SECTION I
SECTION I
INTRODUCTION
The purpose of this document is to provide handling qualities investi-
gators with readily usable data on several representative contemporary air-
craft. Included are those data required to obtain transfer functions relating
the aircraft's response to control inputs. An analytical description of the
aircraft's stability augmentor is also given.
For those aircraft for which complete information was available, the
following summarizes the contents and presentation:
7. Flight conditions for which computations are made
including: a. Configtu_ations (e.g., fuel load_ flaps,
gear, etc.)
b. Mach/altitude combinations
2. General arrangement
3- Control system description
4. Stability augmentation description
5- Tabulations and/or plots of non-dimensional stability
derivatives for trimmed flight
6- Dimensional, mass, and flight condition parameters
7- Dimensional stability derivatives
8. Transfer functions for control inputs
9" Selected_andling qualities parameters
10. Data sources
A page number cross index is presented in Table I-1.
The intention has been to make this 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.
X I
g
o
i i
<_ o_ _ _
_ _ _o_ _ aa
o_ _ _o _ _ _''_'"
. _. . _
The aircraft considered in this report span a wide range of sizes, speeds,
and uses. In each case_ transfer functions and handling qualities parameters
were computed for flight conditions which were selected to cover the flight
regimes of interest. A nominal configuration (generally cruise) was picked
for all up and away flight conditions. For this nominal configuration, plots
of trimmed non-dimensional aerodynamic force and moment coefficients are
presented. Also, in most cases, a power approach case is presented along
with a tabulation of aerodynamic coefficients. The coefficients are based
on rigid wind tunnel data 3 estimated flexible data_ or flight test results,
depending upon availability. This is indicated by the words "rigid, "
"flexible," and "flight" on each aero data plot. Also, the axis system is
indicated by "stability" for a body-fixed stability axis system or 'body"
for a body-fixed system aligned with the F.R.L. (Further clarification of
axis systems used is given in Appendix A.) Descriptions of control systems
and stability augmentation systems are given along with transfer functions.
Where a longitudinal control system has a significant effect on the equations
of motion (as with a bobweight) the stick-free transfer functions and handling
qualities are given.
Transfer functions are always given for body axis motion quantities.
Handling qualities parameters are also given in the body axis. All accelera-
tion transfer functions (a z and 4) are for the pilot's position. Thrust
transfer functions do not include any engine response characteristics.
A substantial portion of this report is in the form of computer printout.
The mnemonics used in this printout are defined in Appendix A.
The handling qualities parameters given in this report represent only a
small fraction of those developed over the years. The majority presented here
are used in past and present versions of MIL-F-8785. Although only SAS-off
values are shown, the definitions given in Appendix A are general and could
be used in conjunction with the HAS-on transfer functions to yield SAS-on
handling qualities parameters.
While complete coverage of each aircraft including only the "latest" and
'_oest" data would be desirable, the major criterion used was that the data be
accessible to the author. This is why only isolated flight conditions are
given for some aircraft, and also why, as those people more intimately familiar
with each particular aircraft will recognize, the data presented may repre-
sent an early estimate in the design process and perhaps the "nominal config-
uration" 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 test data. Every attempt has been made
to insure reliable translation, interpretation, and transcription of the data
from their source documents.
The manufacturers of the aircraft 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.
-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 feel system (pilot's
commands, position or force), attitude and rate gyros, accelero-
meters, dynamic pressure, _ vane and _ probe. This arrangement,
through a response-feedback system, allows the normal T-33
derivatives to be augmented to the extent that the handling
qualities of many existing airplanes, future airplanes or hypo-
thetical 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 functions are given for only the primary surfaces and engine
thrust although the NT-33A also has other control surfaces and a range of con-
trol crossfeed and feedback combinations.
Aerodynamic data, for the most part, was taken from AFFDL-TR-70-71. However,
longitudinal data for the high lift configuration was obtained from LAL 1 27
andMach number derivatives from NACA-RM-7116.
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NT-33A
PITCH AXIS
Variable
Variable
Feel Stability
Input
Input
I
_]ST(in) ] -I0 _._ ---- _.3 Be(rod)
s z +.89s + 22.5
FST(Ib) _..026
ROLL AXIS
Variable Variable
Feel Stability
Input Input
FLAT (ib) I OST _,n I0 _a(rad)
sT
YAW AXIS
Variable
Variable
Feel Stability
Input
Input
I
I_PED(in) I 2.34 _. = _._ 8r(rad)
FpED(Ib)_
Feel system parameter values shown correspond
to the "Front Seat Engage" mode (normal NT-33)
Figure 11-3. NT-33A Control System
TABLE 11-I
Power_oach Non-Dimensional Stability Derivatives
h = sea level
VTo = 228 ft/sec = 139 kt
oo = 2.2 °
Longitudinal Lateral-Directional
( Stability Axis )
cL = .813
cy0 = -.72/r
cD = .139
Cn_ = .049/rad
CLm = 5.22/rad
C_0 = --.127/rad
CD_ = .94/rad
C_p = -.O7/rad
% = --.401/rad
C_p = -.045/rad
C_r = .20/rad
Cmq : -mo/raa
: Cnr = --.16/rad
CL5e = .34/rad
Cn5 a = --.O09/rad
Cm6e = -.89/rad
C_5 a = .14/rad
CYSr = .17/rad
Cnsr = -.O73/rad
C_5 r = -.OO2/rad
' SL NT-33A
.... 20,000 ft 13700 Ib
w
------ 40,O00ft .263
Rigid
B
Cl o
(deg) n
D D
\
4-
Z-
0 o
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oJ
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NT-33A
!
13700 Ib
(red -I )
I
Rigid
4- 4
!
!
!
SL
..... 20,O00ft
2-
-------- 40,000 ft
I I I
I
.6 .8
.2 .4
Mach
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(rad "l)
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l
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Mach
Mach
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I (_ I I I
/
(rad -i)
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SL
NT-33A
..... 20,O00ft
13700 Ib
--"-- 40,O00ft
.263_
-1.2
Rigid
Mach
• _ .2 .4 .6 .8
Cm&
Cmd, -4
Cmq
(rod")
-8
-12
_Cmq
-16
NT-33A
13700 Ib
.263 F.,"
1.0
Rigid
CL M
"21 2 _ 3 6 8 4 i
| _ .4 Mach .6
-I.0
SL
..... 20,O00ft
------- 40,O00ft
.3-
CD M
I
0 .2 .4 .6 .8
Mach
Moch
0 .2 .4 .6 .8
Crn M
-.2
-.4
.4
CL8 e
(rod "l )
NT-33A
.2
Rigid
I I I I
O0 .2 .4 .6 .8
Mach
Moch
.2 .4 .6 .8
0 o
I I I I
-.4
Cm_ e
(rod -j )
-.8
-I.2'
1 _;
Mach
.2 .4 .6 .8
1 I I I
Cy_
(rad-i) -.4 --
NT-33A
SL
13700 Ib
..... 20,O00ft
Stability Axes
------- 40,O00ft
Rigid
.2
Cn/_
(rad -i )
I I I I
.2 .4 Mach .6 .8
f.®." /
-.2
Mach
0 .2 .4 .6 .8
0 I t l
-.2
-.4
c.tp
(rod "I)
m6 Boa
NT-S3A
- - SL
137001b
..... 20,O00ft
Stability Axis
--- "-"- 40,000 ft
Rigid
.O4
Cnp
_4r _,f
(rod "l)
-.04
-,08
SL NT-33A
• 20,000 ft 13700 Ib
------- 40,O00ft 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 r
t9
.2O
.16
C}s a
(rad "l )
.12
' SL
NT-33A
13700 Ib
..... 20,000 ft
40,O00ft
Stability Axis
Rigid
0 I I I I
0 .2 .4 .6 .8
Mach
.01
Mach
.2 .4. .6 .8
Cn8 o
(rod -j )
-.01
¢
So is sum of both right and left
-.02
aileron deflections
2O
Cy_ r
(rod "l )
I I I I
O0 .?_ .4 .6 8
Mach
Mach
.2 .4 .6 .8
I I I I
-.04
Cn8 r
(rad "I)
-.08
NT-33A
, SL
m *== 13700 Ib
--- ?_O,O00ft
Stability Axis
---- _- 40,O00ft
Rigid
.04
C,_sr
(rad "l )
.02
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3O
NT-33A DATA SOURCES
Hall, G. Warren, and Ronald W. Huber, System Description and
Performance Data for the USAF/CAL Variable Stability T-33
Airplane, Air Force Flight' D_nsmics Laboratory Rept. No.
AFFDL TR-70-71, Aug. 1970
Tests of a I/5 Scale Wind Tunnel Model of the TP-80C Trainer,
Lockheed Aerodynamics Laboratory Rept. No. LAL 127, Jan. 23, 1948
Cleary, Joseph W., and Lyle J. Gray, High Speed Wind-Tunnel Tests
of a Model Pursuit Airplane and Correlation with Flight-Test
Results, NACA-RM-7116, .Jan. 21, 1948
Statler, Irving C., et al, The 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. 1967
Flight Manual_ USAF Series T-33A Aircraft, T. O. IT-33A-I.
SECTION III
SECTION III
F-IO4A
F- 104A BACKGROD'AID
The F-IO4A is a single place_ lightweight_ supersonic air superiority
fighter powered by a single turbojet engine with afterburner. The wing has
a full span leading edge flap. Trailing edge flaps have a blowing-type
boundary layer control system. Control is provided by conventional ailerons
and rudder and an all-movable stabilizer. Pitch_ roll_ and yaw dampers are
incorporated_ however their effect is not shown here. Pitch and roll con-
trols are fully irreversible while the yaw control is a cable-actuated rudder
without boost. A bobweight is used in the longitudinal feel system. Its
position is assumed to be at the pilot's location.
The primary source of data was LR 10794. Drag information was obtained
from LR-12873.
The nominal configuration used here is the combat loading for the F-]O4A
based on actual weight and balance data. The PA configuration is a typical
loading at flight manual approach speeds.
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C-_
F-104A
PITCH AXIS
8SsAs(rad)
G
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i
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F B
B
az assumed to be at pilot location
/in)
ROLL AXIS
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F LAT --I I
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ST (Ib) --i 2.7
_! 5"_ _ 8a (rod)
YAW AXIS
SpED(in)
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KDIR_
2.0
K°["/'I b/in_
1.0
o, I I I I I
0 .4 .8 1.2 1.6 2.0
Mac h
Figure 111-3. F-IO4A Control System
Power Approach Non-Dimensional Stability Derivatives
h = sea level
VTo = 287 ft/sec = 170 kt
_o = 2"3°
_s = --7.1°
Longitudinal
Lateral-Directional
(Stability Axis )
CL = .735
Cyp = -1.17/rad
% = .263
cn6 = .5o/r_
CL= = 3.44/tad
C2p = --.175/tad
CDa = .45/rad
C_p = --.285/tad
Cm_ = -.6_/ra_
Cnp = --.14/rad
Cma = --I .6/rad
C_r = .26_/rad
Cmq = ->.8/ra_
Cn r = --.7_/rad
Cg_s = .68/tad
Cnsa = .O0_2/rad
Cm_s = --1.4g/rad
C£5a = .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
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U') v rf % j O. _ _ I O O O
F- 104A DATA SOURCES
Stabi? [ty and Control and Handling Qualities_ F-IO4A, Lockheed Rept.
