Aircraft Stability and Control Data

N69-31783
NASA
AIRCRAFT
STABILITY
AND
By Gary
L.
April
CONTROL
CR-96008
DATA
Teper
1969
Distribution
of this report
is provided
in the interest
of information
exchange
and should
not be construed
as endorsement
by NASA of
the material
presented.
Responsibility
for the contents
resides
in
the author
or organization
that prepared
it.
Prepared
under
Contract
No.
NAS 2-4478
by
Systems
Technology,
Inc.
Hawthorne,
California
for
NATIONAL
Ames Research
Center
AERONAUTICS
AND SPACE
ADMINISTRATION
REPRODUCED
BY
NATIONAL
TECHNICAL
INFORMATION
SERVICE
U.S.DEPARIMENIOF COMMERCE
SPRINGFIELD,
VA. 22161
FOREWORD
This
report
was
prepared
under
Contract
Technologg_
Inc._ Hawthorne_
California
and
and Space Administration.
The _SA
project
The
STI
project
engineer
The
author
gratefully
was
co±lecting_
interpreting_
wishes
to acknowledge
the
in the
preparation
Gary
L.
acknowledges
NAS2-4478
between
the National
monitor
was
Systems
Aeronautics
L. W. Taylor.
Teper.
the
aid
of the
STI
staff
in
and organizing
the data.
The author
also
fine work of the STI publications
department
of this
Precedingpageblank
report.
iii
ABSTRACT
Data of interest to handling qualities investigators is presented
for various current aircraft.
Included are those required to obtain
transfer functions for the aircraft's
response to control inputs. Where
possible, an analytical description of the aircraft's
stability
augmentor
is given, and also the complete flight envelope of each aircraft is
covered for its most commonconfiguration and loading. Computedtransfer
functions for various flight conditions are included.
_V
CONTENTS
Page
I.
INTRODUCTION
]
II.
A-7A
3
III.
A-4D
27
F-]O6B.
49
T-38
57
F-gA
67
IV.
v.
VI.
VII.
VIII_
IX.
X.
XI.
F-104
.
73
F-]OSB.
81
B-58
91
NAVION.
99
DC-8
Io9
APPENDIX
A.
AXIS
APPENDIX
B.
TRANSFORMATION
OF NON-DIMg_SIONAL
DERIVATIVES
TO BODY AXIS
APPENDIX
C.
SYSTEMS_
EQUATIONS
COUPLING
SYMBOLS,
OF MOTION_
NI]MERATORS
AND
DERIVATIVE
TRANSFER
v
DEFINITIONS
STABILI_£
FUNCTIONS,
. .
A-I
AXIS
B-]
AND
C-]
SECTION
I
INTRGDUC
The
gators
those
purpose
with
data
response
_or
required
to
control
those
is
aircraft
y_eneral
obtain
for
the
which
contents
and
is
b.
Flight
c.
Nominal
configuration
location).
d.
References.
e.
Basic
data
of the
and
number
Geometrical
parameters,
TR-176-I
are
information
are
the
aircraft's
of the
aircraft's
was
available,
the
including:
(weight,
geometry.
limits
of
for
inertias,
and
the
versus
nondimensional
altitude
for
longitudinal
some
the
showing
elevator
lateral
aircraft,
given
description
reference
augmentor
and
versus
Mach
ration.
*_ese
relating
Included
and
c.g.
sources.
angle-of-attack
the
aircraft.
investi-
envelope.
s_d
by
qualities
presentation:
gLven_
drawing
Longitudinal
dictated
functLons
complete
Three-view
remaining
cl_rrent
analytical
derivatives,
and longitudin_ml
for the nominal
configuration
These data are usually
given
(body axe s ).
For
handling
given.
description
A block diagram
scheduling.
4.
transfer
a.
Trim
provide
on various
An
also
the
is to
data
inputs.
summarizes
A
document
usable
au_nentor
folIowLng
].
this
readily
to
stability
of
TION
portion
system
I
Mach
number
stability
the
and
trimmed
gains,
and
and
altitude.
derivatives*
nominal
lateral
configu-
dimensional
and lateral
transfer
functions
at various
flight
conditions.
for body-fixed
centerline
axes
available
axis
feedbacks,
of the
above
is presented
data.
of the
data
source.
as
The intention
has been to makethis
report completely self-consistent
insofar as symbols, nomenclature, definitions,
etc. The system used is
described in three appendices. Appendix A covers axis systems, symbols
and notation, and definitions of nondimensional and dimensional stability
derivatives.
Appendix B gives the axis system transformations for the
derivatives.
Appendix C includes the aircraft equations of motion and
transfer functions used herein.
While complete coverage of each aircraft including only the "latest"
s_d "best" data would be desirable, the major criterion used was that the
data be immediately accessible to the author. This is why only isolated
flight conditions are given for someaircraft,
and also why, as those
people 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. As to how well the data can be expected to match the flying
aircraft_ it is assumedthat those for whomthis document is intended
know well the difficulties
of obtaining derivatives from flight test data.
Every attempt has been madeto insure reliable translation,
interpretation,
and transcription
of the data from their source documents.
The manufacturers of the aircraft
described herein can not be held
accou_itable for tile infomnation presented, nor would they be bolmd to
concur in any conclusions with respect to their aircraft which might be
derived from its use.
'lYe- 176-l
2
SECTION
A-TA
3
II
I
c_
i
NOMINAL
CRUISE CONFIGURATION
FLIGHT
ENVELOPE
Cleon Airplane
60%
Fuel
40,000
W = 21,8891bs
CG at 30%MGC
Ix =13,635
Slug ft 2
[y = 58,966
Slug ft z
I z = 67,560
Slug ft 2
Ixz =2,933
Slug ft z
REFERENCE
X
X
X
X
h, (ft)
Body
Ref.
Axes
20,000
GEOMETRY
X
O0
.4
X
.
1.2
S = 375 ft 2
X
c = 10.8 ft
Tronsfer functions given
for these flight condlHons
b = 38.7ft
I) LTV Vought Aeronautics Div. Rept. No. 2-53310/5R-1981,
'_,-TA Aerodynamics Data Report" 21 Moy 1965 (U)
2) LTV Vought Aeronoutics Div. Rept. No. 2-53310/5R-5121,
Rev. I ,"A-7A Estimoted Flying Quollties" 20 August 1965 (C)
3) LTV
Vought Aeronoutics Div. ,"Updoted
LateroI-Directionol
A-TA
Cruise Device Configurotion
BASIC DATA SOURCES
Wind Tunnel Test ond
est,motes u
Some LoteroI-Directionol
Derivotives
Adjusted After Flight Test
Aircraft
Doto, 25 Augur 1967
PITCH
AXIS
GZ
,
X= •
v
(ft/sec
(Ib)
_ep _._ 57.3
.5
Ib
rad
'
_j
55s
+
z)
A-7A
i) }-_:
1-
I
-.25 rad/sec
rad
152.2
rad
i_
5z3 ft/sec2 IROLL
AXIS
. rod
(Ib)
= 5L_
__]
-L!2_iic.,_+,l
rad
_
.10 rad/sec
YAW
pi
(rad/sec)
I_
AXIS
(rad/sec)
_rp
I,__-_,
A-TB
rR6
r --_.
Cos
2.50
b
P
(red/sec)
t -2 5 rad/se_
red
_-J
Sin
2.5 °
I__
F
__+1
_KARI
aa
T.E. up
(rcJd)
l°t/I
_e
1.5
Figtu.e
11-2.
A-TA
[_tabilit¥
5
(deg)
Au{_rtentation
System
=
(red/sec)
=-
14
I
, ,ooof,
12
...........
Sea Level
GO
I0
(deg)
8
\
_
_N35,000ft
i
L
.4
.6
..............
_f
....
2-
°6
.2
M
i
I
.8
1.0
1.2
-I0
I
,15,00Oft
I
Sea Level
(deg)
-6
"
m 4
....
I
-2
0
TR--] 76-I
0
.2
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_
M
.8
1.0
1.2
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I
15,000ft
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eL
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M
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1.0
1.2
1.0
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15,000ft
.12
I
CD
.08
.04
..............
Sea
Le!:
¸-
06
TR-176-1
\
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.6
7
M
.8
6
,
I
,
i
I
i
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....
i
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ft /
t
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,,b/l"
!
/
1
Sea Level
....
i
___
0
.2
2.0
.4
.6
i
M
.8
1.0
1.'2
1.0
;.2
!
i
IZ 15,00Oft
1.6
CD a
Sea Level (_
\
XXX\\,
35,00Oft
.8
\\x.
ii
\
4
.......................
(7)
.:
i
J. ................
f_
............
i
_.J ....
..£-
!
--0
....2"
I
....
oo 0
o.
>
._J
0
0
o
Q
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o.
0
I/
I
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io
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(xl
Od
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i
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o.
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e_
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° I_
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-V
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o
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I
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-v
0
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,
t
,
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...............
//Q
35,00Oft
/
CL M
iI1__.
I
.04
15,000
ft _
,
uu
0
/
/
-.04
-'080
.2
.12
ea Level
I-
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.6
1.........
4
M
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1.0
1.2
T
Oft
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-
Sea Leve!
15,000
_t(__,
C DM
I
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i
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................
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q
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r)
.O4
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I
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',
0
Cm M
-.04
\
-.08
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f,
\
\
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..
\
© ss,ooo,
i
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TR-17,]-i
I
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i
i
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4
I1
M
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1.0
1.2
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_.&.35.oo'o.t
.6
CLB
e
"" _
' \
_.151000ft
........ T"""..
.4
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..............
!
[
l
t
0 o
.2
0
.4
.6
M
.8
1.0
.2
.4
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M
.8
1.0
1.2
J..
-.60
.........
-I
.........
..........
!......
i.......
7/
-.80
CmB
e
Sea Level
__ !___....._?
!
-1.00
,
e_ ,//-_
,,_
15,00Oft
..........
_ 35,00Oft
I
t
-1.20
1
0
.2
.4.
.6
[
Cy.8
-.7
_
-.8
.............
i .........
M
.8
1.0
1.2
1.0
1.2
L
1.---------E_,_
--
1..............
--
------
7..................
............
Sea Level/_
-I.0
0
I
]
i
l
.2
.4
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--'-
-i ....
M
.8
-.06
-.lot-............:f--_-
.............
/Sea
Level "(.D
-.izl
TR- 17c7-1
.......[C-;_- _---
i
13
......
_-C__35_,QQQf
1.....
I
J
I
0
.2
.6
.4
M
.8
1.0
.12
Sea Level
35,000
15,000
Cn/_
,10
li7_
.O8
.06
mR-17<7-1
14
ft
.2
0o
.2
.4
.6
M
,8
1.0
1.2
-.I
C_p
i
Sea Level
_3
35,oo;_i__
-.4
15,ooo.
.....
-,5
.O6
I
I
I
i
.O4
Cnp
.02
15,00Oft
l
0
tSea Level
-.02
-.040
ii135,000,
ft
.2
T
'
L
C._r
Sea Level _'_',,,u _.
O0
--
0
I
15,00Oft
1
.
.4
.6
M
.8
1.0
1.2
.2
.4
.6
M
.8
1.0
.2
Cnr
,
_/"'_
_'_
/'i
,. Sea Level
"\
t
-.s6---
35,00Oft
".-,. -- ,-- 4,,..
:
|I
55, O00f,\
_ "NI5'OOOft
J---_.......
_...........].............
t-----:,
--\ <- --....
!
-.40
.................
[
M
00
.2
z
.6
.8
1.0
1.2
! ,5,ooof,p
-.01
(_._.._
I
See Leve_
/
-.02
-.05
_QR_Q
-
_OL
2
(Includes
Spoiler
(_....
1
Effects)
.O8
I
.O6
C_.8o
(')
.O2
-
o6
TR-176-I
,
.2
x,_
.4
.6
17
M
.8
1.0
1.2
.006
.004
011{}_
)
.002
0
- .002
i']_-1'7"_;-i
1_
.3
Cy_r
.2
0
Sea Level __
i
0
.2
.O3
"-'_
.01
0o
TR- 1yC-I
35,000
ft
Sea Level
i
.2
l
.4
.6
i9
.....
M
.8
1.0
1.2
!
I, I
!
V
!
!
0
!
b
oo
!
b
!
!
b
b
_b
0
0
PO
0
0
TABLE
GEOMETRICAL
Note:
I
-q
Oh
I
Data for body-fixed
S = 375 ft 2,
W = 21,889
centerline
b = 38.7 ft,
ib,
PARAMETERS
axis,
FOR THE A-7A
clean
flexible
airplane
c = 10.8 ft
m = 680 slugs,
Ix = 13,635 slug-ft 2,
II-A
c.g. at 30 percent
!y = 58,966
slug-ft 2,
MGC
!z = 67,560
FLIGHT
slug-ft 2,
Ixz = 2,933
slug-ft 2
CONDITION
I
h (ft)
BO
M (-)
a (ft/sec)
0 (slugs/f@)
I
2
3
0
0
0
0.S5
0.6
0.9
0.3
0.6
0.9
1.1
1,117
1,117
1,117
I,058
I,058
I,058
I,058
0.002378
O. OO2378
O. 002378
4
15,000
0.001496
5
15,000
O. 001496
6
15,000
O. O01496
7
15,000
O. O01496
8
35,000
9
35,000
0.6
0.9
973.3
973- 3
o. 000736
O. 000736
279
670
1,005
317
635
952
1,164
584
876
91.5
534
1,200
75.3
301
677
1,OLO
126
283
11.2
2.9
2.1
13.3
4.0
2.5
2.9
7.Y
3.8
Uo (ft/sec)
274
669
1,004
3O9
633
951
1,163
579
874
Wo (ft/seo)
54.2
33.9
36.8
72.9
44.3
41.5
58.9
76.2
58. I
6eo (deg)
-7.4
-3.35
-3.8
-8.8
-3.8
-3.85
-4.95
-5.4
--a._
0
o
VTo
(ft/sec)
ov
/2(lb/ft2)
s o (aeg)
7o (deg)
0
0
0
0
0
0
0
_" 0_O9 LO0"0-6C_'0-
6L'_C_9ooo"
o
oCC" O-
_'_-_-
L'Lfr-
_?_oo'o
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L_'L-
£0"L--
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C9 Looo" o-
LLLOOO'O-
0C5L0"0-
LL_O0"O--
6_90"0-
"_'66-
_'C_-
O_-
_6C0"0--
C_Co'o
6£_oo'o
_'o--
_C "_-
_L'_-
__0"
O--
LO'L-L9"9
oi'_
C6LO'O-
).CCoo"o
9LCO'O
6"0
000 c_C
6
6"gL--
969"O--
_6_o'o6o_-
_'LL
_OLO0"O
9L LO0"O
£C LO0"O
LOGO0"o
L_" L--
LL'L-
99?'o-
CRL0"0-
£££oo" o-
_o_o" o--
?_0"0-9L'L--
9"C_£ _9o" o._Y" o,f
C9_
o_9oo" o-
LOGO0" o
6CCo'o
9"0
L'L
6"0
000 c_
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O00(_L
000 ( _ L
9
ff
LC_o" o
9"0
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_gLO'O
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0_0" 0--
9
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9"0{-
9£ LO00" 0--
LC_O'O--
9t[LO'O
CgLO0"O
9" 9Y-
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9"66-
CL'6
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T_I_
I
e9 Z
nZ
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_9 X
+_C"T
_£Lo'o.--
_LO'O-
s9 LO'O
79_0"_
99 go" o---
_LO'O--
6"0
9"0
_'0
0
0
0
C
_
L
Od
O4
z
_KIO
I,I,
! CLI_O
0 J_ff-IDl'l,
q
7
<o
b-
7
Gu_Td_T _ elqTx_lj
Um_TO
(sTx_ GuTiz_%u_o
p_xT.j-Xpoq zoj _
VZ-V ZHZ EO_ _ZAIZVAI_{Z(I_IVII0!TK!Zk_CgV__IIC/IZID_I0q
E-If
:EIEVg
m%_C
:_%oz
TABLE
LATERAL
Note:
Data
are
for
body-fixed
DIMENSIONAL
I!-C
DERIVATIVES
centerline
axes,
clean
FOR
_
A-7A
flexible
airplane
I
-q
O_
I
FL!_T
1
2
3
h
0
0
0
M
0.25
0.6
0.9
4
15,000
CONDITION
5
'_
15,000
6
7
I5,000
8
I5,000
9
35,000
35,000
0.6
0.9
i
0.3
0.6
-o.187
-0.162
-0.314
-0.574
-0.722
Y6 a
-O. 00274
-0.oi 05
-0. 0085 7
-O.OO15O
Y6r
o.o43o
0.0769
o.o626
1.1
0.9
-0.310
-o.435
-0. 0847
-o.
145
-o.oo655
-0. OO691
-0. 0021 6
o. 0537
o.o55o
O. 0792
0.0267
-29.2
-66.0
-71 .2
-14.9
-3o. 6
-2.73
-6.79
-7.31
-i .4o
-3. oo
0.857
o .868
0.843
o. 859
o.599
o .563
3.75
17.6
24.1
12.5
7.96
14.2
7.27
11.2
7.27
3.09
6.55
21
I. 38
4.72
0.0307
-0. 00267
-0.00427
I
O. 0347
I
h)
L_
-11.9
-44.8
-98.o
-2. O0
-4.46
-9.75
I .18
i .15
i.38
-8.79
i
!
!
Lr
!
L5 a
-1.38
!
I
i
5.34
28.4
25.2
2.22
11.4
13.2
!
L6 r
!
!
I .82
1.28
5.74
17.2
1
0.948
I
i
I
i
!
E
I
3.12
10,2
!i
9
4
T
Nr
-o. 087o
-0.
-0.369
-0.905
168
-0.379
-i .54
-0.0310
-0.271
-o.116
-0.207
-0.541
-0.975
-0.169
-1.33
!
N$ r
o.4o2
2.08
I .56
o. 28o
-1.93
I8.61
--11 .I
-1.56
i
I
I
I
t
-0.112
-o .247
-o.455
i
i
I
N'
6a
-o.o799
7.37
1.64
-5.54
-8.8O
i
1
t
l
1.o4
0.652
I .01
-4.83
--2.54
-5.17
TABLE II-D
ELEVATOR
Note:
Data for body-fixed
centerllne
LONGI_TDINAL
_ANSF_
axes, clean flexible
FUNCTION
FACTORS
FLIGHT
_L
!
L_
h
M
2
3
0
0
0
0.29
t
i
15,000
35,000
9
35,000
0.3
"0.6
0. 9
I .I
0.6
0.9
0.316
0.316
o.185
0.229
0.230
1.76
4.21
6.76
I .63
3.15
5.48
8.81
2.08
3.68
0.118
0.0620
(o o_4_)
o.589
o.ok49
(0.0616)
o.14o
O. 071 0
(-0.o513)
0.0372
o.o75:
(-0.o9oi)
(1/Tp2)
o.156
0.o698
o .0472
i _-_ (1/%3)
15,OO0
8
0.277
o.79o
_U (!/Tu2)
15,OOO
7
0.9
o.1oo
!,'Tu I
h)
15,000
6
o.39_
o.o99_
i _/Te2
A_
5
0.6
_p ; 1/Tm )
!/T81
CONDITION
0.383
sp
I As
4
0.367
6DSp
8
N5 e
_IE A-7A
airplane
I
I
FOR
-41.6
-4L.3
o.oo716
o.o_43
o. 0422
0.506
1.o9
I .97
2.02
o.516
0.933
11.6
5.63
6.96
9.13
11
5.70
6.61
186
8.5
12O
190
2_
(I .22)
(0.369)
o. 627
0.854
(0.899)
0.929
o.753
1.30
(2.28)
(0.587)
0.89o
1.24
(i .23)
0.466
o.719
-i®
-318
-23.8
-99.6
-209
-22O
-43.2
-99._
126
187
58.9
121
191
2_
110
-0.o_44
o. o5 67
0.0990
0.0386
(o.o918)
(0.o53o)
o.o_9_
24.5
99.8
209
221
43.6
99.7
-5.43
-30.6
_8.4
-45.
