# Propulsion

## Theory

### Propulsion equation

This is the equation that links the electrical power, the propulsive force and the ISP.

P = F x ISP *9,81 / 2n or P= F x Ev /2n

where:

P = power (Watts)

F = Engine force (Newtons)

ISP = Specific impulse (Seconds)

n = efficiency of engine, for an ion thruster this is between 0,2 and 0,8, for a chemical rocket, essentially 1.

9,81 conversion factor

Ev = Exhaust velocity (m/s)

### Specific impulse

ISP = Ev / 9,81

ISP = Specific impulse (Seconds)

Ev = Exhaust velocity (m/s)

### Fuel consumption

m = F/Ev

m = Fuel consumption (kg/s)

F = Force (Newtons)

Ev = Exhaust velocity (m/s)

### Velocity

V = Ev x ln(M_{o}/M_{f})

Ev = Exhaust velocity (m/s)

V = ship final velocity (m/s)

ln = natural logarithm

M_{o} = Initial mass of the ship (kg)

M_{f} = Final mass of the ship (kg)

The propulsive force is the force the engines produce to push the ship. This is factor of the available electrical energy, the engine efficiency and the propulsive system ISP and ejection velocity.