No. LR 10794, 12 Dec. 1955
Andrews, William H., and Herman A. Rediess, Flight-Determined Sta-
bility and Control Derivatives of a Supersonic Airplane with a
Low Aspect-Ratio Unswept Wing and a Tee-Tail, NASA Memo 2-2-59H,
A!or. '1959
Performance t F-IO4D, Lockheed Rept. No. LR-12873, I May 1958
Flight Manualt F-IO4A and F-IO4B USAF Series Aircraft, T. O. IF-IO4A-I,
15 Dec. 1961
Technica ! Manual t Flight Controls t USAF Series F-IO4A and F-I04C
Aircraft, T. O. 1F-104A-2-8, 15 Mar. 1960
6O
SECTION IV
SECTION IV
F-4C
F-_C BAC_DROUND
The F-4C is an Air Force tactical fighter whose primary mission is
all-weather air-to-air missile combat. Lateral control is achieved by
ailerons in combination with spoilers on a swept wing. A swept stabilator
provides longitudinal stability and control. Directional stability and
control is accomplished through a conventional fin-rudder combination.
Landing speed is reduced by full span leading edge flaps and inboard plain
trailing edge flaps in conjunction with blowing-type boundary layer control
(BLC). Boundary layer control is automatically induced when full flap
deflection occurs.
Features distinguishing the USAF F-4C from its Navy counterpart, the
F-4B, are:
• Lack of drooped ailerons with flaps down resulting in
higher landing speeds.
• Dual flight controls resulting in slightly increased
control system inertia.
• Wing bumps to house larger main gear wheels resulting
in a slight drag increase.
Data included here was obtained primarily from MAC Report No. 9842.
Special emphasis is placed on the longitudinal control system because of
its relative complexity when compared to other aircraft. Figure IV-4 has
been addqd to help illustrate this system. Also, care has been taken to
retain s_m% of the control system nomenclaure used by the manufacturer, e.g., qB and PBF (see Fig. IV-5).
The Stability Augmentation block diagrams are shown in Fig. IV-7. The
roll SAS described is not included in lateral directional SAS on transfer
functions since it is faded out with the lateral control stick out of neutral
position.
_p :d q-i O O ,--I
@
O
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II II II .Q IU
F-4C
PITCH AXIS
_SsAs (rad)
Feel System
I _ Gearing / Actuator
8s(rad)
18sT(in)_ _
.0569qePsF
+ .OI57qBPBF -*
FST(Ib__ _-_.0369s 2 +.208s
,:_1 I _'-_ I- _ -I°_'+'1
_-- See Fig and for feel system details
Bobweight
az ts---_- _) of JtB= 39.3 ft
ROLL AXIS
8OsAs (rad)
Feel Spring Gearing /
Sa(rad)
_;T,,_ -I 2"961 =1 _ i -_ Spoiler
-__ 8sp( ra d )
AR! Gain
CLEAN O ,/
PA ARI
C38r {-.46 SAS OFF
= _-.69 SAS ON
__r I___--
<_rAm(rod)
_-:1_
YAW AXIS 8rARl(rad) 3rsAs (rad)
\ / Rudder
Feel Spring Gearing \ / Flexure
.._j_'_ SPED (i n) .___.J__
8r(rad)
_"_°_'_ - I _ I _I _ I- _ - l""txl -
_-- See Fig
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 Control System
ID C O C °_ t_ .J_ C
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.6
qB
-4C
q
/ _---- 35,00Oft 389:)4 Ib
.... 55,00Oft .289
I I I I 1
O0 4 8 12 1.6 2.0
Mach
J.I m
1.0-
PBF
(ft z)
I I L 1 I
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.4 .8 1.2 1.6 2.0
Mach
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40k
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h 3.03 Ib/in/sec
"l//f/[_ I
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b=_
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Mach
Figure IV-5. F-4C Feel System }arameters
6?
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E} (rad/sec) _1 .15s
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- I s+l
ROLL SAS
PG(rad/sec) _I -.265 I _--- 8asAs(rad)
P6 = P (Roll rate gyro assumed aligned with FRL)
Note." Roll GAS faded out with lateral control
out of neutral
YAW SAS
r G (radlsec)
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_I ,s
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' (ftlsecz )
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I
ay = ay + 9.9 _"-.391b
Yaw rate gyro inclined 1.5 ° below FRL and
lateral accelerometer at ES. 198.0and W.L.23.0
Figure IV- 7. F-4C Stability Augmentation
TABLE IV- I
F-_C
Power A_roach Non-Dimensional 8tability Derivatives
h = sea level
VTo = 230 ft/sec = 136 kt
% = 11.7°
_s = -9 .1°
Longitudinal
Lateral-Directional
(Stability Axis )
CL = .915
Cy6 : --.655/rad
CD = .242
Cnl3 : .199/rad
CL_ : 2.8/rad
C26 = -.156/rad
CD_ = .555/rad
C£p = --.272/rad
Cm_ - .098/rad
Cnp = -.013/rad
Cm& - .95/rad
C_r = .20_/rad
Cmq = -2.0/rad
Cnr = -.320/rad
CL5 s = .24/rad CYSa = --.0359/rad]
Spoiler
Effects
C-mss = --.322/tad
Cnsa = --.O041/rad I
Included
CD5 s = --.14/rad
= .o 7/r a j
CYSr = .124/rad
Cnsr = --.072/rad
C_5 r = --.O009/rad
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F-4C DATA SOURCES
Bonine, W. J., et al, Model F/RF-4B-C Aerodynamic Derivatives,
MAC Report 9542, I0 Feb. 1964
Crawford, W. N., and G. Nadler, Static and Dynamic Control System
Characteristics for the F-4 Aircraft, MAC Rept. F21_, 16 Dec. 1966
Bridges, B. C., Calculated Longitudinal Stability and Performance
Characteristics of the F-hB/C/D/J' and RF-hB/C Aircraft plus the
AN/ASA-32H Automatic Flight Control System, MAC Rept F934,
19 Apr. 1963
Bridges, B. C., Calculated Lateral-Directional Stability and Perfor-
mance Characteristics of the F-4B/C/D/J and RF-4B/C Aircraft plus
the AN/ASA-32H Automatic Flight Control System, MAC Rept. F935,
3 May 1968
NATOPS Flight Manual_ Navy Model F-4B Aircraft, NAVAIR 01-245 FDB-I,
I Nov. 1966
SECTION V
SECTION V
X-15
X- 15 BACKGROUND
The X-]_ is a single-place, rocket-powered airplane designed for flight
at hypersonic speeds and extreme altitudes. The airplane is carried aloft
under the right wing of a B-52 and is launched at an altitude of about
45_000 ft and a Mach number of about 0.80. After launch_ the X-J5 performs
a powered flight mission_ followed by a deceleration glide prior to vectoring
for a landing. With this operational technique, the airplane is capable of
attaining a Mach number of 6 and can be flown to and recovered from an altitude
in excess of 300_000 feet.
Flights to high altitudes have been made with all three of the X-J5
airplanes in two configurations: the basic and the ventral off. The basic
configuration is considered here.
Aerodynamic control is provided through conventional aerodynamic surfaces_
with vertical surfaces used for yaw control and the horizontal tail for both
pitch and roll control. All of the aerodynamic control surfaces are actuated
by irreversible hydraulic systems. Control force is provided by bungee for
pilot feel. A conventional center stick is used for pitch and roll control_
and rudder pedals are used for yaw control; however_ a side-located stick is
provided for control of pitch and roll in high-acceleration environments at
the option of the pilot. Most of the X-15 missions have been made with the
side stick_ although the pilots used the center stick on their first flights.
Only the center stick control is shown here.
The augmentation system shown in this report consists of angular rate
feedback loops about all three axes. In addition to the normal p -_$a roll
SAS loop_ there is an r -_5 a feedback known as the YAR loop. The gains for
each SAS loop are manually set by the pilot. The SAS-on transfer functions
given for this airplane assume maximum gain settings for each loop. This may
not have been realistic for actual flights.
The flight conditions considered for this airplane are all for straight
and level trimmed flight. This is definitely unrealistic for this airplane_
however_ the intent here is to show general speed and altitude variation
effects.
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Figure V-3. X-15 Control System
X-15
PITCH SAS
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Roll Gain
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r (rad/sec)
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Note:
Gains variable in 10% increments of the
maximum values which are shown above.
(e.g. roll gains selectable are .05,.I0,.15,
.2_0, .25, .30, .35, .40, .45, and .50)
Figure V-4. X-15 Stability Augmentation
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X-I 5 DATA SOURCES
Revised Basic Aerodynamic Characteristics of X-15 Research Airplane, North
American Aviation, Inc. Report No. NA-59-12033 August 19_9.
Osborne, Robert S., Stability and Control Characteristics of a O.0667-Scale
Model of the Final Version of the North American X-15 Research Airplane
(Configuration 3) at Transonic Speeds, NASA TMX-758, April 1963.
Franklin, Arthur E. and Robert M. Lust, Investigation of the Aerodynamic
Characteristics of a O.067-Scale Model of the X-15 Airplane _ConfigurA-
tion 3) at Mach Numbers of 2.29_ 2.98_ and 4.65, NASA TM X-38, November 1959.
Penland, Jim A. and David E. Fetterman, Jr., Static Longitudinal t Directional,
and Lateral Stability and Control Data at a Mach Number of 6.83 of the
Final Configuration of the X-15 Research Airplane, NASA TMX-236, April 1960.
Tunnell, Phillips J. and Eldon A. Latham, The Static and D_mamic-Rotar_
Stabilit_ Derivatives of a Model of the X-15 Research Airplane at Macb
Numbers from 1.55 to 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, Edwin J. and Darwin J. Garringer, Summary of Full-Scale Lift and
Drag Characteristics of the X-15 Airplane, NASA TN D-3343, March 1966.
Taylor, Lawrence W._ Jr. and George B. Merrick, X-_5 Air_lane Stability
Augmentation System, NASA TN D-1157, March 1962.
Tremant, Robert A., Operational Experiences and Characteristics of the X-15
Flight Control System, NASA TN D-1402, December 1962.
SECTION VI
SECTION VI
HL-IO
EL- I 0 BACKGROUND
The HL-IO is one of a number of lifting body research vehicles. The
airplane is typically launched from a B-52 at 0.8Mach and 4_,000 feet.
In numerous glide and powered flights the HL-IO has been flown in excess
of 1.8 Mach and 90,000 feet.
Following problems involving the loss of roll-control effectiveness,
the leading edge of the tip fins was modified. This became known as the
Mod II configuration. The information contained here is for the Mod II
HL-IO.
Pitch and roll control is obtained by elevons and yaw control by a
conventional rudder. A subsonic or a transonic configuration is selected
using combinations of speed brakes_ elevon flaps, and tip fin flaps. These
combinations are specified in Fig. VI-I.
The stability augmentation system consists of angular rate feedback loops
about all three axes.
The flight conditions shown correspond to actual flight test points.
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Figure Vl-3. HL-IO Control System
HL-I0
PITCH SAS
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Figure VI-4. HL-IO Stability Augmentation
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o o _ o _ o _ _ _ _ _ _ _ _
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"T
.-_ .-i I'M ("-4 r_. _ . ..4 #n £ _, - - % . .
HL- I0 DATA SOVRCES
I • Ladson, Charles L., and Acquilla S. Hill, Aerodynamics of a Model
of the HL-10 Flight Test Vehicle at Mach 0.35 to 1.80, NASA
TN D-6018, Feb. 1971
,
Pyle, Jon S., Lift and Drag Characteristics of the ML-IO Lifting
Body during Subsonic Gliding Flight, NASA TN D-6263, Mar. 1971
_°
Ware, George M., Full Scale Wind Tunnel Investigation of the Aero-
dynamic Characteristics of the HL-IO Manned Lifting Entry
Vehicle, NASA TMX-1160, Oct. 1965-
JETSTAR BACKGROUND
The Jetstar is a four engine utility transport. Controls consist of
conventional ailerons_ elevators_ and rudder. Ailerons and elevators are
mechanically actuated with hydraulic boost. The rudder is mechanically
activated but assisted by a servo tab.
