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Transcript of robertheffley.comrobertheffley.com/docs/Data/NASA CR-2144--Heffley...robertheffley.com
1. Report No. 2. Government Accession No.
NASA CR-2144
4. Title and Subtitle
AII_CHAFT tIANI)LING QUALITIES DATA
7. Author(s)
Robert K. tleff!cy and Wayne F. Jewell
9. Performing Organization Name and Address
Systems Technology, Inc.
ttawthmme, Califon_ia 90250
12. Sponsoring Agency Name and Address
National Aeronautics m_(t Space A(ln_inistration
Washington, I).C. 20546
3. Recipient's Catalog No.
5._Report Datel)ecemoer 1972
6. Performing Organization Code
8. Performing Organization Report No.
Technical Report 1004-1
10. Work Unit No.
11. Contract or Grant No.
NAS 4-1729
13. Type of Report and Period Covered
Contractor Report
14. Sponsoring Agency Code
15. Supplementary Notes
16. Abstract
Available information on weight and inertia, aerodynamic derivatives,
control characteristics, and stability augmentation systems is documented
for 10 representative contemporary airplanes. Data sources are given
for each airplane. Flight envelopes are presented and dimensional deriv-
ativcs, transfer functions for control inputs, and several selected handling
qualities parameters have been computed and are tabulated for 10 different
flight conditions including the power approach configuration. The airplanes
documented are the NT-a3A, F-104A, F-4C, X-15, HL-10, Jetstar,
CV-880M, B-747, C-5A, andXB-70A.
17. Key Words (Suggested by Author(s))
llandling qualities, transfer functions, stability
derivatives, airplanes, control systems
18. Distribution Statement
Unclassified- Unlimited
19. Security Classif. (of this report} 20. Security Classif. (of this page)
Unclassified Unclassified
21. No. of Pages
343
22. Price*
$6.00
' For sale by the National Technical Information Service, Springfield, Virginia 22151
I. INTRODUCTION .
ii. NT-33A • • •
III. F- IO_A . . .
IV. F-4C • • •
v. x-15 • • •
VI. HL-IO • • •
VII. LOCKHEED JETSTAR
viii. CONVAIR 880M .
D{. BOEING 747 • •
x. C-_A ....
XI. XB-70A • • •
TABIZ OF COI_TERTS
• I
• • • • • • •
32
• . . 61
• . . Io8
• • • 137
• . . 166
• • • 193
• . . 210
• . . 2_3
• • • 273
APPENDIX A. AXIS SYSTEMS, SYMBOLS, COMPUTER MNEMONICS,AND DERIVATIVE DEFINITIONS ....
APPENDIX B. TRANSFORMATION OF STABILITY AXIS
DERIVATIVES TO BODY AXIS ......
APPENDIX C. EQUATIONS OF MOTION AND TRANSFER FUNCTIONS . . .
• . A-I
.... B-I
• C-I
iii
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
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._
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 (az 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
3
with each particular aircraft will recognize, the data presented mayrepre-
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, thosedata knownto 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 isassumedthat 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 datafrom 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 anyconclusions with respect to their aircraft which might be derived from its use.
4
-33A ACXSXOmm
"The NT-33A variable stability airplane (Serial No. 51-4120)
is an extensively modified T-33 jet trainer. The elevator,
aileron and rudder controls in the front cockpit are disconnected
from their respective control surfaces and have been connected
to separate servomechanisms that make up an 'artificial feel'
system. In addition, the elevator, aileron and rudder control
surfaces have been connected to individual servos which can be
driven by a number of different inputs. These servos receive
their electrical inputs from the artificial 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 127
andMach number derivatives from NACA-RM-7116.
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VariableFeel
Input
FST(Ib) _..026
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s z +.89s + 22.5
Variable
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_]ST(in) ] -I0 _._---- _.3 Be(rod)
ROLL AXIS
Variable VariableFeel StabilityInput Input
FLAT (ib) I OST _,n I0 _a(rad)sT
YAW AXIS
VariableFeelInput
FpED(Ib)_
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Variable
StabilityInput
I_PED(in) I 2.34 _.= _._ 8r(rad)
Feel system parameter values shown correspond
to the "Front Seat Engage" mode (normal NT-33)
Figure 11-3. NT-33A Control System
9
TABLE 11-I
Power_oach Non-Dimensional Stability Derivatives
h = sea level
VTo = 228 ft/sec = 139 kt
oo = 2.2 °
Longitudinal
cL = .813
cD = .139
CLm = 5.22/rad
CD_ = .94/rad
% = --.401/rad
Cmq : -mo/raa
:
CL5e = .34/rad
Cm6e = -.89/rad
Lateral-Directional
(Stability Axis )
cy0 = -.72/r
Cn_ = .049/rad
C_0 = --.127/rad
C_p = -.O7/rad
C_p = -.045/rad
C_r = .20/rad
Cnr = --.16/rad
Cn5 a = --.O09/rad
C_5 a = .14/rad
CYSr = .17/rad
Cnsr = -.O73/rad
C_5 r = -.OO2/rad
10
Clo
(deg)
14
12
10
8
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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 Testsof 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.
31
SECTION III
F-IO4A
32
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.