I
-0.0214
0.0122
O. 0728
-0.00823
0-731
1.79
3.19
5-75
8,3_
5! .i
129
(0.14-11)
o .665
(i. o3)
-29.o
--18.8
.2
-8.18
-0.
oo316
109
-20.2
O. 0202
1'7'7
i
i
Aw
1/Twl
w
NB e
51.7
.-o.11o
I
(w (1/T_2)
0.%:
(I/Tw 3)
o.1o9
29.6
£
/'l'nl
-o. 0624
o.239
0.0210
165
(-o.oo6o3)
(0.0773)
318
(-0.0o939)
(--0.0!
31 )
-o .o553
178
o.419
0.0219
0 .o_31
O.Oh12
-0.o154
0.0173
11 .8
20.0
22.2
7.64
13.2
-_.92
-I I.o
-18.7
--21 . 2
-7.22
-12.5
-23.8
-99.6
-209
--220
-43.2
-99.4
0.00956
o.o719
-o. O949
15.6
29.3
5.41
-5 -57
-14.3
-23.3
-29.0
-165
-318
-0.oo998
-0.oo2_
-O.00117
o. Ol 20
0.0729
6.33
15.6
25.3
5.55
-5.73
-14.3
-23.3
-5.o8
o. oo225
N6 e
6.21
I/'i_2
1I%,3
Aa z
I/Tazl
I/Taz 2
CG
I/Taz3
/Taz_
-o.
0506
-0.00417
-o. Oh 97
-o.OO139
-o.OO17o
-0. OO25O
O.'O445
o.o_25
---0.0136
o.0197
20.0
22.2
7.69
13.2
-21.3
-7.28
-12. 5
--O.OO4O5
-0.00147
O. OO627
11.8
-I 1 .o
--18.7
I
TABLE
II-E
AILERON
LATERAL
TRANSFER
FUNCTION
FACTORS
FOR
THE
A-TA
Note:Datafor body-fixed
centerline
axes,cleanflexibleairplane
FLIGHT
CC_DITION
I
2
3
4
5
6
h
0
0
0
15,000
15,000
15,0OO
M
O.25
O.6
0.9
0.3
0.6
O.9
I
C_
I
8
35,000
O.6
9
_O00
O.9
0.0214
0.0102
0.0319
0.0191
0.0462
o.o411
0.018o
I/T R
I.62
4.46
9.79
0.968
2.71
6.17
7.15
1.28
2.92
_a
O. 237
0.202
0.218
o.231
o.156
0.179
o.189
o.114
0.128
_d
I.81
2.91
4.68
1.65
2.29
3.66
5.o3
I .81
2,58
Ap
5._
28.4
2_.2
3.79
17.6
2_.I
12.5
7.96
14.2
-o.oo113
-o. 0232
I/T s
A
7
15,0OO
I.I
-o. o219
I/Tpl
-0.0o23_
0.C_35
O.O_L9
-0.oo_7
.
-0.00144
-o.oo137
-o.0o718
-43.00241
_a
_p
0.217
0.217
O. 222
0.191
o.173
o.176
0.173
0.122
0.124
%
I.49
3.05
4.91
I .27
2.34
3.87
5.33
I .62
2.64
5.42
28.5
25.2
3.81
17.7
24.1
12.6
8.0*
14.3
O.210
0.217
0.222
0.183
O. 173
o.177
o.175
0.119
0.124
I.51
3.05
4.91
1.29
2.34
3.87
5.32
I .62
2.6_
0.402
2.08
I.56
0.280
1.37
1.6_
I.O_
0.652
1.01
0.596
I .12
1.13
O.445
0.777
o.9_4
0.581
0.420
0.593
0.0852
0.287
0.597
o.i&6
0.151
o._6
0.638
o.o198
0.193
2.35
2.29
3.26
2.18
2.13
2.78
3.98
-0.O0857
-0.00150
-0.0O655
-0.0o691
hD
N5 a
%
Ar
I/Tr
I
:'
Nr
5a
_r
_r
-0.0O274
%
11%
I
(o.885)
(_IB)
-0.o_05
3.26
7.76
_a
(0.667)
11%2 (_)
-O. 627
-233
63.1
78.2
-0.766
-7.06
-8.61
(o.9_3)
2.29
(o.@8)
5.92
I/T_3
I/Tay
I
(_ay
2)
i/T_Z2(_y2)
CG
_&y
(1/Tay
3)
( 1/T_y4)
-0._4
0.0896
6.37
-0.810
1.76
(0.726)
2.21
(o._71)
-1.63
5.77
-o.245
-0.00216
IO.7
--0.113
23.2
86.8
--0.477
-4.16
-6.58
-2.51
-i .16
(0.798)
1.32
-0.596
-0.146
-i .84
(o._61)
3.12
-2.66
(3.65)
(1o.7)
-391
o. 0673
7.10
--o.29_
.99
188
2.03
-0.00267
2.45
--0.OO427
0.793
(o.872)
0.422
(io.6)
-147
-0.545
-I
-0.o37_
.56
o.29o
(0.801)
-7.93
o.961
(2.Zm)
(3.79)
0.897
O.O_99
-0.113
(-6.63)
9.31
3.92
1.3o
TABLE
RUDDER
Note:
Data
]ATERAL
for body-fixed
TRANSFER
eenterline
II-F
FUNCI'ION FACTORS
axes,
clean
FLIGHT
FOR
flexible
THE A-7A
airplane
CONDITION
.
0
0
15,000
35,000
35,000
0.9
1.1
0.6
0.9
0.9
0.3
o.o462
0.0411
0.0i80
0.04:9
o.0435
0.0214
0.0102
o.o319
0.0191
I/T R
i.62
_ .46
9.75
0.968
2.71
6.17
7.15
1.28
2.92
_d
o. 237
O. 202
o .218
O. 231
o.156
o.175
o. 189
0.114
0.128
2°9i
4.6,%
I .65
2.29
3.66
5.o3
I .81
2.58
7.27
3.09
6.55
2.22
Ap
---0. 0224
I/_1
11.4.
13.2
18.2
-0,00242
-0.00117
-0.0237
©.00352
2.33
4.31
6.63
5.56
3.16
4.39
-4.45
-6.33
-4.55
-3.44
-4.38
I .45
6.89
I0.8
7.03
2.75
6.21
2.!!_
4.3.5
6.64
5.53
3.27
4.4.3
-6.57
-4.76
-3.79
-4.61
-5.54
--8.80
-4.83
-2.54
-5.11
2.68
1/Tp2
-3,38
1/Tp3
1.84
Aq)
/%1
5.35
8.31
-5.31
-7.88
10.9
12.8
8.29
7.27
-2.79
11.2
-0.00147
-o.oo141
-0.00723
-0.00243
2.78
5.37
1/%2
-_.11
-5.53
-8.18
Ar
-I .93
-8.61
-11 .I
I/Trl
I .13
4.33
9°87
0.553
2.35
6.12
7.31
0.578
2.64
_r
o.538
0.475
O. 674
0o41_
o.473
o.535
o.79o
0.440
0.526
%
I .02
o.6_z
0.502
1.17
0.735
0.514-I
o.381
I .12
o,585
%
O. O430
0.0769
0.0626
0.03c7
0.0937
0.0550
0.0192
0.0267
o.o347
0.000578
O. 00271
2.70
6.17
7.11
113
170
272
NS_r
N5 r
15,ooo
0.6
.81
r
15,000
0.25
/Ts
A
0
-<).0624
-0.oo199
I/T_2
I .73
4.45
9.76
I/%3
54.7
12o
186
12.0
51.5
62.9
-O.123
-0.0165
-0.00502
i/%
i.87
-2. O0
2.60
4-.43
_.
0.00_266
9.57
-3.
_8
-4.68
-I .56
-0.O603
-©.00616
1.14
63.6
9._
314.1
-0.10_
O. 0227
I .27
97
-7.84
--I .96
5 °92
9.77
2.45
2.69
-3.69
-o. 00654
22.4
O. 000648
6.16
7.06
-5.78
-8.91
I .32
-0.0021
2.94
'110
160
15.6
30.4.
-0.0436
-0.0107
I.36
2.97
--2.28
-3.81
4.3o
6.80
1o.5
2._1
4.3o
L
TR-i
52.3
-0.0178
(i-1
26
6
SECTION
A-4D
27
Ill
Figo_re
!Ii- ]
A-4D
!
I
FLIGHT
NOMINAL CRUISE CONFIGURATION
Cleon Airplane
ENVELOPE
60,000
W = 17,578 Ibs
CG at25%MGC
Ix = 8090
slug- ft z
I y = 25,900
Iz = 29,200
slu9- ft z
sluo-ft z
Ixz = 1:500 stug-ft 2
Body
Ref.
Axes
40,OOO
h(ft)
20,000
REFERENCE
/
GEOMETRY
S = 260 ft 2
c = 10.8 ft
SL
1.0
0.2
b = ?_7.5ft
X
REFERENCES
I) Abzug, M.J. and R.L. Faith, Aerodynamic Data for Model
A4D-I _OperotiormlFliqht Trainer, Douglas Aircraft Co.
Report ES-26104,
November I, 1955
2) _Johnston,D.E. and D.H.Weir, Study of Pilot-Vehicle'Controller
Integrotion for A Minimum Complexity AFCS, Systems
Technology, Inc. Technical Report No. 127-1, July 1964
BASIC DATA SOURCES
Wind Tunnel Test
Envelope for model A-4D-I
Transfer functions given for
these flight condition
ROLL
PITCH
!
I
az
,_x=?)
.-.j
I
_ep
P
..__+t<
A-4D
A-4D
_ap
t
['0
FilterPass
Low
+
Kp" Gain in deg/deg/sec,scheduied
for indicated air speed
_"
I
K_ , Koz • Scheduled for indicated
airspeed
YAW
L
(_rp
Note:
n
System
used on the A4D-2N
Control
stick
steering
mode
model
only.
shown
Kr
: Gain in deg/deg/sec,
for
Figure
r
A-4D
r_
iii-2.
A-4D
_
Stability
Augmentation
System
scheduled
indicated air speed
14
12
ao
I0
(deg)
8
\\35,000
6
ft
\\
\
4
2
0
0
T_-I 7!]-1
.2
.4
.6
M
_.50
.8
1.0
.8
CL
.6
\ 55,000
ft
"
.4
Sea
.2
Le
......
0
0
.2
.4
.6
.8
1.0
M
i 35,000
.06
ft
/
\
\
.04
O0 ft
.02
00
•2
.4
.6
M
TR-17g-I
31
.8
1.0
5
CLcl
4
_
All Altitudes
5
2
0
.2
.4
.6
.8
1.0
M
1.4
1.2
/
1.0
All Altitudes
/
0.8
]
0
.2
.4
.6
M
Tl_-176-1
32
.8
1.0
q
o.
f
\
/
O
O
O
to
j
0
co
c0
i/
I
,4--.
m
O
0
O
,
r_h
4
i
I
!
i
i
!
Q
00
@
,_-
ea
O
(D
l
(D
oa
_.
I
_0
oo
I
!
O
m
i
¢.2
t_l
I
I
E
E_
-1.0
All Altitudes
-I.2
-I.4
-I.6
-1.8
- 2.0
V
-2.2
0
Z
.2
.8
.6
M
Cmq
All
!
_-
17_- I
34
Altitudes
I.O
It--
0
0
0
0
Q
o
LO
0
o.
o.
_i
._.u_
0
0
C
0
0
0
o---_
co
\\
0
0
\
ro
C_
\
----C_
0
--
ro
L
r_
;0,1
0_1
0,1
0
0
0
0
,_,
cO
-----
'_
o
0
_
I
E
_.
_.
I
I
i
rj
_L
I
E_
o.
/
o.
O
O
o.
O
O
cO
I
OO
¢.D
o__
i
L
_,,.0
O,I
O,1
O
O
_"
I
¢.D
!
O
OO
--_
o
O
"_I
I
O
_7
_0
D--
_7
--.9
Sea Level
c_
-I.0
.......
(r+,)
-I.I
15,0(
..............
ft
-12
0
.2
.4
M
.6
.8
0
1.0
I
Sea Level
.m._.
r_
j
15,000
ft
_ " fl.mil.l_.
35,000
-.2
-
-.3
0
.2
.4
.6
.8
1.0
M
.4
5,000
ft
.3
_/5,000
.2
ft
Sea Level ----
.I
00
.2
.6
.4
M
TR- ; 7__-L
Y(
.8
1.0
-.2
All Altitudes
-.3
-.4
0
.2
.3
.4
.5
.6
M
.06
Cnp
.0,
/
Seo Level/
!
/
/
t
.02
/
/
15,000
/
/
_J
/ 55,000
0
ft
f
.2
.4
.6
M
_-17_-i
38
.8
1.0
.2
15,000 ft _._
Sea Level _-
C_. r
(-).,
Cn r
0o
.2
z
0
.2
.4
5,ooo
-
M
M
_
.6
.8
1.0
.6
,8
1.0
%3
Sea Level
15,000 ft
¢
-._
35,000
-.5
TR-176-I
39
ft
o.
q
L
r_
o
I
\
00
co
m
\
i
i
o
0
i -
I
.J
o
0
_I
0
_D
0
0
_
I'
I
I
if)
J
i
_0
1
ii
IJ
._I
i
o
J
I
i
I1)
oo
0
!
i,
0J
Od
co
0
0
O_
I
I
i
i
B
0
o
i
I
_
aJ
I"
q
I
0
q
0
0
0
q
o.
q
o
q
q
0
I
!
O
0
D
0
v
DI
CY8 r
.2
L
All Altitudes
.I
Cn8
r
0
.2
.4
M
.6
.8
1.0
0
.2
.4
M
.6
.8
1.0
-.06
........
i
' ...............................................
-.12
I
.06
I
.04
seoLeve,
y_
,5,ooo,,_+"_,++-35,ooo,,
l
.02
0
TR-176-]
•2
.4
4]
I
M
.6
.8
1.0
0
0
{'6?
{'@
£'£{
0
0
0
?"g9
9"9
9 "9{
(oas/as)
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9q?
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?'A
9"LL
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9_o t
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9"9
07"0
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6"0
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9£9
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9_o L
9{£ooo'o
9{£ooo'o
967L00"0
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9"0
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k
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967L00"0
967t00"o
95o L
95o L
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9
d
(_ap) %
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s{6
6"0
(_ap) oz
96qtoo'o
9_o L
9£{soo'o
(oas/%j) °SA
9£{soo'o
ILLL
LLLL
oJ
9"0
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gg"o
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(-)
O00'gL
O00'dL
0
0
(a_)
_
L
_
{
_OI$1CAIOO $H0!_£
8%fl_UT_
0£0_
--:
zx! _8%j-_nTs
00_98
= zI _8%J-gnIS
006_8
%J 9"Or
= X I _8%j-gnTS
O_L_9
= xI
7
= o _%g _'£8 = q _8%J 098 = S
<o
b-
:a%o£
C¢[-V _{Z HOg T_Z,I,ZKrV_IVcl_IVOI_Z2MOZO
V-Ill
Z_[V_
7
TABT__
LONGiTUDiI_AL
Note:
Data
are
for
body-fixed
DiY_SIONAL
centerline
IiI-B
DERIVATIVES
axes,
clean
FOR
THE
flexible
A-4D
air!o lane.
!
FLIGHT
C OE_DIT!OI[
!
i
2
3
4
5
6
7
8
h
c
o
15, ooo
_F_ ooo
15_ ooo
15, ooo
35, ooo
35, ooo
x
0.2
0.85
0.4
0.6
0.9
1.o
0.6
0.9
0.052
0.0422
-0.0303
--0.0251
-0.00938
-0.0615
-0.
--19.723
--15.289
Xw
0.0687
-O.0215
Xu
-0.00934
-0.0298
XSe
7.6i2
Zw
-0.899
0.000877
--33.942
6.068
-2.23
-0.535
7.396
-0. 922
-I ._78
_
1343
-i .892
0.0227
--0.O212
0.000806
-0.02_2
6.288
--3.8_:3
-0.3874
-0. 677
I
Zu
--0. 0765
-0.0982
-O. 0704
Z_ e
--42.08
--188.28
I
--22.273
Mw
--0.0228
-0.0502
I
M@
-0. 000763
-0.
0533
--0.1174
-0. 0487
--O. 05 25
-0. 0869
--56.68
--103.23
-94.606
--23.037
-_'3. 149
-0.0131
-0.0204
-0.0379
-0.1072
--0.00908
--0.01739
--0. 00131
-0. 000476
--O. 000555
--0. 000902
-0. 000683
-0. 000270
-0. 000423
Xq
--I. 151
--2.936
--0.670
--I .071
Mu
0.00232
0.00340
0.00253
0.00162
M_e
-13.728
--63.987
-7.400
-19.256
--i .93 k
-0.00906
--33.809
--2.455
0.00263
-7!
.773
--0. LS4
-0.876
0.001824
-$.096
-0.00412
I
I
--14.084
TABLE
LATERAL
Note:
Data
are
for
DIHZFSiONAL
body-fixed
IIi-C
DERIVATIVES
centerline
axes_
FOR
clean
THE
A-4D
flexible
airplane.
I
O_
I
FLIGHT
I
2
3
h
0
0
M
0.4
o.85
0.4
--O.2484
--0.5755
Ysa
-0. 00582
%r
15,000
4
15,000
CONDITION
5
6
7
8
15,000
15,000
35,000
35,000
0.6
o.9
1.o
o.6
o.9
-0. 1476
-0. 228
-0.3628
-0.358
--0.1 034
--0. 1596
-0. 00807
--0.00188
--0.0038
-0. 0055 6
O. 00207
-0. 000819
-0. 002763
O. 044
O. 0898
O. 02561
O. 03958
O. 0549
O. 049
O. 01791
O. 02487
L5
--29.71
--I18. I
--17.52
--35.95
-82.086
-82.02
--17.557
-£0.7
6
--I.813
--3.844
--I.111
--I.566
--2.503
--2.708
--0.761
--1.167
0.8731
I .776
0.613
0.812
I .208
1.113
0.475
0.6227
17.2
6£.359
8.99
21.203
39.282
44.89
8.1704
16.85
8.217
37.214
k.309
10.398
22.103
22.943
4.1675
8.717
13. 203
67. 279
6.706
16. 629
£2.527
39.85
6.352
17.31
Yv
!
T
L8 a
!
