i
I
I
I
I
0
0
(xl
(_]
(x]
--
--
o
143
0
°--
O_l
--
0
C-
®
¢0
U
®
-- Od
o_
'
1
_P
0
_J_
_
'r_
I
I
I
I
I
tl_
N
--:
1.0
t'M
."
J
o
o.
q
0
q
0
©
Od
0000
0000
0000
-JGGGd
o_cx],_-
_O 00
II I!
li
Jj
J__"
i
Q
®
r-
I
I
I
I
I
q
.-I
(_)
144
1
o
0
0
Q
OJ
!
/
#
#
.a
/
' _0
/
l
LI..
/
/
_l.. t@-- _I"
0000
0000
qqoo
.J
cO
oodd
/
}
0
_o
--CO
®
--C_I
i
i
ro
OJ
i
0
i
0
!
.J
-?_
0
145
0
O
0,1
(D
0
IO
N
.c
o
--
4
o
o
'1J
(D
-
I'
ill.
,I$--
_e..
_lj..
000
ooo
ooqo
.ndooo_
0
I
I
I
O
0
O
I"
_.
_r
I"
!
_T
÷
°_
o
E
v
C.)
146
"_
o.
0
0000
0000
.Q
o_
,
J_
'-!-_
oooo
\
/
/
jO000
\
_
/
\
N
m
,F
0
0
(,
,,%
I
I
I
S p
CO--
--CO
0
0
0
0
I
0
0
147
I
1,0•
!
m
-I
I
O4•
E
o
"-
!
\
B
i
\
x
•.= ,,_
_o _ =,,,
, _ID"o
J _1" 0
"r" _4DgD
a_
00
!
!
/
I
®
I
/
0J
N
o._
!
!
!
m
m
o.
o._
!
I
t
U
o
o
CO-
--
01)
I
II
0000
0000
oooo
._10000
, I!
I
I
,
0
I
I
I
I"
q
m
,_
!
!
0
II
I
q
I
1
N
I
"m
o
0
0
I
I
I
I'
I"
I"
0
I
m
0
148
o
llb
¢0
GO
m
U3
¢n
x
0'_
"10
-Ao
O_
C_
(
Q
m
0
o.
__
eU
t(3
t3
QD
GD
GO--
--
LO
L'_I--
l
0
0
I
---:
_
I
I
Q,
_<
C)
i
i
I
I¢)
O_
-_
o
0
I
I
L_I
--_
I
,
"10
c3
1,.
o
0
I
I
I
I°
I
i°
0
D
!
e.
r_
_._
t3
-(_
t_
lb.
lh
149
_
o_
oo
_
(
_oo
II
_\\
I.
0
_0
'W
I
0
I
I
I
#
#
I
7I
I
I
0
o
•
i
q
o
I
o
I
O
q
I
o
q
q
a7
m
_,, n13
0
C_
,-_
o
0
0
o
1
I
I
_"
_
Oa
q
q
q
O
m
,-
v
L
V
150
0
Oa
q
q
!
!
GO
m
°_
0'_
_O
tO
o.
q
-J o
co
GO
I
0,1
I
0
0_1
I
_
"-:
I
0
_
I
0
0
0
I
o.
I
I
o.
o.
I
o.
0
0
0
I
I
Lo
0
0
--
I
t,.
>,
"_3
C.D
Ib
v
151
I
!
!
m
00
ek-
!
"0
0
4-
0
C_
I
÷
C:
-/
0
"
•
+D
1"-
i<_
I'_
r.-
_r_
,
T
7'
•
0
.
o
0
•
?
o
N
I
T
I
Io
0
•
_
t'-
u_
CO
I
0
0
0
0
t
I
/
o
T--
¢-)
0
•
_o
+ .
!
o
c)
•
?
%
0
I
o
I
|
?
II
0
_2
?
I:%
0
•
•
..0
_
_
eq
t'-
_t_
,
I_2
N
0
0
0
0
T
+
T
7
_p
•
I
C
I•
o
0
I*
0
l'
*
I
_
:
I
"
I"
o
I
I
.4
c.d
I
_I
I
I
I
i
I
I
l
I
I
I
,"
'
l"
I'
I
'
I
I
I
I
I
I
ix
c.,
•
v
cJ
/
I
m
"_
I--I
.
0
0.1
n
H
0
H
_
I'
0
o
_
I
I
_
u
.,.-I
0
o
o
4"
I
I--I
l
o
0
o
0
_
I
I
0
e_l
I_-
•
G3
o
F'I
_
1"-
R
0
_
0
I"_
0
I
!
I
0
0
0
I
I
I
I
!
0_
I
0
0
!
•-4
0
0
_
C"
0
_
'_
0
0
0
"_
"f
0
I
I
I
I
r_
_
,D
_,
C
v'
o
0
0"
o
._
o
_
o. o. 8
,4"
_
.0
_. _
I
I
0
o. o
153
o
,--I
•
_
_
_
I
I
_
u.
o
t_1
_D
uJ
I
I
uJ
u_
•d"
i_.
=_
,.0
.
• _
b_,
-,t
...._
•
_C_
_1_ C2 _+
I
+
_'n 0
0
P--
• .'-+ 0 _ C?+
I"- 0
*
•
fM
• Mr i.,_
I
+CCC_
!
•
,0
*
_c_o
"00
I
r_
i_
...i
,--_o
M-I e..4 i_
c,,_
Oo
0
I
I
_w
t_
0,.I
(_
I.
ot+.•
•4
IF,.+
COp.-
.o_
00_
I
x:
o
e fl_, I_
_0_
,,13O0
•
•
I%1 0
et'¢_
!
O_
E-I
_t+
rj
v
o
_0o
eell_
I
.._
Ln
+¢¢_
O_
,
.
,.-4
_
.
I
*Oe'J
'
I
_OOI_-_
I
•
I
O"
g_ f-.. O_
ef_O
,
e_
I
*+--It--,
_OCO
•
(M
•
•
I%1
O0
!
o_
_0_
.*00"
+',o
1])
-p
_0
_.+ N
r'J
I
{MO
I
,
I
_o_
O0
•
•
+=
ih..
•
I
fi+-2
I
I
+
I
I
*
I
_>
0
_
_
•
-O'_O
I E+ ,.-+ •
_0 o o ,,1"
_C.)
+P-
I. °
o_
eet _. 0D
+ ,-I p-cxl 0
_rl
,..+ •
I
++_.+
cx_O
0_,_
"1" 0
0_.
_0_
,_
OU_
O_N_
_Oe
• 0.,I _00
,00
•
I
I
o
N
o
•
• ¢_
_00'0
I
I
II
I
I,+
_C_an
_0
•
.Ocq
Os
•
I
N_
I
•4J 0
•
P+* Pr'i x,+"
I
v
0
0
e L,'_ 0
•-,
o_.
:__ _._
•-¢ 00
.
0
-_" _0
_',,
0
_J
_00_O
et'.-
0
_,.
_
Z
w
ww
_
154
+m+;;
I
000
I_
I
o
_
_+
i_
_÷
+ I-++ ,0
.
r,+- ,.t ..+
•
I
•
I
I
_L
o
_
,
+.+
c+
_+
_
txj t;
c+ oh
(P
_
C.
.
Iz+ G
• u
l',J c+ ..
I,+ .0 ,-<
• r,J
it
. + ,.+ co
+ t+-.j t+ r_
I'
o
*
P.+
• pr_ pr
|
ac
.C+ •
,.-< c._
?_
_
(jl_+_
+ (j
•
cD t-
I
•
c_o
t
,
.
c._
I
y:
o.0
pe_ t_.
cJ
+ rx, .._
0
rr,
t'+ cO .-+
¢
b_
cxl .-+
m /+ _
<,++
P.J 0
*
j_
T
•
I
c_a
• I,<_ <:D P_
G
.,<_
•.D
0
<>
c_O"o
_0_
aO
_0
i_1 o
t'J
I
*
• I+", u-_
I
_
I
_v
IX;
o
O
E4
,d3
_0
t_J ._ N
u'_
coo
c¢_ i:_
,_co
rj
o-
txl
+-t
<t
•
g+o.o
o
,-4
!
I
*O'.'Xl
,--40
0
I
I
,
_
•
m
O"
I
w
O
[-4
_
o_'_
O
,d
b+,, C_ rr.
o_
p+.
(0_o
•
* e+j
e,_ r--
P,j o-
•
<_
t'I
l
a_,
I
I"
I
v
o
a_ co -_
<_ O0
u'x co_, ct_
• I'4
I
"-I
c_
",r,.r... .-i
co o
CXll_
O" _
.
•
i_
*,+o
,o co
o
{_-1
+ l'xt P'J I_
e_J 0
•
I
•
{o txl
+ r_l c,+ ++.T
"40
_0
o_o_
ao
t--
•
++-+_
!
. t+,,l _0 eO
U-x _rl .--t .0
,,00
'
a0o._
o_¢_o,_
+.-+ •
I
I
,'-_ C)
I
'
I
o
|
I
q
I
o
l'-P'-
•
O" _
,0
0
+..+ r..
•
i
,esl
,_
.o
_n 0o
e,l.t
t_
0o
¢'J 01_ t_
_00
I
0
_
N
,_
•
o_ 1_
<<_ p..
*
o
O,,t_
• _.t oO
coo,o
_D 0
<",J +.--+i._
•
+..+ 00
P.J
Pc+ ..t
•
0
?
_
+..+
L_
OOIII
_
z
155
N
o+
I
I
coo
+-I en
CO
Z
, i_
r...
T-.T
_
•
0
•
G(
•
•
r_
•
,,4
•
¢0
I_
•
,-4
0
,o
,_•
I_
,._
ie
C:
|
0
I
I
0
N
l"
!
h-
um
O"
•
,I)
,.4
•
I
0
_
•
•
v
I
,,
o
_*
$
o
0
LU
_,•
l
I_
•
LL
•
•
m
I
_
e¢1
,_
ell
,0
un
o
_)
•
o
_
-,I"
_
rq
_
0
O,
,-_
-,t
I
•
I
v
v
_J
_
_D
-r
u.
156
LU
o
0
,
-.,"
?
T
_
,
,,t"
•
,
;
,
,.,t
O
o
I
I
_
O
0
•
•
I
0
_
I
I
I
I
+
I
•
_
o
_
• _
._ .+
0
. J
l_-
®
.;
I
_
o
a_
I
I
I
I
•
o
,_
I
I
_-
0_
o
o
I
•
I
.4"
,._
C
I
.-+
I_
t._.
_
!
O,
0
u_
_
cO
o_
0
,-,•
o•
_
_
I
I
u',
¢
_
_
_
4"
m
m
,.1
o
_•
.'-'•
0
o
I'
I
I
l
I
•
I
t
I
I
I
I
I
•
I
I
I
I
I
I
I
I"
0 _
l_
0
I
I_ .....
C
I
!
I
,;
•
,
I
I
1
--
_
0
.,P,
I
_
o_
I
0
_
I
_
,0
ao
(.3
I
I
157
I_
•
0
•
I
O'
0
--
o
f_400
um
um O_ 4" _.00
f'- 0
O,
_o_
q
.4
0
a[
0
oO _
G"
_o
_go
o_
@
I
v
o
o
_
00
..d r--
u'_ •
_0
_
•
_0
._t
I
P-
o
um_-,
_-0o_mo
0_0_
',.q_
P"-O
-
c0oo
0_
I
I
w
v
A_
o
a00
LF_
._7,_
oo _
_
o_ _,_-
u-_ ur_
_0 0
"
_o_o
0_
O'4"O
_'b o
I
•
I
÷
v
0
o
o"
_0
oum
0_
ocx_O
•
_0
00_
o_
0_
4"
•-_
o
f'.,i
• 0
0_
0_
_
I
_-_
>
rY_
_>_
I
÷
o_
r_
0
co
I_.
_0_
,ooi%1
_0_
"_0
o
I
I
oA ÷
0,
_o
o:g,O
,0
_0_
0_
,--_
ooo
r.-,
t_
•
._t
I
w
I
0
7
*
_
-4"
o
,
I
_A
°_oo0
¢¢1
I
•
,
mm•
•
I
°
I
v
o_
g_Z _
o_
rq 0
_t ,0
•
• ,0
I
t
158
,i,_
o
•
,t,_
OC
o
•
,
I
(_ o_ r-- I-• o
• •
-,_
,:_
co u%
_ 0- .n e%
• co
•
I
,
ZJJ
I
I
_o
0,
0r-_¢u
,.-4
o.-_c
•
t_
0
I
I
I
I
I
I
..o._
II
!
I
v
•
•
o_,h
• C,
o
•
•
.
°
.0
,rr)
I
I
"
o
_oo _o
o_o
0o_
0
_0_
'
o
o_
I
I
I
o
_0
8
o
•
.u,%
o
• o
b-O-O
u'% _
._4
_0_
I
I
!
o_
°o.._
II
4-
:m
v
8
o
[-4
o_
----
O_N
oo_
_o
_
0_
_o_
I
cO
rj_
,
•
I
I
II
I
I
II
+
CH
o_°
U_
4"
e_J
o'_ ,C
_0_
I
ao
.
o
o
o_
._o_
_o
oo_o
!
0
÷
o
,_c
_0_
!
I
!
I
o
co
o_•
u- .-_
,c_P-
.u',
oo
.o_
.
..4'
I
O[" O_
I
o_
_
II
_v
_N_
_N_
_znzz
7
159
÷
0
p-
o
_J aD ¢_
•
0
.00
C5
o
r.--
•
*_xJ
;.-T_
I'
I
.p.
x'
0
4"
O"
(7_0_
• o
,_-¢
t.
o
o
I
÷
w
P-
_
_o_Z
o,
I
I
aDO
_0_
O0
+
,','_, _'x_
_oN*e
I
a
v
°
0_
_o_
..NN_
0_,
I
I
,_
oe,,J
o_0_o0
_0_*
r--
0
I
_0_0
_0_
00_@
I'
I
I
I
o
I*
o
•-_
o
c_
CO
*_
I
77
160
7
_00_
r'm r--
..T
I_Oooe
p-
oc
•
•
t
l'_
cr _¸ ,4
•
I
•
I
•
g
ON_
o*_
_NOl
_,
...._ 0
c0
•
,t
,-e ,ID
,.-0_._ d
•
•
,O
,._ _r_ N O
,42
,..._ _0 N
0•
O.-0
•
eP.•
• t%l _a'l ,..4
J
,'d
.rl
o0_ee_
_Oe_
•
_ee
O
r...)
¢
0'x
_0
_0_0_
:>
•
rx;.4"
•
I
•
I
eP'-Q
°
°
_e.
I
161
2
o
o
e_
0
,_
h0 "_" •
t_- _
rq _ 0
O0_m
,CO
C;
• ,.--lrl_
• I
,N
_t
O"
¢0 0
•
I
I
4.
_
_m
_o00
I
v
o
O"
,ON
0"
h-
•
0oo_
O0_eO
I%10
,e
• cr_ M'_
!
4-
0
o
•
0_
•
•
I
÷
0
0i'%1
"0
•
• r_
_000
_0
• 0_
0_00_
•
•
tX.;
÷
0
O_
_OOe
c00
00_
0
,_
_°
_g.
-.t,O
_
o_o
_
•
•
• ¢M
.w'
,,1"
o
ON
r_,O
O_
"_
"0_,"
I
0
0
ONO_
_0_0
_0,
o
_0_0
._,m
I
I
o
0
N
_7
162
7
I_",I_
•
•
_o
_ooo
_ite
I
r..- 0
_-
o
Ot_,O
0CO
I
•
I
I
_'_0
1
•
I
O0
•
o_
0_
i'%_
erq
o
oo_o
I
I
•
_I" 0
erl
I
*0
I
I
•
I
I
• 0
I
•
•
I
eO_1"
• .-_ N
_0
t _,i
,,,_
"d
_o_
.,-4
o
r...)
0
N
•
I
o
I
H
,.1-0
ir_l
,_ ,_D
0_
.-_
erXl
• ,.t ,0
I
•
_
I
ww
0
_0000_
_0_
!
I
• Ot_ _,
I
I
e._,--I
I
163
o
o
_
o
_
o
,_
I'_
_
.
..--4
"_
MI"
0
_"
_
_
_
_
_
_
_
_
_
,4-
r_
_
4"
I_
t_
P'%
*
.0
-'%
,0
.4"
,..,
.-,
,,
t'n
aO
O
,4"
*
(_
,,o
i_
o•
0"
_1_
¢0
•
,...,
•
•
,-4
•
(%1
¢'q
•
_•
:'4
I'_*
*
@4
,vl•
,-4
t_i
*
.,I"
,-_
..4
#n
*
•
0
•
_r
•
*
d"
I
I
.
I
I
I
0"
"
_
I
I
I
I
I
i
I
I
I
I
I
I
4-
t_
O
,o
r'.-
E
*
,=4
_
•
•
4"
..,
0
4-
t_
•
_*
,0•
•
,-4
*
i
_
.-,
c_
•
I
÷
0
.
.,11"
.0
_
0
I--
.-_
.-i
I'M
("-4
r_.
£
_,
co
•
.-_
,'.
0
0
"T
_
-- %
164
.
.
.
.0
HL- I0 DATA
I
•
,
_°
SOVRCES
Ladson,
Charles
L., and Acquilla
S. Hill, Aerodynamics
of the HL-10 Flight
Test Vehicle
at Mach 0.35 to
TN D-6018,
Feb. 1971
Pyle,
of a Model
1.80, NASA
Jon S., Lift and Drag Characteristics
of the ML-IO
Body during
Subsonic
Gliding
Flight,
NASA TN D-6263,
Ware,
Lifting
Mar.
1971
George
M., Full Scale
dynamic
Characteristics
Wind Tunnel
Investigation
of the Aeroof the HL-IO Manned
Lifting
Entry
Vehicle,
Oct.
NASA
TMX-1160,
165
1965-
166
JETSTAR
The
Jetstar
is a
conventional
ailerons_
mechanically
actuated
activated
The
but
assisted
primary
aerodynamics
source
were
test
data
engine
elevators_
with
and
hydraulic
of
aerodynamic
the
servo
using
control
latter
transport.
rudder.
boost.
a
The
from
utility
by
estimated
_TC-TDR-62-24C-140.
flight
four
BACKGROUND
Controls
Ailerons
The
rudder
and
consist
elevators
of
are
is mechanically
tab.
data
CR-544
system
and
NASA
flight
description
reference.
167
was
CR-544.
test
was
data
based
Power
approach
from
solely
on
_,
rn
o
r-_
_p
Ca
:>
0
-M
0
.rl
0
C;
%
,--t
_
%
o
L
I
o
I
I
"_o
,
0
o
0
"-"
"-
0
oJ
4._
.i-I
o
4._
®
,-q
v
"7
I-i
I-4
oJ
oJ
z
_o _
O'x OJ
OJ
c_
OJ
r_
o,J
oJ
0_J
4-_
0
I_0
_I
r-I
_,o _ _ _
I--I ._I
.-=1
__Oo
E-_
_
•r-I
0
CO
_
o'_
0
o o__
_g_o
o
oJ
oJ
Ox
0
b_
lf_
_ _
_o_
0
,
_
o.I
_
_
II
N
168
.
_0__
,-I
.,q
¢)
0
11
_
II
.._
LO_
II
0
0
_'_
II)
H
a3
4_
0d
c;
I
..A
t--4
.r4
N
II
II
II
169
JETSTAR
PITCH
AXIS
I' I
FST(Ib)
Note:
-_ 52
Angle
h/nge
ROLL
8e (rad)
+ 2.95CI
of attack
moment
effects
are
on elevator
neglected
AXIS
LAT
F ST (Ib)
YAW
=
.75_q
I
8a(rad)
AXIS
-_ 8r (rad)
FpEo(Ib)
Figure
VII-3.
Jetstar
170
Control
System
TABLE
VII- ]
JETSTAR
Power
Approach
Non-Dimenslonal
h
=
sea
level
VTo
=
224
ft/sec
%
=
6._ o
Longitudinal
Stability
=
132._
Derivatives
kt
Lateral-Directional
(Bod Ax±s)
CL
=
.737
CD
=
.O9_
Cn_
=
.137/rad
C_
=
--.IO3/rad
C_p
=
-.37/rad
Cnp
=
-.14/rad
=
.O/rad
CD a
=
.7D/tad
Cm_
=
-.80/rad
Cm_
=
--3.0/rad
C_ r
=
.]I/rad
Cmq
=
_8.0/rad
Cn r
=
--.T6/rad
CLSe
=
.4/rad
Cn_a
=
--.O07_/rad
CruSe
=
C_Sa
=
.054/rad
CySr
=
.17_/rad
Cn5r
=
--.O63/rad
C_Sr
=
.O29/rad
--.81/rad
171
SL
20,000
ft
40,O00ft
JETSTAR
38204
Ib
12I0-_0
(deg)
8642-
0 o
.2
I
.4
I
.6
Mach
172
I
.8
-- OD
ru
-- 0_
0
w_
o
q
q
q
a
C.)
00
00
_00
o
o
S
--00
_
II
!
J
11
rc_)
--0_
I
0
1,
tO
_
I
I
OJ
-_
0
..J
173
6CLa
5
(rad-i)
4
JETSTAR
38204
Ib
5
2
0
0
1
.2
I
.4
Mach
I
.6
I
.8
I
.6
I
.8
1.2
.8
.4
%%%,
0
0
I
.2
t
.4
Moch
174
Mach
0o
.2
.4
.6
.8
I
I
I
I
-.4Cma
(rad "i )
.....
---- -----
JETSTAR
38204
Ib
.255
SL
20,O00ft
40,O00ft
Mach
0
0
.2
.4
.6
.8
I
!
I
I
-.4
Cm&,
Cmq
(rad-I)
-.8
_'*'_:_)
Cmq
-1.2
175
CDM
.08 t
(rod "l )
.04
-
0
0
.2
.4
.6
.8
Mach
Moch
0o
_o I
.2
.4
.
.8
B
-'.2t
CM M
-.3
-
(rod "l )
-.4
-
I
"o 5
-6
-
SL
....
-
JETSTAR
38204
Ib
.25_
20,O00ft
40,O00ft
176
CL8 e
4
-
.2
m
CL8 e ,
Cm8 e
(rod'=)
0
)
.2
I
.4
I
.6
I
.8
Moch
.2
JETSTAR
-.4
-.6
n
-.8
-I.0
177
Mach
0
0
.2
I
A
I
.6
J
.8
I
-.4
Cy_
(rad -t)
2
5
3
8 4 6
9 " _,,_
-,8
-----
-
SL
20 O00ft
JETSTAR
382041b
40,O00ft
Body Axis
.2
_-"
-"_(_- -_
Cn B
.I
Cn_,
Mach
Cj_
(rod't)
0
•2
.4
.6
.8
I
I
I
I
c_
:2
178
Mach
00
.2I
.4I
.6I
.8I
-.2
C,_p
(rad "I)
-.4
JETSTAR
38204. Ib
Body Axis
SL
-.6
.....
--- ----
20,O00ft
40,O00ft
Mach
0
.2
I
0
-.04
.4
i
.6
I
-
Cnp
(rod "i)
-.08
-.12
--
-
179
.8
I
•
---'----
SL
20,O00ft
40,O00ft
JETSTAR
38204
Ib
Body Axis
.2
C_r
C,t r ,
Cnr
(rod "i )
0
I
I
.2
.4
!