33
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F-104A
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32.2 F BOz
Baz assumed to be at pilot location
G57.3
8SsAs(rad)
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ROLL AXIS
F LAT --I I
ST (Ib) --i 2.7
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I i 2,,4_! 5"_ _ 8a (rod)
YAW AXIS
FpED(Ib)KDIR_
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2.0
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Mac h
Figure 111-3. F-IO4A Control System
36
Power Approach Non-Dimensional Stability Derivatives
h = sea level
VTo = 287 ft/sec = 170 kt
_o = 2"3°
_s = --7.1°
Longitudinal
CL = .735
% = .263
CL= = 3.44/tad
CDa = .45/rad
Cm_ = -.6_/ra_
Cma = --I.6/rad
Cmq = ->.8/ra_
Cg_s = .68/tad
Cm_s = --1.4g/rad
37
Lateral-Directional
(Stability Axis )
Cyp = -1.17/rad
cn6 = .5o/r_
C2p = --.175/tad
C_p = --.285/tad
Cnp = --.14/rad
C_r = .26_/rad
Cn r = --.7_/rad
Cnsa = .O0_2/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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59
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-I04CAircraft, T. O. 1F-104A-2-8, 15 Mar. 1960
6O
SECTION IV
F-4C
61
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 to0
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.
62
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68
4--q.- r-- _1"
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.Q IU
0
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r_
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64
PITCH AXIS
FST(Ib__ _-_.0369s 2 +.208s
F-4C
Feel System_SsAs (rad)
I _ Gearing / Actuator
18sT(in)_ _.0569qePsF
,:_1 I _'-_I- _ -I°_'+'1
_-- See Fig and for feel system details
Bobweight
az ts---_-_) of JtB= 39.3 ft
+ .OI57qBPBF -*
8s(rad)
ROLL AXIS
8OsAs (rad)
Feel Spring Gearing /
_;T,,_ -I 2"961 =1_ i-_
AR! Gain
C38r {-.46 SAS OFF
= _-.69 SAS ON
CLEAN O ,/
Sa(rad)Spoiler
-__ 8sp( ra d )
PA ARI
__r I___--_-:1_ <_rAm(rod)
YAW AXIS 8rARl(rad) 3rsAs (rad)
\ / Rudder
Feel Spring Gearing \ / Flexure
.._j_'_ SPED(i n) .___.J__
_"_°_'_- I _ I _I_ I- _ - l""txl -
K mR G air
V<235KIAS 36.61b/in -11.5deg/in
V>220KIAS 8.51b/in -6.5deg/in
8r(rad)
_-- See Fig
Figure IV-3. F-hC Control System
65
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q
.6
-4C
/ _---- 35,00Oft 389:)4 Ib
.... 55,00Oft .289
I I I I 1O0 4 8 12 1.6 2.0
Mach
PBF
(ft z)
J.I m
1.0-
8
I0
I I L 1 I.4 .8 1.2 1.6 2.0
Mach
h
(ft)
60k
40k
20k
Viscous Damper Off Stop3.03 Ib/in/sec
"l//f/[_ I
Viscous Domper On Stopb=_
I I I I ISLo" .4 .8 1.2 1.6 2.0
Mach
Figure IV-5. F-4C Feel System }arameters
6?
III!i-
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i°
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111
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68
F-4C
PITCH SAS
E}(rad/sec) _1 .15s
- I s+l_SsAs(rad)
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
rG (radlsec)
' (ftlsecz)ay
_I,s_1 S+'5
I--I .0168
_rsAs (rad)
rG = r cos(-I.5 °) +p sin (-I.5 °)
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
69
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
CL = .915
CD = .242
CL_ : 2.8/rad
CD_ = .555/rad
Cm_ - .098/rad
Cm& - .95/rad
Cmq = -2.0/rad
CL5 s = .24/rad
C-mss = --.322/tad
CD5 s = --.14/rad
Lateral-Directional
(Stability Axis )
Cy6 : --.655/rad
Cnl3 : .199/rad
C26 = -.156/rad
C£p = --.272/rad
Cnp = -.013/rad
C_r = .20_/rad
Cnr = -.320/rad
CYSa = --.0359/rad]
Cnsa = --.O041/rad I
= .o 7/r aj
CYSr = .124/rad
Cnsr = --.072/rad
C_5 r = --.O009/rad
Spoiler
Effects
Included
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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
107
SECTION V
X-15
108
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.
109
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Figure V-3. X-15 Control System
112
X-15
PITCH SAS
_(rad/sec) .75 SssAs(rad)
ROLL-YAW-YAR SAS
p (rad/sec)
Roll Gain
Yar Gain
BasAs(rad)
r (rad/sec)
Yaw Gain
.3O BVSAs(rad)
Note:
Gains variable in 10% increments of themaximum 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
1 13
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135
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.
136
SECTION VI
HL-IO
137
EL- I0 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.
138
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PITCH AXIS
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FpED(Ib) 22.2
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(Sr (rod)
Figure Vl-3. HL-IO Control System
141
HL-I0
PITCH SAS
(rad/sec)_eSA S
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p(rad/sec) 8aSAs
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r (rad/sec)J .4s I
= s 7"._,3 _ arsAs
Figure VI-4. HL-IO Stability Augmentation
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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 LiftingBody 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-
165
166
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.
167
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169
JETSTAR
PITCH AXIS
FST(Ib) I'I-_ 52 + 2.95CI8e (rad)
Note: Angle of attack effects on elevator
h/nge moment are neglected
ROLL AXIS
LATF ST (Ib)
I.75_q= 8a(rad)
YAW AXIS
FpEo(Ib) -_ 8r (rad)
Figure VII-3. Jetstar Control System
170
TABLE VII- ]
JETSTAR
Power Approach Non-Dimenslonal Stability Derivatives
h = sea level
VTo = 224 ft/sec = 132._ kt
% = 6._ o
Longitudinal
CL = .737
CD = .O9_
= .O/rad
CD a = .7D/tad
Cm_ = -.80/rad
Cm_ = --3.0/rad
Cmq = _8.0/rad
CLSe = .4/rad
CruSe = --.81/rad
Lateral-Directional
(Bod Ax±s)
Cn_ = .137/rad
C_ = --.IO3/rad
C_p = -.37/rad
Cnp = -.14/rad
C_r = .]I/rad
Cn r = --.T6/rad
Cn_a = --.O07_/rad
C_Sa = .054/rad
CySr = .17_/rad
Cn5r = --.O63/rad
C_Sr = .O29/rad
171
SL JETSTAR
20,000 ft 38204 Ib40,O00ft
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(deg)
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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
192
SECTION VIII
CONVAIR _OM
193
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.
