Minimum chemical rocket energy required
Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. Space propulsion or in-space propulsion exclusively deals with propulsion systems used in the vacuum of space and should not be confused with launch vehicles. Several methods, both pragmatic and hypothetical, have been developed each having its own drawbacks and advantages.
In the ideal case m1 is useful payload and m0 − m1 is reaction mass (this corresponds to empty tanks having no mass, etc.). The energy required can simply be computed as shown here
This corresponds to the kinetic energy the expelled reaction mass would have at a speed equal to the exhaust speed. If the reaction mass had to be accelerated from zero speed to the exhaust speed, all energy produced would go into the reaction mass and nothing would be left for kinetic energy gain by the rocket and payload. However, if the rocket already moves and accelerates (the reaction mass is expelled in the direction opposite to the direction in which the rocket moves) less kinetic energy is added to the reaction mass. To see this, if, for example, 10 km/s and the speed of the rocket is 3 km/s, then the speed of a small amount of expended reaction mass changes from 3 km/s forwards to 7 km/s rearwards. Thus, although the energy required is 50 MJ per kg reaction mass, only 20 MJ is used for the increase in speed of the reaction mass. The remaining 30 MJ is the increase of the kinetic energy of the rocket and payload.
If the energy is produced by the mass itself, as in a chemical rocket, the fuel value has to be ve2 / 2 , where for the fuel value also the mass of the oxidizer has to be taken into account. A typical value is ve=4.5 km/s, corresponding to a fuel value of 10.1 MJ/kg. The actual fuel value is higher, but much of the energy is lost as waste heat in the exhaust that the nozzle was unable to extract. For a given Δv the minimum energy required is as shown here.Related formulas
|E||Minimum chemical rocket energy required (J)|
|m1||Fuel mass (kg)|
|Δv||Maximum change of velocity of the vehicle (m/s)|