I
.6
.8
Moch
-.I
Cn r
-2
180
SL
JETSTAR
20,O00ft
58204
Ib
Body
Axis
40,000
ill
ft
.08
CYaa
(rod -I )
.04
O0
I
.Z
I
.4
I
.6
I
.8
;
8,
Mach
Mach
0o
,2
4,
Cns a -.01 -(rod -l )
-.02 8a is deflection
of aileron
on one slide only
181
Cy8 r
2
5
3
846
""_,o
._
(rod -I )
I
.2
O0
I
.4
I
.6
1
.8
Moch
Mach
0 o
-.04
.2
.4
.6
.8
I
I
I
I
-
Cn8 r
(rad "i )
-.08
-
'
.....
SL
20,O00ft
JETSTAR
382041b
40,O00ft
Body
.04
C_8 r
(rod "l )
.02
0
0
I
.2
I
.4
I
.6
Mach
182
I
.8
Axis
N
C3
C_
•
t_
h
Lr
-.t
_
¢_
t_
t_
,-<
_
_
N
_
•
•
•
o
r,J
_-
C
C:
c
f_
_
O
r_
C
I
I
O
c_
o
c_
r,j
I*
o
I
in
g
I_-
l"-
,_
t_
I%1
O0
u'h
_
0
o
O
_0
o
i°
0_
co
N
c>
H
El
H
¢_
I"-+
0
03
N
r,i
0
0
o
o
N
I
O
_
0
•
i_
0
0_
,_)
cO
I"
P-
"-+
o
_
_
lib
°
°
i°
I
H
•
g
_
•
_
::
.;
-
i_
i_-
.-.+
.
_._
rq
•
co
•
h
O
t}
t_
N
+
u-_
t,3
u_
O
u_
_+._
c_
_-x
0"
,0
0o
,0
r_
I
I
I
_r_
f_
_'_
O
C>
_
*
•
O
•
O
O
e,i
c_
o
•
•
_x_
o
o
I'M
0
0
_1
?1
!
r_
[e
O
*
•
_
c)
bx
183
o
"_
o
u_
,.t
o
o
N
,,0
I,_
I'M
_
,,0
".0
I°
,
oc_
u",
4)
_"
c '¸
c_
':
•
I
%t
_,
_4-
(_.
•
o
C2
0
•
G
|
"4
_
O
0
I_
•
C_
t'-
O
_
42
C_
c.D
C_
O
•
"4"
C'.
0
C._
O
0
.
I
•
I
ie
G
e
0"%
c_
I"
I
•
i
I
I
•
I
_,_
•
I
C.,
0
•
I
•
I
I
I
CO
_
c
I
C
_
•
•
"
•
I
0"
$'j
C._
O
Ca
CJ
N
¢_
•
C,
O
¢_
I
_
_
C)
•
I_
|"
T
_u
o
•
I'
I"
°
'
T
l"
le
0
0
I"
T
P_
_
I
"_
_
•
I
t"
I
I
'
I
I
I
I
"
I
°
0
I"
0"
•
0
0
;
!i
•
o
,
;
.
,
I
•
I
,"
'
I
I
o
I
I
'
I
-
I
I
I
I
•
•
I
e
I
0
e
I
•
!
0
I'
_
i
_-,
._.
I
_
I
0
°
e
I
!
I
¢W
_
t_l
•
0
O
I"
,'_
00
.4
I
I_•
I
0
0
0
0
I"
0
0
I'
_ ,
e_"
I
_
!
"
'_
0
0
O
I
o
0
"_
_r_
I
I
0
_D
?
_
0
•
I
I'
184
0
0
I"
U%
"
l
"
"=_
_"
,=_
"
r_
I
I
0
0
0
u_
I,
c
c
-1" t_
o_
r_l
<10_Lt_
i_
•
*
_,
,l_,r
txj o
_ t/_
_(.
e (_J
I
I
I
I
*
I
I
r-_ Cr_ 0
_
O0
e_
_.._#
"_
?~o.
c_
o
r_.
...-4
C- r,_ 0r.
,--4 0 tr, re, e_
,o_
r--- 0
I
,
•
I
t,-
._
°
°
_0_
I
•
!
I
I
_.o_
ot_
z_J r--
• o,
_o
•
I
•
,0_0
,e_
._t
I
<1- ,-_ O_ U-
•
£'b
I
•
_'_ 0
_
..+
0"
I
..,,_
_
_00_
_
7
I
v
o
ou-_
co
_No
,OC0
o'_ 0
00,_
.e
I
I
•
I
H
o
_0_
o_
t_
o_o_
I
P-'I
•
o" r,.- o
r-d _ 0 _ O"
oo_
.o_
I
_
I
II
r_
l_m • ,or,)
, ._ ..t ..t
o
frl
,-_
_u .-_u_
,.1"
,..i
I
!
t
w
I
w
o
_
_o
_q
_0_
°
•
0"I ,-_ _0 CO
nr_ ..-d ,.4
• 0
•
_00
ol
,_
.,oog
oo,_
•-<o
I
•
•
,ff_
I
o_
r--
ecol'--
r_
rq
ff_
_O,e
I
o
I
_
_0
o
_
_0
,e
_
e_IO
v
I
OIII
z
185
0
•
.
_
. eel
_.L C.D
c(,c
I
(D
0_
CC_
•
°
I
,
u't..
E
¢\J
C,C
"
•
I
!
I
I
!
v
0_
'_
0
U".
,_D
¢_10
O
0 _
r_
1_
0
•
G
Cq
c_
0
e
I
)._J ,..4 ¢'_
0
_.)CF_C
• C_
,_D
•
!
C_
•
!
•
,
•
I
I
00_,0
OOe'_
eel
l
I
O0
_c?_ _.
C,
0
I
txl
,4
o_
0
,,t"
_
•
!
oo_
!
0
O"
W
,._ I_1 CO I'OOr'_
000
O0
_0
O0
,,0
•
_o_..
O_r_
_..7 _
•
• ,-i
?
00_,
OeoN
._
0
•
0
_
o4er_
.0
|
•
•
I
0_
_.,_
N _t u-_
O,D0
_
0_
00_
!
UJ _t" trl
•
I
I
0_+_
00_0
O0
•
•
I
I
•
!
_
_0
0_
•
I
._D
,-_
I
I
•
I
_0
O0
ee
¸
0000
O0
l"
0
OLr_
_
l" I"
I
•
I
,_
0
o_
0o_0
O,,e_
"II
I
u_
U_
0_
0
N O_ r-00,,1"
0
•
e¢_
eOe_
U'_ _
0(7"<)"
! I
I --
,,0 p-
-JO
O0
o
,-_
0_
00_
00_._
•
"
•
,N
o_,_
0
,o
i I
I
!
T
I
_0_
U'_ O_
0_0_
o0_
0_,_
!
I
•
•
I
N
I
•
I" I
•
_0
o_
oo_0
O_
o0_
0
•
• I
t wv
•
•
Ofq
•
•
I
w_
,
I
w_
"
_,'F'_
T
_oo
"",,I'0
0 -,f"--'
0
, •
• I
_
•
I"
!
_0
=JO
u_
0
|
T
_0_
0
•
I
e_
_o_.
•
!
w
I
_N
U_
_ww
.%
U.
w
Z_
Z
186
Z
•
!
I
I
0
F._
C"
0
o
t_
C
_)
•
00
O
*,I
_
o
Go
tf,
tih
,.4
o
o
if.
o
o
N
•
,
,-4
I
v
O
0_
•
C)
_o
_t
0
o
N
I
E_
_o
_
E_
H
q-_
09
uJ
x
uo
I
_
-J
u_
,-_
N
0
o
C)
o
t
,0
u _
N
•
0o
I'__"
_t
"4"
,0
Q
U_
00
_
0
,1"
I
I
I_-,1"
•
I
O
N
O
N
O
O
¢o
lh-
V_
N
0
"r
_..
U
N
-
O
I
•
o
I
•
Zo _
U.
w
187
0
0
0
0
,-,
._
cO
O"
0
",I"
_'%
,0
v"
I'-
U%
•
O_
0
I'
0
I
I
"_
0
•
CO
I
I
I
_
_
_
_
•
o4
I
¢_
I
_
_
_
I
_o _
_
¢'_
I_-
--4
t_
I"
"_
o
_. _
I
""
I
_
U,_
O_
e4
_
un
0
e4
_
-0
I
0
I
0
,-4
I
"4-
l'_
0
O_
0
I
I
•
•
o
•
I
•
•
0
•
"4"
o
_
•
•
•
I
i
_
,-4
U%
"_
I'
_
_
_
_
I
t
_
_
I
I
_
I
_
_
I
t_
t_
I
/
0
0
"4"
un
I",-_
I
0
•
CO
t
m¢'_
•
I
c..)
t_
_
0
0
aO
¢%_
0
eJ
,-4
_F_
I
!
I
'4"
•
"-,2
CO
0
,,-4
0
I
I
I
-_
_
_
I
_
_
¢'4
_
0
•
•
I,
_'%
_
_
_
I
.:
I
•
,
0
_
•
I
,-4
_
_0
o
_
...4
,-4
•
t_
•
0
_
4"
_
,-4
I
_0
,-4
t_4
I
_
t-.-*
0,4
_
_
,'_
,-4
e4
I
!
4"
,"4
•
0
-a"
0
•
I
t_
0"
I
I
_
t"
,,It
C- "_ ._ Z
•
_
•
I
_
_
0
0
I•
•
_, _
.
_
"
"
I'4
t%l
I
o
_
I
4"
_- _
,-I
f_
_
,4)
"4"
_,-
0
0
•
I_"
0
I
®
...4
I
d
I
,4"
t,_
_t
0
_
_
•
,0
,,1"
_
C)
0
_'%
•
I
0
!
0
_%
_)
!
I
_
•
I
I
I
-0
,-*
,
I
I
I*
_---J
I
•
0
0
0
,_ _•
D'-
.
0
I
_
_
I
,0
,-4
_
I
_
"4"
|
I
0
I
,. _
•
O_
0
-4"
,0
,,0
o
t_,
I
_"
cD
_0
0
o
0
e,_
0_
o
I_
,_
I
_
°
0
0
•
I
-,1"
wO
I
i
o
...r.
x
>-
--
-,
z
_
188
z
J
z
>.
_
z
>-
"_
z
o
oo°
_o_o.
0
O
_O_
O
,_
I'_0
+_o++
•
cMO
O
0001 cO
q-
#
.
•
*
0
•
IPM
.,-+
I
•
_
,0
0
....i
I
I
I"
_g
_
aO
_D
_o
O
I'-+.
0,0_0
'_
If_
p--
_,
N
euo_
o
10
_O
,..+i
"_
I
I
I
I
I
0
OC,
o
u_
o
_°_
0
o,o_,
+,
.0.-4
!
I
I
I
"L
°o
_
o
NG
h
cO
t_
O
"0
O,-'+
I_-
N
O
sO
_0
cO
ue_ _
p<i O
•
+OO
'
co
•
<_
0
,
IN
I
I
I
I
p_
p(D._
-I- C_
.0
_0_
_O
co
co
•
O
P•
•
O
+.-,i
O
"-4
I
I
I_-
<1" ¢_
I
!
H
_O
_D
I
G_
cO
0
o_
I_-
•
,-+
,
I
G'J
._
_0
0
,_ o o. q
_o_o
O_O
,.-i
(w_
_0_
_0
,,--I
"N
,-i
I
I
CQ
(2s _
p-+
,--.I
t_
0
.4"
_"
N
N
c'3
0
,--_
+
_
oO
,-I
.1i-_
•
ll'l
i
O
_
,.O
,_
I
b-
_,
N
q_
_N-O
G'
",O
O"
_.3_
<+_,l O
_.
,-i
(:u
•
,--I
•
•
<+_
,
.-,I
N
J
E-I
O
cO
0"
•0
_
t_
•++'._ ."M
co
<:3
•
,-i
,-i
,-.+
+
.,_
+-J
O
o
+.-i
_
t_'+
,_
¢"+.1
,-+
O_
r¢_
+....+
-+,t
tl_ t_
•
.
!
l,l_
_,
O,-4(',I
• .--.i ,.P+
I
_ <,'.+:
U_
0.0
*_-_
0
c,,I
,
I
+-.I
_j
tr_
I
N
I
,
I
"4
0
•
+
._
. .-_
O"
c,l
I'M
,.,...+
•
.
eO
,O
.-i
I
I
I
,,-.4
O.
Z
189
_N
"--+
Z
,
o
o
o
_°_
oo
_-o_
,
r--o
II
I
*
I
I
am
_o_
0
.o _j (,r_
,0
•
•
°_
•
I
t
I
I!
I
4_
o
oo°
o_o
_
_-0
* 0
O
,"_
r,_ r_
o_
°o
°
•
I
I
_o
'
I
li
I
÷
o_
rcl ¢,_
0
'0
*4"
O0
,o-*
•
4"0
o h..
_
*
,0
I
0
,_ q"
• o
0
'
¢XI
Lf_ ,-4 ,-_ o
. 4D _ rJ_0
4"0_0
•
'-40
•
._4
I
!
•
_
•
I
I
_o_
0
oo_
_0
•
I
_>
._
I
I
I
I
01
+
_o_
_0_
O0
0.0
_0_¢
eel 4" 0
o oP-
e4
o
o
,_
0
0_
_7
_
oo
vw
co
:w m- e,%
,0
*
I
v
v
!
o_
a0 oD e_l
o
oo
O0
_
• o
•
•
,_
_
I
!
I
I
_0_
_o_
_o_
"
_
0
*
I
w_
÷
_
r_- _
,
,
I
T
¢
,
I
•
I
w
I!
+
o
f_
,-,
I
O_ oO .:I-
o_
I
I
I
I'
e_l
,
,
I
vv
_v
,..-i
A
_K
e'3
_.
O7y
190
"
• o
•
,
_L
o
_
q-
_j
,...4
,-.4
(_
,...4
!
I_
o
0_
0_
_
o
0
G'I
_
0
i_-
_
0
,-I
•
I_
_7'
0"
_
_
N
0
,-_
0"
0
0"
(_J
,_
,'_
N
_
-0
,._
_
_
_(%1
_
!
"J"
1-
_
r_
r_
i-4
E-I
0
0
_"
.rq
_-u
E-I
M
h-
I
0
©
0
0
fW
G"
A
r_
i
0
N
_.1
L_"I
r,J
G"
u_
0
(_
,0
u
_
r _•
0
_
.-4
u2
o_
"_
a.
191
,JJ
:I[
J_S_4J_
DATA
Myers,
Russell
Air Force
H., Jr., and Carl
Flight
Test Center
Clark,
Daniel
Conceptual
C., and
Design
Flight
Manual_
USAF
T. O. 1C-140A-1
Jetstar
Handbook
Models
C-140A
S. Cross,
Jetstar
Flight
Evaluation,
Rept No. FTC-TDR-62-24C-140,
Feb. 1963
John Kroll,
General
Report,
NASA CR-544,
Series
C-140A_
of Operating
and
SO_CES
VC-140B
and
C-140B_
and
Maintenance
Aircraft,
192
Purpose
Airborne
Aug. 1966
T.
VC-140B
Aircraft,
Instructions
O.
IC-140A-2
Simulator--
for
USAF
SECTION
VIII
CONVAIR
_OM
193
CONVAIR
The
tudinal
and
Convair
and
Lateral
actuated
Elevator,
respective
the
used
control
in
is
directional
rudder.
hydraulic
880M
a medium-size
control
control
880M
BACKGROUND
four
engine
jet
transport.
servo
tab
deflected
consists
consists
of
of
servo
deflected
elevators
ailerons
plus
spoilers.
aileron,
and
rudder
transfer
functions
primary
surface
deflections
with
system
diagram
shows
in
computing
tab
Longi-
transfer
a lag
functions.
194
tab
the
16sses
spoiler
are
in
terms
included.
actuator,
of
Although
none
was
0
•_
+_
0
0
0
,-I
ID
0
.r-I
0
O
-O
o3
O
.,-t
+_
.r-t
_d
-,-I
,--I
I
I
0
0
0
0
0
0
_
"-
I
0
0
,
0
O"
0
_D
©
.H
I
i-
cO
cO
°H
O
rD
H
H
(1)
O
.,-t
-O
.r-t
O
-r-t
C_
_
O
•,-I
_-,
/
rD
4.0
q-t
4o
_
4o
q-I
,
_
,
_
_
0d
I
-o
O
(2)
4-,
O,1
-o
I
I
O
O
O
O
O
_io_o
ff_
03
O
(2)
0
(D
0
O
O
LZh
Oh
0
0
0
o
o
0
0
0
0
0
0
M
®°
O
O
_ _o
m
i1)
_
4._
II
H
ii
Ii
II
_
_
ii
d_
d_
N
1---I
_
H
N
H
195
II
II
r-_
m
O
"7,
O
i
<
O
5
a0
co
O
o
rj
i
H
H
H
>
-H
!
o
o
_-.¢
0
odm
I_1
II
tl
_0
-Q
Io
196
CV-880M
PITCH
AXIS
)
_--
-Ch8te
Oh8
ROLL
8te (rad)
Be(rod)
e
AXIS
I +.Is
t -I.425
8Sp (rod)
8to(rad)
8tac
_--- Ba(rad)
YAW AXIS
(Sir
,.._+
t<
_
-Sr)c
b
St, (rad)
L
8r(rad)
i':':kg',kre
'/! i_ -3.
CV-880M
197
Control
System
TABLE
VIII-I
CV-880M
Longitudinal
Flight
Condition
Configuration
Speed
I
2
L
PA
134
Altitude
Non-Dimensional
KTAS
165
Stability
3
KTAS
4
.6M
.86M
Derivatives
5
6
.7M
.SM
7
.86M
SL
SL
23K
23K
35K
35K
35K
5.2
4.3
5.3
2.8
8.3
4.7
4.0
CL
I .03
0.68
0.36
0 .I75
0.454
0.347
0.301
CD
0.154
0.080
0.022
0.019
0.025
0.024
0.023
_o
(Deg)
CL_
(I/rad)
4.66
4.52
4.28
4.41
4.62
4.8
4.9
CD_
(I/rad)
0.43
0.27
0.14
0.07
0.18
0.15
0.13
Cm_
(I/rad)
-0.381
-0.903
-0.522
-0.572
-0.568
-0.65
-0.74
2.7
2.7
2.44
2.5
2.75
2.75
2.9
Ci_
(I/rad)
7.92
7.72
6.76
6.37
7.51
7.5
7.62
CLq
(I/rad)
-4 .I7
-4 .I3
-4 .I6
Cmc_ (I/rad)
-I 2.2
Cmq
-I 2 .I
-I I .5
-4.66
-I I .8
-4.4
-I 2.
-4.5
-I 2.
-4.6
-I 2.
(I/rad)
CL5 e
(I/rad)
0.22
0.213
0.193
0.141
0.203
0.190
0.180
Cm5 e (I/rad)
-0.657
-0.637
-0.586
-0.438
-0.618
--0.57
-0.532
Ch5 e ( I/rad)
-0.326
-0.328
-0.336
-0.278
-0.342
-0.31
-0.285
CLSte
( I/rad)
(I/rad)
0.055
--0.164
0.0532
-0.159
0.0482
-0.146
0.0352
-0.11
0.0508
-0.155
O. 047
-0.14
0.0450
-0.134
CmSte
( I/rad)
-0.287
-0.285
-0.297
-0.343
-0.31 2
-0. 335
-0.352
chste
198
TABLE
Vlll-2
OV-880M
Lateral-Directlonal
Non-Dimensional
(Stability
Flight
Condition
Configuration
2
L
PA
13 _ KTAS
Speed
Altitude
C_B
I
SL
1 65 KTAS
SL
Axis
Derivatives
System)
3
4
.6M
.86M
23K
23K
5
.7M
35K
.SM
•S<,Iv
35K
3!_X
-I .01 5
-0.877
-0.788
-O .81 5
-0.807
-0 .UI25
-0.239
-O.196
-0.163
-0.145
-0.181
-0. _77
0.145
0.139
0.128
0.122
O.129
-0.395
-0.381
-0.329
-0.243
-0.341
-o.31
-0.087
-0.049
-0.0173
-0.0031
-0.023
-0.011
(I/rad)
c% (1/_d)
C% (1/_d)
Cnp (1/_ad)
C_r
(l/tad)
Cnr
(I/tad)
Cysa
0.129
2
O. 198
0 .I46
0.088
0 .I8O
0.153
-0.21 8
-0 .I85
-0 .I63
-0 .I89
-0 .I66
-0 .I65
0
0
0.309
0 .O01 9
0 .O745
0 .O044
o .00775
o .133
-0.294
-0.oo_
o.146
-0.165
0.00979
(I/rad)
-0.0487
-0.0384
-0.0466
-0.0452
-0.0479
-0 .o_97
-0.0479
C_5 a (I/rad)
0.01862
0.0172
0.00746
0.01061
0.007
o .oo8o3
O .O0975
Cn5 a (I/tad)
-0.607
-0.481
-0.236
-0.258
-0.2233
-0.2005
-0.258
O
0
0
0
0
0
0
-0.0072
-0.0056
-0.0068
-0.0071
-0.0075
-0.0071
0
0
0
0
0
0
-0.249
-0.227
-o .21 5
-0.21 25
-0.226
-0.235
-0.213
-0 _078
-0.031 5
-0.0189
-0.0175
-O.0189
-0.01 89
-0.01 75
0 .o805
0.0405
0.029
0.0281
0.0324
o .0329
0 .o339
0 .o258
0.01 29
0.011 46
0 .oi 09
0.00975
o .01004
o .oo917
0.223
0.21 55
0 .I904
0 .I394
0 .I99
o .I84
o.I 685
0 .O207
0.0226
0.01 76
O .0183
0 .O1 65
0.01 87
0.01 93
-0.O9_)5
-0.0958
-0.0845
-0.0534
-0.0848
-0.0756
-0.0644
-O.2140
-O.2125
-O.1626
-0.1844
-0.1345
-0.1491
-0.1924
0.0493
0.0467
0.0374
0.021 5
0.0404
0.0355
0.0316
0.0021
0.0027
0.001 6
0.001 8
0.001 4
O. O01 9
0.0020
--C,
.020
-O .019
-0.01 5
-0.0077
-0.01 6
-o.o13_
-0.01
--0.25P,
-< .N_;5
-0.267
-0.254
-0.27
-o.267
-0 ._C,5
Ch5 a (I/rad)
(llraa)
(I/rad)
C_a
Cn6ta
(I/rad)
Ch6ta
(I/rad)
Cyss
C_
(1/rad)
s (l/tad)
Cn5 s
I/rad)
Cy_z '
I/rad)
C_6 r
I/rad)
Cn6 r
I/tad)
Ch_ r
7/raa)
CY6t r
(llrad)
C£Str
(I/tad)
CnBtr
(1/rad)
C"
(1/rad;
nst r
-0.0068
0
199
1
O_
•
O
0
P'÷
W
0
h=
,,,F*
_
I'dILl
U'_
c_ 0_ _
0
0
0
o
o
o
o
0
0
0
o
0
I
÷
o
_
0
•
j
_
_
÷
÷
o
o
-, _
,-
0
_
,'-4
0
___
._i 3
o
r_q
o
•
0
_r_
,'-'4
g
• _
•
I
o
o
!
