Maximizing Missile Flight Performance.ppt
imecherif2016
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Oct 19, 2024
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About This Presentation
missile propulsion and effeciency for flight aerodynamics.
Slide Content
10/19/24 ELF 1
Eugene L. Fleeman
Senior Technical Advisor
Georgia Institute of Technology
Maximizing Missile Flight Performance
Eugene L. Fleeman
Senior Technical Advisor
Georgia Institute of Technology
Maximizing Missile Flight Performance
10/19/24 ELF 2
Outline
Parameters and Technologies That Drive Missile Flight
Performance
Missile Flight Performance Prediction
Examples of Maximizing Missile Flight Performance ( Workshop )
Summary
Outline
Parameters and Technologies That Drive Missile Flight
Performance
Missile Flight Performance Prediction
Examples of Maximizing Missile Flight Performance ( Workshop )
Summary
10/19/24 ELF 3
Parameters That Drive Missile Flight
Performance
Nose Fineness
Diameter
Propellant / Fuel
Wing Geometry / Size
Stabilizer
Geometry / Size
Flight Control
Geometry / Size
Length
Thrust
Profile
Flight Conditions ( , M, h )
Parameters That Drive Missile Flight
Performance
Nose Fineness
Diameter
Propellant / Fuel
Wing Geometry / Size
Stabilizer
Geometry / Size
Flight Control
Geometry / Size
Length
Thrust
Profile
Flight Conditions ( , M, h )
10/19/24 ELF 4
Small Diameter Missiles Have Low Drag
10
100
1000
10000
100000
4 8 12 16 20
d, Diameter, inches
D
/
C
D
,
D
r
a
g
/
D
r
a
g
C
o
e
f
f
i
c
i
e
n
t
,
l
b
.
.
Dynamic Pressure =
1,000 psf
Dynamic Pressure =
5,000 psf
Dynamic Pressure =
10,000 psf
Example for Rocket Baseline:
d = 8 inches = 0.667 ft
Mach 2, h = 20K ft, ( C
D
0
)
Powered
= 0.95
q = 1/2 V
2
= 1/2 ( M a )
2
= 1/2 ( 0.001267 ) [( 2 ) ( 1037 )]
2
= 2,725 psf
D
0
/ C
D
0
= 0.785 ( 2725 ) ( 0.667 )
2
= 952
D
0 = 0.95 ( 952 ) = 900 lb
D = C
D
q S
Ref
= 0.785 C
D
q d
2
Note: D = drag in lb, C
D
= drag coefficient, q = dynamic pressure in psf,
d = diameter ( reference length ) in ft
Small Diameter Missiles Have Low Drag
10
100
1000
10000
100000
4 8 12 16 20
d, Diameter, inches
D
/
C
D
,
D
r
a
g
/
D
r
a
g
C
o
e
f
f
i
c
i
e
n
t
,
l
b
.
.
Dynamic Pressure =
1,000 psf
Dynamic Pressure =
5,000 psf
Dynamic Pressure =
10,000 psf
Example for Rocket Baseline:
d = 8 inches = 0.667 ft
Mach 2, h = 20K ft, ( C
D
0
)
Powered
= 0.95
q = 1/2 V
2
= 1/2 ( M a )
2
= 1/2 ( 0.001267 ) [( 2 ) ( 1037 )]
2
= 2,725 psf
D
0
/ C
D
0
= 0.785 ( 2725 ) ( 0.667 )
2
= 952
D
0 = 0.95 ( 952 ) = 900 lb
D = C
D
q S
Ref
= 0.785 C
D
q d
2
Note: D = drag in lb, C
D
= drag coefficient, q = dynamic pressure in psf,
d = diameter ( reference length ) in ft
10/19/24 ELF 5
Supersonic Drag Is Driven by Nose Fineness
While Subsonic Drag is Driven by Skin Friction
0.01
0.1
1
10
0 1 2 3 4 5
M, Mach Number
(CD0)Body,Wave;
lN / d = 0.5
(CD0)Body,Wave;
lN / d = 1
(CD0)Body,Wave;
lN / d = 2
(CD0)Body,Wave;
lN / d = 5
(CD)Base,Coast
Example for Rocket Baseline:
( C
D
0
)
Body, Wave
( C
D
0
)
Body, Friction
( C
D
)
Base
l
N
/ d = 2.4, A
e
= 11.22 in
2
, S
Ref
= 50.26 in
2
, M =
2, h = 20K ft, q = 2725 psf, l / d = 18, l = 12 ft
( C
D
0
)
Body, Wave
= 0.14
( C
D
)
Base
Coast
= 0.25 / 2 = 0.13
( C
D )
Base Powered = ( 1 - 0.223 ) ( 0.25 / 2 ) = 0.10
( C
D
0
)
Body, Friction
= 0.053 ( 18 ) { ( 2 ) / [( 2725 )
( 12 ) ]}
0.2
= 0.14
( C
D
0
)
Body, Coast = 0.14 + 0.13 + 0.14 = 0.41
( C
D
0
)
Body, Powered
= 0.14 + 0.10 + 0.14 = 0.38
( C
D
0
)
Body, Wave = ( 1.59 + 1.83 / M
2
) { tan
-1
[ 0.5 / ( l
N / d )]}
1.69
, for M > 1. Based on Bonney reference, tan
-1
in rad.
( C
D
0
)
Base,Coast
= 0.25 / M, if M > 1 and (C
D
0
)
Base,Coast
= ( 0.12 + 0.13 M
2
), if M < 1
( C
D
0
)
Base,Powered
= ( 1 – A
e
/ S
Ref
) ( 0.25 / M ), if M > 1 and ( C
D
0
)
Base,Powered
= ( 1 – A
e
/ S
Ref
) ( 0.12 + 0.13 M
2
), if M < 1
(C
D
0
)
Body,Friction
= 0.053 ( l / d ) [ M / ( q l )]
0.2
. Based on Jerger reference, turbulent boundary layer, q in psf, l in ft.
( C
D
0
)
Body
= ( C
D
0
)
Body, Wave
+ ( C
D
0
)
Base
+ (C
D
0
)
Body,Friction
Note: ( C
D
0
)
Body,Wave
= body zero-lift wave drag coefficient, ( C
D
0
)
Base
= body base drag coefficient, ( C
D
0
)
Body, Friction
= body skin
friction drag coefficient, ( C
D
0
)
Body = body zero-lift drag coefficient, l
N = nose length, d = missile diameter, l = missile body length,
A
e = nozzle exit area, S
Ref = reference area, q = dynamic pressure, tan
-1
[ 0.5 / ( l
N / d )] in rad
Supersonic Drag Is Driven by Nose Fineness
While Subsonic Drag is Driven by Skin Friction
0.01
0.1
1
10
0 1 2 3 4 5
M, Mach Number
(CD0)Body,Wave;
lN / d = 0.5
(CD0)Body,Wave;
lN / d = 1
(CD0)Body,Wave;
lN / d = 2
(CD0)Body,Wave;
lN / d = 5
(CD)Base,Coast
Example for Rocket Baseline:
( C
D
0
)
Body, Wave
( C
D
0
)
Body, Friction
( C
D
)
Base
l
N
/ d = 2.4, A
e
= 11.22 in
2
, S
Ref
= 50.26 in
2
, M =
2, h = 20K ft, q = 2725 psf, l / d = 18, l = 12 ft
( C
D
0
)
Body, Wave
= 0.14
( C
D
)
Base
Coast
= 0.25 / 2 = 0.13
( C
D )
Base Powered = ( 1 - 0.223 ) ( 0.25 / 2 ) = 0.10
( C
D
0
)
Body, Friction
= 0.053 ( 18 ) { ( 2 ) / [( 2725 )
( 12 ) ]}
0.2
= 0.14
( C
D
0
)
Body, Coast = 0.14 + 0.13 + 0.14 = 0.41
( C
D
0
)
Body, Powered
= 0.14 + 0.10 + 0.14 = 0.38
( C
D
0
)
Body, Wave = ( 1.59 + 1.83 / M
2
) { tan
-1
[ 0.5 / ( l
N / d )]}
1.69
, for M > 1. Based on Bonney reference, tan
-1
in rad.
( C
D
0
)
Base,Coast
= 0.25 / M, if M > 1 and (C
D
0
)
Base,Coast
= ( 0.12 + 0.13 M
2
), if M < 1
( C
D
0
)
Base,Powered
= ( 1 – A
e
/ S
Ref
) ( 0.25 / M ), if M > 1 and ( C
D
0
)
Base,Powered
= ( 1 – A
e
/ S
Ref
) ( 0.12 + 0.13 M
2
), if M < 1
(C
D
0
)
Body,Friction
= 0.053 ( l / d ) [ M / ( q l )]
0.2
. Based on Jerger reference, turbulent boundary layer, q in psf, l in ft.
( C
D
0
)
Body
= ( C
D
0
)
Body, Wave
+ ( C
D
0
)
Base
+ (C
D
0
)
Body,Friction
Note: ( C
D
0
)
Body,Wave
= body zero-lift wave drag coefficient, ( C
D
0
)
Base
= body base drag coefficient, ( C
D
0
)
Body, Friction
= body skin
friction drag coefficient, ( C
D
0
)
Body = body zero-lift drag coefficient, l
N = nose length, d = missile diameter, l = missile body length,
A
e = nozzle exit area, S
Ref = reference area, q = dynamic pressure, tan
-1
[ 0.5 / ( l
N / d )] in rad
10/19/24 ELF 6
Lifting Body Has Higher Normal Force
C
N,
Example
Normal
Force
Coefficient
for l / d = 20
150
100
50
0
0 20 40 60 80 100
, Angle of Attack, Deg
2a
2b
a / b = 3
a / b = 2
a / b = 1
Note:
If negative, C
N
negative
Based on slender body theory ( Pitts, et al ) and cross flow theory ( Jorgensen ) references
Example l / d = length / diameter = 20
d = 2 ( a b )
1/2
= 0°
C
N = [( a / b ) cos + ( b / a ) sin ] [ sin ( 2 ) cos ( / 2 ) + 2 ( l / d ) sin
2
]
C
N
Lifting Body Has Higher Normal Force
C
N,
Example
Normal
Force
Coefficient
for l / d = 20
150
100
50
0
0 20 40 60 80 100
, Angle of Attack, Deg
2a
2b
a / b = 3
a / b = 2
a / b = 1
Note:
If negative, C
N
negative
Based on slender body theory ( Pitts, et al ) and cross flow theory ( Jorgensen ) references
Example l / d = length / diameter = 20
d = 2 ( a b )
1/2
= 0°
C
N = [( a / b ) cos + ( b / a ) sin ] [ sin ( 2 ) cos ( / 2 ) + 2 ( l / d ) sin
2
]
C
N
10/19/24 ELF 7
Large Surface Area Increases Normal Force and
Maneuverability
0
0.5
1
1.5
2
2.5
3
3.5
0 30 60 90
M < 1.35, based on slender wing theory + Newtonian impact theory
M = 2, based on linear wing theory + Newtonian impact theory
M = 5, based on linear wing theory + Newtonian impact theory
(
C
N
)
W
in
g
S
R
E
F
/ S
W
,
W
in
g
N
o
r
m
a
l F
o
r
c
e
C
o
e
f
f
ic
ie
n
t
f
o
r
R
o
c
k
e
t
B
a
s
e
lin
e
’ =
W = + , Wing Effective Angle of Attack, Deg
( C
N
)
Wing
= [ 4sin ’ cos ’ / ( M
2
– 1 )
1/2
+ 2 sin
2
’ ] ( S
W
/ S
Ref
), if M > { 1 + [ 8 / ( A )]
2
}
1/2
( C
N
)
Wing
= [ ( A / 2) sin ’ cos ’ + 2 sin
2
’ ] ( S
W
/ S
Ref
), if M < { 1 + [ 8 / ( A )]
2
}
1/2
Note: Linear wing theory applicable if M > { 1 + [ 8 / ( A )]
2
}
1/2
, slender wing theory applicable if M < { 1 + [ 8 / ( A )]
2
}
1/2
,
A = Aspect Ratio, S
W = Wing Planform Area, S
Ref = Reference Area
Example for Rocket Baseline
A
W
= 2.82
S
W
= 2.55 ft
2
S
Ref
= 0.349 ft
2
= 13 deg, = 9 deg
M = 2
{ 1 +[ 8 / ( A )]
2
}
1/2
= 1.35
Since M > 1.35, use linear wing
theory + Newtonian theory
’ =
W = + = 22
( C
N )
Wing S
Ref / S
W = [ 4 sin 22
cos 22 / ( 2
2
– 1 )
1/2
+ 2 sin
2
22] =
1.083
( C
N )
Wing = 1.08 ( 2.55 ) / 0.349 =
7.91
Large Surface Area Increases Normal Force and
Maneuverability
0
0.5
1
1.5
2
2.5
3
3.5
0 30 60 90
M < 1.35, based on slender wing theory + Newtonian impact theory
M = 2, based on linear wing theory + Newtonian impact theory
M = 5, based on linear wing theory + Newtonian impact theory
(
C
N
)
W
in
g
S
R
E
F
/ S
W
,
W
in
g
N
o
r
m
a
l F
o
r
c
e
C
o
e
f
f
ic
ie
n
t
f
o
r
R
o
c
k
e
t
B
a
s
e
lin
e
’ =
W = + , Wing Effective Angle of Attack, Deg
( C
N
)
Wing
= [ 4sin ’ cos ’ / ( M
2
– 1 )
1/2
+ 2 sin
2
’ ] ( S
W
/ S
Ref
), if M > { 1 + [ 8 / ( A )]
2
}
1/2
( C
N
)
Wing
= [ ( A / 2) sin ’ cos ’ + 2 sin
2
’ ] ( S
W
/ S
Ref
), if M < { 1 + [ 8 / ( A )]
2
}
1/2
Note: Linear wing theory applicable if M > { 1 + [ 8 / ( A )]
2
}
1/2
, slender wing theory applicable if M < { 1 + [ 8 / ( A )]
2
}
1/2
,
A = Aspect Ratio, S
W = Wing Planform Area, S
Ref = Reference Area
Example for Rocket Baseline
A
W
= 2.82
S
W
= 2.55 ft
2
S
Ref
= 0.349 ft
2
= 13 deg, = 9 deg
M = 2
{ 1 +[ 8 / ( A )]
2
}
1/2
= 1.35
Since M > 1.35, use linear wing
theory + Newtonian theory
’ =
W = + = 22
( C
N )
Wing S
Ref / S
W = [ 4 sin 22
cos 22 / ( 2
2
– 1 )
1/2
+ 2 sin
2
22] =
1.083
( C
N )
Wing = 1.08 ( 2.55 ) / 0.349 =
7.91
10/19/24 ELF 8
Wing Skin Friction Drag Is Larger Than Shock
Wave Drag for a Thin Wing
0
0.005
0.01
0.015
0.02
100 1000 10000
q, Dynamic Pressure, psf
M / cmac = 0.01 / ftM / cmac = 0.1 / ft
M / cmac = 1 / ftM / cmac = 10 / ft
( C
D
0
)
Wing,Friction
= n
W
{ 0.0133 [ M / ( q c
mac
)]
0.2
} ( 2 S
W
/ S
Ref
), based on Jerger, turbulent, q in psf, c
mac
in ft
( C
D
O
)
Wing,Wave
= n
W
[ 2 / ( M
LE
2
)]{{[( + 1 ) M
LE
2
] / 2 }
/ (
- 1 )
{( + 1 ) / [ 2 M
LE
2
– ( - 1 )]}
1 / ( - 1 )
– 1 } sin
2
LE
cos
LE
t
mac
b / S
Ref
, based on Newtonian impact theory
( C
D
O
)
Wing
= ( C
D
O
)
Wing,Wave
+ ( C
D
O
)
Wing,Friction
n
W
= number of wings ( cruciform = 2 )
q = dynamic pressure in psf
c
mac
= length of mean aero chord in ft
= Specific heat ratio = 1.4
M
LE
= M cos
LE = Mach number leading edge
LE = leading edge section total angle
LE = leading edge sweep angle
t
mac = max thickness of mac
b = span
Example for Rocket Baseline Wing:
n
W
= 2, h = 20K ft ( q = 2,725 psf ), c
mac
= 1.108 ft, S
Ref
= 50.26 in
2
, S
W
= 367 in
2
,
LE
= 10.01 deg,
LE
= 45 deg,
t
mac
= 0.585 in, b = 32.2 in, M
= 2 ( M
LE
= 1.41 )
( C
D
O
)
Wing,Friction
S
Ref
/ [ n
W
S
W
] = 2 {( 0.0133 ) { 2 /
[( 2725 ) ( 1.108 )]}
0.2
} = 0.00615
( C
D
0
)
Wing,Friction = 0.00615 ( 2 ) ( 367 ) / 50.26 = 0.090
( C
D
0
)
Wing,Wave = 0.024
( C
D
O
)
Wing = 0.024 + 0.090 = 0.11
(
C
D
0
)
W
in
g
,F
r
ic
t
io
n
S
R
e
f / (
n
W
S
W
)
Wing Skin Friction Drag Is Larger Than Shock
Wave Drag for a Thin Wing
0
0.005
0.01
0.015
0.02
100 1000 10000
q, Dynamic Pressure, psf
M / cmac = 0.01 / ftM / cmac = 0.1 / ft
M / cmac = 1 / ftM / cmac = 10 / ft
( C
D
0
)
Wing,Friction
= n
W
{ 0.0133 [ M / ( q c
mac
)]
0.2
} ( 2 S
W
/ S
Ref
), based on Jerger, turbulent, q in psf, c
mac
in ft
( C
D
O
)
Wing,Wave
= n
W
[ 2 / ( M
LE
2
)]{{[( + 1 ) M
LE
2
] / 2 }
/ (
- 1 )
{( + 1 ) / [ 2 M
LE
2
– ( - 1 )]}
1 / ( - 1 )
– 1 } sin
2
LE
cos
LE
t
mac
b / S
Ref
, based on Newtonian impact theory
( C
D
O
)
Wing
= ( C
D
O
)
Wing,Wave
+ ( C
D
O
)
Wing,Friction
n
W
= number of wings ( cruciform = 2 )
q = dynamic pressure in psf
c
mac
= length of mean aero chord in ft
= Specific heat ratio = 1.4
M
LE
= M cos
LE = Mach number leading edge
LE = leading edge section total angle
LE = leading edge sweep angle
t
mac = max thickness of mac
b = span
Example for Rocket Baseline Wing:
n
W
= 2, h = 20K ft ( q = 2,725 psf ), c
mac
= 1.108 ft, S
Ref
= 50.26 in
2
, S
W
= 367 in
2
,
LE
= 10.01 deg,
LE
= 45 deg,
t
mac
= 0.585 in, b = 32.2 in, M
= 2 ( M
LE
= 1.41 )
( C
D
O
)
Wing,Friction
S
Ref
/ [ n
W
S
W
] = 2 {( 0.0133 ) { 2 /
[( 2725 ) ( 1.108 )]}
0.2
} = 0.00615
( C
D
0
)
Wing,Friction = 0.00615 ( 2 ) ( 367 ) / 50.26 = 0.090
( C
D
0
)
Wing,Wave = 0.024
( C
D
O
)
Wing = 0.024 + 0.090 = 0.11
(
C
D
0
)
W
in
g
,F
r
ic
t
io
n
S
R
e
f / (
n
W
S
W
)
10/19/24 ELF 9
Relaxed Static Margin Allows Higher Trim Angle
of Attack and Higher Normal Force
C
N, Trim
, Trimmed Normal
Force Coefficient of
Rocket Baseline
0 4 8 12 16 20 24
16
12
8
4
0
Trim
Trim Angle of Attack, Deg
Note: Rocket Baseline
X
CG
= 75.7 in.