LS r
Hr
-0.029
0.02953
-O.0348
-0.02173
0.01647
-0.0260
-0.02513
i --0.00539
-O.5761
-1.4
-0.3432
-0.5144
-0.899
-0.88
-0.2468
-0.3893
5.484
0.538
1.769
17.43
3.212
0.5703
1.399
-26.642
-3.280
-7.78
-16.36
-16.562
-3.16
I
T
N8 a
1.4875
N'
8m
-6.1953
-6.744
TABLEIII-D
ELEVATOR
LONGITUDINAL
TRANSFER
FUNCTION
FACTORS
FORTHEA-4D
Note: Data are for body-fixed centerline axes, clean flexible
FLIGHT
I
h
M
o.4
2
airplane.
CONDITION
4
5
6
7
8
35,000
35,000
0
15,000
15,000
15,000
15,000
0.85
o.4
o.6
o.9
1.0
o.6
o.9
_sp
0.352
0.435
O. 2838
0.301
0.3435
O. 233
0.214
0.2478
_sp
3.39
7.348
2.445
3.718
6.232
IO. 857
2.358
3.951
A
_p( I/Tpl )
O. 0735
o.195
0.682
o.086
a_o(I/Tp2)
O. 1035
0.08615
o.11o5
0.0747
--13.726
-63.98
-7.4
-19.456
I/Tel
0.0141
0.0319
0.00353
0.0112
1/Te2
0.8234
2.079
0.489
0.76
-34.074
6.076
Ae
N_)e
Au
7.628
I/Tu I
66.931
(-0.o6835) (0.02574)
o.0859
(-0.oso)
(0t1101)
(0,1019)
O. 0822
(0.0563)
-33.805
-33.771
-8.096
-I 4.083
O. 1284
-0.o0o615
1.362
1.572
0.3591
7.4o8
-19.776
-15.32
6.293
-3.878
80.193
99.8
--2O.49
--13.172
115.28
-160.9
(2.615)i
0.725
0.638
(G.98)
0.49
0.8554
(0.3383)
(3.813)
0.4926
(3.733)
2.824
0.3595
(1.337)
--56.68
--103.23
-94.606
--23.034
-43.149
218.67
313.69
357.77
203.34
286.42
0.0835
0.4915
(0,01471)
-0.0238
0.249
--12.608
0.0926
0.02184
o. 6259
N_e
{u(I/Tu2)
0.584
_u(I/Tu3)
0.8481
Aw
--42.08
--188.28
I/Tw I
149.77
325.77
_w(I/Tw2)
0.0614
O. 2653
_4_(I/Tw 3)
O.O761
O. 0602
0.0771
0.o538
0.0546
(0.1'127)
0.0965
o.o516
Ah
42.565
188.o4
22.946
57.02
162.98
94.496
23.728
42.898
-0.01842
-22.274
139.54
0.8042
5e
1/Thl
-0.0172
0.00122
0.0299
--0.02081
o.oo436
o .o5o
0.1270
11.623
27.426
8.454
13.376
21 .62
24.916
0.01593
_e
1/Th2
I/_ 3
-IO.415 -24..502
-188.28
Aaz
-4 2.08
I/Taz I
--0.0085
-0.00025
I/Taz2
0.00962
0.0301
I/Taz3
11.668
27.412
I/Taz 4
--10.471
TR-176-I
-24.484
-I 2.282
8.58o6
13.782
-19.671
-22.453
-8.048
-12.892
-56.68
--I03.23
--94.606
-23.037
-43.149
--0.0228 -0.00404
-0.000431
-0.000214
-...0.0181
-.0.00227
--7.712
--22.274
0.00835
0.05043
8.56
13.405
21.597
--7.84
--12.321
--19.645
0.00187
45
o.127
24.903
-22.437
-0.0oo296
8.7174
-8.203
0.01805
13.762
--12.868
TABLE
AILERON
Note:
Data
for
lATERAL
bod_-fixed
_ANSFER
III-E
FUNCTION
centerline
axes,
FACTORS
clean
FLIGHT
FOR
flexible
2
3
h
0
0
15,0OO
15,000
15,000
M
0.4
0.85
0.4
0.6
0.9
0.00508
o.oo599
o.oo698
I.O152
I.5346
2.48
4
5
I/T s
0.00914
0.00568
I/T R
1.744
3.81
_d
0.112
O. 1207
o.0949
O.0885
o.0966
_od
3.999
_. 293
3.058
4.342
6.618
Ap
17.199
64.36
8.988
21.2<)3
39.282
"-0.00572
-O. 0OO233
-0.01182
-0.003
A-_D
airplane.
CONDITION
1
I/Tpl
_KE
-0.00041
6
7
8
15,000
35,000
35,000
I.0
0.6
o.9
0.00726
0.00_32
o.0067
o.7o13
1.137
O. 0676
0.065
6.392
2.996
4.4o3
44.89
8.17
16.89
2.772
0.09125
-0.000211
-0.0085
-0.00185
NIDsa
O. 0977
0.0923
O. 1015
0.0968
0.O717
0.0669
8.845
2.779
4.442
8.914
6.787
2.742
4.553
17.321
64.398
9.073
21.308
39.495
44.91
8.299
16.921
_(p
O. 1149
O. 121
0.0991
O. 0924
O. 1021
0.0968
0.O70
0.067
%
3.985
8.843
2.798
4.439
8.891
6.789
2.76
4.55
1.4875
5.484
0.5376
i.769
17.4_
3.212
0.5703
I .39
0.9029
4.364
0.4868
0.873
2.601
3.054
0.3965
0.739
O. 1024
0.0571
0.0185
o. 0847
o. 0946
-O. 0646
0.O17
0.0695
3.694
I .521
2.523
4.073
3.519
i_p
0.1149
0.121
%
3.986
Acp
I/T r
N_Sa
3.767
_r
2.655
--6.OO582-0.00807 -0.001883 -0.0o38 -0.0o556 0.oo207 -0.o00819 -O.OO276
%
-0.1615
185a
4.475
I/TGI(_)
(o.9834)
-0.723
-0.0447
-0.2036
(0.974)
-0.369
(0.5504)
1.704
2.537
2.2264
(0.4294)
1.368
629.29
-456
134.99
3048.0
-1396.8
-838.16
197.67
--7.665
-0.7967
--2.413
--5.294
2.193
-O.4781
--2.42
-2.178
1/T#2(a_)
3.287
4. 156
f
I/T#3
19.189
Aay
--2.66
I/Tay1(_e_r2)
(0.7012)
i/%2(4,y2) (1.923)
-0"0505
CG
_y4(I/Tay4)
TR-176-1
3.049
-0.1975
o.3891
(-0.8875) -0.0468
4.248
0.6872
(2.2183)
2.54
2.266
0.4622
1.651
(-16.43)
0.0215
(1.869)
(-32.14)
0.0324
0.00935
(-2.903)
(17.62_)
8.743
(4.149)
(33.046)
23.294
9.772
_6
-o.1843
0.3626
-o.9o3
(3.712)
TABLE
RUDDER
Note:
Data
IATERAL
for body-flxed
III-F
TRANSFER
FUNCTION
centerline
axes,
FLIGHT
I
2
3
4
h
0
0
15,0(90
15,000
M
0.4
0.85
0.4
o.6
o.o0968
FACTORS
FOR
THE A-4D
clean flexible
airplane.
CONDITION
5
15,000
o.9
o.oo5o8 0.00595 o.oo658
6
15,00([)
7
8
35,000
35,000
1.0
o.6
o.9
O. 00726
0.00432
O. 0067
2.772
0.7013
1.137
O. 0676
0.065
2.996
4.403
8.717
I/T s
0.00914
I/TR
I .744
3.81
I .0152
I
.5346
2._,8
_d
o.112
O. 1207
0.o949
0.0885
O. o966
0.09123
3.955
8.293
3.058
4.342
6.618
6.392
37.21t_
_.309
10.398
22. 103
22.944
4.167
-0 .ooo236
-O.0119
--O.003
-0.OOO412
-0.000212
[-0.00851
4.375
2.552
3.208
4.359
4.534
2.587
3.743
-3.207
--4.196
--4.2rF9
-2.664
--3.79
A
Ap
8.217
-0.00186
1/ p1 -O.00576
1/_ 2
3.o_
I/TP3
--3.O29
i
7.7o8
3o86
-3.997
37.028
4.376
--2.6
3.795
9.936
21-9
22.83
3.678
8.379
2.642
3._
4.378
4.539
2.729
3.797
1/T 2 -3.211
-3.98
-2.902
-3.33
-4.227
-4.293
-2.936
Ar
-6.199
-26.642
--3 •28
-7.78
--I6.362
--I6.562
-3.159
I/_r
1.54s_
3.815
0.615
1.348
2.t_95
2.786
0.393
0.930
_r
0.3075
0.363
0.308
0.272
o.1783
o. 1828
o.2o7
0.20
o.7 38
0._63
1.032
0.718
0.578
I .128
0.850
o. 4
o.09
0.Iz_96
0.0396
o.o9_9
_r
%
0.00133
N_Sr
I/% I
-0.0209
-0.o067
-0.0OO321_
1.537
2.485
0.049
0oQ179
0.000941 -0.0175
-3.90
-_744
0.0249
-0.00939
--0.00945
i/% 2
1.7532
3.812
I/T133
156.02
300.91
A_y
20.1
89.33
I/_ayI -0.o219 -0.00154
1/Ta,y. 2
llTar
1.0312
153.O
10.835
5.14
10.957
-4.49
-9.526
TR-176-1
--3._19
1.145
303.67
342.14
210.29
289.01
_.134
52.296
51.83
10.499
21.78_
-o 86
-0.00224 -0.0326
1.54
2.489
2.752
0.717
5.73
8.618
9,46_
3.733
-7.7
--8.63
CG
llTa
0.711
212.32
-0.o39 -0.o147
1.760
2.76
--3.411
-0.0141
1.150
-4.9
SECTION
F- Io6B
Precedingpageblank
49
IV
i
Figure
iV- I
i
F -106B
FLIGHT ENVELOPE
60,000
NOMINAL CRUISE CONFIGURATION
Cleon Airplane
W = 29,776
CG at 50.5%
h(ft)
/_
4o,0oo
MGC
//..
//
j
;
×
/
Ix = 18,634 slug-ft 2 "_
_j'7
o
[y
177,858slug'ft2(
Zz
191,236 slug-ft t (
Ixz
5,539slug
"ftz
Body Ref.
Axes
2%0oo
_q
v.,
X/
)
REFERENCE GEOMETRY
S
= 695 ft 2
c
= 23.755
b
= 58.15 ft
f
-__.m
X
M
Maximum A/B thrust
Military Thrust
Transfer functionsgiven for these conditions
REFERENCES :
Weyel, A.E., A.H.Terp, C.A.Lunder,
Description of F-106B Aircraft
to Be Used as a Variable Stability Trainer, Service Engineering Div.,
Kc_:llYel_:_Ji:_ilbiL::NE:y_;m_cs,DeC'convl_o_, A Compilation of F-106
Data From Various Convair Reports Contained in Letter, 14 May 1963_
I
F-106
I
YAW
PITCH
O_
!
8
F-106
F-_36
$
s+l
T_s.I
SCHEDULED
SCHEDULED
GAIN and TIME
GAINS
CONSTANTS
.2O
.6
-.5
(J
(I)
".4
:_ -.3
Ke
\
"0
_-.2
\
.5
.16
/Kp
.08
.12 !
\
.04 v
0
"0
0
.2
.4
.6
.8
1.0
0
PreSsure Rotio,ow/Po
.2
.4
.6
.8
1.0
Pressure Ratio,/_H/Po
0
200
400
600
Dynamic Pressure, qc, Ibs/ft2
Figure
IV-2.
_-_06
--
Stability
Augmentatiom
System
800
I V-A
G_OME'IRICAL
PARAMETERS _
_
F-IO6B
I
r-J
--j
I
Note:
F-J
Data
are
s=695,
I
for
bo_-f_l
b=38.1_,
e_terlLt_
axe,,
e=2_._,
eoc_itlocatio=:
_=
17._
,
_=-3._
FLIG_
,
CORDITION
2*
20,000
(--)
0.755
(rtl,,_)
p (slug,/rO)
1,037
o.00126?
7_
20,000
0.759
1,037
0.OO1267
10
20,000
0.799
1,o}7
o.001267
l_ss
_3,000
(s1,_s)
!,090
Ix (s1_ -ft2)
_0,0(0)
991
870
Iy (a1_-rt2)
195,196
1_,..._00
Iz
(slug "I_2)
219,262
198,707
187,119
Ixz
(slug-ft
2)
4947.1
18,74
_,
331o.9
6o19.4
xCU/C
0.29
O.305
0.26
%
4.42
_.O_
3.88
(aeg)
• o (eel)
eo (eel)
0
4._
Uo (_l,ec)
wo (_l,,c)
60.6
0.4
1,116
o.00e_77
_3.2
99.3
29,500
28,000
19,8o9
177,6_9
_3,49o
8,5.
0.2
39e
39_
w (_)
S.L.
0
0
791.9
19,800
1_,_1
9,"r"_'
o._o9
29,776
9e4.7
18,6_
18.0
78_
212
99.4
93.1
condition
73
1,037
0.00126?
108.6
29,776
92_,.7
18,6_
S,L.
1,116
0.002377
0.9
1.4
1,057
o.001267
o. 001267
1,4DO
1,199
591
z_3
1,3_'a
29,776
964.7
18, 6_
177,
1 91,2_6
8'38
2.0
0.000987
I,_9
949
o.00o587
1,9}6
1,100
29,776
18,634
1 8, 6_A
18,634
18,6_
18,6_
177,858
177,858
177,898
177,858
177,898
1 91,2_6
191,2_6
191,2_6
191,2_6
191,2_6
964.7
9,939
5,5)9
9,9_9
0._
0._
O._05
O._O5
0._05
2.0
0
2.7
9.4
0
0
0
1.2
0
11.0
2.0
2.7
1,0(0,
_6
933
9.4
868
80
I_0,000
29,776
964.7
9,9_
4O6
1.4
29,776
964.7
9,939
11 .O
40,000
12
1,037
0.ooo987
871
1 91,2_6
_o
20,000
933
1'r/,858
0
O.9
_0,000
100_._
191,2)6
9,9_
0._
20,000
0.9
177,898
4.9
3.88
del_
257.2
4.9
78_
0.4
414
18.0
0
4.O_
*Opt:_
1,116
0.002577
20,000
11
82
1.2
1,490
29,776
964.7
29,776
_4.7
9,9_9
0._05
9,9_9
O._X_5
2.70
I .2
0
0
• 2.7
1.2
I
_9"_"
[6" t9L_
"0-
_%9o'ot" L_
6_'_-
_'L-
_<L"6-
_"
06"_-
8¢'_-
L-
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7
D-AI _I_D_
7
TABLE
RUDDER
IATERAL
TRANSFER
IV-D
FUNCTION
FACTORS
FOR
FS I£bt
5
BASIC
F-I 06B
C_n_ _tion
6
I
I
MBch
No.,
Altitude,
CG
--4
Oh
I
Weight
q,
h
_
20,000
29
20,000
35,0oo
_,000
-O.017O
1.60
59
11 .I
-o.oo914
-0.00286
-0.002T5
(i._)
(i.72)
(I.79)
(0.0736)
(0.0693)
6.86
(o.o7oi)
9.32
10.9
2.76
9.oi
2.12
4.79
9.22
9.97
0.129
o.116
0.099
o.o7_
0.162
0.255
O. 162
2.08
6.17
2.97
-0.049
1.88
-2.64
o.o_7
-0.00111
I/TGr I
I/TOr9
Aa r
I/Tar I ((Oar)I
ay/Sr
1/Tar2(_a
r) I
(CG)
I/Targ(ea
r) 2
I/Tar_(_ar)
2
A_ r
ay/Sr
I/T_'rl
(cockpit)
I/T_r 2
(a_r I )I/T_r5
£_rl)I/T_r4
-0.000727
0.0039
-o.ooo53o
2.11
2.95
89.9
89.8
81 .I
27.9
o.o061_
31.6
[9+.2
1.96
I/T_r 2
0.0402
1.59
-9-3O
9.9e
6.40
o.o646
-8.81
0.00696
2.00
0.00679
2.44
-9._I
-5..49
4.16
4.29
16.6
o.00670
-6.09
29.9
0.00699
-5.96
19.5
11 .I
-0.006
-0.015
-0._I
-0.782
I .85
1.97
-0.001
°0.002
-2.54
0.569
-2.09
o.8e9
5.07
-o.oo9
5.19
9._5
9.1o
-9.40
-9.98
.4.9_
1 9.9
11 .0
-0.406
-0.808
-i.7.4
0.Sa3
i.99
0.4_-2
-I.
63
2.18
2.02
0.5.59
-0.792
-6.1 6
o.43o
9.97
0.680
I -74
(0.
0.21.4
o.419
o.2_
(o._62)
0.028
0.0438
0.02.5
2.4-8
-0.259
-0.053
0.690
2.07
41.9
6.57
(I .02)
(o._)
(1.21)
-(o.2.49)
.4.71
-0.300
0.402
90..4
19.6
-0.067
2.05
-2.4.2
9.25
11.8
-o.o61
-6.36
(9._)
(2.99)
(3.08)
-5.38
(2.17)
(0.890)
(o.73o)
(0.66_)
9.26
(o.9_9)
-0.086
0.780
6o.o
0.067
-o.oo4
9.08
100
9.92
0.90_
6
1.88
5.60
-o.i95
0._28
-5..47
9.99
7.29
-9.9+
9.I_
_.I_
9.19
-9.45
-3.61
3.37
9.10
-3.28
-I .44
-2.90
-I .49
-I .91
2.00
o.739
4.28
I .43
2.71
0.19 °
0.674
o.99_
.7_6
o.43o
o.58e
0.902
0..4_
•610
0.38_
0.059
-0.0O9
I .89
97.8
o.o_9
-0.021
I .07
0.0_.4
-o.oo5
4._6
13o
105
o.o09
-0.004 _
1.98
18,4
o.0o9
-0.010
2.7.4
219
36.6
16.2
34.1
12.2
18.2
-0.004
-0.01 0
-o.o_
-0.012
-O.Oli
-o.o12
6.89
1.89
1.08
-9.92
-2.4-4
67 .2
-0. 999
-1.1
_89)
5.29
-O.O(X)9
-9.29
2.81
1 .85
.4.18
-0.0OI
I._4-
-2.4.9
1.99
7.91
-0.0009
-I .69
6.09
-o.431
A_r
o.159
-2.12
-0.909
(9.28
0.224
1.9_
-o.427
(2.71)
-o.oo9
.4._
-2.75
rr (I/Trr)
o.oiol
2.00
-2.68
(0.975)
0.01 0
1.97
-2.55
(o.365)
I,ioo
0.001
4.59
Ar r
(0.349)
(2._)
29,776
_9
1.0_
-2.98
_r(1 I_)
29,776
I _952
1.84
(I.81)
(0.0582)
-o._36
30.9
5.05
(i44)
(o._9)
I/Trrl
-o.0o6
29,776
-o.o00
(o._)
(I .67)
951
29,776
223
2.0
_o,ooo
14o,ooo
3o.9
3o.9
o. 678
I/_m(;_)
I/T_r I (a_pr)
30.9
29,776
1,199
20,000
0.080
2.&7
9.51
30.0
o.9
20,000
30-5
12
1 .4
o.o_
2.01
7.06
0.9
20,000
30.5
29,776
I..4
0.1 69
2.42
0.178
0.9
S.L.
29,776
109
0.59e
A_r
A_r
-0.0164
29,776
297
2.54
0.175
)
30.9
30.5
2.62
0.16_
$/5r
_/Sr
25,500
0.4
20,000
2.19
So
i/_m
S .L.