÷
H
H
pq
4-
÷
÷
=
•
o
H
_
,-4
,-d
N
,-I
•
_
_•
+
I
_J
200
I_•
i_"
0 _
",I"
tO,
•
I
0
o
0
o
0
o
r_l
0
..-i
_
_1
',,t
0'
o
_
_
_
.o
_
.t
_
-_
_
o
c_.
-1-
cO
0
0
0
0
0
,D
0
0
0
0
0
0
_
*
.-_
t_
•
0
•
{_
l
v
r--
¢v_
I"
*
•
."
I'
_'
_f_
I_
c¢_
El
o
0
t'•
I'
04
_
o_
_
t _"
0
O
•
I
_
0
O
'
I
{_
_
0
0
O
•
oJ
_._
_
O_
0
•
_r_
•
I
N
H
U_
H
H
H
,,,7-
_
uo
o_
O
O
•
I
O
•
I
O
O
O
•
O
0
•
I
O"
I
_r_
0._
,0
tZ_
_•
o
_..
I
I
CO
•
"
O_
•
I
_I
I
WD
I
_
_
w
0
0
0
.-4
C_
P-•
7
•
I"
,--I
._
o,
c,,I
0
O
*
I
C_
0
O
"
I
_
_
O
O
"
I
O
O
O
0
O
0
I'_
_o
t_/
-r_
I
e,,,i
,,,,,
I:I
•
I_0
I"
_
_
'7'
_
"
_
0
0
o
I
0
_
-,t
_
tP,
•
_
._
-0
_
_,-i
.
.-.4
I
_
0
0
o
"
0
,..-4
"
I
o
_--
,,1-
co
(,_
I
_
.-_
I
_'
O
(._
O
t._
CO
•
,._
O
O_
O
_
/
w
I_0_
"
,o
I
•
04
I
O
O
O
0
"
O
'--_
°
I
O_
r"*
u_
"
I
"
I
0_
t _'
E_
Cc_
H
¢_
04
,O•
O
0
O•
"
_0e
I
•
-_ _
_•
_
_
.-e•
I
..I
.O
p.,.
_
O
U'_
_
o,.t
UJ
tlJ
o
_"
_
.; -_
o
'
O
_--i
I
I
_I"
_
u'_
o_
CO
_"
O
o
o"
o
O
.
I
I"
I
I
u_
CO
CO
_
°
I
_
O
c_ _•
I
I
11
_
.
I
201
•
I"
I-
I,I.
_,
•
I'
"r
"r
4
0
• o e0 o.
oOLt_
.40
.
I
e,
O_
_00
•
•
"2
,.n
_n,4
_,._ 0 ,,,.-I ¢10
I.t'_ _", laO he,,,,,4
_o
•.--4
It-
I_-°
•000
oeq
I
I
÷
_o
0
_0_
_0
0
_
,.,,t 0".
_
,,,t
.: o,,,
O0
00_
I
i
I
@
i.n
I'-.- .-4 f.,..,.=._¢0 h.0,,I"
0
_0_
_0_
O0_J
_0
0_00
!
I
_o
_0_
_00_.
O0
,.,_ ¢,..) u -. e._
•
!
!
I"..
_)
u,_ OON
r.- r,,/
u_
e_ O_ ¢0
O0
0_0
eee
N
!
!
•
•
I
I
H
._
f,.- t_l
,,o
,o
_0_"
_000_
_00
I
I
I
I
_o_
_" _o.i
r._ o,i
• _0
C)
•
_
,'-_
o
,0
•
N
I
!
I
•
I
"
÷
GO
I
oo_
_0
0_
,-4
_N
•
0
•
e_ee
!
Z
_
I
!
_
Z
202
t_
.b•,I
I
v
_o
P-
uJ .-_ (_, _
oo_o
_o0
OOen
•
t--
,o
I
I ,o
Lul_-
wo
c_P-
00_
_-I
o
¢_ c._
,.._ _
_o_
o_
...-4
•
I
I
I
I°
I"
,t-.1OC0
c'x_,,_ u"_ u".
o r_ rv_ t_
OOe
_'
0
-.1Lr_
O0_r_
O_ L-_
I.U ,5' O" I_
P'•
I
o
,.0
ogo._
.-_
I
!
÷
p-
-.t
0
_r%
erl D.OOCxl
0.I"
•-_ u
u
I o
Uj _r', wD
.O co cf_
OOU_
00_
wE}
-,1"
OOO_
,,T
!
I!
4,4"
P-- <._ ,o
aO _
00,I"
0", ,..._
0_
00_
Oe'N
0
(%1
•
I
I
-'o
(M _u' 0
N_;
I
I
,o
I
LU r..}
_o_
U_N
_o
Cxl ,ID
00_
oO
o
CO
(xl P.-
•
!
¢0
,.--i
*
,
LU r-- O_ _rM
cO CP. ,4- L._
e,a
.I
I
I
_0_
0_
0_
II
!
U.J O,
_oo
uj ao -_" u_ (M
_ ,.._ co co PO [0 L) .--_
._-_
T
_
CO
UJCO0
OOU_
CO
•
!
I
+
co
co
I
•
•
I
w_
I!
,0
I
_0_
0_
l,iJ
4"
u-, co
8E _
_o_
_,'"
ol0e
I
co
•
I
!
_N
E
EJ
Z
203
•
_N
0
,-4
°
0
I
÷
CO
WD
u_
0
0
c0
_'_
_
0
0_
0
,_
QO
I
,-.4
I"
4.
_r_
_
0
0
_
0
_0
I
,.-i
,-.4
0
uJ
!
O]
v
_
i_i
v
l.J
wD
a)
_J
l_J
,,,1"
--
_._
wD
D'oO
!
H
ca
v
i_
_
U
0
ur_
U_
0
_
h-
•
a
I
,0
N
..J
O"
,,I"
_"
•
,4)
I
0
I
•-q
CO
OD
-J
f_
0
o_
0_
oO
,,I"
,,I"
0
,0•
_0•
_
_n
I
l
_,
I
-
G
p..
-_
I,.9
w
I/_
_J
u.;
,_
IK
_x;
CI--
_'_
L5
14..
204
C_
_
0
_-
r'-
_
_
CO
"
_
0
I"
•
O_I
N
CO
P_I
,-I
I•
_t
I•
_
•
r_
0
I•
_
0
_t
0
•
IX)
•
•
I"
I"
O_
•
0
I
0
i.
-.11"
I
•
_
_0
I
"_
I
<r
co
N
u_
I
_n
I
_
I"
$
I"
o_
_
I°
!
•
_
.
|,
o
.
•
I
_0
0•
I
N
o
0
o'
N
•
N
•
,DO
•
•
.I"
_
f_-
•
/
I
e_l
(X)
_
_
0
•
*
0
_"
I_,
O
_'_
0
_
o
*
*
_0
0_
I
N
<)
_
o
I
01
_'_
_0
_
I
I
•
_
I
_0
_
I
_
o
I
i
e_l
_
I
205
._
I
_0
I
IX)
IX)
_"
o
'
I
N
I
_
I
I
N
0 _
I_-
0
I
N
0_0
O
SS_
*
0
i_-
O_ um
,.'tO
•
I
0
O_0
0
•
•
i°
I"
0
•
*,--4
'4" •
• ...-_
I
er_
•4" ¢
0"0_
•
*_
0
.
u",
rr_
• (_
0_ ti_ c_
,00_
.c_
I
I
I"
i°
°
t,t_ ,4,- r,,_
rq
.4_ 0
o.o_=,o
,"_
I
•
I
!
• c)
•
....
.-_
.
_o _.
o_to,
!
I
I"
_ut
NO
•
I
I"
...'-4
I
I
I
C0_NO
0
I'll
•
-'_o
•
NO
I
..=_
I
I
!
I
4.
N
_
O"'
,,o o', g'_
.....4
!
I'
I
_E
_w
ZZ
Z
206
v
Z
P--
_
o
lJm_
i_0o
,-4
_o_
_0_
o_o
o
co0
oo
°
,._
°
_
°
°,,,
I
I"
_o_
I
I"
..s
o~_
o
0_
_0
. o ej
•
I
t_m r,j
I_0
i._ f,el
r_
_ Z _."_.
_o
co
l_J
I
°,+,
I
I
_°°
II
_o
0_
•
I
I
I
I
, l_j mm
+
I
I
II
P_
, I'_ u'_ 0o um
II
+
H
r.-
°_
• o
•
I
I
I
H
H
t:"
_
q_
tl
._
F7_
F_
_,_
I-+
c"
_0
O)
oo
•
<N
p_
,_
• o
I
•
I
I_ eu
l
I
I
_o_
..A'_
_
.-_,0
0_0
,,IDrex ,-_
• ,,-I
.4
+ ,-i eq
I
,0_
I
I
I
II
I
o
e_
_
"o
_o_
o
o
_
e_R_o
_0
• ,-'4
.-4
I,_,0
I
ZOOWW
v
Z
207
Z
0
0
_
_
_
_
_
_
_
,
I_
I'-
p
I_I
|
.
--
0
_
_
_
0
_
_
_g_lg.._O_O_._
v
+
I_
I_
0
+
f_
CO
.
aO
.
f
J
O
+
0
4_
,--4
_
_•
I_
I
o
u_
_
r-
,+
_
p_
l
+
<%j
q
_
•
p_
ch
_p
o
p_
ir
Q
U'
w
_
_p
•
_
+rt
I
4
I
'4"
_
N
_1
¢O
f_
•
•
0
fJ"
r,_
_
•
"
I
I
CO
+
_0
--
00
•
0
•
P
P"
O
•
P',I
0
+1
_
.,1+
oI_
_
.-w
U
0
.+
v
P
r_l
(P,
,..,I ..,i" w_
_
I
"
!
wD
_
..1"
N
I
O,
,-_
I
co
_
I
I
,,41" _
wO
0
P,,,. _
c'%
P"-
_,
",+"
,
_
•
I"I
.P'
0_
C)
0
_
10,
•
h-
!
•-+
_1
I_
f_
o
lU
0
N
•
_
o
l
I
•
_J
u x
•
P_
•
N
,-4
•
,4"
NO'
_
f_l
,-.4
urs
,--4
_
0_
,_
_
e
¢_1
0
-1"
I
iii
<_
r
r,
UJ
_
w
LU
n.
LU
I_
-.
_
_
+.J
.J
'_
nf
¢'_
,,.,4
_
208
..4
1',,4
O.
1_
I_.
_
_
)¢+
LIJ
U.J
g+.l
0
_
_
IJ
<_
C)
_
+-+
_
es
I
03,
I
_1
_
I--
ID
I-
rJ
I-
I_
_.
"_:
I_
I_
_,.
,'_
CV-880M
DATA
SOURCES
McNeill,
Walter
E., Calculated
Factors
of Three Subsonic
and Flight
Measured
Jet Transports , NASA
Brooks,
Airliners,
Peter
W.,
The
World's
209
London,
Handling-Qualities
TN D-4832,
Nov.
Putnam,
1962.
1968.
_ECTION
IX
BOEING
747
210
BOEI__G
The
Boeing
designed
to
747
operate
necessary
low
flaps
Krueger
the
and
inboard
flaps
through
four
and
only
each
spoiler
are
The
five
as
speedbrakes
Directional
(Boeing
and
this
flaps.
an
spoiler
aircraft
has
and
inboard
aileron
panels
Krueger
slotted
D6-30643).
211
while
which
with
obtained
is
The
operates
each
the
wing
most
from
solely
outboard
the
between
two
obtained
lateral
the
also
con-
inboard
flaps
down
operate
inboard
rudder
of
inboard
with
from
the
trailing
flaps
control
aileron
is obtained
was
To obtain
stabilizer.
on
transport
triple-slotted
Longitudinal
conjunction
control
airports.
The
a movable
outboard
in
intercontinental
wing
cambered
panels_
wing.
for
edge
segments
spoiler
the
unslotted.
an
Information
four-fanjet
international
variable
and
panel.
description
leading
flaps_
symmetrically
large
existing
standard
five
BACKGROUND
characteristics
type
elevator
outboard
on
speed
are
employs
a very
from
nacelle
Krueger
trol
is
747
sixth
segments.
a 747
simulator
2;
(1)
o
X
(1)
o
.i.Ii
4a
ii1
co
o
o
®
gh
0
o
h
i1)
I
I
I
0
0
0
0
o
cf
o
o
"_
o
,d
_
i+
0
_J
or)
_
o
o
O
_
•
c_
o
cu
•
4D
.r-I
_J
O
ea
4_
b8
.H
_H
P_
bbI
i
.H
#
_J
O
b9
.H
o
O
-i-4
O
OJ
-ID
r_
I
,1-1
.,-I
O
O
I"4
o
o
r_
o
I-i
4D
.-a
.H
O
lag
kD
0
_1
o
Od
+_
_H
,
Od
4D
CH
I
rq
r-I
_0
0
X
X
_,
ly_
Ckl
u_
bD
kO
0
,--
kO
0
Io
0
0
GJ
-ID
r._
X
L"-
L¢_
,--
h_
II
II
X
_
•
_
Lr_
OJ
CO
0
4D
cO
II
212
fl
II
CO
a_
_,D ._j
"_I--
°
pr_
a_
f_
,-I
a_
0
lqr)_
!
.J
G
_
o_
||
II
I|
0
b
213
B-747
PITCH
AXI_.
_eSAS
I
Fcc(Ib)
K
-2
4°
k
P" 8e(rad)
57.3
_cc(deg)[
50
e,"s /
20
J"
x
,°t
43
o
0
.2
.4
Mach
I
I
I
.6
.8
1.0
[fj
,-t
0
4_
0
ROLL
AXIS
_t
P
I
I
Fwfib)
r;
I
.161
Sw(deg)
I
57.3
.5
H
(1)
b._
YAW
AXIS
FpED(Ib)
8rsAs(rad)
___
43.5I
}SPeD(in) I
214
7.15
57.3
B-747
YAW SAS
rG (rad/sec)
I
5.05_
I(s,.368)(s
3.68)
Flaps Down
-.688s
s+.368)(s+3.68)
_iNs(rad)
-34.5s
(s+lO)
2
r
=r
*INS:
(Gyro
and
IP dt
INS Aligned
Figure
IX-4.
with
B-747
215
FRL)
SAS
TABLEIX-I
Landing Configuration
h
VTo
Non-Dimensional Derivatives
:
sea level
= 131 KTAS
mo = 8.5 °
5s
=
-6.3 °
Longitudinal
5a
CL
=
I .76
CD
=
CL_
Lateral-Directional
Cy6
=
--1.081rad
.263
C_6
=
--.281/rad
=
5.67/rad
Cn_
=
.184/rad
CD_
=
1.13/rad
C_p
=
--.502/rad
Cm_
=
--I.45/rad
Cnp
=
--.222/rad
CL&
=
-6.7/rad
C_ r
=
.195/rad
Cm&
=
--3.3/rad
Cnr
=
--.36/rad
CLq
=
5.65/rad
C_Sa
=
.0530/rad
Cmq
=
--21.4/rad
CnSa
=
.O083/rad
eLM
=
--I.I
CYSr
=
.179/rad
Cm M
=
.36
C_5 r
=
0
CI6e
=
.396/rad
CnSr
=
--.ll2/rad
Cm5 e
=
--I.40/rad
= total deflection
inboard
aileron
included
of right
inboard
aileron
plus left
with the effect
of outboard
ailerons
216
TABLE
Power Approach
Non-Dimensional
IX- 2
Configuration
Derivative s
h
=
sea level
VTo
=
165 KTAS
co
=
5.7 °
5s
=
--2.1
O
Lateral-Directional
Longitudinal
CL
=
1.11
CyB
=
--.96/rad
CD
=
.102
C_
=
--.221/rad
CI_
=
5.70/rad
Cn_
=
.150/rad
CD_
=
.66/rad
C_p
=
--.45/rad
Cm_
=
--1.26/rad
Cnp = -.121/rad
CL&
=
--6.7/rad
C_r
=
.101/rad
Cnr
-
.30/rad
Cm_ : -3.2/rad
CLq
=
5.4/rad
C_5 a
=
.0461/rad
Cmq
=
--20.8/rad
Cn5 a
=
.O064/rad
c_
= -.81
Cysr
=
.175/rad
CmM
=
.27
C_5 r
=
.O07/rad
CLte
=
.338/rad
Cn5 r
-
.109/rad
crime = -1.34/rad
5a = total deflection
of right inboard
aileron plus left
_nboard
aileron with the effect of outboard
ailerons
included
217
SL
i
_m
mmm
B-747
20,000
40,000
_m
em mmme
ft
ft
636600
.25 _"
Flexible
Ib
k
i
k
k
k
12
I0
m
GO
(deg)
8
m
6
42-
o
I
I
0
4I
.2
.6
"
.8
1.0
Mach
2
,_i_,
° " _0
I
.2
(deg)
I"
.4..""_
.6
.8
Mach
-2
-4
218
._
I
I
1.0
_o.
u
o
I
I
I
I
o.
o.
m
0
0
_0
b- _D
i P0
m_p
O0
O0
o.
qQ
_00
u) od
,_'-
11
li
_5
I
I
I
I
o.
o
_
c_
Od
_1
o
219
CL
SL
B-747
20,000
ff
40,O00ft
636600
Flexible
Ib
a
(rad-')
4l
2-
0o
I
.2
I
.4
I
.6
I
.8
I
1.0
.8
I
1.0
Mach
I
CD a
(rad-')
.8
l
l
m
,
\
.4-
0o
I
.2
.4
.6
Mach
220
Mach
0
2_
.4
.8
.6
1.0
7------V---
0 ,--------T-------T-------_
B - 74T
636600
Ib
.25E
Flexiable
-.4
:8
Cm a
(rod -j )
-I.2
-I.6
Mach
.Z
I
.4
r
.6
I
.8
I
1.0 _
I
-8
Cm&, Cn_q
(rod "t )
SL
20,O00ft
40,O00ft
....
.-.. -..-
-12
Crnq
--------®.
]
J
221
I
m
CL M
0
I
.2
.4
Mach .6
.8
(_
1.0
!
SL
B-747
20,000 ft
40,O00ft
636600
.25
Flexible
.3-
I
/
CD M
#
.I
//
m
0o
l
.2
1
.4
j
.6
®_/
,
.8
1.0
.4
.2
Cm M
I "(_._
0
-,2
-4
222
t
II
I
Ib
B-747
"
SL
20,000
ft
--------- 40,O00ft
.4
.3
CL8 e
(rod -=)
I
.2
O0
I
.4
I
.6
I
.8
I
1.0
.6
I
.8
I
1.0
I
Mach
.2
00
.4
I
-.4/
I
-.8
--
I
/
I
Cm8 e
(red-I )
y
-I.2
-
-I.6
-
/
'
." 7/
223
Mach
00
.2
I
.4
I
.6
I
.8
I
1.0
I
-.4
Cy,o
(rad "I)
-.8
B-747
SL
-I,2
20,000
ft
636600
40,O00ft
Ib
Flexible
Stability
Axis
.2Cn_
( rad-I )
O0
I
.2
I
.4
I
.6
I
.8
I
1.0
.4
.6
.8
1.0
1
I
I
Mach
0
0
.2
(rad "=)
\j
-3-
224
/
SL
B-747
636600
20,O00ft
40,O00ft
Stobility
Flexible
Ib
Axis
Mach
0
0
.2
I
.4
I
.6
I
.8
I
1.0
I
-.2
Cyp
(rad "l)
-.4
.O4
I
I
0
Cnp
.2
1.0
(rad "i)
-.04
-.08
225
SL
B-747
20,000 ft
40,O00ft
636600
Ib
StabilityAxis
Flexible
.3C_ r
\
l
(rad-')
I
.2
O0
I
.4
I
.6
I
.8
I
1.0
.6
i
.8
I
1.0
I
Mach
00
.2
I
.4
I
-.I--
-2-Cn
r
(rad"l)
-'.3--
--.4
--
226
....
-----
B-747
636600
Flexible
SL
20,000 ft
40,O00ft
Ib
.016
.012
.008
!
t
t
t
DO4
0 0
i
.2
I
.4
I
.6
I
.8
I
1.0
Mach
Note:
• Because spoilers operate
around a dead band their
effect is neglected here
• 8a is the total differential
deflection of right and
left inboard ailerons
.004
Cn8
a
.!
(rad)
0
.2
.4
.
Mach
-.004
227
1.0
\
SL
B-747
6366001b
Flexible
....
20,O00ft
"-------- 40 O00ft
I
CY8 r
(rod "l )
I
.2
O0
I
.4
I
.6
I
.8
I
1.0
.6
I
.8
I
1.0
I
Moch
0o
-.04
-
-08
-
.2
I
.4
I
Cnar
/
(rod")
-.12 -
.02
O0
-
.2
.4.
.6
Mach
228
.8
1.0
co
I¢
¢o
tc,
t_
c_
.
eo
rt
<o
D-
.-_
r_
_
,,t
C
I_
r -
r-I•
_:
"_
t_,
I_
_
__ _.
0
I'M
O
0
_-_
0
_
03
C
,-_
I
r,J
¢,j
0
r_
_,
0
0
if.
0
_,
C
r-J
Pw
0
0
0
_
o
0
0
__ _
0
C
/
•
_
0
ILl
l.L
I_
,0
It"
_.,
•
•
0
(3
,.0
c,
_
t
/
v
_0
+
UA
OJ
H
E'_
M
N
_-
0_
eq
O,
N
+
_a
4.
ILl
i__
_0
*
_
0
c,J
o
_
S
ce,
I
JI
.° o
_c_
CO
H
kf'x
O_
•
o
G
_
_
_
$
.
_
_
o
_- o
-_ ®. o
0
0
_
c_ _
I
tO
,_
¢_
•
0
_¢LJ
UJ
+
ILl
,0
•
°
0
C_
U_
0
0
0
0
_0
oO
0
•
0
I
H
0
Lr_
LF_
0_
"
_
0
O0
¢C
CO
+
'JJ
÷
LLI
UJ
+
o
0
t'_
_0
0
0
0
0
,(J
0
I
D--
0
0
0
"
0
I
-.ID--
oc,
•
•
,_
(D
.
uJ
_
ILl
o
U'_
0
229
o
-'_
_-
0
o
0
0
0
0
0
4
g
_
_
o
I
I
I
•
I
"
I
"
*
I
I
I
I
!
•
•
I
•
÷
_o_
_
•
,0
•
_
I
•
I
•
o
0
•
o
I
g
_
•
•
0
I•
•
I
•
I
•
I
S
S
If_
¢_;
_
•
;
,"
I_-
0_
4"
_
0
o
0
0
0
i_
I
•
o
•
•
I
_"
•
•
o
0_
o• _
'
o
o
,.