Mach 2
( + )
Max = 21.8 Deg, ( C
N
Trim
)
Max
/ = 0.75, ( Static Margin = 0.88 Diam )
/ = 1.5, ( SM = 0.43 Diam )
/ = , ( SM = 0 )
Relaxed Static Margin Allows Higher Trim Angle
of Attack and Higher Normal Force
C
N, Trim
, Trimmed Normal
Force Coefficient of
Rocket Baseline
0 4 8 12 16 20 24
16
12
8
4
0
Trim
Trim Angle of Attack, Deg
Note: Rocket Baseline
X
CG
= 75.7 in.
Mach 2
( + )
Max = 21.8 Deg, ( C
N
Trim
)
Max
/ = 0.75, ( Static Margin = 0.88 Diam )
/ = 1.5, ( SM = 0.43 Diam )
/ = , ( SM = 0 )
10/19/24 ELF 10
Scramjet
High Specific Impulse Provides Higher Thrust and
Reduces Fuel Consumption
Turbojet
Ramjet
Solid Rocket
4,000
3,000
2,000
1,000
0
T
h
r
u
s
t
/ (
F
u
e
l F
lo
w
R
a
t
e
)
, S
p
e
c
if
ic
Im
p
u
ls
e
, I
S
P
, S
e
c
o
n
d
s
0 2 4 6 8 10 12
Mach Number
Ducted Rocket
Scramjet
High Specific Impulse Provides Higher Thrust and
Reduces Fuel Consumption
Turbojet
Ramjet
Solid Rocket
4,000
3,000
2,000
1,000
0
T
h
r
u
s
t
/ (
F
u
e
l F
lo
w
R
a
t
e
)
, S
p
e
c
if
ic
Im
p
u
ls
e
, I
S
P
, S
e
c
o
n
d
s
0 2 4 6 8 10 12
Mach Number
Ducted Rocket
10/19/24 ELF 11
Solid Rockets Have High Acceleration Capability
1,000
100
10
1
0 1 2 3 4 5
Ramjet
T
Max = ( / 4 ) d
2
V
2
[( V
e / V
) -
1 ]
Solid Rocket
T
Max = 2 P
C A
t = m
.
V
e
M, Mach Number
(
T
/ W
)
M
a
x
, (
T
h
r
u
s
t
/ W
e
ig
h
t
)
M
a
x
,
Note:
P
C = Chamber pressure, A
t = Nozzle throat area, m
.
= Mass flow rate
d = Diameter,
= Free stream density, V
= Free stream velocity,
V
e = Nozzle exit velocity ( Turbojet: V
e ~ 2,000 ft / sec, Ramjet: V
e ~ 4,500 ft / sec, Rocket: V
e ~ 6,000 ft / sec )
Turbojet
T
Max
= ( / 4 ) d
2
V
2
[( V
e / V
) -
1 ]
Solid Rockets Have High Acceleration Capability
1,000
100
10
1
0 1 2 3 4 5
Ramjet
T
Max = ( / 4 ) d
2
V
2
[( V
e / V
) -
1 ]
Solid Rocket
T
Max = 2 P
C A
t = m
.
V
e
M, Mach Number
(
T
/ W
)
M
a
x
, (
T
h
r
u
s
t
/ W
e
ig
h
t
)
M
a
x
,
Note:
P
C = Chamber pressure, A
t = Nozzle throat area, m
.
= Mass flow rate
d = Diameter,
= Free stream density, V
= Free stream velocity,
V
e = Nozzle exit velocity ( Turbojet: V
e ~ 2,000 ft / sec, Ramjet: V
e ~ 4,500 ft / sec, Rocket: V
e ~ 6,000 ft / sec )
Turbojet
T
Max
= ( / 4 ) d
2
V
2
[( V
e / V
) -
1 ]
10/19/24 ELF 12
High Thrust for a Ramjet Occurs from Mach 3 to
5 with High Combustion Temperature
0
5
10
15
20
25
0 1 2 3 4 5
M, Mach Number
T
/
[
P
H
I
(
p
0
)
(
A
3
)
]
,
N
o
n
d
i
m
i
m
e
n
s
i
o
n
a
l
T
h
r
u
s
t
i
f
S
p
e
c
i
fi
c
H
e
a
t
R
a
ti
o
=
1
.
2
9
T4 / T0 = 3T4 / T0 = 5T4 / T0 = 10T4 / T0 = 15
T / ( p
0 A
3 ) = M
0
2
{{[ T
4 / T
0 ] / { 1 + [( - 1 ) / 2 ] M
0
2
}}
1/2
- 1 }
Note: Ideal ramjet, isentropic flow, exit pressure = free stream pressure, 1, T in R
Example for Ramjet Baseline:
M = 3.5, h = 60 Kft, T
4 = 4,000 deg R, ( f / a ) =
0.06, = 0.900, T
0
= 392 Rankine, p
0
= 1.047
psi, A
3 = 287.1 in
2
, = 1.29
T / ( p
0 A
3 ) = 1.29 ( 3.5 )
2
{{[ 4000 / 392 ] / { 1 +
[( 1.29 – 1 ) / 2 ] ( 3.5 )
2
}}
1/2
– 1 } = 14.49
T = 14.49 ( 0.900 ) ( 1.047 ) ( 287.1 ) = 3920 lb
Note:
T = Thrust
p
0 = Free stream static pressure
A
3 = Combustor flameholder entrance area
= Specific heat ratio
M
0
= Free stream Mach number
T
4
= Combustor exit temperature
T
0
= Free stream temperature
= Equivalence ratio
High Thrust for a Ramjet Occurs from Mach 3 to
5 with High Combustion Temperature
0
5
10
15
20
25
0 1 2 3 4 5
M, Mach Number
T
/
[
P
H
I
(
p
0
)
(
A
3
)
]
,
N
o
n
d
i
m
i
m
e
n
s
i
o
n
a
l
T
h
r
u
s
t
i
f
S
p
e
c
i
fi
c
H
e
a
t
R
a
ti
o
=
1
.
2
9
T4 / T0 = 3T4 / T0 = 5T4 / T0 = 10T4 / T0 = 15
T / ( p
0 A
3 ) = M
0
2
{{[ T
4 / T
0 ] / { 1 + [( - 1 ) / 2 ] M
0
2
}}
1/2
- 1 }
Note: Ideal ramjet, isentropic flow, exit pressure = free stream pressure, 1, T in R
Example for Ramjet Baseline:
M = 3.5, h = 60 Kft, T
4 = 4,000 deg R, ( f / a ) =
0.06, = 0.900, T
0
= 392 Rankine, p
0
= 1.047
psi, A
3 = 287.1 in
2
, = 1.29
T / ( p
0 A
3 ) = 1.29 ( 3.5 )
2
{{[ 4000 / 392 ] / { 1 +
[( 1.29 – 1 ) / 2 ] ( 3.5 )
2
}}
1/2
– 1 } = 14.49
T = 14.49 ( 0.900 ) ( 1.047 ) ( 287.1 ) = 3920 lb
Note:
T = Thrust
p
0 = Free stream static pressure
A
3 = Combustor flameholder entrance area
= Specific heat ratio
M
0
= Free stream Mach number
T
4
= Combustor exit temperature
T
0
= Free stream temperature
= Equivalence ratio
10/19/24 ELF 13
Maximum Specific Impulse And Thrust of Rocket
Occur at High Chamber Pressure and Altitude
220
240
260
280
0 5 10 15 20
Nozzle Expansion Ratio
Is
p
, S
p
e
c
if
ic
Im
p
u
ls
e
o
f
R
o
c
k
e
t
B
a
s
e
lin
e
h = SL, pc = 300 psi h = SL, pc = 1000 psi
h = SL, pc = 3000 psih = 100K ft, pc > 300 psi
I
SP = c
d {{[ 2
2
/ ( - 1)] [ 2 / ( + 1)]
( - 1 ) / ( + 1 )
[ 1 – ( p
e / p
c )
( - 1 ) /
]}
1/2
+ ( p
e / p
c ) - ( p
0 / p
c ) } c* / g
c
T = ( g
c
/ c* ) p
c
A
t
I
SP
= {[ 2 / ( + 1)
1 / ( - 1 )
][( -1) / ( + 1 )]
1/2
]} / {( p
e
/ p
c
)
1 /
[ 1 - ( p
e
/ p
c
)
( - 1 ) /
]
1/2
}
Note:
= nozzle expansion ratio
p
e
= exit pressure
p
c
= chamber pressure
p
0
= atmospheric pressure
A
t = nozzle throat area
= specific heat ratio = 1.18 in figure
c
d = discharge coefficient = 0.96 in figure
c* = characteristic velocity = 5,200 ft / sec in figure
Example for Rocket Baseline:
= A
e / A
t = 6.2, A
t = 1.81 in
2
h = 20 Kft, p
0 = 6.48 psi
( p
c )
boost = 1769 psi, ( I
SP )
boost = 257 sec
( T )
boost
= ( 32.2 / 5200 ) ( 1769 ) (1.81 )( 257 ) = 5096 lb
( p
c
)
sustain
= 301 psi, ( I
SP
)
sustain
= 239 sec
( T )
boost
= ( 32.2 / 5200 ) ( 301 ) (1.81 )( 239 ) = 807 lb
Maximum Specific Impulse And Thrust of Rocket
Occur at High Chamber Pressure and Altitude
220
240
260
280
0 5 10 15 20
Nozzle Expansion Ratio
Is
p
, S
p
e
c
if
ic
Im
p
u
ls
e
o
f
R
o
c
k
e
t
B
a
s
e
lin
e
h = SL, pc = 300 psi h = SL, pc = 1000 psi
h = SL, pc = 3000 psih = 100K ft, pc > 300 psi
I
SP = c
d {{[ 2
2
/ ( - 1)] [ 2 / ( + 1)]
( - 1 ) / ( + 1 )
[ 1 – ( p
e / p
c )
( - 1 ) /
]}
1/2
+ ( p
e / p
c ) - ( p
0 / p
c ) } c* / g
c
T = ( g
c
/ c* ) p
c
A
t
I
SP
= {[ 2 / ( + 1)
1 / ( - 1 )
][( -1) / ( + 1 )]
1/2
]} / {( p
e
/ p
c
)
1 /
[ 1 - ( p
e
/ p
c
)
( - 1 ) /
]
1/2
}
Note:
= nozzle expansion ratio
p
e
= exit pressure
p
c
= chamber pressure
p
0
= atmospheric pressure
A
t = nozzle throat area
= specific heat ratio = 1.18 in figure
c
d = discharge coefficient = 0.96 in figure
c* = characteristic velocity = 5,200 ft / sec in figure
Example for Rocket Baseline:
= A
e / A
t = 6.2, A
t = 1.81 in
2
h = 20 Kft, p
0 = 6.48 psi
( p
c )
boost = 1769 psi, ( I
SP )
boost = 257 sec
( T )
boost
= ( 32.2 / 5200 ) ( 1769 ) (1.81 )( 257 ) = 5096 lb
( p
c
)
sustain
= 301 psi, ( I
SP
)
sustain
= 239 sec
( T )
boost
= ( 32.2 / 5200 ) ( 301 ) (1.81 )( 239 ) = 807 lb
10/19/24 ELF 14
Cruise Range Is Driven By L/D, I
sp, Velocity, and
Propellant or Fuel Weight Fraction
Typical Value for 2,000 lb Precision Strike Missile
Note: Ramjet and Scramjet missiles booster propellant for Mach 2.5 to 4 take-over speed not included in W
P
for cruise. Rockets require thrust magnitude control ( e.g., pintle, pulse, or gel motor ) for effective cruise.
Max range for a rocket is usually a semi-ballistic flight profile, instead of cruise flight.
R = ( L / D ) I
sp
V In [ W
L / ( W
L – W
P )] , Breguet Range Equation
Parameter
L / D, Lift / Drag
I
sp,
Specific Impulse
V
AVG ,
Average Velocity
W
P
/ W
L
, Cruise Propellant or
Fuel Weight / Launch Weight
R, Cruise Range
10
3,000 sec
1,000 ft / sec
0.3
1,800 nm
5
1,300 sec
3,500 ft / sec
0.2
830 nm
3
1,000 sec
6,000 ft / sec
0.1
310 nm
5
250 sec
3,000 ft / sec
0.4
250 nm
Solid Rocket
Hydrocarbon Fuel
Scramjet Missile
Liquid Fuel
Ramjet Missile
Subsonic Turbojet
Missile
Cruise Range Is Driven By L/D, I
sp, Velocity, and
Propellant or Fuel Weight Fraction
Typical Value for 2,000 lb Precision Strike Missile
Note: Ramjet and Scramjet missiles booster propellant for Mach 2.5 to 4 take-over speed not included in W
P
for cruise. Rockets require thrust magnitude control ( e.g., pintle, pulse, or gel motor ) for effective cruise.
Max range for a rocket is usually a semi-ballistic flight profile, instead of cruise flight.
