Optimal performance of a dual-fuel single-stage rocket

Abstract

The theory of optimal control is used to maximize the performance of a single-stage rocket that is powered by liquid oxygen (LOX)/kerosene (RP-1) engines in parallel with LOX/liquid hydrogen engines. For the sake of simplicity and because of the theoretical nature of the work, the rocket motion is analyzed in the absence of gravitational and aerodynamic forces; either the vehicle gross mass or the dry mass is minimized for the required payload and velocity increment. The analysis provides the optimal values of the constant mixture ratios of the engines and the best time for switching off the hydrocarbon engine. The results cone rm that the use of a hydrocarbon engine at liftoff is recommended for minimum system dry mass, whereas it is required only for the highest velocity increments in the case of minimum gross mass. The ine uence of the thrust level and engine mass on the rocket performance is also discussed. Nomenclature A = parameter; see Eqs. (19) and (20) a = thrust acceleration B = parameter; see Eq. (21) c = effective exhaust velocity D = parameter; see Eq. (26) f = hydrogen-engine thrust fraction at liftoff H = Hamiltonian; see Eq. (8) m = mass r = hydrogen-engine propellant fraction S = switch function T = thrust t = time V = velocity ® = oxygen/fuel mixture ratio 1V = characteristic velocity ≤ = structural coefe cient ¸ = adjoint variable Ω = bulk density ’ = performance index; see either Eq. (18) or Eq. (25) Â = constraint Subscripts