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ID-A165 38 AIRCRAFT PERFORMANCE OPTIMIZATION WITH THRUST VECTOR 1/238 CONTROL(U) AIR FORCE INST OF TECH MRIGHT-PATTERSON AFB

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AIRCRAFT PERFORMANCE OPTIMIZATION

' I THRLST VECTOR CONTROL

THESIS

Mark S. Fellows

3, AFIT,'GAEiAA/85D-6

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ApProvod tor public relgahIi

.Distbution Uniml%.d

,E?ARTMENI OF THE AIR FORCE

AIR UNIVERSIY" AIR FORCE INSTITUTE OF TECHNOLOGY

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AFIT/GAE/AA/85D-6

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WITH THRUST VECTOR CONTROL

THES IS

Mark S. Fellows,-p

AFIT/GAE/AA/85D-6

Approved for public release; distribution unlimited

AFIT/GAE/AA/85D-6

A


WITH THRUST VECTOR CONTROL

THESIS

Presented to the Faculty of the School of Engineering

of the Air Force Institute of Technology

Air University

In Partial Fulfillment of the

Requirements for the Degree of

Master of Science in Aeronautical Engineering

Accesion For

NTIS CRA& IDTIC TAB

Unannounced 0

Justification

Mark S. Fellows, B.S.A.E.By ... ........................Dist. ibutior, I

Availability Codes

Ava,; ard/or

V. December 1985 Dist Special

A-Approved for public release; distribution unlimited 1

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Table of Contents1Page

Acknowledgements ....... .... ......................... i

List of Figures ........ ... .......................... iii

List of Tables ........ ..... .......................... vi

List of Symbols ..... .............. ......... .... vii

Abstract ........ ...... ............................. ix

I. Introduction .I...... ....... ........ .. 1

Background ....... ..... ........................ 1Problem Statement ........ .. ..................... 2Assumptions ........ .... ........................ 3Summary of Current Knowledge ....... ............... 3Approach ....... ........ ..... .......... 5

II. The Aircraft Performance Problem ....... .............. 6

Phases of Flight ........ .. ..................... 6Equations of Motion ....... ... .................... 7Aircraft Characteristics ........ ................. 10Atmospheric Model ....... ..................... .... 12

g' Control Variable Constraints .... ............... .... 13

III. Aircraft Performance Equations of Motion ... .......... ... 15

Trimmed Flight ........ ...................... .. 17Functional Relationships ...... ................. ... 18Flight in the Vertical Plane .... ............... .... 20Flight in the Horizontal Plane ..... .............. ... 27Summary ....... ... .......................... ... 31

IV. Aircraft Performance Computer Program....... .... 32

V. Optimization Techniques . ....... ....... ... 36

VI. Results ....... ... .......................... ... 39

VII. Conclusions and Recommendations ........ ...... 53

Appendix A: Aircraft Performance Computer Program Data Input . . . 54

Appendix B: Results From Using the Traditional Equations of Motion 67

Appendix C: Results From Using the Complete Equations of Motion 88

% %

Appendix D: Results for Subsonic Cruise.................... 109

Bibliography......................................... 116

-* Vita..............................................1i17

* "7

I.

-

.

A'

Acknowledgements

I would like to thank my thesis advisor, Dr Curtis Spenny, for

contributing much time and effort in helping me complete this project.

I also appreciate the help and advice given by my thesis committee,

consisting of Dr Robert Calico, Capt Lanson Hudson and Dr Peter Torvik.

I would also like to thank the members of the sponsoring organization

that contributed to this effort, in particular, Jerome Forner, Richard

Dyer, Jacqueline Harris, Richard Johnson and Lt Charles Brink. Finally,

I would like to thank my wife, Kathy, for her support and understanding

during the 18 month program at AFIT.

iZ.

7'.

List of Figures

Figure Page

1. Aircraft Performance Problem. . .............. . . 9

2. Definition of Thrust Vector Angle .... ... .............. 15

3. Trimmed Flight ......... ........................ ... 18

4. Thrust's Contribution to Lift .... .. .............. ... 33

5. Flight Envelope, Military Power .... ............... .... 42

6. Flight Envelope, Maximum A/B Power ..... .. .............. 43

7. Sustained Turn Rate, Sea Level (Case 1) ... ........... ... 68

8. Sustained Turn Rate, 10,000 ft (Case 1) ... ........... ... 69

9. Sustained Turn Rate, 20,000 ft (Case 1) .... .......... ... 70

10. Sustained Turn Rate, 30,000 ft (Case 1) ... ........... ... 71

11. Sustained Load Factor, Sea Level (Case 1) ... .......... ... 72

12. Sustained Load Factor, 10,000 ft (Case 1) ... .......... ... 73



15. Specific Excess Power, Military Power, Sea Level (Case 1) . 76

16. Specific Excess Power, Military Power, 10,000 ft (Case 1) . . 77

17. Specific Excess Power, Military Power, 20,000 ft (Case 1) . . 78

18. Specific Excess Power, Military Power, 30,000 ft (Case 1) 79

19. Specific Excess Power, Maximum A/B Power, Sea Level (Case 1) 80

20. Specific Excess Power, Maximum A/B Power, 10,000 ft (Case 1) 81



23. Thrust Required, Sea Level (Case 1) .... ............. ... 84

24. Thrust Required, 10,000 ft (Case 1) .... ............. ... 85

iii

25. Thrust Required, 20,000 ft (Case 1) .... ............. ... 86

26. Thrust Required, 30,000 ft (Case 1) ...... ....... 87

27. Sustained Turn Rate, Sea Level (Cases 2 & 3) ........... ... 89

28. Sustained Turn Rate, 10,000 ft (Cases 2 & 3) ........... ... 90

29. Sustained Turn Rate, 20,000 ft (Cases 2 & 3) ...... ... 91

30. Sustained Turn Rate, 30,000 ft (Cases 2 & 3) ........... ... 92

31. Sustained Load Factor, Sea Level (Cases 2 & 3) ........ .... 93

32. Sustained Load Factor, 10,000 ft (Cases 2 & 3) .... ........ 94

33. Sustained Load Factor, 20,000 ft (Cases 2 & 3) ...... .... 95

34. Sustained Load Factor, 30,000 ft (Cases 2 & 3) .......... ... 96

35. Specific Excess Power, Military Power, Sea Level (Cases 2 & 3) 97

36. Specific Excess Power, Military Power, 10,000 ft (Cases 2 & 3) 98



39. Specific Excess Power, Maximum A/B Power, Sea Level(Cases 2 & 3) ...... .... ....................... ... 101

40. Specific Excess Power, Maximum A/B Power, 10,000 ft(Cases 2 & 3) ...... ... ........................ ... 102



43. Thrust Required, Sea Level (Cases 2 & 3) ... ........... ... 105

44. Thrust Required, 10,000 ft (Cases 2 & 3) ... ........... ... 106



47. Specific Range, 30,000 ft (Case 1) ....... .............. 110

48. Specific Range, 35,000 ft (Case 1) ..... .............. ... 111

iv

(.

9''

49. Specific Range, 40,000 ft (Case 1) ...... ............ .. 112

50. Specific Range, 30,000 ft (Cases 2 & 3) ... ........... .. 113

51. Specific Range, 35,000 ft (Cases 2 & 3) ........... 114

52. Specific Range, 40,000 ft (Cases 2 & 3) ... ......... .. 115

I-

'4

List of Tables

Table Page

I. Results: 0.7 Mach, 10,000 feet ..... ............... ... 44

II. Results: 0.8 Mach, 10,000 feet ..... ............... ... 45

III. Results: 0.9 Mach, 10,000 feet. .. .............. 46

IV. Results: 1.0 Mach, 10,000 feet ............... 47V. Rsut: 0. ac,2,00fet.........................4

V. Results: 0.8 Mach, 20,000 feet ....... ............... 48

Vi eut:10Mc,2,0 et... . . . . . .. .. . 49

VII. Results: 1.2 Mach, 20,000 feet ..... ............... ... 50

VIII. Results: 0.9 Mach, 30,000 feet ..... ............... ... 51

*IX. Results: 1.4 Mach, 30,000 feet. .. .............. 52

.4.

vi

'A A*4* ***N

List of Symbols

CD -drag coefficient

CL - lift coefficient

CL - lift curve slope due to angle of attack

CL - lift curve slope due to canard deflection

CD - drag

E - energy

F - gross thrustg

FN - net thrust

g - gravitational constant

h - altitude

K - induced drag coefficient

lc - distance from canard to center of gravity parallel to x-axis

1c - distance from canard to center of gravity parallel to z-axisz

1 - distance from nozzle to center of gravity parallel to x-axisx

IN - distance from nozzle to center of gravity parallel to z-axisZ

L- lift

m - aircraft mass

M - Mach number

n - load factor

P - specific excess powerS

q - dynamic pressure

Q - sideforce

sfc - specific fuel consumption

S - wing reference area

t - fuel flow slope with thrust-pf

Vii

., ,%

to0 - fuel flow at zero thrust

T - thrust

V - velocity

W - aircraft weight

X - downrange

Y - crossrange

a - angle of attack

K Y - flight path angle

- canard deflection angle" C

6N - nozzle deflection angle

E. - thrust angle of attack

S- bank angle

SV - thrust sideslip angle

7T - thrust power setting

P - air density

T -aircraft angle

X - heading angle

Subscripts

c - canard

WB - wing/body

0 - zero lift condition

'."

viii

_V• ."

- - 'A' *. -.

*Abstract

The objective of this investigation is to determine to what extent a

highly-maneuverable aircraft's overall performance capability is

enhanced by thrust-vectoring nozzles. The resulting performance

capabilities are compared to a baseline configuration with non-thrust-

vectoring nozzles to determine the effects and advantages of thrust

vectoring.

The results indicate that the use of vectored thrust can

significantly increase an aircraft's performance capability in turning

flight. The greater the demand on the aircraft in a turning combat

"- scenario, the more the aircraft utilizes its thrust-vectoring capability

to complete the task. The results also indicate that the use of

vectored thrust in other phases of flight -- such as cruise,

acceleration and climb -- only slightly increases an aircraft's

performance capability.

e

ix

.7N

AIRCRAFT PERFORMANCE OPTIMIZATION WITH THRUST VECTOR CONTROL

I. Introduction

Background

A fighter aircraft's performance capability mainly consists of a

combat mission radius associated with its close-in combat

maneuverability. By evaluating the aircraft's performance

characteristics in segments which, when added together, define the

combat mission profile, the design of the fighter aircraft can be broken

down into three parts: climb, cruise and combat. The aircraft's

maximum climb performance is determined by the engine's maximum

available thrust; optimum cruise performance is determined by its

aerodynamic and propulsive efficiency; and combat performance is

determined by maximum turning capabilities -- dictated by structural and

angle of attack limits.

In an effort to improve a fighter aircraft's performance without

changing the basic design, the Air Force is currently investigating the

use of vectored engine thrust by developing the F-15 short takeoff and

landing (STOL) demonstrator. By installing advanced aerodynamic and

!V propulsion control concepts on an "off-the-shelf" F-15, the Air Force

expects the F-15 STOL/maneuver technology aircraft to "yield combat

performance and runway flexibility improvements of a magnitude normally

associated with the development of an entirely new aircraft" (1). The

primary modifications to the F-15B two-seat flight test aircraft will be

"the addition of controllable canards above the engine inlets forward of

the main wing of the aircraft" and "two-dimensional nozzles at the rear

i- %

. . . . . ..

- of the F-15's Pratt and Whitney F1O0 engines." The F-15 STOL

demonstrator is expected to begin flying in 1988, testing these

potential applications to the next generation of Air Force combat

aircraft." The Advanced Tactical Fighter, nicknamed as a

*superfighter," might employ vectored engine thrust -- "an especially

welcome feature In a superfighter because of its small wings" (2).

Several studies present optimal controls and trajectories to

7minimize an aircraft's turning time, one aspect of an aircraft's overallperformance capability. Humphreys, Hennig, Bolding and Helgeson (3)

investigated three-dimensional aircraft dynamics. Johnson (4) included

the possibility of in-flight thrust reversal. Finnerty (5) constrained

- " the maneuver to the vertical plane. Brinson (6) considered the effects

of sideforce and Schneider (7) considered the effects of vectored thrust

in reducing the time to turn. Johnson, Brinson and Schneider all found

"substantial benefits in utilizing additional controls to reduce an

aircraft's turning time in three-dimensional flight. This study, in

contrast, investigates a highly-maneuverable tactical aircraft's overall

performance capability enhanced by thrust-vectoring nozzles and

restricts turning flight to the horizontal plane.

Problem Statement

This investigation seeks the thrust vector angle schedules which

will optimize various air combat energy maneuverability parameters --

including specific excess power, maximum sustained and instantaneous

turn rate, and the power setting required to sustain a given load factor

and energy level.

2

4NJ

The controls to be optimized are nozzle deflection angle and thrust

sideslip angle (where applicable). These controls are to be considered

unconstrained initially and subsequently constrained to practical

physical limits as dictated by the F-15 STOL demonstrator design.

To evaluate the effects of thrust vectoring on fighter aircraft

performance, the optimal thrust vector angle schedules and associated

performance results will be obtained and compared against the results of

a non-thrust-vectoring configuration.