The primary source of aerodynamic data was NASA CR-544. Power approach
aerodynamics were estimated using CR-544 and flight test data from
_TC-TDR-62-24C-140. The control system description was based solely on
flight test data from the latter reference.
_, rn
o _p
r-_ Ca
:> 0 0
-M .rl
0 C;
%
,--t _ %
o
4._
.i-I
o
I
L I "_o
4._
, ®
o
o
,-q
I
0 "-" 0
"- oJ
v
"7
I-i
I-4
oJ
oJ
z
_o _
c_ oJ 0_J
O'x OJ OJ OJ
o,J 4-_
r_
I_0 _I r-I
I--I ._I
_,o _ _ _ _ _
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__Oo
Ox
o o__ _g_o
o oJ oJ .._
E-_ 0 CO 0 0
_o_ _ o.I _ _ _ LO_
II 11 II II
_ , . _0__
• r-I b_ N
,-I .,q ¢) 0
_'_
II)
H
a3
4_
0d c; I
..A t--4
.r4
N
II II II
JETSTAR
PITCH AXIS
8e (rad)
FST(Ib)
-_ 52 + 2.95CI
I' I
Note: Angle of attack effects on elevator
h/nge moment are neglected
ROLL AXIS
LAT
= 8a(rad)
F ST (Ib)
.75_q
I
YAW AXIS
-_ 8r (rad)
FpEo(Ib)
Figure VII-3. Jetstar Control System
TABLE VII- ]
JETSTAR
Power Approach Non-Dimenslonal Stability Derivatives
h = sea level
VTo = 224 ft/sec = 132._ kt
% = 6._ o
Longitudinal
Lateral-Directional
(Bod Ax±s)
CL = .737
CD = .O9_
Cn_ = .137/rad
= .O/rad
C_ = --.IO3/rad
CD a = .7D/tad
C_p = -.37/rad
Cm_ = -.80/rad
Cnp = -.14/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 = --.81/rad
C_Sa = .054/rad
CySr = .17_/rad
Cn5r = --.O63/rad
C_Sr = .O29/rad
SL JETSTAR
20,000 ft 38204 Ib
40,O00ft
12-
I0--
_0
(deg)
8-
6-
4-
2-
I I I
0 o
.2
.4 .6 .8
Mach
-- OD
r-
u
-- 0_
w_ o q q q
a
C.)
o o
S _
--00
_00
II
! J
r-
c_)
--0_
I 1, I I
0 tO OJ -_
_ 0
..J
6-
CLa 5
(rad-i) 4
JETSTAR
38204 Ib
1 I I I
0 .2 .4 .6 .8
Mach
1.2
.8
.4
%%%,
I t I I
0 .2 .4 .6 .8
Moch
Mach
.2 .4 .6 .8
0 o
I I I I
-.4-
Cma
(rad "i )
JETSTAR
SL
38204 Ib
..... 20,O00ft
.255
---- ----- 40,O00ft
Mach
0 .2 .4 .6 .8
I ! I I
-.4
Cm&,
Cmq
(rad-I )
-.8
_'*'_:_) Cmq
-1.2
CDM .08 t
(rod "l )
.04 -
0 .2 .4 .6 .8
Mach
Moch
0 o
.2 .4 . .8
_o I B
-'.2-
t
CM M -.3 -
(rod "l ) -.4 -
I
"o 5
-6 -
SL JETSTAR
38204 Ib
.... 20,O00ft
.25_
- 40,O00ft
CL8 e
4 - m
.2
CL8 e ,
Cm8 e
(rod'=) 0
) I I I
.2 .4 .6 .8
Moch
.2
JETSTAR
-.4
n
-.6
-.8
-I.0
Mach
0 .2 A .6 .8
0 I I J I
-.4
Cy_
(rad -t)
2 5 3 8 4 6 9 " _,,_
-,8
SL JETSTAR
382041b
- - 20 O00ft
Body Axis
----- 40,O00ft
.2
_-" -"_(_- -_ Cn B
.I
Cn_,
Mach
Cj_
• 2 .4 .6 .8
(rod't) 0
I I I I
c_
:2
Mach
00 .2 .4 .6 .8
I I I I
-.2
C,_p
(rad "I)
-.4
JETSTAR
SL
-.6
38204. Ib
..... 20,O00ft
Body Axis
--- ---- 40,O00ft
Mach
0 .2 .4 .6 .8
0 I i I I
-.04 -
Cnp
(rod "i)
-.08 --
-.12 -
S L JETSTAR
• 20,O00ft 38204 Ib
---'---- 40,O00ft Body Axis
.2
C_r
C,t r ,
Cnr
(rod "i )
I I ! I
.2 .4 .6 .8
Moch
-.I
Cn r
-2
SL JETSTAR
20,O00ft 58204 Ib
ill
40,000 ft Body Axis
.08
CYa a
(rod -I )
.04
I I I I
O0 .Z .4 .6 .8
Mach
Mach
0 o
,2 4, ; 8,
Cns a -.01 --
(rod -l )
-.02 -
8a is deflection of aileron
on one slide only
Cy8 r
2 5 3 846 ""_,o ._
(rod -I )
I I I 1
O0 .2 .4 .6 .8
Moch
Mach
.2 .4 .6 .8
0 o
I I I I
-.04 -
Cn8 r
(rad "i )
-.08 -
' SL JETSTAR
382041b
..... 20,O00ft
40,O00ft Body Axis
.04
C_8 r
(rod "l )
.02
0 I I I I
0 .2 .4 .6 .8
Mach
o N C r,J C3 C_ • t_ _ t_ t _ ,-< _ N • • C: O C _-
h Lr -.t ¢_ _ _ • f_ c _ r_
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in
g
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El
I
H
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• _ o ': "
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_7 _ oo
I vw v v !
o _ ,_ _ r_- _ 0 a0 oD e_l o oo O0 _ • o • , • I I ! * I w_ I ÷ _0_ _o_
_o_
¢ , •
_ " _
, T
I I I I!
w + o f_ ,-, O_ oO .:I-
o_
• o • , I' e_l , , I I I I I vv _v ,..-i A _K e'3 _.
O- 7y " _L
o _
q- _j ,...4 ,-.4 (_ ,...4 !
I_ 0 G'I i_- _ ,-I _ 0 • I_ 0" o 0 _ 0_ _ o _7' _ _ N 0 ,-_ r_ r_ i-4 E-I 0 0 _" .rq _-u h- I 0" 0 0" (_J ,_ ,'_ 0
E-I ©
0 0 fW
M
G" r_
A
i G" ,0 _ 0 N -0 _ _- "J" N _.1 L_"I 0 u_ u r _- _ _ ,._ _ (%1 r,J (_ • _ .-4 !
u2 o_ "_ a. ,JJ 1- _ :I[
J_S_4J_ DATA SO_CES
Myers, Russell H., Jr., and Carl S. Cross, Jetstar Flight Evaluation,
Air Force Flight Test Center Rept No. FTC-TDR-62-24C-140, Feb. 1963
Clark, Daniel C., and John Kroll, General Purpose Airborne Simulator--
Conceptual Design Report, NASA CR-544, Aug. 1966
Flight Manual_ USAF Series C-140A_ C-140B_ and VC-140B Aircraft,
T. O. 1C-140A-1
Jetstar Handbook of Operating and Maintenance Instructions for USAF
Models C-140A and VC-140B Aircraft, T. O. IC-140A-2
SECTION VIII
SECTION VIII
CONVAIR _OM
CONVAIR 880M BACKGROUND
The Convair 880M is a medium-size four engine jet transport. Longi-
tudinal and directional control consists of servo tab deflected elevators
and rudder. Lateral control consists of servo tab deflected ailerons plus
hydraulic actuated spoilers.
Elevator, aileron, and rudder transfer functions are in terms of
respective primary surface deflections with tab 16sses included. Although
the control system diagram shows a lag in the spoiler actuator, none was
used in computing transfer functions.
0 0 0 •_ .r-I +_ 0 0 0 ,-I O ID -O o3 O .,-t +_ -,-I .r-t ,--I _d
I I
_D
0 0 0
I
0 0
, ©
0 _ 0
.H
0 "- O"
I
i- cO cO °H O rD H H (1) O .,-t -O .r-t O -r-t C_ _ 0d 03 O,1 O
I -o 4-, -o
• ,-I _-, 4.0 4o 4o / q-t _ q-I I I O O O O
, , _
rD _ _ O M
_io_o o o
0 0 0 0 (D LZh 0 0 O O O 0 Oh 0 0 0
ff_ (2) (2) O ®° _ _o
O O m i1) _ 4._ r-_ m O II ii II II II H ii Ii
d_
d_
N _ N _ _ 1---I H H "7, O i < O a0 co O o rj i H H H > -H !
o o _-.¢
0 odm
I_1 II tl _0 -Q Io
CV-880M
PITCH AXIS
)
_-- 8te (rad)
-Ch8te
Be(rod)
Oh8 e
ROLL AXIS
8Sp (rod)
I +.Is
t -I.425
8to(rad)
8tac
_--- Ba(rad)
YAW AXIS
,.._+ t<
b
(Sir -Sr)c _ St, (rad)
L
8r(rad)
i':':kg',kre '/! i_ -3. CV-880M Control System
TABLE VIII-I
CV-880M
Longitudinal Non-Dimensional Stability Derivatives
Flight Condition I 2 3 4 5 6 7
Configuration L PA
Speed 134 KTAS 165 KTAS .6M .86M .7M .SM .86M
Altitude SL SL 23K 23K 35K 35K 35K
_o (Deg) 5.2 4.3 5.3 2.8 8.3 4.7 4.0
C L 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
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)
7.62
7.92 7.72 6.76 6.37 7.51 7.5
CLq (I/rad)
-4.6
-4.5
-4 .I7 -4 .I3 -4 .I6 -4.66 -4.4
Cmc_ (I/rad)
-I 2. -I 2.
-I 2.2 -I 2 .I -I I .5 -I I .8 -I 2.
