Nuclear Rocket Thrust Optimization Using Dynamic Programming
The problem considered is that of maximizing the burnout velocity of a solid core nuclear rocket. The optimal thrust schedule was shown, for a range of realistic parameter values, to differ from the well-known result for chemical systems because of the necessity to remove core fission product decay afterheat. This afterheat, which must be removed if the core is to remain intact, is a function of the reactor operating power schedule. The criterion of optimality is the maximization of the rocket final velocity under the constraints of a maximum and minimum allowable reactor power level corresponding to engine throttleable limits and a fixed initial propellant loading that is to be allocated either as useful thrust-producing propellant or as a core afterheat removal coolant yielding no useful thrust. The method of dynamic programming is used to perform the optimization. Numerical results are presented for an example problem that considers vertical, drag-free liftoff from a stationary earth with a uniform gravitational field. Means to relax all of these restrictions, along with other important extensions, are discussed. The effect of varying the problem parameters also is indicated, and implications thereof are pointed out.