Assumptions

Several assumptions regarding the aircraft, its dynamics and the

controls are incorporated into this study. These issumptions are not

only necessary to reduce the complexity of the problem to manageable

proportions, but are common in this type of study as a source of

meaningful comparison of results. The assumptions are:

1. the aircraft is a point mass

2. flat, non-rotating earth

3. NASA 1962 Standard Atmosphere (8)

4. constant gravitational acceleration

5. coordinated turn (no sideforce)

F. instantaneous controls

Summary of Current Knowledge

Aircraft performance analyses done within the Air Force and industry

have traditionally been done using graphical and analytical methods with

underlying assumptions that the angle of attack and thrust vector angle

are small and consequently neglected. In the case of highly-

3

maneuverable aircraft utilizing large angles of attack and high thrust-

to-weight ratios (such as the F-15 and F-16), the negligible angle of

attack assumption becomes less accurate but will yield acceptable

conservative results. In the case of the F-15 STOL demonstrator where

thrust-vectoring nozzles will be used, the thrust vector angle becomes a

primary control variable and will directly influence the canard

deflection.

Current aircraft performance computer programs in use throughout the

Air Force are typically generic -- meaning that they are applicable to

nearly every type of Air Force aircraft, such as cargo, transport,

trainer, attack and fighter aircraft. To keep the programs from

becoming too complex, the small angle of attack and thrust vector angle

assumptions were built into the logic since there was no real need for

these capabilities at the time. With the advent of the F-15 STOL

demonstrator program and its eventual Advanced Tactical Fighter

applications, the inclusion of angle of attack and thrust vector angle

as additional control variables in optimal performance analyses has

become a necessity for aircraft performance engineers.

There is only one aircraft currently in production and service in

the United States that utilizes thrust-vectoring nozzles -- the AV-8

Harrier, flown by the United States Marine Corps. The Harrier is

capable of vectoring its four exhaust nozzles through angles of

approximately 100 degrees, giving it vertical and short takeoff and

landing capability (V/STOL). Low speed pitch, roll and yaw attitudes

= are controlled by six small reaction control jets placed in appropriate

locations on the aircraft and are integrated into the flight control

*4

Ie l W I ' N = }n - Ih' - I l I I ' - -I I -

system. The Harrier uses its thrust-vectoring capabilities mainly to

provide direct lift since the exhaust nozzles are symmetrically located

about the aircraft's center of gravity. The F-15 STOL demonstrator, on

the other hand, uses its thrust-vectoring capabilities to provide both

direct lift and pitch control through its integrated control system that

governs the nozzle deflection angle/canard deflection interaction.

Approach

Definitions of all aspects of the aircraft performance problem

.i including models and constraints are discussed in Section II. The

derivations of the equations of motion of an aircraft in straight and

level flight, climbing flight and turning flight are presented in

Section III. These equations of motion include the angle of attack and

thrust vector angle contributions which are traditionally neglected. A

direct comparison of the traditional equations of motion is also covered

in this section. The changes necessary to transform the traditional

equations of motion in an existing aircraft performance computer program

to those that include angle of attack and thrust vector angle are

discussed in Section IV. The methods used in optimizing the aircraft's

performance with vectored thrust are presented in Section V. The

results of this study are then discussed and the use of thrust vectoring

is compared to the non-thrust-vectoring baseline in Section VI.

Finally, conclusions and recommendations are given in Section VII.

5

?J. Q - - :,

II. The Aircraft Performance Problem

Before results can be analyzed and compared, it is necessary to

completely define all aspects of the problem. The problem will be

defined in terms of the different phases of flight to be investigated,

the characteristics which model the aircraft, atmospheric properties,

and practical physical constraints on the control variables.

Phases of Flight

The different phases of flight are determined by setting certain

state variables and/or their derivatives equal to zero and letting the

other state variables vary within the optimization. The phases of

flight included in this study are:

1. straight and level flight

a. acceleration

b. cruise

2. climbing flight

3. turning flight

a. sustained turn

b. instantaneous turn

The takeoff and landing phases are not included since they require an

optimal trajectory analysis beyond the scope of this study. This study

concentrates on the aircraft's mission performance applications, which

treat the takeoff and landing portions of a mission profile as segments

of flight that use fuel with no time or range considerations. With the

*1 6

.2-%

phases of flight included in this study and appropriate approximations

for takeoff and landing, a typical fighter aircraft mission profile can

be analytically performed.

Equations of Motion

The equations of motion for flight of a point mass aircraft over a

flat, non-rotating earth are derived by Miele (9:42-49) as

X = V cosY cosX (i) *'ii

Y f V cosY sinx (2)

h V sinY (3)

mV T cosE cosv- D -mg sinY (4)

1

X cosP cosy - Ysil = mV {T cose sinv - Q + mg sinp cosy) (5)

X sl cosy + YcosU fT sinE + L - mg cos cosY) (6)

The definitions of all the variables used in this study are contained in

the List of Symbols preceding the Abstract and are shown pictorially in

Figure 1. Since this study does not allow for sideforce, Q = 0.

Rearranging, the equations of motion become

X - V cosy cosx (7)

7 '

'%N

Y V cosYsin X (8)

h -V sin Y (9)

g (T cos ecos v- - sinY} (10)

X X y cos sinv cosP + sine sinp) + L sinli (11)

Y = ( (sine cosP - cose sinv sin) + L cosU - cosY, (12)

These equations are written in the wind axes and describe the aircraft

motion with respect to an earth-fixed coordinate frame. The state-.N

variables are X, Y, h, V, X and Y. The variables P, C and V are

control variables. The aircraft weight (W) is considered constant for

the point performance calculations, but will vary when used in quasi-

steady integrations.

The lift, drag and thrust forces will be discussed in the next

paragraphs and will give rise to three more control variables.

.4-

84

,.4.

I ,

LCOS I'

HoHiorio

Figure 1 -- Aircraft Performance Problem

91I]

Aircraft Characteristics

IThe common coefficient forms of the aerodynamic lift and drag forcesare

2p L= ov S CL (13)

D= PV S CD (14)

From incompressible aerodynamic and thin airfoil theories, the lift and

drag coefficients can be expressed as

CL C +CLCL +C ciC CL S6 (15)

LwB + c c

CC

tL C

""CD = CDw + = CD + KWB C.+ CDO + cC(6

WB OW

which shows that the lift coefficient is a linear function of angle of

attack (a) and canard deflection angle (6c) and that the drag

coefficient varies parabolically with lift coefficient. These simple

yet descriptive relationships give rise to the terms "linear lift curve

slope" and "parabolic drag polar" and identify the control variables

associated with the aircraft's aerodynamics. The aerodynamic lift and

.. drag data used to model the aircraft in this study, however, have been

derived from flight test and analytical methods and exhibit the same

trends as the linear lift curve slope and parabolic drag polar. These

10

°*

- . . . . . .

data, contained in Appendix A, realistically model the aircraft's

aerodynamics with angle of attack and canard deflection angle as control

variables.

The engine data is also derived from flight test and analytical

methods and does not resemble the ideal jet theory where engine thrust

is considered only as a function of altitude. The thrust and fuel flow

characteristics can be written ideally as

T = T Tr (17) sfc - Te, = max (T ff T 0 o )(B

where Tmax is a function of velocity and altitude and the thrust power

setting (n) is the control variable associated with the aircraft's

propulsion system. These data are also contained in Appendix A.

The formulation of the lift, drag and thrust relationships has

introduced several aircraft parameters and three control variables: a ,C

and 7T. Approximate values for the aircraft parameters in the case of

5 the F-15 STOL demonstrator at a Mach number of 0.8 and an altitude of

30,000 feet are:

p.- CL 0.1 CL 0L0 L0* T ,E c

C = 0.0200 CD 0.0013

0 c

CL = 0.05 (1/degree) CL = 0.0145 (1/degree)

t KWB- 0.25 K - 0.105

V--\' md ','' ' , A. ** " % ". . . -- *, . ,, *,*, . . . ". , .* . 1..o .P'.r% .. I. -

\"- 2

S =608 ft W = 35,000 lb

Tmax = 10,900 lbT (Military Power)

Tmax = 22,968 lbT (Maximum Afterburner)

tff = 0.833 lbf/(lbT hr) (Military Power and below)

tff = 2.142 lbf/(lbT hr) (Maximum Afterburner)

t o 1000 lbf/hr

These values were used initially with the linear lift curve slope,

parabolic drag polar and engine thrust equations to test the techniques

developed for optimizing aircraft performance with thrust vector angle,

while the results presented in this study are based on the data ini

p. Appendix A.

Atmospheric Model

The NASA 1962 Standard Atmosphere (8) was used for this study and is

limited to the first two layers of the lower atmosphere. This

atmosphere is modelled from sea level to the tropopause (36,089 feet) as

a linearly decreasing temperature layer, and above the tropopause as an

isothermal layer -- the troposphere and stratosphere, respectively. The

aircraft performance program used in this study is programmed with the

complete set of equations to model the NASA 1962 Standard Atmosphere.

12

Control Variable Constraints

i Three control variables -- the throttle setting (7), angle of attack

...- (a) and canard deflection (6c) -- are constrained by physical

considerations. The thrust can neither be greater than the maximum

Pthrust nor less than the minimum thrust of the particular power settingbeing used. The F-15 is capable of throttling both the military and

afterburner power settings. The minimum thrust for the military power

Asetting is taken to be zero, while the minimum thrust for the

afterburner power setting is taken to be 100% military power. The scope

*of this study, however, will only be concerned with throttling military

and not the afterburner power setting for cruise and turning performance

calculations. Since the throttle setting is defined in equation (17) in

terms of the maximum thrust, the throttle setting is limited to

0 <<T< 1 for military power

fiT 1 for afterburner power

Each lifting surface is limited by its own aerodynamic lift limit

and the total lift generated is limited by the aircraft's maximum load

* qfactor. Individually, the angle of attack and canard deflection can not

exceed their stall points; collectively, the angle of attack and canard

deflection can not generate more lift than is tolerated by the

aircraft's maximum load factor. Since the canard is used to trim out

the pitching moment caused by the deflection of the thrust vector, the

canard surface is assumed to be designed such that its stall point is

never reached in normal hrust vectoring applications to maintain pitch

13

.4.

*-.

' ,control authority. In this case, the aircraft is constrained by an

angle of attack limit (defined by a CL of 1.6) and a thrust vectormax

angle limit and not constrained by a canard deflection limit.

In turning performance, the velocity where the aircraft is at its

maximum angle of attack and maximum load factor is the corner velocity.

.}. The corner velocity is the velocity at which the aircraft achieves its

maximum turn rate. At speeds below the corner velocity, the aircraft is

limited by its maximum angle of attack. At speeds above the corner

velocity, the aircraft is limited by its maximum load factor (9 g's).

_ . No constraints were placed on the thrust angle of attack (E) and

-thrust sideslip angle (). While the F-15 STOL demonstrator will have

limits on its nozzle deflection angle (6

0 0-20 6N<+20

this angle was allowed full range in order to determine how much range

7 of thrust vectoring would be exploited if it were available. The

.! -" effects of constraining the two thrust vector angles were later examined

and are discussed in Section VII.

The aircraft's velocity is constrained by the lesser of the

following: a dynamic pressure limit determined by the aircraft's

2structural and flutter characteristics (q = 2131 lb/ft ); or the

aircraft's Mach number limit determined by temperature or engine limits

(M = 2.5). No constraint was placed on the bank angle (i).-4

14

. .* ze

_ RFR N..

III. Aircraft Performance Equations of Motion

Miele's equations of motion for flight of a point mass aircraft over

a flat, non-rotating earth as discussed in Section II use the thrust

sideslip angle (v) and thrust angle of attack (e) as the angles of

successive rotation to which the wind axes must be subjected in order to

turn the velocity vector in a direction parallel to the thrust vector.

When a pair of body-fixed reference lines are introduced into the

derivation of the equations of motion (as depicted in Figure 2), the

thrust angle of attack control variable is found to be dependent upon

the aircraft's angle of attack (a) -- a control variable derived from

the aircraft's aerodynamic characteristics.

Lco

.8.

OLC

0Y

Horizon L

mg

Figure 2 -- Definition of Thrust Vector Angle

15 *1% "

%'E-F r . . . .- .

I.

The nozzle deflection angle (5N) replaces the thrust angle of attack as

i the second angle of rotation in the definition of the thrust vector

orientation, with the body-fixed engine centerline replacing the

velocity vector as the reference orientation. Since this study allows

for no sideslip, the thrust sideslip angle definition is unchanged. The

nozzle deflection angle and thrust angle of attack are related by the

equality

S N + T + a (19)

The equations of motion now become

X - V cosy cos X (20)

Y = V cosy sinx (21)

h V siny (22)

V f g { cos(N + T + a) cosv - - sinyl (23)

T

x"= Vos {_[cos(6N + T + a) sin v cos i + sin(N + T + a) sinu]L

+ L sin p) (24)w

y Rf 1w[sin(6N + T + a) cosp - cos( 6N + T + a) sinv sinn]

+ it cosp Cos y} (25)

16

',t"., 1.6 "°

The first three equations are kinematic relationships and the second

three equations are dynamic relationships.

Trimmed Flight

Since the aircraft is considered to be a point mass with all forces

acting at the center of gravity, there must be no net moments acting on

the aircraft. In the case of the F-15 STOL demonstrator, however, a

deflection of the nozzle will cause a moment since the nozzle's point of

action is not at the center of gravity. The addition of the canard in

the F-15 STOL demonstrator design allows for balancing the moment

induced by the nozzle deflection by deflecting the canard appropriately.

This interaction results in an additional constraint equation relating

the canard deflection and the nozzle deflection. Since the F-15 STOL

demonstrator design does not have a sideforce generator to balance a

moment caused by deflecting the nozzle out of the aircraft's plane of

symmetry, the thrust sideslip angle (v) must be set to zero for trimmed

flight.

