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Chapter 7 / Missile Trajectory Optimisation
_ _
Yang [Y.8] . In more practical applications the cost is a balance between
impact time, impact speed, miss distance, control effort, etc.
7.4.2 Impact speed
7.4.3 Miss distance
7.4.4 Control effort
7.4.5 Approach angle
φ
2
: =
7-12
− P&
o,
m
( t )
F
Equation 7.4-5
T
T T
( ∂ φ ∂ X , ∂ φ ∂ U ) : = ( ( 0 , −1
, 0 ) , 0 )
2
⎛
⎜
⎝
φ
3
⎛
⎜
⎝
2
C
( ) ( ) ( ) 2
XA 2 YA 2 ZA
P + P P
: =
+
A
m,
t
m,
t
A
t
m,
t
P : = P −
3
A ( t ) P ( t )
( ∂ φ ∂ X , ∂ φ ∂ U )
3
− 2 ⋅ P
φ
m,
t
⋅
F
3
m
F
m,
t
: =
A T T
( ) ⎞ T ⎞
Pm
, 03
⎟ , 02
⎟
⎠ ⎠
( ) ( ) 2
MV 2 MV
Ψ +
4 : = B ΘB
C
2
2
Equation 7.4-6
Equation 7.4-7
Equation 7.4-8
Equation 7.4-9
Equation 7.4-10
MV MV
( ∂ φ ∂ X , ∂ φ ∂ U ) : = ( 0 , 2 ⋅ ( Θ , Ψ ) )
4
4
C
6
B
B
Equation 7.4-11
Minimising the head-on aspect angle at impact increases the kill probability.
For a target travelling towards the missile,
φ
5
A 147 MV
( − nˆ ( Pt
) • )
−1 &
: = cos
ϕ
A
Equation 7.4-12