194
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CV-880M
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Be(rod)
ROLL AXIS
t -I.425I +.Is 8Sp (rod)
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YAW AXIS
,.._+t<(Sir -Sr)c _ b
L
St, (rad)
8r(rad)
i':':kg',kre '/! i_ -3. CV-880M Control System
197
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
Ci_ (I/rad)
CLq (I/rad)
Cmc_ (I/rad)
Cmq (I/rad)
2.7 2.7 2.44 2.5 2.75
7.92 7.72 6.76 6.37 7.51
-4 .I7 -4 .I3 -4 .I6 -4.66 -4.4
-I 2.2 -I 2 .I -I I .5 -I I .8 -I 2.
2.75
7.5
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2.9
7.62
-4.6
-I 2.
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
198
TABLE Vlll-2
OV-880M
Lateral-Directlonal Non-Dimensional Derivatives
(Stability Axis System)
Flight Condition
Configuration
Speed
Altitude
C_B (I/rad)
c% (1/_d)
C% (1/_d)
Cnp (1/_ad)
C_r (l/tad)
Cnr (I/tad)
Cysa (I/rad)
C_5 a (I/rad)
Cn5 a (I/tad)
Ch5 a (I/rad)
C_a (I/rad)(llraa)
Cn6ta (I/rad)
Ch6ta (I/rad)
Cyss (1/rad)
C_ s (l/tad)
Cn5 s I/rad)
Cy_z ' I/rad)
C_6 r I/rad)
Cn6 r I/tad)
Ch_ r 7/raa)
CY6t r (llrad)
C£Str (I/tad)
CnBtr (1/rad)
C" (1/rad;nst r
I 2 3 4 5
L PA
13 _ KTAS 165 KTAS .6M .86M .7M
SL SL 23K 23K 35K
-I .01 5 -0.877 -0.788 -O .81 5 -0.807
-0.239 -O.196 -0.163 -0.145 -0.181
0.145 0.139 0.128 0.122 O.129
-0.395 -0.381 -0.329 -0.243 -0.341
-0.087 -0.049 -0.0173 -0.0031 -0.023
0.309 O. 198 0 .I46 0.088 0 .I8O
-0.21 8 -0 .I85 -0 .I63 -0 .I89 -0 .I66
0 0 0 .O019 0 .O745 0 .O044
-0.0487 -0.0384 -0.0466 -0.0452 -0.0479
0.01862 0.0172 0.00746 0.01061 0.007
-0.607 -0.481 -0.236 -0.258 -0.2233
O 0 0 0 0
-0.0072 -0.0056 -0.0068 -0.0068 -0.0071
0 0 0 0 0
-0.249 -0.227 -o .21 5 -0.21 25 -0.226
-0 _078 -0.031 5 -0.0189 -0.0175 -O.0189
0 .o805 0.0405 0.029 0.0281 0.0324
0 .o258 0.01 29 0.011 46 0 .oi 09 0.00975
0.223 0.21 55 0 .I904 0 .I394 0 .I99
0 .O207 0.0226 0.01 76 O .0183 0 .O1 65
-0.O9_)5 -0.0958 -0.0845 -0.0534 -0.0848
-O.2140 -O.2125 -O.1626 -0.1844 -0.1345
0.0493 0.0467 0.0374 0.021 5 0.0404
0.0021 0.0027 0.001 6 0.001 8 0.001 4
--C,.020 -O .019 -0.01 5 -0.0077 -0.01 6
--0.25P, -< .N_;5 -0.267 -0.254 -0.27
199
.SM
35K
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0.129
-o.31 2
-0.011
0.153
-0 .I65
o .00775
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o .oo8o3
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0
-0.0075
0
-0.235
-0.01 89
o .0329
o .01004
o .I84
0.01 87
-0.0756
-0.1491
0.0355
O. O01 9
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-o.267
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o .133
-0.294
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o.146
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0.00979
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-0.213
-0.01 75
0 .o339
o .oo917
o.I 685
0.01 93
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0.0316
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208
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.
209
_ECTION IX
BOEING 747
210
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).
211
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213
B-747
PITCH AXI_.