0
h-
N
o
0
0
I
0
•
•
*
I
0
I
0
_
0
,_
_•
0
o
o•
0
o
_
_
"
I
_
o
I
"
I
•
_•
I
E)
•
I
I
I
I
•
I•
•
ie
8
_
o
_
_ -_
• _
,"
,
•
_
._
o•
-r
r_
o"-_
0
I
•
o
I
3
_"
"
I
I
"
.
o
.
o
I
I
I
I
o
_
fM
o
I
•
"
I
•
_
_
-.
,
o
_
,
o
I
I
"
"
I
CO
o
i°
I
I
_,
_ o
A
,
I
_J
o
_
,8 o
I
I
I
Q
o
;
I
I
_I
I°
o
0
I•
I*
•
IT
I"
0
I
• o
;
_
. _
_'_
I
_
• o
-'_
I
_
OJ
o
"
I
[..--
_J
_I"
.-_
•
"
l
_
0
'
I
0
0
•
.-_
"
l
o. _. o
I
I
0
•
•
I
r,_
_r_
0
•
rI
0
o
I
•
I
230
•
I
o
I
;_'
I
_
I
h.
•
0
0_
_
0
,n
I
I
•
I
I"
"
•
3
I
•
I
e_
,
I"
•
r-
I__
_r
I
C
Co C
•
I
I
_._
T"
,,1,
I
o+ c
•
.
+ o. T 'r+
I:_oc
,.-i
I
o_
_0
0, ._
•
o
_
,_
c0
-o
°_u-,
I
t',J
r--
i,,,
I
,1_ r),
I"
"
u_
_o0
I.--_
_,_
F'- 0
I
t,IP CO
_
,_i_
,o,o
''+.
I
0
OO
•
_000
o
t_m
COtP
O C_
• O ('_ O
_D O
• •
NO<
u_
• I
_
oo
I
_'
I
,-400
•
I
mo
H
O
,-4_
,,1" _
OO
um
,O ,,t"
u_ r,-
,o
O-
rq_uh
c'u_o
0,-+0
'0_"
I
_
f"O
,_I
°
f_•
I
•
I
•
I
I
•
I
•
•
I
H
u
,y_
t,"_ .._ (7,
•
o_
,-'* O _D
•
•
•
,,..i
I
I
I
o_+ _
r.j
um
,_ ,-1 .-+
,_OrM
,-*r,i
•
N_O0
°
!
-or-
r_o_
I
•
I
I
g¢_
•-J_
v1¢'4
¢,_
0
_o
_
tx/
,,.4 ,,_
.+_++
,.4
i_
P- em
I
P-
!
I
I
-oo
f_o_
,o+,
I
II
I
"-_N
_
_
___
Z
231
Z
c
0
I
h-
C,
O0
Ul ¢0 0-.
e,_ .4" I'.fM _,
• I
I
o
•
¢c_
.
•
e.
I!
" .o_
C_
,,1
,¢3 co
,o
OCN_
O(:N
¢% ,-4
•
I
!
¢o
•
O
O
•
e=
II
,?
T
C.
OO
,4- P.-
•
uu_
0,0
_rt
•
I
g-
O
¢¢_
_r_a)
•
_Oee_
I
o
oO
! m
_o
_OU't
eO
i!
I U"o
UJ ¢Y f¢'l
eO_
•
0w.._
_O_O
(
_o
OO_0
NO,_
ee
I
O
I
er_
|e
I
_l
_8_
_.
•
_D
I 00
uuOO
_-
O_
_
P'- t_ Od
00,4
.
ee..4
• _r_ _o -4r
00
.-_ ,
_
_7,'"
_o
_¢0
•
I
•
•
¢¢t
•
•
I
_e
II
d"
O
Oo
00.4"
_n_NO
00_%
*
•
(%J _
• |
I
•
•
_1
•
•
•
0_0
_O__oe_
_o
tttO
_P-
_U
I_
_o_
•
,.-.e
•
• tl% r--
¢.d0 _
•
(
I
I
•
I
O¢..;,(7,
f¢3
•
•
OOtt_
•
,0
I
OOU_
•
•
I
•
u_
I ,u
IJ.I ¢o
uu
oo_
e,-.4
¢%J_0
•
I
I
¢,--
NOlO
Nee_
I
'41"
I 0"1
O
,,,J_
•
•
00,"4
ff-_
I
I¢1
N
(7"
.J,4"
_N
p..
O
..-_ ,0
vrt
_-
•
•
(¢t
•
00
O
I
I
04
•
I
•
I
E)
¢'_t
•
_7,"
01
,4"
I
_;..._
i
_ww
232
,,-4
o
_oe_
Q
Z_
•
t-- e4 _'% ,0 ,-_
"
_N
IlL
•
I
u._ _0
I
U
NO_
o
•
I_
u._ _1 .,¢ 0,,
I_
• ('¢'_co
¢00'
0 ,.-_
u_h.•
•
r_I£_
•
N_
_0,
f_lW
•
I
!
I_
w
_._
Y
I
O'¢ON
r'_ ."_ ,.0 0,
ur_ •
•
•
• !
eeee
O
•
o
C
o
c
_c
.-4
o
_
_
0_
,,.4
I
C
_
o
C_
_
I_
_r_
I_
O
O
U_
LJ
_
_O
v
P_
O
O
0
rn
_rj
iI
0
wD
0
I
O
•H
O
_0
C_
U
I
o
H
_0
O
b-
0_
O
O
N
0
"_
r,.,-
!
I_
_J
@o
N
-
G
,,ii.
233
_:_
,,-4
.J"
,o
O"
0
_
R
_
O"
!
I
'T'
i
-4"
I
f,'t
I
I
I
•
_
,,1"
_1"
--
0.1
I
•
o
•
•
l
•
I
•
I
I
t
I
_
_
_
C'
.._
,-4
j,
0
7
o
•
0
0
!
•
I
•
_
0
_
_
"
0
,,1"
s"
•
•
!
I
•
_
_
_
0
I
I
I
I
!
I
0
_
I_
I
I
I
I
I
I
I
I
I
I
I
I
I
I
0
N
0
0
04
_B
4"
•4"
vt,
.0
.-_
-.t
•
I
I
•
,
I
0
(_
_
I
0
_
_'_
_r_
0
0
0
tel
0 _
I
I
_o
04
I
I
I
I
I
I
I
o
I
I
I
I
,4"
!
_"
g-
,4-
txl
I
!
I
o
I
¢
I
I
I
I
......
,o
I
,_
234
_.
_
I
c_
(J
"",,
(._I
(...}
(..I,
÷
• v
o
IG
e_
:M rx/
aD_a_
_C_
_0_
c,j
._oc-
o
Io
•
•
•
I"
I
I
I
I
.4-
o
i:_
o
.,r
0"-
c
co
cq@
_
o_og"
o
•
•
*G
•
•
,0
_°.oQ
I
I
÷
v
o °
lX_
_t
(q
I'll
_ID OO
u-,
,.Ih
I'.-- P-
oo ,--_
,f'
I'--OO
O
•
•
t
•
!
I
I
I
./
0
,-
0
o o
0
,0
,-_
"0
C'
•
O_,D
o_ o
•
I
,0
o°
.-4
.
_.-4
• _
ooo
0
00_
,-_I
•
,r,
r.q.4
t;
.
I
.to.o_
I
I
I
I
c_O
_0
o
_0
_0_
OCMO_
I
I
I'
0
H
r_
,::o _e_JMD _D
_J i"- _
O0
o,-i
0
•
0
e,l _"
•
•
*o
•
*
I
0_
c..Q
H
O
:?
CQ
rm
o
_um
N
IA'_ i1"_ <1"
2-- 20`0
rq-_
•
O"
• 0
m
.0
-t -_
,._
•
• .-4
I
A
I
I
I
I
+
°
_J
if',
_40,J
Cxl 0
0
• ,--I
•
I'-I
_
i'_" cq t:_o u.r,
-.tO_"-
_0
0_
I"
C_ C
*
,.._
•
_o_
Nt
I*
I
•
1
•
I
÷
o
u
I _
r.,0
• r_l
I
_5
._lq_
0
eO_-
_o
0
°_
,i'_I
C3":t
"N.
u_
::':
%<<Z:
Z
:<<
g
235
I
I
. ,-I
+
C
0
OC._,
,_
P--
cO
,'_J
("1
P-
0",
0
cO
,,m
_m
. m;
*
C
G
•
•
O"
•
°
,
I
mj
r_
f--
•
°
pro
I
t
,
I
,
,
I
I
0
0"
rq
Ok
-T
,,L,eel
C
-t
I'_I ,.,ir--
aO
',.r 0
0
1.1" G,
.,?-
cz_
_I-
•
rq_
oc
,C7.
_
_0
•
,
•
0
l'J _
t
•
•
,
•
• (";
-.1"
I
I
I
+
_0
O:.
I--
O
,F.,_
.._
P'--
,C
r_o'O
r,j
0
_
(j
_,
Oi
r-- r--
co
'_-
•
I
•
I
I
0
0
0
,'_j i_)
•-_
II
I
I
÷
r--
._
*
0
0
0"
t"'l
*0
_"
r',-
l'W
u-_
.-w ¢,
•
00
_0
i_
4 -
0,,
O"
co
._-
•-I
o
_-
.-*
,
I
I
I
I
I
4-
o°
(_f'4
-f
oT_ o.
,0
000
O0
,,¢
oJ
o
•
• 0
r_
W)_O0
•
•
_r_
•
,
-4"
I
I
•
I
,
I
I
I"
°
,--_
I
4-
g_
or-..
_o_
_o_-
o
_0_
It
I
_:) ,,o ,.,m o
,-I
OCO
0
,0
cI) O_
0
_
u'_°0_ t,.-
r--
•-_
0
•
..i
,
I$_
,--I
_0_
wD
I
I
!
,,-_
!
,,-_
I
I
0
u'J
O0
gO
r_
,
L"-.-IF
IL'--
rl)
..,I"
0
•
•
c-) l_J ;_,
I
•
r¢_
I
I
I
,
i
•
i
I
+
-.[,.,I"
_0
,--I,.-4..--I
{.P '---' " l"m
I
_
I
I
._o_
_
°
_T
I
I-
0
0
.-i ,.,P
_
_em
0
o_
I
,..--_
I
I
°
•
0..,.,
I
!
II
.-,f_
:ll
•
=J
I--
I-"
OC
_-"_ Cy..__
OC
_L
_.
Of
_N
c_
ft.
7_
236
_-_
7
°,...._
,
v
c_
_,_g
o
F,
_
_i- ej c_ C rm
o_o..o
o
c
.4
c
c_
_
I'4
,',%...*
,o
C_
•
-4 _
u_, _
.
14",
•
rq
t'F', ,,0 IF
"-
,_
•
.,'-' _'1
4
r,.,
•
I"
i_
,.-4f_ _-..
rq C_ _ _J <t
Cb
• • cq
•
°_oG
.l,r
i_
o
t-J c_c m", _,
C. nm•
(2.
•
t
I
c_rr_
og
_
.--, c_
.D llm I/'._4 u-_ .-,
¢- ,.-. t'x_ 0_ m- e,
•
,_r_
c,
co
°
c)
0r
a"
m", O
to_: _.._,_
......
_:.
re,
o
•
I
C_
o
r_cc;
(_
00...
i°
r.,Q
r_.,_o0
0
q3 0"
,£,
o
•
,,,,-,
r,.-,
.
,
I
_
v
o
E-I
4D
[9
C_
O1._
i._l -O
o @- ,--S _."
_g.
t-._ o
I
,.,0
_o, r.o co o9
.
_
c
r,,,,
I
i
o
H
oZ
m.- _
.,._ co
I
I
I
r_,Q
rj_
.,-I
_D
_jum
u
o9 e,j
--v
....
re, .Z_
•
I
.
,,-_crl
•-_
• 1"-4
D
-P
-.f
0
.-4 ,'q
•
r
,
• ¢_,
•
I
°
t
o
a
o
t--
I
I
t-I
III
_ 0 -.t 0 '4 0":0
,,-4 • .U_-.t..,t CO
0 n_ ,,.,-..-4
..r c,u •
C).-,_n"I
, • .C.,l
_o.o.
.4"
i0o_.
,_1 ,-i
IN
r,_ ,3
L¢_ ,4",
•
_4 ,"_
,_
uJ
_
237
r.--
_
r,,i cq
'_.
"_
_
-q
.1:--4
_
61_0
!
et
_
•
I
o_._
eg_oe
!
o_
_ttO_
I
_0_
o_
,-.a (%1
•
•
!
•
•
.(%1
'0
(])
r-I
0
0_
0
0_0_0
_eee_
oeNoo
0
•
I
!
!
vv
0_
!
oQ
_
e_N_ee
I
_0_0_
_.._
,.-.e r.,.i g_
_.:_._.
.4-
w
238
•,t
o
CO
oc
Q
.
0_
tr..,,t
•
I
c
u',
,_
o_'1
•
0
*
u-
cr_
t_J
0D
•
•
e.,_r,,,
0
0
¢'x.
fx.I
OF,
_O
I..-
f<_
,4_
h...,_j
0
C._
n'_
,,1"
•
aO
•
°_0
"
I
CO
•
,,0
I
I
v.
It
o
Go
_
c0
_.
co
I_
,,,t
,,0
_
_j
Cj
CJ
re5
_-_
FJ
"
¢'_
•
•
•--I OC
C._
_
_"_
<r
l_m _0
O"
I_-
",,t
•
•
I
I
i°
w
,,.I"1"-f,.-
cx_o0
.-_
0
•
O."4
wDl"-I"•
0"
,00'
-0
•
,t_l'.-
•
•
.r,J
GO
•
• ..._ 0
*
o0
.Oh-.'--'
f_
•
*
•
_
•
rnu_
I
!
I"
I
0
WD
e,J_O
CO
0"
",0
O"
0,0
•
C_
.,--4.-._
l"-
0
.,,tO"
°
•
°
•
I
I
I
!
I
•
,_0
I
I--I
._
o
_ ,__.._,_ _.
e.e_,
,,,Imm
I
•
_w
I
r_
m
•
•
r..-
w_
•
I
I
I
O0
•
b-
•
,
,
,
_on,
*,
•
*
.-e
I
I
!
I
E,--
•
00_
,*°0_
"
0
"
"0_I
'
!
_'_.
'
eO
_'_
0
0
_.
*
I
.o_
I
239
t
c
I
I
I
._" 0o oo *1% _q
¢," _
4w l_'.c
_ooj
I
_xlo
I
!
I
4%
l--orqoO
,0
,
I
I
,_q
,.-_
•
,.-_
0
II
I
_d
(D
_d
0
r.5
v
;
II
I
II
CU
7
_q
I
II
,o
O_ oo co ;-- oo _o
I
o
o
0
i
_v
C
__00
I
_.__
240
_O
*
GO
•
•
•
•
CO
#
...-4
•
•
.,f
I
I_
0
0
0"
_
O
_n
_0
_._
O
O
o
0
4"
•_"
O3
h_
4J
•
r-
I
_
•
_-*
_'_
_
_
•
•
N
•
wD
.--_
0
_
•
N
_o
,-_
--
,o
_
•
•
•
•
I
J
0_
.,-4
_
_
o _ _
$
_
_ _, _
l o
_
_
_
_
_ _ _
_
_
-o
.
O
I
_
_
o
_
• o
_
N
I
I
_'_
l
"4
0
..a
wD
0
"
I
G
0
5
v
X
II.
_
uJ
,-
0
0
rxl
_.
w
o_.
24_
--
--
1
tJ
B-747
DATA SOURCES
I-_.nke_ C. Rodney and Donald R. Nordwall 3 The Simulation of a Large Jet
Transport Aircraft, Boeing Rept. No. D6-306433 Vols. I and II,
Sept. 1970.
242
SECTION X
C-SA
243
C-_A RACm_ROU_D
The
C-5 A
is
a very
large
turbofan
engines.
sections
with
ailerons
and
spoilers,
surfaces
are
irreversible.
A
bobweight
The
of the
Longitudinal
an
bobweight
all-movable
SAS
is
and
is used
position
C-5 A
military
not
control
stabilizer
yaw
in the
is assumed
employs
stability
included
logistics
control
consists
for
be
at
the
augmentation
here.
244
trim,
of
feel
powered
elevators
roll
a conventional
longitudinal
to
transport
in
control
four
four
employs
rudder.
system.
by
All
The
control
effective
pilot.
about
all
axes.
A
description
0
.rt
b_
°,-I
CH
0
Q.)
°H
0
,--I
rO
m
0
•_
4a
_
.rt
4_
,)
)
4u
or-I
r_
cl
I
r-I
I
0
0
_1
0
0
o
d
,'-t
0
"d
c,l
0
o
o
I
i
I
4_
.H
0
®
X_
b9
,.-I
LFX
I
"7
(1)
,rl
.M
0
4_
OJ
OJ
0,1
OJ
LF_
_0
OJ
r'-I
o _ _
i
_o_o%_o
_
o
'._
_
II
4a
X
_
X
-I_
X
,_
_,
4_
X
_c_
_-
_
C--
Io
0
_
___
I
-I"a
_
I
4-_
r_
I
CXJ
4a
c+_
I
_n
_a
m
,'M
0
0
0
×x×_
_
_
'_0
0
0
X
_
II
II
II
II
_._
245
_
II
II
II
II
It
4-)
r--I
aJ
I
&
i
X
¢J
D
b
N
.J
246
C-5A
PITCH
AXIS
8esAs (deg)
I
Fcc('b)---_;)_"
K
I 8cc(in)_l
_-'(_)_''se(r°d)-I
-2'92
57..3
t
32.2
8.3
a zB at
_.
_B
30
i II
?"
20_
/
KIlbl
.._/,/
I0
o,ooo,,
40,O00ft
I
.2
O0
ROLL
I
.4 Moch
I
.6
1
.8
1
1.0
AXIS
8asAs(deg)
I
Fw(Ib)
8w(deg)
8a(rad)
KLAT
Config.
K LAT
8sp(rod)
YAW
Cleon
.121b/deg
PA
.155 Ib/deg
AXIS
8rsAs(rad)
_
63.5
F'i_re X-3.
-I
57.3
C-_DA Control System
247
TABLE
Power
A_&ch
X-I
Non-Dimensional
h
=
sea
level
VTo
=
247
ft/sec
=
2.7 °
c:qO
Longitudinal
Derivatives
=
Lateral-D
146
kt
irect ional
(Stability
Axis )
CL
=
I. 29
CylB
=
-.77/rad
CD
=
.145
Cn#
=
.075/rad
CI_
=
6.08/rad
C_IB
=
--.123/rad
CD_
=
.622/rad
C_p
=
--.458/rad
Cm_
=
Cnp
=
-.098/rad
Cm&= - .3/rad
C_r
=
.290/rad
Cmq
Cnr
=
--.293/rad
Cysa
=
--.O044/rad
Cnsa
=
.0091/rad
C_sa
=
.089/rad
CYSr
=
.211/rad
Cnsr
=
-.106/rad
C_Sr
=
.0209/rad
CLUe
--.827/rad
=
--23 . 2/rad
=
.385/rad
= --1.6/r d
248
Spoiler
Effects
Included
C -5A
654562
14
m
12
m
IO
m
8
1
Ib
Flexible
SL
....
_-
_
20,000
40,000
ft
ft
(deg)
6
1
4_
2_
I
0
0
.2
I
.4
.8
Mach
249
1.0
0
rU
I
I
I
I
OJ
O0
O0
o O
tl
i0
iI
U
0
L,.
j
_-
.lj
o
.a
0J
i LO
(-) _0
OJ
I
I
I
Q
_
J
0
250
I
_
_o
C-5A
654:562
Flexible
SL
- 20,000
40,000
Ib
ft
ft
_
5-4-5-2-I -0
0
I
I
.2
.4
I
I
.6
.8
I
1.0
Moch
1.2
--
,8
--
.4
--
CD a
f_
(rad -I)
o
0
I
I
.2
.4
.6
Moch
251
.8
1.0
Mach
0
.2
.4
.6
.8
i
I
I
I
1.0
I
C -5A
654362
-.4
--
Ib
.30 E
Flexible
,
SL
--- --- -----. - --
20,000
40,000
ft
ft
Croci
=-.%
(rad -i )
.\
-1.2
-t
Mach
0o
_..,,-._
.2
.4
.6
.8
1.0
I
I
I
I
I
-4-Cm_
,
Cmh
Cmq
(rad -I )
-12
--
-16
--
-20
Cmq
--
-24
--
-28
-252
Moch
0
0
.2
.4
-__--
I_
.6__-'L-_._.8
'_'_" I
1.0
C-5A
CL M
-I.0
--
-I.5
--
-2.0
--
-2.5
-
-3.0
--
654362
Flexible
SL
D
CD M
.12
--
.10
--
.08
--
.06
--
.04
--
.02
--
D--,,.
20,000
ft
40,000
ft
I
0
0
.2
.8
n
o6
n
I
.4
.6
.8
1.0
Mach
o4
Cm M
.2
0
m
I
I
.2
1.0
-,2
253
Ib
C -5A
654362
Flexible
Ib
-----.,--------
SL
20,000
40 000
1
CLSe
(rad "t )
,J
0
0
t
I
.2
.4
I
I
I
.6
.8
1.0
Mach
0
-,4
--
_=8
J
.2
.4
.6
.8
1.0
I
i
I
t
1
CruSe
-¢
(rad -I)
-I.2
--
254
ft
ft
Mach
0
0
.2
1
.4
.6
.8
I
I
I
1.0
I
C-5A
-.4
c_
-.8
(rod -I )
-I.2
SL
-- -- -- 20,000
--- - --
.I
____--_:_:
_o=. _,, c._
I
0
.2
I
.4
.8
Mach
(rad "l)
40,000
I ,_
.8/
t
I
1.0
C_
-.I
-.2
255
654362
Ib
Stability
Flexible
Axis
Moch
0
0
•2
1
.4
.6
I
I
.8
1.0
1
I
C -5A
-.2
C_p
654562
Ib
Stability
Flexible
Axis
-.4
(rod -I )
.----.(_...
_
I,_'_
-.6
SL
-------
20,000
ft
----------
40,000
ft
Mach
0
.2
I
.4
1
- .04
Cnp
//
- .08
(rad-')
- .12
-.16
256
.6
.8
1.0
I
I
I
C -5A
654562
.50
Ib
E
Stability
Axis
Flexible
.4--
,SL
\
•----.---- 20,000
ft
--------- 40,000
ft
\,
C_ r,
Cn r
°2
(rad -I)
C_ r
0
.2
t
I
.4
.6
I
.8
l
1.0
Mach
-t2
--
_,__,___j_,,L_"
257
Cnr
.04
....
_----"
SL
20,000
40,000
I
.2
I
.4
C -5A
654326
ft
ft
Ib
-
C_.$o
-I
(red)
.02_.--
0 I
0
I
.6
I
.8
Mach
.02
.01
Cn_ o
-I
(red)
0
-.01
-.02
/
]i
-.03
258
I _
/
tf
I
1.0
Mach
0
.2
1
0
-.002
-
-.004
-
-.O06
-
.6
I
.4
I
2
5
5
6
1.0
I
.8
I
4
87
9
C-5A
6545621b
.O8
%%%
.O4
0
0
I
.2
........