2.o9
2.37
I/Tprs(_Pr
r/Sr
20,000
-0.01 66
_b
I/Tpr2(_Pr)
k_q
kJq
S.L.
3_
I/T R
P/Sr
_.5
0.4
0.2
o. 755
20,000
26
ib/ft _
I/Ts
2_iat
0._5
0.795
M
11
I0
7
i
-5.65
5.1 7
.4.99
2.4.9
16.9
-o.oo_
-0.01 0
-16.1
(9.81)
(0.709)
2.88
8.03
-0.091
2.69
0.844
-8.19
-9 •89
5.99
3.39
4.29
-9.97
6.16
7.89
-0.012
-21 .5
8.69
I .99
2.74
-.4-99
-5.69
9.0_
o.78_
-0.010
9.99
2.52
-0.012
1.99
2.90
-91.o
-_.4
10.9
8.94
BECTION
_-38
Preceding
pageblank
_7
V
_-3
I
c_
!
NOMINAL
CRUISE
Clean
Ix
60,000
at 23%MGC
= 1438
slug-ft 2
Iz = 26,779slug
"ft2
T.y = 25,874
slug-ft2
[xz = 0 (assumed)
I
40,000
Ref.
Axes
Body
h(ft)
/
20,000
REFERENCE
co
ENVELOPE
Airplane
W = 90001bs
CG
FLIGHT
CONFIGURATION
/
/
GEOMETRY
I
S = 170 ft 2
i
I
c
= 7.73 ft
b = 25.25
SL
I
0.2
ft
Augmented Power
---REFERENCES
I) T-38
Report
BASIC
X
Dynamic Stability,
NAI 58-704,April
DATA SOURCES
Wind Tunnel
Tests
Norair
1959
Military
Power (J85-GE-5)
Lateral transfer functions
given for these flight candltlon=
PITCH
__ _e
T-38
8"
Io.__
_
IO.Ss+,! I -° I
YAW
8rp
SCHEDULED
8r
GAINS
1.8
1,4
1.6
o
{D
Kr
1.2
1.0
\
.8
Y
C
.6
(.D
KSo
.2
0
0
2_
6
4
8
Impact
Figure
Tk- _76-i
V-2.
T-38
--
I0
Pressure
Stability
59
12
14
16
qc ,I bs/ft2
Augmentation
System
18
20xlO0
OL_L
9LOL
t_LL
0
<0
0 = zxI _g%J-_nI_
000_9[
= Zl
# %J-BriTs 000_0{
OVA _{_ %_ "_'o
= £I
#s_nI_ O'LL{
# %@-_nIs
009#9
- m ¢_ql O00_OL
= xI
=
7
<o
b-
uolg_u_ljuoo
_sTu_o
Cs_x_ OUTl_Ogu_o
$_-,T,,_HZ _0£ T_,V,T,
ZNV_V£
V-A [_I_VZ
p_xT_-£poq
qVOIH,T,
ZNO,_O
_o$ _%_6
:_%o_
7
TABLE
Note:
Data
LATERAL
NONDT}_SIONAL
are
body
for
fixed
V-B
STABILITY
centerline
DERIVATIVES
axes,
cruise
FOR
THE
T-38
configuration
I
FLIGHT
CONDITION
-4
Gh
I
2
3
4
5
7
h (ft)
0
M (--)
o.6
o.8
1.0
O.L
1.0
o.8
1.0
i .25
67o
893
1117
4O6
1017
774
968
1210
--I.27
-i .35
-i .26
VT o
cy 6
( f$/sec
)
-o.715
0
25,000
25,000
-i .35
50,000
-I .26
50,000
-1.41
40,000
--1.20
o
0
0
0
o.155
o.172
O. 103
o.16o
C_6
-o. o57
-O. 063
-0. o85
-0. 097
-o.o86
-o.o86
-o. o8o
-o. 052
C_p
-0.320
-0.330
--O.275
-0. 270
-0.365
-0.335
-0.390
-0.295
CY$ a
CY$ r
0
0.132
o. 183
Oh
o.126
0.097
C_ r
o. 080
o. 095
0.110
o.155
o.115
0.140
o.135
o.13o
C_6 a
O. 037
o. o3o
o. o069
O. 040
0.026
o.o53
0.032
o.o19
o.o16
o.o_8
0.012
0.017
o.o15
O. 021
o.o16
0.oio3
o. 262
o.315
o.332
o. 24o
0.335
O. 286
o.340
o.31o
o. o76
o.o78
0.084
o. 085
0.078
o. o52
O. 070
O. 076
--0.340
-o.49O
C_6 r
Cn_
Cnr,
Cnsa
Cn5 r
-0.470
o.o13
-0. 092
-0.435
o.o143
-0.092
-0.490
0.0126
-o. o63
-o.38o
-o.5oo
O. 0069
0.0126
0.0149
0.0137
-0. Io3
-0.o86
-o. io6
-0. o86
-o.53
0.0149
-o.
060
TABLE V-C
LATERAL
DIMenSIONAL
DERIVATIVES
FOR THE T-38
_9
I
Note:
Data
-4
O_
are
for body-fixed
centerline
axes,
cruise
configuration
I
FLIGHT
1
2
3
4
h (ft)
0
0
0
25,000
M (-)
o.6
o.8
1.o
o.4
-O.311
-0.737
--0.98
-O.151
0
0
0
O
0.0675
0.1
o.o75
-29.69
-58.29
Yv
Y8 a
Ysr
o_
rO
L
!
P
L
!
r
!
%a
L
!
6r
I
Nr
-3.14
-4.5
6
7
8
50,000
50,000
40,000
o.8
1.o
1.25
--0.0982
-O.137
-0.232
0
0
O
0.0391
o.o143
0.0122
o.o188
-8.491
--46.24
-9.293
-13.46
-21 •73
-0.727
-2.435
-0.588
--0.8544
-].286
o.191
5
25,000
_.o
-0.4
0
1.8
0.4]7
0.767
0.246
0.296
0.567
27.75
9.987
3.5o3
13.98
5.727
5. 383
7.941
8. 334
16.65
17.37
1.489
8.065
2.269
2.691
4.305
17.65
37.71
62.18
2.72
23.31
4.0
7.402
16.77
o. o965
0.132
O. 178
0.296
0.0673
o.o198
0.0429
-0.597
-0.736
o.876
1.712
-6.2
-11.01
0.785
1.242
19.27
!
N$ a
-4.3]6
-123.03
CONDITION
-1.037
2.36
-11.8
-0.1185
-0.423
0.0782
o.877
-1. ] 67
-5.984
o.0118
-0.O86
0.2084
--1.482
-0.142
o. 298
-1.872
-0.30
0.806
-3.245
TABLE
AILERON
Note:
IATERAL
Data
for
TRANSFER
V-D
FUNCTION
body-fixed
FACTORS
FOR
axes,
cruise
centerline
FLIGHT
h
0
0
0
M
o.6
0.8
1.0
A
N_
i/T
R
3.Ol97
4.145
4.185
o. 6o5
(d
0.121
0.133
o.146
_d
4.251
6.2
7-97
Ap
19" 273
I/Tpl
-0.00091
-o.oo14
0.oo141
27.75
10.0
-0.0005
-o.ooo3
configuration
8
5
25,000
0.4
o.oo25
1.0
0.8
50,000
1.0
40,000
I •25
-o. 00594
-o.oo31
2.275
o.548
o.8o3
1 •236
0.102
0.t
0.0527
0.0585
0.0705
I.98
4.94
2.187
2.847
4.151
13.98
5.727
5.383
7.941
i-0.00082
-0.00362
-o.o018
-o.o13
3.50
-0.012
o.ooo16
50,000
-0.0043
-o.ooo554
_p
0.108
0.12
0.127
0.0852
0.085
0.0473
0.052
0.0675
%
4.382
6.473
9.628
1.703
5.137
2.081
2.856
4.365
5-745
5.4
7.96
Am
19.29
!27.78
N_a I/T% (_) (o.Io8) (o.12)
1/%p2(_cp)
(4.381)(6.471
r
25,000
I/Ts
T-38
CONDITION
4
2
THE
I0.01
3.515
14.0
(0.127)
(0.0829)
(o.o853)
(0.047)
(0.0522)
(0.068)
) (9-617)
(1.719)
(5.135)
(2.086)
(2.856)
(4.361)
Ar
0.876
1.712
2.36
0.782
0.877
0.2084
O. 298
o.8o6
I/Tr
4. 439
5.4o5
4.80
o.535
I .52
0.484
o. 638
1 •401
_r
0.267
0.423
0.47
0.192
0.405
0.0827
0.129
0.143
car
2. 127
2.113
1.523
4.345
2.95
3.19
2. 765
1.884
A_
--0.511
0.446
-O.511
N5 a
I/TPl
(_#) -0. 167
-1 •323
-2.255
-0.0832
-o. o353
7.439
5. 334
(0.706)
--0.0843
-0.0074
-0.64
(o.58)
-0.21
-0.o66
(0.283)
t8.624
O. 289
N5 a
1/Tl_2(_
p)
6.926
(0.287)
1/T_ 3
TR-176-I
63
4.90
I .795
TABLE
RUDDER
Note
Data
&re
LATERAL
for
TRANSFER
body-fixed
V-E
FUNCTION
centerline
FLI_IT
I
h
0
M
O.6
2
0.8
3
FACTORS
axes,
FOR
cruise
_HE
T-38
configuration.
CONDITION
4
5
0
25,000
29,000
I .O
0.4
I .0
-O.013
O.0OO16
6
50,000
0.8
-0.OO594
7
50,000
1.0
8
40,000
1.29
-0.0043
I/Ts
0.0025
-0.OO14
I/TR
3.O197
I_.145
4.185
0.605
2.275
0.9/48
0.803
1.236
O.121
0.133
O.146
0.102
0.1
0.527
0.585
o.o7o5
4.251
6.2
7.97
I .98
4.94
2.187
2.847
4.151
16.65
17.37
1.49
8.065
2.27
2.691
4.305
-o.0oo92
-o.ooo5
-0.0003
-0.O119
-0.00082
-0.00361
--O.OO18
-0.000583
-2.07
-o. 797
-4.522
-2.o6
--3.311
--I.454
--I.395
(O.O081)
8.33
Ap
0.00141
-o.oo31
N_Sr I/Tpl
I/Tp2
(_p)
I/Tp3
((Op)
8.215
AS
N_r
I/T$I
(_)
I
IITrl
r ( I/Tr2)
a_
(I/Tr3)
%
1 .I0
4.79
16.5
17.245
--2.11
--0.827
-4.557
2.15
i.09
-6.2
Ar
r
N5 r
2.1.94
3.o
-I 1.01
4.114
I .905
3.341
I .423
I .408
i.31
7.91
2.14
2.59
4.237
-3.372
-1.526
-1.443
!(-O.O103)
1.42
(0.608)
-2.293
4.79
I .994
--II .8
--I.167
3.390
-9.984
1.451
-1.482
-1.872
(0.605)
-3.245
4.196
O.561
2.252
0.519
0.78
-0.0_71
0.206
(0.0302)
0.674
O.14
0.373
O.11
O.196
(O.193)
0.309
(0.367)
0.465
0.833
0.456
0.502
0.346
(1.23)
0.067
0.0998
0.o748
o.o191
0.0391
0.0143
0.0122
0.188
-o.ooo63
--o. ooi 6
-0.0034
-O.OLO7
--0.0052
-0.oo41
2.994
4.075
2.302
0.558
0.810
1.23
117.48
64.64
178.02
39.77
11.08
11.88
22.72
-o.oo561
-0.o14
-0.0063
-o.00398
-0.00212
-0.0372
N_Sr 1/TI31
I/%2
II/T03
Aay
I/Tay I
NS_r I/Tay 2
CG
I/Tay 3
I/Ta_%
TR-176-1
94.93
113.63
4.2o5
161.56
45.24
89.16
83.53
-0.0057
-0.0018
-0.00447
3.89
3.799
4.223
-3.027
-6.248
-9.098
2.882
7.327
10.416
0.65.5
72.21
7.852
-0.0496
o. 683
-2.525
2.736
64
159.0
2.322
0.565
0.813
1.226
-5-987
-2.536
-3.709
-4.732
2.66
3.90
6.529
5.096
SECTION
F-SA
6_
VI
I
Figure
Vl-]
I
F-5A
(_ONFIGURATIONS
GAR-8I
-
GAR-8 on wing tips
Centerline Tank
150gal.tanks
40,000
at W.S.85
h(ft)
7501b. stores at W.S. 114.5
50gaL tip tanks
T-A -
as I with 50%
11" -
20001b
I000
7501b
X
X
20,000
w
fuel
centerllne store
Ib stores at W.S. 85
0
stores at W.S.I14.5
w_
0
°
•
.5
w
w
M
IJO
50 gal. tip tanks
REFERENCE
GEOMETRY
X Longitudinal data given at these
flight conditions,see Table E .5a
for conflguratlon,_ ,and 7'e
S = 170 ft =
b • 25.25ft
c • 7.75 ft
REFERENCE
I) Jex,H.R.
and J.Nakagawa,Typical
F-SA
J=_oon_tudinolAergdynomk_ Data and
Transfer
Functions for 14 Conditions,
Systems Technology, Inc., Technical
Memorandum No. 239-4,
March 1964
BASIC DATA SOURCES
Wind tunnel tests with corrections
made per flight test.
1.5
I
._=
F -5A
I
YAW
PITCH
8
F-5A
o5---2%
°'5s*'
SCHEDULED
SCHEDULED
GAINS
I
L__
GAIN
K8 = 0.2 deg/deg/sec
1.8
K_ = 1.35 deg/deg/sec
I00
1.4
Q_
1.6
o.
1.2
.c_
._o 1.0
u
.c_
.o
,o
\ \
n_
\
O.8
KI
2O
0.6
p-
e-
£
\
0.4
0
I-
0.2
-_
2O
40
Impoct Pressure,
60
q'c, Ibs/ft2
80
Figure Vi-2.
IO0
I
00
2
4
6
8
I0
Impact Pressure,
F-SA -- Stabilit_
Au_memtation
System
12
qc, Ibs/fte
14
16
18
20 x I00
!
I
_%BLE _q-A
_ICAL
Rote :
S - 170
Data
tt 2,
b -
25.2_
are for body-fixed
_,
c - 7.73
stability
t%,
PAn
ZrOR _BE F-_A
_o " 0.5
axes.
FLI_IE
1
ConfiKurat1_ns
0Aa-8
k0,000
h (_t)
2
G_-8
_O,0_0
5
gAa-8
0
M
0.87_
1.25
0.875
70
(_eg)
0
0
o
a,-
:./w
1.0
1.0
1.0
3.2
1.0
0.8
_o,
(Ibl_ 2)
w
(zbs)
[email protected]./8
70
85O
1210
98o
210
_28
1150
1o, o00
511
6eo(_g)
-I. 15
5O,0CO
ix (_zot)
10,000
10,0GO
0.22
12.o
O. _c'
O. _'_
2
5
GAR-8
+ DL_ Bz_Xe
gAa-8
F_ps + Slate
20,000
1 ._
-6o
0.5
0
o.2o_
0.286
1_-5o
15_I0
10,000
30,000
12.0
_'Dl_
20,000
)0,000
0.8
_0,000
12.0
1.0
30,000
12.0
TT E_pty
I-A
0.875
I-A
13
II
Fuel
50_
12
II
Fuel
50_
0
0
0
0
0
0
0.875
0.875
0.70
0.70
0.50
0.50
0
0
0
0
0
0
0
0
1.0
1.0
0.5
1.0
_.0
1.0
4.0
1.0
2.0
9.0
2.8
1.2
2.8
2.8
7.0
2.2
8.0
12
228
61.9
122
19,000
O. _'_
--4.28
51,000
12.0
-60
980
980
1,130
1,1_0
720
725
570
570
12,000
I_,000
I_,000
17,000
17,000
910
282
17,000
0.1k
--6.26
_,600
11._
521
I_,000
14,000
0.12
0.1._
.05
_55
590
--0._-5
Bz_ke
12
1.0
21
-1.80
11
o
10,000
0.2
1o
I-A
I
+ Flaps
0
12
0
CCRDITI_
--2.5'7
P,,6oo
11.2
0.52
57,900
11.2
0.17
57_
-I .55
_,
700
1o.5
--2.62
57,100
11.6
0.15
_55
--I.13
57,900
11._
0.15
_
0.15
526
-_.62
57,900
11. b,
--2.86
_4,400
11.5
0.I_"
528
-5.77
_,_00
11._
"R.,TST.Is
"o_'0
oC_-
O00_--
0_" L--
O_'t-0
0
8"9--
g'9--
Ot "0-
Ot "O-
oL9"o-
989 "o_o'o
068OO "0
OgCe"
_" L0
O_LL--
ooo_ =.
_-_--
"_g"t-
0
OL "0-
o_9"o_6_oo'o
L'6Ot "O-
L'o-
6_g"0-
gkg"O--
_00"
0
9gtLooo'o
0
0
o_o'o
o
o
0
Q_O'O
o
o
o
_9_ "o
9o_'o
L_Zg'O
_8"o
0
_'CS
o
C-g
98"_-
_9"_-
o'8
_'_
o'L
ggr.o'o
L_(O "0
LL_O'O
/Z'O
_g_'o
_g'O
0
og'o
o
.
0
o_'o
o
Ii
ii
_t
_L
Lg_'oGLGooo"o
0
0
0
0_0"0
0_0"0
_o'o
0
0
O_'L
L_",
_05"0
g_L'O
8Sg'O
o_'o
_'g
_'0
oL'o
C'g
C'g
Lg "8'--
98 "9-
g'g
0
V-I
eL
8"_
o
Y-I
L--
gg°
_g'O
8"L
L6LO'O
8iZO'O
8_'o
_Lo'o
6Lo'o
o
o
CL8"O
X%c_
OL
/,Z
o_'o
8_'g
g_'o-
0_" !.-
gLLO'O
gg_'O
86"o
_6"o
_o'o
_Go'o
o
o
000'0_
t
8
_o_'o
o
_d_Ix
I
v-I
o
9_'o
0
o9-
000 tog
o
GLS"O
0
+
g-h'VO
0"_
8"0
o+_-t
8-h'vO
8-h'VO
(we=It)
_o
_o'_
_'z
8_-g
o
(w,_/_) _o
g-g
g_'_
L_O "o
_t
"o
o
_-_.
ooo'o_
wco
o
on'o
_o" _
o_
(_,=I_)
_
6_'o
oL'o--
g-_
0_O'0
000 '0_
6
gt_L"0
_t
8"o
_@I
_'o
0St "0
o9-
0
0
"_-
og_o "o
_09 "0
_t
0"6
_0"0
gL8"o
gL_ "o
_'C
0
_6"L
(_.q_)._b
_.9_'o- ..(_,=/_)
0
0
o
_o
.(_'=/0_o
_o6ooo'o
o
_9_o'o
9"O-
_'g
9tl" _.9_tO0"O
_6LO'O-
O_L"0
g'_
_o'o
o
OCO'O
o
0
_'C
8"8
oL'o
o
0
ga "o-
o
o
0
o
0
o
_g_'o
9'6"0
_L'O
0
0
og'og'g
OOt "0
_9_o'o
9L6"0
_"
_._-
g+_LtOO'O
0
_9°8
C
_t_O'O
_LL "o
o_o'o-
L'O-
G69LO0"O
pe%oea.zoo,,,
SaAI:%'_AT,IOG.