R = ( L / D ) I
sp
V In [ W
L / ( W
L – W
P )] , Breguet Range Equation
Parameter
L / D, Lift / Drag
I
sp,
Specific Impulse
V
AVG ,
Average Velocity
W
P
/ W
L
, Cruise Propellant or
Fuel Weight / Launch Weight
R, Cruise Range
10
3,000 sec
1,000 ft / sec
0.3
1,800 nm
5
1,300 sec
3,500 ft / sec
0.2
830 nm
3
1,000 sec
6,000 ft / sec
0.1
310 nm
5
250 sec
3,000 ft / sec
0.4
250 nm
Solid Rocket
Hydrocarbon Fuel
Scramjet Missile
Liquid Fuel
Ramjet Missile
Subsonic Turbojet
Missile
10/19/24 ELF 15
Slurry Fuel and Efficient Packaging Provide
Extended Range Ramjet
Propulsion / Configuration Fuel Type / Volumetric
Performance (BTU / in3) /
Density (lb / in3)
Fuel Volume (in3) /
Fuel Weight (lb)
ISP (sec) / Cruise
Range at Mach 3.5,
60K ft (nm)
Liquid Fuel Ramjet
RJ-5 / 581 / 0.040 11900 / 476 1120 / 390
Ducted Rocket ( Low Smoke )
Solid Hydrocarbon / 1132 /
0.075
7922 / 594 677 / 294
Ducted Rocket ( High
Performance )
Boron / 2040 / 0.082 7922 / 649 769 / 366
Solid Fuel Ramjet
Boron / 2040 / 0.082 7056 / 579 1170 / 496
Slurry Fuel Ramjet 40% JP-10, 60% boron
carbide / 1191 / 0.050
11900 / 595 1835 / 770
Note: Flow Path Available FuelR
cruise
= V I
SP
( L / D )
ln [ W
BC
/ ( W
BC
- W
f
)]
Slurry Fuel and Efficient Packaging Provide
Extended Range Ramjet
Propulsion / Configuration Fuel Type / Volumetric
Performance (BTU / in3) /
Density (lb / in3)
Fuel Volume (in3) /
Fuel Weight (lb)
ISP (sec) / Cruise
Range at Mach 3.5,
60K ft (nm)
Liquid Fuel Ramjet
RJ-5 / 581 / 0.040 11900 / 476 1120 / 390
Ducted Rocket ( Low Smoke )
Solid Hydrocarbon / 1132 /
0.075
7922 / 594 677 / 294
Ducted Rocket ( High
Performance )
Boron / 2040 / 0.082 7922 / 649 769 / 366
Solid Fuel Ramjet
Boron / 2040 / 0.082 7056 / 579 1170 / 496
Slurry Fuel Ramjet 40% JP-10, 60% boron
carbide / 1191 / 0.050
11900 / 595 1835 / 770
Note: Flow Path Available FuelR
cruise
= V I
SP
( L / D )
ln [ W
BC
/ ( W
BC
- W
f
)]
10/19/24 ELF 16
Flight Trajectory Shaping Provides Extended Range
Altitude
Range
R
MAX
Apogee or Cruise
Glide
Climb
Rapid Pitch Up
Line-Of-Sight Trajectory
R
MAX
Design Guidelines for Horizontal Launch:
–High thrust-to-weight 10 for safe separation
–Rapid pitch up minimizes time / propellant to reach efficient altitude
–Climb at a 0 deg with thrust-to-weight 2 and q 700 psf minimizes drag / propellant to
reach efficient cruise altitude for ( L / D )
MAX
–High altitude cruise at ( L / D )
MAX
and q 700 psf maximizes range
–Glide from high altitude at ( L / D )
Max
and q 700 psf provides extended range
Flight Trajectory Shaping Provides Extended Range
Altitude
Range
R
MAX
Apogee or Cruise
Glide
Climb
Rapid Pitch Up
Line-Of-Sight Trajectory
R
MAX
Design Guidelines for Horizontal Launch:
–High thrust-to-weight 10 for safe separation
–Rapid pitch up minimizes time / propellant to reach efficient altitude
–Climb at a 0 deg with thrust-to-weight 2 and q 700 psf minimizes drag / propellant to
reach efficient cruise altitude for ( L / D )
MAX
–High altitude cruise at ( L / D )
MAX
and q 700 psf maximizes range
–Glide from high altitude at ( L / D )
Max
and q 700 psf provides extended range
10/19/24 ELF 17
Rocket Baseline Missile Range Driven by I
SP
,
Propellant Weight, Drag, and Static Margin
-1
-0.5
0
0.5
1
1.5
IspProp.
Weight
CD0Drag-
Due-to-
Lift
Static
Margin
ThrustInert
Weight
Parameter
Nondimensional
Range
Sensitivity to
Parameter
Note: Rocket baseline:
h
L = 20k ft, M
L = 0.7, M
EC = 1.5
R
@ ML = 0.7, hL = 20K ft = 9.5 nm
Example: 10% increase in propellant
weight 8.8% increase in flight range
Rocket Baseline Missile Range Driven by I
SP
,
Propellant Weight, Drag, and Static Margin
-1
-0.5
0
0.5
1
1.5
IspProp.
Weight
CD0Drag-
Due-to-
Lift
Static
Margin
ThrustInert
Weight
Parameter
Nondimensional
Range
Sensitivity to
Parameter
Note: Rocket baseline:
h
L = 20k ft, M
L = 0.7, M
EC = 1.5
R
@ ML = 0.7, hL = 20K ft = 9.5 nm
Example: 10% increase in propellant
weight 8.8% increase in flight range
10/19/24 ELF 18
Ramjet Baseline Range Is Driven by I
SP
, Fuel
Weight, Thrust, and Zero-Lift Drag Coefficient
-1
-0.5
0
0.5
1
1.5
Inert
Weight
Fuel
Weight
CD0, Zero-
Lift Drag
Coefficient
CLA, Lift-
Curve-
Slope
Coefficient
Thrust ISP
Parameter
N
o
n
d
im
e
n
s
io
n
a
l R
a
n
g
e
S
e
n
s
it
iv
it
y
t
o
P
a
r
a
m
e
t
e
r
Sea Level Flyout at Mach 2.320 Kft Flyout at Mach 2.5
40 Kft Flyout at Mach 2.860 Kft Flyout at Mach 3.0
Example: At Mach 3.0 / 60K ft altitude
cruise, 10% increase in fuel weight
9.6% increase in flight range
Ramjet Baseline Range Is Driven by I
SP
, Fuel
Weight, Thrust, and Zero-Lift Drag Coefficient
-1
-0.5
0
0.5
1
1.5
Inert
Weight
Fuel
Weight
CD0, Zero-
Lift Drag
Coefficient
CLA, Lift-
Curve-
Slope
Coefficient
Thrust ISP
Parameter
N
o
n
d
im
e
n
s
io
n
a
l R
a
n
g
e
S
e
n
s
it
iv
it
y
t
o
P
a
r
a
m
e
t
e
r
Sea Level Flyout at Mach 2.320 Kft Flyout at Mach 2.5
40 Kft Flyout at Mach 2.860 Kft Flyout at Mach 3.0
Example: At Mach 3.0 / 60K ft altitude
cruise, 10% increase in fuel weight
9.6% increase in flight range
10/19/24 ELF 19
Ramjet Baseline Flight Range Uncertainty Is +/- 7%, 1
Parameter Baseline Value at Mach
3.0 / 60k ft
Uncertainty in Parameter
R / R due to Uncertainty
1. Inert Weight 1205 lb +/- 2%, 1
+/- 0.8%, 1
2. Ramjet Fuel Weight 476 lb +/- 1%, 1
+/- 0.9%, 1
3. Zero-Lift Drag Coefficient 0.17 +/- 5%, 1
+/- 4%, 1
4. Lift Curve Slope Coefficient 0.13 / deg +/- 3%, 1
+/- 1%, 1
5. Cruise Thrust (
= 0.39 ) 458 lb +/- 5%, 1
+/- 2%, 1
6. Specific Impulse 1040 sec +/- 5%, 1
+/- 5%, 1
Level of Maturity of Ramjet Baseline Based on Flight Demo of Prototype and Subsystem Tests
Wind tunnel tests
Direct connect, freejet, and booster firing propulsion tests
Structure test
Hardware-in-loop simulation
Total Flight Range Uncertainty at Mach 3.0 / 60K ft Flyout
R / R = [ (R / R )
1
2
+ (R / R )
2
2
+ (R / R )
3
2
+ (R / R )
4
2
+ (R / R )
5
2
+ (R / R )
6
2
]
1/2
= +/- 6.9%, 1
R = 445 nm +/- 31 nm, 1
Ramjet Baseline Flight Range Uncertainty Is +/- 7%, 1
Parameter Baseline Value at Mach
3.0 / 60k ft
Uncertainty in Parameter
R / R due to Uncertainty
1. Inert Weight 1205 lb +/- 2%, 1
+/- 0.8%, 1
2. Ramjet Fuel Weight 476 lb +/- 1%, 1
+/- 0.9%, 1
3. Zero-Lift Drag Coefficient 0.17 +/- 5%, 1
+/- 4%, 1
4. Lift Curve Slope Coefficient 0.13 / deg +/- 3%, 1
+/- 1%, 1
5. Cruise Thrust (
= 0.39 ) 458 lb +/- 5%, 1
+/- 2%, 1
6. Specific Impulse 1040 sec +/- 5%, 1
+/- 5%, 1
Level of Maturity of Ramjet Baseline Based on Flight Demo of Prototype and Subsystem Tests
Wind tunnel tests
Direct connect, freejet, and booster firing propulsion tests
Structure test
Hardware-in-loop simulation
Total Flight Range Uncertainty at Mach 3.0 / 60K ft Flyout
R / R = [ (R / R )
1
2
+ (R / R )
2
2
+ (R / R )
3
2
+ (R / R )
4
2
+ (R / R )
5
2
+ (R / R )
6
2
]
1/2
= +/- 6.9%, 1
R = 445 nm +/- 31 nm, 1
10/19/24 ELF 20
US Tactical Missile Follow-On Programs Provide
Enhanced Performance
Year Entering EMD
AIM-9X ( maneuverability ), 1996 - Hughes
AIM-120 ( speed, range ), 1981 - Hughes
Long Range ATS, AGM-86, 1973 - BoeingAGM-129 ( RCS ), 1983 - General Dynamics
PAC-3 (accuracy), 1992 - Lockheed MartinLong Range STA, MIM-104, 1966 - Raytheon
1950 1965 1970 1975 1980 1985 1990 1995 >2000
AGM-88 ( speed, range ), 1983 - TI
Man-portable STS, M-47, 1970 - McDonnell Douglas
Anti-radar ATS, AGM-45, 1961 - TI
Short Range ATA, AIM-9, 1949 - Raytheon
Javelin ( gunner survivability,
lethality, weight ), 1989 - TI
Medium Range ATA, AIM-7,1951 - Raytheon
Medium Range ATS, AGM-130, 1983 - RockwellJASSM ( range, observables ),
1999 - Lockheed Martin
Hypersonic Missile, ~2005
Hypersonic Missile ~2005
Long Range STS, BGM-109, 1972 - General DynamicsHypersonic Missile ~2005
US Tactical Missile Follow-On Programs Provide
Enhanced Performance
Year Entering EMD
AIM-9X ( maneuverability ), 1996 - Hughes
AIM-120 ( speed, range ), 1981 - Hughes
Long Range ATS, AGM-86, 1973 - BoeingAGM-129 ( RCS ), 1983 - General Dynamics
PAC-3 (accuracy), 1992 - Lockheed MartinLong Range STA, MIM-104, 1966 - Raytheon
1950 1965 1970 1975 1980 1985 1990 1995 >2000
AGM-88 ( speed, range ), 1983 - TI
Man-portable STS, M-47, 1970 - McDonnell Douglas
Anti-radar ATS, AGM-45, 1961 - TI
Short Range ATA, AIM-9, 1949 - Raytheon
Javelin ( gunner survivability,
lethality, weight ), 1989 - TI
Medium Range ATA, AIM-7,1951 - Raytheon
Medium Range ATS, AGM-130, 1983 - RockwellJASSM ( range, observables ),
1999 - Lockheed Martin
Hypersonic Missile, ~2005
Hypersonic Missile ~2005
Long Range STS, BGM-109, 1972 - General DynamicsHypersonic Missile ~2005
10/19/24 ELF 21
Example of Missile Technology State-of-the-Art
Advancement: Missile Maneuverability
0
10
20
30
40
50
60
1950196019701980199020002010
Year IOC
O
p
e
r
a
t
i
o
n
a
l
A
n
g
l
e
o
f
A
t
t
a
c
k
,
D
e
g
r
e
e
s
AIM-7A
AM-9B
R530
AA-8
AIM-54
R550
Skyflash
Python 3
AA-10
Aspide
Super 530D
AA-11
AIM-120
Python 4
AA-12
MICA
AIM-132
AIM-9X
Controls Augmented
with Propulsion
Devices ( TVC,
Reaction Jet )
Example of Missile Technology State-of-the-Art
Advancement: Missile Maneuverability
0
10
20
30
40
50
60
1950196019701980199020002010
Year IOC
O
p
e
r
a
t
i
o
n
a
l
A
n
g
l
e
o
f
A
t
t
a
c
k
,
D
e
g
r
e
e
s
AIM-7A
AM-9B
R530
AA-8
AIM-54
R550
Skyflash
Python 3
AA-10
Aspide
Super 530D
AA-11
AIM-120
Python 4
AA-12
MICA
AIM-132
AIM-9X
Controls Augmented
with Propulsion
Devices ( TVC,
Reaction Jet )
10/19/24 ELF 22
Example of Missile Technology State-of-the-Art
Advancement: Supersonic Air Breathing Missiles
0
1
2
3
4
5
6
7
1950196019701980199020002010
Year Flight Demonstration
M
c
r
u
i
s
e
,
C
r
u
i
s
e
M
a
c
h
N
u
m
b
e
r
Cobra
Vandal / Talos
RARE
Bloodhound
BOMARC
Typhon
CROW
SA-6
Sea Dart
LASRM
ALVRJ
3M80
ASALM
Kh-31
ASMP
ANS
Kh-41
SLAT
HyFly
Scramjet
Ramjet
Example of Missile Technology State-of-the-Art
Advancement: Supersonic Air Breathing Missiles
0
1
2
3
4
5
6
7
1950196019701980199020002010
Year Flight Demonstration
M
c
r
u
i
s
e
,
C
r
u
i
s
e
M
a
c
h
N
u
m
b
e
r
Cobra
Vandal / Talos
RARE
Bloodhound
BOMARC
Typhon
CROW
SA-6
Sea Dart
LASRM
ALVRJ
3M80
ASALM
Kh-31
ASMP
ANS
Kh-41
SLAT
HyFly
Scramjet
Ramjet
10/19/24 ELF 23
New Technologies That Enhance Tactical Missile
Performance
Dome
Faceted / Window
Multi-lens
Seeker
Strapdown
High Gimbal
G & C
GPS / INS
In-flight
Optimize
, Feedback
Propulsion
Liquid / Solid Fuel Ramjet
Variable Flow Ducted Rocket
Scramjet
High Temperature Combustor
High Density Fuel / Propellant
High Throttle Fuel Control
Endothermic Fuel
Composite Case
Pintle / Pulsed / Gel Motor
Insulation
Hypersonic
High Density
Flight Control
TVC / Reaction Jet
Power
MEMS
Airframe
Lifting Body
Neutral Static Margin
Lattice Fins
Low Drag Inlet
Mixed Comp. Inlet
Composite
Titanium Alloy
MEMS Data
Collection
Split Canard
Free-to-roll Tails
New Technologies That Enhance Tactical Missile
Performance
Dome
Faceted / Window
Multi-lens
Seeker
Strapdown
High Gimbal
G & C
GPS / INS
In-flight
Optimize
, Feedback
Propulsion
Liquid / Solid Fuel Ramjet
Variable Flow Ducted Rocket
Scramjet
High Temperature Combustor
High Density Fuel / Propellant
High Throttle Fuel Control
Endothermic Fuel
Composite Case
Pintle / Pulsed / Gel Motor
Insulation
Hypersonic
High Density
Flight Control
TVC / Reaction Jet
Power
MEMS
Airframe
Lifting Body
Neutral Static Margin
Lattice Fins
Low Drag Inlet
Mixed Comp. Inlet
Composite
Titanium Alloy
MEMS Data
Collection
Split Canard
Free-to-roll Tails
10/19/24 ELF 24
Outline
Parameters and Technologies That Drive Missile Flight
Performance
Missile Flight Performance Prediction
Examples of Maximizing Missile Flight Performance ( Workshop )
Summary
Outline
Parameters and Technologies That Drive Missile Flight
Performance
Missile Flight Performance Prediction
Examples of Maximizing Missile Flight Performance ( Workshop )
Summary
10/19/24 ELF 25
Flight Envelope Should Has Large Max Range,
Small Min Range, and Large Off Boresight
Rear Flyout Range
•Max
•Min
Forward Flyout Range
•Max
•Min
Beam Off Boresight
Flyout Range
•Min
•Max
Flight Envelope Should Has Large Max Range,
Small Min Range, and Large Off Boresight
Rear Flyout Range
•Max
•Min
Forward Flyout Range
•Max
•Min
Beam Off Boresight
Flyout Range
•Min
•Max
10/19/24 ELF 26
Examples of Air Launched Missile Flight
Performance
Examples of Air Launched Missile Flight
Performance
10/19/24 ELF 27
Examples of Surface Launched Missile Flight
Performance
Examples of Surface Launched Missile Flight
Performance
10/19/24 ELF 28
Conceptual Design Modeling Versus Preliminary
Design Modeling
Conceptual Design Modeling
1 DOF [ Axial force ( C
D
O
), thrust, weight ]
2 DOF [ Normal force ( C
N ), axial force, thrust, weight ]
3 DOF point mass [ 3 forces ( normal, axial, side ), thrust,
weight ]
3 DOF pitch [ 2 forces ( normal, axial ), 1 moment
( pitch ), thrust, weight ]
4 DOF [ 2 forces ( normal, axial ), 2 moments ( pitch,
roll ), thrust, weight ]
Preliminary Design Modeling
6 DOF [ 3 forces ( normal, axial, side ), 3 moments ( pitch,
roll, yaw ), thrust, weight ]
C
D
O
C
N
C
N
C
N
C
m
C
A
C
A
C
A
C
A
C
A
C
l
C
l
C
N
Cm
C
N
Cm
C
n
C
Y
C
Y
Conceptual Design Modeling Versus Preliminary
Design Modeling
Conceptual Design Modeling
1 DOF [ Axial force ( C
D
O
), thrust, weight ]
2 DOF [ Normal force ( C
N ), axial force, thrust, weight ]
3 DOF point mass [ 3 forces ( normal, axial, side ), thrust,
weight ]
3 DOF pitch [ 2 forces ( normal, axial ), 1 moment
( pitch ), thrust, weight ]
4 DOF [ 2 forces ( normal, axial ), 2 moments ( pitch,
roll ), thrust, weight ]
Preliminary Design Modeling
6 DOF [ 3 forces ( normal, axial, side ), 3 moments ( pitch,
roll, yaw ), thrust, weight ]
C
D
O
C
N
C
N
C
N
C
m
C
A
C
A
C
A
C
A
C
A
C
l
C
l
C
N
Cm
C
N
Cm
C
n
C
Y
C
Y
10/19/24 ELF 29
3 DOF Simplified Equations of Motion Show
Drivers for Configuration Sizing
Configuration Sizing Implication
y
..
q S
Ref
d C
m
+ q S
Ref
d C
m
High Control Effectiveness C
m
>
C
m
, I
y
small ( W small ), q large
( W / g
c
) V
.
q S
Ref
C
N
+ q S
Ref
C
N
- W cos Large / Fast Heading Change C
N
large, W small, q large
( W / g
c ) V
.