1
.4
I
.6
,.,,
1
.8
1.0
Mach
SL
20,000
40,O00ft
.O2
C n 8sp
(tad-l)
.01
o
[
0
.2
I
I
.4
.6
Mach
259
I
.8
I
1.0
ft
.2Cy8 r
(rod -j )
.l
--
0
0
I
.2
I
.4
]
.6
I
.8
I
1.0
.6
.8
1.0
Mach
Moch
00
.2
.4.
I
I
I
I
i
-.04.
Cn8 r
(rad "t }
-.08
SL
20,000
40,000
C-5A
ft
ft
654..362
Stability
Rigid
Ib
Axis
C,ts r
O0
....
I!0
Mach
260
_t"
_
,,1
C_
,0
,,t
er,
f'_
.--4
,_,
,,1"
..-4
tr,
•
!
I
c3
.--,
0
C)
0
0
0
_7
_3
*
O0
I
r_"
_
•
f_
0
0
0
0
2
..
o
o
__
0
{3
0
•
_0
0
"4
0
*
*
O'
O"
I
0
"4.
UJ
÷
ill
4"
UJ
4111
•
*
0
d
,0
0
0
•
0
U'_
•
,,0
.-4
•
•
•
•
I
I
O_
(_
0
4UJ
4W
+
W
÷
W
,--4
.
_
0
O0
CO
_
,0
O_
0_
.
0
er_
0
_-
0
,,II
•
II
vll
,,0
_
_
07
4-
_
_D
0
•
e
•
O_
_"
"
0
o.}
÷
W
,....4
,40
,,,,1"
*
'
'
_
I
_
CO
4LU
_
4W
P"
"_"
IJJ
r -_
O"
*
0
0
u7
0
0
0
I
I
•
.'-*
t.,"x
t--
0
0
I
•
{3"
,_'_
fq
_
O"
-4r
•0
r_
CO
4-
03
4-
eO
4,
I_+
I_-
,--i
,0
,_
.
.
_
|
o
261
•
I
t'_
_
•
0
I_-
0
0
0
0
_
co
!
_
e,_
,4
_"
C.
I_
I
_"
c
_I_
0
_
I_-
-,1"
_£
u',
°
I°
I"
"
_
_
_
"_
r_
0
N
C,
_
0
_
0
;
c
0
I
_',
0
I_
_
"..I
;
l
I"
|"
";i.O.
I
v
o
N
0_
•
¢'ft
co
t
_
O
0
_
O
o
_-_
0 _
t"
_
I"
¢e_
"
0
O..I"
•
_
_0
-
•
CO
I_
_
._
0
,0
_
oo
_
0
0
0
0
I"
0
6)
-4"
_•
0
0
_'_
*
0"
0
cO
N
0
0
o--
c_
I"
_
"
'
I
I
0
0
I.[J
¢o
.,I"
O
0
_r_
_0
"-_
,0
0
cO
"
0
0
0
0
0
•
I
0
I
e_
N
¢_1
_I
0
_
,0
cO
•
N•
¢_l
I
*
I.L
LL
LU
C
(Y
t_
_I"
•
,.
-_
_
•
N•
_
I
I
I
.-4
O"
_
__t
_
(_
,#.4
I
I
I
I
I
•
•
;
"
I
•
•
I
.
0 "
I
I"
•
I
0
0 "
|
I
_
_
.--I
I
•
o•
_
l
__I
•
.
I
c
_r_
C_
0"
'4"
_v_
o
0
0
°
I
I
_0
•
I
_
•
o
0
07._._...
Ie
I
"
•
I
l"
e_
0
0 "
I
•
0
0
I'
I
"4"
_
l"
I
_-
I
_0
I
_
I
I
•
O"
P--
,I"
_1"
I
.--I
_t"
.--_"
I
'
aO
_
-,1"
I
LLI
u_
I
U._
,_)
I
ILl
I_•
.0
¢_
I
_
-,1"
•
.._
I
O"
-,I"
"
r _.-4
•
,4"
.-_
"
,,1"
I
U_
I
.0
I
.-_
_M
N
"4I
I•
o_
•
-'_
t
0
I
I
_0
(7"
0
_
f_-
_l
•
0
I_-
I_"
•
I_-
l
I
I
r.)
I"
'-'
U
"It
_t.
I
"
I
'-'
"'
"'
I
I
I"
•I_
.U.
'R"
X
_4
_
I
t"-
_
_
I
X
N
M.
262
I•
I"
_,
_,
"-"
=
I'
_.
I
I"
_
N
_
o
o
l
_
._
I
X
_1
•
I
=
'."
I
•
IL
•
l'
I
"'
I
'"
I"
"
T
-r
"I"
X
N
E
,/.
,c
0
C_
_
co
wt
F
O
•-" (_
_
- wE. CO
"_
.[
C. _F"
C
0
C_ CJ
•
•
"('_
0
•
o
_0
F'I#
r:
I
&F
_2
0
c,_
_
•
,4" t _C.PO_t
•
•
U" .f_ O0 (_r
• Or_
.f
wD 0
"
°
l.fl,'_}
0
0
'
. ,.-w
I
•
•
f_co
O.C_
• c)
I
•
0
• -.I
r-_
CP C_ C_
•
•
I
I
I
I%:
C,
o,#J_
I_) _t F'- O"
<I" _D u", •
O0
• ,-,-_
r.J _i_ ..* u
,o_:
mm
,TI •
I
,urn
0
°
_:
cr .c_
f
v_
, m-,
..®o
0
.,_ rxl 0
oO
_00
o
o
•
I
.-io
I
°
u',
•
f-j o
l_J .-_ eq
•
o
_00
i_
O_
o
,f'.J
I
•
I
o
Oo
.-_
•
I
,o
F- _o
O" _0
f-..
t4_
_00
,...1 o
_
•
I
I
e¢_
!
I
CZ)
_"
um
o
._i i.i_,
u'),O
0
,.-_I_ wO rwJ
• 00{_
0
O0
, •
l_l {_) (I"
•
If_O
C) erl r_ ,0
_y (Y; 0 o
,i _!
!
_A
o
._I i.(_
•
I
rw
0
_- (-,_oO
_o°_
I
O"
f.- .,7-
_j_
,or'-
0o_,
wOO
•
,
_oo
!
•
t'-
0
_
,-4
I
I
o
0_
ii_,(_0 aO F•
"00
I
0
,..w_
I
0
•
I
I
I
w
o
0 .._ (-w
l_o _o or_
2 _
•4" u'_
,,_
O_
_o_
•
_,
v
_N
Aw_
L
D_
Z
263
o
•
I
I,M 0,5
I
_
_0
_
.O
!
u_
.40_
I.L, C
('c, _C_ f.-
.
•
7,"
I
"i
•
I
I
,,f
C)
LU ,._
PJ_
m
M
*
I
I
I"
I"
O, p.
OrN
I[_
• I
I
un
,0
•
"O
!
w
"
,,t"
UJ<t
oo
..t" .-_
_
•
I
•
I
4"
I.-.4
0
•
I
I
|
_
PJ
Ot¢_
•
O"
I
*
I
•
p..
II
!
u.l P-- _"
O0
_0_
OOZe
ea*_
•
(
•
I _)
_J
tO
p,_ _i_ c_I
_o_,_
,
•-._0
!
,(%1
I
_w
,0
o
!
Oo
e,4
UJ ,,1 ,¢
,0
w
b-
,,t
u_
I
w o" iJ'_ p-
00_
,...i f¢_
•
.@
•
t_'i 0
!
•
I
•
i
•
I
_ju_
.-.t ¢M _
O
c,
•
I
•
I
I
•
_OC_O
•
I
u_
I
tu ,c _
,¢ t',4
_!r ,--t p._
00_'
•
6
4"
I
O
I
•
I
I
_
_o_ _.
•
,,D
m
I o
.,-JO
_00_
-,t"
*
•
I
o,,,.i
7?0. •
@
•
!
,0
T
I
.,lr
! 0
m_
m
•
•
!
o
•
_.? ,-•
I
_N
00_00
Z
264
I
rxl Ck_
,
_oc
,_o
•
"_
0
i_. ,,,0 a.+
*
O O
O ",G
•
C)
C._ct_
•
•
_
<_-+ ,4 f.-. <<-+
G+. c...
•
•
I
I
+C.,
I
•
I
I
I
•
.C_l
m_
o
c_
oo._
r,,+
•
Ca,_
•
•
C._O
•
+ +,
C
•
I"
I
P,,- ++
C.+
•
I
++'_
v
p-f_,
,,o IlL
0,_0 *_O_ O
..+P
.C)
._
IZ,
OO
"
I*
• I,_ ,O
,i+) +j: u., _+- e
•
+
I
0
O01f_
,
•
0_0_
+000
00,
o+I.FX.,-,,_
f.cl
0_
0_o*
O0
.I_CO
,
• 00
•
o
.r_
I-I
I
Pl
+t +-,
_5
tf_ rr_
CO 0
U'_ Oa
O0
,,0
.
+
I
ro
El
_e
0
o.--.
,4-¢o
0
oa
O0
t_
,._
_0
_+gg
_000+
BI
I
|
_
°
I
I
I
I
,Do
:z, 4;
NOlO
o
0
•
_O
O O
fel _,.- _0
I
I
•
"
o
,-_
I
ml
,INO"
r..)
H
r/_
iz_
cr_
• 0,I 0
oo_
0
o
•
•
OO+
*O_
I.I
.OO'_
I
0_1
0
6
0_0_
O0
o_
o
_OO_0
00*
•
•
!
•
I
_00
g4 _
o_
0":
i_
_0
0
oo_
o.
•
•
• 0
o_
i_
,-,I I%11_
z
265
_
i'1
_
+'+_
•
".1"
QI
_•
o_ o. _
u-_
,4 C_ _,
_I
C_
i-_ c_ ,.-,cj
•
I'
I
"_C,
" P_
I
I
I
'4"
_D
I
I_, ..1- ¢7
•
Oo-.t
I._ P_ l:c.a
•
CA
•
o
I
I
_
I
._
°
I
I
I
I
#
m
h-N_
,....I
_0
• N
0
•
!
I
. ,0
I
I
-=4
•
•
I
•
•
•
I
I
.IN
_t
O0
cO 0
O0
•
I
uj f_l
L.U _.-_
_t_ N
•
•
I_"
. _
•_" ,0
I I
•
,,-i
•
I
_
_O_N
.-.4 N
.=_ .
f'..- n.J ,,t
LU
_
o
I
__)
..o
0
0_
bJ ,..-I _Of_
°
I
,?
t,LJ ,o
,,_
_0 nJ r_l
0 ,4r .._
Nr_1"I • _._
I
I
0
•
_,_o
•
•
I
.,.-i
I
I
it-,
I
un
,,,,_ O_u
,o
-.It
NllmN
f'@ _-
•
I
I
I
I
r
I
?
A_
O_r.O_D
uJ
f_
0"0
•
_0_"
"_
I
I
o
•
,o
I
•
1
I
l
0
I
I
tu
f_
f_
UJ 0
_0
•
_Ul _-
I_
!
I"
•
I" I
I
,0
I .o
LUc_
I 0
ua..f
ua
P_
.-4
•.-4 .
I"
•
._0
•
I
I" 'T'
i
_N
w_w_
w
a
I
_N
_0_
266
N
w
°
• c_j
O"
0
-,i
t-00
N
,.4
C_
e
"
i_I
C)
r_
I
i
_xj
•
I
I•
_'¢
I•
0 _
0
_t
P'_
I_-
•
G
_
I
0
0
0
I•
,0
•
_
o
t_
,.-*
•
v
0
N
IM
E--I
0
0
"4)
O"
0
0
-.-,
.-_
!
•
0
0
0
c_
Ud
X
UJ
UJ
U-
0
./
_J
0
ul_
•
,-4
I
_*
C)
,_')
¢Xl
_U
_0
,.0
¢'_
_)
I
0
H
¢'_
.J
0
0
nr_
,_U
¢_
C)
:)
•
!
•
..-4
n,I
00
0
I_
•
I_
N
O"
N
_l)
i_-
,,1"
N
0
_
..-I
•
N
,,1"
,-.
•
,,I"
!
I
l]O
0
I'
-
g
I-
;le
_.)
"I-
_.
v
U-
g
...'4 2
,,
9 2
-,,_,
,_.
267
LI.
F--
0
e_
0
cO
•
_
_
_i
,.=e
*
i'_
oD
_
•
,_"
•
.=.4
O_
0
0
_
c_J
•
0
0
_
_q
•
oD
0
•
_
0
•
0 _
_
•
r_
aO
•
I"
I
N
X
N
I
!
4,
_J
U_
268
•
I
!
,,t
I eq
o_O.
.4r_,
c_ cO (_ 0
O Lc, ..-4 .iD
ea0
(_o
i
I
I_
I'
0
0
•
•
IT,d
I
I
I
÷
0
0
r'.._O_
O_O_
o
•
•
•
I*
I
4-i
u'_
I
o
0
oO
0
Q.-d
o,-_
O_t-N
P-_'N
er_ ,...4
o
_£__-_ _0
oo@_
o
•
._0
• I
I
•
_,-4
•
.O_OI
!
I"
÷
"4
0
I
LU_t_
O0
0
.
_0_
• ..-4
.
•
I"
_._
o
0
H
!
I
_
N.,t
o
_o_
_
u
•
•
N
•.0
•
.O
* ,-d ,-_
e,.N
II
I
I"
O
r._
I
U'/
I
I
÷
I
!
vw
÷
m
X
H
_-c_
*.-_
e..-4
•
•
I
_
A
_
i,-4
e,-_
I
I
+
_
o
-_r
0
0_
_0_
o0_o_
O
•
I
o
!
u',
_0_
*0
• ,-_ _l
I
•
r_
a0
•
I
I
I
N
uJ p.. _
-JO
•
_O_
_0_0
O•
•
I
• .-_ u'_
I
!
0_
•
I
•
•
I
e,.I-
Y
w_
÷
n4
a0
t_
0
oo_._
oe_
• _4
•
•
o
• N
o_O
it.,
_o_
.
l',I'
I"
I
_.0ii
I
!
_N
t_
_N_
_Z
269
•
÷
0"-
.o
um
o i',.,,tad
,._ ,0
.4- ,0
_o
CD
•
I
,
I
.-_ 0
oO
, 4"
•
I
o_r
e4
•
,.--_
I
I
•
I
I
II
-I-
oO
co
oo
,,1-1 _-
¢
o
•
•
O" 4" nn
0
_0
r-.o_
•
•
I
•
t
!
I
I0
vw
÷
_L
o
o
o
O0 .-_
_=_'
0 (_' _1 _
..,q q,- 0-. _-,_
aO . .--4 _4
o_
o, -i _e4
_0,0,
O_-,t
!
I
I
I
I
.I.
_o
o
o_
-,t_
e.4 ..._ -.,_ :%1
_
0 _,% ..._
u',
• ,.-¢ e.4
o
0
•
*..-.4
O0
•
•
,Cr'
* .-I e4
I
, o
,-, e4
I
_o h%
I
I
v
w_
o°
0
O_
_0_
_,J _'4 e4
0
"
•
, ,-4 u_
!
OO_O
0',"
I
I
!
I
r_
tl
_v
¢'J4"
0
r_ e44"
• 0
e4 _4
I
I'
I-.0,.-4
I
"
I
,,-4
_A
_4C_
• 4"
• ,-_ e4
I
r,4
, .-4 ¢_4
I
_v
0
0,_
I
_v
"
,_0
_0
o
r.,.i
_jo
I/I f¢l
_-j _%1-.,t ,o
_0 O0
_"
¢'4 ,_4 I"4
JZ_
#,,
•
I°
I
,.-4 e_l
I
I
O, ,-4 -0
"_ZZ
,.-I 4 I
II
,r ._r --¢
0"00
Of-•
• • t-4
I
0
I
0
,0
÷
i"..4o
_
.-I
Cgllm
oo
¢..0 _1
_4
,
,o
r_
*o
,,-4
I
q
|
_
_-3 tu
,,-i 0
I
*
,
_
.-4 _, ,..¢
in
z
,
u.l
._. i'=
270
_i. 13_
!
•
÷
÷
0 _
0
O
I'_0
•
•
0
w.4
0
I"-
N
--
_
•
_
"J
_
N
I
I
N
d
I
I
0
..4
I
I
I
_
_)
I
I
0
,-4
r,-.
N
I
I
o
,-.
_0
0_
•
0
,'_
•
I_
O0
w-G
_
_
•
N
,-4
•
,4
rq
,,,o
_
,,
aO
N
0_
._.
0"
.4"
¢_
I
h-
O
O
.4
I
a0
_
_r_
.4
,.-4
l_
41.
N
r_
_0
c@
•
I
_
f_
_r_
O
0_
O
O
•
.-'6
I
_n
o
o
o
•
co
_n
-
o,
m
,-.4
_
•
N
¢
•
r
_
.-4
Ie
o
=
-4
o
o
_
00
N
o
m
_
-
m
o
o
o
"0
I¢
•
f1_
i
•
_
.-4
•
_
rg
0•
N
',.I
_1"
eq
O
rq
,-4
i_
÷
o
•.,1"
j
_r_
,4
_
I
N
u_
_
_t
r_
.-_
e_
.j
tn
f,_
0_
I
O
.4
N
0_
O
ur_
I
A
I
.e
N
J
O
O
u'_
•
0_
,0
I
,0
r_
0_
0_
O
I
r_
rn
O
_
,,1"
_
O
0•
0_
u'_
0 _
ur_
N
_0
•
I
I
C_
•..4
,..J
e
I
rx)
I
IJLI
3
"
G
u.,
1-
uJ
_
w
_.
_
_
_
271
_
I
C-SA DAT_
SOURCES
C-5 Flight Control Report (Aerospace Vehicle) Stability and Control,
Lockheed-Georgia
Rept. No. LGIUS_2-1-1, 8 Feb. 1966
272
SECTION
XB-70A
273
XI
XB-70A
The
XB-70A
supersonic
craft
was
cruise
to
two
SST-related
XB-7OA's
had
zero
The
first
airplane
Pitch
control
geometric
in takeoff
is used.
Yaw
45
flight
identical
dihedral
while
is considered
Roll
control
is obtained
is provided
aircraft
except
that
systems
built
with
became
long
range
research
air-
the
second
by
the
Lad
the
first
5 deg
airplane
geometric
(XB-7OA-I)
dihedral.
here.
elevon
canard
rotation
is
through
of
the
and
locked
canard
and
a
differential
vertical
surfaces
fixed
except
canard
action
stabilizers
of
flap
the
about
elevons.
a
line.
shown
test
two
interconnected
where
airplane
Data
were
employs
as a weapons
problems.
landing
hinge
The
The
and
control
deg
designed
capabilities.
explore
The
originally
BACKGROUND
is
here
data
equipped
is
where
with
stability
a composite
of many
possible.
274
augmentation
sources.
The
in
all
object
axes.
was
to
use
o
.,-i
4_
o
r.D
bO
.,-i
r_
0
b-
i
H
275
0
o
\
\
4-)
o
E
,--t
J
0
0
&
!
I,--I
X
°,-t
N
;!
OD
'+-
o
I.D
--
II
II
1'_
II
276
XB-70A
PITCH
AXIS
(_eSAS (red)
I
.025s
i -
z +.35s+K
See
Fig.
PA o/t
Clean
Config
--
a z at 1B
50
_
SL
_
20,O00ft
40,O00ft
/
60,O00ft
/
_/
l
FS i
I0 Ib/g__852/2
14 tb/g
1479.2
Clean
PA
8c(rad)
Effective
Bobweight
B
_....... -
//
f
"/'-
--e
I0
0
0
ROLL
I
1
I
I
4
.8
1.2
1.6
AXIS
I
I
I
2.0
2.4
2.8
1
:5.2
8uSAS(rad)
I
FLAT/
CC ,in/Ib)
Much
=--
8cc
Meg)
.41
=
57.:5
_
I
1+.075
I
I
.-_ 8a(rad]
I
YAW
AXIS
8rsAs(rad)
FpE D(lb)
KDIR
I
I _PED(in)
Config.
Gear
Gear
Figure
K DIR
UP
281b/in
DN
3lib/in
XI-5.
XB-70A
277
8r(rad)
GDIR
57.:3
G D.R
.96deg/in
4.0deg/in
Control
System
B
j-2169ft
I0 96ft
XB-70A
PIT.___CH
SAS
8 (rad/sec)
-_
az'
34.8ft
at -_x' = 1 36.4ft
Normal
8¢¢(in)-_-4'65
ROLL
at F.S. 1174
}
SAS
p(rcd/sec)
|
-
j
YAW
Accelerometer
Clean
PA
_
8OsAs(rad)
SAS
r (rod/sea)
_rsA s (rad)
Figure
XI-4.
278
XB-70A
SAS
TABLE
Power
Approach
XI- I
Nondlmensional
h
:
sea
level
VTo
:
347
ft/sec
ao
=
7.5
deg
Stability
:
209
Derivatives
kt
Lateral-Directional
Longitudinal
CL
=
-333
Cy_
=
--.183/rad
CD
=
.055
Cn_
=
.132/rad
CL_
:
2.6/rad
C_
:
--.072/rad
CD_
=
.56/rad
C_p
=
--.18/rad
Cm_
:
-.23/rad
Cnp
=
--.26/tad
Cm&
=
+.09/rad
C_r
=
--.03/rad
%q
: -1.9/ra_
Cnr
=
-.25/tad
CL_e = .46/ra_
CY$a
:
-.063/rad
%_e
c_ a
:
.042/rad
Cn5 a
=
--.O052/rad
CYSr
=
.12/rad
C_5 r
=
-.O018/rad
Cn_r
=
-.103/rad
: -.19/raa
279
GJ
®
/
CO
N
/
Oea
¢'*"
1'7. LQ I_
Xt¢_
/
T_
J
v,,i,.
,I,I,-.
q
i-
/
'ILII--
00
O0
oo
0
_O
_10"00
I
I!l
III
I I
'1
N
CO
I
I
I
I
I
I
0
o
.._
0
5,
_.
---Oj
_
Q
I_'_
ID
0
3;
00_
,
m
X
z
q00
2
I
I
I
I
I
0
tO
o00
00o
o0o
_ c_o"
03
c_
I,I
o.
¢o
If)
(M
I
O.
--
I
I
tO
(x.I
.
¢.)
281
I
-_
0
I
tO
Q
0
0,1
0,I
,,i
J_
i
wl-.w_
w,-
®
000
000
o_'_
I_. LO .-
'_
ooo
I
Xl_ll
m
-I000
•
III
I:il
g'l
tD
/
0
O,J
®
q
r
¢-
o
o
o
(.0
OJ
I!
I-
/
Od
#
cq
0
--CO
II
I-
o
f
sJ
_
_
4 _
I
o
e6
I
o.
_
I
o
--
0
1
o o
0
o'r
_._
I
o'r
¢'_ "o
o
282
Od
0
I',.-Io
r_--
"-
×_.,T
\
Od
oL
C_J
f-
I
_
)
0
O0
I
I
_ 17i
I
0
I
I
I
I
0
0
I"
I°
I
I
OJ
I
I
_" .aT
E E "0
0
283
I
I
_
388
I
,!1
u
I
,11
N
I
I
I
I
I
I
0
I
I
I
I
I
0
!