Cmq (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) 0.055 0.0532 0.0482 0.0352 0.0508 O. 047 0.0450
(I/rad) --0.164 -0.159 -0.146 -0.11 -0.155 -0.14 -0.134
CmSte ( I/rad) -0.287 -0.285 -0.297 -0.343 -0.31 2 -0. 335 -0.352
chste
TABLE Vlll-2
OV-880M
Lateral-Directlonal Non-Dimensional Derivatives
(Stability Axis System)
I 2 3 4 5
Flight Condition
L PA
Configuration
.SM •S<,Iv
13 _ KTAS 1 65 KTAS .6M .86M .7M
Speed
35K 3!_X
Altitude SL SL 23K 23K 35K
-0 .UI25
-I .01 5 -0.877 -0.788 -O .81 5 -0.807
-0. _77
-0.239 -O.196 -0.163 -0.145 -0.181
C_B (I/rad)
o .133
0.129
0.145 0.139 0.128 0.122 O.129
c% (1/_d)
-o.31 2 -0.294
-0.395 -0.381 -0.329 -0.243 -0.341
C% (1/_d)
-0.011 -0.oo_
-0.087 -0.049 -0.0173 -0.0031 -0.023
Cnp (1/_ad)
o.146
0.153
0.309 O. 198 0 .I46 0.088 0 .I8O
C_r (l/tad)
-0 .I 65 -0.165
-0.21 8 -0 .I85 -0 .I63 -0 .I89 -0 .I66
Cnr (I/tad)
0 0 0 .O01 9 0 .O745 0 .O044 o .00775 0.00979
Cysa (I/rad)
-0.0479
-0.0487 -0.0384 -0.0466 -0.0452 -0.0479 -0 .o_97
C_5 a (I/rad)
o .oo8o3 O .O0975
0.01862 0.0172 0.00746 0.01061 0.007
Cn5 a (I/tad)
-0.2005 -0.258
-0.607 -0.481 -0.236 -0.258 -0.2233
Ch5 a (I/rad)
0 0
O 0 0 0 0
-0.0075 -0.0071
-0.0072 -0.0056 -0.0068 -0.0068 -0.0071
C_a (I/rad) (llraa)
0 0
0 0 0 0 0
Cn6ta (I/rad)
-0.235 -0.213
-0.249 -0.227 -o .21 5 -0.21 25 -0.226
Ch6ta (I/rad)
-0.01 89 -0.01 75
-0 _078 -0.031 5 -0.0189 -0.0175 -O.0189
Cyss (1/rad)
0 .o339
0 .o805 0.0405 0.029 0.0281 0.0324 o .0329
C_ s (l/tad)
o .01004
0 .o258 0.01 29 0.011 46 0 .oi 09 0.00975 o .oo917
Cn5 s I/rad)
o .I84
o.I 685
0.223 0.21 55 0 .I904 0 .I394 0 .I99
Cy_z ' I/rad)
0.01 87 0.01 93
0 .O207 0.0226 0.01 76 O .0183 0 .O1 65
C_6 r I/rad)
-0.0644
-0.0756
-0.O9_)5 -0.0958 -0.0845 -0.0534 -0.0848
Cn6 r I/tad)
-0.1491 -0.1924
-O.2140 -O.2125 -O.1626 -0.1844 -0.1345
Ch_ r 7/raa)
0.0316
0.0355
0.0493 0.0467 0.0374 0.021 5 0.0404
CY6t r (llrad)
0.0020
O. O01 9
0.0021 0.0027 0.001 6 0.001 8 0.001 4
C£Str (I/tad)
-0.01 1
-o.o13_
--C, .020 -O .019 -0.01 5 -0.0077 -0.01 6
CnBtr (1/rad)
-0 ._C,5
-o.267
--0.25P, -< .N_;5 -0.267 -0.254 -0.27
C" (1/rad;
nst r
O_ P'- h= I'- ÷ ,,,F* d- O • 0 0 W _ ILl U'_ 0 0 0
c_ 0_ _ o o o
I ÷ ÷ ÷ _r_ o 0 o
o • j _ o o -, _ ,- ._i 3 o
• ,'-'4 0 0 0 _ 0 _ 0 _ ,'-4 ___ 0 r_q
g • _ •
o
I
o
o
! ÷
H
H
pq
4- ÷ ÷ tO, 0 0 0
= • o o o
• _ ,-4 ,-d N • _ _ I_ i_" 0 _ ",I" ,-I • • I
o
H +
I
_J
..-i oJ I_- _I WD v r_l 0 _ _1 ',,t 0' _._ 0 I I
o _ _ _ .o _ .t _ -_ _ o c_. -1- _ _ _ w
r-- ¢v_ cO 0 0 0 0 ,D 0 0 • 0 _ * t_ • 0 0 C _ 0 * 0 0 {_ 0 .-_ 0 .-4 P-- • 0 I" • ." l '7' 7 • • I' I' I" I" _' 0 4 _ _ {_ _ ,--I I'_ 0 I / w
o o_ _ _ _ _ ._ o, _o _ _ _ ._ _- _
I_ 0 t _" 0 O_ c,,I C_ t_/ 0 tP, -- ,-i 0 I_- _f_ c¢_ t'- 0 0 0 0 _r_ 0 0 -- 0 -,t • 0 . 0 0 0 _ • O O O • • O O r _ o _ _ .-.4 o ,..-4
El
• ' • I * " I I " " " I I I I I e,,,i o _-- ,,1- ,o ,,,,, ,,,7- _ uo o _ _ _ co (,_ I I
I:I
N CO O O O O O _ O O _ _' CO • O • O O 0 _ • O • O • • O O .-_ O ,._ O_ 04 O _ t _- • I " I " " I I " " ' I I I I
H U_ E_
H
H Cc_
H
¢_ 04 ,O O O O O _0 O O (._ O _ • _ • O O O _ • 0 " 0 • e 0 0 t._ _ _ .-e 0 '--_ r"-
H
• I " I • ° I I " ° * I I I I u_ _ u_ ..I .O tlJ _r_ 0._ ,0 tZ_ O _I" _ u'_ o_ p.,. _ O U'_ _ o,.t UJ
CO
-_ _ _ o _ c_ _ _ o o o o _ _ .; -_ o _, • .. CO • " O " O " ' O _--i
CO
I I • • I I I . I I" I I I' I" 11 _ . I- "r "r I,I.
0 _n,4 ,.n
"2
_,._ 0 ,,,.-I ¢10 O_ • o e0 o.
I.t'_ _", laO h- _00 oOLt_
_o °
• • e,,,,,4 •.--4 It- I_- • 000 oeq .40 .
I e, I I ÷ _o _0_ 0 _ ,.,,t 0". ,,,t _0 _ O0
.: o,,, 00_
i I I @ i.n
_o
_0_ I'-.- .-4 f.,..- _0_ _0_ _0 ,.=._ ¢0 h- O0_J 0_00 .0,,I" O0 _00_.
,.,_ ¢,..) u -. e._ I ! • !
!
I".. u_ _) u,_ r.- r,,/ OON e_ O_ ¢0 0_0 O0 eee N ! • • I !
I f,.- t_l ,o
H ._ ,,o
_0_" _00 _000_ I I I I
_o_
_" _o.i
C) ,'-_ ,0 r._ o,i • _0 _ • o • N • " t_ ! I I I ÷ oo_ 0_ _0
GO
I ,-4 _N • 0 • e_ee I ! !
Z _ _ Z .b- • ,I ,o v I ,o I t-- I Lul_- wo _o c_P- uJ .-_ (_, _ _-I ¢_ c. _ P- _o0 oo_o o ,.._ _ _o_ OOen 00_ o_ • ...-4 • I I I ° I" I ,t- -.1- OC0 I.U ,5' O" I_ ,.0 c'x_,,_ u"_ u".
o r_ rv_ t_ -.1Lr_ O_ L -_ P'- o .-_ O0_r_ OOe _'
ogo._
• I I !
÷ p- -.t I o Uj _r', wD .O co cf_ _r% erl D.- OOO_ OOU_ 00_ OOCxl 0.I" • -_ u u ,,T
!
I!
4- ,4" wE} -,1" P-- <._ ,o uj ao -_" u_ (M _ ,.._ co co P- aO _ 0", ,..._ 0_ O [0 L) .--_ 0 (M _u' 0 00,I" 00_ (%1 ._-_ Oe'N • I I I I I ,o I LU r-- O_ _rM _o_ LU r..} _o
-'o N_; U_N
cO CP. ,4- L._ _0_ Cxl ,ID 0_ 00_ oO e,a 0_ ¢0 * , o • ,.--i .I !
II I
T
!
CO U.J O, _ CO
_oo UJCO0
(xl P.- OOU_ CO • • • I I I w_ I!
!
+
co
,0 4"
co
I l,iJ u-, co _0_ 0_ _o_
8E _
co • • ol0e
_,'"
I I !
_N _N E EJ Z ,-4 ° 0 I ÷ CO _'_ 0 _ ,_ WD u_ 0 ,-.4 0 _ 0 QO I c0 I" 4.
,.-i _r_ _ 0 _ 0 _0 I ,-.4 uJ O] !
v v l.J _J ,,,1" _._ D'- _ wD l_J -- wD oO i_i a) !
H v
ca
U ur_ i_ _ 0 U_ 0 _ h- • a I ,0 O" N ..J ,,I" _" • ,4) I 0 I f_ o_ 0 _ oO ,,I" _n • -q -J 0 ,,I" ,0 • _ I _, CO 0 • _0 l OD I
- G
p.. -_ w _J I,.9 I/_ u.; _'_ C_ ,_ _x; 0 14.. L5 _ IK CI-- _- _ N r _ r'- _ CO _ 0 • CO _t _ 0 _ 0 IX) " I" O_ P_ ,-I • • • 0 _t • • • I I I• I I I" I" O_ 0 $ _0 • i. _ _0 "_ I" I" • |, 0 • N • • . I" I I I 0 -.11" <r co N o_ _ _ o o 0 N ,DO _ f_-
• u_ _n _ . . • o N • • • -
I I I I° ! I ' / I
I
e_l (X) _ _ 0 • * 0 _" I_, O _'_ 0 * * I
N <) _ o • _ _ o _" ._ o _ o _0 0_
I I I i I ' I I _'_ _0 _ _0 _ e_l _ _0 N _ N 0 _ I _- 0 I I I I I I I
IX)
IX)
I N O
SS_
0_0 * 0 i_- O_ um *,--4 • ,.'tO • ...-_ '4" • • I i ° I I" 0 0 er_ • 4" ¢ u", rr_ (_ 0_ ti_ c_ 0"0_ • ,00_ • O_0 • 0 • *_ 0 . .c_ I I I" i°
°
t,t_ ,4,- r,,_
rq .4_ 0 ,"_ o.o_=,o
• I I !
o_to, _o _.
• c) .-_ .
• !
I I" ....
_ut NO ...'-4 • I I I I I" C0_NO -'_o 0 I'll • • NO ..=_ I I I !
I 4.
N _ ,,o o', g'_ ! I' I _E _w v ZZ Z Z o _ ,-4
_o_
lJm_ _0_ P-- i_0o _o_ o_o oo co0 ° _ ° °,,, o ° ,._ I" I I I" ..s
o~_
o 0_
r_ _ Z _."_.
_0 _o . o ej l_J °,+, _°° I I II • I I
t_m r,j i._ f,el _o
I_0 co 0 _ , l_j mm • I I + II I I
+
H r.- °_ • o • I I I II I I H _ q_ F7_ H tl _,_ I-+ t:" ._ F_ c" , I'_ u'_ 0o um _0 <N P_ p_ oo ,_ O) • • o I_ eu I • l I I I
_o_
..A'_ 0_0 .-_,0 _ ,,ID rex ,-_ • ,,-I .4 + ,-i eq ,0_ I I I I II I o e_
_ "o
_o_
e_R_o
_0 o • ,-'4 o _ .-4 I,_,0 I ZOOWW v Z Z 0 0 _ _ _ _ _ _ _ _ _ 0 _g_lg.._O_O_._ v I_ + I_ 0 + _ , I_ I'- p I_I f J + 0 _ _ _- f_ CO . aO | . . -- 0 O 4_ ,--4 _ • I_ I o u_ _ p_ <%j _ p_ ch _p o p_ _p _ r- ,+ _ l + q • ir Q U' w _ • +rt I I P '4" _ _1 f_ I CO _0 00 0 P" P',I +1 N ¢O • • I + -- • • O • 0 _ , v oI_ 0 fJ" r,_ _ .,1+ _ .-w _
P
r_l _ • " I " I I I I U 0 .+ • I"I (P, ..1" wD O, co ,,41" _ P,,,. _ _, .P' C) ,..,I ..,i" w_ N ! _ ,-_ _ wO 0 c'% P"- ",+" 0_ 0 !
f_ 0 _ _J P- N ,4" f_l urs 0_ e _ h- • -+ _1 o N o l u x _ ,-4 NO' ,--4 ,_ ¢_1 10, I_ l U • • I • • • _ ,-.4 _ _ 0 • -1" I iii <_ UJ r LU _ r, w _ _ )¢+ LIJ U.J g+.l n. -. .J 0 _ _ I _ ID rJ LU _ '_ _ IJ +-+ 03, I-- I- I- I_ _ nf <_ _ I +.J ..4 1',,4 C) es _1 ¢'_ ,,.,4 _ O. 1_ I_. I_ _. "_: I_ I_ _,. ,'_
CV-880M DATA SOURCES
McNeill, Walter E., Calculated and Flight Measured Handling-Qualities
Factors of Three Subsonic Jet Transports , NASA TN D-4832, Nov. 1968.