The additional constraint equation relates the canard's aerodynamic

characteristics to the thrust (T), nozzle deflection angle, the aircraft

angle of attack and the aircraft's dimensional characteristics (1 ,

x

I N 1, 1N ) by balancing the moments induced by the nozzle and canard

z x zdeflections:

1c [Lc cosa + D sinal + 1c [Lc sina -D c cosa]X Z

+ IN [T sin( N+ )] + 1 N [T cos(N+t)] - 0 (26)x z

17

The lift and drag of the canard (L and D) are functions of the canard

deflection control variable in the same manner as the lift and drag of

the aircraft are functions of the angle of attack control variable.

) Tcos(6 +r

x147Figure 3 -- Trimmed Flight

Functional Relationships

The final set of equations governing the motion of the point mass

aircraft is composed of three kinematic relationships, three dynamic

relationships and one trim constraint equation. The trim constraint

equation transforms the aerodynamic characteristics of the aircraft from

a function of four variables to a function of six variables:

L = L(h, V, a, 9 ) trim L = L(h, V, a 6N , IT)

D D(h, V, a, ) constraint D = D(h, V, a , ' N'" C C N.

The kinematic and dynamic equations have the following functional

relationships:

18

'N

X = X(V, y, X)

Y - Y(V, y, x)

h = h(V, y)

V = V(h, V, Y, a,6c ,8N , T)

x = x(h, V, y, a,6 9 N ', ,96 6N

y = y(h, V, Y, c,6c ' 6N ' I , i)

The aircraft performance computer program used in this study

utilizes point performance optimization, treating the kinematic

"- equations as integrals of motion and the dynamic equations as the

differential system. To accomplish this, the aircraft's downrange (X)

and crossrange (Y) locations along with its altitude (h) and velocity

(V) must be known prior to optimization. Since the program already has

° .routines to optimize the various aircraft performance parameters with

altitude and velocity, the optimization of the aircraft's performance

with thrust vectoring can be considered as a point sub-optimization

problem, or an optimization within an optimization.

Of the twelve state and control variables, seven remain unspecified

and are considered dependent variables. Since there are four equations

in the differential system (including the trim constraint equation),

there are three degrees of freedom in which to optimize the aircraft's

performance (9: 48-51). By restricting flight to the vertical and

horizontal planes and defining a phase of flight by constraining certain

variables within that plane, the number of degrees of freedom in which

to optimize the aircraft's performance can be reduced significantly.

19

%.

Flight in the Vertical Plane

This category of trajectories is represented by a vertical plane of

symmetry which implies

Y - constant (27)

S= 0 (28)

Equation (27) implies that Y = 0, and equation (21) implies that

x = X = 0. The equations of motion become

X = V cos Y (29)

h = V sin Y (30)

V = [T cos( 6N + T + C) - D - W siny] (31)

;'i WV

X 0 (33)

0 = 1 [L cosa + D since]+ 1 [L sin - D cosci]C C C C CX Z

+ 1N [T sin(C N + T)] + 1 N [T cos( 5N+T )] (34)x z

Rewriting, the remaining equations of motion are

20

ft

X = V cos Y (35)

h = V sin Y (36)

V IT cos(N + + a) D -W sin (37)

y [T sin(N + Tr + a) + L - W cosy] (38)WV N

0 = 1 c [L c cosa + D sina] + ic [Lc sina - Dc cosa]

x z '

+ 1 N IT sin(6N+ )] + 1 N [T cos(6N +T)] (39)x z

This reduced system of equations for flight in the vertical plane has

.- two kinematic relationships and three dynamic equations. Of the

seven dependent variables previously unspecified for point performance

optimization, five variables -- 6, 5N' a , 6 and Y -- remainN) C

unspecified, yielding two degrees of freedom.

One common application of flight in the vertical plane is that of

straight and level flight, where the flight path angle (Y) and its

derivative (Y) are set to zero. This implies that the aircraft will

maintain a constant altitude during this flight phase. The equations of

motion reduce to

X= V (40)

I'

V- [T cos( 6 N+ T ) - D] (41)

21

, - , ,- - ..- ,...... % ...- -'- . - - -- '5 ,- I .- , , - , --- ,. -'-

0 =T sin( 6 N + T + a) + L W (42)

0 1 c [L c cosa + D e sina] + 1 [L c sina - Dc cosa]x z

+ 1 N [T sin( 6 N +T)] + 1 N [T cos(N + ) (43)X Z

with dependent variables n '6N a and 6c Two cases of straight and

level flight are of primary interest to the aircraft performance

2 engineer -- acceleration and cruise. Although the equations of motion

are the same, the techniques involved in finding the aircraft's optimal

.9 acceleration and cruise controls are entirely different.

In the case of maximizing an aircraft's acceleration, the throttle

setting control variable is set at some constant value (normally at the

maximum -- 7T 1 for maximum acceleration). This reduces the number of

dependcnt variables to three (6N, a and6 c ), but since the performance

parameter to be optimized (V) is solved for explicitly in the first

dynamic equation (41), the number of equations in the differential

system is also reduced by one. The resultant differential system has

* three dependent variables and two equations, leaving just one degree of

freedom in optimizing the aircraft's acceleration capability. Since

this study is interested in finding the effects of thrust vectoring on

the performance of an aircraft, the one control variable chosen to be

the degree of freedom is the nozzle deflection angle (6N).N

In the constant altitude cruise case, the throttle setting (7r) is

the parameter that is to be minimized. Since the cruise condition is a

22

-4~~ 4 ".

non-accelerating flight phase, the aircraft's acceleration (V) must be

I set to zero. The throttle setting appears explicitly in all three

dynamic equations but also appears implicitly in the first two as a

functional dependency. Thus the differential system has four dependent

Fvariables and three equations, leaving just one degree of freedom.Again the nozzle deflection angle is the control variable that is chosen

to be the single degree of freedom.

The traditional equations of motion for level flight in the vertical

plane neglect the angle of attack and thrust vector angle contributions:

X -V (44)

V - [T -D] (45)

L W (46)

Since the aircraft weight is known, the lift, drag and subsequently the

aircraft's acceleration or cruise throttle setting are easily calculated

-- results from a system of equations with no degrees of freedom.

Another common application of flight in the vertical plane is that

of climbing flight, where the parameter to be optimized is the time rate

of change of the altitude or climb rate (h). The climb rate is solved

for explicitly in the second kinematic equation but can be inserted into

the first dynamic equation by a direct substitution. The equations of

motion reduce to

23

- - .. .-.. ..A - .. .- .. . , - . . . . . . . . .., ? . . -.-. . . .-. .. '. , ' -,

.4

X - V cos y (47)

V Wh - [T cos(6 + T + a)- D -- V] (48)W N g

y - [T sin(6 + T + a) + L - W cosy] (49)WV N

0 = 1 [L cosa + D sina] + 1 [L sini - D cosa]

x z+ 1N [T sin(6N +T) + IN [T cos(8N +T)] (50)

x z

An alternate way of expressing the climb rate is

[T cos (6N + T + c) -D] Vh -- -V (51)

g dh

where V dV is the acceleration correction term. For climbing flight atg dh

a constant true airspeed, the acceleration terms are zero:

V W V VdVj[g V] = gV - Th h 0 (52)

W V dVor V 0 and g dh (53)

The equations of motion for non-accelerating climbing flight become

X V cos Y (54)

24

h f [T cos(6N + T + a) -D] (55)

y g [T sin(6 N + T + a) + L - W cosy] (56)

0 = 1 [L cos a+ D sina] + 1 [L sina - D cosa]C X CZ C C

+ 1 N [T sin(6 N + ) + 1N [T cos( 6N +T)] (57)

x z

The climb rate equation (55) is identical to the equation for the

aircraft's level acceleration (41) when multiplied by a constant factor.

Since the non-accelerating climb rate and level acceleration are the

parameters to be optimized in their respective cases, their

optimizations should result in the same values for the control

variables.

This relationship between the constant altitude acceleration and the

non-accelerating climb is the basis for the specific energy concept

*. described by Rutowski (10). In his approach to the performance problem

using energy concepts, the author computes the time rate of change of

the aircraft's energy in terms of its climb rate and acceleration:

-()= P + Vg V W [T cos(6 N + t + a) - D) (58)

V

For the constant altitude case, Ps = V. For the non-accelerating

case, Ps = h. Optimizing the specific excess power (Ps) optimizes the

accelerating climb rate or the varying altitude acceleration providing

25

% Air.

the desired simplification with no loss in accuracy."

Since the optimization of the specific excess power can be done by

the techniques developed for the level acceleration, the dynamic

equation for the time rate of change of the flight path angle (y) is not

used when optimizing climb rate. This parameter can be calculated,

however, for the non-accelerating climb by making use of the

relationship between the climb rate and the flight path angle:

h V sinY (59)

Once P and h are optimized by the techniques developed for the level

acceleration, the flight path angle and its derivative can be calculated

j directly.

The traditional equations for non-accelerating flight in the

vertical plane neglect the angle of attack and thrust vector angle

contributions:

X V cosy (60)

Vh-V sinY - (T - D) (61)

, WV (L- W cosY) (62)

Once the optimal climb rate is found, the flight path angle and its

derivative are easily calculated.

• "26

Flight in the Horizontal Plane

This category of trajectories is represented by the mathematical

condition

h = constant (63)

Equation (63) implies that h = 0, and equation (30) implies that

Y f 0. The remaining equations of motion are

X = V cos x (64)

Y = V sin X (65)

V [T cos( 6 N + T + a) - D] (66)

X = - [T sin(6N + T + a) sinP + L sinP] (67)

0= T sin(5 N + T + a) cosP + L cosP - W (68)

0 = ic [Lc cosa + D c sina]+ lc [Lc sina - Dc cosalx Z

+ iN [T sin( 6N + T)] + 1N [T cos(6N + T)] (69)x z

This reduced system of equations for flight in the horizontal plane has

L two kinematic relationships and four dynamic equations. Of the seven

dependent variables previously unspecified for point performance

27

. %.. - 4

optimization, six variables -- a, c' and X -- remain

unspecified. The heading angle (X) is only used in the kinematic

relationships and is not included in the dynamic equations, so the

differential system has only five dependent variables, yielding one

degree of freedom.

A common application of flight in the horizontal plane is that of

the instantaneous turn, where the aircraft is accelerating or

decelerating (V 0). This implies that the aircraft will maintain a

prescribed turn rate at the specified throttle setting but will not turn

at a constant altitude, constant velocity combination (energy state)

during this flight phase. Since this study restricts the aircraft to

turn only in the horizontal plane, the altitude must remain constant and

any change from the initial energy state will be reflected in a change

in velocity. By maximizing the aircraft's acceleration (or minimizing

its deceleration), the aircraft's energy gain (or loss) is optimized.

The performance parameter to be optimized (V) is solved for explicitly

in the first dynamic equation (66), so the number of equations in the

differential system is reduced by one. Since the throttle setting is

specified, this leaves one degree of freedom: the nozzle deflection

angle (6.

Another application of flight in the horizontal plane is that of thesustained turn, where the aircraft is not accelerating or decelerating

(V = 0). This implies that the aircraft will maintain a constant

altitude and velocity during the flight phase. The equations of motion

reduce to

28

*. ,

X = V cos X (70)

Y = V sinX (71) -*

0 T cos(N + T +a ) - D (72)

x __ [T sin( 6N+ T +a) sinP+ L sin]'] (73)W= WV

0 = T sin( 6N+ T + a) cosl1+ L cosi'- W (74)NI

0 1 [L cos a+ D sina] + I [L sin - D cosa]C CC C C Cx z

1 1N [T sin( 6 N+t ] + 1 N [T cos(6N +T )] (75)x z

with dependent variables ", N , and 1. There are two cases of the

sustained turn flight phase that are of primary interest to the aircraft

performance engineer -- the maximum sustained turn rate and the minimum

'. throttle setting required to maintain a specified sustained turn rate.

Although the equations of motion are the same, the techniques involved

in finding the maximum sustained turn rate and the minimum throttle

setting are entirely different.

In the case of maximizing the aircraft's sustained turn rate, the

throttle setting control variable is set at some constant value

(normally at the maximum -- 1 1). This reduces the number of

dependent variables to four ( 6 N, at 6c and p), but since the performanceU

parameter to be optimized (X) is solved for explicitly in the second

29

ON

dynamic equation (73), the number of equations in the differential

system is also reduced by one. The resultant differential system has

one degree of freedom and again will be chosen to be the nozzle

deflection angle.

In the case of finding the minimum throttle setting required to

maintain a specified sustained turn rate, the throttle setting appears

explicitly in all four dynamic equations but also appears implicitly in

the first three as a functional dependency. Thus the differential

system has five dependent variables and four equations, and will use the

same control variable as the degree of freedom as the other turn cases.

The traditional equations for turning flight in the horizontal plane

neglect the angle of attack and thrust vector angle contributions:

JLn - L (76)

X = V cos X (77)

Y = V sin X (78)

V - , (T - DI (79)

y, 2 ~X -9 L sinP - [n - 1] (80)

WV

For a sustained turn the thrust is equal to the drag, which determines

the load factor through the drag polar and in turn determines the turn

rate. For an instantaneous turn the specified turn rate determines the

30

-" "--

° r w w w . - r-- . .. 4

load factor, which in turn determines the drag and the aircraft's

acceleration.

Summary

Restricting flight to the vertical and horizontal planes greatly

reduces the magnitude and complexity of the aircraft performance

problem. Applications of this study reduces the flight in the

vertical and horizontal planes to optimization problems with one degree

of freedom.