I"
_E
E
c_
284
O
Jr"
Xtj_
¢q
\
o
-{D
__A
I
I
l
eO
¢q
--:
I
I
O
!
®T
285
t_
t_
_O
mOO._
XrOnr
/
CO
l
¢q
¢q
÷
t_
J
tM_D
o
¢X]
|
¢q
o
¢q
/
e(.)
e(.)
o
_D
I
I
/
I
/
¢q
tM
I
|
{
I
--{D
I
-- CO
I
O
o
t_
I
¢j
u
--:
U
E
C.)
v
I..
C.)
286
_-
O
O
e_
OOJ
I,.LO
4e-
mGO-X
rr) LL
o
oJ
O,l
_D
ii
oJ
OJ
,¢._
t_
oJ
o_
0
oJ
Od
e(J
¢t.)
0
o
L_
OJ
¢q
OJ
Od
I!
%I--
II
i-
$0
0
0
I
I
CO
e_l
I
m
I"
I
_T
eO
oL
t(J
v
287
"13
0
0
0
e_
o_._
I_,
,.)
r
mCO-X I_ I.I-
o
txl
o
tt')
LD
oJ
II
Q_
¢q
tO
0,l
o,I
(D-
-S
0
O0
l
i
CO
n
l-
tA)
O
I
I
l
!
i°
i°
J
O
I
-_
o
I
I
m
Q.
c
I
O
288
iX]
,6
CO
o4
00
t_
oJ
0
0
0
i
-d
®
OOO4
!I
cq
®
0
Od
0
(x]
r
0
13
O0
O0
O0
II
®
\
0
0
n
¢q
(
o_
00 --
m
-Xl_l,
I
I
I
0
0
0
I
I
I
I
I
O4
I
_.....
m
L.
0
&,.
v
289
I
"0
0
a _-
o<_
O4
04
.5
mOO
o-X_mb_
.5
.9
®
CO
N
OOO
OO
000
04
_0
,,
_-
O
¢M
oJ
¢¢J
o
/
oJ
>
_.
I
-_.
1,
O
o
O
>'
O
I
I
I
_t
___1_
_
.9
e4
--
9
o
o
o
o
I
o
0
N
o
I
--
O
Q
O
c
O
290
I
04
O
I'
o
I
!
D
L.
I
--
I
O
_-
X l,,r) m I,,L
rd-
0J
000
000
ooo
i_0 N
t_I" I.D
!1
o
'5
I
I.O
I.D
0J
0d
/
1,
0J
!
I
--¢0
0
0
I_0--
0
0
I
I
,¢
0
QO
0
_.
I"
-_"
291
I
I"
I
0
I'
o
,--*
0
o
.I: _;
0
0
_.
,0
+
_; _, _
o
_
c;
o
o
_
o
o
_
.;
_,
_
_
0
_M
_•
_
0
N
I
I
•
r_
co
o.1
•
t _-
0
0
i%1
J
N
I
I
o
P_
_
co
w
uJ
uJ
L_
co
0
P,I
0
J
_
o
o
0
•
!
I
•
I_-
_0
a0
c_
P'-
0
0
o,1
!
0
_° _
CO
_
_
_
_= _
_
UJ
LU
LU
If,
_
o
_
_
oo
U'%
_o o
0
lb..
_-
tl
o
N
0
•
o
_
0
0
_
o
•
I%1
I
Io
I
v
0
-4"
o
*
_
r_
_
•
_I"
_0
÷
LL/
r,-
,_-
N
coo
÷
UJ
4.
UJ
0
tt_
_
0
0O
•
N
-P"
0
P•
0
0
I',-
•
0
o4
•
N
I
_{_
I_
4.
aO
4.
CO
+
(:_
o
_.o
o
0
_
o
0
_O
o
N
o
,0
.
N
_
.0
_
r',,.,
_
_
_
<I*
_
_.
o
o
0
N
•
N
I
CH
I
O0
0
_
o
•
li
,0
N
..,I
V)
o
0
.
r,_
0_
;
_
U_
_
_
@
+
÷
o
_
_
_
_
"4
0
_
. ;
CO
0
o
_4
J
P-
0
A
_"
J
o
N
•
U
0
(;
o
•
!
I
o
-
i,_
• -
_
r'+
_
co
÷
_
00
÷
_
un•
_
®
-
• o
o
_
0
N
N
I
I
292
•
•
I
I
0
0
0
0
0
_G
0
0
•
I
I
,
I
77"?T
em
0"
_0
•
v"
v
o
;_"
0
"4"
¢-J
0
0
0'_
I'
I
•
,0
O"
I
I
o0
,,I-
_00
S
I
O
I•
I
I
0_
o
H
_
_,
•
!
E4
0
_
C
I
I
,0
,4)
4"
,43
_
.._
o"
T
-.1I
w
h-
0
(:3
I
|
!
I
'
I
o',
I
•
0
_
_
_
_
_
0
O
O
O
t;_
I•
O
4"
_
_
I
_
_I"
_
!•
"-_
._•
_
I_"
I•
I
•
I
_I
LU
O
O
O
0
o
!
I
I
_
0
•
I
o
_
I'
I
,_
o•
_
_
#
_. o
_.
I
4"
•
.-_
0 _
4"t
_.
I")
_0
I
I
O
4"
I
bJ
_
.-4
_"
_O
I
O
41"
I
I
•
O
_xl
N
l
O
rq
I
I
,o
I
tU
I
'
I
H
r/)
I
A
03
H
4"
O
_
O
_
O
0
_x_
o
•
,-,
O
0
I
O
o
•
_
_
I
O
o
•
0
0
_
,-'4
I
•
•
•
_
I
•
I
.
I
•
#_l
.
l
I
_
I"_
_0
•
0
o
•
g
,o
I
IJJ
o
t'-!
,_
o
_0
_
o
I
_
o
I
_
o
_
•-_
_
rn
O
I
O
I
_
o
I
_•
I
O
c_
c;
I
I
O
293
_
_:
r_
I
._
_
I
o
._
I
I
_
O
__
o
h-
_,_
_
•
I
I
I
_
em
I
_
I
e_
*,0
_
,-4
•
"
I_
,
O
I
_•
4"
o,
I'-
_
o
"
0
_O
_
o
c
.
o
_'_
•
¢
CC_
c
_
N
•
.u
c,
r_
¢¢
q.
u
t.r
"
_
_
C
•
•
.
L
.
.
t
•
r..
-,*
u
,_ _s 2 j
P
I
*
•
*
{
C
r,_
¢..
.7.
u-,
_,
o
*p
U
L, •
¢%
q
v.
I
I
•
e,
I
p
(_
•
:2'
c_,
(%,
a
"*
U,
•
*.L
.-
C,
•
"T
_''
.._
¢
p.
,.I
U.
*
{.-
•
*
¢¢C.C
C.,
•
c
•
¢"
•
•
I
c¢:
<
.acl
.¢
.4o
c.
,J
C
•
T ":.
o
I
I
r_,
¢-
C,
¢_,
*c_
c_
_.
_.-)
_¢-.
•
p,.
•
_
r_
•
*
._-
•
I
C ¸
•
•
E.
pr,
•
I
(7
I
(D
u%
"_
•
.
*
E2
..C
I
f-.
@
o
PI
C)
*
¢:r-_
_CC"
O"
_
O'
_C'C>O
¢_
I
!
°
•
(.,'
I
•
*
I
I
i
i
0r-[
_I_
¢q
_,
¢qO"
,u"
_
cCC5
4.*
•
-,._ g7
Lr
4
..I
(7
¢_
o_
C2" L;'
,_
I
_',
;_.
v'*
0
r_.
_-U_
•
-
..T
_
I
I
•
,
Cr
°
C>
C._•
.
LC
•
q-
O"
LP,
•
_._,i
._
r, _, _
_c, ¸
I
r_
C
_
C_eM
_
0
•
r,
I
I
°
C
I
_'C"
I
e,x,
¢,-
O"
o
_
I
I
!O':
.-_
•
•
I
v
I
tr
,D
t_,
r--
,:r
.
*
_¢._
I
*to
i
_-I
C,
C
LF
r'-'
C
("
_
C,
_"
•
I
t
0
r--
_J,._
C"
ex; _.
C"
r_j
._
_o,_
0
u*.,£_
U._
.,./
_
b-
L_
.
.
LU
I*
_.2_ :£
U
,-..
"_
_,,.
t-,4
•
_J
L_
tL
'
,._
_--)_
7_ 7
294
F-
t--
.,I
l"
"_
(_:
•
_(,
C,
•
_
-
r"
_
I
C
+
v
c_
.-Ic
ccu'_
(¢
,_
G
U
L_
¢
4
,-
u
•
I
f,[_.
ix,
c
I
•
,,1
c
C
I
,,£
i
cr , /
b
u-
_"
c
c
I
I
(7
•
I
•
*U"
¢
c
_.
¢,_
•
.
,
.'4
t_
+
.4
o,L
•
ck
_
pr._"
u-, (<
"4
4"4(I_
¢.c
u
p-- _
t
c.
U. r-
-+,,p c
,_
•,_ u
I'- u"
(.. C_C
•
CM
•
o
rk c_
I
v
i°
P-
. i ,.L ,/,
u.+ .t
_,
_; L+, .,C,
OC.C,
.¢.4
+
.
¢,. c
I
I'
.
n-
I"
o
c
,_
..I"
¢_
r.- ct
l--- p,
en_O
c_,
I
•L
c, rq
LL ..,_ ,,',
u% o ,_
o
•
¢,j
c_ (_+
c
,
i°
,,t
(-
c,c_
_r
•
.r,
{•
•L
I
c_
C
I
+¢
c.
_,CC."
c,
tk
_'(_
_
•
I
,4
o
u-+,d-c,d
U
t-O
u_ eq
uh _
c
r,_ c',J
OGcC
•
C_O
.04
¢_J •
•
c,- e,_ c_
LP _ L_
evC_
I
I
•
C_
I
ID
,c
.I
<D
I
t_C:
.-+ o
I-4
_
0
•
•
I
r'_
cr
•
,
I
I
I
_r
• r{
,,1"
e,.
,ZJ
0
O'
o
. ,--+
•
C
b_
Ix: •
• I
•
4
O0
u, ['_1
•
_
,,t
P--- +"+ OP++.
",1 C"
'
"
u
0
.4J
I
I•
•
* 1"4
,-"
P+O
•
I
I
0
,
I
i
.,..+
LU .-'_ U ' ,O ..T
_÷ P"- P'+.: ,/' O"
C"
_,j •
•
_
<I-
,0
_SZ*,
07 _ O'
c_ r r,
.
r..
• l
£u
Ol
e0
•
I
u
.
-,t
i,
LUU'
t-00.-4
o
o
_J
•
I
•
I
•
I
I
•
C
o
i
4
_
I
('_
c_
....J c,
t,9 c._
I
"-'
l
p_ t'4 N
POC
_
•
I
°
,..+
•
0
o
oo
*f'4
.
I
-4
I O
u-¢_
o¢-J
CC3_,
C_
,-+
q-- ,_
•
I
I'o
eq
,--,
•
I
04
•
_.-+
I
"4
•
•
I
_-
,.,..i
'4 e.,l C.+ o++
_P_
"0'4
e,,l ._.j
•
•
•
l
I
I
,C
,-_
C+
I
Uu_ P++.Ie,_
c,J
,
,-,
i°
I'
v
•-, t,J
c,9 ..
_
L;_-I- c_
D
..¢ ,..,
_,-F-
v
7_
295
I
C+ ,.",I
_: ,-
"4
C
c.
_
(:
• Is_
c.
(•
I
c. ,r, c
, .c_c_
t-
• _- o:
•
•
ir c
I
°
.
•
o c
• •
o.c
(r _
I
• i
c
•
,t-
,,c
L,
4
(
• <
e-
.c
u-
r-
c
.-
,
,4
G r-
• .TT
.c
°
.,
_
°
u-, f. _
°
.- c
(L c.£
.
•
I
e,
i,'(-_
•
•
_,_i
_.
I
c_
¢
L
r-.
_
o
°
°
rJc
c
c
c,
•
°
I
i
_._
• r--
_,hr-
c
_
L
°c
u,
• p
_.,
_ _
_e_
_.
f
° r
c "
.
o
c.c
I
°
i
_CT-
•
_7 4
c.) ,
o
c.t-..* ,q
w. _+ o
_'E c,_ .
•
0
I.-4
0
eL _,
I
°
0
•
I
• i
+
G
• c
c.
o
c
c_ _
• • _
I
_
.euqJ
• f,J • r_r
°_"
_r,
_
c
t- -_
,F. _
_._.
L
I
.
I
_0
4
I
•
I
I
I
I
I
I
I
•
l
•
I
cl
"
I
•
I
x
• el
_.}
_
H
U
'.J t..'
_ ¢¢,o
_
4m
• -L: O,
I
._
• it. _T
I-4
_ o_
0
._,
u,._m
r,_ C" C,
t-(?
_,
._-
0
° _
I
t'-
r_
t_
,
I
o_
,¢¢,
°_-
-4
u,_t-
_
e_C_
'"_ c r _,
• "'4
I
I
_'"_
• ,_
eC_
,
I
I
• ¢,
I
I
r._
I
.
_
c.:
I
°
• ,r
c_
c_L'
•
_n.t
I
°
.
_c._
u_
.rein
_.o
'
_e-oc
•
'-/, 0
_
°
_
t:,-
c.; v',
LL
I
I- F-
_" .......
_u
r-
;f
y
7"
296
°
°
T-
i
='2 _,_
_:_._F:
4
v
c
c
¢ ,.7_
,4:
0
_r_
c
c
0-4(:'
P"
0
P"
C
•
n
_
C
_
CL
C
•
•
I
I
•
•
I
_
r
,4
c
¢
U
1"-4
cx.
_._C
C
_i"
#
r_
u"
c
c.
r"-
',.h"
e.. c
g
._.
_.
h
_',,
-,L
I
"4
,.I
('.
Z.
C_
d_
f_
r,.
_'
0
U,
f_,n',
(
¢-,
Cs t_
, I_,
I
t"
C.
_÷
CJ
r_
•
oF
o.h•
I
cch
C
_eo
C,
C)
G
,eq
i°
÷
C
I_
t£
C,
rj
I
4,C
CC- r_
4c
o
c_'0
f_.
o:
•
I
C/3
rj3
I
o
t-_
¢,_
.f,¢
8
¢xJ_O
r_
•
q
.49
,-'_
eq
I
•
I
,-_
,(%
CM _L. iv
0
tl
-,D ",,1 _
.i
C_
0
0
0
1_'3 ,,0
•
"N
I
.,I-
v
q
,.ju
C.
_.
g
0
rJ3
t'-I
,-4
,,.-_
I
-t
c3
4-
•H
0
4-
I--4
q'4
q"4
0
O_
,°
0
,-I
a
CXl _
C)
¢)
I
•
•
!
,-4
-.7.) ,,-'_
• I
I
•
+
.4
C,
C_
f-..- _..
C70.
p-
..._- C-_
g
_'_
,L e-,
C.
I
C
_J.-_
•
•
I
I
I
C.,_
_,
4"
_
4
4"
u'-,
_-,
C.: _.-
•
•
•
G::3:
kY
297
_")
I*
I
.....
_7
w
7
_"
{_.
•
_
r,.
t
•
_
•
I
•
I
_
I
_o.. r,.
,_
,[% c,. c.
,,G
_r_
t_
I
_
I
iI
¢
4"
LL_
,G _
ab
,&
_
o_
oO _
I
P'- P_
o
,G
.,._
l"
I
,O
!
<D
P- c
I°
u_, -.!-
,_
,4"
Lb
o _..:_ _' _,_
•
0
c,D
v
l
•
,0
I
•
1
-d"
• I
I
,,j.
L'I
i-I
I
I
|
t_
L,LJ C" L_" _::, ,,0 Cd K'_._
•
I
•
I
.d"
•
I
I
"_
I
• _"
"'l
II
..G
t
•
P"
_'WO° '
l
..4"
I
l" --'
C_
P'_
i
-,1"
I
t
_ _ _,_ _ _. _,_.
•
t
' .=_
_
....
PJ
_.._
=_
2_
7
298
I
.....
v
C';
C
•
_,._._"
c
u-
c
cL
_
r_,O
u
f_
o
*C
•
I
l
U_
I
•
i
P
o"
_-
P_
r'_._ c...L
c.
IL:,
,.: U"
•
*_,U*,
• fN
*
•
•
_-
r r.
C
(_
"._.
I
C.
C-¢x.,
•..C, I¢
0
O
t'_
C,
II
,_ _ &_: ....
._
¢xj
•d•
,'-_
C
* _-20"_
rr, ¢r'¸
Cx/ C
0
O.,C
,,--i
o"
¢_J ._ o_
• o_
l_
I
o °
H
E-*
C
C
0
v"
U
I
•
*0_0
0
c0
!
I'--I
X
•d"
• r-I
(.._ u
I'N,_
O0
•
.
O'u_r'-
CQ
I
I
"
E-, _
o I
E-I
(',_
c.i
O
o"_, .,o
,_j_"
_
L_
C_ r,_
0.., ,-,,I U"
*_'_t_,
-_
,",'_ _0 /--- I_. _I_T
*C"
.re-.
*o'h
I
_c_ cr
0
I
*
-JC
o_o_,_
._ _.o_
o__ _ _ _ _.
c-_
X
• rq
u
C
_
.J,-_
_
*"_C
_
r_. _
U'. U_
_0_
" I_"
*
•
•"qO
_._, ('M LC
L-: _J
Z
(TJ
C} _
U:
k-
_- *......
U-, LU LIJ
23_
UJ
7
299
•
*
•
,
,-_ -£
_.eq
_'I'I/ 0
c¢, ¢x
•
,'--" c
_"
er
¢X. OC
• +---+
(x.
,Ix.
+ r,C_ C
_
•
_
+ (x, ,_
.<"
.
.l
.
TM
I
l
¢_.
i--
_.
_
,I+ .'
• (X. ,+¢_ _++ I_
.4 +
I_
(%o,
I#,
c,
*
,_',
_
'
p+
l+ir ,,t
_I
_
.1%.
I
I
C,
¢,.
c_
I".
,_
p•
•
pr., r.•
O"
c,
u
T
+-it+
_
,,-+
,_x.
I
_
• G
t.+'x ¢_
1_
C+,I '_
, ..I-i<, l_i
G
I_ CJ
I
(.+ ,..-4
_
,r<_
I
tlm
<<- c_
+.o _-
I_
0
pf2) _
I
i+'¢%,-+
•
4_1 /_-
I
1
r_
<D
C,+C
'--I
0
,4-
C"
Pc'+
0
+--+ ¢._
I
°
.,._
s_
.
.c_J
•
I
v
cO
I
I
IN
p.- ,-i l._t_T
I
¢_m p- _-xj
•
H
<%1 _
,-+ iX,
l _.# LI_
X
I
_+'
"
•
I
Um 0
"0
On
0
I
I
e_j
• PP, P+
• l_m ,+._I+i _, i_+.i
0
0
I_
I
I
i_
<_
l
•
p,-. em
i_
,:tm
I
,,t
,,? C
,-..., pr
I-,
_
• l.P
•
I
•
• ,.--+
,,'%1
e_; C5
•
I
,---4 I'X+ r,_ -,I-
_-_,--:____+
,,,,.
--.:.
300
opec+
*
I
,-i
c-.
• c-+
"4"
(-
(
•
u
l.f
e"
r_
q_
('-
f,,
t;
I_',
r_
o¢
r_- (%
C
_
If
_x'
tc
r_
_
r
L.L.L.
I_'t 'P"
,_
O
I_
r,
• ..? ,,_
r_. ,',_
,
I
-#
y
Lr
_,
rc
c_
_,-. ,
r(
_
°
•
C
c-_
l
I
4
c
I
•
ul
--
I
,d
C_
c,
h-
c-_ ,.r
_,
CG _.
• _,
r"
¢,.
(Nj C_
--_
*
:
er_ Lm
¢_
c
•
I
I
er, _
_
<_" O'
r,_ ee
-:r CC
_t
_,
• IN
I•
LL_ _
I
0
_
O"
P--
I
.,
I_'
H
_
I
!
H
_
,¢
"_
i_
°r-I
I
(._
,43 I._
(..." I"_ l,¢h
,,S" r_
N
o%
, t
5"
,
c,,
_,
•
I
!
I
_
0
_
o
m
I%1 0
me
w
_
• ,--,I
_0
or_
"0
.l%1
I
I
c
I_
_0_0"
I
I
C,
I
r-_
•
•
• _
(ma
"
•
I
.-I ,-._¢'M I'_I
_d
U22
Z
_"_J_N_
_'1¢
2L --
_L'-b
301
.-_--I
,-,I
_I
_
O,
Cc _
_
!J.-r
_
•
I
u"
I
o
<x. _
i--
P_
I
I
I
r,',
c
0% C.
_'
¢_,
I_
_
".'_.
I
I
I
c
U.
,-_
_C
C,J t_', C_ ,0
I
Uh
I
4"
tO-dO
,r_
OOCr_O
I'
_0
I"
CCO(qC
_0
_
_
_
_
!
I"
II
,-I
.4"
C)
_'_o.
o
o
v
•
I
Oh
!
II
I
H
X
!
w
co
I_00
_J_ _
O_ c.j
,,0
I
I
II
I@
cO, _0
_J"
.0"
I
I
i
l
t_
I
IJ_' ,_,
_
r,"
(2
ip
Tr
• •
I I
I
4-
i,
•
I
I
N
302
I
t(-
C.
C
,4
_
¢t
C
O_C
LC
r,
r
NC
*o
I
I
v
C
.
•
t'
O
c_
u',
U
C_
C_
f;
C
I
I
C
c_
C,C_
•
(.
¢,._
t_
C
_
U',
¢x
ff'_
C7
C_
I_
_10_,
rq
f_
,-_
t-,j
t--
..+
C_
ed
¢D
I_
G)
O
,,C'
,'--'
•
•
I
C_
(%
O"
f'_
rr',
-,i'
i'_-
•
¢_.
•
I.f_
u",
,-4
(',a
03
C"
_
•
•
I
!
C2,
C _
',_
.,I
•
,t'_
Ima
U'7
_
,,I-
t'.-
_
h
•
r_
P*
f_
•
,0
I
D'J
le;
0
H
I
o
C_
0
(.20
I_
,.I
0"
•
o
CO
0
•
I
M
_
0
'.-_
em
_
*
M
,--4
*C'
¢_j
*t_J
*
,
N
C,C
tu
OI
C_
*
er3
I
0
f_
_,
No
M
_/"
_
_0
I_
oi'_
_
0
,,1"
•
QI_I
-
e_
I
_
t--!
,.:1
O"
I
0
_._C,
0 _
C7
_
,--_
•
°
_
t',/
I
I
C,
_
.
_
A
V'Io7
<_"
I
"C
"l;
'
•
•-4
C_
_
F-
F-
t--
7
_
_
_
_
N
•
•
t"",
,.,I
_
_:_
L_L_J
IU
lU
_
,(]
UJ
L)
_ _ .b._ _-..
U.
LU
rm
303
W_qq
_
I
I
I
*0
_1.. l%
I
I
¢L
•
i°
0
¢%
I
co
or'-
*i"-
I
•
*
I
!
