[NASA] Aircraft Handling Qualities Data

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

I

g

o

i

i

<_ o_ _ _

_ _ _o_

o_ _ _o _ _ _''_'"

_ aa

. _. . _

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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NT-33A

PITCH AXIS

VariableFeel

Input

FST(Ib) _..026

I

s z +.89s + 22.5

Variable

StabilityInput

_]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)_

I

78

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

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(deg)

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12

10

8

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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 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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35

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F-104A

FST(Ib)

i

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32.2 F BOz

Baz assumed to be at pilot location

G57.3

8SsAs(rad)

8s(rad)

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ROLL AXIS

F LAT --I I

ST (Ib) --i 2.7

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2.0

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Figure 111-3. F-IO4A Control System

36

Power Approach Non-Dimensional Stability Derivatives

h = sea level


_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

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0

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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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I I I I 1O0 4 8 12 1.6 2.0

Mach

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J.I m

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8

I0

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Mach

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60k

40k

20k

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"l//f/[_ I

Viscous Domper On Stopb=_

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Mach

Figure IV-5. F-4C Feel System }arameters

6?

III!

i- I, 00

I_://,,,/

//7i °

/

000000oOOq

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l I I I

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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


% = 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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106

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

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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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Figure Vl-3. HL-IO Control System

141

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Figure VI-4. HL-IO Stability Augmentation

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0 .,11" .0 _ 0 I-- co .-_ ,'. 0 .,I" ,-_ .0

.-_ .-i I'M ("-4 r_. _ . ..4 #n

£ _, -- % . .

164

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

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

L I "_oo0o0 "-" 0"- oJ

v

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o _pr-_ Ca

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0 C;

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oJ

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o o___g_oOxo oJ oJ .._

o.I _ _ _ LO_

II 11 II II

"7I-iI-4

168

00

_'_

..A

N

II II II

II)

H

a3

4_0d

c;I

t--4

.r4

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

_0

(deg)

12-

I0--

8-

6-

4-

2-

0 o .2I I I

.4 .6 .8Mach

172

0

w_ o q q q

a

C.)

-- OD

-- 0_

r-

u

0000o o

_00

II! J

11

S _

I 1, I I0 tO OJ -__ 0

..J

--00

r-c_)

--0_

173

CLa 5

(rad-i) 4

5

2

6-

00

JETSTAR38204 Ib

1 I I I.2 .4 .6 .8

Mach

1.2

.8

.4

00

%%%,

I t I I

.2 .4 .6 .8Moch

174

0 o

Mach.2 .4 .6 .8

-.4-

Cma

(rad "i )

I I I I

SL

..... 20,O00ft

---- ----- 40,O00ft

JETSTAR

38204 Ib

.255

00

-.4Cm&,

Cmq

(rad-I)-.8

-1.2

Mach.2 .4 .6 .8

I ! I I

_'*'_:_) Cmq

175

CDM .08 t

(rod "l )

.04 -

00 .2 .4 .6 .8

Mach

0 o

_o I B

-'.2-

CM M -.3 -

(rod "l ) -.4 -

"o 5

-6 -

Moch

.2 .4 . .8

t

I

SL

.... 20,O00ft- 40,O00ft

JETSTAR

38204 Ib.25_

176

.2

CL8 e ,

Cm8 e

(rod'=) 0

.2

-.4

-.6

-.8

-I.0

4 -

m

n

) I I I.2 .4 .6 .8

Moch

CL8 e

JETSTAR

177

Mach

-.4

Cy_

(rad -t)

-,8

0 .2 A .6 .80 I I J I

2 5 3 8 4 6 9 " _,,_

SL- - 20 O00ft

----- 40,O00ft

JETSTAR382041b

Body Axis

.2

.I

Cn_,

Cj_

(rod't) 0

:2

_-" -"_(_- -_ Cn B

Mach•2 .4 .6 .8

I I I I

c_

178

Mach

00 .2 .4 .6 .8I I I I

-.2

C,_p

(rad "I)

-.4

-.6SL

..... 20,O00ft--- ---- 40,O00ft

JETSTAR38204. Ib

Body Axis

Mach

0 .2 .4 .6 .80 I i I I

-.04 -

Cnp

(rod "i)

-.08 --

-.12 -

179

S L JETSTAR

• 20,O00ft 38204 Ib

---'---- 40,O00ft Body Axis

C,t r ,

Cnr

(rod "i )

.2

0

-.I

-2

I I ! I.2 .4 .6 .8

Moch

C_r

Cn r

180

ill

SL JETSTAR

20,O00ft 58204 Ib

40,000 ft Body Axis

.08

CYaa

(rod -I )

.04

I I I IO0 .Z .4 .6 .8

Mach

0 o

Cns a -.01 --

(rod -l )

-.02 -

Mach

,2 4, ; 8,

8a is deflection of aileronon one slide only

181

Cy8 r

(rod -I )2 5 3 846 ""_,o ._

I I I 1O0 .2 .4 .6 .8

Moch

0 o

Mach.2 .4 .6 .8

-.04 -

Cn8 r

(rad "i )

-.08 -

I I I I

' SL

..... 20,O00ft

40,O00ft

JETSTAR382041b

Body Axis

.04

C_8 r

(rod "l )

.02

0 I I I I0 .2 .4 .6 .8

Mach

182

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191

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

0

0,-IID

-,-I,--I

I I0 00 00 _ 00 "- O"

i-

0

O

0

0 0•_ .r-I+_0 0

-Oo3

I, ©

I

O.,-t+_.r-t_d

0_D

.H

cOcO

°H

OrD

O-r-t

•,-I _-, 4.0 4o 4o/ q-t _ q-I

, , _rD _ _

O O Off_ (2) (2) O

4._

II H ii Ii

d_N _ N

_ _ 1---I H H

O.,-t-O

O

O

O

OO

C_

_ 0d 03 O,1I -o 4-, -o

I I

_io_o o o0 0 0 0(D LZh 0 0 00 Oh 0 0 0

II ii II II

d_

O O O

M

®° _ _o

m i1) _

r-_ m O

HH

(1)

.r-t

195

"7,i

o o _-.¢0 odm

I_1 II tl

_0 -Q Io

O

O

!