PII

31

-. -z

IV. Aircraft Performance Computer Program

NSEG (11), a segmented aircraft performance analysis program widely

in use throughout the Air Force, uses the traditional equations of

motion to calculate an aircraft's performance capability. Implementing

the full equations of motion discussed in Section III would require a

major overhaul of the existing equations which would necessitate a

complete checkout for all applications. On the other hand, adjusting

the thrust and drag data to account for the changes in the equations of

motion would leave the existing equations intact while only changing the

data lookup routines. Currently, the aircraft's aerodynamic drag data

is input as a function of the required lift force, Mach number,

altitude, drag index and center of gravity. The engine's propulsion

characteristics (net thrust and fuel flow data) are input as a function

of power setting, Mach number and altitude.-'..'

The NSEG program utilizes a thrust-drag accounting system that

treats the airframe and throttle-dependent drags (ram, spillage and

nozzle drag) as separate and unrelated. This system, when coupled with

the small angle of attack and thrust vector angle assumptions, reduces

Miele's equations of motion (20-25) to the traditional equations ofS

motion (60-62 and 76-80), where the thrust (T) is actually the net

thrust (F) defined byN

F =F - D -D D(1N g ram spillage nozzle (81)

9: and is the resultant propulsive effort of the engine. The thrust and

drag appear in the traditional equations of motion only as the quantity

32

(T - D), which renders the thrust-drag accounting system arbitrary as

long as it remains consistent.

This thrust-drag accounting system becomes very important, however,

when the complete equations of motion are used. In this case, the

thrust (T) is the engine's gross thrust (Fg), which is the actual force

being exerted through the nozzle. The total drag (D) will then have to

include the throttle-dependent drags as discussed above. As the gross

thrust is vectored through a positive angle (6 N+ T + a), there is a

loss in thrust corresponding to a gain in lift. To illustrate this

point, part of Figure 1 is repeated here with additional definitions.

tug

Figure 4 - Thrust's Contribution to Lift

When 6N + T +a) -0, the engine's propulsive force is just Fg. When

(6N + T + a) > 0, the propulsive force along the flight path is

F COs + T + a). The loss in thrust along the flight path is then

the difference between these two forces:

• "; 33

1 % .

F Fg [1 cOs( N + T +a) (82)

In flight, this loss in thrust may be expressed as an increase in drag.

In drag coefficient form, this increase is given by

F [I - cos (6 + T + a)]N D= 2 (83)

D V2 S

The corresponding increase in lift due to vectoring the thrust, as shown

in Figure 4, is

AL-F sin( N + r+a) (84)g N

In lift coefficient form, this increase is given by

F sin (6 + t + a)

AC g (85)L P V 2 S

The total lift and drag can then be expressed as

CL =CL + ACL (86)aero

CD =CD + ACD (87)aero

where C is the lift generated by the aircraft's aerodynamics and CDLDaero aerois its corresponding drag. For v - 0, NSEG's traditional equations of

*motion and thrust-drag accounting system defined by equation (81), along

with these adjustments to the aerodynamic data will provide the same

34

4,

results as if the complete set of equations of motion were reprogrammed

into NSEG. The required data now includes the aircraft's aerodynamic

data and the engine's net thrust and fuel flow characteristics as

before, as well as the aircraft's lift curve slopes and the engine's

gross thrust characteristics. The program uses the gross thrust data to

adjust the aeodynamic data accordingly and uses the net thrust as

before. For 0 O, the turn rate equation (24) and the time rate of

* change of the flight path equation (25) each have an additional term to

be considered and programmed. Since v has been determined to be zero

for this aircraft in Section III, the v- 0 case has not been addressed.

'J. Included in the programming changes to account for thrust vectoring

is the trim constraint equation (26). The moment induced by vectoring

the thrust is counteracted by inducing an equal and opposite moment with

the canard. With the canard deflection, additional lift and drag are

added and taken into account in C L and CD respectively. Theaero

thrust (T) in the trim equation is actually the gross thrust (F ) being

exerted through the nozzle that creates the moment about the center of

gravity.

.S.

35

%6'

V. Optimization Techniques

As discussed in Section III, the aircraft performance problem can be

broken down into several distinct phases of flight, each of which are

one degree of freedom optimization problems. Since the functional form

of the performance parameters to be optimized are not explicitly known,

numerical techniques must be used to search for the optimal control

values. Two techniques -- equal interval search and quadratic

interpolation -- were coupled together to provide an efficient and

effective optimization algorithm with an acceptable interval of

uncertainty.

The equal interval search technique was used to find the interval in

which the optimal solution is located. In this procedure, the control

variable chosen to be the degree of freedom is set at some lower bound

and is incremented until an upper bound is met or until an optimal

interval has been detected. At each point, the performance parameter to

be optimized is calculated and compared to its value at the previous

point. The optimal interval is detected when the performance parameter

calculated is not the optimal value when compared to its previous value.

The optimal interval is then defined as the interval bounded by the

points on either side of the optimal solution determined by the equal

interval search.

The quadratic interpolation technique uses the three points that

define the optimal interval along with their functional values to

determine the coefficients of a quadratic equaLlon that approximates the

performance parameter function in this interval. By elementary

calculus, the optimal control value can then be determined analytically

36

and the optimal performance parameter value can be calculated directly.

Using a second order Lagrangian interpolation polynomial, the quadratic

equation can be represented by

F(x) - ax 2 + bx + c = F1(x(x) + Fx) + F3(x) (88)

-"J where

F -(x) 2 3 f(x 1 ) (89)

x x-x x -x. 21 Xl-X2 X-X 3 ,",

F2(x) " 1 3 f(x2 ) (90)x2-x1 x2-x3

F W X-X1 X-X2 f(x) (91)

3 3x 3_x1 x 3-x 2 .

Equating coefficients, the quadratic equation's coefficients are found

to be

a (x3-x2) f(x1 ) + (xl-x3) f(x2) + (x2-xI) f(x3) (92)(x3-xl) (x3-x2) (x2-x1 )

b = (x 2+x 3 ) (x2-x3)f(x1 ) + (x1 +x3)(x3-x1 )f(x2) + (x1 +X2 )(X l -x 2 )f(x 3 )

(x 3 -x 1 ) (x 3 -x 2 ) (x 2 -x 1 ).'

31 3 2 1

37

4I "

= - • |' • - I r . .... ... ..

2 x2 x3 (x 3 -x 2) f(xI) + x 1 x 3 (x 1 -X 3) f(x 2 ) + XX2 (X2 -x1 ) f(x 3 )C f (x( x - x - 94)

S(x-x 1 )(x3-x 2 ) (x 2 -x 1

The quadratic equation is then differentiated once and set to zero, and

the optimal control value is easily determined:

2F(x) - ax + bx + c (95)

F (x) = 2ax + b = 0 (96)

Equation (89) implies that

"j b

Xopt 2a (97)

Even though this optimization algorithm is not the best algorithm

that could be used to find a function's optimal value, it was used

because the NSEG program already utilizes the quadratic interpolation

technique in optimizing simple functions. In these existing

applications, NSEG systematically picks three points in a given

interval, calculates their functional values, and "curvefits" the

function to find an approximate optimal solution. The equal interval

search and quadratic interpolation techniques were coupled together in

this new application so that a fairly accurate optimal solution would

result.

38

VI. Results

Since the objective of this investigation is to determine to what

extent a highly-maneuverable aircraft's overall performance capability

is enhanced by thrust-vectoring nozzles, the results are shown against a

* baseline configuration with non-thrust-vectoring nozzles such that a

direct comparison can be made. The results are shown for three cases:

Case 1: Results from using the traditional equations

.,2 of motion with angle of attack and thrust

vector angle neglected

Case 2: Results from using the complete equations of

motion with no thrust vectoring

Case 3: Results from using the complete equations of

motion at the optimum nozzle deflection angle.

With the thrust-vectoring nozzles being used in flight to enhance

the aircraft's combat maneuverability, the results are shown for various

points throughout the air battle arena. Parrott (12) defines the air

battle arena as the part of the fighter aircraft's envelope in which

S most of its close-in combat maneuvering takes place. The air battle

arena definition assumes a threat engagement at a high velocity, high

altitude condition. As the dogfight develops, the aircraft dissipates

its energy by maneuvering outside of its sustained envelope and

eventually ends up at a low velocity, low altitude condition. In order

to be effective in a dogfight, the aircraft must be able to maneuver

without excess energy loss and must be able to disengage from the

39

opponent at any time. This requires high sustained load factors and

high level flight acceleration capabilities throughout the air battle

arena.

Figures 5 and 6 illustrate the F-15 STOL's air battle arena

qsuperimposed on the aircraft's sustained envelope for various load

factors. Tables 1 through 9 show the results for the critical Mach-1,.

altitude points of the air battle arena for the cases previously

__ discussed. Appendix B contains graphical data for the first case and

Appendix C contains graphical data for the second and third cases.

Appendix D contains graphical data for subsonic, high altitude, long

range cruise conditions for mission range comparisons. The units for

the different aircraft performance parameters are as follows:

i Specific Excess Power (PS) : ft/sec

Sustained Load Factor : g's

0Sustained Turn Rate : /sec

Thrust Required : lb

Specific Range : NM/lbf

Figures 27 through 34 show that an aircraft's sustained load factor

and turn rate are significantly improved through the use of thrust

vectoring, especially at low altitudes and low velocities. The tables

of results quantitatively show an increase in sustained load factor as

much as 0.5 g at maximum A/B power and 0.25 g at military power, and an

0increase in sustained turn rate as much as 1.5 /sec at maximum A/B and

00.5 /sec at military power in the air battle arena. Figures 35 through

40

141

V''" , ; i - ; "' -'- -.. *-;-,, . ...... V." : '--' ): 4": ; . , - . .- . - ,. -' - .---- ' - ", "-- '---

I-IU.

42 show that an aircraft's specific excess power is increased

*substantially through the use of thrust vectoring, especially at higher

load factors. The aircraft's specific excess power is shown unchanged

" at level 1 g flight. Figures 43 through 46 show that lower thrust is

required to sustain a specified load factor with thrust vectoring,

especially at lower speeds that are not part of the air battle arena.

Figures 50 through 52 show that the aircraft's high altitude, subsonic

cruise performance is improved slightly with thrust vectoring.

L

4!4

. . . . . . . . . - . - - - - - . -

. . . . . . . . . . * .. * *. . 1 , . . . , ' . - -

tqr-

LLJ~ cr UJ

o 0 i zYCL CC 0 LJ L

-~~~ z -.. zZ

-cr -jJLLL uj C3 0x C'

Z -JZZ L

0

C.C)u. . o...... * . ... ...

. . . . . . . . . . . . . . .

. . . cj~ . . ... . .

*L LUJX............ ... ..------ - -

- - - - -------2-

)) . . . . . .. ... . . . . . . . . . .

-4I

N* 0

.- . . ..

.. .. .. .. .. . 009o o o ~ o c

44

CD %z MCiD

Luj U LLJ CDM Z LuJ - e0f

CO L U

DL CC LUE

mr 0 L L

X 0 CCco

Ir .

I~ 0

.. ..... ....1. ......... .(1C)

LL. - 0Ccro

N.,.

LV . .. . ...

LL- 0r . . .... . . .. . . .

U) (f --

LL J CC. ,

LUJ0

&-43

--- -- - - -- -- - -- - - -

TABLE I

Results: M =0.7/10,000 feet

Case 1 Case 2 Case 3

Military Power

P @ ig 266 267 267 @00S

P S@ 3g 188 190 194 @60

P @ 5g -48 -30 9 @140S

Sustained Load Factor 4.74 4.83 5.04 @ 140.4

Sustained Turn Rate 11.3 11.6 12.1 @ 140

% Thrust Required for 55.0 54.1 53.5 @ 103g Sustained Turn

Maximum A/B Power

P @lig 687 687 687 @ 00S '4

P @ 5g 372 401 442 @ 80

S

P s @ g -1 5 5 1 0 6 4- 6 7 8 @ 2 0*Sustained Load Factor 6.28 6.47 7.10 @ 21~

Sustained Turn Rate 15.2 15.6 17.2 @21~

44-

TABLE II

Results: M = 0.8/10,000 feet


Military Power

p P @ 18 259 259 259 @ 0'

Ps @ 3g 201 202 204 @ 3'

Ps @ 5g 51 56 65 @ 8 °

N Sustained Load Factor 5.38 5.45 5.65 @ i00


% Thrust Required for 57.6 57.5 57.1 @403g Sustained Turn

Maximum A/B Power

" s @ ig 794 794 794 @ 00

Ps @ 5g 587 594 606 @ 50

PS @ 9g -595 -484 -169 @ 210

Sustained Load Factor 7.59 7.78 8.43 @ 190


.%

;': 45"

".I

TABLE III


'


Military Power

Ps @ ig 232 232 232 @ 00

Ps @ 3g 181 183 184 @ 2°

Ps @ 5g 58 61 67 @

Sustained Load Factor 5.55 5.61 5.75 @ SP


% Thrust Required for 67.0 66.6 66.4 @3g Sustained Turn

Maximum A/B Power

Ps @ lg 906 906 906 @ 00

Ps @ 5g 732 737 747 @ 5°

Ps @ 9g -40 19 164 @ 150


Sustained Turn Rate 16.7 17.0 17.0 @ 17'

46

-. ---- - --------------------.- --- , , l 9i ,

TABLE IV


Case I Case 2 Case 3

Military Power

P @ Ig -6 -6 -5 @ 10

Ps @ 3g -96 -94 -86 @ 60

Ps @ 5g -283 -278 -252 @ 100

Sustained Load Factor - -

Sustained Turn Rate

% Thrust Required for -.-3g Sustained Turn

Maximum A/B Power

P @ ig 837 837 838 @ 10

Ps @ 5g 560 569 603 @ 70

Ps @ 9g -291 -248 -65 @ 150



-.r. . -.