I'
I
*
f
_m
_J
©
_J
I
•
I
r_
r-4
O
o
L)
• i_- _YJ I_
--_0
*
-0
I
•
i
o
7
_u
H
r_
Ij_
0"00"
I
•
I
I
I
,m'_C
°
I
_OC_N
I
I
I
0
I
."
I
I
C
I
I
I
•
I
om
•
P--<N
0"I w_
e,lCD
I
•
_- Or, C0
',0
I
-IN
304
v
•.
,4
•
f'r
• f-.,
cL
IO" &.(" Ix-
_"
C
t',
L _¸
t-
t_
(. l\J
_
(.
u-
•
o
o
_
• _,
c,,
f,
I
c:
(
u-,
•
t_
•
_/,
_t
C_
L( F- "_ C_ I"
O. C
('. (",.
, _
rf._.
*
•
e¢._f(
C ('-.I'-
4
I
-,C r,-,
•
•
I
c
c
c
I
I
b"
wL _
•
*
w(
_'I_,
_
C¢
--_
(% (_l
, ,,(_,
I
<l
!
c
•
C_. c_O C_
u',
1"-- ,_-
C_e
o
OCC_IO
!
c)
(_
E-_
E.)
rd
[;_
0
0
H
r..D
_
,,+
,¢_,r
o_'_'_
-_
l
_,
c
I,r_
,4"
<1
I (7"
LL_ _0 .,-_ ,-,_ _
C
oo
I-'l
0
I _r, C'
LU _
O" U"
O" UT
_0
O
I%1C"
I
.r-I
r_
_"
L_
• ,,--_ -._
t('_
r'4
I
,¢
X
(0
_o_._'_.:_.,
'4"
I_,
Lr
eJ
_-_ _
•
_,
t--
,-_
(.._
_,_ r ¸
l
I
,,,t
_
..1
h-
....j u _
cn ,-w oo
o
I
I
t--!
0
IJ. 0",
(J
,.o
_
_,0
•
aOO_
l_
O_
e,
I
I
I
_t
h.-
(.
-,o F-
.(2
(._
l'_,
C,•
le
r_2 _,..
eO"
0_
-,t
• ,-..
LC
IM
..,
k_
LL;
305
....
_0
t./1 cQ
*c_
A= _
.1:
.A:
4D O.
I_
I.L
t.F
I.IJ P--
_0
P,+@
_
._<_k<_++ •
P-
_,
I
_
• _
I
I
I
1¢
¢-._o
C C,
or.
,,L
_
C_
• -c
rqC
(_.
u
(_
r".-
(%
t
I
I
)
.j
I
LL
rr_ CJ
u,
,Z.
C. _0"+ ,,C., _[,
(,+ _)
•
+
I
I
I
l
i_
.1
u_ LC, _t aL
•_" G
,
,
P,-- C
C; 0
•
-0
,=..i
p.+..-, _
e_
,
c+,.l
P,-+
I
1°
I " -.o
nO
cc_ oc
0
-_" C
P- _,_
cog
_ ¢"_ ,-,
I
I
•
_
•
Cq
_
c_j _
,u _
C%, ,I
i"
_j
,tj
I
,-+
u.I/_"
_r_-O
0
_
C"
<P T',J tl'_
c_
._o._ .., . ..¢._-
-
o
o
C
C;
0-,'i __-
I'q-_q_"
_,0
I
I
4"
+;
/
H
X
P+ +--, On
0
(,t,
._
O_ C+.+
,_
i
I
I
I
L_oof
UJ
-.T CI* O0
ur_c_
c.J C
C_J C_J
+r,o
o:
rn
gr
_~_
it,
•
t
L_; ,.(n _
.o
.4+
I cP
/,,..
t.D
_
o3
,-+
r,a
C
.,,I
_
O-
0+, i.._ ..
@.
-_
_t
_t
•
.j-
,.j. 0
c'.J
I"
"_
I
pr
c.j
)
_
?_
_
I-- _-- I-+ /_ "_
_
.") __
"TS .T
T
_
C ¸
.. _
306
_._ _._
c
0c
_
_
cc
_
o
_
_
c,r,
C
I'_
.?
t.i
C
c_
I"
.4
I"
C.
17
I_
I"
u,
g
I
_o
I
l
c_
,_
o
i
I
Y
c_
,_, _,
I'_
_
_..
I,D.
w,
a,
c_-
o,
ua
4_
-4-
O
o
..-4
I
_o
O"
G
.-i
I
I
C"
x
•
I
o-i
_
I--
I"-,I
0
o
I"-4
I
_'
1.2.
Fu
u..
_
_,.
..D I--
tJ
%
I._
307
I.L
o
o
o
_
_
I
I
_
_
_
I
_
_
I
0
¢
I
o
I*
..I
I
I_
0
o
e,J
,.
._
I
_,
r,,I
I"
.¢-
•
,-4
I
_
I
.
_
_
I
_
|
|
I"
I.In
o
_,,,0
..C',
r.-.
!
.
,_
I
•
I
I
o
r,I
_
0
D
!
•
0
0
,"'
'-'
0
r_
°o
,-,
o
¢
I
I
_
÷oo?
I
I
I
0
•
a0
I
¢o,
0
!
_
I
•
I•
o
_
_
_
_
I
I
,_
!
:Ira
I
_I
i
¢
.
_:
_
_
t"-I
,_ o
• j
_
-
I"
Ie
er_
_
_
_
_
_
_
_
I
!
I
I
J7,
_
o
_
_
_
o
_
_
I
1
I
I
i
-
-
308
-
",11"
!
°'
,_
-
_4
_
I
I
-
I
7
I
0
I
i
!
_
_
•
t
.-, ,_
I
_m
o
h-
_D
o_ °
o_--0
0,4"_
O0
,
0,--4
I
•
.O
,_
•
I
!
I"
o
o
N
_o_
O_C:;
_ OO
Gtl-_
OO
,0
o_.
I
._1"
MI"
0
0"
P-O
,,o.¢
oo
_r'l 0
(:7'N
¢.r_ N
I
0
N
,-_ o
_
O0
I
o
°
|
I
I
I
O_N_
-oo
NO_O*
_
I
UP, O
•
I
I
I
I
!
I
l
÷
N
o2
o
O
OO
O
.,-I
n'l O
I_.
,<I"
H
_-um
I_ O _I" _I_,
tO_-I
,
"_
I
I
i
I
÷
-o
o
o
o
NOCM
o
•
P-I
X
•
,--4
•
I
,
¢_1 .0
,c,3
I
•
mm•
I
I
I
II
G_
0
+
-,r
o
og
m-.
_
Mr"-
,--_ ,0
¢¢3
o um -._
0_1
_-
_oo_
O4
,-IN
.o
I
o
@
r,... f_.
r_
I
I
I
"'7,
mm
o') 0-,
O
O0
,tel
;
,ON
I
O
N
I
I
II
O_O_N
oo _m
_¢_ _-_
•
I
•
I
•
I
t.-
..I
0
o
N
_tX_
,-_ °
•
I
!
N
I
•
,
•
v_
O"
0
NO0_
O
,O
OO
•
I
,i_I ,-_ Od
I
• o .-,I
IN
,
I
•
l'%1
I
•
•
I
I
N
i_)
LI_
w
7
309
I
"4
O
O
I.(',
_I"
_4
OO
0
o
_I .-4 •
• • ,--J
0_
o0_
_OOW
I
I"
•
.O,_oO_"
_o,,f
NOC
I
I
I'
I
N
_2 2,..
O
O_r_
wD
•
N
C
0
,,,_
•
o
0
_oO
_ID o
I
O0
O
o_
,elo
I
I
!
o
,,-,_
N,O
_o
OO
I
,
oo
_o
00_
0
0
_o_.
•
I
I
_0_
_,,,e
I
I
i
I
w_
0
_0
_o_
_o_
0_
o_
_-o
.o
00,_
o_
I
I
I
÷
c_
°
_o
o_
..d
00'_
_c0_
,o
O0
"_
e,.-4
I
I
I
I
I
v_
H
O_
oo
o_
O0
q_
0
_o
"_
I
I
._o_
_Oc_
,.,e
I
I
•
,N
I
÷
o
o
0_
oo
o_
I
o
_o_
_o
o_
I
_0-I"
o
aD .-_
(-_ , •
,(_qt
e,,e
I
_?
I
I
I
@
_o
000_
_0
-,I" •
I I
0
I
!
I
• _D-I
I
I
I
,0
I
o
_o
_8°j
_0_
_oo
I
I
I
I
II
O
0
_
_0_
r..0_
o
I
I
•
,_0o"
I
_N
w
w
Z
ZZ
310
•
I
Z
_o._
II
I
(7,
..,1"
0
0
O0
r_
01_
u'% .-* 0
0 ,'l (_ e4
.
0
•
• • .-4
m- .o ,m
OOumO0
0_@
o. 4-
_0_
i°
4-
0_
0
_r_
•
r_
C
,o
0
_0_
_0_
Oi,oo
• 0
•
•
•
|'
I
"
• ,Th-'_
I
÷
,,e
c
eo
I0
o(:3
_o
.0
P- I_- .0 1_
•
_O_
0_.,
Oill,
•
0
I
•
•
•
I
"4
,,0
o,
0
Or_
0_
tM
O_
•
iN
•-_0
•
,-_
I
I
I
I
+
0
_3
0"¢
4"
'
_0_
_0 ,m I_ .1% mD
4D I_IDtel (_. ID_
I*_ .-_ .4- 01,1%
• 0
O'l C',l *
0
I
"i
!
I
+
0
ur_
Oo
I'- -_
o
o
0
,0
Um
•
..+ _C
e4 ._" ,o
• •
.I_
I
e¢_ 0
i°
-.II"
0
'
.-_
"
,
7
I
+
"O
-.,t
oo
cM,o
_0_0
_o0_
_0_
0
0_@
" _
'
•
0
"_
,
•
°
•
•
,_N
I
I
4"
o
-.Jr/
.o_.
I
I
i''I
"'e
÷
0
Jo
v: 00
I
!
I
I
...j
w_
o
,...4
I
I
I
I
_N
u
u_
,,-i
"_¢L
_222
_q_..
_
v
7
311
!
7
....
tM I_1 ,.lr
N
_@_0_
C;
u"_ 0
e_-i
N
C
J
I
_y rr,
...., ,'_
oO_"l
our',
I
u,
.@ _¢
_2_
li",
I
t_o
I
I
!
,d
0
t
I
x.O
0_
I
,<
_'_ i.f"
r_
O0_J.
..I- u_ _'xJ .,t
_"d -..1 i'_-. -.._
g ,_ r'•
I
_O_C_
II
7
w
7
312
•
,/
.,I
O
O
,-i
OO
q_
•
0_0
_O_W,
c_
O
•
•
ee%
P'-
•
ii
!
I
•
I
•
I
O
O
0_
E;t_
,0
*
(%1
WO_OO,,
•
OO,,_
e,
feel
"'_
I
OeO
i_, ,_
0
(DO
tf,
o
O
00
O
,..i
nn _
_D
('4
Oo,
•
,C
o,--4
!
I
I
O"
E
Q
_Lr_Oa0N
Of,4
(D
N
OP_
,l%/
•
OO_
_
_O_O
O_O
e,J e_4
,_
•-_O
,el
I
I
I"
O
4D
O,0
4"
N
_O_
0_0
_O_
•
0
_
_
I
I
'D
OO
4"0",
..I 4"
_m O
o_;;
O
I
!
I°
O
Or_)
r.4,-
,.-i u.'., .,I-
I
O" u,_
,_ co _
r-4 (_
OO_
r,.-
_'_ ocq
.
o
!
!
o4 P.I-- ,
,C0
I
!
I"
A_
O
o_
_*
,o_oI
I
I
O
.JO
r-.2 £.,_ Pr', • _T
• O
• 45 _"J
I°
._J
_
L# (j
-C
I
•
|
•
O
.-I
_r;
,rj
,GfM
I
Jl
_
,-a4"
.O
CO
• O
r_
oP, fl- .-_
•
•
-2
-t
•
I
_LU_
CL
D_
_7
313
,-4
--_
7
_
0- ...,0_
0(_4
•
-
•
"
• r_
I"
•
i_0
i
•
i
•
!
'
I
•
I
•
I
.=..
•
_" 0
I
•
eel
.0,."4
i
0
•
•
I
0
0_
I
I
.,-I
4_
0
0
O_
•
i
_
._-j
II
"7
N
om_ • o.
•
I
I
I
I
o
,
7
I
I
I
•
!
!
_aaa
_-_-
314
_
o.-.o o•
N
.-,
_0
•
.-.I
.,_ o
®
_
e_
eel
,41"
41
_
,o
_
.-, j
•
,.-,I
_
I_
•
• -4
r'J
•
._
g
÷
,,f
÷
÷
0
•
I_
OJ
0
0 '_
Od
I_
Od
_
_
0,8
,,I"
0
•
t_
r%l
_1
0,1
•
•
t",,I
_
o
•
•
÷
÷
0',
•.
_
,_
0, _
I
_
t
o
,,,
o
_,
,,,
_0 o
I
i-
_<
it,.
315
ILl
XB-70A
DATA
SOURCES
Estimated
Aerodynamic
Derivatives.,
No. 'NA-61-707,
29 June 1962
Aerodynamic
Coefficients
North American
Rept.
XB-70 , North
American
Rept.
Obtained
from Flight
Test Data_
No. TFD-67-277,
]4 Apr.
]967
XB-70,
Wolowicz,
Chester
H., et al, Preliminary
Flight
Evaluation
._f the
Stability
and Control
Derivatives
and Dynamic
Characteristics
of the Unaugmented
X_B-70-1 Airplane
Znciuding
Comparis_i_s
k_th
Predictions,
Estimated
North
XB-70
NASA
TND-4578,
Performance
Report
American
Rept. No.
Flight
Control
System
Rept. No. NA-_6-360,
30
May
]968
for the XB-70A
Air
NA-6h-660,
26 Oct.
Summary
Test
Sept. 19'66
316
Report,
Vehicle
190_
North
_o.
I,
American
APPENDIX
A
AXIS SYSTEMS, SYMBOLS,
MNEMONICS, AND DERIVATIVE
I.
AXIS
COMPUTER
DEFINITIONS
SYSTEMS
.XB,U,P
_-_ _
YB ,Ys ,V,q
_
/
_-_ Inertial
Ref.
Za ,W, r
g
XB, YB, ZB
--
The Body-Axis System consists of right-handed,
orthogonal
axes whose origin is fixed at the nominal aircraft center
of gravity.
It's orientation remains fixed with respect
to the aircraft, the XB and ZB axes being in the plane of
symmetry.
The exact alignment of XB axis is arbitrary, herein
it is taken along the body centerline reference.
XS, YS, ZS
-
The Stability-Axis
System is that particular body-axis
system for which the Xs_axis is coincident with the
projection
of the total steady-state
velocity vector (VTo)
on the aircraft's plane of symmetry.
It's orientation
remains fixed with respect to the aircraft.
A-I
2.
SYMBOLS
a
S_peed of
ay
Lateral
at the
sound
in
ft/sec
air
acceleration
along the y-body
axis
center
of gravity
(positive
out right
ft/sec 2
wing)
Lateral
acceleration
axis
a distance
at
parallel
_x and
to
the
_z from
y-body
the
c.g.,
ft/sec 2
a_ = ay + _x_- _z_
T
Normal
a Z
axis
acceleration
at
a distance
az = az
axis
_x
from
the
z-body
c.g.,
ft/sec 2
acceleration
at
parallel
a distance
b
Reference
wing
B
Bobweight
gain
B.L.
Buttock
_B from
to
the
the
z-body
c.g.
ft
span
ib/g
line
Reference
ft
chord
C
Longitudinal
C. ,g.
Center
D
Aerodynamic
force (drag)
velocity
vector
(positive
FRL
to the
_xq
r
Normal
parallel
of
Fuselage
feel
system
ib/in./sec
damping
gravity
reference
line
along
aft)
the
(parallel
total
ib
to
x-body
axis)
Fuselage
F°S.
FST
T
Fped
station
Longitudinal
control
Longitudinal
stick
Lateral
Rudder
stick
pedal
g
Acceleration
G
Pilot
control
force
force
force
due
to
column
to
force
(+ aft)
(+ aft)
ib
ib
(+ right)
ib
(+ right )
ib
gravity
surface
A-2
gearing
ft/sec 2
deg/in,
deg/deg
or
h
Altitude
I
Longitudinal
Ix_ ly_ I z
][XZ
ft
feel
system
Moments
(unless
of inertia
otherwise
referred
specified)
to
Product
(unless
of inertia
otherwise
referred
specified)
to
The imaginary
portion
able s = J ±jc_
_B
Effective
(positive
distance
forward)
Distance
along
c.g. (positive
_X
Sth
Perpendicular
line
(positive
due to thrust)
Longitudinal
KTAS
Knots
true
KCAS
Knots
calibrated
K
Feel system
pressure
torques
M
Pitching
slug- ft 2
complex
varirad/sec
the x-body
forward)
from
axis
c.g.
from
the
ft
the z-body
down)
system
axis
from
the
ft
spring
constant
ib/in.
unit
(ib/in.
airspeed
constant
about
per
the
x-axis
(positive
right
Aerodynamic
force
the total velocity
plane of symmetry
Mach
axis
ft
spring
moment
M
body
due
dynamic
to
wing
aero-
down)
!lift) perpendicular
to
vector
in the aircraft's
(positive
up)
ft-lb
ib
s_igs
number
aerodynamic
2
airspeed
dynamic
Mass
axis
slug-ft
of bobweight
feel
Rolling
m
the
body
2
ft
K
T
of
ib/in./sec
distance
from c.g. to thrust
for nose-up
pitching
moment
Distance
along
c.g. (positive
_Z
inertia
moment
about
torques
MAC
Mean
aerodynamic
MGC
Mean
geometric
the
y-axis
rpositive
chord
chord
A-3
due
nose
to
up)
ft-lb
ft
ft
)/psf
N
Aerodynamic
axis,
normal
but
force
positive
along
the
Ib
Yawing
moment
about z-axis
due
torques
_positive
nose right)
P
Roll rate, angular
velocity
(positive
right wing down)
Pitch rate, angular
(positive
nose up)
q
r
rRG
Dynamic
pressure,
Yaw rate,
(positive
Yaw
rate
I/2
y-axis
lb/ft 2
about
z-axis
rad/sec
rad/sec
TED
Trailing
edge
down
TEU
Trailing
edge
up
TL
Thrust
U
Linear
perturbed
velocity
(positive
forward)
operator,
wing
rad/sec
a + j_
ft 2
area
line
Linear
steady-state
x-axis
(positive
Stall
speed
Total
linear
along
the
x-axis
ft/sec
velocity
along
the
forward)
Linear
perturbed
velocity
(positive
out right wing)
forwaz_
about
signal
Reference
VT o
x-axis
2
o VTo
S
V s
ft-lb
rad/sec
Laplace
V
aerodynsmic
rad/sec
velocity
S
Uo
to
about
angular
velocity
nose right)
gyro
z-body
up
steady-state
ft/sec
along
the
y-axis
ft/sec
velocity
Cpositive
)
W
Linear
perturbed
(positive
down)
W°L.
Water
W
We ight
Wo
Linear
steady-state
z-axis
(positive
kt
velocity
along
the
x-axis
line
in.
lb
velocity
down)
A-4
along
the
ft/sec
X
Aerodynamic force along the x-axis
forward )
Y
Aerodynamic force along y-axis
out right wing)
Z
(positive
(positive
lb
Aerodynamic force along z-axis (positive
down)
lb
(L
Perturbed
rad
_o
Steady-state
relative
to
angle
Sideslip
_O
_a
_e
of attack
(trim)
the FRL
path
angle
deg
deflection
(includes
(positive
for posirad
Elevator
surface
deflection
from
(positive
for nose-down
pitching
for aft surface)
elevator
trim
control
(positive
Lateral
stick
tive right)
column
deflection
aft)
deg
deflection
from
Spoiler
_V
Vertical
tive for
trim
in.
deflection
from
trim
(posiin.
Lateral
wheel deflection
tive about x-axis)
$sp
rad
deg
Rudder
pedal deflection
from
tive right pedal
forward)
Stabilizer
(positive
trim
moment
deflection
Longitudinal
stick
(positive
aft)
_r
deg
Aileron
control
surface
spoiler
effects,
etc.)
tive rolling
moment)
from
_S
attack
rad
flight
Longitudinal
_w
of
angle
Steady-state
Trim
Sped
angle
surface
for TED)
surface
yawing
moment
trim
(posideg
deflection
from
trim
rad
tail deflection
nose-left
yawing
de_ection
(posiin.
from
deflection
Rudder
trim
(positive
from trim
moment)
[positive
(negative
A-5
N)]
for
up)
rad
(posirad
nose-le_
rad
A
g
Denominator
of
airframe
transfer
Angle between
principle
(positive
about y-axis)
Damping
ratio
particularized
inertia
Inclination
tive gives
Mass
axis
of linear
second-order
by the subscript
of
The real portion
s = a ±j_
mode
and level
rad
of thrust line with FRL
negative
(--) z force]
density
and FRL
deg
Pitch angle, fq dt for straight
flight,
positive
nose up
iTH
function
[posi-
slugs/ft3
air
of the
complex
variable
rad/sec
Roll angle,
(cos eof p dtstraight
and level flight
wing down)
sin eofr dt) in
(positive
right
Undamped
natural
frequency
of a second-order
mode, particularized
by subscript
Special
Subscript
a
Aileron
cc
Control
d
Dutch
e
Elevator
G
Gyro
INS
Inertial
P
Phugoid
r
Rudder
R
Roll
S
Spiral
SAS
Stability
sp
Short
ST
Stick
column
roll
navigation
deg
system
subsidence
augmentation
system
period
A-6
rad
rad/sec
Special
Superscript
DIR
Directional
LAT
Lateral
S_mbols
Unique
to
control
control
S_eclflc
system
(e.g.,
Aircraft
Aileron-rudder
interconnect
BLC
Boundary
control
KDIR
FLEX
Rudder
flexure
PBF
Bellows
force
qB
Bellows
pressure
5d
Yaw damper
surface
deflection
(positive
for nose-left
yawing
layer
Aileron
$tac
Commanded
5t e
Elevator
(_te
-- _e)c
5tr
(Str
-- 5r)c
tab
coefficient
parameter
tab
tab
F-4)
(F-4)
(F-4)
ft 2
(F-4)
deflection
aileron
(F-4)
(F-I04,
tab
deflection
lb/ft 2
deflection
(F-I04)
moment)
(CV-880M)
deflection
Commanded
rudder-rudder
servo tab
combination
(input
linkage)(CV-880M)
A-7
(CV-880M)
servo tab
(CV-880M)
(CV-880M)
rad
rad
(CV-880M)
Commanded
elevator-elevator
combination
(input
linkage)
Rudder
pedal)
system
ARI
St a
rudder
tad
rad
tad
rad
tad
3-
COMPUTER
PRINTOUT
MNEMONICS
a.