T - C
A S
Ref q - C
N
2
S
Ref q - W sin High Speed / Long Range Total
Impulse large, C
A
small, q small
+ Normal Force
<< 1 rad
W
+ Moment
V
+ Thrust
+ Axial Force
Note: Based on aerodynamic control
3 DOF Simplified Equations of Motion Show
Drivers for Configuration Sizing
Configuration Sizing Implication
y
..
q S
Ref
d C
m
+ q S
Ref
d C
m
High Control Effectiveness C
m
>
C
m
, I
y
small ( W small ), q large
( W / g
c
) V
.
q S
Ref
C
N
+ q S
Ref
C
N
- W cos Large / Fast Heading Change C
N
large, W small, q large
( W / g
c ) V
.
T - C
A S
Ref q - C
N
2
S
Ref q - W sin High Speed / Long Range Total
Impulse large, C
A
small, q small
+ Normal Force
<< 1 rad
W
+ Moment
V
+ Thrust
+ Axial Force
Note: Based on aerodynamic control
10/19/24 ELF 30
1.00E+05
1.00E+06
1.00E+07
1.00E+08
0 0.10.20.30.40.50.60.70.8
WP / WBC, Propellant or Fuel Weight / Weight at Begin of Cruise
R
, C
r
u
is
e
R
a
n
g
e
, f
t
(VISP)(L/D) = 2,000,000 ft(VISP)(L/D) = 10,000,000 ft
(VISP)(L/D) = 25,000,000 ft
For Long Range Cruise, Maximize V I
sp, L / D,
And Fuel or Propellant Weight Fraction
Example: Ramjet Baseline at Mach 3 / 60 Kft alt
R = 2901 ( 1040 ) ( 3.15 ) ln [ 1739 / ( 1739 - 476 )]
= ( 9,503,676 ) ln [ 1 / ( 1 - 0.2737 )] = 3,039,469 ft =
500 nm
R = ( V I
sp ) ( L / D ) ln [ W
BC / ( W
BC - W
P )] , Breguet Range Equation
Note: R = cruise range, V = cruise velocity, I
SP
= specific impulse, L = lift, D = drag,
W
BC = weight at begin of cruise, W
P = weight of propellant or fuel
Typical Rocket
Typical Ramjet with Axisymmetric AirframeRamjet with High L / D Airframe
1.00E+05
1.00E+06
1.00E+07
1.00E+08
0 0.10.20.30.40.50.60.70.8
WP / WBC, Propellant or Fuel Weight / Weight at Begin of Cruise
R
, C
r
u
is
e
R
a
n
g
e
, f
t
(VISP)(L/D) = 2,000,000 ft(VISP)(L/D) = 10,000,000 ft
(VISP)(L/D) = 25,000,000 ft
For Long Range Cruise, Maximize V I
sp, L / D,
And Fuel or Propellant Weight Fraction
Example: Ramjet Baseline at Mach 3 / 60 Kft alt
R = 2901 ( 1040 ) ( 3.15 ) ln [ 1739 / ( 1739 - 476 )]
= ( 9,503,676 ) ln [ 1 / ( 1 - 0.2737 )] = 3,039,469 ft =
500 nm
R = ( V I
sp ) ( L / D ) ln [ W
BC / ( W
BC - W
P )] , Breguet Range Equation
Note: R = cruise range, V = cruise velocity, I
SP
= specific impulse, L = lift, D = drag,
W
BC = weight at begin of cruise, W
P = weight of propellant or fuel
Typical Rocket
Typical Ramjet with Axisymmetric AirframeRamjet with High L / D Airframe
10/19/24 ELF 31
Efficient Steady Flight Is Enhanced by High L / D
and Light Weight
Steady Level FlightSteady Climb Steady Descent
T = D
L = W
L
D T
W
C
SIN
D
= ( D – T ) / W = V
D
/ V
V
D
= ( D – T ) V
/ W
R
D = h / tan
D = h ( L / D )
T – D
L
D
T
W
V
CV
C
D – T
L
D
T
W
DV
D
D
•Small Angle of Attack
•Equilibrium Flight
•V
C
= Velocity of Climb
•V
D = Velocity of Descent
C
= Flight Path Angle During Climb
D
= Flight Path Angle During Descent
•V
= Total Velocity
h = Incremental Altitude
•R
C
= Horizontal Range in Steady Climb
•R
D
= Horizontal Range in Steady Dive ( Glide )
Note:
Reference: Chin, S.S., “Missile Configuration Design,”
McGraw Hill Book Company, New York, 1961
V
T = W / ( L / D )SIN
c
= ( T – D ) / W = V
c
/ V
V
c
= ( T – D ) V
/ W
R
C = h / tan
C = h ( L / D )
Efficient Steady Flight Is Enhanced by High L / D
and Light Weight
Steady Level FlightSteady Climb Steady Descent
T = D
L = W
L
D T
W
C
SIN
D
= ( D – T ) / W = V
D
/ V
V
D
= ( D – T ) V
/ W
R
D = h / tan
D = h ( L / D )
T – D
L
D
T
W
V
CV
C
D – T
L
D
T
W
DV
D
D
•Small Angle of Attack
•Equilibrium Flight
•V
C
= Velocity of Climb
•V
D = Velocity of Descent
C
= Flight Path Angle During Climb
D
= Flight Path Angle During Descent
•V
= Total Velocity
h = Incremental Altitude
•R
C
= Horizontal Range in Steady Climb
•R
D
= Horizontal Range in Steady Dive ( Glide )
Note:
Reference: Chin, S.S., “Missile Configuration Design,”
McGraw Hill Book Company, New York, 1961
V
T = W / ( L / D )SIN
c
= ( T – D ) / W = V
c
/ V
V
c
= ( T – D ) V
/ W
R
C = h / tan
C = h ( L / D )
10/19/24 ELF 32
Small Turn Radius Requires High Angle of Attack
and Low Altitude Flight
R
T
, E
x
a
m
p
le
In
s
t
a
n
t
a
n
e
o
u
s
T
u
r
n
R
a
d
iu
s
, F
e
e
t
= Increment in Angle of Attack Required to Turn, Degrees
h = 100 K ft ( M
(L/D)
Max
= 7.9 )
h = 80 K ft ( M
(L/D)
Max
= 5.0 )
h = 60 K ft ( M
(L/D)
Max
= 3.1 )
h = 40 K ft ( M
(L/D)
Max
= 1.9 )
10,000,000
1,000,000
100,000
10,000
1,000
0 5 10 15 20
• • • •
•
•
•
•
•
•
•
•
Note for Example:
W = Weight = 2,000 lb
a / b = 1 ( circular cross section ), No wings
C
N
= sin 2 cos ( / 2 ) + 2 ( l / d ) sin
2
l / d = Length / Diameter = 10
S
Ref
= 2 ft
2
C
D
O
= 0.2
( L / D )
Max = 2.7, q
( L / D )
Max
= 1,000 psf
( L / D )
Max
= 15 degrees
T
( L / D )
Max
= 740 lb
Example:
= 10 deg
C
N
= 0.99
h = 40K ft ( ρ = 0.00039 slugs / ft
3
)
R
T
= 2 ( 2,000 ) / [( 32.2 ) ( 0.99 ) ( 2 ) ( 0.00039 )] = 161,000 ft
R
T
= V /
.
2 W / ( g
c
C
N
S
Ref
)
Small Turn Radius Requires High Angle of Attack
and Low Altitude Flight
R
T
, E
x
a
m
p
le
In
s
t
a
n
t
a
n
e
o
u
s
T
u
r
n
R
a
d
iu
s
, F
e
e
t
= Increment in Angle of Attack Required to Turn, Degrees
h = 100 K ft ( M
(L/D)
Max
= 7.9 )
h = 80 K ft ( M
(L/D)
Max
= 5.0 )
h = 60 K ft ( M
(L/D)
Max
= 3.1 )
h = 40 K ft ( M
(L/D)
Max
= 1.9 )
10,000,000
1,000,000
100,000
10,000
1,000
0 5 10 15 20
• • • •
•
•
•
•
•
•
•
•
Note for Example:
W = Weight = 2,000 lb
a / b = 1 ( circular cross section ), No wings
C
N
= sin 2 cos ( / 2 ) + 2 ( l / d ) sin
2
l / d = Length / Diameter = 10
S
Ref
= 2 ft
2
C
D
O
= 0.2
( L / D )
Max = 2.7, q
( L / D )
Max
= 1,000 psf
( L / D )
Max
= 15 degrees
T
( L / D )
Max
= 740 lb
Example:
= 10 deg
C
N
= 0.99
h = 40K ft ( ρ = 0.00039 slugs / ft
3
)
R
T
= 2 ( 2,000 ) / [( 32.2 ) ( 0.99 ) ( 2 ) ( 0.00039 )] = 161,000 ft
R
T
= V /
.
2 W / ( g
c
C
N
S
Ref
)
10/19/24 ELF 33
Turn Rate Performance Requires High Control
Effectiveness
.
= g
c
n / V = [ q S
Ref
C
N
+ q S
Ref
C
N
- W cos ( ) ] / [( W / g
c
) V ]
Assume Rocket Baseline @ Mach 0.8 Launch, 20K ft Altitude
(C
m
)
xcg=84.6
= (C
m
)
xcg=75.7
+ C
N
( 84.6 – 75.7 ) / d = - 0.40 + 0.68 ( 8.9 ) / 8 = 0.36 per deg
(C
m
)
xcg=84.6
= (C
m
)
xcg=75.7
+ C
N
( 84.6 – 75.7 ) / d = 0.60 + 0.27( 8.9 ) / 8 = 0.90 per deg
/ = - C
m
/ C
m
= - 0.90 / 0.36 = - 2.5
’ = + < 22 degrees,
max = 30 deg = 30 deg, = - 12 deg
.
= [ 436 ( 0.349 )( 0.68 )( 30 ) + 436 ( 0.349 )( 0.27 )( - 12 ) – 500 ( 1 )] / [( 500 / 32.2 )( 830 )] = 0.164 rad / sec or 9.4 deg / sec
Assume Rocket Baseline @ Mach 2 Coast, 20K ft Altitude
/ = 0.75
’ = + = 22 degrees = 12.6 deg, = 9.4 deg
.
= [ 2725 ( 0.349 )( 0.60 )( 9.4 ) +2725 ( 0.349 )( 0.19 )( 12.6 ) – 367 ( 1 )] / ( 367 / 32.2 )( 2074 ) = 0.31 rad / sec or 18 deg / sec
Note: High q, statically stable, forward wing control, lighter weight higher climb capability
Note: Forward wing deflection to trim increases normal force
Turn Rate Performance Requires High Control
Effectiveness
.
= g
c
n / V = [ q S
Ref
C
N
+ q S
Ref
C
N
- W cos ( ) ] / [( W / g
c
) V ]
Assume Rocket Baseline @ Mach 0.8 Launch, 20K ft Altitude
(C
m
)
xcg=84.6
= (C
m
)
xcg=75.7
+ C
N
( 84.6 – 75.7 ) / d = - 0.40 + 0.68 ( 8.9 ) / 8 = 0.36 per deg
(C
m
)
xcg=84.6
= (C
m
)
xcg=75.7
+ C
N
( 84.6 – 75.7 ) / d = 0.60 + 0.27( 8.9 ) / 8 = 0.90 per deg
/ = - C
m
/ C
m
= - 0.90 / 0.36 = - 2.5
’ = + < 22 degrees,
max = 30 deg = 30 deg, = - 12 deg
.
= [ 436 ( 0.349 )( 0.68 )( 30 ) + 436 ( 0.349 )( 0.27 )( - 12 ) – 500 ( 1 )] / [( 500 / 32.2 )( 830 )] = 0.164 rad / sec or 9.4 deg / sec
Assume Rocket Baseline @ Mach 2 Coast, 20K ft Altitude
/ = 0.75
’ = + = 22 degrees = 12.6 deg, = 9.4 deg
.