Brooks, Peter W., The World's Airliners, London, Putnam, 1962.
_ECTION IX
BOEING 747
BOEI__G 747 BACKGROUND
The Boeing 747 is a very large four-fanjet intercontinental transport
designed to operate from existing international airports. To obtain the
necessary low speed characteristics the wing has triple-slotted trailing
flaps and Krueger type leading edge flaps. The Krueger flaps outboard of
the inboard nacelle are variable cambered and slotted while the inboard
Krueger flaps are standard unslotted. Longitudinal control is obtained
through four elevator segments and a movable stabilizer. The lateral con-
trol employs five spoiler panels_ an inboard aileron between the inboard
and outboard flaps_ and an outboard aileron which operates with flaps down
only on each wing. The five spoiler panels on each wing also operate
symmetrically as speedbrakes in conjunction with the most inboard sixth
spoiler panel. Directional control is obtained from two rudder segments.
Information for this aircraft was obtained solely from a 747 simulator
description (Boeing D6-30643).
2;
(1)
o
o X
.i.Ii (1)
co 4a
ii1
o
o
gh
®
o
h
i1)
o
,d
_ _ o
I
c_
I I
0 o
o _ cu
0 0
_J
O • • 4D
0 0 or) i +
.r-I
_J
o o
cf "_ o O
ea
4_
b8
.H
_H
P_
b-
b-
I
i
.H
#
b9
_J
.H
o
O
O
-i-4
O
GJ
OJ Od Od -ID
-ID +_ 4D r._
,1-1
r_ _H CH
I , I bD
o
o
.,-I
rq r-I
kO
4D
r_
O
kD _0 kO 0
.-a
O
_1 0 0 0 ,--
o
.H
I-i
I"4
o Io X
O
0 X X X
0 ly_ Lr_
_, Ckl L"- L¢_ _ OJ
lag
• CO
u_ ,-- h_ _ 0
4D
cO
II II II fl II
CO a_ _,D ._j "_I-- ° pr_ a_ f_ ,-I a_ lqr)_ !
.J
G
_ o_
|| II I| b
B-747
PITCH AXI_.
_eSAS
I
-2
Fcc (Ib)
K
57.3 P" 8e(rad)
_cc(deg)[
4° k
s / J"
e,"
x
,° t
[fj
I I I
o
,-t
0 .2 .4 .6 .8 1.0 0
Mach
4_
ROLL AXIS
_t P I I r; I
F w fib)
.161 57.3
Sw(deg) I .5 H
(1) b._
YAW AXIS
8rsAs(rad)
___ 7.15
FpED(Ib)
43.5 57.3
I }SPeD(in) I
B-747
YAW SAS
I 5.05_
r G (rad/sec)
I(s,.368)(s 3.68)
Flaps Down
-.688s
s+.368)(s+3.68)
_iNs(rad)
-34.5s
(s+lO) 2
r =r
*INS: IP dt
(Gyro and INS Aligned with FRL)
Figure IX-4. B-747 SAS
TABLEIX-I
Landing Configuration Non-Dimensional Derivatives
h : sea level
VT o = 131 KTAS
mo = 8.5 °
5s = -6.3 °
Longitudinal Lateral-Directional
C L = I .76
Cy6 = --1.081rad
CD = .263
C_6 = --.281/rad
CL_ = 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
5a = total deflection of right inboard aileron plus left
inboard aileron with the effect of outboard ailerons
included
TABLE IX- 2
Power Approach Configuration
Non-Dimensional Derivative s
h = sea level
VTo = 165 KTAS
co = 5.7 °
O
5 s = --2.1
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
C_r = .101/rad
CL& = --6.7/rad
Cm_ : -3.2/rad Cnr - .30/rad
C_5 a = .0461/rad
CLq = 5.4/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
i
SL B-747
_m _m
20,000 ft 636600 Ib
mmm em mmme
40,000 ft .25 _"
Flexible
k
i
k
k
m
I0
k
GO
m
(deg)
4-
2-
I
o I
4I .6 " .8
1.0
0 .2
Mach
,_i_, ° " _- ._
I
I
0 I
1.0
I" .4..""_ .6 .8
.2
(deg)
Mach
-2
-4
_o.
u
o
I I I I
m o. o.
_0
b- _D
i P0
m_p
O0
O0
qQ o.
_00
u) od ,_'-
li
_5
I I I I
o. o _ c_
Od
_1
o
SL B-747
20,000 ff 636600 Ib
40,O00ft Flexible
CL a
(rad-')
4-
l
2-
I
I I I I
0 o
.2
.4 .6 .8 1.0
Mach
I
CD a
(rad-')
l
l
.8 m
, \
.4-
I I
0 o
.2
.4 .6 .8 1.0
Mach
Mach
.8 1.0
0 2_ .4 .6
7------V---
0 ,--------T-------T-------_
B - 74T
636600 Ib
-.4 .25E
Flexiable
:8
Cm a
(rod -j )
-I.2
-I.6
Mach
.Z .4 .6 .8 1.0 _
I r I I I
-8
Cm&, Cn_q
SL
(rod "t )
.... 20,O00ft
-12
.-.. -..- 40,O00ft
Crnq
--------®. ]
J
I m
CL M
I
.2
Mach
.4 .6 .8 (_ 1.0
!
SL B-747
20,000 ft 636600 Ib
40,O00ft .25
Flexible
.3-
I
CD M
/
#
.I m
//
j ®_/ ,
l 1
0 o
.2 .4
.6 .8 1.0
.4
.2
Cm M
I "(_._ t II I
-,2
-4
B-747
" SL
20,000 ft
--------- 40,O00ft
.4
.3
CL8 e
(rod -= )
I I I I I
O0 .2 .4 .6 .8 1.0
Mach
.4 .6 .8 1.0
.2
0 0
I I I I
-.4-
/
I
-.8 -- I
/
I
Cm8 e
/
(red-I )
y '
-I.2 -
." 7/
-I.6 -
Mach
00 .2 .4 .6 .8 1.0
I I I I I
-.4
Cy,o
(rad "I)
-.8
B-747
SL
-I,2
20,000 ft 636600 Ib
40,O00ft Flexible
Stability Axis
.2-
Cn_
( rad-I )
I
I I I I
O0 .2
.4 .6 .8 1.0
Mach
0 .2 .4 .6 .8 1.0
1 I I
(rad "=)
/
\j
-3-
SL B-747
636600 Ib
20,O00ft
40,O00ft
Stobility Axis
Flexible
Mach
.2 .4 .6 .8 1.0
I I I I I
-.2
Cyp
(rad "l)
-.4
.O4
I
I
Cnp
.2
1.0
(rad "i)
-.04
-.08
SL B-747
20,000 ft 636600 Ib
40,O00ft Stability Axis
Flexible
.3-
C_ r
\ l
(rad-')
I I I I I
O0 .2 .4 .6 .8 1.0
Mach
.2 .4 .6 .8 1.0
0 0
I I i I I
-.I--
-2--
Cn r
(rad "l )
-'.3--
--.4 --
B-747
SL
636600 Ib
.... 20,000 ft
Flexible
----- 40,O00ft
.016
.012
.008
! t
t
t
DO4
i I I I I
0 0
.8 1.0 .6
.2 .4
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
.! 0
(rad)
.2 .4 . 1.0
Mach \
-.004
SL
B-747
6366001b
.... 20,O00ft
"-------- 40 O00ft Flexible
I
CY8 r
(rod "l )
I I I I I
O0 .2 .4 .6 .8 1.0
Moch
.2 .4 .6 .8 1.0
0 o
I I I I I
-.04 -
Cnar
(rod")
/
-08 -
-.12 -
.02 -
O0 .2
.4. .6 .8 1.0
Mach
co eo <o O 0 _-_ 0 0 I¢ rt D- C I_ "_ t _, 0 _ C C
• _
¢o tc, t_ c_ .-_ r_ ,,t r - r-I I_ I'M 03 ,-_ r,J ¢,j I 0 r_ _, 0
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24_
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.
SECTION X
SECTION X
C-SA
C-_A RACm_ROU_D
The C-5 A is a very large military logistics transport powered by four
turbofan engines. Longitudinal control consists of elevators in four
sections with an all-movable stabilizer for trim, roll control employs
ailerons and spoilers, and yaw control a conventional rudder. All control
surfaces are irreversible.
A bobweight is used in the longitudinal feel system. The effective
bobweight position is assumed to be at the pilot.
The C-5 A employs stability augmentation about all axes. A description
of the SAS is not included here.
.rt b_ °,-I CH Q.)
°H 0 rO ,--I m •_ .rt _ 4a 4_
,)
)
o r-I r_ 4u cl ,'-t "d c,l
r-I I I
_1
0 0
0 0 0
o o
4 _ .H
d o
I
i ®
X_ b9
I
,.-I LFX I
"7
(1) ,rl .M 4_ OJ OJ 0,1 OJ LF_ _ -I"a 4-_ CXJ _0 ___ _ r_ 4a OJ I I I c+_ I r'-I _n _a m ,'M ,_ 0 0 0 '_0
o _ _ _o_o%_o
_, _c_ Io 0 i _ 4a _ -I _ 4_
X X X X _- _ ×x×_
C-- 0 X _ _ 0
o '._ _
_ II II II II II _._ _ II II II II It 4-) r--I aJ I
&
i X ¢J
D
b
N
.J
C-5A
PITCH AXIS
8esAs (deg)
I
Fcc('b)---_;)_"
I 8cc(in)_l -2'92 t _-'(_)_''se(r°d)-I 57..3
K
32.2 a z at _B
8.3 _. B
i II ?"