Fcc(Ib)I
K _cc(deg)[
-2
57.3
_eSAS
P" 8e(rad)
4°k50
20
,°to
0 .2 .4Mach
ROLL AXIS
Fwfib)
s / J"e,"x
I I I.6 .8 1.0
I
.161 Sw(deg) I .557.3
43
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(1)
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YAW AXIS
FpED(Ib)I }SPeD(in) I
___ 7.1543.5 57.3
8rsAs(rad)
214
B-747
YAW SAS
rG (rad/sec)
_iNs(rad)
I 5.05_
I(s,.368)(s 3.68)
-.688s
s+.368)(s+3.68)
-34.5s
(s+lO) 2
Flaps Down
r =r
*INS: IP dt
(Gyro and INS Aligned with FRL)
Figure IX-4. B-747 SAS
215
TABLEIX-I
Landing Configuration Non-Dimensional Derivatives
h : sea level
VTo = 131 KTAS
mo = 8.5°
5s = -6.3 °
Longitudinal
CL = I .76
CD = .263
CL_ = 5.67/rad
CD_ = 1.13/rad
Cm_ = --I.45/rad
CL& = -6.7/rad
Cm& = --3.3/rad
CLq = 5.65/rad
Cmq = --21.4/rad
eLM = --I.I
CmM = .36
CI6e = .396/rad
Cm5 e = --I.40/rad
Lateral-Directional
Cy6 = --1.081rad
C_6 = --.281/rad
Cn_ = .184/rad
C_p = --.502/rad
Cnp = --.222/rad
C_ r = .195/rad
Cnr = --.36/rad
C_Sa = .0530/rad
CnSa = .O083/rad
CYSr = .179/rad
C_5 r = 0
CnSr = --.ll2/rad
5a = total deflection of right inboard aileron plus left
inboard aileron with the effect of outboard ailerons
included
216
TABLE IX- 2
Power Approach ConfigurationNon-Dimensional Derivative s
h = sea level
VTo = 165 KTAS
co = 5.7 °
O
5s = --2.1
Longitudinal
CL = 1.11
CD = .102
CI_ = 5.70/rad
CD_ = .66/rad
Cm_ = --1.26/rad
CL& = --6.7/rad
Cm_ : -3.2/rad
CLq = 5.4/rad
Cmq = --20.8/rad
c_ = -.81
CmM = .27
CLte = .338/rad
crime = -1.34/rad
Lateral-Directional
CyB = --.96/rad
C_ = --.221/rad
Cn_ = .150/rad
C_p = --.45/rad
Cnp = -.121/rad
C_r = .101/rad
Cnr - .30/rad
C_5 a = .0461/rad
Cn5 a = .O064/rad
Cysr = .175/rad
C_5 r = .O07/rad
Cn5 r - .109/rad
5a = total deflection of right inboard aileron plus left_nboard aileron with the effect of outboard ailerons
included
217
i
_m _m
mmm em mmme
SL B-747
20,000 ft 636600 Ib40,000 ft .25 _"
Flexible
GO
(deg)
12
I0
8
6
m
m
4-
2-
o I0 .2
kik
kk
4I .6 " .8
Mach
I1.0
(deg)
2
0
-2
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218
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219
SL B-747
20,000 ff 636600 Ib40,O00ft Flexible
CL a
(rad-')
4-
2-
0 oI.2
l
I I I I.4 .6 .8 1.0
Mach
CD a
(rad-')
.8 m
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0 oI.2
I
l
l
, \
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I1.0
220
Mach
0 2_ .4 .60 ,--------T-------T-------_
.8 1.07------V---
-.4
:8
Cm a
(rod -j )
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B-747 DATA SOURCES
I-_.nke_ C. Rodney and Donald R. Nordwall 3 The Simulation of a Large Jet
Transport Aircraft, Boeing Rept. No. D6-306433 Vols. I and II,
Sept. 1970.
242
SECTION X
C-SA
243
C-_A RACm_ROU_D
The C-5 A is a very large 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.
244
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PITCH AXIS
Fcc('b)---_;)_" I
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I 8cc(in)_l -2'92 t_-'(_)_''se(r°d)-I57..3
8.3 _. B32.2 a z at _B
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I I I 1 1O0 .2 .4 Moch .6 .8 1.0
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Fw(Ib)I
KLAT
Config. K LAT
Cleon .121b/deg
PA .155 Ib/deg
8w(deg)
8asAs(deg)
8a(rad)
8sp(rod)
YAW AXIS8rsAs(rad)
_ 63.5 -I 57.3
F'i_re X-3. C-_DA Control System
247
TABLE X-I
Power A_&ch Non-Dimensional Derivatives
h = sea level
VTo = 247 ft/sec = 146 kt
c:qO = 2.7 °
Longitudinal
CL = I.29
CD = .145
CI_ = 6.08/rad
CD_ = .622/rad
Cm_ = --.827/rad
Cm&= - .3/rad
Cmq = --23 . 2/rad
CLUe = .385/rad
= --1.6/r d
Lateral-D irect ional
(Stability Axis )
CylB = -.77/rad
Cn# = .075/rad
C_IB = --.123/rad
C_p = --.458/rad
Cnp = -.098/rad
C_r = .290/rad
Cnr = --.293/rad
Cysa = --.O044/rad
Cnsa = .0091/rad
C_sa = .089/rad
CYSr = .211/rad
Cnsr = -.106/rad
C_Sr = .0209/rad
Spoiler
Effects
Included
248
(deg)
14
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C-5 Flight Control Report (Aerospace Vehicle) Stability and Control,Lockheed-Georgia Rept. No. LGIUS_2-1-1, 8 Feb. 1966
272
SECTION XI
XB-70A
273
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.
274
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276
XB-70A
PITCH AXIS
I
.025s z +.35s+K
(_eSAS (red)
i -See Fig.