AAII

TABLE V



Military Power

*" Ps @ig 216 216 216 @ 00

PS @ 3g 117 119 123 @ 70

P @ 5g -266 -239 -158 @ 230o



o0% Thrust Required for 67.8 67.3 66.4 @ 7

3g Sustained Turn

Maximum A/B Power

Ps @ g 603 604 604 @ 1.

PS @ 5g 121 163 260 @ 140~o

P @ 9g -2473 -2068 -1403 @ 29

0• Sustained Load Factor 5.34 5.50 6.00 @ 18

0Sustained Turn Rate 11.7 12.0 13.2 @ 18

48

,

A 8,.-

I.1

t v ,v.. .' ',,, v . .,". * , ."'." :,"- .,, 'k ,:"-'. -""'- --- " '.." ' .; ' " •--.,-•-: ' ,

TABLE VI

Results: M 1.0/20,000 feet


Military Power

P @ ig 51 51 52 @ 1'S

P@3g -80 -77 -67 @ 9'

t @ 5g -399 -386 -337 @ 140


Sustained Turn Rate 3.1 3.2 3.3 @ 7 °

% Thrust Required for - -3g Sustained Turn

Maximum A/B Power -

" @ ig 664 665 665 @ 0'sPs @ 5g 214 236 300 @ 120

P @ 9g -1099 -995 -789 @ 210


Sustained Turn Rate 10.2 10.4 11.3 @ 17'

A49.

.'A°

%; . '"J L'". %" . [ .

J. '.' ,'-.' .- . ... J .'.'. ' ' ....... ' '.'.",' .-- '-"'.r -. •,-., " • " =, h ,, ' ,- , * ,

TABLE VII



Military Power

P @ ig -525 -525 -525 @ 00'° S

P @ 3g -539 -537 -534 @ 50

P s @ 5g -815 -806 -763 @ 130

Sustained Load Factor . -

Sustained Turn Rate -

% Thrust Required for - -

3g Sustained Turn

Maximum A/B Power

. @ ig 410 410 410 @ 0'

P @ 5g 121 136 192 @ 80

P @ 9g -1262 -1175 -889 @ 210



50

L ,-

TABLE VIII



Military Power

P @ lg 144 144 144 @ 0'sP s @ 3g -18 -12 7 @ 10'

P @ 5g -698 -651 -474 @ 27'

Sustained Load Factor 2.89 2.94 3.05 @ 10'


Z Thrust Required for 99.9 @ 1003g Sustained Turn ?A.

Maximum A/B Power

p" @ Ig 479 480 480 @00£" Ps

P s @ 5g -362 -286 -92 @ 200

Ps @ 9g -5592 -4777 -3092 @ 480



51

%

t .. .. .. .. " . ,.. . _ ;,. ;, .... > . ,; .,.. ,,i~ ..- X - -... ,.t,,; .. ,,, ,..e. ,. ..... i...,..g.... :...:.,.;,"d U..

TABLE IX


Case I Case 2 Case 3

Military Power

PS @ Ig -592 -592 -592 @ 0'

PS @ 38 -701 -698 -691 @ 7'

Ps @ 5g -1197 -1177 -1078 @ 14°

Sustained Load Factor - - -

Sustained Turn Rate

% Thrust Required for3g Sustained Turn

IMaximum A/B Power

Ps @ ig 378 378 378 @ 0

Ps @ 5g -228 -191 -74 @ 130

PS @ 9g -2366 -2215 -1733 @ 23



52 'SO

'5 5*' 5 -. .. ..52%.'. - * -

Ir (I -I.

A

VII. Conclusions and Recommendations

Two major conclusions are drawn based upon the results of this study:

1. Thrust-vectoring nozzles can substantially increase a fighter

aircraft's turning performance throughout the air battle arena.

0SnThe + 20 nozzle deflection angle constraint would limit

the aircraft's optimal performance in only a few instances.

2. Level 1 g flight does not benefit from the use of vectored thrust

since the aircraft's wing loading is small compared to that of

turning flight.

Two recommendations are offered for future research:

1. This study concentrated on the air-to-air combat applications of

a fighter aircraft's performance. Air-to-ground applications

should be investigated for the ordnance delivery scenario.

2. Investigate the class of aircraft that might utilize thrust

sideslip vectoring and sideforce generation and the type of

trajectories that may result.

53

I? Jo de V ".A r- .

._

V

V

P APPENDIX A

1'L

Aircraft Performance Computer Program Data Input

4. 5

I

.4!

,7, , ",. , :"

'' ' ' '.',.",,, '"..'+. "..- .;,''"-- ,-' _.-. . -'.'- .+-+,-+ .'+ " ."..+ +7 ".."- ." .'+. .,-'"._ ,.,,',, ' ",' """- :.,, -',

WMWWMWWMWMWMWMWMWMWWMWMW MWMW MWMWMIWMW wM41liMr A MWMM MWMMM mwmwpmwmwIIM

.. REYNOLOOS NUMBER CORRECT104S

* INDAG1uL,

I AO IX-8,I A01Y-1I,AIAB01=o. 910000. ,20000. ,30000. ,40000. ,50000. ,b0uOO. 70000.,

-. 00179-.0012,-.00069.0, .0.)099-00209.00339.00479 $M -. 2-. 00139-.00099,-.00059.09. 00379 .00159.002 5,.0036, s M -.b-. 0012,-.00)08,-.0004, .0,.OO0b,.OOi4,.00O23,.0033, isl-.8-. 001Z,-o0008,-.0004,.O, .00)b,.0ul3,.002)2,.,)u3l, sM=1.o-. 0011,-.00079-.0004,.0,.0005, .00i2,.0020,.0029, SM-L.2

-.0010,-.OO0o,-.0003,v.0,.0005, .O012,.Oild,.0027, &M-1.4-. 00109-.0006,-.00C3, .0,.0005,..00110017,.0023, sm1i.d-.00099-.00069-.0003, .0, .0004 .Q010,.0017,.0022, SM2.0d-.00089-.00069-.0003, .0, .C003.00109.015,.0022, $M-2.0

-. 00079-.0005,-.0002, .0, .0003,.0008,.0013,.0019, SM=2.5

se F-15 FLIGHT TEST DRAG POLARS

I NA02-1 7,

I AO02 Y - 1.,ATABO2-.0,.05,.l,.L5,.2,.259.3,.35,.4,.45,.5,.559.6,.65,

.7, .75,.8,.8d5,9,.95,1.0,1.05,1.1,1. 15s1.2,.4,1.6,

.02289.02259.02309.0-,42,.C254,p.02d4,p.t320, .U360, .04i20,.L'4939 .0580,9.0 685, .0825,. 1005, .1180,. i400 ,.16b3(i,. 16502105, .2400,.27l5,. 2945,. 3367, *38 109,4409 . 8700,lo. 3100

.",222,.0215,.c1220,.023.02O459.02739.03059.03479.039U,.04509.0530,.0635,.u78o0,.0)b0,1ll63,. i396,.1640,i.1873,.21b39,2465,.2793,.3135,v.3ob,,).4lU5,.47)u.9,1j~.3400,

0 .0220,.O2l3,.O2l59o0225, 02't2,.O2b8,.O2')9,.0341,.03909.0453, .0523,. 0b25, .0765, .09!579.*115b,.1395,. 1650,.190',,.2203,.2525,.2880,.32859.3770,.4t3259.5040f.9200,1l.3b5J,0217, .0213, .02 16, .22 5, .0242, 0265, .0298, .0 33 7,.0 383,.04 3 7, .05 2 0 0 63 3, .0 7 80 .094It6, 9 1150 J 9 13 95 9 . 16 6 8,. 19 60,.22909.2643,.3O000.34609.39tui,4550,.52ZdUo935091.4o00u,

q .02l59.02l39eO2209.02319.02449.02699.U3009.0336,.03db,.O445, o053i,.e0646, .078 3,.0953, *li529. 140() ,.i66b,.2000,.23459.2700,.30759.3540,.4075,.4t)539,559,.9t(00,1.42009

o0216,.02l3,.0224,.0236,.0249),.02749.0304,')343,.03969.0466,.0560,.0673,.08C,3,.o973,.ll163,.l413,.170,,v.2045,

* .C530,"3,bS23o790.25lb,ol2b,o0,.75,ol3l,.l70,.215,8

.2470,.28359.32209.3725,.4t2d0,.4850,.o10O,1.0500,1.52009C0300,e0299, .03109.03359.03b1,.0'tiO,.04b5,.05't0,.0623,oC735, .0870 , .1000, * 150,.1330, .1 8,. Ibis,. 1990,.v275,o2 5 b 5. 2 9 15,.p 3 3 2!,. 3 82, 'Y ItJti0i.49CJ9.o330 ,1.rj8uO,1. 580(it

o '3 9 4,.U 3 6 9 .U3 8 99,U4 (o7 0 43 8 *0 4 8 Itp.J34t2 1. 062 5 9. 07 2 8G08489ok)9909.11359.13339 ol5U,.1678,.ltb6s,.Z13U,o2,00,oZ69O,.300,34P4t0 9 ItC b 9. 146 30 o5 "0 0 9. 6 o5 91 15 0G1b2 0 0

.2 8 2 5 .32 15 9. 3 b0 0 15 G .4700, .54U0,.bt'5J,1. 1JOUu,155009*.,1495,.o0473,. t)If52 04tbi ,o jtwd, .()54, t15,oj .01 04t5 q

.09939. 1150,. 13'),. 1555,.- 17J-it. 19 75 9~ 30 1) 27u Ici 0,

w- -0-5,.-- - -, --I-,I - -- v--, . - . /5,.555OWLS VR. wa I . b ,

.3150, . 3S0,. 3703,. 4,,:u ,. 4 ,J, . jo ,. 5Gt'u, . , A. .',o,"0596,.0486,.0490,o 051:,,.'sC5),.,6d2, .753,.,),, iui9 ,

.102 -0,.[ZO0 .14590,.lbtu,.164,%, Z%)93t. , 35G, . t7Z1 .2d309

" U50,O 9 3,.J 4 96,.U51 ,.U53J 6)UUI35,*Lbi4,2.-9J i. LU52,.1239.12 14,.I 5,.17b5,.21O.9.2300,.25 2 0,.2o74,,.296o,. 3170, 3,00, . 3 7 34%, .4 lo ), . 't'U,.4 ,*, .o u0,u.930,U

" 048boO5,1486o042,. 015b )Jb3 9 723,.3,.b oU92C, .109 ,.1300, .1505 .1723, .8 960, .! 19o, .22bU,. 2640,. Zb . 3090,

.3320,.3550,.3850,.4lJ,.45,0U,.4d0O,.51j5O,.6770,0.91St,0.0 *0482,.09490,.0552, .57,.Obbt.,u 90,., 93d,.9IJ2 ,* 1330,•*1575, .ldO), .20"0, .2 , .25k 0.2 75O,•3O00,. 32)0,) 350,. 3700,. 3It 50, .3 0,. J8j . 95j , 5250,0 .550, 4. 950,

• 047, .067 85O .085, .0519,.9 2 53,. 085, .bbb 6, .59 3 o ,. 1087,

•L385,.1b45,.1875,.1960,.237U,.20U2,.2850,. 31d,.330,.3570,.325,.3•075, .41G14 30,s •2Uo0,9.550,'q.5970,0.750,

.0#739 .62,.0483,.0475,.052,.0575,,.0602,.u850,.U025,.237,

. 3450,. 1710,. 3950, .22 10,.• 25, 2 903 ,. 29t0 ,. 3200,. 3 950,

.3700, .3950,.2O03,. ,0, .9", .5OJ,.5700,O. 7100,O.8520,

" • (' ,0, . 04,37, .04,55, .C5u2, .OhiOL, .0 740, .09 Ib, .110L5, .1t 3o* 51609, . 1870, .2 130, .2i30, * 2b50, .2690,.3 150,. JO0,. 3650,* .3950,.41b0,.4o0,.,75u, .qd00,.5350,.5700,.600,30.b00,

.4 204 63 , .0I32, .08U 7, .0529, .0802, .80997, .122 5, . 1500,.1780,.2050,.2300,.2620,.255), .3£00,..:]'),.3650,.39 ,

• ~*,2d, .4,80,.750,.5,0,.5 10, .5J,.s00,.6ds0,0.7900,

4t2 .'LACE CANOPY .R0G

I A030 1,

-)20A9ICi)79., 8000u. ,

U.l,L. 31,1.5",,1.55,2.J5,3.0,.10050, .00050,

2 1) 00 , It ItOO3 0 , ,0 5z70,. )5t

" ".'" .00083, • u0083,

.- 000 .00100, O

.0000,.0.0.

.. •,, F-i 5 CL.-AL.PH"A CURVES

I CLAX- 29,r: ".,ICLAY=L•,

r.-.', CLATAS=O.,•t,. 2,.],.4, .5,.s5,.b, .65,.7,rF" .75,.d6, .85, .99.95, .,.05 ,11,1 s.I, 1.2,I.25, .A0,,2 * ., 5, *5, ,

"",. ,2.2,.09,1.,l.2, 1.',.,.235.,z .5, ,2, 3,2.

