Space Propulsion - IAP/TU Wien

Space Propulsion
• a fixed total mass M of propellant is available for
….acceleration of a payload of mass m L
• compare the velocity gains, when the propellant is
….consumed in a single – stage or a multi – stage rocket
Assumptions:
• initial / final mass ratios identical = R for all stages
• mass of supporting structure in each stage is same fraction φ
….of propellant mass of respective stage (φ = „tankage factor“)
1. St.
2. St.
3. St.
( + φ)
mL
+ m1 1
R =
mL
+ φm1
mL
+
R =
m +
R =
m
L
L
m
+
( m1
+ m2
)( 1+
φ)
m1( 1+
φ) + φm2
L
+ ( m1
+ m2
+ m3
)
( m1
+ m2
)( 1+ φ ) + φm3
m
1
R −1
=
1−φ
m
L
( R −1)
)
R −1
m2 =
L
1 φ
1−φ
[ m + ( + ) m1
]
( R −1)
)
R −1
m3 =
L
1 φ +
1−
φ
[ m + ( + )( m1
m2
)]
( R −1)
R −1
ρ =
1−φ
( R −1)
ψ = ( 1+ φ)ρ
m
i
= ρmL
+ ψ . Si−1
propellant mass for i th stage;
S i
… sum of propellant masses m 1
,
m 2
, …, m i