PA o/t Clean
-- a z at 1B 8c(rad)
Effective lConfig B Bobweight FS i B
Clean I0 Ib/g__852/2 j-2169ftPA 14 tb/g 1479.2 I0 96ft
50
I0
00
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20,O00ft_ 40,O00ft / / _....... -
60,O00ft _/ // f "/'-
--e
I 1 I I I I I
4 .8 1.2 1.6 Much 2.0 2.4 2.8
1:5.2
ROLL AXIS
FLAT/CC ,in/Ib)
8uSAS(rad)
I 8cc Meg) .41 I I
=-- _ = 57.:5 1+.075 I
I
.-_ 8a(rad]
YAW AXIS
FpE D(lb)I I _PED(in)KDIR
8rsAs(rad)
GDIR57.: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
8r(rad)
277
PIT.___CHSASXB-70A
8 (rad/sec) -_
ROLL
8¢¢(in)-_-4'65 }
SAS
' ' 1 34.8ft Cleanaz at -_x = 36.4ft PA
Normal Accelerometer at F.S. 1174
p(rcd/sec) - |j _ 8OsAs(rad)
YAW SAS
r (rod/sea) -
_rsA s (rad)
Figure XI-4. XB-70A SAS
278
TABLE XI- I
Power Approach Nondlmensional Stability Derivatives
h : sea level
VTo : 347 ft/sec : 209 kt
ao = 7.5 deg
Longitudinal
CL = -333
CD = .055
CL_ : 2.6/rad
CD_ = .56/rad
Cm_ : -.23/rad
Cm& = +.09/rad
%q : -1.9/ra_
CL_e = .46/ra_
%_e : -.19/raa
Lateral-Directional
Cy_ = --.183/rad
Cn_ = .132/rad
C_ : --.072/rad
C_p = --.18/rad
Cnp = --.26/tad
C_r = --.03/rad
Cnr = -.25/tad
CY$a : -.063/rad
c_ a : .042/rad
Cn5 a = --.O052/rad
CYSr = .12/rad
C_5 r = -.O018/rad
Cn_r = -.103/rad
279
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315
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
316
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, orthogonalaxes 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-axissystem for which the Xs_axis is coincident with the
projection of the total steady-state velocity vector (VTo)on the aircraft's plane of symmetry. It's orientation
remains fixed with respect to the aircraft.
A-I
2. SYMBOLS
a
ay
T
a Z
b
B
B.L.
C
C. ,g.
D
FRL
F°S.
FST
T
Fped
g
G
S_peed of sound in air
Lateral acceleration along the y-body axis
at the center of gravity (positive out right
wing)
Lateral acceleration parallel to the y-body
axis at a distance _x and _z from the c.g.,
a_ = ay + _x_- _z_
Normal acceleration parallel to the z-body
axis at a distance _x from the c.g.,raz = az _xq
Normal acceleration parallel to the z-body
axis at a distance _B from the c.g.
Reference wing span
Bobweight gain
Buttock line
Reference chord
Longitudinal feel system damping
Center of gravity
Aerodynamic force (drag) along the total
velocity vector (positive aft)
Fuselage reference line (parallel to x-body
axis)
Fuselage station
Longitudinal control column force (+ aft)
Longitudinal stick force (+ aft)
Lateral stick force (+ right)
Rudder pedal force (+ right )
Acceleration due to gravity
Pilot control to surface gearing
ft/sec
ft/sec 2
ft/sec 2
ft/sec 2
ft
ib/g
ft
ib/in./sec
ib
ib
ib
ib
ib
ft/sec 2
deg/in, or
deg/deg
A-2
h
I
Ix_ ly_ I z
][XZ
_B
_X
Sth
_Z
K
KTAS
KCAS
K T
m
M
M
MAC
MGC
Altitude
Longitudinal feel system inertia
Moments of inertia referred to body axis
(unless otherwise specified)
Product of inertia referred to body axis
(unless otherwise specified)
The imaginary portion of the complex vari-
able s = J ±jc_
Effective distance of bobweight from c.g.
(positive forward) ft
Distance along the x-body axis from the
c.g. (positive forward) ft
Perpendicular distance from c.g. to thrust
line (positive for nose-up pitching moment
due to thrust) ft
Distance along the z-body axis from the
c.g. (positive down) ft
Longitudinal feel system spring constant ib/in.
Knots true airspeed
Knots calibrated airspeed
Feel system spring constant per unit dynamic
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
Mass s_igs
Mach number
Pitching moment about the y-axis due to
aerodynamic torques rpositive nose up) ft-lb
Mean aerodynamic chord ft
Mean geometric chord ft
A-3
ft
ib/in./sec 2
slug-ft 2
slug- ft 2
rad/sec
(ib/in. )/psf
N
P
q
r
rRG
S
S
TED
TEU
TL
U
Uo
V
V s
VT o
W
W°L.
W
Wo
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
(positive right wing down)
Pitch rate, angular velocity about y-axis
(positive nose up)
2Dynamic pressure, I/2 o VTo
Yaw rate, angular velocity about z-axis
(positive nose right)
Yaw rate gyro signal
Laplace operator, a + j_
Reference wing area
Trailing edge down
Trailing edge up
Thrust line
Linear perturbed velocity along the x-axis
(positive forward)
Linear steady-state velocity along the
x-axis (positive forward)
Linear perturbed velocity along the y-axis
(positive out right wing)
Stall speed
Total linear steady-state velocity Cpositive
forwaz_ ) kt
Linear perturbed velocity along the x-axis
(positive down)
Water line in.
We ight lb
Linear steady-state velocity along the
z-axis (positive down)
A-4
rad/sec
rad/sec
lb/ft 2
rad/sec
rad/sec
rad/sec
ft 2
ft/sec
ft/sec
ft/sec
ft/sec
X Aerodynamic force along the x-axis (positiveforward )
Y Aerodynamic force along y-axis (positiveout right wing) lb
Z Aerodynamic force along z-axis (positivedown) lb
(L Perturbed angle of attack rad
_o Steady-state (trim) angle of attack
relative to the FRL deg
Sideslip angle rad
_O Steady-state flight path angle deg
_a Aileron control surface deflection (includes
spoiler effects, etc.) (positive for posi-
tive rolling moment) rad
_e Elevator surface deflection from trim
(positive for nose-down pitching moment
for aft surface) rad
Trim elevator deflection
Longitudinal control column deflection
from trim (positive aft)
deg
deg
Longitudinal stick deflection from trim
(positive aft)
Lateral stick deflection from trim (posi-
tive right)
in.
in.
Sped Rudder pedal deflection from trim (posi-
tive right pedal forward) in.