GG',-" I .(v,=ll)
_)'_b
_'o_-
LQgO0"O
_LL "0
6_'L--
6-
L_ ° [-
_8_oo'o
,zo,;
aA.llg,
oo_
OOL"0--
o_'_
og'oL69
"_'o
o%= T
L'6-
g'_'L • O-
0
C_'L-
o
%u'nooo_
_R_.
6 "9-
Coo"o-
L_8"O
_o'o
8"9--
9_'_--
R_'O-
96_ "o
_-g
0t0"0-
0
8"9-
OOOc_-
_O'L--
GOO'O-
0_90"0
0
9_'L--
o]:_,s'_le
_I)om
O-
t8%'C,-
gL'_
gL'_
LL'9-
0
O
g'6-
o_ t
oAt(t-
O_'t-
0_0"0
o" _-
L--
g_too'o
o
6_"L--
g" _L-
L'o-
o
o
oLa'O-
L'6-
gO"
0
_£_'o
00_'0_
OG6-
oo_t
+_)_"_-
%g" t-
9t "0
8"L-
o
_
_:_
_'i8"C
.(_,_/:)
_o
w_o
t
(_)
%q
(_,_) %0
6Lso'o
(Io
0(_ "0
"IO
o
(_) oz
_/8"o
ooo'o_
Oh
(_,_I_)
_o
w
(_)
q
8-1_vo
9
NOLLI G_OD _OIq_
I
\D
[.._
_H
V_-_I
_}_
_
8SAI&VAI_G
XV_OIB/_HI(INO_
E-IA
T_II(II%_O._Oq
I
_-3
I
TABLE
Oh
VI-C
I
LONGITUDINAL
Note :
Data
are
for
body-fi_ed
stability
axes,
quasi-steady
aeroelastic
corrections
DI)_SIGNAL
D_IVATIVES
FOR
Configurations
GAR-8
h (ft)
40,000
M
Xw
o
-O •01 R6
-0.01 O9
-o.oo589
zw (llsec)
-0.754
-I .05
(11se_)
-0.124
o.118
X_
O
(11sec)
-I19
%e (ftlsee21r_a)
(11sec-ft)
_& (11ft)
M_
Note:
The
transfer
equations
of
(®_)z_
functions
Appendix
given
C with
(_)_
93
Table
additional
E.gc)
are
based
corrections
+ Uo_(z_-z@%)
- KazZ_
: (_--_)Z__
the
above
for
Inertial
(First
(DC_aln)_
-o.oo838
Bending
subscript
%
_,000
_
I-A
0
0
0.70
0.90
0.90
0.873
O.87D
0.875
o.7o
0.ooo_8
0.oi17
0.0e22
0.0e76
0.0178
o.o167
0.00128
o.o14-4
-o.o_o9
-o.oi 82
-o.o919
-I
-1.0_
-0.828
-O.Olge
-2.2_
-I .74
-o.0975
-o.71_
-0.0696
-_e9
-I 81
-78.6
-9.91
-0.0910
-2_6
value
+ quasi-steady
corrections
-0.119
-99.1
-O._'P9
-97.7
-0.00061
-0.0408
-0.C_93
-0.0174
-o._ooa
-o.m 7_
-o.oi 69
-0.00(X)891
-0.000109:
-0.000114
-0.0OO019
-0.0000199
-0.000o176
-0.000o176
-0._88
-0.888
-i ._8
-_ .99
-o.979
-o.969
-o.667
-o.66e
o.ooo_
-O.0109
-o.eo_99
-26.1
-99.8
0.00589
0.000166
-62.1
-91.9
the
corrected
_3
-O.O000_a7
follows:
R _ rigld-body
aeroelastic
-0. _7
-0.0822
-_79
.61
-O.00892
-14. 9
• (first
Fuel
0.8
-o.o9o9
O.O(X)626
II
_1_
0
-I .86
_9
Fuel
0
-o.o_Yo
-o._72
90%
0
-1.10
-o.o138
I-A
O
-0.0362
=_I
IBm
Empty
El
@_
+TT _t_
-0.521
0
and
as
II
-0.0198
0
derlvatives
I0
-o._,91
-26.9
o.o001
+
9
I-A
Dive Brake
-o.o_oI
-o.197
-0.276
coefficient)13
where
(_S_)R
(PC_n)z_
on
msde
30,000
-o.o3oi
-3.16
-63.2
-73. i
O.286
o.c964
-0.00099
O.OOOO757
O.20_
-o.296
-1.08
-I .9_
0
-o.9o8
o.oo_47
-O.0001_I
-e4.e
in
-o.o993
-o.oi87
8
+ Flaps
0
-24.1
-439
-599
-0.001
-14.3
_e (11sec2/r,_)
o.4oI
-0.289
-o.9_o
-O.O00_6e
(llsec-ft)
I
-o.o6o9
-0.0909
.2.22
0.000149
-0.429
(I18eo)
0.(_o09
-0.045Z
-o.c_2?
-0.0000599
GAR-8
COIDITION
?
I
1.40
0.0101
-IT_
-0.00399
6
+Slats
20,000
.879
1.25
-0.00805
(I/eee)
GAR-8
+ Dive
Brake
C_R-8
40,000
O . 875
9
3
CAR-8
F-gA
included.
FLIGW_
2
THE
coefficient)
R
Ka z
:
-- 0.000162
red/ft/sec
2
o.oooe66
-_I .O
o.ooo_7
-17.0
o.ooo_77
-16.7
TABLE
LONGiTUDL-_AL
Note :
Data
for
are
for
Inertial
0ody-fixed
TRANSFER
stability
VI-D
FUNCTIONS
a_es;
FOR
corrections
THE
F-SA
have
been
made
Bending
FLIGHT
CONDITION
I
I
2
5
4
5
6
7
8
9
I0
11
12
!3
14
Oh
I
h
(ft)
40,000
o.875
_z/7o (de_)
Wt.
1.25
1.olo
I 0,0OO
CG
A
0
40,000
M
1.olo
0.22
0.22
0.22
5.65
_sp
0.266
0.121
O. 325
(-0.O721)
O.0856
(-0.05465
0.257
(o.io_)
0.0_7
(I/Tp2)
0.0761
(0.0750)
-80.4
ACe
-14.6
I/_eeI
0.0995
-2_.0
O.0461
o.oo778
I/T%2
0.703
0.885
Aue
0.970
2.26
3 • 3O
-6.15
5e
I/Tuel
0.580
I/Tue2
586
1/Tw e I
aWe
_w e
_ 03
(I/T_e2)
(I/Tve3)
0.0673
0.0809
121
Abe
O.0O309
J_e
0.602
0.286
1.0/0
11.4
0.128
-68.3
0.0457
I. 81
20,000
0.8
1.0/0
1 9,000
0.22
30,000
1.0/0
1 7,000
0.1 4
0.875
0.5/-60
1 4,000
0.12
0
0
0
0
0
0
0 • 875
o.819
0.70
0.70
0.50
0.5o
12,000
0.15
0.15
0._5
O._5
8.05
7._9
4.95
5.5O
5. _6
0.215
0.26_
0.285
0.262
0.243
0.223
0.126
o.o6o_
o.115
0.0852
o.118
o.197
o.157
o.129
0.1o6
0._32
0.I 88
0.I 82
0.197
0.147
O.O555
(-0.053O)
(-0.0964)
0.1o8
0.142
o.155
(0.1165
(o.1285
0.0170
0.0225
0.0159
0.484
O. 379
-9.91
1-47
O.810
-0.O269
-I .95
0.512
0.280
0.478
-294
100
98.6
-610
-474
-24.1
273
-26.9
0.O571
O. 474
-17,450
I. 03
_
-64.0
-67.0
-_.6
I/_3
-18o
168
I _I
(-o.o563)
(o.o622)
180
o.o117
0.0969
0.233
610
0.0432
-8.25
-12.o
-19.6
8.72
12.4
21.7
54.0
a'
0
I/T_' el
(°_el
I/T_'_2
(;'zel
Cpi ot o
-_2.2
-17.3
-17.o
O.0534
0.O516
o. 0202
o.o_8
0.01 6_
0.0;_
I. 58
2.04
1.6o
1.46
O. 991
O. 724
-_._8
-4.06
2.79
2.42
-2.19
-9.74
2.91
4.68
-68.6
2.0/0
17,000
4.81
0.286
-14.6
I .O/0
17,000
o.15
2.82
0.270
14,000
o.17
2.1 4
-5.31
3.78
4..olo
1.0/0
14,0OO
0.05
1.43
-5.16
_.olo
1.0/O
1 4,000
-71.4
-14.1
9.55
-52.6
-I 57
-i 54
210
29. 5
(-0.03585
(0.105)
238
0.0680
0.199
0.159
-26.9
62. I
0.145
0.139
24.1
26.9
-0.0718
-0. 357
-79.5
146
0.04_2
O.161
79.5
0.0108
-186
-515
-438
1 51
0.0501
0.666
93.4
O.O661
145
-246
-244
(-O.00410)
(0.0576)
438
0.0355
lO5
129
o._-_
-0.1 _
o.9_2
-4.210
!
"_!
-_ .4_
0.969
-288
o.5o9
51 3
O.O5O5
o.oo3o9
12.8
0.o476
120
355
-18.8
1 9.6
346
0
o
o.oI_
0.0117
0.o432
0.0499
15.0
0.0559
27.1
0.101
22.7
0.0720
-5.59
3.81
-4.50
4.95
-8.04
8.56
-11.0
1 2.0
1 5.9
95.6
0.116
O.O82O
o.116
o.165
o.1_
0.111
o.I 57
24.6
O.01_D
-15.5
-12._
17.o
13._
26_
-99.7
I_5
244
101
0.025_
-11.9
12.8
124.
0.0110
-9.05
9.75
9_.6
99.7
c.o_ 8o
-7.98
8.67
95.2
55.6
84.8
o
o
o
(o.o538)
o
o
0
0
O
0
0.01o8
(0.984)
0.0555
O.O5O5
0.01 80
0.02_4.
0.O110
o.o18o
9-7o
8.6o
0.0613
o.o_68
-o.o536
4.76
4.25
8.05
0.0871
0.O509
0.0276
1_.5
0.0381
255
96.5
1 3.8
-o.o714
11 9
-14.3
-I 01
lO_
0.0585
I/_'_I
I/The2
NsZ
4.72
O
0 •204
525
-I 21
Awe
N_e
0.22
5.84
)
0
10,OOO
2.29
_p
NI _
0.5/-60
I 0,000
%p
a_p (I/Tpl
_T e
I •40
1.0/0
I 0,000
I 0,000
20,000
0.875
20.6
0.0379
22.5
0.0618
18.1
0.0781
17.2
0.0699
SECTION
VII
F-I04
Preceding
pageblank
75
i
Figure
ch
Vii-
]
F-104
I
FLIGHT
CONDITIONS
I
2
3
Takeoff
Start
Cruise
End
Cruise
h(ft)
Sea Level
M
.273
W(Ib)
24,000
23,510
.046
.040
xcslc
Tlp
External
Tanks
Pylon
Loterol
196
:
s
ft =
C = 9.53ft
REFERENCES
Unpubllsh_Dota
1.9
1.36
14,960
15,000
15,000
.18
.18
Sea Level
.18
Cleon
Clean
On
On
Clean
Clean
Cleon
-3o
-3o
.3 °
0 °
0°
0°
GEOMETRY
b = 21.9ft
30,000
1.0
Clean
dofo not ovoiloble
REFERENCE
l
Note:
30,000
On
15°
Trailing Edge
.84
VMAx
5
VMAX
Sea Level
On
-15 °
Leading E_e
Flaps
30,000
4
.3 °
IS °
PITCH
"
8
r
_ep
F-104
ROLL"
F-104
L _s __.
_'s+l
--
YAW"
I
r
F-104
TS+I
Figure
T_:- 176-1
VIi-2.
F- i<)l_ --
Stability
7>
Augmentation
System
TABLE VII-A
GEOMETRICALAND
Note:
Data
INERTIAL
are for body-fixed
S = 196.1 ft 2
,
PARAMETERS
stability
c = 9.53 ft
axes
,
b = 21.9 ft
FLIGHT
]
FOR THE F-I04
CONDITION
2
START
CRUISE
3
END
CRUISE
Vmax
5
Vmax
SEA LEVEL
Sea Level
30,000
30, O00
30,000
Sea Level
M (-)
0.273
o.84
1.0
1.9
I .36
a (ft/seo)
1117
995
995
995
1117
TAKEOFF
h (St)
(slugs/ft
3)
0.00238
VT° (ft/sec)
3o5
_= _v2/2(ib/ft
2)
w (ib)
m (slugs)
ly (slug-ft
2)
Xo.g./_
]]0.5
o.0oo889
O .000889
0.00238
836
995
1892
1519
31o
44O
159o
2740
15,ooo
15,ooo
24,000
23, 31o
746
724.5
65,000
O .O46
O. 000889
4
14,960
465
466
64,500
56, 65O
56, 65o
O.040
0.18
o.18
0.18
466
56,650
19.6
4.0
2.0
1.4
1.1
7o (_eg)
IO
0
O
o
0
e o (deg)
29.6
4.0
2.0
1.4
1.1
so
(deg)
TR-176-1
76
TABLE
LONGITUDINAL
Note:
Data
are
for
NONDIMLmNSIONAL
body-fixed
VII-B
DERIVATIVES
stability
FLIGHT
I
h
(ft)
0
2
FOR
THE
F-104
axes.
CONDITION
3
4
5
30,000
30,000
30,000
0
M (-)
o.237
0.84
I.0
1.9
I .36
CL
1. 125
o.342
O.1375
o.o383
O. 0278
CD
O. 185
o.o365
O. 04
0.041
0.045
4.44
4-.97
5.10
2.92
4.18
CL(_
eL&
0
0
C_
0
0
O. 6925
CL6e
CD_
CD M
I
0.762
1 .O15
I. 071
0
0.1094
0.0255
0
o.o38
0
0
o.8035
0
O
o.040
O. 042
0.045
0
0
0
CD6e
Cm_
--I.496
-I .319
-I. 564
-i.255
-I .8o
Cmc_
--3•44
-3.90
-4.99
-3 •04
-2.oo5
0
0
0
0
0
Cm M
Cmct
TR-176-I
-5.615
--8.O3
--8.6O
77
--4.59
-6.825
TABLEVII-C
LONGITUDINAL
DIMENSIONAL
DERIVATIVES
FORTHEF-IO4
Note:
Data are for body-fixed stability
axes.
FLIGHT
2
I
TAKEOFF
(ft)
M(-)
Xu
(I/sec)
xw (I/see)
XB e
[(ft/sec2)/rad]
Zu
(I/see)
z_
(-)
Zw
(I/see)
ZBe
[(ft/sec2)/rad]
Sea
Level
CONDITION
3
START
CRUISE
END
CRUISE
30,000
30,000
1.0
4
Vmax
30,000
o. 273
0.84
-0.0352
-0.O106
-0.0224
-0. 0573
o. IO7
O. 0234
O. 0209
0.0136
o
0
-o.214
-o. 0688
0
-o.o513
0
o
o
-0.504
-0.959
--22. I
-85.3
-199
0
O
--0.0005 6
-0.000239
-0.o156
-0.0142
-o. 0228
-0.440
0
1.9
0
-O. 0271
0
-1.05
-464
o
5
Vmax
SEA
LEVEL
Sea
Level
I.36
-0.115
O. 0211
0
--0. 0422
0
--3.21
-927
0
Mu
(I/see-ft)
M_
(11ft)
Mw
(11sec-ft)
Mq
(11sec)
-0. 279
-O.412
-o.598
-0. 607
-I. 94
MBe (I/sec2)
--4.67
-17.8
-30.8
-57.2
--140
_-176-1
78
-o.
o00349
-0.000212
-0. 000375
-0.0348
-O. 107
TABLE
E_ATOR
Note:
Data
are for
LONGITUDINAL
VII-D
TRANSFER
hod ,-fixed stability
FUNCTION
FACTORS
Altitude,
CG
M
(--)
h
(ft)
(_ o)
Weight,
_sp
Along
_sp
_p
(I/Tpl)
N_e
Vmax
O.273
O.84
1.0
1.9
1.36
30,000
30,000
Sea Level
Sea
Level
24,000
30,000
18
4.0
23,310
14,960
SEA
LEVEL
18
18
15,0(0)
I0,000
0.220
o.2o6
O.161
O. 197
0. 126
2.21
3.48
4.83
8.16
o.o932
0. 102
0.277
(0.0o959)
(o.008o8)
O. 140
o.o01
O.O4O2
(o.o4w)
(o.1o7)
-17.8
-30.7
-57. I
13.0
-14o
I/Te I
o.133
0.01_
0. 0237
o .o_78
o.115
I/Te 2
o.269
0.432
o.812
O. 767
2.51
-2.37
I/Tu I
-0.0391
I/Tu2
6.17
-22. I
Aw
I/Tw I
_w (1/Tw2)
a_
( 1/T1_3 )
_.7
-2.00
-4.19
2.26
I .11
-113
-85.7
-85.3
-199
175
1.55
-6.29
-19.6
3.61
24.8
--62.2
-_3.2
-_6_
-927
23_
231
o.o966
O. 102
0.275
(0.00967)
(0.00833)
o.147
0.O914
0.0_07
(0.0476)
(O.107)
21.8
199
89.3
46_
o.o971
IITI_
i
0.0185
0.00816
II_2
5.21
9.03
11.7
13.9
-8.41
-1o.7
-12.9
-_.76
TR-176-1
5
Vm_
TAKEOFF
END
CRUISE
-_.66
Ae
4
START
CRUISE
4.6
W (ib)
CONDITION
3
2
I
No.,
THE F-I04
axes
FLIGHT
Mach
FOR
79
o. o217
927
0.115
29.2
--22.7
SECTION
VIII
F-IOSB
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I
_0
p-I
E-_
PITCH •
8
-_(_
_ep
Se_-
F- 05
i
T
I
K_} = Scheduled
of impact
function
pressure
qc
Kp = Scheduled
function
of impact pressure
qc
ROLL'
F-105
YAW'
P
/
_rp
ay
8r
F-105
....
4,
Ks
1.15s+l
K_,, Kpr = Fixed gains
Ka = Scheduled function
of impact pressure
Pigmre
T_- 17(;- 1
VIII-2.
qc
F-I05-
gtabilit:F
83
Aug_nent_tion
System
TABLE
GEOMETRICAL
Note:
AND
INERTIAL
Inertia
data
are
for
S = 385
ft 2,
b = 34.9
VIII-A
PARAMETERS
principal
ft,
C
=
2
TAKEOFF
h (ft)
Sea
Level
M (-)
o.261
a
1117
(ft/sec)
o (slugs/ft3)
VTo
(ft/sec)
0v2/2(lb/ft
2)
w (ib)
O. 00237
35, O00
F-105B
11.D
ft
CONDITION
4
3
END
CRUISE
C LEAN
35,0OO
5
POWER
APPROACH
CLEAN
CLEAN
Sea
40,000
Level
Vmax
0.9
0.9
O.241
2.1
973.3
973.3
1117
968.5
0.00237
o. ooo587
O. 00o738
o .000738
291
875
875
269
2030
IO0
283
283
86
1210
30,000
35,37O
1098
932
1098
Io, 300
1 2_ 600
I0_ 300
41,230
m (slugs)
START
CRUISE
THE
axes.