20_
/
KIlbl
I0
.._/,/ o,ooo,,
40,O00ft
I I I 1 1
O0 .2 .4 Moch .6 .8 1.0
ROLL AXIS
8asAs(deg)
8w(deg)
I
8a(rad)
Fw(Ib)
KLAT
Config. K LAT
8sp(rod)
Cleon .121b/deg
PA .155 Ib/deg
YAW AXIS
8rsAs(rad)
_ 63.5 -I 57.3
F'i_re X-3. C-_DA Control System
TABLE X-I
Power A_&ch Non-Dimensional Derivatives
h = sea level
VTo = 247 ft/sec = 146 kt
c:qO = 2.7 °
Longitudinal Lateral-D irect ional
(Stability Axis )
C L = 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_ = --.827/rad
Cnp = -.098/rad
Cm&= - .3/rad
C_r = .290/rad
Cmq = --23 . 2/rad Cnr = --.293/rad
CLUe = .385/rad
Cysa = --.O044/rad
Spoiler
Effects
= --1.6/r d
Cnsa = .0091/rad
Included
C_sa = .089/rad
CYSr = .211/rad
Cnsr = -.106/rad
C_Sr = .0209/rad
C -5A
654562 Ib
Flexible SL
m
.... 20,000 ft
_- _ 40,000 ft
m m
IO
(deg)
4_
2_
I
I
.4 1.0
0 .2 .8
Mach
r-
U
I
I I I
OJ
O0
O0
o O
tl
i 0
U
iI
L,. _-
j .lj o
.a
0J
i LO
(-) _0
OJ
I I I I
Q _ _ _o
J
C-5A
654:562 Ib
Flexible
SL
- 20,000 ft
40,000 ft
_
5--
4--
5--
2--
I --
I I I I I
0 .2 .4 .6 .8 1.0
Moch
1.2 --
CD a
f_
,8 --
(rad -I)
.4 --
I
o I
0 .2 .4 .6 .8 1.0
Moch
Mach
0 .2 .4 .6 .8 1.0
i I I I I
C -5A
, SL
654362 Ib
.30 E --- --- -- 20,000 ft
-.4 --
----. - -- 40,000 ft
Flexible
Croci
=-.%
(rad -i )
.\
-1.2 --
t
Mach _..,,-._
1.0
.2 .4 .6 .8
0 o
I
I I I I
-4--
Cm_ ,
Cmh
Cmq
(rad -I )
-12 --
-16 --
Cmq
-20 --
-24 --
-28 --
Moch I_
1.0
0 .2
.4 .6__-'L-_._.8
-__-- '_'_" I
C-5A
CL M
654362 Ib
-I.0 --
Flexible
-I.5 --
-2.0 --
-2.5 -
-3.0 --
SL
D D--,,. 20,000 ft
40,000 ft
.12 --
.10 --
CD M
.08 --
.06 --
.04 --
.02 --
I I
0 .2
.4 .6 .8 1.0
Mach
.8 n
o6 n
o4
Cm M
.2 m
I
I
.2
1.0
-,2
C -5A
654362 Ib
SL
Flexible
-----.,-- 20,000 ft
------- 40 000 ft
CLSe
(rad "t )
,J
t I I I I
0 .2 .4 .6 .8 1.0
Mach
0 .2 .4 .6 .8 1.0
I i I t 1
-,4 --
CruSe
_=8 J
-¢
(rad -I)
-I.2 --
Mach
.2 .4 .6 .8 1.0
1 I I I I
C-5A
654362 Ib
-.4
Stability Axis
Flexible
c_
-.8
(rod -I )
-I.2
SL
-- -- -- 20,000
--- - -- 40,000
.I
____--_:_: _o=. _,, c._
I I I ,_ I
.2
.4 .8 .8/ 1.0
Mach t
(rad "l)
C_
-.I
-.2
Moch
•2 .4 .6 .8 1.0
1 I I 1 I
C -5A
654562 Ib
-.2
Stability Axis
Flexible
C_p
-.4
(rod -I )
.----.(_... _ I,_'_
-.6
SL
------- 20,000 ft
---------- 40,000 ft
Mach
0 .2 .4 .6 .8 1.0
I 1 I I I
- .04
Cnp
//
- .08
(rad-')
- .12
-.16
C -5A
654562 Ib
.50 E
Stability Axis
Flexible
.4--
,SL
• ----.---- 20,000 ft
--------- 40,000 ft
\
\, C_ r,
Cn r
°2
(rad -I)
C_ r
t I I l
.2 .4 .6 .8 1.0
Mach
-t2 -- _,__,___j_,,L_" Cnr
SL C -5A
.... 20,000 ft 654326 Ib
_----" 40,000 ft
.04 -
C_.$o
-I
(red)
.02_. --
I I I I I
0 I
.2 .4 .6 .8 1.0
Mach
.02
.01
Cn_ o
-I 0
(red)
-.01
-.02
/ ]i I _ tf
/
-.03
Mach
.2 .4 .6 .8 1.0
1 I I I I
-.002 -
-.004 -
-.O06 - 2 5 5 6 4 87 9
C-5A
6545621b
.O8
%%% ,.,,
.O4
I ........ 1 I 1
1.0
.2 .4 .6 .8
Mach
SL
20,000 ft
40,O00ft
.O2
C n 8sp
(tad -l )
.01
o [ I I I I
0 .2 .4 .6 .8 1.0
Mach
.2-
Cy8 r
(rod -j )
.l --
I I ] I I
.2 .4 .6 .8 1.0
Mach
Moch
00 .2 .4. .6 .8 1.0
I I I I i
-.04.
Cn8 r
(rad "t }
-.08
SL C-5A
20,000 ft 654..362 Ib
40,000 ft Stability Axis
Rigid
C,ts r
O0 .... I!0
Mach
_t" _ ,,1 C_ ,0 ,,t er, f'_ .--4 ,_, ,,1" ..-4 tr, • !
I c3 0 0 0 • .--, C) 0 _7 _3 * " • O0 r_ _ I _0 I O' "4. ÷ 4" 4- f_ 0 0 0 0 "4 0 * * O" 0 UJ ill UJ 111 • * 0
d 2 .. o o __
I ,0 • • • • I O_ 4- 4- + ÷ _- 0 0 {3 0 0 • • (_ 0 UJ W W W ,--4 . . 0 0 0 U'_ ,,0 .-4 _ 0 O0 CO _ ,0 O _ 0 _ er_ 0
,,I-
I • .'-* 0 0 u7 vll ,,0 _ _ 07 4- _ ,....4 ,40 ,,,,1" _ _ O" t.,"x
II
I _D " * ' ' I I • o.} CO _ P" O_ ÷ 4- 4- "_" t-- 0 0 0 0 0 • e _" 0 W LU W IJJ r -_ • * 0 I • CO 03 eO I _- {3" 4- 4- 4, + I _- 0 0 0 0 ,_'_ fq _ O" -4r r_ I_- ,--i ,0 ,_ • t'_ _ • 0 _ co _ e,_ ,4 !
• 0 _ . . I |
o
_" C. I _ -,1" _£ u', I I I I " ° I° I" I ° I" * _" _ _ _ "_ _0 CO I 0 r_ 0 N C, I _ I_ _ _0 C_ _ _ I.L LL LU
c _ _ _ c _', _ ._ _ • o c o _ -_ _
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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
SECTION XI
SECTION XI
XB-70A
XB-70A BACKGROUND
The XB-70A was originally designed as a weapons systems with long range
supersonic cruise capabilities. The two aircraft built became research air-
craft to explore SST-related problems.
The two XB-7OA's were identical except that the first airplane (XB-7OA-I)
had zero geometric dihedral while the second Lad 5 deg geometric dihedral.
The first airplane is considered here.
Pitch control employs interconnected elevon and canard surfaces except
in takeoff and landing where the canard is locked and a fixed canard flap
is used. Roll control is obtained through differential action of the elevons.
Yaw control is provided by rotation of the vertical stabilizers about a
45 deg hinge line.
The airplane is equipped with stability augmentation in all axes.
Data shown here is a composite of many sources. The object was to use
flight test data where possible.
o .,-i 4_ o r.D bO .,-i r_ b- i H
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XB-70A
PITCH AXIS
(_eSAS (red)
I
.025s z +.35s+K
i -
See Fig.
PA o/t Clean
Effective l
Config B Bobweight FS i B
Clean I0 Ib/g__852/2 j-2169ft
PA 14 tb/g 1479.2 I0 96ft
-- a z at 1B 8c(rad)
_ SL
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I
YAW AXIS
8rsAs(rad)
8r(rad)
FpE D(l b)
GDIR
I I _PED(in) KDIR 57.:3
Config. K DIR G D.R
Gear UP 281b/in .96deg/in
Gear DN 3lib/in 4.0deg/in
Figure XI-5. XB-70A Control System
XB-70A
PIT.___CH SAS
8 (rad/sec) -_
' ' 1 34.8ft Clean
az at -_x = 36.4ft PA
Normal Accelerometer at F.S. 1174
8¢¢(in)-_-4'65 }
ROLL
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|
p(rcd/sec) -
j _ 8OsAs(rad)
YAW SAS
r (rod/sea) -
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Figure XI-4. XB-70A SAS
TABLE XI- I
Power Approach Nondlmensional Stability Derivatives
h : sea level
VTo : 347 ft/sec : 209 kt
ao = 7.5 deg
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
Cnr = -.25/tad
%q : -1.9/ra_
CL_ e = .46/ra_ CY$a : -.063/rad
c_ a : .042/rad
%_e : -.19/raa
Cn5 a = --.O052/rad
CYSr = .12/rad
C_5 r = -.O018/rad
Cn_r = -.103/rad
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XB-70A DATA SOURCES
Estimated Aerodynamic Derivatives., XB-70 , North American Rept.
No. 'NA-61-707, 29 June 1962
Aerodynamic Coefficients Obtained from Flight Test Data_ XB-70,
North American Rept. No. TFD-67-277, ]4 Apr. ]967
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, NASA TND-4578, May ]968
Estimated Performance Report for the XB-70A Air Vehicle _o. I,
North American Rept. No. NA-6h-660, 26 Oct. 190_
XB-70 Flight Control System Summary Test Report, North American
Rept. No. NA-_6-360, 30 Sept. 19'66
APPENDIX A
APPENDIX A AXIS SYSTEMS, SYMBOLS, COMPUTER MNEMONICS, AND DERIVATIVE DEFINITIONS I. AXIS SYSTEMS .XB,U,P _-_ _ / _-_ Inertial Ref.
YB ,Ys ,V,q _ 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 ft/sec a S_peed of sound in air Lateral acceleration along the y-body axis ay at the center of gravity (positive out right ft/sec 2 wing) Lateral acceleration parallel to the y-body axis at a distance _x and _z from the c.g., ft/sec 2 a_ = ay + _x_- _z_ T Normal acceleration parallel to the z-body a Z axis at a distance _x from the c.g., r ft/sec 2 az = az _xq Normal acceleration parallel to the z-body axis at a distance _B from the c.g.
ft b Reference wing span ib/g B Bobweight gain B.L. Buttock line ft Reference chord ib/in./sec C Longitudinal feel system damping C. ,g. Center of gravity D Aerodynamic force (drag) along the total ib velocity vector (positive aft) FRL Fuselage reference line (parallel to x-body axis) F°S. Fuselage station ib Longitudinal control column force (+ aft) ib Longitudinal stick force (+ aft) FST ib Lateral stick force (+ right)
T
ib Rudder pedal force (+ right ) Fped ft/sec 2 Acceleration due to gravity g Pilot control to surface gearing deg/in, or G deg/deg A-2
h Altitude
ft
I
Longitudinal feel system inertia ib/in./sec 2
Ix_ ly_ I z Moments of inertia referred to body axis
(unless otherwise specified) slug-ft 2 ][XZ Product of inertia referred to body axis (unless otherwise specified) slug- ft 2 The imaginary portion of the complex vari- able s = J ±jc_ rad/sec Effective distance of bobweight from c.g.
_B (positive forward) ft _X Distance along the x-body axis from the c.g. (positive forward) ft Perpendicular distance from c.g. to thrust Sth line (positive for nose-up pitching moment due to thrust) ft _Z Distance along the z-body axis from the c.g. (positive down) ft K Longitudinal feel system spring constant ib/in.
