A general optimization for maximum terminal velocity

A numerical model is developed to determine the maximum velocity which can be attained by a rocket propulsion system. Particular attention is given to the ratio of active mass, that which can be converted to propulsive energy, to inert mass, which remains after the propulsive energy is expended. Calculations are based on the law of conservation of energy applied to a spaceship with chemical, laser-sail, interstellar ramjet, and annihilation engines. Limits on the exhaust velocity of the thrust system are neglected. Specific attention is given to relativistic calculations involving the annihilation reactions, noting that classical propulsion systems have critical mass values significantly lower than the propulsion required by extra-solar system flight. Numerical results are presented of critical values of propellant which produce an optimal jet speed, which is determined to be a constant.