_w Lateral wheel deflection from trim (posi-
tive about x-axis) deg
_S Stabilizer surface deflection from trim
(positive for TED) rad
$sp Spoiler surface deflection (positive up) rad
_V Vertical tail deflection from trim (posi-
tive for nose-left yawing moment) rad
_r Rudder de_ection [positive for nose-le_
yawing moment (negative N)]
A-5
rad
A
g
iTH
Denominator of airframe transfer function
Angle between principle inertia axis and FRL
(positive about y-axis)
Damping ratio of linear second-order mode
particularized by the subscript
Pitch angle, fq dt for straight and level
flight, positive nose up
Inclination of thrust line with FRL [posi-
tive gives negative (--) z force]
Mass density of air
The real portion of the complex variable
s = a ±j_
Roll angle, (cos eof p dt- sin eofr dt) in
straight and level flight (positive right
wing down)
Undamped natural frequency of a second-order
mode, particularized by subscript
Special Subscript
a
cc
d
e
G
INS
P
r
R
S
SAS
sp
ST
Aileron
Control column
Dutch roll
Elevator
Gyro
Inertial navigation system
Phugoid
Rudder
Roll subsidence
Spiral
Stability augmentation system
Short period
Stick
deg
rad
deg
slugs/ft3
rad/sec
rad
rad/sec
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)
KDIRFLEX Rudder flexure coefficient (F-4)
PBF Bellows force parameter (F-4) ft 2
qB Bellows pressure (F-4) lb/ft 2
5d 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- COMPUTERPRINTOUTMNEMONICS
a. DIMENSIONAL,MASS,ANDFLIGHTCONDITIONPARAMETERS
COMPUTER rRINT OUT
S
B
C
F/C#
H(_)
SL
M(--)
VTO(FPS)
VTO (KTAS )
w( s)
IX
IY
IZ
IXZ
_SI_N(DEG)
Q(PSF)
QC(PSF)
ALPHA(DEG)
_(DEG)
LXP(FT)
up(n)
ITH(DEG)
XI(DEG)
LTH(FT)
STANDARD NOTATION_ DEFINITION
S, wing reference area
b, wing span
E, mean geometric chord
Flight Condition number
h, altitude, feet
Sea Level
M, Mach number
VTo , true airspeed, knots
VTo , true airspeed knots
VTo , calibrated airspeed, knots
W, weight, pounds
c.g., center of gravity relative to
mean geometric chord
IxIIy
Iz
Ixz
Body axis (FILL) moments of
inertia, slugs-ft 2
e, inclination of principle axis with
respect to FRL, degrees
q, dynamic pressure, psf
qc, impact pressure, psf
So, FRL angle of attack, degrees
7o, flight path angle, degrees
£x, x distance to pilot, ft
_z' z distance to pilot, ft
ith , thrust incidence with respectto FRL, degrees
_o' ith + %' degrees
/th, perpendicular distance to
thrust line from c.g., ft
A-8
b. LONGITUDINALPARAMETERS
COMPUTER PRINT OUT STANDARD NOTATION_ DEFINITION
XU* X u ]/sec
zu* z_ 1/see
MU* M_I I/sec-ft
XW Xw 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 Z5 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 aileronDDD = DA
A-9
C° LATERAL-DIRECTIONALPARAMETERS
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/seety*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. TRANSFERFUNCTIONPARAMETERS
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
where k + 2_
: _j;_nj , j : I to
= n, the order of the polynomial
COMI_ER PRINT OUT
DET
N(X/Y)
A(X)
'i/T(X)I
,z(x)J
tw(x)j
For example:
STANDARD NOTATION 2 DEFINITION
Roots of the denominator
Numerator N_
Gain of the transfer function x/y
I/Txi , rad/sec
_j
Cenj, rad/sec
OE NCM INATOR
I/T(OET }I .0318
I/_IOET}2 2.2C
Z{DET} I .06C9
W[DET] 1 1.13
Translates to:
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 + _2.3/6r (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 + ... so )
x/y = a (Sn + Sn-1 + ... SO)
_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
COMIKITER PRINT OU
DCO)fO(U) (D_I_)
DEIo (_1_)
CAP(mDI_clsECIG)
l/c(_/_o)
STANDARD NOTATION I DEFINITION
_/_u, de_rees/knot
Nz_ , g/rad
5e/g , degrees/g
Control anticipation
parameter, rad/sec2/g
The phugoid time to
double amplitude, seconds
Short period inverse cycles
to 1/10 amplitude
EQUATION--r W^ U o 1
l. cs /68 L _O O J
(I. 9)(97.3) Uo u Wo w , for s=O
•-uo _(s)for s =0
¢ _(S)'
for s = 0
a(s) ! '
in 2
---_, for _Ph < 0
2_ll_ for O <' -_sp < I
in 10 _I -- _sp
Fs_/n (,.-/l=) Stick force per knot,
l_unds/knot
Stick force per g, pounds
per g
_S_/G(uVG)
The parameter has no meaning
or is not defined at this flight
condition
*The hat (2) notation implies constant speed (u = e o = 0).