= [ 2725 ( 0.349 )( 0.60 )( 9.4 ) +2725 ( 0.349 )( 0.19 )( 12.6 ) – 367 ( 1 )] / ( 367 / 32.2 )( 2074 ) = 0.31 rad / sec or 18 deg / sec
Note: High q, statically stable, forward wing control, lighter weight higher climb capability
Note: Forward wing deflection to trim increases normal force
10/19/24 ELF 34
For Long Range Coast, Maximize Initial Velocity
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2
Example for Rocket Baseline:
•W
BO
= 367 lb, S
Ref
= 0.349 ft
2
, V
BO
= 2,151 ft / sec, = 0 deg, C
D
0
= 0.9, h = 20,000 ft ( ρ = 0.00127 slugs / ft
3
), t = 10 sec
•t / [ 2 W
BO
/ ( g
c
ρ S
Ref
C
D
0
V
BO
)] = 10 / { 2 ( 367 ) / [ 32.2 ( 0.00127 ) ( 0.349 ) ( 0.9 ) ( 2151 ) ]} = 10 / 26.6 = 0.376
•V / V
BO
= 0.727, V = 0.727 x 2151 = 1564 ft / sec, R / [ 2 W
BO
/ ( g
c
ρ S
Ref
C
D
0
)] = 0.319, R
= 18,300 ft or 3.0 nm
t
/ [ 2 W / ( g ρS C
D
0
V
BC )], Non-dimensional Coast Time
V / V
BO = 1 / { 1 + t / { 2 W
BO / [ g
c ρ
AVG S
Ref ( C
D
0
)
AVG V
BO ]}}
R / { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
(C
D
0
)
AVG
]} = ln {1 + t
/ { 2
W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
BO
]}}
Note: Based on 1DoF
dV / dt = - g
c
C
D
0
S
Ref
q / W
Assumptions:
= constant
0 deg
• D > W sin
V
= velocity during coast
V
BO
= velocity @ burnout ( begin coast )
R = coast range
V
x = V cos , V
y = V sin
R
x = R cos , R
y = R sin
For Long Range Coast, Maximize Initial Velocity
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2
Example for Rocket Baseline:
•W
BO
= 367 lb, S
Ref
= 0.349 ft
2
, V
BO
= 2,151 ft / sec, = 0 deg, C
D
0
= 0.9, h = 20,000 ft ( ρ = 0.00127 slugs / ft
3
), t = 10 sec
•t / [ 2 W
BO
/ ( g
c
ρ S
Ref
C
D
0
V
BO
)] = 10 / { 2 ( 367 ) / [ 32.2 ( 0.00127 ) ( 0.349 ) ( 0.9 ) ( 2151 ) ]} = 10 / 26.6 = 0.376
•V / V
BO
= 0.727, V = 0.727 x 2151 = 1564 ft / sec, R / [ 2 W
BO
/ ( g
c
ρ S
Ref
C
D
0
)] = 0.319, R
= 18,300 ft or 3.0 nm
t
/ [ 2 W / ( g ρS C
D
0
V
BC )], Non-dimensional Coast Time
V / V
BO = 1 / { 1 + t / { 2 W
BO / [ g
c ρ
AVG S
Ref ( C
D
0
)
AVG V
BO ]}}
R / { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
(C
D
0
)
AVG
]} = ln {1 + t
/ { 2
W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
BO
]}}
Note: Based on 1DoF
dV / dt = - g
c
C
D
0
S
Ref
q / W
Assumptions:
= constant
0 deg
• D > W sin
V
= velocity during coast
V
BO
= velocity @ burnout ( begin coast )
R = coast range
V
x = V cos , V
y = V sin
R
x = R cos , R
y = R sin
10/19/24 ELF 35
For Long Range Ballistic Flight, Maximize Initial
Velocity
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2
t
/ [ 2 W / ( g ρS C
D
0
V
i
)], Non-dimensional Time
V
x
/ ( V
i
cos
i
) = 1 / { 1 + t / { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
i
]}}
( V
y
+ g
c
t ) / ( V
i
sin
i
) = 1 / { 1 + t / { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
i
]}
Assumptions: T = 0, = 0 deg, D > W sin , flat earth
Nomenclature: V
= velocity during ballistic flight, V
i = initial
velocity, R
x = horizontal range, h = altitude, h
i = initial
altitude, V
x
= horizontal velocity, V
y
= vertical velocity
Example for Rocket Baseline:
•W
BO
= 367 lb, S
Ref
= 0.349 ft
2
, V
i
= V
BO
= 2,151 fps,
i
= 0 deg, ( C
D
0
)
AVG
= 0.9, h
i
= 20,000 ft, ρ
AVG
= 0.001755 slugs / ft
3
, t = 35 sec
•t / [ 2 W
BO
/ ( g
c
ρ S
Ref
C
D
0
V
i
)] = 35 / { 2 ( 367 ) / [ 32.2 ( 0.001755 ) ( 0.349 ) ( 0.9 ) ( 2151 ) ]} = 35 / 19.22 = 1.821
•V
x
/ ( V
i
cos
i
) = 0.354 V
x
= 762 ft / sec, ( V
y
+ 32.2 t ) / ( V
i
sin
i
) = 0.354 V
y
= - 1127 ft / sec, R
x
/ [ 2 W
i
cos
i
/ ( g
c
ρ S
Ref
C
D
0
)] = 1.037 R
x
= 42,900 ft or 7.06 nm, ( h – h
i
+ 16.1 t
2
) / [ 2 W
BO
cos
i
/ ( g
c
ρ S
Ref
C
D
0
)] = 1.037 h = 0 ft
R
x
/ { 2 W
BO
cos
i
/ [ g
c
ρ
AVG
S
Ref
(C
D
0
)
AVG
]} = ln { 1 + t
/ { 2
W
BO
/ [ g
c
( ρ )
AVG
S
Ref
( C
D
0
)
AVG
V
i
]}}
( h – h
i
+ g
c
t
2
/ 2 ) / { 2 W
BO
sin
i
/ [ g
c
ρ
AVG
S
Ref
(C
D
0
)
AVG
]} =
ln { 1 + t
/ { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
i
]}
For Long Range Ballistic Flight, Maximize Initial
Velocity
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2
t
/ [ 2 W / ( g ρS C
D
0
V
i
)], Non-dimensional Time
V
x
/ ( V
i
cos
i
) = 1 / { 1 + t / { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
i
]}}
( V
y
+ g
c
t ) / ( V
i
sin
i
) = 1 / { 1 + t / { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
i
]}
Assumptions: T = 0, = 0 deg, D > W sin , flat earth
Nomenclature: V
= velocity during ballistic flight, V
i = initial
velocity, R
x = horizontal range, h = altitude, h
i = initial
altitude, V
x
= horizontal velocity, V
y
= vertical velocity
Example for Rocket Baseline:
•W
BO
= 367 lb, S
Ref
= 0.349 ft
2
, V
i
= V
BO
= 2,151 fps,
i
= 0 deg, ( C
D
0
)
AVG
= 0.9, h
i
= 20,000 ft, ρ
AVG
= 0.001755 slugs / ft
3
, t = 35 sec
•t / [ 2 W
BO
/ ( g
c
ρ S
Ref
C
D
0
V
i
)] = 35 / { 2 ( 367 ) / [ 32.2 ( 0.001755 ) ( 0.349 ) ( 0.9 ) ( 2151 ) ]} = 35 / 19.22 = 1.821
•V
x
/ ( V
i
cos
i
) = 0.354 V
x
= 762 ft / sec, ( V
y
+ 32.2 t ) / ( V
i
sin
i
) = 0.354 V
y
= - 1127 ft / sec, R
x
/ [ 2 W
i
cos
i
/ ( g
c
ρ S
Ref
C
D
0
)] = 1.037 R
x
= 42,900 ft or 7.06 nm, ( h – h
i
+ 16.1 t
2
) / [ 2 W
BO
cos
i
/ ( g
c
ρ S
Ref
C
D
0
)] = 1.037 h = 0 ft
R
x
/ { 2 W
BO
cos
i
/ [ g
c
ρ
AVG
S
Ref
(C
D
0
)
AVG
]} = ln { 1 + t
/ { 2
W
BO
/ [ g
c
( ρ )
AVG
S
Ref
( C
D
0
)
AVG
V
i
]}}
( h – h
i
+ g
c
t
2
/ 2 ) / { 2 W
BO
sin
i
/ [ g
c
ρ
AVG
S
Ref
(C
D
0
)
AVG
]} =
ln { 1 + t
/ { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
i
]}
10/19/24 ELF 36
High Propellant Weight and High Thrust Provide
High Burnout Velocity
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.1 0.20.3 0.40.5
Wp / Wi, Propellant Fraction
D
e
lt
a
V
/ (
g
IS
P
)
, N
o
n
d
im
e
n
s
io
n
a
l
In
c
r
e
m
e
n
t
a
l V
e
lo
c
it
y
DAVG / T = 0DAVG / T = 0.5DAVG / T = 1.0
V / ( g
c I
SP ) = - ( 1 - D
AVG / T ) ln ( 1 - W
p / W
i )
Example for Rocket Baseline:
W
i = W
L = 500 lb
For boost, W
P
= 84.8 lb
W
P
/ W
L
= 0.1696
I
SP = 250 sec
T
B
= 5750 lb
M
i
= M
L
= 0.8, h
i
= h
L
= 20,000 ft
D
AVG = 635 lb
D
AVG
/ T = 0.110
V / [( 32.2 ) ( 250 )] = - ( 1 -
0.110 ) ln ( 1 - 0.1696 ) = 0.1654
V = ( 0.1654 ) ( 32.2 ) ( 250 )
= 1331 ft / sec
Note: 1 DOF Equation of Motion with 0 deg, = constant, and T > W sin , W
i = initial weight, W
P =
propellant weight, I
SP
= specific impulse, T = thrust, M
i
= initial Mach number, h
i
= initial altitude, D
AVG
= average
drag, V = incremental velocity, g
c = gravitation constant, V
x = V cos , V
y = V sin , R
x = R cos , R
y = R sin
Note: R = ( V
i + V / 2 ) t
B, where R = boost range, V
i = initial velocity, t
B = boost time
High Propellant Weight and High Thrust Provide
High Burnout Velocity
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.1 0.20.3 0.40.5
Wp / Wi, Propellant Fraction
D
e
lt
a
V
/ (
g
IS
P
)
, N
o
n
d
im
e
n
s
io
n
a
l
In
c
r
e
m
e
n
t
a
l V
e
lo
c
it
y
DAVG / T = 0DAVG / T = 0.5DAVG / T = 1.0
V / ( g
c I
SP ) = - ( 1 - D
AVG / T ) ln ( 1 - W
p / W
i )
Example for Rocket Baseline:
W
i = W
L = 500 lb
For boost, W
P
= 84.8 lb
W
P
/ W
L
= 0.1696
I
SP = 250 sec
T
B
= 5750 lb
M
i
= M
L
= 0.8, h
i
= h
L
= 20,000 ft
D
AVG = 635 lb
D
AVG
/ T = 0.110
V / [( 32.2 ) ( 250 )] = - ( 1 -
0.110 ) ln ( 1 - 0.1696 ) = 0.1654
V = ( 0.1654 ) ( 32.2 ) ( 250 )
= 1331 ft / sec
Note: 1 DOF Equation of Motion with 0 deg, = constant, and T > W sin , W
i = initial weight, W
P =
propellant weight, I
SP
= specific impulse, T = thrust, M
i
= initial Mach number, h
i
= initial altitude, D
AVG
= average
drag, V = incremental velocity, g
c = gravitation constant, V
x = V cos , V
y = V sin , R
x = R cos , R
y = R sin
Note: R = ( V
i + V / 2 ) t
B, where R = boost range, V
i = initial velocity, t
B = boost time
10/19/24 ELF 37
High Missile Velocity and Lead Are Required to
Intercept High Speed Crossing Targets
V
M / V
T
4
3
2
0
0 10 20 30 40 50
L, Lead Angle, Degrees
1
A = 90°
A = 45°
Note:Proportional Guidance
V
M= Missile Velocity
V
T= Target Velocity
A= Target Aspect
L= Missile Lead Angle
Seeker Gimbal
V
M
V
T
LA
V
M sin L = V
T sin A, Proportional Guidance Trajectory
Example:
L = 30 degrees
A = 45 degrees
V
M / V
T = sin ( 45 ) / sin ( 30 ) =
1.42
High Missile Velocity and Lead Are Required to
Intercept High Speed Crossing Targets
V
M / V
T
4
3
2
0
0 10 20 30 40 50
L, Lead Angle, Degrees
1
A = 90°
A = 45°
Note:Proportional Guidance
V
M= Missile Velocity
V
T= Target Velocity
A= Target Aspect
L= Missile Lead Angle
Seeker Gimbal
V
M
V
T
LA
V
M sin L = V
T sin A, Proportional Guidance Trajectory
Example:
L = 30 degrees
A = 45 degrees
V
M / V
T = sin ( 45 ) / sin ( 30 ) =
1.42
10/19/24 ELF 38
Example of Spreadsheet Based Conceptual
Sizing Computer Code - TMD Spreadsheet
Define Mission Requirements [ Flight Performance ( R
Max
, R
Min
, V
AVG
) , MOM, Constraints ]
Establish Baseline ( Rocket , Ramjet )
Aerodynamics Input ( d, l, l
N, A, c, t, x
cg )
Aerodynamics Output [ C
D
0
, C
N, X
AC, C
m
, L / D, S
T ]
Propulsion Input ( p
c, , c*, A
b, A
t, A
3, H
f, , T
4, Inlet Type )
Propulsion Output [ I
sp, T
cruise, p
t
2
/ p
t
0
, w
.
, T
boost, T
sustain, V
Boost ]
Weight Input ( W
L
, W
P
,
max
)
Weight Output [ Q, dT
skin
/ dt, T
skin
,
skin
, t
skin
,
buckling
, M
B
, ( F
t
)
Motor
, W, x
cg
, I
y
]
Trajectory Input ( h
i, V
i, Type ( cruise, boost, coast, ballistic, turn, glide )
Trajectory Output ( R, V, and versus time )
Meet
Performance?
Measures of Merit and Constraints
No [ p
Blast
, P
K
, n
Hits
,
V
fragments
, P
KE
,
KE
Warhead,
Total,
HE,
MAN, R
detect,
C
Weight, C
unit x ]
No [ R
Max, R
Min, V
AVG ]
Yes
Yes
Alt Mission
Alt Baseline
Resize / Alt Config /
Subsystems / Tech
Example of Spreadsheet Based Conceptual
Sizing Computer Code - TMD Spreadsheet
Define Mission Requirements [ Flight Performance ( R
Max
, R
Min
, V
AVG
) , MOM, Constraints ]
Establish Baseline ( Rocket , Ramjet )
Aerodynamics Input ( d, l, l
N, A, c, t, x
cg )
Aerodynamics Output [ C
D
0
, C
N, X
AC, C
m
, L / D, S
T ]
Propulsion Input ( p
c, , c*, A
b, A
t, A
3, H
f, , T
4, Inlet Type )
Propulsion Output [ I
sp, T
cruise, p
t
2
/ p
t
0
, w
.
, T
boost, T
sustain, V
Boost ]
Weight Input ( W
L
, W
P
,
max
)
Weight Output [ Q, dT
skin
/ dt, T
skin
,
skin
, t
skin
,
buckling
, M
B
, ( F
t
)
Motor
, W, x
cg
, I
y
]
Trajectory Input ( h
i, V
i, Type ( cruise, boost, coast, ballistic, turn, glide )
Trajectory Output ( R, V, and versus time )
Meet
Performance?
Measures of Merit and Constraints
No [ p
Blast
, P
K
, n
Hits
,
V
fragments
, P
KE
,
KE
Warhead,
Total,
HE,
MAN, R
detect,
C
Weight, C
unit x ]
No [ R
Max, R
Min, V
AVG ]
Yes
Yes
Alt Mission
Alt Baseline
Resize / Alt Config /
Subsystems / Tech
10/19/24 ELF 39
Outline
Examples of Parameters and Technologies That Drive
Missile Flight Performance
Missile Flight Performance Prediction
Examples of Maximizing Missile Flight Performance
( Workshop )
Summary
Outline
Examples of Parameters and Technologies That Drive
Missile Flight Performance
Missile Flight Performance Prediction
Examples of Maximizing Missile Flight Performance
( Workshop )
Summary
10/19/24 ELF 40
Rocket Baseline Missile Configuration
STA 60.8
19.4
3.4
18.5
STA 125.4
LE
MAC
at STA 67.0
BL 10.2
= 45
40.2
STA 0 19.2 46.1 62.6 84.5 138.6
Note: Dimensions in inches
Source: Bithell, R.A. and Stoner, R.C., “Rapid Approach for Missile Synthesis, Vol. 1, Rocket Synthesis
Handbook,” AFWAL-TR-81-3022, Vol. 1, March 1982.
Nose Forebody Payload
Bay
Midbody Aftbody Tailcone
Rocket Motor
= 57
12.0
LE
MAC
at
STA 131.6
BL 8.0
16.1
8.0 d
cg
BO
cg
Launch
143.9
Rocket Baseline Missile Configuration
STA 60.8
19.4
3.4
18.5
STA 125.4
LE
MAC
at STA 67.0
BL 10.2
= 45
40.2
STA 0 19.2 46.1 62.6 84.5 138.6
Note: Dimensions in inches
Source: Bithell, R.A. and Stoner, R.C., “Rapid Approach for Missile Synthesis, Vol. 1, Rocket Synthesis
Handbook,” AFWAL-TR-81-3022, Vol. 1, March 1982.
Nose Forebody Payload
Bay
Midbody Aftbody Tailcone
Rocket Motor
= 57
12.0
LE
MAC
at
STA 131.6
BL 8.0
16.1
8.0 d
cg
BO
cg
Launch
143.9
10/19/24 ELF 41
Rocket Baseline Missile Propellant Weight Is
27% of the Launch Weight
1Nose ( Radome ) 4.1 12.0
3Forebody structure 12.4 30.5
Guidance 46.6 32.6
2Payload Bay Structure 7.6 54.3
Warhead 77.7 54.3
4Midbody Structure 10.2 73.5
Control Actuation System 61.0 75.5
5Aftbody Structure 0.0 –
Rocket Motor Case 47.3 107.5
Insulation 23.0 117.2
6Tailcone Structure 6.5 141.2
Nozzle 5.8 141.2
Fixed Surfaces 26.2 137.8
Movable Surfaces 38.6 75.5
Burnout Total 367.0 76.2
Propellant 133.0 107.8
Launch Total 500.0 84.6
Component Weight, lbs. C.G. STA, In.
Rocket Baseline Missile Propellant Weight Is
27% of the Launch Weight
1Nose ( Radome ) 4.1 12.0
3Forebody structure 12.4 30.5
Guidance 46.6 32.6
2Payload Bay Structure 7.6 54.3
Warhead 77.7 54.3
4Midbody Structure 10.2 73.5
Control Actuation System 61.0 75.5
5Aftbody Structure 0.0 –
Rocket Motor Case 47.3 107.5
Insulation 23.0 117.2
6Tailcone Structure 6.5 141.2
Nozzle 5.8 141.2
Fixed Surfaces 26.2 137.8
Movable Surfaces 38.6 75.5
Burnout Total 367.0 76.2
Propellant 133.0 107.8
Launch Total 500.0 84.6
Component Weight, lbs. C.G. STA, In.