KTAS Knots true airspeed KCAS Knots calibrated airspeed K T Feel system spring constant per unit dynamic (ib/in. )/psf pressure Rolling moment about the x-axis due to aero- dynamic torques (positive right wing down) ft-lb Aerodynamic force !lift) perpendicular to the total velocity vector in the aircraft's plane of symmetry (positive up) ib m Mass s_igs M Mach number M Pitching moment about the y-axis due to aerodynamic torques rpositive nose up) ft-lb MAC Mean aerodynamic chord ft MGC Mean geometric chord ft A-3
N
Aerodynamic normal force along the z-body axis, but positive up Ib Yawing moment about z-axis due to aerodynsmic torques _positive nose right) ft-lb Roll rate, angular velocity about x-axis
P
(positive right wing down) rad/sec Pitch rate, angular velocity about y-axis (positive nose up) rad/sec lb/ft 2
q
Dynamic pressure, I/2 o VTo r Yaw rate, angular velocity about z-axis (positive nose right) rad/sec Yaw rate gyro signal rad/sec rRG S rad/sec Laplace operator, a + j_ ft 2 S Reference wing area TED Trailing edge down TEU Trailing edge up TL Thrust line U Linear perturbed velocity along the x-axis (positive forward) ft/sec Linear steady-state velocity along the
Uo
x-axis (positive forward) ft/sec V Linear perturbed velocity along the y-axis ft/sec (positive out right wing) Stall speed V s Total linear steady-state velocity Cpositive VT o forwaz_ ) kt W Linear perturbed velocity along the x-axis (positive down) W°L. Water line in.
W We ight lb Linear steady-state velocity along the
Wo
z-axis (positive down) ft/sec A-4
X
Aerodynamic force along the x-axis (positive
forward )
Y
Aerodynamic force along y-axis (positive
out right wing) lb
Z
Aerodynamic force along z-axis (positive
down ) lb
(L rad Perturbed angle of attack Steady-state (trim) angle of attack _o relative to the FRL deg Sideslip angle rad Steady-state flight path angle _O deg _a Aileron control surface deflection (includes spoiler effects, etc.) (positive for posi- rad tive rolling moment) Elevator surface deflection from trim _e (positive for nose-down pitching moment for aft surface) rad Trim elevator deflection deg Longitudinal control column deflection from trim (positive aft) deg Longitudinal stick deflection from trim (positive aft) in.
Lateral stick deflection from trim (posi- tive right) in.
Rudder pedal deflection from trim (posi- Sped tive right pedal forward) in.
Lateral wheel deflection from trim (posi- _w tive about x-axis) deg Stabilizer surface deflection from trim _S (positive for TED) rad rad Spoiler surface deflection (positive up) $sp _V Vertical tail deflection from trim (posi- rad tive for nose-left yawing moment) _r Rudder de_ection [positive for nose-le_ rad yawing moment (negative N)] A-5
A Denominator of airframe transfer function
Angle between principle inertia axis and FRL g deg (positive about y-axis) Damping ratio of linear second-order mode particularized by the subscript Pitch angle, fq dt for straight and level rad flight, positive nose up Inclination of thrust line with FRL [posi- iTH deg tive gives negative (--) z force] slugs/ft3 Mass density of air The real portion of the complex variable s = a ±j_ rad/sec Roll angle, (cos eof p dt- sin eofr dt) in straight and level flight (positive right rad wing down) Undamped natural frequency of a second-order rad/sec mode, particularized by subscript Special Subscript Aileron a cc Control column d Dutch roll Elevator e G Gyro INS Inertial navigation system Phugoid P r Rudder Roll subsidence R S Spiral SAS Stability augmentation system Short period sp ST Stick A-6 Special Superscript DIR Directional control system (e.g., rudder pedal) LAT Lateral control system S_mbols Unique to S_eclflc Aircraft ARI Aileron-rudder interconnect (F-4) BLC Boundary layer control (F-I04, F-4) KDIR FLEX Rudder flexure coefficient (F-4) PBF Bellows force parameter (F-4) ft 2 qB Bellows pressure (F-4) lb/ft 2 5 d Yaw damper surface deflection (F-I04) (positive for nose-left yawing moment) rad St a Aileron tab deflection (CV-880M) rad $tac Commanded aileron tab deflection (CV-880M) tad 5t e Elevator tab deflection (CV-880M) rad (_te -- _e)c Commanded elevator-elevator servo tab combination (input linkage) (CV-880M) tad 5tr Rudder tab deflection (CV-880M) rad (Str -- 5r)c Commanded rudder-rudder servo tab combination (input linkage)(CV-880M) tad A-7
3- COMPUTER PRINTOUT MNEMONICS
a. DIMENSIONAL, MASS,ANDFLIGHTCONDITION PARAMETERS
COMPUTER rRINT OUT STANDARD NOTATION_ DEFINITION S S, wing reference area B b, wing span C E, mean geometric chord F/C# Flight Condition number H(_) h, altitude, feet SL Sea Level M(--) M, Mach number VTO(FPS) VTo , true airspeed, knots VTO (KTAS ) VTo , true airspeed knots VTo , calibrated airspeed, knots
w( s) W, weight, pounds
c.g., center of gravity relative to mean geometric chord IX IY Body axis (FILL) moments of Iy IZ Iz inertia, slugs-ft 2
Ix I
IXZ Ixz e, inclination of principle axis with _SI_N(DEG) respect to FRL, degrees Q(PSF) q, dynamic pressure, psf QC(PSF) qc, impact pressure, psf ALPHA(DEG) So, FRL angle of attack, degrees _(DEG) 7o, flight path angle, degrees
LXP(FT) £x, x distance to pilot, ft
up(n)
_z' z distance to pilot, ft ith , thrust incidence with respect ITH(DEG) to FRL, degrees XI(DEG) _o' ith + %' degrees /th, perpendicular distance to LTH(FT) thrust line from c.g., ft A-8
b. LONGITUDINAL PARAMETERS
COMPUTER PRINT OUT STANDARD NOTATION_ DEFINITION XU* X u ]/sec zu* z_ 1/see MU* M_I I/sec-ft XW X w 1/sec ZW Zw 1/see MW M w 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 Z 5 ft/sec2-rad MDDD M5 1/sec 2 DTH 5th Thrust FST Fst Stick force U u fps W w fps THE e rad HD _ fps AZP a_ 1"t/sec 2 at X = Ax _DDD signifies a control surface, e.g., for elevator DDD = DE; for aileron DDD = DA A-9
C° LATERAL-DIRECTIONAL PARAMETERS
COMPUTER P:_INT OUT STANDARD NOTATION t DEFINITION YV Yv I/sec YB Y_ ft/sec 2 LB' 1% I/sec 2 NB' N% I/sec 2 LP' I_ 1/see
_, _ 1/see
_' L_ 1/seo
_' N_ 1/sec
* 1/see ty*DDD Y_ L'DDD I_ l/sec 2 N'DDD N_ I/sec 2 B _ rad P p rad/sec R r rad/sec PHI _ rad t AYP ag ft/sec 2 at _x, _z tDDD signifies a control surface, e.g., for elevator DDD = DE; for aileron DDD = DA.
A-IO
d. TRANSFER FUNCTION PARAMETERS
The following shorthand notation is used to print the factored
polynomials for all transfer functions*:
(s + ]/Tx) i : ]/Txi , i : ] to k
(_2 + 2_%s + %2)j
: _j;_nj , j : I to where k + 2_ = n, the order of the polynomial COMI_ER PRINT OUT STANDARD NOTATION 2 DEFINITION Roots of the denominator DET N(X/Y) Numerator N_ Gain of the transfer function x/y A(X)
'i/T(X)I I/Txi , rad/sec
,z(x)J
_j
tw(x)j
Cenj, rad/sec OE NCM INATOR For example: I/T(OET }I .0318 I/_IOET}2 2.2C Z{DET} I .06C9 W[DET] 1 1.13 NU M ERATOR S N| 8 /OR } A{B } .0295 I/T|B _I -.0494 I/T (B }2 2.05 I/T (8 } 3 42.3
A. : .o_(s- .o494)(s + 2.o_l(s + _2.3/
Translates to: 6r (s + .0318)(s + 2.20)(s 2 + 2 X .0609 X 1.13s + 1.132s 2) *The transfer function x/y is written as: N_y Ax( sm + sm-1 + ... s o ) x/y = a (S n + Sn-1 + ... S O) _Any roots enclosed in parentheses imply the opposite order of what is specified, e.g., Z(DET)I = (O.OO132)_I/T(DET)I = 0.00132 A-II e. LONGITUDINAL HANDLING QUALITY PARAMETERS EQUATION COMIKITER PRINT OU STANDARD NOTATION I DEFINITION --r W^ U o 1
l. cs /
68 L _O O J _/_u, de_rees/knot DCO)fO(U) (D_I_) (I. 9)(97.3) Uo u Wo w , for s=O •-u o _(s) for s =0 Nz_ , g/rad ¢ _(S)' for s = 0 5e/g , degrees/g DEIo (_1_) a(s) ! ' Control anticipation CAP(mD I_clsEC IG ) parameter, rad/sec2/g in 2 The phugoid time to double amplitude, seconds ---_, for _Ph < 0 2_ Short period inverse cycles l/c(_/_o) ll_ for O <' - _sp < I to 1/10 amplitude in 10 _I -- _sp 1.689 (s for s = O Stick force per knot, Fs_/n (,.-/l=) l_unds/knot -I Stick force per g, pounds _S_/G (uVG) per g The parameter has no meaning or is not defined at this flight condition *The hat (2) notation implies constant speed (u = e o = 0).
A-12 f. LATERAL-DIRECTIO?_AL _ANDLING QUALITY PARI_4ETERS COMPUTERPRIf[U OUT STANDARD _DTATIONj DEFINITION EQUATION DR PERIOD(SEC) Dutch roll period, seconds 2_/ahd _ -- _d 2 Dutch roll inverse cycles iic(i12) for _d _ 0 in 2 to I/2 amplitude SPIRAL (2) (SEC) Spiral time to double Ts in 2, for I/Ts £ 0 amplitude, seconds Roll rate at peak I for a unit step input of 5 a Pl + P3 - $2 for _d _ 0.2 P l + P3 + 2P2 ' A measure of the oscillatory P(OSC)IP(AV) to the average roll rate Pl -- P2 for _d > 0.2 Pl + P2 Ratio of the roll frequency to the dutch roll frequency DEL-B-_gbX 2_.m : Maximum sideslip excur- slon at the c.g., occurring within two seconds or one half- period of the dutch roll, which- ever is greater for a step aileron-control command PHI to BETA, PHASE _/_ at s = (_; C0n)d, degrees PHI TO BETA
I /BI at s = (_ O_)d, radlrad
PHI TO VE "_/Vel at s = (_; o.h)d, deg/fps *v e : (8)(VEAS) , VEAS : _p2_ 0 A-IS 2. NGNDIMENSIONAL DERIVATIVE DEFINITIONS a) Longitudinal Body Axis N CN = _-_ , positive up X CX = - _-_ , positive aft M
c_ = _--_/_ CM = _ Sc
2Vmo _c_/_
c_ = _cW_
V-
2Vmo _cW_
c_ : -'-T-
c_ = _cWM
et% -- _CN/_,
2v_°_c_/_q
Cxa = _Cx/_
CMq - c
CxM = _Cx/_M
Cx_ : _cx/_
ID) Longitudinal Stability Axis L CL - _ S ' positive up D CD - _ S ' positive aft :
2Vmo _Cn/_
Pitching moment
c_ - c
derivatives are
c_ = ac_aM
identical to those for body axis
c_ = acD/_
A-14
c) Lateral Body and Stability Axis
Though physically 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.) al
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.
