Near-optimal operation of dual-fuel launch vehicles

A near-optimal guidance law for the ascent trajectory from earth surface to earth orbit of a fully reusable single-stage-to-orbit pure rocket launch vehicle is derived. Of interest are both the optimal operation of the propulsion system and the optimal flight path. A methodology is developed to investigate the optimal throttle switching of dual-fuel engines. The method is based on selecting propulsion system modes and parameters that maximize a certain performance function. This function is derived from consideration of the energy-state model of the aircraft equations of motion. Because the density of liquid hydrogen is relatively low, the sensitivity of perturbations in volume need to be taken into consideration as well as weight sensitivity. The cost functional is a weighted sum of fuel mass and volume; the weighting factor is chosen to minimize vehicle empty weight for a given payload mass and volume in orbit. Nomenclature L H e LOX D = drag, lb M E = total mechanical energy per unit M,, weight, ft M, -° g = gravitational acceleration on the R earth surface, tVsec e T h = altitude, R Tv Ise = specific impulse, see K = weighting parameter, ib/t_ 3 t K" = value of K for minimum empty V weight, lb/R 3 ve L = lift, lb = liquid hydrogen = liquid oxygen =Mach number = transition Mach number = optimal transition Mach number = radius of the earth, t_ = thrust, lb = magnitude of thrust component along velocity vector, lb = time, see = speed, fps = propellant volume, R3 • Professor and Chairman, Department of Mechanical Engineering. Associate Fellow AIAA. ' Graduate Research Assistant, Department of Mechanical Engineering. Student Member AIAA. ' Aerospace Engineer, System Analysis Branch. Member AIAA. Copyright © 1995 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. 303