10/19/24 ELF 42
Rocket Baseline Missile Has Boost-Sustain
Thrust - Time History
Time – Seconds
0 4 8 12 16
0
2
4
6
8
Thrust – 1,000 lbs
Note: Sea Level, 60°F
Rocket Baseline Missile Has Boost-Sustain
Thrust - Time History
Time – Seconds
0 4 8 12 16
0
2
4
6
8
Thrust – 1,000 lbs
Note: Sea Level, 60°F
10/19/24 ELF 43
Rocket Baseline Missile Has Higher
Maneuverability at High Angle of Attack
4
0
0 4 8 12 16
, Angle of Attack – Degrees
12
8
20
C
N
, N
o
r
m
a
l F
o
r
c
e
C
o
e
f
f
ic
ie
n
t
20
16
24
1.2
0.6
M = 1.2
1.5
2.0
2.35
2.87
3.95
4.60
S
Ref
= 0.349 ft
2
, l
Ref
= d = 0.667 ft, C.G. at STA 75.7, = 0 deg
Rocket Baseline Missile Has Higher
Maneuverability at High Angle of Attack
4
0
0 4 8 12 16
, Angle of Attack – Degrees
12
8
20
C
N
, N
o
r
m
a
l F
o
r
c
e
C
o
e
f
f
ic
ie
n
t
20
16
24
1.2
0.6
M = 1.2
1.5
2.0
2.35
2.87
3.95
4.60
S
Ref
= 0.349 ft
2
, l
Ref
= d = 0.667 ft, C.G. at STA 75.7, = 0 deg
10/19/24 ELF 44
Rocket Baseline Missile Control Effectiveness
and Drag Are Driven by Mach Number
0.4
0
0 1 2 3 4
M, Mach Number
1.2
0.8
5
C
A
a
t
=
0
°
0.1
0
Power Off
Power On
0.2
0.3
C
N
~
P
e
r
D
e
g
r
e
e
Rocket Baseline Missile Control Effectiveness
and Drag Are Driven by Mach Number
0.4
0
0 1 2 3 4
M, Mach Number
1.2
0.8
5
C
A
a
t
=
0
°
0.1
0
Power Off
Power On
0.2
0.3
C
N
~
P
e
r
D
e
g
r
e
e
10/19/24 ELF 45
-5
0
5
10
15
0 5 10 15 20 25
t, Time, sec
n
x
, A
x
ia
l A
c
c
e
le
r
a
t
io
n
, g
Rocket Baseline Has High Boost Acceleration
Note:
t
f
= 24.4 sec
M
L
= 0.8
h
L = 20,000 ft
T
B
= 5750 lb
t
B
= 3.26 sec
T
S
= 1018 lb
t
S
= 10.86 sec
D = 99 lb at Mach 0.8
D = 1020 lb at Mach 2.1
W
L
= 500 lb
W
P
= 133 LB
n
X = ( T - D ) / W
Boost
Sustain
Coast
-5
0
5
10
15
0 5 10 15 20 25
t, Time, sec
n
x
, A
x
ia
l A
c
c
e
le
r
a
t
io
n
, g
Rocket Baseline Has High Boost Acceleration
Note:
t
f
= 24.4 sec
M
L
= 0.8
h
L = 20,000 ft
T
B
= 5750 lb
t
B
= 3.26 sec
T
S
= 1018 lb
t
S
= 10.86 sec
D = 99 lb at Mach 0.8
D = 1020 lb at Mach 2.1
W
L
= 500 lb
W
P
= 133 LB
n
X = ( T - D ) / W
Boost
Sustain
Coast
10/19/24 ELF 46
0
1000
2000
3000
0 5 10 15 20 25
t, Time, sec
V
, V
e
lo
c
ity
, ft / s
e
c
Rocket Baseline Missile Has Nearly Constant
Velocity During Sustain
Boost
Sustain
Coast
V / ( g
c
I
SP
) = - ( 1 - D
AVG
/ T ) ln ( 1 - W
p
/ W
i
), During Boost
V / V
BO
= 1 / { 1 + t / { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
BO
]}}, During Coast
Note:
M
L = 0.8
h
L = 20K feet
0
1000
2000
3000
0 5 10 15 20 25
t, Time, sec
V
, V
e
lo
c
ity
, ft / s
e
c
Rocket Baseline Missile Has Nearly Constant
Velocity During Sustain
Boost
Sustain
Coast
V / ( g
c
I
SP
) = - ( 1 - D
AVG
/ T ) ln ( 1 - W
p
/ W
i
), During Boost
V / V
BO
= 1 / { 1 + t / { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
BO
]}}, During Coast
Note:
M
L = 0.8
h
L = 20K feet
10/19/24 ELF 47
Rocket Baseline Missile Maximum Range Is
About Eight Nautical Miles
0
2
4
6
8
10
0 5 10 15 20 25
t, Time, sec
R
,
F
li
g
h
t
R
a
n
g
e
,
n
m
Boost
Sustain
Coast
R = R
boost + R
sustain + R
coast
Note:
M
L = 0.8
h
L = 20K feet
Rocket Baseline Missile Maximum Range Is
About Eight Nautical Miles
0
2
4
6
8
10
0 5 10 15 20 25
t, Time, sec
R
,
F
li
g
h
t
R
a
n
g
e
,
n
m
Boost
Sustain
Coast
R = R
boost + R
sustain + R
coast
Note:
M
L = 0.8
h
L = 20K feet
10/19/24 ELF 48
Rocket Baseline Missile Has About 30 G
Maneuverability
( n
Z
) = ( n
Z
)
Body
+ ( n
Z
)
Wing
+ ( n
Z
)
Taill
Rocket Baseline @
•Mach 2
•20,000 ft altitude
•367 lb weight ( burnout )
Compute
Wing
= ’
Max
= ( + )
Max
= 22 deg for rocket baseline
= 0.75,
Body =
Tail = 9.4 deg
( n
Z
)
Body
= q S
Ref
( C
N
)
Body
/ W = 2725 ( 0.35 ) ( 1.1 ) / 367 = 2.9 g ( from body )
( n
Z
)
Wing
= q S
Wing
[( C
N
)
Wing
(S
Ref
/
S
Wing
)] / W = 2725 ( 2.55 ) ( 1.08 ) / 367 = 20.4 g ( from wing )
( n
Z
)
Tail
= q S
Tail
[( C
N
)
Tail
( S
Ref
/
S
Tail
)] / W = 2725 ( 1.54 ) ( 0.50 ) / 367 = 5.7 g ( from tail )
n
Z
= 2.9 + 20.4 + 5.7 = 29 g
Rocket Baseline Missile Has About 30 G
Maneuverability
( n
Z
) = ( n
Z
)
Body
+ ( n
Z
)
Wing
+ ( n
Z
)
Taill
Rocket Baseline @
•Mach 2
•20,000 ft altitude
•367 lb weight ( burnout )
Compute
Wing
= ’
Max
= ( + )
Max
= 22 deg for rocket baseline
= 0.75,
Body =
Tail = 9.4 deg
( n
Z
)
Body
= q S
Ref
( C
N
)
Body
/ W = 2725 ( 0.35 ) ( 1.1 ) / 367 = 2.9 g ( from body )
( n
Z
)
Wing
= q S
Wing
[( C
N
)
Wing
(S
Ref
/
S
Wing
)] / W = 2725 ( 2.55 ) ( 1.08 ) / 367 = 20.4 g ( from wing )
( n
Z
)
Tail
= q S
Tail
[( C
N
)
Tail
( S
Ref
/
S
Tail
)] / W = 2725 ( 1.54 ) ( 0.50 ) / 367 = 5.7 g ( from tail )
n
Z
= 2.9 + 20.4 + 5.7 = 29 g
10/19/24 ELF 49
Example of Boost Climb - Ballistic Trajectory
Assume Rocket Baseline @
i
= 45 deg, h
i
= h
f
= 0 ft
Velocity, Horizontal Range, and Altitude During Initial Boost @ = 45 deg
V = - g
c I
SP ( 1 - D
AVG / T ) ln ( 1 - W
p / W
i ) = -32.2 ( 250 ) ( 1 – 419 / 5750 ) ln ( 1 – 84.8 / 500 ) = 1,387 ft / sec
R = ( V
i + V / 2 ) t
B = ( 0 + 1387 / 2 ) 3.26 = 2,260 ft
R
x
= R cos
i
= 2260 ( 0.707 ) = 1,598 ft
R
y
= R sin
i
= 2260 ( 0.707 ) = 1,598 ft
h = h
i + R
y = 0 + 1598 = 1,598 ft
Velocity, Horizontal Range, and Altitude During Sustain @ = 45 deg
V = - g
c
I
SP
( 1 - D
AVG
/ T ) ln ( 1 - W
p
/ W
i
) = -32.2 ( 230.4 ) ( 1 – 650 / 1018 ) ln ( 1 – 48.2 / 415.2 ) = 585 ft / sec
V
BO = 1387 + 585 = 1,972 ft / sec
R = ( V
i + V / 2 ) t
B = ( 1387 + 585 / 2 ) 10.86 = 18,239 ft
R
x = R cos
i = 18239 ( 0.707 ) = 12,895 ft
R
y = R sin
i = 18239 ( 0.707 ) = 12,895 ft
h = h
i
+ R
y
= 1598 + 12895 = 14,493 ft
Example of Boost Climb - Ballistic Trajectory
Assume Rocket Baseline @
i
= 45 deg, h
i
= h
f
= 0 ft
Velocity, Horizontal Range, and Altitude During Initial Boost @ = 45 deg
V = - g
c I
SP ( 1 - D
AVG / T ) ln ( 1 - W
p / W
i ) = -32.2 ( 250 ) ( 1 – 419 / 5750 ) ln ( 1 – 84.8 / 500 ) = 1,387 ft / sec
R = ( V
i + V / 2 ) t
B = ( 0 + 1387 / 2 ) 3.26 = 2,260 ft
R
x
= R cos
i
= 2260 ( 0.707 ) = 1,598 ft
R
y
= R sin
i
= 2260 ( 0.707 ) = 1,598 ft
h = h
i + R
y = 0 + 1598 = 1,598 ft
Velocity, Horizontal Range, and Altitude During Sustain @ = 45 deg
V = - g
c
I
SP
( 1 - D
AVG
/ T ) ln ( 1 - W
p
/ W
i
) = -32.2 ( 230.4 ) ( 1 – 650 / 1018 ) ln ( 1 – 48.2 / 415.2 ) = 585 ft / sec
V
BO = 1387 + 585 = 1,972 ft / sec
R = ( V
i + V / 2 ) t
B = ( 1387 + 585 / 2 ) 10.86 = 18,239 ft
R
x = R cos
i = 18239 ( 0.707 ) = 12,895 ft
R
y = R sin
i = 18239 ( 0.707 ) = 12,895 ft
h = h
i
+ R
y
= 1598 + 12895 = 14,493 ft
10/19/24 ELF 50
Example of Boost Climb - Ballistic Trajectory
( cont )
Velocity, Horizontal Range, and Altitude During Ballistic Flight
h
f
= h
i
= 0 ft t
ballistic
= 59 sec )
V
x
= V
i
cos
i
/ { 1 + t / { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
BO
]}} = 1972 ( 0.707 ) / { 1 + 59 / { 2 ( 367 ) / [ 32.2 ( 0.001496 ) ( 0.349 ) ( 0.95 ) ( 1972 )]}} = 395 ft / sec
V
y = V
i sin
i / { 1 + t / { 2 W
BO / [ g
c ρ
AVG S
Ref ( C
D
0
)
AVG V
BO ]} – 32.2 t = 1972 ( 0.707 ) / { 1 + 59 / { 2 ( 367 ) / [ 32.2 ( 0.001496 ) ( 0.349 ) ( 0.95 ) ( 1972 )]}} – 32.2 ( 59 ) = - 1,505 ft / sec
R
x
= { 2 W
BO
cos
i
/ [ g
c
ρ
AVG
S
Ref
(C
D
0
)
AVG
]} ln { 1 + t
/ { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
BO
]}} = { 2 ( 367 ) ( 0.707 ) / [ 32.2 ( 0.001496 ) ( 0.349 ) ( 0.95 )]} ln { 1 + 59 / { 2 ( 367 ) / [ 32.2
( 0.001496 ) ( 0.349 ) ( 0.95 ) ( 1972 )]}} = 40,991 ft
h = h
i
+ { 2 W
BO
sin
i
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
]} ln { 1 + t
/ { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
BO
]} - 16.1 t
2
= 14493 + { 2 ( 367 ) ( 0.707 ) / [ 32.2 ( 0.001496 ) ( 0.349 ) ( 0.95 )]} ln { 1 + 59
/ { 2 ( 367 ) / [ 32.2 ( 0.001496 ) ( 0.349 ) ( 0.95 ) ( 1972 )]}} – 16.1 ( 59 )
2
= 0 ft
Total Time of Flight and Horizontal Range
t = t = t
boost
+ t
sustain
+ t
ballistic
= 3.26 + 10.86 + 59 = 73 sec
R
x
= R
x
= R
x,boost
+ R
x,sustain
+ R
x,ballistic
= 1598 + 12895 + 40991 = 55,894 ft = 9.2 nm
Example of Boost Climb - Ballistic Trajectory
( cont )
Velocity, Horizontal Range, and Altitude During Ballistic Flight
h
f
= h
i
= 0 ft t
ballistic
= 59 sec )
V
x
= V
i
cos
i
/ { 1 + t / { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
BO
]}} = 1972 ( 0.707 ) / { 1 + 59 / { 2 ( 367 ) / [ 32.2 ( 0.001496 ) ( 0.349 ) ( 0.95 ) ( 1972 )]}} = 395 ft / sec
V
y = V
i sin
i / { 1 + t / { 2 W
BO / [ g
c ρ
AVG S
Ref ( C
D
0
)
AVG V
BO ]} – 32.2 t = 1972 ( 0.707 ) / { 1 + 59 / { 2 ( 367 ) / [ 32.2 ( 0.001496 ) ( 0.349 ) ( 0.95 ) ( 1972 )]}} – 32.2 ( 59 ) = - 1,505 ft / sec
R
x
= { 2 W
BO
cos
i
/ [ g
c
ρ
AVG
S
Ref
(C
D
0
)
AVG
]} ln { 1 + t
/ { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
BO
]}} = { 2 ( 367 ) ( 0.707 ) / [ 32.2 ( 0.001496 ) ( 0.349 ) ( 0.95 )]} ln { 1 + 59 / { 2 ( 367 ) / [ 32.2
( 0.001496 ) ( 0.349 ) ( 0.95 ) ( 1972 )]}} = 40,991 ft
h = h
i
+ { 2 W
BO
sin
i
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
]} ln { 1 + t
/ { 2 W
BO
/ [ g
c
ρ
AVG
S
Ref
( C
D
0
)
AVG
V
BO
]} - 16.1 t
2
= 14493 + { 2 ( 367 ) ( 0.707 ) / [ 32.2 ( 0.001496 ) ( 0.349 ) ( 0.95 )]} ln { 1 + 59
/ { 2 ( 367 ) / [ 32.2 ( 0.001496 ) ( 0.349 ) ( 0.95 ) ( 1972 )]}} – 16.1 ( 59 )
2
= 0 ft
Total Time of Flight and Horizontal Range
t = t = t
boost
+ t
sustain
+ t
ballistic
= 3.26 + 10.86 + 59 = 73 sec
R
x
= R
x
= R
x,boost
+ R
x,sustain
+ R
x,ballistic
= 1598 + 12895 + 40991 = 55,894 ft = 9.2 nm
10/19/24 ELF 51
Boost Climb – Ballistic – Glide Trajectory
Provides Extended Range
Rocket Baseline @
i = 45 deg, h
i = h
f = 0 ft
From Previous Example, the Boost Climb – Ballistic Conditions at Apogee are:
t = 36 sec
= 0 deg
V = 702 ft / sec
h = 28,994 ft
R
x = 36,786 ft
q = 227 psf
M = 0.7
( L / D )
max
= 5.22
( L / D )
max
= 5.5 deg
Incremental Horizontal Range During the ( L / D )
max Glide from Apogee to the Ground is given by
R
x = ( L / D ) h = 5.22 ( 28994 ) = 151,349 ft
Total Horizontal Range for a Boost Climb – Ballistic – Glide Trajectory is
R
x = R
x = R
x,BoostClimb-Ballistic + R
x,Glide = 36786 + 151349 = 188,135 ft = 31.0 nm
Boost Climb – Ballistic – Glide Trajectory
Provides Extended Range
Rocket Baseline @
i = 45 deg, h
i = h
f = 0 ft
From Previous Example, the Boost Climb – Ballistic Conditions at Apogee are:
t = 36 sec
= 0 deg
V = 702 ft / sec
h = 28,994 ft
R
x = 36,786 ft
q = 227 psf
M = 0.7
( L / D )
max
= 5.22
( L / D )
max
= 5.5 deg
Incremental Horizontal Range During the ( L / D )
max Glide from Apogee to the Ground is given by
R
x = ( L / D ) h = 5.22 ( 28994 ) = 151,349 ft
Total Horizontal Range for a Boost Climb – Ballistic – Glide Trajectory is
R
x = R
x = R
x,BoostClimb-Ballistic + R
x,Glide = 36786 + 151349 = 188,135 ft = 31.0 nm
10/19/24 ELF 52
Glide at ( L / D )
max
Provides Extended Range
0
10
20
30
0 10 20 30 40
R, Range, nm
h
, A
lt
it
u
d
e
, K
ilo
F
e
e
t
S
u
s
ta
in
B
a
llis
tic
Note: Rocket Baseline
End of boost, t = 3.26 sec, = 45 deg, V = 1387 ft / sec
End of sustain, t = 14.12 sec, = 45 deg, V = 1972 ft / sec
Apogee, t = 36 sec, = 0 deg, V = 702 ft / sec
Ballistic impact, t = 73 sec, = - 65 deg, V = 1556 ft / sec
Glide impact, t = 286 sec, = - 10.8 deg, V = 500 ft / sec
B
a
l
l
i
s
t
i
c
G
l
i
d
e
a
t
(
L
/
D
)
m
a
x
Glide at ( L / D )
max
Provides Extended Range
0
10
20
30
0 10 20 30 40
R, Range, nm
h
, A
lt
it
u
d
e
, K
ilo
F
e
e
t
S
u
s
ta
in
B
a
llis
tic
Note: Rocket Baseline
End of boost, t = 3.26 sec, = 45 deg, V = 1387 ft / sec
End of sustain, t = 14.12 sec, = 45 deg, V = 1972 ft / sec
Apogee, t = 36 sec, = 0 deg, V = 702 ft / sec
Ballistic impact, t = 73 sec, = - 65 deg, V = 1556 ft / sec
Glide impact, t = 286 sec, = - 10.8 deg, V = 500 ft / sec
B
a
l
l
i
s
t
i
c
G
l
i
d
e
a
t
(
L
/
D
)
m
a
x
10/19/24 ELF 53
Soda Straw Rocket Design, Build, and Fly
Objective – Hands-on Learning of Rocket Physics Based on
Design
Build
Fly
Furnished Property
1 Launch System
1 Target
1 Weight Scale
Furnished Material
1 Soda Straw: ¼ in Inside Diameter by 11 in Length
1 Strip Tabbing: ½ in by 6 in
1 Tape Dispenser
1 Wood Dowel: ¼ in Diameter by 1 in Length
Soda Straw Rocket Design, Build, and Fly
Objective – Hands-on Learning of Rocket Physics Based on
Design
Build
Fly
Furnished Property
1 Launch System
1 Target
1 Weight Scale
Furnished Material
1 Soda Straw: ¼ in Inside Diameter by 11 in Length
1 Strip Tabbing: ½ in by 6 in
1 Tape Dispenser
1 Wood Dowel: ¼ in Diameter by 1 in Length
10/19/24 ELF 54
Soda Straw Rocket ( cont )
Design – Soda Straw Rocket
Compatible with Furnished Property Launch System
Launch tube outside diameter: ¼ in
Launch tube length: 6 in
Launch static gauge pressure: up to 30 psi
Design Body and Tails for
Maximum flight range
Accurate and stable flight
Calculate Aerodynamic Drag Coefficient
Skin friction drag
Base drag
Calculate Thrust and Thrust Duration
Measure Weight
0.1 gram accuracy
Predict Flight Range and Altitude for Proscribed
Launch pressure
Elevation angle
Soda Straw Rocket ( cont )