1.689 (s for s = O
-I
A-12
COMPUTERPRIf[UOUT
DR PERIOD(SEC)
iic(i12)
SPIRAL (2) (SEC)
P(OSC)IP(AV)
DEL-B-_gbX
PHI to BETA, PHASE
PHI TO BETA
PHI TO VE
f. LATERAL-DIRECTIO?_AL _ANDLING QUALITY PARI_4ETERS
STANDARD _DTATIONj DEFINITION EQUATION
Dutch roll period, seconds 2_/ahd _ -- _d2
Dutch roll inverse cycles
to I/2 amplitudein 2 for _d _ 0
Spiral time to double
amplitude, seconds
Ts in 2, for I/Ts £ 0
Roll rate at peak I for a unit
step input of 5 a
A measure of the oscillatory
to the average roll rate
Pl + P3 - $2
P l + P3 + 2P2 '
Pl -- P2
Pl + P2
for _d _ 0.2
for _d > 0.2
Ratio of the roll frequency to
the dutch roll frequency
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
_/_ at s = (_; C0n)d, degrees
I /BI at s = (_ O_)d, radlrad
"_/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
c_ = _--_/_
2Vmo_c_/_V-
et% -- _CN/_,
Cxa = _Cx/_
CxM = _Cx/_M
Cx_ : _cx/_
M
CM = _ Sc
c_ = _cW_
2Vmo _cW_c_ : -'-T-
c_ = _cWM
2v_°_c_/_qCMq - c
ID) Longitudinal Stability Axis
L
CL - _ S ' positive up
D
CD - _ S ' positive aft
:
2Vmo _Cn/_c_ - c
c_ = ac_aM
c_ = acD/_
Pitching moment
derivatives are
identical to
those for body axis
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.) alphysically 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
Cy_
Y
= BCylB_
= _Cy/_
L N
C1 - qSb Cn - _Sb
Cl_ = _CI/8 _ Cn_ = _C_8_
2VTo 8cml_ ev_°Clp - b Cnp - b 8CNI_
2v_° _ci/8r 2VTo 8c_/8rClr - 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
_u = Xu+ Tu cos_o I/see
__ 0_o(_ We)m - 2 CxM - Cx + _ cxcz I/sec
!OSUo
[- CX_ -Xw - 2m
osv_ox8e = - _ CXse
Wo M ]2 _o (cx+ _ %) 11sec
ft
sec2rad
Z*u = Zu - Tu sin_ o
oS_o(_ _)Zu - m - _ CNM - CN + CN(_
ooo[wo .Zw - 2m -CN(_ - 2 _oo (CN + _ CNM
pSc Uo
z_ = - 4m Vmo cN&
PS_T o
ZSe - 2m CNSe
I/sec
I/sec
I/sec
ft
sec2rad
_thM_ = Mu +-_--_I
sec-ft
A-16
MII =
oScUo Cm_ + (Cm +
pSc2 Uo Cm_= l_-y VTo
pSC2VTo
pScVT2o
MSe = - 2Iy- CruSe
% =
I
sec-ft
I
sec-ft
I
sec-ft
I/sec2
I/sec
I/SeC
_/SeC
b) L_ter_-% Body Axis
Yv = (pSVTo/2m) CY_
Y_ = VToYv
Ysa = (pSV2To/2m)CYSa
YSr = (pSV_o/Zm)CYSr
YSr = (pSVTo/2m) CySr
= (_SV_ob/_I_)c_
Lr = (pSVTob2/_Ix) Clr
I/sec
ft/sec2
ft/sec2
ft/sec2
I/sec
_/_
1/sec
I/sec
A-17
L5 a
L_r
YS_
Nr
Nsa
N5 r
NSr
G
2
= (DSVTJ/2Ix)C15
= (PS_TJ/2Ix)C15 r
: (_SV_o/2m)Cy_a
: ( SV ob/21,.)c
: (psv_J/41z)C_p
: (pSVTob2/4Iz) Cnr
= (oS_TJ/2Iz)Cnsa
: (PS_T2/2Iz)Cn5 r
= (L8 + IxzN_/Ix)G
= (Lp + IxzNp/Ix)G
= (Lr + IxzNr/Ix)G
: (_6r+ IxzNSr/IX)G
= (%_ + IxzNS_/Ix)O
= (N_ + IxzL_/Iz)G
: (_p+ I_zLplIz)G
= (Nr + IxzLr/Iz)G
= (NSr + IxzLSr/Iz)G
= (Nsa + IxzI6a/Iz)G
I
IIxlz
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I/sec2
I/sec
I/sec 2
I/sec
I/sec
I/sec2
I/sec2
I/sec 2
I/sec
I/sec
I/sec 2
I/sec 2
I/sec
I/sec
I/sec 2
I/sec 2
A-18
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B-I
b. TRANSFORMATION OF DIMENSIONAL DERIVATIVES
FROM STABILITY AXIS TO BODY AA_IS
(Xu) b
(X )b
(Xw)b
(x,) b
(Xq;5) b
(Zu)b
Longitudinal
= Xu cos2 _o - (Xw + Zu) sin c% cos _o + Zw sin2 _
= Z@ sin 2 ao
= Xw cos2 _o + (Xu-- Zw) sin c_o cos ao -- Zu sin 2 ao
= X@ cos 2 ao -- Z@ sin c_o cos _o
= Xq; 5 cos ao -- Zq;5 sin _o
= Zu cos2 _o -- (Zw--Xu) sin _o cos oo --Xw sin 2 _o
(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-_-) b
(Zq;5)b
(MU)b
(M )b
(_)b
(Mq;5) b
(ly)b
= Z@ cos 2 c_0 + X@ sin oo cos ao
= Zq;8 cos ao + Xq;8 sin c%
= Mw cos ao --Mu sin ao
= -¢4@ sin ao
= M w cos c_o + Mu sin _o
= M, cos _o
= Mq; 8
B-2
(Yv; )b
(Y÷)b
(YP)b
(Y )b
f
(Lr) b
!
(N$) b
(N )b
(Nr)b
(IX)b
(Iz) b
(IXZ)b
Lateral-Directlonal
= Yv;5
= Y@
= Yp cos co -- Yr sin co
= 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
= L_ cos 2 _o -- (Nr -- _) sin ao cos Go -- N_ sin 2 _o
T
= N_; 5 cos C_o + L_;5 sin co
! !
