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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
OH CCHOOL OF ENGINEERING M S FELLOWS DEC 85UNCLASSIFIED AFIT/GAE/RR/85D-6 F/G 1/2 NL
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AIRCRAFT PERFORMANCE OPTIMIZATION
' I THRLST VECTOR CONTROL
THESIS
Mark S. Fellows
3, AFIT,'GAEiAA/85D-6
8 ________N
ApProvod tor public relgahIi
.Distbution Uniml%.d
,E?ARTMENI OF THE AIR FORCE
AIR UNIVERSIY" AIR FORCE INSTITUTE OF TECHNOLOGY
W- I I I I I I O h io
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AFIT/GAE/AA/85D-6
I (
AIRCRAFT PERFORMANCE OPTIMIZATION
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
AIRCRAFT PERFORMANCE OPTIMIZATION
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
13. Sustained Load Factor, 20,000 ft (Case 1) ... .......... ... 74
14. Sustained Load Factor, 30,000 ft (Case 1) ... .......... ... 75
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
21. Specific Excess Power, Maximum A/B Power, 20,000 ft (Case 1) 82
22. Specific Excess Power, Maximum A/B Power, 30,000 ft (Case 1) 83
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
37. Specific Excess Power, Military Power, 20,000 ft (Cases 2 & 3) 99
38. Specific Excess Power, Military Power, 30,000 ft (Cases 2 & 3) 100
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
41. Specific Excess Power, Maximum A/B Power, 20,000 ft(Cases 2 & 3) ...... ... ........................ ... 103
42. Specific Excess Power, Maximum A/B Power, 30,000 ft(Cases 2 & 3) ...... ... ........................ ... 104
43. Thrust Required, Sea Level (Cases 2 & 3) ... ........... ... 105
44. Thrust Required, 10,000 ft (Cases 2 & 3) ... ........... ... 106
45. Thrust Required, 20,000 ft (Cases 2 & 3) ... ........... ... 107
46. Thrust Required, 30,000 ft (Cases 2 & 3) ... ........... ... 108
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
Case 1 Case 2 Case 3
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
Sustained Turn Rate 11.3 11.5 11.9 @ 100
% 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
Sustained Turn Rate 16.1 16.5 17.9 @ 190
.%
;': 45"
".I
TABLE III
Results: M = 0.9/10,000 feet
'
Case 1 Case 2 Case 3
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
Sustained Turn Rate 10.4 10.5 10.8 @ 90
% 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 Load Factor 8.86 9.00 9.00 @ 17
Sustained Turn Rate 16.7 17.0 17.0 @ 17'
46
-. ---- - --------------------.- --- , , l 9i ,
TABLE IV
Results: M = 1.0/10,000 feet
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
Sustained Load Factor 7.98 8.13 8.73 @ 160
Sustained Turn Rate 13.6 13.8 14.9 @ 160
-.r. . -.
AAII
TABLE V
Results: M = 0.8/20,000 feet
Case 1 Case 2 Case 3
Military Power
*" Ps @ig 216 216 216 @ 00
PS @ 3g 117 119 123 @ 70
P @ 5g -266 -239 -158 @ 230o
Sustained Load Factor 3.93 3.99 4.17 @ 120
Sustained Turn Rate 8.5 8.6 9.0 @ 12
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
Case 1 Case 2 Case 3
Military Power
P @ ig 51 51 52 @ 1'S
P@3g -80 -77 -67 @ 9'
t @ 5g -399 -386 -337 @ 140
Sustained Load Factor 2.03 2.05 2.12 @ 70
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 Load Factor 5.82 5.95 6.44 @ 170
Sustained Turn Rate 10.2 10.4 11.3 @ 17'
A49.
.'A°
%; . '"J L'". %" . [ .
J. '.' ,'-.' .- . ... J .'.'. ' ' ....... ' '.'.",' .-- '-"'.r -. •,-., " • " =, h ,, ' ,- , * ,
TABLE VII
Results: M = 1.2/20,000 feet
Case 1 Case 2 Case 3
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
Sustained Load Factor 5.50 5.63 6.07 @ 120
Sustained Turn Rate 8.0 8.2 8.9 @ 120
50
L ,-
TABLE VIII
Results: M = 0.9/30,000 feet
Case 1 Case 2 Case 3
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'
Sustained Turn Rate 5.6 5.7 5.9 @ 100
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
Sustained Load Factor 4.23 4.34 4.71 @ 190
Sustained Turn Rate 8.5 8.7 9.5 @ 190
51
%
t .. .. .. .. " . ,.. . _ ;,. ;, .... > . ,; .,.. ,,i~ ..- X - -... ,.t,,; .. ,,, ,..e. ,. ..... i...,..g.... :...:.,.;,"d U..