Design – Soda Straw Rocket
Compatible with Furnished Property Launch System
Launch tube outside diameter: ¼ in
Launch tube length: 6 in
Launch static gauge pressure: up to 30 psi
Design Body and Tails for
Maximum flight range
Accurate and stable flight
Calculate Aerodynamic Drag Coefficient
Skin friction drag
Base drag
Calculate Thrust and Thrust Duration
Measure Weight
0.1 gram accuracy
Predict Flight Range and Altitude for Proscribed
Launch pressure
Elevation angle
10/19/24 ELF 55
Soda Straw Rocket ( cont )
Build - Soda Straw Rocket Using Either
Furnished Material
Or Can Use Own Material
Fly - Soda Straw Rocket
Proscribed Target Location, Launch Location, Launch Pressure, and Launch Angle
Compare Flight Test Results for Alternative Concepts
Highest vertical location of impact
Smallest horizontal dispersal from impact aim point
Discuss Reasons for Performance of Alternative Concepts
Soda Straw Rocket ( cont )
Build - Soda Straw Rocket Using Either
Furnished Material
Or Can Use Own Material
Fly - Soda Straw Rocket
Proscribed Target Location, Launch Location, Launch Pressure, and Launch Angle
Compare Flight Test Results for Alternative Concepts
Highest vertical location of impact
Smallest horizontal dispersal from impact aim point
Discuss Reasons for Performance of Alternative Concepts
10/19/24 ELF 56
Example Baseline Configuration Geometry,
Weight, and Balance
Example Baseline Configuration
Diameter = d = ¼ in = 0.0208 ft
Outside Length = l = 5 in = 0.417 ft
Inside Cavity Length Available for Launch Tube = l
c = 4 in = 0.333 ft
Hemispherical Nose
Reference Area = S
Ref
= ( / 4 ) d
2
= 0.0491 in
2
= 0.000341 ft
2
4 Tail Panels ( Cruciform Tails, n
T = 2 )
Each tail panel ½ in by 1 in
Mean aerodynamic chord = c
mac
= 1 in = 0.0833 ft
Exposed area of 2 tail panels = S
T
= 1 in
2
= 0.00694 ft
2
Exposed aspect ratio of 2 tail panels = A = b
2
/ S
T
= ( 1 )
2
/ ( 1 ) = 1.0
Example Baseline Weight and Balance
W = 1.9 gram = 0.0042 lb
X
cg / l = 0.55
ll
cc
ll
Example Baseline Configuration Geometry,
Weight, and Balance
Example Baseline Configuration
Diameter = d = ¼ in = 0.0208 ft
Outside Length = l = 5 in = 0.417 ft
Inside Cavity Length Available for Launch Tube = l
c = 4 in = 0.333 ft
Hemispherical Nose
Reference Area = S
Ref
= ( / 4 ) d
2
= 0.0491 in
2
= 0.000341 ft
2
4 Tail Panels ( Cruciform Tails, n
T = 2 )
Each tail panel ½ in by 1 in
Mean aerodynamic chord = c
mac
= 1 in = 0.0833 ft
Exposed area of 2 tail panels = S
T
= 1 in
2
= 0.00694 ft
2
Exposed aspect ratio of 2 tail panels = A = b
2
/ S
T
= ( 1 )
2
/ ( 1 ) = 1.0
Example Baseline Weight and Balance
W = 1.9 gram = 0.0042 lb
X
cg / l = 0.55
ll
cc
ll
10/19/24 ELF 57
Example Baseline Boost Performance
During Boost, Thrust ( T ) Provided by Pressurized Launch Tube
T = ( p – p
0 ) A = p
gauge ( 1 – e
– t /
) A
A = S
Ref = 0.0491 in
2
, = Rise Time to Open Valve
Assume p
gauge = 20 psi, = 0.2 sec
T = 20 ( 1 - e
– t / 0.2
) ( 0.0491 ) = 0.982 ( 1 - e
– 5.00 t
)
Actual Thrust Lower ( Pressure Loss, Boundary Layer, Launch Tube Friction )
Acceleration ( a ), Velocity ( V ), and Distance ( s ) During Boost
a 32.2 T / W = 32.2 ( 0.982 ) ( 1 - e
– 5.00 t
) / 0.0042 = 7528.667 ( 1 - e
– 5.00 t
)
V = 7528.667 t + 1505.733 e
– 5.00 t
– 1505.733
s = 3764.333 t
2
– 301.147 e
– 5.00 t
– 1505.733 t + 301.147
End of Boost Conditions
s = l
c
= 0.333 ft t = 0.0382 sec
V = 25.8 ft / sec
q = ½ V
2
= ½ ( 0.002378 ) ( 25.8 )
2
= 0.791 psf
M = V / c = 25.8 / 1116 = 0.0231
Example Baseline Boost Performance
During Boost, Thrust ( T ) Provided by Pressurized Launch Tube
T = ( p – p
0 ) A = p
gauge ( 1 – e
– t /
) A
A = S
Ref = 0.0491 in
2
, = Rise Time to Open Valve
Assume p
gauge = 20 psi, = 0.2 sec
T = 20 ( 1 - e
– t / 0.2
) ( 0.0491 ) = 0.982 ( 1 - e
– 5.00 t
)
Actual Thrust Lower ( Pressure Loss, Boundary Layer, Launch Tube Friction )
Acceleration ( a ), Velocity ( V ), and Distance ( s ) During Boost
a 32.2 T / W = 32.2 ( 0.982 ) ( 1 - e
– 5.00 t
) / 0.0042 = 7528.667 ( 1 - e
– 5.00 t
)
V = 7528.667 t + 1505.733 e
– 5.00 t
– 1505.733
s = 3764.333 t
2
– 301.147 e
– 5.00 t
– 1505.733 t + 301.147
End of Boost Conditions
s = l
c
= 0.333 ft t = 0.0382 sec
V = 25.8 ft / sec
q = ½ V
2
= ½ ( 0.002378 ) ( 25.8 )
2
= 0.791 psf
M = V / c = 25.8 / 1116 = 0.0231
10/19/24 ELF 58
Example Baseline Drag Coefficient
Total Drag Coefficient C
D
0
= (C
D
0
)
Body + (C
D
0
)
Tail
During Coast, C
D0
= ( C
D0
)
Body,Friction + (C
D
0
)
Base,Coast
+ ( C
D0
)
Tail,Friction = 0.053 ( l / d ) [ M / ( q l )]
0.2
+ 0.12 +
n
T
{ 0.0133 [ M / ( q c
mac
)]
0.2
} ( 2 S
T
/ S
Ref
)
C
D
0
= 0.053 ( 20 ){ 0.0231 / [( 0.791 ) ( 0. 417 )]}
0.2
+ 0.12 + 2 { 0.0133 { 0.0231 / [( 0.791 ) ( 0.0833 )]}
0.2
}[
2 ( 0.00694 ) / 0.000341 )] = 0.62 + 0.12 + 0.88 = 1.62
Above Drag Coefficient Not Exact
Based on Assumption of Turbulent Boundary Layer
Soda Straw Rocket Is Small Size and Low Velocity Laminar Boundary Layer
Example Baseline Drag Coefficient
Total Drag Coefficient C
D
0
= (C
D
0
)
Body + (C
D
0
)
Tail
During Coast, C
D0
= ( C
D0
)
Body,Friction + (C
D
0
)
Base,Coast
+ ( C
D0
)
Tail,Friction = 0.053 ( l / d ) [ M / ( q l )]
0.2
+ 0.12 +
n
T
{ 0.0133 [ M / ( q c
mac
)]
0.2
} ( 2 S
T
/ S
Ref
)
C
D
0
= 0.053 ( 20 ){ 0.0231 / [( 0.791 ) ( 0. 417 )]}
0.2
+ 0.12 + 2 { 0.0133 { 0.0231 / [( 0.791 ) ( 0.0833 )]}
0.2
}[
2 ( 0.00694 ) / 0.000341 )] = 0.62 + 0.12 + 0.88 = 1.62
Above Drag Coefficient Not Exact
Based on Assumption of Turbulent Boundary Layer
Soda Straw Rocket Is Small Size and Low Velocity Laminar Boundary Layer
10/19/24 ELF 59
Example Ballistic Flight Performance
Horizontal Range Equation
R
x
= { 2 W cos
i
/ [ g
c
ρ S
Ref
C
D
0
]} ln { 1 + t
/ { 2 W / [ g
c
ρ S
Ref
C
D
0
V
i
]} = { 2 ( 0.0042 ) cos
i
/ [ 32.2 ( 0.002378 ) ( 0.000341 ) ( 1.62 )]} ln { 1 + t /
{ 2 ( 0.0042 ) / [ 32.2 ( 0.002378 ) ( 0.000341 ) ( 1.62 ) ( 25.8 )]} = 199 cos
i
ln ( 1 + 0.130 t )
Height Equation
h = { 2 W sin
i
/ [ g
c
ρ S
Ref
C
D
0
]} ln { 1 + t
/ { 2 W / [ g
c
ρ S
Ref
C
D
0
V
i
]} + h
i
- g
c
t
2
/ 2 = { 2 ( 0.0042 ) sin
i
/ [ 32.2 ( 0.002378 ) ( 0.000341 ) ( 1.62 )}
ln { 1 + t / { 2 ( 0.0042 ) / [ 32.2 ( 0.002378 ) ( 0.000341 ) ( 1.62 ) ( 25.8 )]} + h
i – 32.2 t
2
/ 2 = 199 sin
i ln ( 1 + 0.130 t ) + h
i – 32.2 t
2
/ 2
Assume
i
= 45 deg, t = t
impact
= 0.9 sec
R
x
= 199 ( 0.707 ) ln [ 1 + 0.130 ( 0.9 )] = 15.5 ft
h = 199 ( 0.707 ) ln [ 1 + 0.130 ( 0.9 )] + h
i
– 32.2 ( 0.9 )
2
/ 2 = h
i
+2.5
Example Ballistic Flight Performance
Horizontal Range Equation
R
x
= { 2 W cos
i
/ [ g
c
ρ S
Ref
C
D
0
]} ln { 1 + t
/ { 2 W / [ g
c
ρ S
Ref
C
D
0
V
i
]} = { 2 ( 0.0042 ) cos
i
/ [ 32.2 ( 0.002378 ) ( 0.000341 ) ( 1.62 )]} ln { 1 + t /
{ 2 ( 0.0042 ) / [ 32.2 ( 0.002378 ) ( 0.000341 ) ( 1.62 ) ( 25.8 )]} = 199 cos
i
ln ( 1 + 0.130 t )
Height Equation
h = { 2 W sin
i
/ [ g
c
ρ S
Ref
C
D
0
]} ln { 1 + t
/ { 2 W / [ g
c
ρ S
Ref
C
D
0
V
i
]} + h
i
- g
c
t
2
/ 2 = { 2 ( 0.0042 ) sin
i
/ [ 32.2 ( 0.002378 ) ( 0.000341 ) ( 1.62 )}
ln { 1 + t / { 2 ( 0.0042 ) / [ 32.2 ( 0.002378 ) ( 0.000341 ) ( 1.62 ) ( 25.8 )]} + h
i – 32.2 t
2
/ 2 = 199 sin
i ln ( 1 + 0.130 t ) + h
i – 32.2 t
2
/ 2
Assume
i
= 45 deg, t = t
impact
= 0.9 sec
R
x
= 199 ( 0.707 ) ln [ 1 + 0.130 ( 0.9 )] = 15.5 ft
h = 199 ( 0.707 ) ln [ 1 + 0.130 ( 0.9 )] + h
i
– 32.2 ( 0.9 )
2
/ 2 = h
i
+2.5
10/19/24 ELF 60
Soda Straw Rocket Range Driven by Length,
Gauge Pressure, Valve Open Time , and Weight
-0.4
-0.2
0
0.2
0.4
0.6
0.8
l pgauge tau W CD0
Nondimensional
Range
Sensitivity to
Parameter
Note: Soda Straw Rocket Baseline:
W = Weight = 0.0042 lb
l = length = 5 in
= Time constant to open valve =
0.2 sec
p
gauge
= gauge pressure = 20 psi
V = Launch Velocity = 25.8 fps
C
D
0
= Zero-lift drag coefficient =
1.62
i
= Initial flight path angle = 45 deg
t
impact
= Time from launch to impact
= 0.9 sec
R
x
= Horizontal range = 15.5 ft
Example: 10% increase in rocket length
7.1% increase in range
Soda Straw Rocket Range Driven by Length,
Gauge Pressure, Valve Open Time , and Weight
-0.4
-0.2
0
0.2
0.4
0.6
0.8
l pgauge tau W CD0
Nondimensional
Range
Sensitivity to
Parameter
Note: Soda Straw Rocket Baseline:
W = Weight = 0.0042 lb
l = length = 5 in
= Time constant to open valve =
0.2 sec
p
gauge
= gauge pressure = 20 psi
V = Launch Velocity = 25.8 fps
C
D
0
= Zero-lift drag coefficient =
1.62
i
= Initial flight path angle = 45 deg
t
impact
= Time from launch to impact
= 0.9 sec
R
x
= Horizontal range = 15.5 ft
Example: 10% increase in rocket length
7.1% increase in range
10/19/24 ELF 61
Outline
Examples of Parameters and Technologies That Drive
Missile Flight Performance
Missile Flight Performance Prediction
Examples of Maximizing Missile Flight Performance
( Workshop )
Summary
Outline
Examples of Parameters and Technologies That Drive
Missile Flight Performance
Missile Flight Performance Prediction
Examples of Maximizing Missile Flight Performance
( Workshop )
Summary
10/19/24 ELF 62
Summary
Flight Performance Analysis Activity in Missile Design and Analysis
Compute Range, Velocity, Time-to-Target, Off Boresight
Compare with Requirements and Data
Maximizing Flight Performance Strongly Impacted by
Aerodynamics
Propulsion
Weight
Flight Trajectory
Lecture Topics
Aerodynamics Parameters, Prediction and Technologies
Drag Coefficient
Normal Force Coefficient
Propulsion Parameters, Prediction, and Technologies
Thrust
Specific Impulse
Summary
Flight Performance Analysis Activity in Missile Design and Analysis
Compute Range, Velocity, Time-to-Target, Off Boresight
Compare with Requirements and Data
Maximizing Flight Performance Strongly Impacted by
Aerodynamics
Propulsion
Weight
Flight Trajectory
Lecture Topics
Aerodynamics Parameters, Prediction and Technologies
Drag Coefficient
Normal Force Coefficient
Propulsion Parameters, Prediction, and Technologies
Thrust
Specific Impulse
10/19/24 ELF 63
Summary ( cont )
Lecture Topics ( continued )
Flight Performance Parameters and Technologies
Cruise Range
High Density Fuel and Packaging
Flight Trajectory Shaping
Range Sensitivity to Driving Parameters
Missile Follow-on Programs
Examples of State-of-the-Art Advancements
Summary of New Technologies
Flight Performance Envelope
Videos of Flight Performance
Modeling of Degrees of Freedom
Equations of Motion and Flight Performance Drivers
Steady State Flight Relationships
Flight Performance Prediction
Steady Climb and Steady Dive Range Prediction
Cruise Prediction
Summary ( cont )
Lecture Topics ( continued )
Flight Performance Parameters and Technologies
Cruise Range
High Density Fuel and Packaging
Flight Trajectory Shaping
Range Sensitivity to Driving Parameters
Missile Follow-on Programs
Examples of State-of-the-Art Advancements
Summary of New Technologies
Flight Performance Envelope
Videos of Flight Performance
Modeling of Degrees of Freedom
Equations of Motion and Flight Performance Drivers
Steady State Flight Relationships
Flight Performance Prediction
Steady Climb and Steady Dive Range Prediction
Cruise Prediction
10/19/24 ELF 64
Summary ( cont )
Lecture Topics ( continued )
Flight Performance Prediction ( continued )
Boost Prediction
Coast Prediction
Ballistic Flight Prediction
Turn Prediction
Target Lead for Proportional Homing Guidance
Tactical Missile Design Spreadsheet
Workshop Examples
Rocket Boost-Coast Range
Rocket Maneuverability
Rocket Ballistic Range
Rocket Trajectory Optimization
Soda Straw Rocket Design, Build, and Fly
Summary ( cont )
Lecture Topics ( continued )
Flight Performance Prediction ( continued )
Boost Prediction
Coast Prediction
Ballistic Flight Prediction
Turn Prediction
Target Lead for Proportional Homing Guidance
Tactical Missile Design Spreadsheet
Workshop Examples
Rocket Boost-Coast Range
Rocket Maneuverability
Rocket Ballistic Range
Rocket Trajectory Optimization
Soda Straw Rocket Design, Build, and Fly
10/19/24 ELF 65
Configuration Sizing Criteria for Maximizing
Flight Performance
Body Fineness Ratio5 < l / d < 25
Nose Fineness Ratiol
N
/ d 2 if M > 1
Efficient Cruise Dynamic Pressureq < 700 psf
Missile Homing VelocityV
M / V
T > 1.5
Subsystems Packaging Maximize available volume for fuel / propellant
Trim Control Power / > 1
Missile Maneuverabilityn
M / n
T > 3
Configuration Sizing Criteria for Maximizing
Flight Performance
Body Fineness Ratio5 < l / d < 25
Nose Fineness Ratiol
N
/ d 2 if M > 1
Efficient Cruise Dynamic Pressureq < 700 psf
Missile Homing VelocityV
M / V
T > 1.5
Subsystems Packaging Maximize available volume for fuel / propellant
Trim Control Power / > 1
Missile Maneuverabilityn
M / n
T > 3
10/19/24 ELF 66
Bibliography 0f Reports and Web Sites
“Missile.index,” http://www.index.ne.jp/missile_e/
AIAA Aerospace Design Engineers Guide, American Institute of Aeronautics and Astronautics, 1993.