COMPUTER
DIMENSIONAL,
MASS,ANDFLIGHTCONDITION
PARAMETERS
rRINT
OUT
STANDARD
NOTATION_
DEFINITION
S
S, wing
reference
B
b,
wing
span
C
E,
mean
geometric
F/C#
Flight
H(_)
h,
SL
Sea
M(--)
M,
VTO(FPS)
VTo , true
airspeed,
VTO (KTAS )
VTo , true
airspeed
W,
altitude,
number
feet
Level
Mach
number
weight,
c.g.,
IX
IY
IZ
IXZ
knots
airspeed,
knots
pounds
Ix
I
e,
knots
center
of gravity
relative
mean geometric
chord
Body
Iy
Iz
Ixz
_SI_N(DEG)
chord
Condition
VTo , calibrated
w( s)
area
inclination
respect
to
axis (FILL) moments
inertia,
slugs-ft 2
of principle
FRL, degrees
axis
Q(PSF)
q, dynamic
pressure,
psf
QC(PSF)
qc,
impact
pressure,
psf
ALPHA(DEG)
So,
FRL
_(DEG)
7o,
flight
LXP(FT)
up(n)
£x,
x
distance
to pilot,
ft
_z'
z distance
to pilot,
ft
ITH(DEG)
ith , thrust
incidence
to FRL, degrees
XI(DEG)
_o'
/th,
LTH(FT)
A-8
ith
angle
of
path
+ %'
attack,
angle,
degrees
degrees
with
respect
degrees
perpendicular
thrust
line
distance
from c.g.,
to
ft
to
of
with
b.
COMPUTER
PRINT
LONGITUDINAL
PARAMETERS
OUT
STANDARD
NOTATION_
XU*
Xu
]/sec
zu*
z_
1/see
MU*
M_I
I/sec-ft
XW
Xw
1/sec
ZW
Zw
1/see
MW
Mw
I/sec-ft
ZWD
Z_
I/sec 2
ZQ
Zq
I/sec
MWD
M@
l/sec-ft
MQ
Mq
I/sec
tXDDD
X8
ft/sec2-rad
ZDDD
Z5
ft/sec2-rad
MDDD
M5
1/sec 2
DTH
5th
Thrust
FST
Fst
Stick
U
u
fps
W
w
fps
THE
e
rad
HD
_
fps
AZP
a_
1"t/sec 2 at
_DDD
DDD
signifies
= DA
a control
surface,
e.g.,
A-9
for
DEFINITION
force
elevator
X =
DDD
Ax
= DE;
for
aileron
C° LATERAL-DIRECTIONAL
PARAMETERS
COMPUTER
P:_INT OUT
STANDARD
NOTATION
YV
Yv
I/sec
YB
Y_
ft/sec 2
LB'
1%
I/sec 2
NB'
N%
I/sec 2
LP'
I_
1/see
_,
_'
_'
_
L_
N_
1/see
1/seo
1/sec
ty*DDD
Y_*
1/see
L'DDD
I_
l/sec 2
N'DDD
N_
I/sec 2
B
_
rad
P
p
rad/sec
R
r
rad/sec
PHI
_
t DEFINITION
rad
t
AYP
tDDD
DDD
ag
signifies
= DA.
a control
surface,
e.g.,
A-IO
ft/sec 2 at
for
elevator
_x,
DDD
_z
= DE;
for
aileron
d.
TRANSFER
FUNCTION
PARAMETERS
The following shorthand notation is used to print
polynomials for all transfer functions*:
(s + ]/Tx) i
(_2 + 2_%s + %2)j
where
COMI_ER
PRINT
k
+ 2_
:
]/Txi
,
i
:
] to k
:
_j;_nj
,
j
:
I to
=
n,
OUT
the
order
of
the
STANDARD
NOTATION
DET
Roots
of
the
N(X/Y)
Numerator
N_
A(X)
Gain
'i/T(X)I
,z(x)J
tw(x)j
For
the
2 DEFINITION
denominator
transfer
function
x/y
_j
Cenj, rad/sec
example:
to:
OE NCM INATOR
I/T(OET
}I
I/_IOET}2
.0318
2.2C
Z{DET}
W[DET]
I
1
.06C9
1.13
NU M ERATOR
N| 8
/OR
A{B
I/T|B
I/T (B
I/T (8
S
}
A.
transfer
}
.o_(s(s +
function
x/y
N_y
x/y
=
.0295
-.0494
2.05
42.3
_I
}2
}3
:
6r
_Any roots
specified,
of
polynomial
I/Txi , rad/sec
Translates
*The
the factored
a
.0318)(s
is written
.0609
X
1.13s
as:
Ax( sm +
(S n +
.o494)(s + 2.o_l(s + _2.3/
+ 2.20)(s 2 + 2 X
sm-1
Sn-1
+
+
enclosed
in parentheses
imply the
e.g., Z(DET)I
= (O.OO132)_I/T(DET)I
A-II
...
...
so )
S O)
opposite
order
= 0.00132
of what
is
+
1.132s 2)
e.
COMIKITER
PRINT
OU
LONGITUDINAL
STANDARD
HANDLING
NOTATION
QUALITY
PARAMETERS
EQUATION
I DEFINITION
--r
W^
l. cs
DCO)fO(U)
(D_I_)
_/_u,
68
de_rees/knot
L
(I.
U o
_O
9)(97.3)
Uo
O
u
Wo
w
•-uo _(s)
Nz_
¢
DEIo (_1_)
Control
'
for
phugoid
to
Fs_/n (,.-/l=)
time
period
1/10
Stick
seconds
inverse
---_,
per
Stick
The
or
force
in
10
1.689
knot,
per
g,
pounds
g
parameter
is
not
has
defined
no
meaning
at
this
flight
condition
notation
implies
constant
speed
(u
=
eo
_Ph
<
<'
-_sp
0
2_
cycles
amplitude
force
for
ll_
_I
for
=
0).
A-12
O
-- _sp
(s
-I
per
0
2
l_unds/knot
_S_/G(uVG)
=
to
amplitude,
Short
s
rad/sec2/g
in
l/c(_/_o)
=0
anticipation
parameter,
double
(2)
!
a(s)
The
hat
s
_(S)'
, degrees/g
5e/g
CAP(mD I_clsEC
IG)
*The
for
, g/rad
for
s
=
O
<
I
1
/
J
,
for
s=O
f.
LATERAL-DIRECTIO?_AL
COMPUTERPRIf[UOUT
STANDARD
DR PERIOD(SEC)
Dutch
roll
iic(i12)
Dutch
roll
to
SPIRAL
(2)
(SEC)
I/2
_DTATIONj
_ANDLING
QUALITY
PARI_4ETERS
DEFINITION
EQUATION
period,
seconds
2_/ahd
inverse
cycles
in
2
Ts
in
_
-- _d2
for
_d _
0
amplitude
Spiral
time
amplitude,
Roll
rate
step
input
to
double
2,
for
I/Ts
£
0
seconds
at peak
I for
a unit
of 5 a
Pl + P3 - $2
P l + P3
P(OSC)IP(AV)
Ratio
the
DEL-B-_gbX
of the
dutch
roll
roll
frequency
to
frequency
2_.m : Maximum
sideslip
excurslon at the c.g., occurring
within
two seconds
or one halfperiod
of the dutch
roll, whichever
is greater
for a step
aileron-control
command
PHI
to
BETA,
PHI
TO
BETA
PHI
TO
VE
*v e :
(8)(VEAS)
+ 2P2
for
_d _
for
_d
0.2
'
A measure
of the oscillatory
to the average
roll rate
PHASE
_/_
at
s =
(_;
C0n)d,
degrees
I /BI at
s =
(_
O_)d,
radlrad
"_/Vel
, VEAS
at
s =
(_;
o.h)d,
: _p2_ 0
A-IS
deg/fps
Pl
-- P2
Pl
+ P2
> 0.2
2.
NGNDIMENSIONAL
a)
DERIVATIVE
Longitudinal
Body
CN
=
N
_-_
CX
=
X
- _-_
c_
DEFINITIONS
Axis
, positive
, positive
up
aft
= _--_/_
CM
2Vmo_c_/_
V-
M
_ Sc
=
c_
= _cW_
c_
:
-- _CN/_,
c_
= _cWM
Cxa = _Cx/_
CMq
-
et%
2Vmo
-'-T- _cW_
2v_°
_c_/_q
c
CxM = _Cx/_M
Cx_ :
ID)
Longitudinal
_cx/_
Stability
Axis
CL
-
L
_ S
CD
-
D
_ S ' positive
' positive
up
aft
:
c_
_Cn/_
- 2Vmo
c
Pitching
c_
= ac_aM
derivatives
identical
c_
= acD/_
those
A-14
moment
are
to
for body
axis
c)
Lateral
Body and Stability
Though physically
Axis
and numerically
different,*
samesymbols are used for body axis and stability
see Appendix B, the
axis lateral
rolling
and yawing momentderivatives.
The sideforce derivatives (Cy, etc.)
physically and numerically the same in both axis systems. Whenthe
al
rolling or yawing momentderivatives are given in this report the axis
system is specified.
Whenusing the following all quantities should be
for the sameaxis system.
Cy
Y
L
Cy_ = BCylB_
= _Cy/_
*The
exception
is
C1
-
qSb
Cl_
=
Clp
N
Cn
-
_Sb
_CI/8 _
Cn_
=
_C_8_
-
2VTo
8cml_
b
Cnp
-
ev_°
b
8CNI_
Clr
-
2v_°
_ci/8r
b
Cnr
-
2VTo
8c_/8r
b
c_
= _/_
c_
= _cJ_
the
zero
trim
A-15
angle
of
attack
condition.
5.
DIMENSIONAL
STABILZTY
DEF_I_ATrWE DEFINITIONS
The same symbols
derivatives.
quantities
a)
are used for body-
Care should
be exercised
so that a consistent
_u =
Body
set of
Axis
I/see
Xu+ Tu cos_o
__ 0_o(_
m
-
We)
- 2 CxM - Cx + _
OSUo
2m
cxcz
=
[-
CX_ -
Wo (cx
M %)
2 _o
+_
-_
I/sec
Zu
-
oS_o
(_
Zw
-
ooo[wo .
- _ CNM - CN +
2m
_)
CN(_
-CN(_ - 2 _oo (CN + _ CNM
pSc
11sec
sec2rad
Zu - Tu sin_ o
m
]
ft
CXse
Z*u =
z_ =
I/sec
!
osv_o
x8e
dimensional
are used.
I_ngitudinal
Xw
and stability-axis
I/sec
I/sec
Uo
- 4m Vmo
cN&
PS_T o
ZSe
-
2m
M_
=
_th
Mu +-_--_I
ft
CNSe
sec2rad
sec-ft
A-16
I
sec-ft
MII
=
oScUo
Cm_ +
pSc2
Uo
I
sec-ft
(Cm +
I
sec-ft
Cm_
= l_-y VTo
I/sec 2
I/sec
I/SeC
pSC2VTo
pScVT2o
MSe
- 2Iy-
=
CruSe
_/SeC
%
b)
=
L_ter_-% Body Axis
I/sec
Yv
=
(pSVTo/2m) CY_
ft/sec 2
Y_
=
VToYv
ft/sec 2
Ysa
=
(pSV2To/2m)CYSa
ft/sec2
YSr
=
(pSV_o/Zm)CYSr
I/sec
YSr
=
(pSVTo/2m) CySr
_/_
= (_SV_ob/_I_)c
_
1/sec
I/sec
Lr
=
(pSVTob2/_Ix) Clr
A-17
2
I/sec 2
L5 a
=
(DSVTJ/2Ix)C15
L_r
=
(PS_TJ/2Ix)C15
YS_
: (_SV_o/2m)Cy_a
I/sec
: ( SV ob/21,.)c
I/sec 2
: (psv_J/41z)C_
p
I/sec
Nr
:
(pSVTob2/4Iz) Cnr
I/sec
Nsa
=
(oS_TJ/2Iz)Cnsa
N5 r
:
(PS_T2/2Iz)Cn5
=
(L8 + IxzN_/Ix)G
I/sec 2
=
(Lp + IxzNp/Ix)G
I/sec
=
(Lr + IxzNr/Ix)G
I/sec
I/sec 2
r
I/sec 2
I/sec 2
r
: (_6r+ IxzNSr/IX)
G
NSr
= (%_ + IxzNS_/Ix)O
I/sec 2
=
I/sec 2
(N_ + IxzL_/Iz)G
: (_p+ I_zLplIz)G
I/sec
=
(N r + IxzLr/Iz)G
I/sec
=
(NSr + IxzLSr/Iz)G
I/sec 2
=
(Nsa + IxzI6a/Iz)G
I/sec 2
I
G
I
Ixlz
A-18
,,,'t
"r4
_
_
r_
c_
r,_
U
i
i
0
-t-
+
o
0
¢..)
U
I-¢
0
k
'o
0
0
/.-,
'
'
0
÷
'o&
0
_
I
0
¢0
H
r,_
o
t_
o
eJ
0
m
I
II
¢O
II
II
H
II
n
tl
H
11
0
r.,3
A
_q
¢0
0
r_
H
m
r.3
4,r
!
cr_
H
_1
r_
c.)
r_
F-I
rj_
o
o
n
tl
C_,
H
CO
II
!
d
B-I
II
II
II
II
II
II
U
il
II
b.
TRANSFORMATION
OF DIMENSIONAL
FROM STABILITY
AXIS TO BODY
DERIVATIVES
AA_IS
Longitudinal
(Xu) b
=
Xu
cos2
(X )b
=
Z@
sin 2 ao
(Xw)b
=
Xw
cos2
(x,) b
=
X@
cos 2 ao -- Z@
(Xq;5) b
=
Xq; 5 cos
(Zu)b
=
Zu
(Z_) b
=
--Z@ sin
(Zw) b
=
Zw
cos 2 ao
(Z-_-) b
=
Z@
cos 2 c_0 + X@
=
Zq;8
(MU)b
=
Mw
(M )b
=
-¢4@ sin
=
M w cos
c_o + M u
(_)b
=
M,
_o
(Mq;5) b
=
Mq; 8
(Zq;5)b
_o -
_o
cos2
cos
+
+ Zu)
(Xu--
Zw)
sin
a o -- Zq;5
_o
ao
cos
+
c% cos
_o
sin
c_o cos
ao -- Z u
sin 2 a o
sin
+ Zw
sin2
_
_o
_o
sin
_o
cos
oo
--Xw
sin 2 _o
sin
ao
cos
c_
+ Xu
sin 2 _o
cos
ao
c_o
(Zu
+ Xw)
sin
+ Xq;8
ao --Mu
sin
c_o cos
_o -- (Zw--Xu)
cos
cos
(Xw
oo
sin
sin
ao
sin
_o
ao
(ly)b
B-2
c%
Lateral-Directlonal
(Yv; )b
=
Yv;5
(Y÷)b
=
Y@
(YP)b
=
Yp
cos
co -- Yr
sin
co
(Y )b =
Yr
cos
co
sin
cO
+ Yp
T
!
=
L_; 5
cos
c_ -- Nv; 5
=
L_
cos
=
_
cos 2 _o-
=
L_
cos 2 _o -- (Nr -- _)
=
N_; 5 cos
=
N_
cos
(N )b =
N_
cos 2 Go -- (N_ -- _)
(Nr)b :
N$
cos 2 ao
+
(IX)b
=
Ix
cos2
(Iz) b
(IXZ)b
c_o --
sin
(L_
sin
c_
co
+ N_)
sin
c_
cos
_o
+ N_
sin 2 oo
sin
ao
cos
Go
-- N_
sin 2 _o
sin
Go
cos
ao -- L_
sin 2 co
+ N_)
sin
ao
cos
Co
sin 2 Go
+ 2Ixz
sin
a o cos
co
+ Iz
sin 2 ao
=
I z cos 2 Go -- 2Ixz
sin
co
co
+ Ix
sin 2 c_o
=
(I z -- Ix)
f
(Lr) b
T
!
(N$) b
C_o + L_;5
!
sin
co
!
c%
Go
+ L_
sin
sin _o
(L_
ao
cos
B-3
ao
cos
+ Ixz(COS
+ _
2 _o -- sin2
Go)
APPENDIX
C
EQUATIONS
OFMOTION,TRANSFER
FDT_CTIONS,
ANDCOUPLING
hq]_RATORS
I
•
Longitudinal
a.
Eouations
(I-xa)s-x;
-X_ s - X w
(I-z_)s-zw
-z_s - z[
--_s-N
q.
=
.SO
fi
=
--w cos
Oo + u
=
sw -- Uoq
_z,
=
a z -- ixS2O
h'
: h +_x oos _o
Transfer
_e
5e
A
A
Denominator,
A
+ (g
=
(1--Z_)
=
-(Mq
=
sin
w
8
s2 --MqS
O 0 + W o sin
=
ZSe
M{5e
0o)8
00)8
Terms
As 4 + Bs 3 + Cs 2 + Ds
+ XU)(J
- Xw_
NOTE:
sin 8 o
I" X$e-
Functions
e
I)
(--Zq--Uo)s+g
sin O 0 + (U o cos
az
b.
cos
-(M,_+ Mw)
u
8o -]
(-Xq+Wo)s+g
including
-- Z_) -- Z w-
+ Wo[M_
Xd,
+ E
M_
+ M_(]
Zfl, Mfl_ X@
C-I
-
Z_)]
+ g_
are neglected
sin
80
in polynomial
expressions.
[Se]
D ---x_(Mqz_-._)
-MuX
_ +Mqx_z_
+g[%z_+M_(_-z_ oo_eo+Wo(M_z_
-._z_)
+ g(Mw-%X_)sin
eo
E = g(%Z* - MuZw)oOS
eo+ g(MuXw
- _,X_),i,, eo
2)
Numerators
N_
=
Ass2
+ Bes + C8
= %_ + %(, - %)
B0 = xs[_z_+
._(,
-%)]÷%(_- %x_)-%[m.+×*!_
-%)]
ce ="xs(%,,z
_ -M_z_)+zs(M_x
_. %,x*)+%(ZwX
_ - x,z*)
I_E =
IA u = X5(I
Au S3 + Bus2 +Cus
+D u
- Z.)
W
Bu = -_[Mq(,
- z_)+ z_+ _] + %x_ - Wo[%% + _o('- %)]
+ Wo(Zw%-MJ_) + gX8% sineo
D u = g(ZwM 5 - MwZs)cos
N_
Aw=
=
eo + g(XsM w - MSXw)Sin
80
Aw s3 + Bw s2 + CwS + Dw
Z5
B_= -%(Mq+ xu)+ UoM
5 + xs_
Cw = X_(ZsMq-
UoM_) + Wo(ZsM u - _Z_)
D w = g(Zs_ u - %Z_)cos
H-747
eo + gMsX _
sin
C-2
- gM 5 sin eO+
@o-
XSM_g
sin
X5(M_U o - Z_Mq)
eO
N_ :
A_s3 + B_s2 + Cis + Di
A£ = - cos
eoAw+
B_
=
- cos
eoBw
+
sin
eoB u +
(U O cos
e O + W O sin
eo)A e
O_
=
- cos
@oCw
+
sin
@oCu
+
(U O
cos
@o
+ Wo
sin
eo)B @
D_
=
- cos
@oDw
+
sin
@oDu
+
(U O
cos
@o
+
sin
@o)C@
sin OoAu
Wo
N_Z--Aa_s
4 + Ba[_3
+C_[s
_+ D_ls
+ Ea z'
A_ = A_ - ixAe
Ba_
= Bw
- ixB e
- UoA @
Ca_
= Cw
- ixC 8
- UoB 8 +
Da_ " = D w
Ea_
To
2.
obtain
= +
az,
- UoC @ +
g
sin
let
g
sin
g
sin
8oB @
+ g
cos
eo
@oA9
@oC@
ix
=
O.
Lateral
a.
Equations
Wos
Uos--g
sin
t
eo-
s-Y v
Y5 a Y5 r
VToS
VT o
!
P
V
-b
s(s-_)
--Lr
s
!
!
L5 a
L5 r
!
t
Ia]
r
!
r
s--N r
v
=
VToO
=
_p_ +---r
s
s
sv
+ Uor
ay
+ lXlat
N5 a N5 r
-- WoP--
g(cos
!
]
cos
tan
8o
ay =
r
eo
s
C-3
sr
-- izS p
8o) _
b.
Transfer
Functions
r
N_Sr
m
5a
a
=
Denc_Linator,
etc.
m
5r
Alat
4
I)
_.
Alat
+ bs 3 +
Lhlat = as
cs 2 +ds+e
I
b - -CY +
+ Nr)
Uo
C
-
WoL_
N_
+ _(Yv
+ N_)
-
NSL_+
YvN_
VT o
d
VT o
U°
VT o
L_N_)
(N_-
L_oNr)---_-
+ Yv(N_L_-
(_
cos
sin
80]
e o + N_
VT o
W o
v%
=
_
VT o
2)
[(_N_--
5
(5 a
N_L_)
or 5r)
=
%
=
C0
=
-Y_[_
+ N_]
Y_ (_N_
Wo
+ _
VTo
D_
=
_VT°
(N_L_
(N_
=
-
L_)
A_s 3 + B_s 2 + C_s
, Uo
Wo
--N 5+--L
VT o
VT o
"'_'_
-- _pLr/
_ __----g
+ L_ VTo cos
, ,
, ,
(NsL r -- LSNr)
-
e O-
Numerators
N66
%
cos
L_N_)
cos
,
5
eo +
,
g
+ N5 _ T
o
(N_-
sin
e 0 +_9_gVT
° (N_L_
C-4
+ D6
L_N_)
U°
--VT
°
8o
-- N_)
sin
80
sin
e o)
N_5 = Aps3 + Bps2 + Cps + Dp
!
Ap
=
L5
=
LS(Nr
+ Yv)
+ NSLr
VT o
Dp
=
-- g
VT
(L_
-- N_)
sin
eo
O
N_
=
Ar s3
+ Br s2
+ Crs
+ Dr
f
Ar
=
N8
.
_,
f
!
f
Br = Y_N_+ n_Np-Ns(Y
_ + $)
Wo
Cr
=
Y_(I%N_-
N_%)-
L_YvN _
+ N_Yv%
+VT o
Dr
-----g
(L_N%-NgL%)ooseo
VTo
N_
A¢
=
Ap
+ A r tan
8o
Be
=
Bp
+
tan
8o
C¢
=
Cp
+ C r tan
eo
Br
=
Acs 2 +
C-5
Bcs
+ C
(LgN%--NgL%)
_a'
AT
+_4
___
ay
!
H-747
_4s4+_2 +CayS2 +_
VToA_
+ lxlatAr-
lzAp
ay
=
VToB _ + UoA r - WoA p + iXlatBr
c_
=
VToC _
+ UoB r-
WoB p-
g
D_
=
VTD
+ UoC r-
WoC p-
g cos
E_
=
UoD r-
To
obtain
__
_
ay,
_
let
WoD p-
lxlat
g cos
eoC ¢
= i z = 0.
C-6
cos
-
8oA¢
lzB p
+ lxlatC r -
eoB ¢ +
iXlatD r -
izC p
izD p
k
L-
[=.
=_
--
_-_. ....
:7
.....
_ _
_
__
"
.....
.
•
-
_
.
p
-
Z
--
-Lg'.
3
....
_
.-