Space Propulsion - IAP/TU Wien

Space Propulsion
m
i
= ρmL
+ ψ . Si−1
S
S
S
S
1
2
3
4
= ρm
= m
= m
= m
2
3
4
L
+ S
+ S
1
2
+ S
3
= ρm
= ρm
L
= ρm
L
L
+ ψS
1
+ ψS
+ ψS
2
3
+ S
1
+ S
+ S
2
3
= ρm
L
= ρm
= ρm
L
L
+
+
+
( 1+
ψ ) S1
= ρmL[ 1+
( 1+
ψ )]
2
( 1+
ψ ) S2
= ρmL[ 1+
( 1+
ψ ) + ( 1+
ψ ) ]
2
( 1+
ψ ) S = ρm
1+
( 1+
ψ ) + ( 1+
ψ ) + ( 1+
ψ )
3
L
3
[ ]
S
n
n
( 1+
ψ ) −1
( 1+
ψ )
n
−
= ρ ∑ − 1
i
1
mL
( 1+
ψ ) = ρmL
= mL
ψ
1+
φ
0
n
total propellant mass for n
stages with equal tankage factor
φ and equal initial / final mass
ratio R
In an n – stage rocket, velocity gain in each stage is
ΔV
i
=
I
sp
ln R
and total velocity gain of n stages is
ΔV
=
nΔV
i
=
nI
sp
ln R