FLIGHT
I
FOR
41 _23o
128o
128o
8 _700
8 _700
35,37o
Ix
(slug-ft
2)
ly
(slug-ft
2)
140,000
140,000
14o, 00o
140 _000
140,000
I z (slug-ft
2)
185,000
185,000
181 ,ooo
177,000
181 _000
Ixz
(slug-ft
Xc.g./_
2)
0
0
o
0
0
O. 295
O. 295
o. 3o8
o. 3o8
o, 308
7.4
7.2
7.0
5.2
3.5
(deg)
10.0
0
0
eo (deg)
17.4
7.2
7.0
7o
TR-176-I
84
-5.0
0.2
0
3.5
TABLEVIII-B
DI_[F_ _,LJlJAL DERIVATIVES
j
LONGITUDINAl,
Note:
Data
are
for
_-
body-fixed
stability
1
TAKEOFF
(ft)
M
(-)
Se&
Level
0.261
Xu
(I/sec)
-0.029
Xw
(1/sec)
0.0793
XSe
Zu
[ (ft/sec2)/rad]!
(]/see)
-0.1585!
Zw
Z8 e
Mu
(I/sec)
[ (ft/sec2)/rad]
(I/sec-ft)
o
35,000
35,000
Sea
0.9
-0.00565
O. 00693
o.o264
-0.01386
0
-o.0263
o.o86
0
-0.05 27
Level
o.241
0.9
-0. oo582
o
-0.1719
5
40,000
2.1
-0.00751
0.0132
0
-0.0265
o
0
o
--0.311
-0.4
-O .466
-0.406
--17.3
-65 •19
-75.97
-I 9.88
L] 35.9
-0. 0000101
-0. oooo 198
-0. 0000119
0
Mw
( 1/sec-ft)
-0.00575
Mq
(1/see)
TR-176-I
4
3
START
CRUISE
-_0.000259 -0.000117
(I/sec 2)
CONDITION
POWER
APPROACH
CLEAN
Mg- (I/ft)
M6e
F-IOSB
END
CRUISE
CLEAN
0
0
(-)
2
ThE
axes.
FLIGHT
h
FOR
,-
-0.
345
--2.60
--o.oo819
-o .485
-12.o3
85
O
-0. 00011 7 -O. 000259
-O. OO4 68
-o .485
--12.03
-0.
003£4
-0.59o
-0.0oooo5
-0. O1 25 2
-0.319
-0.303
-2.7o3
-21.0
35
TABLEVIII-C
LATERALDIMENSIONAL
DERIVATIVES
FORTHEF-IO5B
Note:
Data are for body-fixed stability
axes, lateral
avaiJ able for flight conditions I and 2.
FLIGHT
CONDITION
4
3
END
CRUISE
CLEAN
POWER
APPROACH
35,000
Sea
CLEAN
I/sec)
[(_/seo)/r_d]
Y_r [(I/sec)/r&d]
I/sec 2 )
I/see)
L_ (I/see)
2)
L_ (I/see
L_
-0.00173
0.0234
--_1.1
-2.8
I .709
40,000
2.1
-0.1878
-0.213
-0.0021
O. 0241
-21
.5
-i. 185
i .251
-0.
00221
O. 0837
-I 39.8
-3.14
i .966
IO.71
3.72
26.5
(I/sec 2)
14.37
2.86
12.97
I/see 2 )
12.39
4.38
18.81
I/see)
_ (I/see)
N ' (I/see
2)
6a
(I/seo
2)
_r
TR-176-I
-0. 1497
Level
o.241
0.9
Yv(
0.324
O. 0729
O. 1341
-0.382
--0.242
--0.386
-i. 08 6
-0.277
-I. 339
-4.71
-0.975
-I .989
86
data not
TABLEVIII-D
ELEVATOR
LONGITUDINAL
TRANSFER
FUNCTION
FACTORS
FORTHEF-IOSB
Note:
Data are for body-fixed stability
axes.
FLIGHT
I
TAKEOFF
Mach No., M (--)
Altitude
CG
(¢
Weight,
START
CRUISE
4
3
END
CRUISE
CLEAN
POWER
APPROACH
CLEAN
0.241
5
Vmax
CLEAN
2.1
o.9
o.9
35,000
35,000
29.5
29.5
3o.8
30.2
3o.8
41,230
41,230
35,37o
30,000
35,370
_sp
o.281
o.1819
0.253
0.398
0.0893
_sp
1.338
2.71
2.o8
0.998
5.o6
{p
0.0297
0.1295
o.o631
O.1016
o.1869
0.1247
0.0223
0.0429
O. 1342
0.0201
--2.60
-I 2.03
--I2.02
-2.70
--21.0
0.1026
O.OO6]
0.00891
0,200
O.355
o.433
-o.452
--2.002
h (ft
_)
W
0.261
2
CONDITION
(ib)
Sea
Level
Sea
Level
40,000
Along
A9
1/Te 1
1/Te 2
-1.367
N_e
0.0742
0.335
--1.708
1/Tu1
1 .o18
0.438
1.511
1.266
1/T, 2
-17.0
-696
-55.8
--15.02
-65.2
-76.0
-19.88
-17.27
0.00827
0.508
--1.792
2.94
-65.2
-135.9
44.2
162
-139
36.9
o. 0372
0. 129
0.0642
o.1258
o.1838
O. 1287
0.0225
0.044
o.1435
0.0204
17.28
65.2
76.0
19.88
135.9
I/Th I
O. 01292
O. 004 66
O. 00439
0.01094
0.00737
I/Th 2
-3.37
-7.29
-7.48
--3.49
I/Th 3
3.80
7.88
8.07
3.89
1/Tw 1
315
_e
TR-176-I
87
-12.49
12.8
TABLEVIII-F
AILERONLATERAL
TRANSFER
FUNCTION
FACTORS
FORTHEF-IOSB
Note:
Data are for body-fixed stability
axes; lateral
data not available for flight conditions I and 2.
FLIGHT
C OND ITION
4
3
END
CRUISE
CLEAN
MachNo., M (--)
Altitude,
ca
_o
h (ft)
W
0.241
o.9
Sea
35,000
(_ _)
Weight,
POWER
APPROACH
CLEAN
30.8
(ib)
35,370
7.0
(deg)
l/ms
-0.00870
Level
5
Vmax
CLEAN
2.1
40,000
3o.2
3o.8
30,000
35,370
5.2
3.5
o.ooo676
0.00631
I/T R
2.13
1.382
2.95
_a
0.184
O. 0545
o. 1531
_d
3.29
2.13
4.16
Ap
10.71
3.72
26.5
Alat
0
l/Tpl
O.OLO3
0
N_a
_p
r
o. 0635
0.101
0.0744
2.87
1. 674
3.44
--1.339
Ar
-i.o86
-0. 277
1/Trl
--I.524
-1.503
-I .3
N5 a
(r
o.465
0.564
o.6o0
_r
I .398
1.718
1.686
-0.00174
--622
1/T#1
--0. 00210
-0.00221
O. 1427
0.1379
_a
1/T#2
([_)
I/T_
3 (_)
TR-176-I
(-o.0573)
(0.276)
i.655
-133.7
88
0.658
6oi
TABLE
RUDDER
lATERAL
Note:
Data
data
TRANSFER
are
not
VIII-F
FUNCTION
for body-fixed
available
for
FACTORS
No.,
Altitude_
M
(--)
4
POWER
APPROACH
h
(ft)
o.9
30.8
Weight,
_o
(lb)
W
5
Vmax
CLEAN
0.241
2.1
Level
30.2
30,000
35,370
lateral
1 and
CLEAN
Sea
35,000
F-IOSB
CONDITION
3
END
CRUISE
CLEAN
THE
stability
axes;
flight
conditions
FLIGHT
Mach
FOR
40,000
30.8
35,370
7.0
5.2
3.5
I/Ts
--O.OO87O
0.000676
o.oo631
I/T R
2.13
1.382
2.45
_d
0.184
0.0545
o.1531
_d
3.29
2.13
4.16
%
14.37
2.86
12.97
O.01 O3
0
(deg)
Alat
P
Nf_)
r
1/%1
0
1/%2
-I. 109
-I. 82
-I .499
1/%3
I .014
I. 63
I.738
-0.975
-1.989
Ar
1/Trl
--4.71
1.848
I.4 63
2.31
_r
_r
4r
TR-176-1
1/T_1
0.1028
-0.246
0.1601
0.259
O. 838
0.342
0.0233
0.0241
0.00538
-0.0395
0.00369
1.371
2.36
-0.0103
1/% 2
1.927
1/% 3
203
140.6
89
37O
2.
""4
?RECED_F_G
PAG!
SECTION
B-58
Precedingpageblank
91
IX
NQI"
_L_AED
Figure
IX- ]
B-58
I
I
NOMINAL
CRUISE
FLIGHT
CONFIGURATION
CONDITIONS
See Table 1T-A
50,000
X
40,000
h(ft)
X
30,000
20,000
I0,000
<D
REFERENCE
0
GEOMETRY
_"
0
,4
.8
M 1.2
1.6
2.0
S = 1542 ft =
b • 56.8 ft
c • 36.2
ft
REFERENCES
I) Bright, B.E., EIIIngton,J.D.,"Applicotlon
Selfodoptlve
Stobillty
Concept
Augmentation
to the B-58
Thesis, Air Force Institute
of Technology, GGC/E E/64-5,
System", Gen. Dyn. Fort Worth,
3) Jones, L.S. ,"U.S. Bombers BI-B70"
Unknown
Directional
System'.'
2) Anon. ,NB-58 Flight Control
SOURCE
of the Limit-Cycle
Lateral
May 1964
FZE-
Aero Publishing Inc., 1962
4-049,
Nov. 1962
ROLL
PITCH
I
8
I
B-58
)
YAW
L_
/
ay
NOTE :
K s , K4,
K5,
KT,
Ke...Gains
Scheduled
for Moch- Number
K 2 , K 3 , K 6 , K 9 , Kjo...Goins Scheduled
for Altitude
(Air
doto computer
r
___L
not shown)
The Augmentotion
System
is of 1962
os documented
vintoge
for
this oirplone
Figure
is known to hove undergone
in GD. Convair
Report
IX-2.
--
B-58
FZE
4-052,
Stability
severol
modificotions.
The
Dec. 196=?, being the Iotest
Augmentation
System
system
shown
ovoiloble
doto
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{{'0
0{'0
0
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O00_06L
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S_L
oh
g9LL
gggO00 "0
6L6
699000"0
L99
9{6L
9L?ooo'o
494000"0
kk{¢oo'o
LL{eoo'o
996
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LLLL
LLLL
LLLL
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0"¢
t6"O
t6"O
t6"O
¢{'0
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000'0{
00_'_
000'0_
o
o
o
{
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L
L
9
6
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MOI$1QZO0
(_/S_T_)
LL{¢oo'o
o
(o_s/%#)
(-)
(_)
q
SHO!ff£
%J LL'9{
= o :%j sg"9g = ct :e%j S?g'L
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96-_ Z}KZ HO£ _ZmZIgV_V£
V-XI Z_I_V_
_IVOIKZZNOZ©
TABLE
LATERAL
Not e :
NONDIMENSIONAL
Data are for body-fixed
IX-B
STABILITY
stability
DERIVATIVES
axes_
cruise
FOR THE B-58
configuration.
I
.-a
FLIGHT
CONDITION
o_
I
I
2
3
h (ft)
0
0
0
40_ 000
M (-)
o.32
o.91
o.91
0.91
2.o
0.98
i.2
357.3
1016
1016
880.9
1936.2
975
1161.7
-0.7665
-0. 6275
-0.732
VTo (ft/sec)
Cy_
-0. 6395
-0. 6375
-0. 674
4
5
44,200
6
30,000
7
40,000
-0.801
CYSa
O. 1511
0.08655
0.0890
O. 1790
0.0187
O. 1862
O. 1791
Cyst
O. 0929
O. 0527
O. 05725
0. 0954
O. 0232
O. 68075
0. 0545
kO
k_
C_
-0. 1584
-O.0551
-0.0851
-0. 1345
-0.03942
-0. 1096
-0.1158
C_p
-0. 1936
-0. 1585
-0. 1576
-0.2173
-0.2317
-0.2107
-0.2238
C_r
C_$ a
0.04479
-0.1112
0.08568
0.08553
O. 1102
0.07207
-0.04043
-0.03892
-0. 1041
-0.01782
0.09543
-0.0729
O. 1071
-0.0010
C_6 r
0.001927
0.00729
0.007395
0.01227
0.003115
0.01328
0.0078
CuB
O. 1014
O. 1242
0.0624
O. 1029
0.03207
0.0788
O. 1117
Cnp
-0. 1143
-0.01082
-0.02935
-0.06118
0.01241
-0.03713
-0.04215
Cnr
-0.2494
-0.2449
-0.2312
-0.2868
-0.2132
-0.2611
-0.2823
Cn6 a
-0. 0405
-0. 03318
-0. 03317
-0. 0664
-0. 02038
-0. 0725
-0. 09275
Cn6 r
-0. 06415
-0. 03561
-0. O35 63
--0.O633
-0.01382
-0. 053O
-0. 03255
TABLE
LATERAL
Note:
I
Data
for
body-fixed
DIMENSIONAL
stability
-4
O_
I
IX-C
DERIVATIVES
axes,
cruise
FLIGHT
H (-)
0.32
--0.09
_e
YSa
Y
*
_r
!
Lr
0
40,000
0.91
0.91
o.91
6
44,200
3O,OOO
2.o
-o.o962
o.98
-0.105
7
40,000
1.2
-0.09
o.o153
o.oo287
O. 0267
0.0201
0.0131
0.0382
o.o229
0.00814
o.oo356
o.o116
0.00613
-5.828
-16.875
-23.14
--7.575
-8.394
-i i. 163
-0.736
-0.63
-0.469
-I. 424
-i. 238
-0.381
0.221
0.724
o. 6o3
0.212
--3.516
0.395
I1858
I_
-o.o654
5
o. o356
-13.19
-11.194
!
LSr
configuration.
o. 0578
!
L5 a
--0.27
B-58
0.0212
LO
O_
L_
0
-0.426
THE
CONDITION
4
(ft)
FOR
2.108
13.71
--5.597
o.214
-3.965
o. 278
-7.538
-11.08
-0.524
O. 251
-0.953
0.748
1.71
0.789
0.608
1.313
3.818
1.946
1.895
2.317
3.202
-O.OO473
-O.0388
--O.0293
-0.02
N_
--0.0141
-0.0631
--0.I05
N_
-0.222
-0.76
-0.459
-o.159
-0.198
--0.231
-0.198
-4.021
-2.865
-0.909
-1.413
--2.29
-2.654
--3.986
-2.589
-1.o69
-0.884
-1.614
-0.932
N{a
0.157
f
NSr
-0.669
_
TABLE IX-D
AILERON
Note:
IATERAL
TRANSFER FUNCTION FACTORS
Data are for body-fixed
FOR THE B-58
stability axes, cruise
configuration
FLI(_IT CONDITION
h (ft)
M (-)
Np
5a
2
3
4
9
6
7
0
o
0
40,00O
44,200
30,000
40,000
0.32
0.91
O.91
0.91
2.0
0.98
1.2
I/Ts
0.o58
0.00426
0.0334
0.026
0.0134
0.029
0.017
I/TR
0.698
1.927
1.75
0.556
0.802
0.889
0.687
_a
0.009
o.144
0.044
0.0O86
0.0772
o.oi65
0.0296
_d
i.403
3.796
2.126
I .42
I.40
I-98
I.81
Ap
-3.516
--11.194
-9.597
-3.965
-7.938
-o.953
0
0
-13.19
0
I/Tp
1
_p
Ar
r
i
1/T R
0
0.132
0.192
O.0784
0.085
0.096
0. I04
1.274
3.151
I •786
2.217
2.398
5.89
0.197
-1.148
-4.021
-2.865
1.881
1.498
--0.213
--0.249
--0.909
1.002
-I.413
-2.29
0.983
1.082
--0.174
-O.331
-2. 654
0.934
N5 a
(r
0.678
-0.420
-0.295
1.677
1.o21
0.897
0.845
o.481
0.797
0.602
0.0212
0.0978
0.0356
o.o193
0.00287
0.0267
O. 0202
-O.018_
-0.073
I/T81 (_8)
0.1624
-0.0838
-O.0941
I/T#2 (_B)
2.1616
1.198
0.798
-O.191
--O.0171
_a
I/T#3
-9.008
0.226
0.695
0.467
70.64
81.472
60.03
493.37
7.994
98.73
36.17
13.46
9.99
26.063
23.42
1/Tay 1 (_ay2)
0.12
-0.210
-0.183
0.15
-0.02
-O.161
-0.036
i/T_2 (_2)
I.OO9
o.948
0.993
0.69
O.35
I .839
CG
_ay3 ( I/TaY3)
a_y 3 ( I/Tay 4 )
TR-176-1
--0.127
1.733
(-3.3)
(4.7_)
(-3._)
(4.896)
97
-o.892
(-6.618)
0.89
(6.883)
86.19
0.920
(-2.255)
(2.927)
131.87
0.458
(-2.8)
(3.097)
TABLE IX-E
RUDDER lATERAL TRANSFER FUNCTION FACTORS FOR _{E B-58
Note:
Data for body-fixed stability axes, cruise configuration
FLIGHT CONDITION
h (ft)
3
4
5
6
7
0
0
0
40,000
44,200
30,000
40,000
O.91
O.91
O.91
_.o
o.98
1.2
I/Ts
0.058
0.00426
0.0334
0.026
o.o134
0.09
o.o17
I/TR
0.698
1.527
1.79
0.556
0.8O2
0.885
0.687
_d
0.009
o.144
0.044
0.0086
O.0772
O.0165
o.o_96
I.hO3
3.796
2.126
I .42
1.40
1.58
1.81
0.399
2.108
I .711
O. 789
0.608
I.313
o.748
I/TPl
0
0
0
0
O
0
0
I/Tp2
--2.969
--4.554
I/Tp3
2.713
4.065
9.365
-O. 669
-3.986
0.964
_r
-3.247
-3.433
-3.319
2.818
3.181
3.329
3.204
-2.589
-I •069
-0.884
I.607
I .615
0.786
-0.326
0.167
-0.O561
-0.317
_r
0.665
0.436
0.636
0.534
%
O.0131
O.0382
0.0229
O.00814
Ar
r
2
0.32
M (-)
A
I
I/Tr
-5.859
--2.959
N5 r
I/T01
-0.0149
-0.00689
-0.00709
I/T_2
0.946
I.482
I .337
-0.008
N_ r
I/T_3'
Aay
I/Ts.j1 (_aY2)
51.355
150.05
113.43
4.669
38.813
23.266
-0.0966
-0.O122
-O.O167
0.431
131.44
-1.614
-0.932
I.o
0.88
-0.2_26
-o.255
0.362
0.553
o.518
0.00355
0.O116
0.00613
-0 .o0171
-0.0043
-0 .O0445
0.693
o.574
o.9oi
-0.1o
0.793
248.84
7.173
6.886
-0.0229
-0.0032
139-37
152.06
11.303
7.126
-0.0135
-0.0131
........................
