Reaction engine

A reaction engine is an engine or motor which provides thrust by expelling reaction mass, in accordance with Newton's third law of motion. This law of motion is most commonly paraphrased as: "For every action force there is an equal, but opposite, reaction force".

Examples include both jet engines and rocket engines, and more uncommon variations such as Hall effect thrusters, ion drives, mass drivers and nuclear pulse propulsion.

For all reaction engines which carry their propellant onboard prior to use (such as rocket engines and electric propulsion drives) some energy must go into accelerating the reaction mass. Every engine will waste some energy, but even assuming 100% efficiency, the engine will need energy amounting to

(where M is the mass of propellent expended and ${\displaystyle V_{e}}$ is the exhaust velocity), which is simply the energy to accelerate the exhaust.

Comparing the rocket equation (which shows how much energy ends up in the final vehicle) and the above equation (which shows the total energy required) shows that even with 100% engine efficiency, certainly not all energy supplied ends up in the vehicle - some of it, indeed usually most of it, ends up as kinetic energy of the exhaust.

Interestingly, if the specific impulse (${\displaystyle I_{sp}}$) is fixed, for a mission delta-v, there is a particular ${\displaystyle I_{sp}}$ that minimises the overall energy used by the rocket. This comes to an exhaust velocity of about ⅔ of the mission delta-v (see the energy computed from the rocket equation). Drives with a specific impulse that is both high and fixed such as Ion thrusters have exhaust velocities that can be enormously higher than this ideal, and thus end up powersource limited and give very low thrust. Where the vehicle performance is power limited, e.g. if solar power or nuclear power is used, then in the case of a large ${\displaystyle v_{e}}$ the maximum acceleration is inversely proportional to it. Hence the time to reach a required delta-v is proportional to ${\displaystyle v_{e}}$. Thus the latter should not be too large.

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