L N
Y
Cy
C1 - qSb Cn - _Sb
= BCylB_
Cl_ = _CI/8 _ Cn_ = _C_8_
Cy_
2VTo 8cml_ ev_°
= _Cy/_
Clp - b Cnp - b 8CNI_
2v_° _ci/8r 2VTo 8c_/8r
Clr - b Cnr - b
c_ = _/_ c_ = _cJ_
*The exception is the zero trim angle of attack condition.
A-15 5. DIMENSIONAL STABILZTY DEF_I_ATrWE DEFINITIONS The same symbols are used for body- and stability-axis dimensional derivatives. Care should be exercised so that a consistent set of quantities are used.
a) I_ngitudinal Body Axis I/see
_u = Xu+ Tu cos_o
__ 0_o(_ We)
m - 2 CxM - Cx + _ cxcz I/sec
!
OSUo
Wo M ]
Xw - 2m 2 _o (cx + _ %) 11sec
[- CX_ -
osv_ o
ft
x8e = - _ CXse
sec2rad I/sec Z*u = Zu - Tu sin_ o I/sec
oS_o (_ _)
Zu - m - _ CNM - CN + CN(_ I/sec ooo[wo .
Zw - 2m -CN(_ - 2 _oo (CN + _ CNM pSc U o
z_ = - 4m Vmo cN&
PS_T o ft ZSe - 2m CNSe sec2rad _th M_ = Mu +-_--_I sec-ft A-16 I sec-ft MII = I sec-ft oScUo Cm_ + (Cm + I sec-ft pSc2 Uo 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 I/sec 2 L5 a = (DSVTJ/2Ix)C15 I/sec 2
L_r
= (PS_TJ/2Ix)C15 r I/sec
YS_
: (_SV_o/2m)Cy_a
I/sec 2
: ( SV ob/21,.)c
I/sec
: (psv_J/41z)C_ p
I/sec Nr : (pSVTob2/4Iz) Cnr I/sec 2
Nsa = (oS_TJ/2Iz)Cnsa
I/sec 2 : (PS_T2/2Iz)Cn5 r N5 r I/sec 2 = (L8 + IxzN_/Ix)G I/sec = (Lp + IxzNp/Ix)G I/sec = (L r + IxzNr/Ix)G
: (_6r+ IxzNSr/IX) G
I/sec 2
= (%_ + IxzNS_/Ix)O
I/sec 2 = (N_ + IxzL_/Iz)G I/sec
: (_p+ I_zLplIz)G
I/sec = (N r + IxzLr/Iz)G I/sec 2
NSr = (NSr + IxzLSr/Iz)G
I/sec 2 = (Nsa + IxzI6a/Iz)G I G I Ixlz A-18 ,,,'t "r4 _ _ r_ c_ r,_ U + i i -t- o 0 0 0 ¢..) U 0 0 I-¢ k /.-, I 0 0 0 'o ' ' ÷ 'o& _ ¢0 H r,_ o o ¢O II II H II n tl H 11 eJ m t_ 0 0 r.,3 I II A _q ¢0 r_ H m r.3
4,r
!
cr_ H _1 r_ c.) r_ F-I rj_ o o C_, H CO II II II II II II II U il II n tl !
d B-I b. TRANSFORMATION OF DIMENSIONAL DERIVATIVES FROM STABILITY AXIS TO BODY AA_IS Longitudinal = Xu cos2 _o - (Xw + Zu) sin c% cos _o + Zw sin2 _ (Xu) b = Z@ sin 2 ao
(X )b
= Xw cos2 _o + (Xu-- Zw) sin c_ o cos ao -- Z u sin 2 a o
(Xw)b
= X@ cos 2 a o -- Z@ sin c_ o cos _o
(x,) b
(Xq;5) b = Xq; 5 cos a o -- Zq;5 sin _o = Zu cos2 _o -- (Zw--Xu) sin _o cos oo --Xw sin 2 _o
(Zu)b
(Z_) b = --Z@ sin _o cos c_ o (Zw) b = Zw cos 2 ao + (Zu + Xw) sin ao cos c_ + Xu sin 2 _o = Z@ cos 2 c_ 0 + X@ sin oo cos ao (Z-_-) b (Zq;5)b = Zq;8 cos ao + Xq;8 sin c% = Mw cos ao --Mu sin ao
(MU)b
= -¢4@ sin a o
(M )b
= M w cos c_ o + M u sin _o = M, cos _o (_)b (Mq;5) b = Mq; 8
(ly) b
B-2 Lateral-Directlonal
(Yv; )b = Yv;5
= Y@
(Y÷)b
(YP)b = Yp cos co -- Yr sin co
(Y )b
= Yr cos co + Yp sin cO T !
= L_; 5 cos c_ -- Nv; 5 sin c_ = L_ cos c_ o -- sin co = _ cos 2 _o- (L_ + N_) sin c_ cos _o + N_ sin 2 oo f = L_ cos 2 _o -- (Nr -- _) sin ao cos Go -- N_ sin 2 _o (Lr) b T = N_; 5 cos C_o + L_;5 sin co ! ! !
= N_ cos c% + L_ sin _o (N$) b
(N )b = N_ cos 2 Go -- (N_ -- _) sin Go cos ao -- L_ sin 2 co
(Nr)b
: N$ cos 2 ao + (L_ + N_) sin ao cos Co + _ sin 2 Go = Ix cos2 Go + 2Ixz sin a o cos co + I z sin 2 ao
(IX)b
= I z cos 2 Go -- 2Ixz sin co cos co + Ix sin 2 c_ o (Iz) b = (I z -- Ix) sin ao cos ao + Ixz(COS 2 _o -- sin2 Go)
(IXZ)b
B-3
APPENDIX C
APPENDIX C
EQUATIONS OFMOTION, TRANSFER FDT_CTIONS,
ANDCOUPLING hq]_RATORS
I • Longitudinal a. Eouations u I" X$e- (-Xq+Wo)s+g cos 8o -] (I-xa)s-x; -X_ s - X w w
[Se]
(I-z_)s-zw (--Zq--Uo)s+g sin 8 o = ZSe
-z_s - z[
M{5e
-(M,_+ Mw) s2 -- MqS
--_s-N
q. = .SO fi = --w cos O o + u sin O 0 + (U o cos O 0 + W o sin 0o)8 a z = sw -- Uoq + (g sin 00)8 , = a z -- ixS2O _z
h' : h +_x oos _o
b. Transfer Functions
e _e
5 e A I) Denominator, A = As 4 + Bs 3 + Cs 2 + Ds + E A = (1--Z_) = -(Mq + XU)(J -- Z_) -- Z w- M_ - Xw_ + Wo[M_ + M_(] - Z_)] + g_ sin 80 NOTE: Terms including Xd, Zfl , Mfl_ X@ are neglected in polynomial expressions.
C-I
D -- -x_(Mqz_-._) -MuX _+Mqx_z_ +g[%z_+M_(_ -z_ oo_ e o +Wo(M_z_ -._z_)
+ g(Mw-%X_)sin eo
E = g(%Z* - MuZw)oOS eo + g(MuXw - _,X_),i,, e o
Numerators
2)
N_ = Ass2 + Bes + C8
= %_ + %(, - %)
B0 = xs[_z_+ ._(, -%)]÷%(_- %x_)-%[m.+×*!_ -%)]
c e ="xs(%,,z _ -M_z_)+ zs(M_x _. %,x*)+%(ZwX _ - x,z*)
I_E = Au S3 + Bus2 +Cus +D u IA u = X5(I - Z.)
W
Bu = -_[Mq(, - z_)+ z_+ _] + %x_ - Wo[%% + _o(' - %)]
+ Wo(Zw%-MJ_) + gX8% sin e o
D u = g(ZwM 5 - MwZs)cos e o + g(XsM w - MSXw)Sin 8 0 N_ = Aw s3 + Bw s2 + CwS + Dw Aw= Z5
B_= -%(Mq + xu)+ UoM 5 + xs_
C w = X_(ZsMq- UoM_) + Wo(ZsM u - _Z_) - gM 5 sin e O+ X5(M_U o - Z_Mq) D w = g(Zs_ u - %Z_)cos e o + gMsX _ sin @o- XSM_g sin e O H-747 C-2
N_ : A_s 3 + B_s 2 + Cis + D i
A£ = - cos eoAw+ sin OoA u
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 + Wo sin @o)C@
N_Z--Aa_s 4 + Ba[_3 +C_[s _+ D_ls +E '
a z
A_ = A_ - ixA e
Ba_ = B w - ixB e - UoA @ Ca_ = C w - ixC 8 - UoB 8 + g sin @oA9 Da_ " = D w - UoC @ + g sin 8oB @ Ea_ = + g sin @oC@ To obtain az, let ix = O.
2. Lateral a. Equations t Wos + g cos e o Uos--g sin eo- s-Y v Y5 a Y5 r VToS VT o !
! !
V P
-b --Lr
s(s-_) L5 a L5 r
s
I a]
r ! t !
r s--N r N5 a N5 r v = VToO sv + Uor -- WoP-- g(cos 8o) _ !
= _p_ +---r tan 8 o
s s ay =
ay + lXlat sr -- izS p ] r cos e o s C-3 b. Transfer Functions r N_Sr m _. m etc.
5r Alat 5 a Alat + bs 3 + cs 2 +ds+e I ) Denc_Linator, Lhla t = as a = I
b - -CY + + Nr)
U o WoL_ C - N_ + _(Yv + N_) - NSL_+ YvN_ VT o VT o d U° (N_- L_N_) + Yv(N_L_- L_oNr)---_- (_ cos e o + N_ sin e o) VT o VT o W o
v%
= _ [(_N_-- N_L_) cos e O- (N_ - L_) sin 80] VT o 2) 5 (5 a or 5r) Numerators N66 = A_s 3 + B_s 2 + C_s + D6
=
%
, Uo Wo , % = -Y_[_ + N_] --N 5- +--L 5 VT o VT o C 0 Y_ (_N_ "'_'_ _ __----g (N_- L_N_) U° = -- _pLr/ + L_ VTo cos e o + --VT ° Wo , , , , , g + _ (NsL r -- LSNr) + N5 _ T sin 8o VTo o D_ = _VT° (N_L_ - L_N_) cos e 0 +_9_gVT ° (N_L_ -- N_) sin 8 0 C-4
N_5 = Aps3 + Bps2 + Cps + Dp
!
Ap = L5 = LS(Nr + Yv) + NSLr VT o g (L_ -- N_) sin eo Dp = -- VT O N_ = Ar s3 + Br s2 + Crs + D r f A r = N 8 . _, f ! f
Br = Y_N_ + n_Np-Ns(Y _ + $)
W o
C r = Y_(I%N_- N_%)- L_YvN _ + N_Yv% +- (LgN% -- NgL%)
VT o
-- ---g (L_N%- NgL%) ooseo
Dr VTo N_ = Acs 2 + Bcs + C A¢ = Ap + A r tan 8 o Be = Bp + Br tan 8 o C¢ = Cp + C r tan e o C-5
a' CayS 2 _ _4s 4+_2 + +_ +_4
AT ___ ay VToA_ + lxlatAr- lzAp !
= VToB _ + UoA r - WoA p + iXlatBr - lzB p ay = VToC _ + UoB r- WoB p- g cos 8oA¢ + lxlatC r - izC p
c_
= VTD _ + UoC r- WoC p- g cos eoB ¢ + iXlatD r - izD p
D_
= UoD r- WoD p- g cos eoC ¢
E_
To obtain ay, let lxlat = i z = 0.
H-747 __ _ C-6 k - L- [=. ..... _ __ " =_ -- _-_. .... :7 _ _ ..... . • - _ .
p Z .... _ .- -- -Lg'. 3