I/Troy2 (a_y2)
CG
_ay3 (I/TaY3)
°_y 3 (1/T&y 4)
TR-176-1
0.446
1.46
(--1.486) (-9.179)
(I.828)
(5-915)
1.243
(-4.926)
(5-398)
98
0.394
(--2.492)
(2.662)
0.748
(-4.597)
(4.788)
0.649
0.537
(--3.394) (--3.14)
(3.62)
(3.338)
flFDTION X
NAVION
99
Figure
X-I
NAVION
I
NOMINAL
FLIGHT
CONDITION
oh
I
h(ft)
= 0
; M = .158
W = 2750
; VTo = 176 ft/sec
Ibs
CG at 29.5 % MAC
Tx = 1048 slug ft 2
Ty = 3000
slug ft 2
Tz = 3530
slug ft z
Ixz = 0
REFERENCE
0
S
= 184 ft z
c
= 5.7 ft
b
= 33.4
ft
GEOMETRY
TABLE
X-A
GEOMETRICAL
FOR
Note:
S
PARAMETERS
THE
Data
stability
TABLE
NAVION
for
axes,
X-B
TABLE
LQN,GIT_INAL
DERIVATIVES
NONDIMEN_IONAL
FOR THE NAVION
Note:
are
lATERAL
NONDIMENSIONAL
DERIVATIVES
FOR THE
level
flight
Data
stability
_8o
(ft 2)
for
Data
axes
33.4
c (ft)
w (ib)
2,750
(ft)
85.4
M
(--)
29.5
2)
I,o48
(-_lug-_ 2)
3,000
(slugs)
e.g. (_ MAC)
Tz (sl_-_
2)
_z
h
3,930
0
stability
I
h
(ft)
0
0.198
M (-)
o. 158
CL
0.41
VTo
176
CD
O. 05
c_o
CL=
4.44
Cy6
(ft/sec)
(deg)
-0.564
CL&
0
CYSa
CLM
0
CYSr
CLSe
0._5
C_
-o .o74
CDc_
0.330
C_p
-0.410
CDM
O
C_r
O. 1o7
CDSe
O
C$5 a
O. 1342
C_5 r
O. 0118
Cn_
o.o7oI
Cr_
-o.o575
Cnr
-0.125
Cn5 a
-0.00346
Cn5 r
-0.0717
0
0
O. 197
0
(ft)
M
a
1
h
for
FLIGHT
CONDITION
CONDITION
5.7
are
axes
FLIGHT
( sl_-_
STABILITY
NAVION
body-fixed
b (ft)
m
X-C
O. 158
(ft/see)
P (slugs/ft
1117
3)
0.002378
VTo (ft/see)
176
-4=VTo2/2
(
36.8
ib/ft 2)
cLo
(deg)
0.6
7o
(deg)
0
TR-176-1
- .36
M
o
-9.96
Cmq
i01
TABLE
TABLE
X-D
LATERAL
LONGITUDINAL
DIMENSIONAL
DERIVATIVES
FOR TI-IEN&VION
FLT.
Xw
FLT.
O.03607
-0.O45]
XSe
0
Zw
--2.0244
Zu
-0.3 697
Zse
DIMENSIONAL
DERIVATIVES
FOR THE NAVION
COND.
Xu
YSa
y*
5r
r,f;.
--8.402
2.193
-28.17
--<).
04997
Lsi
M_
--O.005 ]65
L_ r
Mq
--2.0767
MSe
COND.
-0. 2543
Yv
Mw
M_
X-E
28.984
2.548
4. 495
0
-O. 3498
--II. 1892
g
-0.7605
N
-O.2218
'
5a
-4.597
TR-176-1
102
TAB I _E' X-[ _'
TAB[,E
E ] _VA TO I_ 1,0 t'qt_I TUD IN A ]iJ
AILERON
j [ NC2ION
r
TRANSI,'I,:]_
]_
U1ACTORS ]!'OR ']'H_J NAVION
FLT.
o. dgP'{
"'sp
3. (;083
A
RUDDER
FLT.
1/%
o.oo87(;
I/TR
8. h3b
1/T S
o. 008'( 6
1/T R
8.435
A
0.204
_d
o. 204
._
O.2137
._
2.385
md
Ap
28.984
%
O.0'.)231
1/T_b
1.9164
Au
2.385
2.548
0
11Tpl
N_a
--1.0161
COND.
VLT.
O. 0801
I/THI
FACTORS
NAVION
COND.
<p
--II .0114
X-H
libTEI{AI, T]{ANS],']:]I
{
FUNCTION
L;'ORTHE
A
Ao
N 0
LAI_'h",[lA.l_,'_{ANSFER
FUNCTION
FACTORS
FOB TLI]!]
NAVION
(]ON]).
< sp
TAB],E
X-G
1/Tpl
N_.P,r
0
_p
o. P33 6
c%o
2.136
-6.991
1/Tp2
3. 6064
IITp 3
u
Nb e
I/Tul
2.401
I/Tu2
Aw
_.
F
r
N_)a
]/Tr 1
--1. 253
(1.98h
I/mr 3
_e
O. 086u
_%
o. 25 63
Ah
fl
1/Thl
28. 171
--I0.
I08
8. 639
<r
0.1335
N_',r
O. 5345
N w
rw
I/T r
1.543
I/Tr2
1/%
2218
-280.39
--;'8. 171
-4. 997
A r
Ar
54.071
0.0707
Af{
N_Ba
A_
0.2218
1/T_ 1
0.2285
I/T_2
77.78
1/Tpl
-0.0366
I/%_
8.795
1/T[_ 3
65.352
A_
12.489
N_ e
1/Th2
I/Th3
Aaz
O. 01 65
13. 122
1/Tay
1
-o.o591
--28.171
1/Tay
2
8.335
a Z
NB e
I/Tazl
0
I/Taz2
--10.108
#x:0
I/Taz3
0.0165
CG
i/Taz4
13.122
TR-176-1
CG
1/% 3
I/Tay 4
103
--3.0074
3.894
p_EcED_NGPAGE BLANK
8F_TION
DC-8
Precedingpageblank
_o5
XI
NOT
FILMED,
P-3
I
Figure
XI-]
I
DC-8
FLIGRT
Flight
CONDITIONS
Approach
Condition
h(ft)
0.219
W(Ibs)
[x (slug-ft
Iy (slug-ft
Iz
190,000
2)
3.09
z)
2.94x10
5.58
=)
3:5,000
0.88
250,000
250,000
3.11xlO
3.77x
3.77x
e
IO s
10 6
2.94x106
3.56x106
3.56x10
s
x I0 s
5.88x106
7.13 x IO s
7.13
x 106
53.7
x I03
z
-64.5x10
0.15
s
45x105
0.15
Axes
Stability
0.15
GEOMETRY
S = 2600
ft 2
b = 142.3
ft
REFERENCES
0.84
190,000
0.15
REFERENCE
:55,000
0.443
s
28x10
Xce IE
c = 23
x I0 s
15,000
VNE
t
(slug "ftz)
Ixz (slug-ft
Cruise
Holdh_g
ft
: Unpublished
Dota
/9
TABLE
GEOMETRICAL
Note :
Data
are
S = 2600
for
ft 2
AND
INERTIAL
body-fixed
,
b =
142.3
XI-A
PARAMETERS
stability
ft
,
c = 23
,j
•
M (-)
a
o (s1_gs/ft
3)
VTo (ft/seo)
=
oV2/2
(ib/ft 2)
w (Zb)
Yo = 0 deg
CONDITION
3
0
15,000
33,000
0.218
0.443
0.84
1o58
o. 002378
0.001496
468.2
243.5
71.02
163.97
190,000
m (slugs)
,
CRUISE
1117
(ft/sec)
ft
DC-8
HOLD ING
APPROACH
h (ft)
THE
axes
FLIGHT
]
FOR
190,000
59oo
5900
982
0.000795
4
VNE
33,000
0.88
982
o. 000795
824.2
863.46
270.0
296.36
230,000
7t43
230,000
7143
Ix
(slug-ft
2)
3,090,000
3,110,000
3,770,000
3,770,000
ly
(slug-ft
2)
2,940,000
2,91,0,000
3,560,000
3,560,000
I z (slug-ft
2)
5,580,000
5,880,000
7,130,000
%,130,000
Ixz
(slug-ft
XCG/C
2)
28,000
-64,5 O0
o.15
o.15
o
o
45,000
o.15
o
53,700
0.15
@O
(deg)
Uo
(ft/sec)
243.5
468.2
Wo
(ft/sec)
0
0
0
0
35
0
0
0
_F
(deg)
TR-176-I
107
824.2
0
863.46
TABLEXI-B
LONGITUDINAL
NONDIMENSIONAL
DERIVATIVES
FORTHEDC-8
Note:
Data are for body-fixed stability
FLIGHT
axes.
CONDITION
4
2
h
0
15,000
33_ 000
33,000
M
0.21$
0.443
0.840
0.S8
CL
0.98
0.42
0.308
0.279
CD
O. 1095
0.0224
0.0188
0.0276
c:4 _
4.81
4.8762
6.7442
6.8989
0
0
0
0.02
0.048
0
CL_ e
O. 328
0.328
o. 352
o. 358
0.487
0.212
0.2719
0.4862
CD_
CD M
O. 0202
0.00208
o. lOO5
o. 3(;'.) 3
CLg
CLM
0
0
CD6e
-0.97]
-1.2
0
2
Cm_
--1.478
-1.5013
-2 .ol 7
-2.413
Cm_
-3.84
--4.10
--6.62
-6.83
-o. 006
-0.02
-0.17
-0.50
Cm m
Cmq
-o.ool
17
--o .97t
2
-14.6
-_5.2
TABLE
LATERAL
Note:
NONDIMENSIONAL
Data
are
for
XI-C
STABILITY
body-fixed
FLIGHT
h (ft)
0
1D,O00
DERIVATIVES
stability
FOR
THE
DC-8
axes
CONDITION
33,000
33,000
M (-)
o.218
0.443
0.84
0.88
VTo
243.5
468.2
824.2
863.46
(ft/sec)
-0.87268
-O.
6532
0
-O.7277
-0.7449
O
CY_ a
CY_r
0.18651
C_p
-O.15815
C_p
--O.385
C_r
0.248
C_6 a
-0.08595
C_$ r
0.02189
cR_
o. 1633
Cnp
-0.0873
Cnr
-O.196
Cn6 a
-O.O106
Cn_ r
-0.08337
TR-176-1
o.18651
o.18651
O. 18651
-0.137D2
-0.16732
-0.17362
-o.4]6
-O.516
-o .538
0.132
0.147
-0.o83o8
-0.07965
0.146
-0 .o79o7
o.o]9195
0.021086
0.02166
0.12319
O. 15471
O. 16044
-0.0307
-0.0107
-0.00587
-0.161
-0.190
-0.199
-0.00354
-0.003701
-0.003999
-0.08337
-0.O8337
-O.O8337
109
TABLE
LONGITUDINAL
Note:
Data
are
XI-D
DIMENSIONAL
for body-fixed
DERIVATIVES
stability
M (-)
% (i/seo)
xw (I/sec)
33,000
33,000
0.218
o.443
o.84
o .88
O. 000D99
o. 000733
-0. 000595
-o.
-0.o2891
-o. oo7o7
-o.o145
-0.0471
-o.o291
-o. oo714
-o. Ol Ii
-0.04
o.o629
000084(5
0.0321
0
-0.1
Zu
-0. ,_)06
-o.1329
0
(-)
Z6 e
[(ft/sec2)/rad]
0.0043
0
-o. 25 o6
( I/sec)
CONDITION
19,000
ZU ....(]/sec)
Zw
DC-$
0
x6e [(ft/sec2)/rad]
(I/sec)
THE
axes
FLIGHT
h (ft)
FOR
329
o
-0.75g
-lO.19
0
0 0622
-0.073[3
0
-o
.806
0622
0
0
-o .845
-38.6
-34.6
-23.'7
oP59
-0.0735
0
-0.6277
-o.
63
-o.
000063
-0.
000786
-o.
oo254
-0.0000077
-0.
o00003
-o.
ooo 78 6
-0.
00254
M@ (I/ft)
-0.
-o.
00072
-o .o0o51
-0.
00052
£w (I/sec-ft)
-o. 0o8 7
-o.
o107
-0.0111
---0.01
14q(I/see)
-0.7924
-o.
991
-0.924
-I. 008
Iv]u
....
(I/sec-ft)
-o.
%
(i/_oo-ft)
0000077
O01 u(_
-3.24
M8e (I/see2)
TT- 1 7.'-1
{'1
1 10
-4.59
39
TABLE
IATEI_&L
Note:
Data
are
for
DIMK_SIONAL
XI-E
DERIVATIVES
body-fixed
stability
FOR
h (ft)
M (-)
Yv (I/see)
DC-8
axes
FLIGHT
1
THE
2
•
0
15,000
0.218
0.443
-0.1113
-0.1008
CONDITION
3
33,000
33,000
0.84
0.88
-0.0868
-0.
o931
YS_
[(11sec)Irad]
0
0
0
o
YS_
[(11sec)Irad]
o. 0238
o. 0288
0.0222
0.0233
L_
(1/see
2)
½ (l/sec)
L_
-i. 328
-2.71
-4.41
-5.02
-o. 951
-I. 232
-i. 181
-I. 29
O. 397
O. 334
O. 609
(I/see)
L5 A (I/sec 2)
-0.
726
-1.62
-2.11
0.346
-2.3
0.1813
o. 392
0.549
o.612
0.757
I .301
2.14
2.43
-0. 124
-0. o346
-0.0204
-0.01715
-o. 26>
-0.257
-0.228
--o.25
N_ (i/_ee _)
-o.
-0.01875
-0.065 2
-0.0788
N_ (1/_ec2)
-0. 389
-o.864
-0.o1164
-1.
L6#
N#
(I/sec 2)
(1/see
2)
N5 (l/_eo)
N_
(I/sec)
O
TR-176-I
0532
111
277
TABLE
Note :
ELEVATOR
LONGITUDINAL
Data
for
are
TRANSFER
body-fixed
XI-F
FUNCTION
stability
FACTORS
_}IE DC-8
FOR
axes
FLIGHT
CONDITION
4
2
Mach No.,
M (-)
Altitude,
h
0.218
0.443
0
(ft)
15,O00
15
Weight
W
(ib)
190, OO0
_sp
0.522
O .434
msp
1.619
2.40
0.O606
o.o31o
O.1635
O. 0877
A0
--l. 358
-3.22
I/TOl
o. o6o5
0.01 354
l/T82
o.535
O. 075
(I/Tpl)
%
N8
_e
(I/Tp2)
--0.641
A m
u
l/Tu l
0.88
33,000
33,000
15
15
230,000
2.50,000
15
190,000
ZSlong
0.8h
o. 342
0.325
3.59
o. 241
O. 0243
(--0.0708)
(o.zo8)
-4 .>7
-5.
I
O. 01436
O. 0493
O. 7,9',;
o. 76
--O.1489
I . O0
I .08
I.279
o.816
o .449
-35.3
-72.7
-#{79
279
-,'3.7
-34.
G5. o
110.2
O. 13{3,
N8 e
1/Tu2
-/o.19
A W
33.0
I/Tw 1
G
-38.6
-o.
o361,
w
(I/%2)
o.o781
o .o37
ov (I/%3)
o.1798
o. 0947
N5 e
O.ODl
l
<
,%
(O.U3_7)
(1 15.5
A_
10.19
25.7
34.
d
38.6
1/T]4_ 1
-3.75
-5.95
-8.24
-8.63
1/m 2
--0. 00182
0.O107
o.o_31
_ .83
1/__ 3
-I0.19
Aaz
1/Taz
-0.
I
I/maz2
1/Taz 3
O
O0002G
7.29
9.P9
-23.7
-3_4.4
0
-3.75
-5.95
-O. O0182
O
i oo .9
o
-8.24
--0. 000026
0.010'7'
o.o531
7.29
9.59
1oo.9
CG
1/maz4
TR-176-1
4.83
112
)
TABLE
XI-G
AILERON
LATERAL
TR_,iSFER FUNCTION
FACTORS
Data are for body-fixed
stability
axes
Note :
FLIGHT
Mach No.,
(-)
Altitude,
h
CG
(_
Weight,
(ft)
_)
W
0.218
0.443
0
I5,000
15
15
FOR
'I_{EDC-8
CONDITION
3
4
o.84
0.88
33,000
33,000
15
15
190,000
190,000
230,000
230,000
1/T s
-0.013
O. 00649
O. 00404
O. 00447
1/T R
1.121
I .329
1 .254
I .356
{a
o. Io96
O. 1061
O. 0793
O. O855
_d
o .996
1.197
1.495
I.589
(ib)
Alat
Ap
1/Tpl
Np
$a
(p
A_
A r
N5 a
0
0
-2.3o
--2.11
0
0
0.223
o. 1554
O. 1072
O. 1094
0.943
I .166
1.515
1.620
-1.52
-0.726
--2.11
-2.3o
O. 223
o. 1554
o. 1072
o. 1o94
0.943
t .166
i .515
1.620
-0.0532
-o.o1875
-o. 065 2
-o. 0788
I.644
I. 757
1.589
(r
-O. 656
-o. 727
_r
I .242
2.23
I.323
I .259
O. 0532
O. 01875
o. 0652
-0. 0788
1/T 1
1/T72
-0.392
-1.036
-2.75
0.203
0.291
1/TB3
TR-175-I
.62
O. 998
1/Trl
r
-1
-0.725
113
-O. 345
-0. 704
0.404
TABLE
RUDDER
Note
:
Data
are
LATERAL
for
TRANSFER
body-fixed
XI-H
FUNCTION
stability
FACTORS
FOR
THE
DC-8
axes.
FLIGHT
CONDITION
4
2
Mach No., M (-)
Altitude,
h
(ft)
(¢
Weight,
0.218
0
15,000
15
15
W
0.88
33,000
33,000
15
15
190,000
190,000
230,000
230,000
I/ms
-o.o13
0.00649
o. 00404
O. 00447
I/T R
I .121
1.329
i.254
1 .356
o. 0793
O. 0855
1.197
I .495
1 .D89
0.392
0.545
0.612
o
0
[d
o.Io96
COd
o.996
Ap
I/Tpl
NP r
0.84
(lb)
Alat
I/Tp2
I/T>
3
A_
q)
0.443
I I/Tqpl
N_r
I/Tep2
0.1061
0.1813
0
0
1. 028
i.85
2.43
2.57
-2.13
-2.56
-3.oi
-5.15
o.1813
0.392
o.545
0,612
1.o28
I.85
2.43
2.57
-2.13
-2.56
-3.oi
-3.15
-o. 389
--0.864
--1 . 165
I
A r
I .124
1.335
I.276
1.377
_r
-o. 0743
-O.O451
--0.0619
-0.0475
_r
o. 339
0.330
o. 323
0.323
0.0238
o. 0288
0.0222
1/mpl
-O.O559
-o, o14 7)
--0.00726
1/T 2
1,141
1.297
1.217
1/Tp3
16.47
3o .2
52.6
Aay
5.79
13.hS
18.33
I/Tr I
r
N5 r
P
N6 r
Cd
TR-176-1
-1.277
1/may 1
-O.819
I/may 2
-4).I 077
1/may 3 ( _ay)
( O. 994 )
l/may
(1.078)
-O. 0347
i .535
--1.157
i.147
114
-0 .ot883
1 .122
--1 .418
1 ,723
0.0233
-0.00637
1.323
f
r
pp. 0
20. I
-o .Ol 7146
I .231
-1.494
I .819
APPENDIX
A
AXIS SYSTEm,
SYMBOLS,
AND DERIVATIVE DEFINITIONS
I.