<

O

5a0co

orj

iHHH>

-H

196

PITCH AXIS

CV-880M

)

-Ch8te

Oh8 e

_-- 8te (rad)

Be(rod)

ROLL AXIS

t -I.425I +.Is 8Sp (rod)

8tac 8to(rad)

_--- Ba(rad)

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

-4.5

-I 2.

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

-0 .UI25

-0. _77

0.129

-o.31 2

-0.011

0.153

-0 .I65

o .00775

-0 .o_97

o .oo8o3

-0.2005

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

-o.o13_

-o.267

•S<,Iv

3!_X

o .133

-0.294

-0.oo_

o.146

-0.165

0.00979

-0.0479

O .O0975

-0.258

0

-0.0071

0

-0.213

-0.01 75

0 .o339

o .oo917

o.I 685

0.01 93

-0.0644

-0.1924

0.0316

0.0020

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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

®

I I0 00 0o ocf "_ o

ea

co

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r_

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212

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0

COa_

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pr_

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b

a_f_

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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

[fj

,-t0

4_

0

_t

PI

r;

I

H

(1)

b._

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

-4

I.2

,_i_,° " _- ._

I" .4..""_ .6 .8Mach

II

1.0

218

0_0

b- _Di P0m_p

I I I I

o. o.

_o.

m

0

uo

O0O0qQ

_00u) od ,_'-

11li

I I I Io. o _ c_Od

_1

o

o.

_5

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

.4-

0 oI.2

I

l

l

, \

.4 .6 .8Mach

I1.0

220

Mach

0 2_ .4 .60 ,--------T-------T-------_

.8 1.07------V---

-.4

:8

Cm a

(rod -j )

-I.2

-I.6

Mach.Z .4 .6 .8 1.0 _I r I I I

B - 74T636600 Ib.25EFlexiable

-8

Cm&, Cn_q

(rod "t )

-12

SL.... 20,O00ft.-.. -..- 40,O00ft

--------®. ]

J

Crnq

221

I m

CL M

CD M

0

.3-

.I m

0 o

I

.2.4 .6 .8 (_ 1.0Mach

!

SL B-747

20,000 ft 636600 Ib40,O00ft .25

Flexible

l.2

1.4

I

/#

//j ®_/ ,

.6 .8 1.0

Cm M

.4

.2

0

-,2

-4

I "(_._ t II I

222

" SL20,000 ft

--------- 40,O00ft

B-747

.4

.3

CL8 e

(rod -=)

I I I I IO0 .2 .4 .6 .8 1.0

Mach

.20 0

-.4-

-.8 --

Cm8 e

(red-I )

-I.2 -

-I.6 -

.4 .6 .8 1.0I I I I

/

y '

II/

I

." 7//

223

Mach

-.4

Cy,o

(rad "I)

-.8

-I,2

00 .2 .4 .6 .8 1.0I I I I I

SL

20,000 ft

40,O00ft

B-747

636600 Ib

Flexible

Stability Axis

Cn_

( rad-I )

.2-

IO0 .2

(rad "=)

-3-

I I I I.4 .6 .8 1.0

Mach

0 .2 .4 .6 .8 1.00 1 I I

/\j

224

SL

20,O00ft40,O00ft

B-747

636600 Ib

Stobility AxisFlexible

00

-.2

Cyp

(rad "l)

-.4

Mach

.2 .4 .6 .8 1.0I I I I I

.O4

0Cnp

(rad "i)

-.04

-.08

.2

I

I1.0

225

SL B-747

20,000 ft 636600 Ib40,O00ft StabilityAxis

Flexible

C_ r

(rad-')

.3-

\ l

I I I I IO0 .2 .4 .6 .8 1.0

Mach

0 0.2 .4 .6 .8 1.0

Cn r

(rad"l)

-.I--

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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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Fcc('b)---_;)_" I

K

C-5A

8esAs (deg)

I 8cc(in)_l -2'92 t_-'(_)_''se(r°d)-I57..3

8.3 _. B32.2 a z at _B

30

20_

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ROLL AXIS

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


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)

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12

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6

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m

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1

4_

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654562 Ib

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C-5A654:562 IbFlexible

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I1.0

251

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(rad -i )

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Cmq

(rad -I )

0

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-12 --

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-20 --

-24 --

-28 --

Mach.2 .4 .6 .8 1.0

i I I I I

C -5A

654362 Ib

.30 E

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, SL

--- --- -- 20,000 ft----. - -- 40,000 ft

=-.%

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252

CL M

CD M

Cm M

00

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654362 Ib

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253

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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

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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60,O00ft _/ // f "/'-

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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

I/sec 2

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

¢0H

t_

A_q

¢0

0

r_

H

cr_H

F-I

rj_

C_,HCO

!

o o

eJ m0 0

I II

4,r

d

,,,'t "r4 _ _

r_ c_ r,_ U

+ i i -t-

o 0 0 0

¢..) U 0 0

I-¢ k /.-,

'o ' ' ÷ 'o& _0 0 0

II II H II n tl H 11

I

r,_

¢O

r.,3

m

_1 r_ c.) r_

o o

II II II II II II II U il II n tl

r.3

!

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

k

Z .... _ .-

- L-

[=. ..... _ __ "

=_ -- _-_. .... :7 _ _ ..... . • - _ .

p

-- -Lg'. 3

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