S.1 Spacecraft Propulsion Systems Chapter 1: Introduction to ...

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The mass of propulsion systems can be determined with help of the overall ‘Propulsion
System Mass Fraction’
m
m
PS
S / C
∆v
⎛ − ⎞
⎜ ve
I = − ⎟
tot vem
S / C 1 e
⎜ ⎟
⎝ ⎠
[Ns]
I tot
I ssp =
m
⇒ I tot = I sspm
PS [Ns/kg]
m
m
PS
S / C
=
I
PS
v
e
ssp
⎛
⎜1−
e
⎜
⎝
∆v
−
v
e
⎞ I
⎟ =
⎟
⎠
I
:
sp
ssp
⎛
⎜1−
e
⎜
⎝
∆v
−
v
e
⎞
⎟
⎟
⎠
Propulsion System Mass Fraction
mPS = mass of propulsion system (including propellant) [kg]
mS/C = total mass of spacecraft (vehicle) [kg]
Isp = thruster specific impulse [Ns/kg] → ve = thruster exhaust velocity [m/s]
Issp = system specific impulse [Ns/kg]
ve = thruster exhaust velocity [m/s]
The first equation above is obtained from the rocket equation. The second equation is just the
definition of Issp, and the final expression follows from the first two.