.a_:T.8
IB_r_TEI_B
_XB,U,P
f v,
--_/_ ............
"_,
_--Inerticll
Ref.
YB,Ys,v,q
ZB,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
Speed
a
of
Lateral
at the
sound
in
ft/sec
air
acceleration
along the Y-Body
Axis
center
of gravity
(positive
out right
ft/sec 2
acceleration
parallel
to
Axis at a distance
i x and
ft/sec 2
wing)
!
ay
Lateral
Y-Body
c.g.,
az
I
a z
the
_ = _ + ix_- iz_
Normal
at the
acceleration
along the
c.g. (positive
down)
Normal
acceleration
Axis
the
i z from
at
c.g._
parallel
a distance
i x from
Z-Body
to
the
Axis
ft/sec 2
Z-Body
ft/sec 2
the
a z, = a z - lx_
ft
b
Reference
wing
C
Reference
chord
CG
Center
D
Aerodynamic
force (drag)
velocity
vector
(positive
g
Acceleration
h
Altitude
Ix, ly, Iz
Moments
of inertia
referred
to body
axis
slug-ft 2
Ixz
Product
of
referred
to body
axis
slug-ft 2
jcD
The imaginary
portion
variable
s = _±j_
ix
Distance
along
c.g. (positive
the X-Body
forward)
Iz
Distance
along
c.g. (positive
the Z-BodyAxis
down)
L
Rolling
moment
about the X-axis
due
aerodynamic
torques
(positive
right
span
ft
of gravity
due
to
along
aft)
the
total
lbs
ft/sec 2
gravity
ft
inertia
_own)
A-2
of the
rad/sec
complex
Axis
from
the
ft
from
the
ft
to
wing
ft-lb
L
Aerodynamic
force
(lift) perpendicular
to the total velocity
vector
in the aircraft's
plane
of symmetry
(positive
up)
ibs
m
Mass
M
Mach
M
Pitching
moment
about the Y-axis
due to
aerodynamic
torques
(positive
nose up)
ft- ib
MAC
Mean
aerodynamic
ft
MGC
Mean
geometric
N
Aerodynamic
slugs
number
Axis
chord
ft
chord
normal
force
bu___t
positive
along
the
Z-Body
ibs
up
N
Yawing
moment
about Z-axis
due
torques
(positive
nose right)
P
Roll rate, angular
velocity
(positive
right wing down)
q
Pitch
rate_ angular
(positive
nose up)
to
about
velocity
aerodynamic
ft-lbs
X-axis
rad/sec
about
Y-axis
rad/sec
2
Dynamic
pressure,
]/2
ibs/ft 2
p VTo
r
Yaw rate_
(positive
rRG
Yaw
s
Laplace
S
Reference
T.E.
Trailing
u
Linear
X-axis
perturbed
(positive
U o
Linear
X-axis
steady-state
velocity
(positive
forward)
v
Linear
perturbed
velocity
(positive
out right wing)
along
VT o
Total
linear
steady-state
(positive
forward)
velocity
rate
angular
velocity
nose right)
gyro
about
Z-axis
signal
operator,
wing
_+
rad/sec
rad/sec
jw
rad/sec
ft 2
area
edge
velocity
forward)
A-3
along
the
along
the
ft/sec
the
Y-axis
ft/sec
ft/sec
ft/sec
perturbed
(positive
velocity
do_m)
along
ft/sec
w
Linear
Z_-axis
the
W
Weight
Wo
Linear
Z-axis
X
AeroCy_;lamic force
(positive
forward)
along
t!_c X-axis
ibs
Y
Aerody_lamic
force
out right wing)
along
Y-axis
_]0s
zj
Perpendicular
line (positive
due to thrust)
Z
Aerodynamic
lbs
steady-st_/Le
velocity
(positive
dovm)
alonf{ the
(positive
distance
from c.g. to
for nose up pitching
force
along
Z-axis
thrust
moment
(positive
;l't/sec
ft
ibs
down)
Pert_irbed
_o
angle
Steady-state
Sideslip
rad
of attack
(trim)
angle
rad
angle
flight
path
deg
7o
Steady-state
8a
Aileron
control
surface
deflection,
(includes
spoiler
effects,
etc.),
for positive
rolling
moment)
_e
angle
Elevator
surface
deflection
from
(positive
for nose down pitching
for
aft
surface)
Trim
(leg
of attack
elevator
tad
(positive
trim_
moment
deflection
rad
deg
F
Rudder
left
A
deflection
yawing
Denominator
of
Damping
ratio
particularized
e
Pitch
angle,
level
flight,
Ipositive
moment
(negative
airframe
for
transfer
of linear
second
by the subscript
fq
dt
for
positive
A-4
straight
nose
rad
nose
N)]
up
function
order
and
mode
rad
_o
IncJ.ination
[positive
Mass
Special
of
gives
density
thrust
line
negative
of
air
The real portion
s = _± j_
of
with
X-axis
deg
(--) Z force]
slugs/ft3
the
complex
rad/sec
variable
Roll angle,
(cos @o _P
dt -sin e o _r
in straight
and level flight,
(positive
right wing down)
dt)
rad
Undamped
natural
frequency
of a second
mode, particularized
by subscript
order
rad/sec
Subscript
a
Aileron
d
Dutch
e
Elevator
P
Phugoid
r
Rudder
R
Roll
s
Spiral
sp
Short
roll
subsidence
period
A-5
3,
NONDIMENSIONAL
a)
DERIVATIVE
Longitudinal
Body
N
_-_
CN
=
CX
=
X
_ S
:
_CN/_
DEFINITIONS
Axis
, positive
up
' positive
aft
IV[
c_
CM
-
Sc
2VT o
CN_ -
c
bc_/_
c
CNs :
_c_/_s
cxa
8Cx/_
2VT o
b)
:
CMq
CxM :
_Cx/_M
cxs
8cx/_s
=
Longitudinal
Stability
-
c
Axis
CL
-
L
_
qS'
positive
up
CD
-
D
_
qS'
positive
aft
Ci_
=
_CL/_
CI_
-
2VT o
C
Pitching
_Cn/_
CLM =
_CL/_M
derivatives
Cr_
_C_/_
identical
CDc :
_CD/a_
those
CI_
:
_CD/_M
CD5
=
_CD/_5
:
_cM/_q
A-6
moment
are
to
for body
axis
c)
Lateral Body and Stability
Thoughphysically
Axis
and numerically different_*
see Appendix B, the
samesymbols are used for body axis and stability
axis lateral
rolling
and yawing momentderivatives.
The sideforce derivatives (Cy, etc.) are
physically and numerically the same in both axis systems. Whenthe
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
Cl
_s
-
_Sb
N
Cn
-
{Sb
_Cn/_ _
Cy_
=
_Cy/_
CI_
=
_CI/_
Cn_
=
Cy_
=
_Cy/_
CIp
-
2vb °
Cnp
_ 2vb °
Clr
-
Cnr
-
Cl8
=
cn_
=
*The
exception
is the
zero
2VTo _Cl/_r
b
_Cx/_
trim
A-7
angle
of
attack
2VTo _c_/_r
b
8Cn/8_
condition.
4.
DIMENSIONAL
The
STABILITY
same
symbols
derivatives.
quantities
a)
DERIVATIVE
Care
are
are
used
should
be
DEFINITIONS
for
body-
exercised
and
so
stability-axis
that
a consistent
dimensional
set
of
used.
Longitudinal
Body
Axis
X{_ =
Xu + mu cos_o
Xu
-
pSUo
(- _M
m
Xw
_
0SU2mO I- CX_
CXM
I/sec
- CX + _Wo CX_
2U o
)
- 2 U_o
Wo (Cx _ -2
M CXM)
I/sec
'
]/sec
oSVT2o
ft
X_e
=
Z_
-
Su
Zu
-
OSUo
m
M
- _
Zw
-
p
-CNc_ - _ _oo
Z_
:
_
CX_ e
- Tu
sec'-rad
I/sec
s:i.n[ o
CNM
_ CN +
p2_
Uo
4m
VTo
C N 4. _
=
-
_n
CNM
] / S (-:_C
]/sec
CN&
0SV_ o
ZSe
CN _
uo[
wo
I M )]
2m
-
o
ft
CN6 e
rb
see'
r:Ad
Zjm
sec-ft
k-8
Nil
-
-
OScU°
21y
I_
Cram + Cm
I
2Iy
Cmo_ + _
sec-ft
- 2U----o
(Cm
1
+ _ CraM)
sec-ft
pSc2
Uo
_
=
_zy
V_o C_
I_
:
UoM w
]/sec 2
=
UoM_
]/sec
sec-ft
pS C2VTo
]/sec
Mq
-
41y
Cmq
oS CV2o
I/sec 2
M6e
-
21y
Cm_e
]/sec
b)
Lateral
Body
Axis
Yv
:
(oSVTo/2m)Cy
Y_
=
VToY v
Y_
]/sec
_
ft/sec 2
ft/sec 2
: (pSV_omm)%5
Ys_ : (0SV_o/2m)%
%
ft/sec 2
Y6_
I/sec
:
(pSVTo/2m)dy6r
_B : (_SV_ob/2_x)C_
_
Lr
]/sec 2
= (pSVTob2/4Z_)Clp
]/sec
=
]/sec
(oSVTob2/41x)Clr
A-9
2
_5_ = (oSV_ob/21_)Clb
I/sec 2
_r
I/sec 2
= (oSV$ob/21xlCl_r
l/sec
Y_a = (oSV_o/2m)CYS_
_
= (oSV$ob/2I_IC_
_
I/sec 2
Np = (oSV_ob2/_I
z)c_.P
I/sec
Nr
I/sec
N_
=
(oSVTob2/41z)Cn
r
l/sec 2
-- (pSV$ob/2Zz)C_
_
F]
N_
I/sec 2
= (_SV_ob/21_)c_
_
I/sec 2
I/sec
]/see
Lt_r
=
(L_ r +
IxzNSr/Ix)G
/sec 2
],t_
:
(L_ a +
lxzNSa/Ix)@
]/sec 2
N'
:
(N@
]/sec 2
+ IxzL_/Iz)G
I/see
N_
:
(N r + IxzLr/Iz)G
_!_'
" r
:
(N_r
_q
: (_
_
IxzLSr/Iz)
]/sec
]/sec 2
G
+ I_z_/z_)_
]/sec 2
1
G
I
Ixlz
A-tO
I
--4
©_
I
./_
Xe, Uo
CN
J
U o
=
VToCOS
a o
Wo
=
VToSln
_o
Cx
_a_o_
Ys---Ye
Zs,Wo
Zs
I
ON
=
CL
cos
ao+
CD
sin
_o
(C_)B :
C16
cos
CX
=
CD
cos
_o-
CL
sin
Go
(c_;)
B =
CIp
cos£ao
- (Clr+
=
C1 r
ces!_e
- (C_ r
=
C16
cos
a o-
Cn_
sin
a e
ao+
CI_
sin
a e
CN_ =
CL_c°s _o-CLsln ao + CD_Sln ao+ CD cos ao
(Clr)
CN& =
CL_ cos _o
(c_)_
CNM
=
CLM
cos
Go
CN8
=
Ci6
cos
Go+
CX_
=
CD_
cos
_o'CD
CXM
=
CDM
cos
_o-
CL M
sin
<_o
CX 8
=
CD5
cos
_o-
C_
sin
_o
Cram ,
Cm_
-t_NCHANGED
Cm,
Cm_
,
Cm_
,
Cmq
+
,
B
_o"
C_
sin
ab
Cnp)Sln
-Clp)sin
ae
c_
_o+
Cnr
sin2ao
_e
cos
&o"
Cn F
sin2_o
r
sinlAe
CDM
sin
_o
(end) B =
Cn_
cos
CD5
sin
_o
(c_)B =
Cnp
cos2_o
- (Cn r-clp)sin
_e
cos
&o'CI
(Cnr)
=
Cnr
coS2ao
+
o_
cos
_o
=
Cn6
cos
sin
o_-CL_
sin
_o-CL
cos
_o
B
(c_)_
Cy_,
CYSr
, CYsa
ao+
-
(Clr+
CI_
C_p)sin
sin
t_CHANDEP
a e
+ Cip
sin_%e
]
.L
y
APPENDIX
EQUATIONS
I
•
OF
AND
MOTION,
COUPLING
C
TRANSFER
FUNCTIONS,
NUmeRATORS
Longitudinal
a.
E quat i on s
s-X_
-X w
-4
(1-Z_)s-Z
--(M_s
b.
I)
q.
=
-se
}_
=
--w cos
cos
ej
u
-Uos+g
sin
80
w
-
@
* Mw)
@o
az
=
sw-
Uoq
a z'
--
az
ixS2@
Transfer
w
Wos+g
s2-
+ u
sin
eo +
(g
sin
eo)e
+
MqS
(U o cos
XSe
=
Z6e
M6 e
e o + w o sin
eo)e
Functions
@
N_e
5e
A
Denominator,
A
=
As 4 + Bs 3 + Cs 2 + Ds
+ E
A -B
=
--(Mq + Xu)(I
c
=
MqZ w-
-- Z_) -
Mc_ + Xu[(Mq)(1
-- XW_
+ WO[M_Z
u
Zw -
Mc_
-- Z_)
+ _(I
C-I
+ Z w + M_]
-- Z_)]
+ g_
sin
@O
t
D ---x_(Mz_-_.h)
-M_y=+MqK_z_
+g[%z_+M_(I-z,_oos0o+Wo(ti>_
-t_Iz_)
+ g(%-%x_)_inOo
E --g(MwZ
_ - M_Z_)oos
eo+ g(M_IXw
- %X_)_i_Oo
2)
5
_umerator
s
N_
Ao --z_
B8
=
Aes 2 + Bes
+ Ce
+ M_(1 - z_)
= XS[M_Z_+
Mu(1
- Z_.)]+
Zs(Mw-I%X
_)
% -"x8(_vz_i-M_zw) + z_,(M_x_-_)+
N_
Au
= X5(I
Bu
= -XS[Mq(I
=
-MS[Zw+
XI_(I - ZQ)]
_,%(
zj,_- x_, u)
Aus 3 + Bu s2 + CuS + Du
- Z.)
w
- ZQ)
+
Zw
+ M_]
+
ZsX w
- Wo[ZsM
_ +
_o(I
- ZQ)]
Cu--x_(M_z.-vh)z_(g% oos0o+Mqx_)+ _%[_- (_ oo_eo)(1-z,)]
+ Wo(ZwM_-_) + _x_% _i._o
Du : g(ZwM5
- MwZs)c°s
N_
Aw=
=
00 + g(XsMw
- Ms_psin
Aw s3 + Bw s2 + CwS
_o
+ Dw
Z6
Bw = -%(Mq+ x_)+ Uo_ + x_z_
Cw
= X_(ZsM
Dw
" g(ZJ_
q - UoMs)
- %Z_)cos
+ Wo(ZsM
0o +
u
- MsZ _)
gMsX*
C-2
sin
- gM 5 sin
0 o-
XsMug
00 + Xg(M_Uo
sin
0o
- Z_Mq)
N_
=
A_s 3 + B6s 2 + C_s
+ D_
A_ = - cos eoAw + sin 0oAu
=
- COS
@OBW
+
sin
@OBU
+
(U O cos
e O + W O sin
0o)A @
O_
=
- cos
@OOw
+
sin
eoC u +
(U O cos
@o
sin
0o)B @
D_
=
- cos
@oDw
+
sin
eoD u +
(U O cos
e O + W O sin
eo)C @
+ No
.t
_f'= _a[?+B_'zS3
+c4__+_ab+E '
&z
To
2.
Ba_
= Bw
- ixB e - UoA 0
Ca_
= Cw
- ixC e - UoB 0 + g
Da_
= Dw
- UoC e +
Ea_
: +
obtain
az,
g
sin
let
g sin
sin
@oAe
0oB e
0oC 8
ix = O.
Lateral
a.
Equations
Wos + g cos
s- Yv
-
VT o
0o
Uos-g
sin
- _o _
8o]
E-
IF
Y5 a Y5 r
=
L5 a L5 r
!
!
--I_
-._
v
--L
S(S--%)
VTo _
:
_p_ + _r
s-N
r
sv + Uor
_
--WoP-
iNsa ,N5 r
g(cos
!
S
DO
ay + iXlat
S
]
COS
tan
r
8 0
!
!
-._
:
r
S
c-3
sr -- izS p
8o)C_
b.
Transfer
Functions
___=
N_a
_a
r
Alat
;
N_r
_r
-
4
I)
a
=
Denominator,
etc.
Alat
2
Ala t = as
+ bs 3 +
cs
+ ds
+ e
I
!
b = -(y_+ L_+ Nr)
Uo
WoL _
o ---N_ + L_(Y_
+ _) - N_L_+
Y_
VT o
U o
d _ --(_VT o
VT o
_) + Yv(_9_r_)
_ (_ cos0° +
VT o
Wo
VT o
e
=
2)
-_g
VT o
[(I%N_-
8
(5 a or
N_I$)
5r)
cos
e o-
(N_-
L_)
sin
0o]
Numerators
=
_s 3 + _s 2 + c_s + D_
A_ : Y_
+ N_]- N___Uo
+ __w°
L_'
B_ ---Y_[_"
VT o
VT o
,
c_
--
Y_(_'_-_r) + L_--g
co__o+ (%_ - %_)
VT o
Wo
+ -VTo
D6
=
, ,
, ,
(NgL r -- LgNr)
-_g (N_L r -- L_Nr)
VT o
cos
, g
+ N_ V_T
0 o + -_g
VT o
c-4
o
sin
Uo
VT o
0o
(N_I,_ -- N_I_)
sin
0o
N_
sin
O o)
[__ •
N_5
=
Ap s3 + Bp s2 + Cps
+ Dp
!
Ap
=
L5
- LS(Nr
, ,+
=
.
Cp
=
Dp
-
Yv)
,,
+ NSLr
, ,
,
Y_(LrN _ -- L_N'r)
,
+ L_YvN' r -- NsYvLr
UO
+
(L_N_
+ Crs
+ Dr
-- N_L_)
VT °
VT
o
N_
Ar
=
=
Ar s3 + Br s2
N_
*
T
!
!
T
Wo
Cr
Y_(I,_N_-
N_%)-
L_YvN _
+ N_YvL _
+-
=
Dr
VTo
VTo
N_
A¢
:
Ap
+ A r tan
6)
o
Be
:
Bp
+ Br
tan
8o
C¢
:
Cp
+ C r tan
8o
=
Acs 2 + Bcs
c-5
+ C
, ,
(LsN_ -- N_L_)
•
N_
ay
VToA_
+ iXlatAr
+ UoAr
izAp
B'ay
=
VToB_
C_
=
VToC _ + UoB r -- WoB p -
g cos
QoA¢
+ iXlatC
r -
izCp
V T D_
o
g cos
0oB ¢ + iXlatD
r -
izD p
D
!
obtain
ay,
-WoAp
+ UoC r -
UoD r-
To
= A'ays4 + B_ s3 + C_ys2 + D_s + E'ay
let
WoD p-
Ixlat
+ iXlatBr
WoC p -
g cos
-
eoC ¢
= i z = O.
c-6
IzBp