= N_ cos c% + L_ sin _o
= N_ cos 2 Go -- (N_ -- _) sin Go cos ao -- L_ sin 2 co
: N$ cos 2 ao + (L_ + N_) sin ao cos Co + _ sin 2 Go
= Ix cos2 Go + 2Ixz sin ao cos co + Iz sin 2 ao
= Iz cos 2 Go -- 2Ixz sin co cos co + Ix sin 2 c_o
= (Iz -- Ix) sin ao cos ao + Ixz(COS 2 _o -- sin2 Go)
B-3
APPENDIXC
EQUATIONSOFMOTION,TRANSFERFDT_CTIONS,ANDCOUPLINGhq]_RATORS
I • Longitudinal
a. Eouations
(I-xa)s-x;
-z_s - z[
--_s-N
-X_ s- Xw
(I-z_)s-zw
-(M,_+Mw)
(-Xq+Wo)s+g cos 8o -]
(--Zq--Uo)s+g sin 8o
s2 --MqS
u
w
8
I" X$e-
= ZSe
M{5e
[Se]
q. = .SO
fi = --w cos Oo + u sin O0 + (U o cos O0 + W o sin 0o)8
az = 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_)
NOTE:
= -(Mq + XU)(J -- Z_) -- Z w- M_
- Xw_ + Wo[M_ + M_(] - Z_)] + g_ sin 80
Terms including Xd, Zfl, Mfl_ X@ are neglected in polynomial expressions.
C-I
2)
D ---x_(Mqz_-._)-MuX_+Mqx_z_+g[%z_+M_(_-z_ oo_eo+Wo(M_z_-._z_)
+ g(Mw-%X_)sineo
E= g(%Z* - MuZw)oOSeo+ g(MuXw- _,X_),i,, eo
Numerators
N_ = Ass2 + Bes + C8
= %_ + %(, -%)
B0 =xs[_z_+._(,-%)]÷%(_- %x_)-%[m.+×*!_-%)]
ce ="xs(%,,z_-M_z_)+zs(M_x_. %,x*)+%(ZwX_ - x,z*)
IAu = X5(I - Z.)
I_E = Au S3 + Bus2 +Cus +D u
W
Bu = -_[Mq(,-z_)+ z_+ _] + %x_ -Wo[%% + _o('-%)]
+ Wo(Zw%-MJ_) + gX8% sineo
Du = g(ZwM 5 - MwZs)cos eo + g(XsM w - MSXw)Sin 80
N_ = Aw s3 + Bw s2 + CwS + Dw
Aw= Z5
B_= -%(Mq+ xu)+ UoM5+xs_
Cw = X_(ZsMq- UoM_) + Wo(ZsM u - _Z_) - gM5 sin eO+ X5(M_U o - Z_Mq)
Dw = g(Zs_ u - %Z_)cos eo + gMsX _ sin @o- XSM_g sin e O
H-747 C-2
N_ : A_s3 + B_s2 + Cis + Di
A£ = - cos eoAw+ sin OoAu
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_s4+Ba[_3+C_[s_+D_ls+E 'a z
A_ = A_ - ixAe
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
s-Y v
!
-b
Wos + g cos e o
VT o
s(s-_)
Uos--g sin eo-
VToS
V
--Lr
!
s--N r
Ps
r
t
Y5 a Y5 r
! !
L5 a L5 r
! t
N5 a N5 r
Ia]r
v = VToO
= _p_ +---r tan 8os s
] r
cos eo s
!
ay =
sv + Uor -- WoP-- g(cos 8o) _
ay + lXlat sr -- izS p
C-3
b. Transfer Functions
5 a Alat
r N_Srm _. m
5r Alatetc.
4I) Denc_Linator, Lhlat = as + bs 3 + cs 2 +ds+e
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 eo + N_ sin e o)VT o VT o
W o
v%
= _ [(_N_-- N_L_) cos eO- (N_ - L_) sin 80]VT o
2) 5 (5a 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
C0 Y_ (_N_ "'_'_ _ __----g (N_- L_N_) U°= -- _pLr/ + L_ VTo cos eo + --VT°
Wo , , , , , g
+ _ (NsL r -- LSNr) + N5 _ T sin 8oVTo o
D_ = _VT° (N_L_ - L_N_) cos e0 +_9_gVT° (N_L_ -- N_) sin 80
C-4
N_5 = Aps3 + Bps2 + Cps + Dp!
Ap = L5
= LS(Nr + Yv) + NSLr
VT o
g (L_ -- N_) sin eoDp = -- VTO
N_ = Ar s3 + Br s2 + Crs + Dr
f
A r = N8
. _, f ! f
Br = Y_N_+ n_Np-Ns(Y_ + $)
W oCr = Y_(I%N_- N_%)- L_YvN _ + N_Yv% +-
VT o
-----g(L_N%-NgL%)ooseoDr VTo
(LgN%--NgL%)
N_ = Acs 2 + Bcs + C
A¢ = Ap + A r tan 8o
Be = Bp + Br tan 8o
C¢ = Cp + Cr tan eo
C-5
a' CayS2_ _4s4+_2 + +_ +_4
AT ___
ay VToA_ + lxlatAr- lzAp
!
ay
c_
D_
E_
= VToB _ + UoA r - WoA p + iXlatBr - lzB p
= VToC _ + UoB r- WoB p- g cos 8oA¢ + lxlatC r - izC p
= VTD _ + UoC r- WoC p- g cos eoB ¢ + iXlatD r - izD p
= UoD r- WoD p- g cos eoC ¢
To obtain ay, let lxlat = i z = 0.
H-747 __ _ C-6