25.25,27.900., l.0 7J,3 04.04*Q'40,$=

-0.4,5, 1.07, 2.a, ',. 1, 5.93, 1.19, 7.90, 16.., 9.,i 30, __

"-'-25.25,27.90,30.b5, 3.00,37.Ju,37'.,9.b5,42.UO, .'0, $M=0U.2

" it. L7,CO0509 .0 9,/. 50,bOI3,L~~2.0,.

- -0.51, 0.85, 2.28, 3.6t,, 5.u7, 6.45, 7.13, 7.9o, 8.b- , 9.4,5,1-3-l. 33,11.44,12.,13 .90, 1S. 30, lb.d85, 18.50, 20.25 ,22. 10, 24.00,

.. ,...2b.u5,28o iOo3O.30,32.4,, 34.50t3b.35,38. 1O,39. Su,39.50, SM=, .85

" .90, LL .09, 1.2. 37, 13. I , is. 12 ,1b.67, 13. 3 3,20. 10, 21L.110, Zi. 75,

& . T 1 5. ()0075.000759S ]e ~l) .~ . O 9 9 ,Ot #.O -M ,.

• w" . . "

""," " . 000 83'," '.6008 39 " ,' ' .' " " ", % w% """'. "%

"" ', " - ' "' " "" %' % ' ' - "'vv, ',',,;.._' .-;.-.. 0 1 . 30 . ,0 0 , --.-0.0 .,'.: ."- .. ,.',- -:: -. ,v . : .. '.i Z . .:.'.'..'... .. .: '- -" -". .--9'

- 3 u, .9 , 2.25, 3 . c, 5C ., , t*l(, 7. 5v ?.3 , t;.00, o.75,.0,25.3O,2.00,l. 31,4759.,6.20,1i..L7,29.2u,2u . 2 i. 30

23.I, 70 q*9 5,vZb . 10O,2 1. 2u , 2tj.. O, 9 , Z 0,J6.2u,3L.10931. 10, iM- 1.0-0.J~ V o 1. 14 2. t)5 , s. 1 7, ', t. O .,5v 7 0 3. 3 (1 9 1 . 1~ (. 9 1?. 140 i u. 7 011 55 b 12.-50 , 3o 0, 1 1 i,. tit' , 16 . Ou, 9 17. iv, 1i'4. 3, 920. 7 5, 2 z..-j , 2 3. 2 u2 0 2. 3 0 9 Z6 .3092 7.oz( ,2z7 .2 , e .oeoZ .o ,0 2 7. 2 0,2 7. 2U, M"-L .2

-0.92, 1.01, 3. 10 , .i,, 7 . ,v 1 . uu . , 1 2 .) 13 .dO, 15 . ,1 6.30,17.50, 18. 75,20. ,22. lue3. do,2. uo.,20,bo2,,2 d.20,/ 2.G,2 8.20,28.2, 2. ,,2d.2'),e8.2U, 2d. u, 2d.29,28.20, iM= i .0-0.q6, 2. ll, 4. 93, v .8t qIV'6 1 13.o ? ,9L .CO,9Id. 2gZ , .411.,922. 70,

22.70,22.70,22.70,22. ?U, 2.7u,22 . 70,2 .1u,22.70,22.1u,22.70,22.70,22.70,22. 70,22.7,22. 70,U.?0,22. 70,2Z.70,22.7o, iMaZ .2

-,J.bb, 2.17, 5.03, 7.1?,1). 461J.O,io. z0,1.5,2u.s5,2u.6s,

2.5,20.85 ,20.85,2 ,0. 510 ,0 ,20.05,20.5, 20u. 5, 2U 2. 5

-0.25, 2.55, 5,30, d._l0 J..90,14.90,it.o9,14,.9,O,14.90,91.90,

14. 90,14.909 14.90, 4.9L *149 , 9,14. 90 t.g9 ,1.90,14. 90, 14. 90,14 .1, 0914 .90, 14.90, ).91, L19J. 90, 4.90,14.90, 14.90, 14.90, $M-2.5

• . CANARD DRAG POLAR

|NDA04=11,IAO4Xm23,IAO4Y2,AI B0-.27,-.20,-.1d,-. 16,-. 14,-. 17,-.iO,-.08,-.O6,-.O4,-.02,

0.,,.02, .04, .06, .08,.* 0,. 12,.* 1,,. 16, .18, .20, .22,• 2t.4t6,-8,t .0,L.2,1.4,i.6,L.8,2.O,2.2,2.4,

* i .'i C. 2

.0635,. 0525, .O'd, .u34,, .0262,

.0146, .0140, .0093, .0057, .0o32, .0016,

.0011,.0016, .0032, .0057, .0093, .0i40, .319b,.02b2,i .U34V, .64289 .J52D, .ub35,

.0717, .C' 5, .4079, .0324, .u2St0,. 0 b6s o 132 . OSd , .:054I .u0 2 9 , .UG159.0010,- 00 159 OJ029v . 09514 .3088, .0 132, J, 18 t

.0250, .u32 4, .OSJ7, .U533, .J717,

o 10139 o0719, .05 129 .0U302, .oZ5z,

.0182, .029, .0086, .U053, .j,29, .0014,

.0013,

.0014s, .0029, .0053, .008b, o129, .0182,

.0252, .0362, .C2, .719, .1013,$ 1=0.8

.2732, .1553, .J961, .O61b, .0 a99,.0255, .0159, .004s , .00,2 , .6028 .OC',14.0009,.0014, .0028, a0052, .0094, .0159, .o255,.0399, .Oi, .0')6i, .1553, .2732,

1e181, .32014, *1552, .087o, .0523,.0317, . 18 , .u109, .0059, ..U 3k, .1001,.0014,

0 U 17 , .00319 00s), 109, .1d9, .0317,

.0523, .087b, 7 j511, .3204, .181,$ "1= 1.2

4 .84It2, .0o)7, .05t)5, 04'id U .3',4,#.0255, .Lso, .00')0 .0073, .LUl,, .3022,.001 a•0022, .00,0, .io073, .0119, .ulO, .0255,

=$ 1=. 410#8, .odto, .-)702, 9 5, .9 , t,

.0i1S, G. 22 1 . It , .9 o 0 8 7 . 9L O . 2 24,"

! • 001.9,-

.002 4 .0J4b, .C01l, .0145, .021, .0j15,

.04269 . )515, 1.U702,L .c.sb 6 l104?j,S M=I1.6

.1255, .109, .,d 39, .Uob, .0508,

.0374, .O2 h', .C 17C, .0101, .UO52, .0U25,

.0019,_.0025, .3U52, .Z1ul d,170 .u2b2, .'J374,,

.0508, .066e, .U639, .1139, .L/-S5,-+.. $ ,'1 1.8

.1453, .1199, .0970, .J 76, .054o,

.0431, .0301, .u195, .114, .o658, .0026,

.0019,

.002o, .0058, .0114, .01959 .U301, .0431,

.058b, .07db, .0910, .1199, . L45 3 ,

.1646, .135, .1098, .08bb, .UbbZ,

.U4869 .03389 .0216, .31269 .00639 OO02lq

.0019,

.0027, .O63, .0126, .0218, .0338, .0486,

.Ob62, .08bb, .1098, .1358, .1646,

.18359 .1514,1 .12239 .09b4 .0737,

.0540, .0375, .0241, .01392 .U067, .o0279

.0018,

.0027, .0067, .U139, .0241, .0375, .0540,

.0737, .0964, .1U23, .1514, .1835,* $ M=2.4

.2022, .1667, .1347, .1062, .d10,

.05949, .01412, .Z64, .0151, .0072, .0028,

.0018,0028, .0072, .0151, .02b64 .0412, *059 ,

.0810, .1)6, .13s7, .Ibt7, .2u22,

.. , CANARD LIFT CURVE

I CLCX=,I CLCY= ,ri

" . CLCT I -0.2, t.2,

-27.5, 27. ,-27.0, 27.0,

"".-'-20.0, 26.1. 9

-24.5, 24It.5,9-22. 3, 22.3,

S -19.6, 19.6,-20.2, 20.2,-20.2, 20.2,

.. F-15 MILITARY POWER (FN wIrH SFC ANU FG HOOKS)

INOTOI= 1,or ITOX- b,

IT T O1Y- 9," T AH 0 1 0. I00O., 2 0000., 3000t)., 'oo00., 50000.,0.00, .20, .40, .60, o80, .85, .90, .95, 1.00,

11790., 861,., 6099., 4 1 3t . , 254t2, 1546. , tMO.klu12030., 9117., o09'. , 413-t., 2512. , 1546., M- .2'J1 1970., 9339., bJ0o., 4t13., 2542., 1546., Ma .40

12050., 9775., 154., 6 53., 33,32., u2., S.= .3O

1 190., 91, ., lb"t3., 5378., 34?., 2141., ,i= .9C11680., 91u1., 6o. , 5099. , 35q8., 22u i - .'- )1 1400. )5.,7., / 2 1. , 5 711 7 lO. , z e , 5M-1. "

S 2 - -d --- . , , -

~I r~2x 12,

I TOZYM 9,IT02/Z 6,

* 60.009 71)•.uO .0.,Ok), 90 tC, '05•U(; 100. ,O,

S0.009 •2 , U •99, . q,, du, •9 •9v, . 9 •0 ,

0., 103,, j 30 . 3Csuu., itO() ., 50JU6.,

$ ALTIrUDE =1.357, 1.135, .835, •7o, . 738, .725, S .4- O

.723, .7 , 7, 75$, . 763, .768,2 138, 1.354, L.u12, .1uu, v .847, .817, $,- .20

.60 -2, 12, . t2, .di7, .b18, .820,2€: -.66}9, 9 .08 1, 1.02I5, 9 1. Os I, .9bo, . 9 1 ,) 9 M .• 0

.891t .d8, .dtg .do4, .8849 .683,

3.716, 2.221, 1. 4b7, 1.210, 1u9b, 1.033, SM- .60

• 991, .962, .970, *9., .957, .953,

5.343, 3.008, 1.837, 1.473, 1.293, 1.195, im- .

1.138, 1*104, 1.078, 1.058, 1.050, 1.0',2,

5.827, 3.238, 1.9,19, 1.551, 1.353, 1.242, i-a.o851.179, 1.139, 1 .u9, 1.085, 1.075, 1.066,6.427, 3.53 , 2 .10b, 1.6539 1.429, 1.303, SM = .90

1.230, 1.182, 1 .11, 1119, 1L. 107, 1.o96,7.396, 4.023, 2 .33, .816, 1.555, 1. j4, Sm- .95

1. 317, 1.257, 1.22, 1.17o, 1.161 1, 1.18,8.548, 4.599, 2.65t, 2.005, 1.698, 1.518, $.'i-1.00

1.415, 1.34G, 1.265, 1.242, 1.223, 1.207,$ ALTITUOE = 10000.

1.134, 1.luz, .d15, .7, 7, .711, .709, 1i-0.•0)

.708, .10, .733, .755, .764, .173,

1.867, 1.276, .96J, .881, .s,14 .787, M- .20

.779, .175, .7"0, .d10, .816, .822,

.U8, 10 35, 1. 11i, .975, .907, •87G, $M -t•')

.8549, .d5, .863, .d71t, .b75, .878,

3.233, 1.981, 1.323, 1.i18, 1.020, .9o9, & ,= .0. 44Z . 9 .937, .937, .93t), .9 3 , .)b,

1.o62, 1.0,1. 1•dJ26, 1.31t, 1.009, 1.004,

t.b!3, 2.75e, 1.112, 1.363, 1.2 4, 1.14G, M= •a5

I.U9, 1.067, 1. 09, 1.0314, , 1. , 1.j23,5.321, 2.469, 1. z1, 1.4t58, I.2 81, 1.185, 1*= • U

1.129, 1.100, 1.078, 1.0bI, 1.U54, 1.%48,t• .uo,9 3. 3719 2. 1 )9, 1.593,t 1.*3 60, •1 M .2o19 -'

I. 194, 1.156, 1.127, 1.L05, 1.096, 1.uo ,_7.002, 3.82,, .250, 1.7,4, 1.491, 1.346, S'i= .Cu

1.26b, 1.219, 1.184, 1.156, 1. 1.45, 1.i34,

$ ALTITUDE = 20000.

- 1.155, 1. 15h, .9b4, .13 , .802, .73, S. .. J

:. 763, . lout . 176, .700 , . 793, • 798,1' l.913, 1.5169 i. 095,q .95't •.887, .tj,9, 9 ' s

38)4, .127, .39, .840 , .852, .05b,2 :.91) , 1.829 , 1 . ! 49, i•.0(56, .9779 -o 30,9 vM= •

.910, .9, .907, .915, 919, .922,3.•838, 2.2 3',t 1 . '9, 1.202, 9 1 093, 1 .•O SI , o • Lu

16995, ' , 15, .67 , .987, .9b ,4.12 ., 2.374, 1.v17, 1.250, 1.127, 1. 59, .1 j5

4.491, 2.56, 1.61 , 1. 31b ib,1.176, 1 .u9 8, s .C.1 . 0 0, 1.,J)3 b, 1.O , 1 u I. u2 , .0239 1 *.02i,

5.159, 2.893, 1. 1132, 1.8, 1.253, 1. 18, b 1 .15

1. 102, 1. dJ, i.070, 1.08o, 1.056, I .Cs2,

5.907, 3.t),3, 1.9b5, 1.54 , 1 .341, 1.231, &1=1. (C

1.1OZ, 1.3 3, i.I/, .u2, 1.096, 1.191,

ALTITOJF 30CI'.

. . . .- * . . . '. . -. ...*¢ ,,' , . - - . *... . . , - ,, '. ...- . ". '. ....-.