TABLE IX
Results: M = 1.4/30,000 feet
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
Sustained Load Factor 4.27 4.36 4.71 @ 120
Sustained Turn Rate 5.5 5.6 6.1 @ 120
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 '
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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..
2579.,37500., 3334t0., 29310., 25250., 21860., 18b90., $m= .90
15530., 1l9oO., 9828o, 7 Pt5. , 5612., #233.,
3033..40620., 36290., 32010., 27780., 23920., 20440., M1-1.00
17130., 13480., 1110., 55Z., b276., 9658.,
3354-.,42570.. 38270., 3330., 30210., 26090., 22340., SM=1.10
18850., 14960.. 12340., 9501., 6929.. 51b2.,
A, . 47050., 41980., 37550., 33300., 28940., 24940., 19-1.20
21080., L6740., 137oJ., U6JO., 7993., 5847.,
4233.,524 *0., 46760., 41250., 3b600., 31980., 27490., $=1.30
23460... 18780., 15330., 1160., 9043o, bb30o.
4728..54830.* 52520., i,622U., 0 03h0., 35Z20O., 304b0., $,4=-'.q
Z5960. 21070., 11120.. 1319., 10030., 7370.,
5313..54830.. 57060., 51720., 4502U., 38940., 33580., $M1. 50
28760., 23290., 189 0., 1S570., 11150., 8301.,
6021.95,4830. 57060.9 57100., 504t50., 35b0., 37320., M1- 60
3 1750., 2530., I 0?90., 101. 12430., 9393"I! 6831..
5 830.9 570h0.. 57100., 593 b. 531., bO 0 11 M- .16O
39090., 31,t20., 257bo., 19860. , 152,0.9 11630.,
8720.,54,830., 570o0.9 5 710U., 64370. , 56640. , 49930., 1M:1.90
42780., 34450., 26290.. 218!0., 16770., 121790.,o,,o 9685. ,
54830., 57060., 57100., o,30., 020., 9j500., 7i=.0 0.7U046540.. 37670., 30810., 23d7U., 18390., 4t1zo.,
10770.54830., 57060., 5 7Lj., 6437N., 61020., 620., $0.20
13080.
57090., 9 47o'~0 3 445). q 3069U0., 2391 i 46 L'b. ,
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APPENDIX D
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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).
- 11. Fellows, Mark S. "NSEG--Segmented Mission Analysis Program,ASD/ENFTA User's Manual," ENFTA-TM-84-01, March 1984.
12. Parrott, Edward L. "Combat Performance Advantage: A Method of
- Evaluating Air Combat Performance Effectiveness," ASD-TR-78-36,*December 1978.
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.
.
Permanent Address: 311 Kenderton Trail
Beavercreek, Ohio 45430
I
117
i z&
UNCLASSIFIED
SECURITY CLASSIFICATION OF THIS PAGE
REPORT DOCUMENTATION PAGEIa REPORT SECURITY CLASSIFICATION 1b. RESTRICTIVE MARKINGS
UNCLASSIFIED
2s. SECURITY CLASSIFICATION AUTHORITY 3. DISTRIBUTION/AVAILABILITY OF REPORTApproved for public release; distribution
2b. OECLASSIFICATION/OOWNGRAOING SCHEDULE unlimited
4. PERFORMING ORGANIZATION REPORT NUMBER(S) 5. MONITORING ORGANIZATION REPORT NUMBER(S)
AFIT/GAE/AA/85D-66. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7s. NAME OF MONITORING ORGANIZATION
(If applicable)
School of Engineering AFIT/ENY
6c. ADDRESS iCity. State and ZIP Code) 7b. ADDRESS (City. State and ZIP Code)
Air Force Institute of TechnologyWright-Patterson AFB, Ohio 45433
Is. NAME OF FUNDINGISPONSORING Sb. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBERORGANIZATION (if applicable)
S. ADDRESS (City. State and ZIP Code) 10. SOURCE OF FUNDING NOS.
PROGRAM PROJECT TASK WORK UNITELEMENT NO. NO. NO. NO.
11. TITLE dinclude Security Clasification)
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
20. DISTRIBUTION/AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION
UNCLASSIFIED/UNLIMITED 9 SAME AS RPT. DTIC USERS UNCLASSIFIED
22. NAME OF RESPONSIBLE INDIVIDUAL 22b. TELEPHONE NUMBER 22c. OFFICE SYMBOL(Ilnclude A.trea Code)
Dr. Curtis H. Spenny 513-255-3517 AFIT/ENYDO FORM 1473,83 APR EDITION OF 1 JAN 73 IS OBSOLETE. UNCLASSIFIED
--. , : ."SECURITY CLASSIFICATION OF THIS PAGE
-rwt c - .U - % --. W SW SW S_ 1. W I .w- I . . - .-W 1 . -% r rI I
UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE
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.
U .
'I
p.
I UNCLASSIFIED
DT II
"Mow
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