Bonney, E.A., et al, Aerodynamics, Propulsion, Structures, and Design Practice, “Principles of Guided Missile
Design”, D. Van Nostrand Company, Inc., Princeton, New Jersey, 1956
Chin, S.S., Missile Configuration Design, McGraw-Hill Book Company, New York, 1961
Mason, L.A., Devan, L., and Moore, F.G., “Aerodynamic Design Manual for Tactical Weapons,” NSWCTR 81-156, 1981
Pitts, W.C., Nielsen, J.N., and Kaattari, G.E., “Lift and Center of Pressure of Wing-Body-Tail Combinations at
Subsonic, Transonic, and Supersonic Speeds,” NACA Report 1307, 1957.
Jorgensen, L.H., “Prediction of Static Aerodynamic Characteristics for Space-Shuttle-Like, and Other Bodies at
Angles of Attack From 0 to 180,” NASA TND 6996, January 1973
Hoak, D.E., et al., “USAF Stability and Control Datcom,” AFWAL TR-83-3048, Global Engineering Documents, Irvine,
CA, 1978
“Nielsen Engineering & Research (NEAR) Aerodynamic Software Products,”
http://www.nearinc.com/near/software.htm
Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design, “Principles of Guided Missile Design”,
D. Van Nostrand Company, Inc., Princeton, New Jersey, 1960
Schneider, S.H., Encyclopedia of Climate and Weather, Oxford University Press, 1996
Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 1997
US Army Ordnance Pamphlet ORDP-20-290-Warheads, 1980
Nicholas, T. and Rossi, R., “US Missile Data Book, 1996,” Data Search Associates, 1996
Bithell, R.A., and Stoner, R.C., “Rapid Approach for Missile Synthesis,” AFWAL TR 81-3022, Vol. I, March 1982
Fleeman, E.L. and Donatelli, G.A., “Conceptual Design Procedure Applied to a Typical Air-Launched Missile,” AIAA
81-1688, August 1981
Hindes, J.W., “Advanced Design of Aerodynamic Missiles ( ADAM ),” October 1993
Bibliography 0f Reports and Web Sites
“Missile.index,” http://www.index.ne.jp/missile_e/
AIAA Aerospace Design Engineers Guide, American Institute of Aeronautics and Astronautics, 1993.
Bonney, E.A., et al, Aerodynamics, Propulsion, Structures, and Design Practice, “Principles of Guided Missile
Design”, D. Van Nostrand Company, Inc., Princeton, New Jersey, 1956
Chin, S.S., Missile Configuration Design, McGraw-Hill Book Company, New York, 1961
Mason, L.A., Devan, L., and Moore, F.G., “Aerodynamic Design Manual for Tactical Weapons,” NSWCTR 81-156, 1981
Pitts, W.C., Nielsen, J.N., and Kaattari, G.E., “Lift and Center of Pressure of Wing-Body-Tail Combinations at
Subsonic, Transonic, and Supersonic Speeds,” NACA Report 1307, 1957.
Jorgensen, L.H., “Prediction of Static Aerodynamic Characteristics for Space-Shuttle-Like, and Other Bodies at
Angles of Attack From 0 to 180,” NASA TND 6996, January 1973
Hoak, D.E., et al., “USAF Stability and Control Datcom,” AFWAL TR-83-3048, Global Engineering Documents, Irvine,
CA, 1978
“Nielsen Engineering & Research (NEAR) Aerodynamic Software Products,”
http://www.nearinc.com/near/software.htm
Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design, “Principles of Guided Missile Design”,
D. Van Nostrand Company, Inc., Princeton, New Jersey, 1960
Schneider, S.H., Encyclopedia of Climate and Weather, Oxford University Press, 1996
Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 1997
US Army Ordnance Pamphlet ORDP-20-290-Warheads, 1980
Nicholas, T. and Rossi, R., “US Missile Data Book, 1996,” Data Search Associates, 1996
Bithell, R.A., and Stoner, R.C., “Rapid Approach for Missile Synthesis,” AFWAL TR 81-3022, Vol. I, March 1982
Fleeman, E.L. and Donatelli, G.A., “Conceptual Design Procedure Applied to a Typical Air-Launched Missile,” AIAA
81-1688, August 1981
Hindes, J.W., “Advanced Design of Aerodynamic Missiles ( ADAM ),” October 1993
10/19/24 ELF 67
Bibliography of Reports and Web Sites ( cont )
Bruns, K.D., Moore, M.E., Stoy, S.L., Vukelich, S.R., and Blake, W.B., “Missile Datcom,” AFWAL-TR-91-3039, April 1991
Moore, F.G., et al, “Application of the 1998 Version of the Aeroprediction Code,” Journal of Spacecraft and Rockets,
Vol. 36, No. 5, September-October 1999
Fleeman, E.L., “Tactical Missile Design,” American Institute of Aeronautics and Astronautics, Reston, VA, 2001
Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, New York, 1974
“Missile System Flight Mechanics,” AGARD CP270, May 1979
Hogan, J.C., et al., “Missile Automated Design ( MAD ) Computer Program,” AFRPL TR 80-21, March 1980
Rapp, G.H., “Performance Improvements With Sidewinder Missile Airframe,” AIAA Paper 79-0091, January 1979
Nicolai, L.M., Fundamentals of Aircraft Design, METS, Inc., San Jose, CA, 1984
Lindsey, G.H. and Redman, D.R., “Tactical Missile Design,” Naval Postgraduate School, 1986
Lee, R. G., et al, Guided Weapons, Third Edition, Brassey’s, London, 1998
Giragosian, P.A., “Rapid Synthesis for Evaluating Missile Maneuverability Parameters,” 10th AIAA Applied
Aerodynamics Conference, June 1992
Fleeman, E.L. “Aeromechanics Technologies for Tactical and Strategic Guided Missiles,” AGARD Paper presented at
FMP Meeting in London, England, May 1979
Raymer, D.P., Aircraft Design, A Conceptual Approach, American Institute of Aeronautics and Astronautics, Reston, VA,
1989
Ball, R.E., The Fundamentals of Aircraft Combat Survivability Analysis and Design, American Institute of Aeronautics
and Astronautics, Reston, VA, 1985
Eichblatt, E.J., Test and Evaluation of the Tactical Missile, American Institute of Aeronautics and Astronautics, Reston,
VA, 1989
“DoD Index of Specifications and Standards,” http://stinet.dtic.mil/str/dodiss4_fields.html“
Periscope,” http://www.periscope.usni.com
Bibliography of Reports and Web Sites ( cont )
Bruns, K.D., Moore, M.E., Stoy, S.L., Vukelich, S.R., and Blake, W.B., “Missile Datcom,” AFWAL-TR-91-3039, April 1991
Moore, F.G., et al, “Application of the 1998 Version of the Aeroprediction Code,” Journal of Spacecraft and Rockets,
Vol. 36, No. 5, September-October 1999
Fleeman, E.L., “Tactical Missile Design,” American Institute of Aeronautics and Astronautics, Reston, VA, 2001
Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, New York, 1974
“Missile System Flight Mechanics,” AGARD CP270, May 1979
Hogan, J.C., et al., “Missile Automated Design ( MAD ) Computer Program,” AFRPL TR 80-21, March 1980
Rapp, G.H., “Performance Improvements With Sidewinder Missile Airframe,” AIAA Paper 79-0091, January 1979
Nicolai, L.M., Fundamentals of Aircraft Design, METS, Inc., San Jose, CA, 1984
Lindsey, G.H. and Redman, D.R., “Tactical Missile Design,” Naval Postgraduate School, 1986
Lee, R. G., et al, Guided Weapons, Third Edition, Brassey’s, London, 1998
Giragosian, P.A., “Rapid Synthesis for Evaluating Missile Maneuverability Parameters,” 10th AIAA Applied
Aerodynamics Conference, June 1992
Fleeman, E.L. “Aeromechanics Technologies for Tactical and Strategic Guided Missiles,” AGARD Paper presented at
FMP Meeting in London, England, May 1979
Raymer, D.P., Aircraft Design, A Conceptual Approach, American Institute of Aeronautics and Astronautics, Reston, VA,
1989
Ball, R.E., The Fundamentals of Aircraft Combat Survivability Analysis and Design, American Institute of Aeronautics
and Astronautics, Reston, VA, 1985
Eichblatt, E.J., Test and Evaluation of the Tactical Missile, American Institute of Aeronautics and Astronautics, Reston,
VA, 1989
“DoD Index of Specifications and Standards,” http://stinet.dtic.mil/str/dodiss4_fields.html“
Periscope,” http://www.periscope.usni.com
10/19/24 ELF 68
Bibliography of Reports and Web Sites ( cont )
Defense Technical Information Center, http://www.dtic.mil/
“Aircraft Stores Interface Manual (ASIM),” http://www.asim.net
“Advanced Sidewinder Missile AIM-9X Cost Analysis Requirements Description (CARD),”
http://web2.deskbook.osd.mil/valhtml/2/2B/2B4/2B4T01.htm
Briggs, M.M., Systematic Tactical Missile Design, Tactical Missile Aerodynamics: General Topics, “AIAA Vol. 141
Progress in Astronautics and Aeronautics,” American Institute of Aeronautics, Reston, VA, 1992
Briggs, M.M., et al., “Aeromechanics Survey and Evaluation, Vol. 1-3,” NSWC/DL TR-3772, October 1977
“Missile Aerodynamics,” NATO AGARD LS-98, February 1979
“Missile Aerodynamics,” NATO AGARD CP-336, February 1983
“Missile Aerodynamics,” NATO AGARD CP-493, April 1990
“Missile Aerodynamics,” NATO RTO-MP-5, November 1998
Nielsen, J.N., Missile Aerodynamics, McGraw-Hill Book Company, New York, 1960
Mendenhall, M.R. et al, “Proceedings of NEAR Conference on Missile Aerodynamics,” NEAR, 1989
Nielsen, J.N., “Missile Aerodynamics – Past, Present, Future,” AIAA Paper 79-1818, 1979
Dillenius, M.F.E., et al, “Engineering-, Intermediate-, and High-Level Aerodynamic Prediction Methods and
Applications,” Journal of Spacecraft and Rockets, Vol. 36, No. 5, September-October, 1999
Nielsen, J.N., and Pitts, W.C., “Wing-Body Interference at Supersonic Speeds with an Application to Combinations
with Rectangular Wings,” NACA Tech. Note 2677, 1952
Burns, K. A., et al, “Viscous Effects on Complex Configurations,” WL-TR-95-3060, 1995
“A Digital Library for NACA,” http://naca.larc.gov
Spreiter, J.R., “The Aerodynamic Forces on Slender Plane-and Cruciform-Wing and Body Combinations”, NACA
Report 962, 1950
Simon, J. M., et al, “Missile DATCOM: High Angle of Attack Capabilities, AIAA-99-4258.
Bibliography of Reports and Web Sites ( cont )
Defense Technical Information Center, http://www.dtic.mil/
“Aircraft Stores Interface Manual (ASIM),” http://www.asim.net
“Advanced Sidewinder Missile AIM-9X Cost Analysis Requirements Description (CARD),”
http://web2.deskbook.osd.mil/valhtml/2/2B/2B4/2B4T01.htm
Briggs, M.M., Systematic Tactical Missile Design, Tactical Missile Aerodynamics: General Topics, “AIAA Vol. 141
Progress in Astronautics and Aeronautics,” American Institute of Aeronautics, Reston, VA, 1992
Briggs, M.M., et al., “Aeromechanics Survey and Evaluation, Vol. 1-3,” NSWC/DL TR-3772, October 1977
“Missile Aerodynamics,” NATO AGARD LS-98, February 1979
“Missile Aerodynamics,” NATO AGARD CP-336, February 1983
“Missile Aerodynamics,” NATO AGARD CP-493, April 1990
“Missile Aerodynamics,” NATO RTO-MP-5, November 1998
Nielsen, J.N., Missile Aerodynamics, McGraw-Hill Book Company, New York, 1960
Mendenhall, M.R. et al, “Proceedings of NEAR Conference on Missile Aerodynamics,” NEAR, 1989
Nielsen, J.N., “Missile Aerodynamics – Past, Present, Future,” AIAA Paper 79-1818, 1979
Dillenius, M.F.E., et al, “Engineering-, Intermediate-, and High-Level Aerodynamic Prediction Methods and
Applications,” Journal of Spacecraft and Rockets, Vol. 36, No. 5, September-October, 1999
Nielsen, J.N., and Pitts, W.C., “Wing-Body Interference at Supersonic Speeds with an Application to Combinations
with Rectangular Wings,” NACA Tech. Note 2677, 1952
Burns, K. A., et al, “Viscous Effects on Complex Configurations,” WL-TR-95-3060, 1995
“A Digital Library for NACA,” http://naca.larc.gov
Spreiter, J.R., “The Aerodynamic Forces on Slender Plane-and Cruciform-Wing and Body Combinations”, NACA
Report 962, 1950
Simon, J. M., et al, “Missile DATCOM: High Angle of Attack Capabilities, AIAA-99-4258.
10/19/24 ELF 69
Bibliography of Reports and Web Sites ( cont )
Lesieutre, D., et al, “Recent Applications and Improvements to the Engineering-Level Aerodynamic Prediction Software
MISL3,’’ AIAA-2002-0274
Sutton, G.P., Rocket Propulsion Elements, John Wiley & Sons, New York, 1986
“Tri-Service Rocket Motor Trade-off Study, Missile Designer’s Rocket Motor handbook,” CPIA 322, May 1980
Chemical Information Propulsion Agency, http://www.jhu.edu/~cpia/index.html
Bibliography of Reports and Web Sites ( cont )
Lesieutre, D., et al, “Recent Applications and Improvements to the Engineering-Level Aerodynamic Prediction Software
MISL3,’’ AIAA-2002-0274
Sutton, G.P., Rocket Propulsion Elements, John Wiley & Sons, New York, 1986
“Tri-Service Rocket Motor Trade-off Study, Missile Designer’s Rocket Motor handbook,” CPIA 322, May 1980
Chemical Information Propulsion Agency, http://www.jhu.edu/~cpia/index.html
10/19/24 ELF 70
Follow-up Communication
I would appreciate receiving your comments and corrections on this
text, as well as any data, examples, or references that you may offer.
Thank you,
Gene Fleeman
4472 Anne Arundel Court
Lilburn, GA 30047
Telephone: +1 770-925-4635 ( home )
+1 404-894-7777 ( work )
Fax: +1 404-894-6596
E-mail: [email protected] ( home )
[email protected] ( work )
Web Site: http://www.asdl.gatech.edu
Follow-up Communication
I would appreciate receiving your comments and corrections on this
text, as well as any data, examples, or references that you may offer.
Thank you,
Gene Fleeman
4472 Anne Arundel Court
Lilburn, GA 30047
Telephone: +1 770-925-4635 ( home )
+1 404-894-7777 ( work )
Fax: +1 404-894-6596
E-mail: [email protected] ( home )
[email protected] ( work )
Web Site: http://www.asdl.gatech.edu
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