.824, .1C, .25, .63L, .831, .836,

1 O1 0, 9 1.Lu,., I . . , .gvo .9i .€dL 9$ 19 i,. .20.82')4 d61, .625, .63, .d34, .636,

1. 7259 leZ b 7.-& L O+ , 9 9 .'412,9 $,Ml .,0

88 .s7 0 . , . ') q g891, .d93,3. 685 , 2. 1,79 1. 33, 1.lbu, l.Oto, 1.000, SM- .dJ.968, •94,6, .9t,, .959, .961, .9639

3.i23, 221 , 0. 9, L~ b . 8L•v1 0779 1.0139, SM= .d5

.980, .95b, .965, .97 1, . 973, .975,4 u 3b , 2. 2 , o.4i, .Z23, 1. lb, 1. 3, M= .901.001, .976, .9ti5, .991, .993, .996,4.4o9, 2 .5't,8, 1~ L .0 1• e30C) 1 0 6 Z, I•o081, tm- .95

I1039, l.uli, i./0, 1.025, 1.027, 1.U29,5.038, 2.830, lo 7,2, 1.393, 1.229, 1.13b, 1-I.001.08I, 1.059, 1.062, 1.064, 0.OeS, .066,

S ALTITUDE - 40000..8429 .6429 .4,2, .8429 .8412, 08492, LlsO.0

o842, .429 0842, .842, 6429, .di2,p m .20.827, .816, .822, .627, .t29, o831,842, .842, .8,2, .842, .842, .842, SM- .400827, 0dIt, .d2, 82 , 0829, 831,

.9669 .966, .966, .966, .9579 .910, SM= .60

.885, .670, .875, .87ts, .880, .681,* 1.28b, 1.266b, 10db, L.1L, 1o056, .99 , SM- .60

.960, .9389 .9,12,9 .9f6, 9, .9489I.454, I*56, 1397, iit7, l.06, 1.003, SM= .85096'), .94 79 .952, .9,16 .9, o959,

1. 76, 1.760, 1.4789, 1Z13, 1.095, 1.o2A, SM .')0

.989, .')bb, .9 7, •975, .977, .97992.609t 2.482, 1.562, 1.283, 1.146, 1.0b5, 'i" .951.024, .9'9, 1.04, 1. 009, .01 , 1.Q i2,4.863, 2. 739, 1.b91, 1.3s7, .2u 1 1.011, i 1.1. 1, 1. 36, I.o,2, .04,, .q4 100, . O,

ALTITUOE 500jo..877, .171, •. 77, .677, .877, .877, = . ' ).876, .876, .o76, .87t, . 876,0 .78,877, .677, . 77, .d77 .8?7, .d77, SM- .2(

.876, .d7b, .876, .7b, .876, .8/8,

.d77, .. 779 d.77, .677, .7d7, .877, 11- .',o

.876, .67, , .87,, d7t, .87b, .a7 b

.895, .89t) .d97, .Id96 .899, . 9 0u, tM .6C

.9019 .902v .903, .9Ub q .914, .920,

.991. .990, .99u, .998, .990, .99u, L,1- .dl

.990, o983, .984, .'84 , . 985, .9b5,1. 011, 1.010, 1.olO, .uLo, . lu, .0lu, I = . 51.007, .984, .')dh .1988 .989, .990,1.005,. 1.054. 1. 054 1.054, [.053 1.053, SM= .'40.940, 1.302, 1.105, 1.07, 1. u u, 1.0U9,

1o127, 1.127, 1.127, 1.127, .126, 1.262, 1M- .9)s1 .06, 1.034, 1.637, 1.O40, [.0,1, 1.02, _1.l

1.231, 1.231, 1.231,p [.231, 1 , .162, 19=. 2Cl107, 1.077, 1 1.079, i.j79, 1.079,

INOTL- 1,ITIIX- [2,

lIT1Ya 9,

TTAHL1=5.00, 10.00, z.o0, 30.Cv, 40.00, 50.0060.00, 70.Q0, do.00, 90.iOu 90.ou, lOU.tfO,

0.00,9 .0 O 'eo 9 .6O .80, . 5, .90, .95, 1. o JO,

u., [O)JO., 060J., 30000., t0o., OO5OUL'.,ALTITUoE = ',,

I... . .... . ..-... '. -. +. - ... - ...... ,.... . .. -... ...

no. I -i M 0 1 I 1 5 a i.

I n 3 i . - i

,7074. , 5 3 5 .t q ,0 J2. , 106b i. 9 11 2%L. L . L 79G0.

1127., 1dbd., 32bl., . i., 3o 9 b., 7Zb., = ..0

51 l., 9769., 1 i023. , 1227b., 1 903., 13530.,21L2 7. 2 )36 ., '" / , 59 v 7 . 7 312 ., do6)9,7. , b =

10060., 11373., 12o . 13I)1., £ 1464. 9 L53(0.,3924 ip ' 737. 9 3 1 Lo d 7. i M"

12230.. 13618., j54h5., £o393., 1708b. 177d0.,6706 v/ . 74# d 0.,v ,Gi 3., 9, . L2 J4 3., L 35 5 4., M

S15 017:., 164 6., 9 L 7 4t., 9 0302.- o 2UO0T ., 20730.,

7652. 8'08., 41., 11423., 12929., 14419., SM .35

15909., 17337.. 1t17b5. , 20192., 20906., 21620.,

8'79. 942391 ., 123 7. , L38bd., L5395., M- .90

1683d. 18256.. 1974o. j . 9 21801., 22510.,• •1 7i 8., 13bi , 6 15065 . 9 lb~ l9q , g

10 o21. 10739. 1 z 5

17915., 19301., 3b6S9., 22074.. 22767.. 23460.,

11509., 12194., 1357J., 947., 16353., 17765., S M1.00

.,9116., 204t7.. 21a13., 23119. 238,,5 ., 2i520. ,

-- ALTITUDE * 1000C.826. .67., 1735., 2biJ., 3470 4337., .MP0.00

5204., 6072. b93., 7807., 8240 ., 8674.,

885., 1385., Z, 37., 3448. 4437., 5119 - .

6387., 7354., 8303., 9251., 972b., 10200.,

1525.. 2148., 3315., 4435. 5519.. 6594., SM= .40

7650., 8689., 9102., 10716., 11223 , 11730.,

2739., 33b2., 4513.. 5745., 6897., 8042., $ .60

9180.. 10274., 11356., 12438., 12979., 13520.,

-: 4645., 5251., ot58.9 766i., ,862*9 10070 . M- .80

011274. 124L0., 135't., 7 146d4' ., 15252., 15820..

5298., 5900 ., 7115., 8334., 9554., 10783., tM- .85

11998., 13 15 .. 1t 314., 15472., lb051., lbb30.,

6012., 6008., 128., 9056., 10287., 11533., -M" .90

12754. , 13923., vi 92.q 16261., 168s6., 1743u.,

h939., 7523.. d7l6.. 9912. , [1109.. 12320., $M= .95

13507., 14bul., 15b2d.. lo'd9., 17570., 18150.,

7967., 8j3?., 9o91., iOd52., 12017.. 13199., .1A1.GGO

14364., 15 5., 1bo2., 17d2.. 18403., 1 9d .,

i ALTITUDE - 0oOS3102., 1132., 129., 2306.1 246

4273o, 4')18., 5552., b186., 6503., 0820.,

1102., 1102. £629.. 23Lb., 296., 3625., iM= .26

4273., 4918.. 5552.. 6186. 6503.. 6820.,

1182.. I149.. 224 ' 3., 30u5., 3741., 4 ,73., I 0

f519£, 5905., 659't., 723 ., 76?7., 7972.,

1870., 2325., 3212., ',Oob., ,9U., 57479, i. .60

6579., 7408., 819o.• 8'82., 931., 9782.,

3150., 3631., 4577., 5519., 647.. 7416., i = .bU

8366., 9282., 10168. 11054., 11497.. 1194.,

3579., 4051., I')9 4. 5'94., I19b.. 78U., .b

8802., 972L•, 1U2I a 152 ., 11970.. 12420.,

4052.. 4 520- ,' oi, 't1., 7373., 8330., * .90

9Zd1., 1C205.9 11120., 12035., 12493., L2 9 5 U.,

4089., 5144. 6Oob., o997., 793',., 8874., 3# .. 5

9815., 10735., 11653., ll25e., 1303L., 13490.,

538., 5 1 .e bZ4. 7 ,/638. , 855'., 9477., M1.-O

S04. ., 11320.. 12240., 1316..0 13620., 08 0 .,:.$ ALTITUD)E * 3000(C•

T.7b., £476., £76., 1949.. 2427/., 2903., iM-'). 0

S3370., 3833., 279., 4,726.. It')50., 5173.,1 476., 176., £476., 1949.. 2427., 903., SM 0LI"3370., 333., o 169., I 950 5173.,£4 ' L76., jh., 1416., 19'9., 2427.. 2903., LMM- .

370., 3333 2- , ,72., 950., 173.,

1563., 1563., 2cdb., 26',., 319£., i7",., = .6)"I2049. 3' 70 7. 3 3.

2335., 2boh., 33"b., 39%. ' ',9-d., 5127., . .85

5990., b(50. , 7274., ld9o., 21 1., d '3.,

265t., 29)j., 3b7"., ' 4 )., 5063., 5/5., . '1" .906itt,3 ., 7 1, ., /Ib I. , d 4,5t). , .3783. , '-) 111.,

3071., 3 4 1,., Jo,. ,O ., 5 5 U 3., U 7 ., $A=- .95

o917 ., P)24t. ,3u-. 9 d.Wdf. 9 3/e ., 96 4,.

352't., 3d)3 ., 45',3 . , 5 b J-)., 59 3-1., ot, 7 ?. I ,i 1. 6 r

7350.t 005d ., 3" I 5' 9 , # 9 3., l 861 ., I u15% 1 ,

ALTITUDE - 40000.1859., 1359., Ilib6o., 10ou. 1859., 1659., u.U0

2075. 2360., £b3)., 2911., 304ts. , 318b.,1859., 11 9 ., 1860., 1 iou ., 9 L859., I Ib 9 ., $0si= .ZO

1859)., 1359., 18buo, idbO. 9 1 d5 9 ., 9 ib 9. 9 $Sl" .4,0

2075., 236u., 2635., 291109 3048., 3156.,191.9 191]9.9 T -914.1 1919.v 1.965.9 2juo.g i.Ma .60

2632., 2963., 3278., 3:92., 3750., 3907.,

2016., 201b., 2o17. 22b5., 265., 364., $.M .60

3458., 3850-, 4,219., I589., 4773., ,958.,

2035., 2035., 2035. , 2179. 2896., 3313., sM- .85

3726., 4137., ,5 5., 4913., 5107.s 5301.,

2069., 2069., 2291., 272L., 3156., 3590., $lI .90

402S . 4457., 4865. 5274., 5479. s 1bd3.,

2107., 2107., 255., 3003., 3147., i92., $M .95

4341., 47b1., Sflsa 5643., 5857., 6071.,

2203., 2,#22., 2864., 33i. , 3766., -#222., i£-1.00

4bd7. 1 41 9., 5598., 604b. , 6271-, b95.,

ALTITUDE = 5J000.1856., 1857., 1859., 18600 1862., L863., M-O.00

1865., 1866., 18cU., 1d69. , 1871., 1942.,

1856., 1157., 1859., Ide., I162., 1863., SM= .2U1865., ldbb., n~bi., 9 18b9 . , 18 71-, 19It2 .,v

1d5b., 1857., 1859., 1bO., 1862., 1863., b1 .. a 6lbs. 13 bh., Io b d. ld69. , L8 7 1. 9 i9 I?2.,v

2151., 2153., 214i., 215o., 2158., 2U16., . 6

2162., 21b3., 2 1 t35. , 2222., 231 ., 2t06.,2 2 t,9. 9 225)0.9 z 2 e., 9 e2 53.,9 2254., 2255., 9 .80

2257., 2 .371. e 227., 291., 3055.,

2269., 2269., 22b#. 269., 229., .,2b-, ',,i. .8e

2291., 2543., 27dz., 3022., 31,41., 32bL.,

229b., 2296., 2296., 229b., Z296., 229b., S-= .90

2246., Z736., 298 q, 3239., 3364., 349u.,

2331., 233u., 2129., 2328., 2327., 238b., .- .'5

2bbO., 2934., 3197., 34b0., 3592., 3723.,

2353., 2353.' 2353., e354. 2 354 ., 2581., 1-.0

286?., 314#1.t 3qt14.v 38bd8., 3124., 3961.,2e

°

a 0 F-15 MAX A/B (FN AITH SFC AND F G -- 100.

INOT05 = 1 ,I rcsX- 13,

IrO5Y- 22,

rTAHOSA 0., 5000.9 100U0. I5uOGj., 20000., 25000.9

30000., 300., 4,oO., 'uOO., 503LO., 55060.,

huOOo.,0.00, .20, .'0, .50, .bo, .7, .do, .90,1.00,l.0U,L.20,1..30, L.4 1, 1. 5U, L~bO, I- O, 1 .90,2. uO,92 .20,,Z °309

2.4092. 50,18790., 161t0., 14070., 11670., 975 ., 77o.5, iM.C'.On

6211., 5057., IZ ., 34 ')., 281-., 2530.,

1731.,

Z0350., 183J0., lbO'j., ±2'10., 1)730., "., $" "M-

6)15., 5/7, N012., 40., 23145.5, 2530. ,

173 1.,l11o70., 19150., Lh6U)., 14290., 11170., '471,., t ., C-

'4, %

8436., 6155., 4 699.,v 36b9',., v 12 9 2530..9L'. 1731.,17 3 1g , .*/ ~ , 1 b 2 UlL., L 7C,0 . , .14= .60

2 37 22 0 . 2• ~. 1 " t1011 c

1731.,24610., 22 170. 3O., 173 3.u, s4 1bU., 1146., $v. 1 .7u

1731.,25940., .23260.. 1335., 1020., 1500., 13380.. SN- .8

217330. 2 460., 9 01o., u1. 11 ., 3bco., 14530., i- .90

2241.,

28370.9, 25650., 2320o., 2047u. s 0

13070., ic o., 86106.9 51., 4b99, 3425.

2396* 1 t .,29580., 26 60., 2250., 21620., 18900., 1Z400., 50 *.00

14650., 11290., 9283., 7109., 499., 3Wt5.,

2537.,31660., 28590., 25920., 23200., 20320., 17890., $M=1.20

15310., 12'.20., 1U140., 7788, 5741., 'O08.,

33330., 30500.9 2152G., ,870., 22070., 19270., v8=1-30

* b710.9 13b'.0ei 11090., 85'.1., 6453., *$595*9

-r 3132.,31730., 33020., 30070., 26700., 23140., 20770., $8=1.40

b180O.,, 15)70.1 1ALb0o, 9335., 7030.,, 5012.,

3 t62.-,3 1730., 3 'v't. u. 32d. , 29123., 256 o), 2 e25t0. , .i-150

19760., i6320., 13Z30., luO9 O., 7b58.9 5559.,

3d26.,31730., 34440., J531')., 32010., 282k) 2., 2490., %8=I.6O

21320., 17063., 142L0., luddO. , 3325., b156.,

42 14.31730., 34,440., 3531U., 3'2U., 32670., 29020., 19 .d

25120, 2055u., 16O00., 1281u., 9b68t., 7216.,~5231.,

231730., 3'0., 35310., 590U. , 33330., 30490., SMI,90

26760o, 21480., 18b5O., 13730., 1815., 799.,

5742a.%,-31730., 340., 35310., 359U0. , 34,30., 31250., tM=2.u0

28040., 23350., 19090., 1462., 11160., 82.,8229.,

631730., 340., 35310., 35900. , 344 30. 32110., tMi2.2 0

29810. 25200., o .0730. 1 6140., l2 LO-, 9675.,

7248.,

31730., 3h440., 35310., 359000., 3','30., 30360., $1-=2.30

29800., 25840., 21480. 9 16710., 1290., 99144. ,

7155.o31730., 34440., 35310., 35900., 34430., 30360., LM=2.40

29020., 21110., 1720., 17050., L3 4U., 10060. ,

.373. 7 3454,". 3531U., 35900., 34430., 30360., M= . 50

29020., e5650., 21550., 13940.1,, 13050.. 9956.,' ' 747,.

I',OT06 1,I "robx 13,i ,I[ObY" 22,

TTA806- 0., 5000., CO0)o, 15006., 20)u., ,00,

30000., 36.J0., ',1'50J0., 4 00. , 5uuU'). 5 50uG.,

000 z ,.Q 0 .~ 0 d, 9,.01 L

j v .9

2 .40,2.5092.356, 2.Z8i., 2.2 1, 2.13'3, e.u9, 2.042, $,.m0. uu1.955, 1.397, 1. 0 d, L.dJb, . 95, 1.93b,2. 143,2.403, 2.312, 2.2-,?, 2.172, 2.1''., 2.080, I- .201..9939 1.897, 1 .300 t .d3 , .. 98o 9 5, 1.*93b 9

2.143,2.1509 2.388, 2.314, 2.221, 2.L74, 2.122, SM- .40

2.056, 1.951, 1.905, l.d3b, 1.895, 1.936,

L' " 2.4,66, 2.420, 2.331, 2.251, 2.),75, 2.135, Sri- .50

2.143,2.488, 2.435, 2.359, 2.251, 2.1759 2.141, $A- .60

2.084 1.991, 1.969, 1.903, 1. 8)95, 1.936,

S2.143,

2.521, 2.442, 2.3d6, 2.30Z, 2.219, 2.140, si- .70

2.090, 2.013, 1.980, 1.952, 1.859, 1.9369

*2.143,2.54#3, 2.,68, 2.409, 2.326, 2.Z37, 2.145, SM- .802.094, 2.334, 1.992, 1.992, 1.91u, 1.891,2.0749,2,574, 2.484, 2.It4, 2.348, 2.263, 2.173, SM- .90

2.091, 2.030, 2.01o, 1.973, 1.962, 1.874,1 .986,2.63b, 2.536, 2.446, 2.381, 2.290, 2.205, S'-1.00

2.114, 2.038, 2.025, 2.003, 2.021, 1.948,0 1.987,

2.679, 2.597, 2.520, 2.437, 2.362, 2.263, S -. 10

2.169, 2.071, Z.063, 2.064, 2.105, 2.052,

2.030,2.708, 2. 634 2. ',, 2. 4bd, 2.401, 2.287, iM- 1. 20

2.196, 2.070, 2.070, 2.074, 2.074, 2.098,

2.05?,2.7799 2b9t6t 2.6, 2.501, 2.412, 2.320, i-I L. 302.218,6, 097, 2.0L,, 2.071, 2.087, 2.061,2.08692.900, 2.736 26, 2. 5'4, 2.440, 2.370, M 1. 4J2.2579, 2.lb6, 2.od5, 2.060, 2.102, 2.027,

2.109,2.900, 2.679, 2.624, 2.549, 2.473, 2.380, sm-1.50

2.2799 2.154, 2.1259 4.106, 2.122, 2.126,2.0137,2.900, 2.679, 2.569, 2.54?, 2.64, 2.391, &M-1.60

2.3209 2.209, 2.187, 2.147, 2.154, 2.195,

2o900, 2.679, 2.5610, 2.585, 2.,495, 2.434, $M-1.80

2.036, 2.310, 2.le2, 2. 3, 2.273, 2.85,

-, 2.328,2.900, 2.679, 2.5 9, 2.542, 2.550, 2.462, SM-1.90

2.402, 2.339, 2.332, 2.36 , 2.271, 2.304,2.3659,2.900, 2.679, 2.569, 2.542, 2.535, 2.533, 1-2.)0

2.9519, 2.378, 2.38 , 2.831,7 2.3i1, 2.329,

S2.53899

2.900, 2.67q, 2.569, 2.542, 2.535, 2.b25, $m=2. 20Z.5939 2.i13v 2.522, 2.5349 2.516, 2.4689

2.45792.900, 2.679,, 2.569s, 54.2 2.535,p 2 .78d1 , %A-2.3 0

2.676, 2.b02, z.cob, 2.o12, 2.627, 2.588,2.7092.570, 2.79s 2• S,' 2.542, 2.535, 2.781, 1 M=.4O

2.759, 2.713, 2.706, 2.707, 2.722, 2.79,

2.722,2.9O0, :.b 79, 2.5b), 2.5 2, 1.535. 2.70i, , =2.5 '

rMe.s

, -, " 1 ! ..... 2 . 855.-,! 2:I ...... 2.o. ,, 2 ..... . . .. . .. .'

I 2.889,

INDTI3- 1.IT13X- 13,IT13Y- 22,TTABI3- 0. 5000. 1OO6'J., 15000., 20000., 25000.,

30000.. 3609U., 1,60kO. 9 ' ouo., OOJoU., 55000.,

* 60000...00o .20, .40, .50, .b3, .709 .80s .9G,.0091.10,1.20,L. 30,l. ,0,i,50, L.6O, 1. O, L.90,2. 0,92.20' 2"30'

2 40,2.50,18790., 16430., 14070., i1670., 9755., 7961., $M=0.00

b211.9 5404.9 4359o 3957., 3335., 3199.,2248.,

21850.. 19370., lbbdO., 1d310., 11'50., 962., SM- .20

7437. 5404., 4359., 3957., 3335.. 3199.,

2248.,24960., 21930., 19160., 16260., 133b0., 11030., SM- .40

8897.. 6486., 5197., 3957., 3335., 3199.,

2248.,21030., 23510., 20730., 17840., L1690., 12080., S.4= .50

9855., 7183,9 5750., 4362., 3335., 3199.,

22 18.,29250., 25560., 22390., 1940., 16370.. 13390.. S.9 .60

10950., 8098., b53., 4927., 3761., 3199.,

-K. 2248.,314o50.9 28000., 2I220., 21170., 18030., 14940., SM- .70

12190., 9190., 739d., 5573., 4220., 3199.,

2248.,34300., 30380., 26510., 23040., 19990., 16830., SM- .80

13700., 10520., 8470., b362., 4853., 3684..

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Bibliography

1. Ropelewski, Robert R. "Modified F-15 Will Investigate AdvancedControl Concepts," Aviation Week & Space Technology: 51-53(February 11, 1985).

2. Kinnucan, Paul. "Superfighters," High Technology: 36-48(April 1984).

3. Humphreys, Robert P., George R. Hennig, William A. Bolding, andLarry A. Helgeson. "Optimal 3-Dimensional Minimum Time Turnsfor an Aircraft," The Journal of the Astronautical Sciences, XX

, -'(2): 88-112 (September-October 1972).

4. Johnson, Capt Thomas L. Minimum Time Turns with Thrust Reversal,MS Thesis, School of Engineering, Air Force Institute of Technology

. (AU), Wright-Patterson AFB, OH, December 1979 (AD-A079.851)

5. Finnerty, Capt Christopher S. Minimum Time Turns Constrainedto the Vertical Plane. MS Thesis. School of Engineering, AirForce Institute of Technology (AU), Wright-Patterson AFB, OH,December 1980 (AD-Alll.096)

6. Brinson, Michael R. Minimum Time Turns with Direct Sideforce.MS Thesis. School of Engineering, Air Force Institute of Technology(AU), Wright-Patterson AFB, OH, December 1983 (AD-A136.958)

K' 7. Schneider, Capt Garrett L. Minimum Time Turns Using VectoredThrust. MS Thesis, School of Engineering, Air Force Institute of

* Technology (AU), Wright-Patterson AFB, OH, December 1984

8. NASA. U.S. Standard Atmosphere. Washington, D.C., December 1962.

9. Miele, Angelo. "Theory of Flight Paths," Flight Mechanics, 1.- Massachusetts: Addison-Wesley Publishing Company, Inc., 1962.

' 10. Rutowski, Edward S. "Energy Approach to the General Aircraft

Performance Problem," Journal of the Aeronautical Sciences,Vol 21: 187-95 (March 1954).

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116

VITA

Mark S. Fellows was born on 25 July 1957 in Dayton, Ohio. He

• -graduated from high school in Kettering, Ohio in 1975 and attended the

University of Cincinnati from which he received the degree of Bachelor

of Science in Aerospace Engineering in June 1980. After graduation, he

was employed as an aeronautical engineer in the Aerodynamics and

Performance Branch, Flight Technology Division of the Deputy for

Engineering within the Aeronautical Systems Division at Wright-Patterson

Air Force Base until entering the School of Engineering, Air Force

Institute of Technology in June 1984.

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Permanent Address: 311 Kenderton Trail

Beavercreek, Ohio 45430

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2s. SECURITY CLASSIFICATION AUTHORITY 3. DISTRIBUTION/AVAILABILITY OF REPORTApproved for public release; distribution

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6c. ADDRESS iCity. State and ZIP Code) 7b. ADDRESS (City. State and ZIP Code)

Air Force Institute of TechnologyWright-Patterson AFB, Ohio 45433

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See Box 1912. PERSONAL AUTHOR(S)

Mark S. Fellows, B.S.13a. TYPE OF REPORT 13b. TIME COVERED 14. DATE OF REPORT (Yr., Mo.. Day) 15. PAGE COUNT

MS Thesis FROM TO 1985 December 2 11716. SUPPLEMENTARY NOTATION

17. COSATI CODES 18. SUBJECT TERMS (Continue on reverse if necesary and identify by block number)FIELD GROUP SUB. GR. 'ircraft Performance, Optimization, Vectored Thrust,12 01 Thrust Vectoring. "01 03

t1. ABSTRACT (Continue on reverse if necesary and identify by block number)

TITLE: AIRCRAFT PERFORMANCE OPTIMIZATION WITH THRUST VECTOR CONTROL

THESIS ADVISOR: Dr. Curtis H. Spenny

; 5 n .n . d O p e a s e : L A W A F E 1 9 0 .1

NE.WOLAVER /,060) (6Dean lor Resoatch and Pre. oal DeIvelopmouAir Force Instiute at Te/A g (406fWright-Patterson ArI 03 45W

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Dr. Curtis H. Spenny 513-255-3517 AFIT/ENYDO FORM 1473,83 APR EDITION OF 1 JAN 73 IS OBSOLETE. UNCLASSIFIED

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The objective of this i is to determine to what extent a highly-

maneuverable aircraft's overall performance capability is enhanced by thrust-vectoring

-. nozzles. The resulting performance capabilities are compared to a baseline configuration

with non-thrust-vectoring nozzles to determine the effects and advantages of thrust

vectoring.

The results indicate that the use of vectored thrust can significantly increase

an aircraft's performance capability in turning flight. The greater the demand on

the aircraft in a turning combat scenario, the more the aircraft utilizes its thrust-

vectoring capability to complete the task. The results also indicate that the use of

* vectored thrust in other phases of flight -- such as cruise, acceleration and

climb -- only slightly increases an aircraft's performance capability.

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