Control strategies for space boosters using air collection systems

Abstract

A simple and efficient performance analysis method is developed for evaluating vehicle pitch and engine throttle controls to minimize booster fuel required to fill second-stage liquid oxygen (LOX) tanks and deliver the vehicle to the staging point. An optimization methodology finds a throttle schedule that controls both the air-breathing engine and the LOX collection rate. The altitude-velocity profile is derived from a variational calculus/energy management contouring method. Automatic adaptive-gain pitch-rate and throttle controls are developed. Results from a parametric study show that collecting on the run for an optimum schedule results in a 17% fuel savings over collection at a constant Mach number. Nomenclaturecollection ratio of LOX to hydrogen fuel, W C^ = engine throttle setting D = drag force, Ib E = specific energy, h + 1 / 2 V 2 /g 9 ft F FCN = fuel integrand, WIP S , Ib/ft FA STOIC = stoichiometric H 2 -fuel/air ratio f s =fuel specific energy, P S /W, ft/lb g = gravity constant, ft/s 2 h = height above sea level, ft I SP = specific impulse, s L FCN = LOX integrand, W LOX /^ lb/ft L = lift force, Ib M = Mach number m = vehicle mass, slug P s = specific excess power, V(T-D)/W, ft/s q = dynamic pressure, lb/ft 2 R -radius from Earth's center, ft R E = Earth radius, ft S = vehicle wing surface reference area, ft 2 s = distance downrange from vehicle launch point, n.mi. T = thrust, Ib t = time, s V = flight velocity, ft/s W A = engine air flow, Ib/s W = engine fuel flow, Ib/s W = vehicle weight, Ib a = angle of attack, deg OQ = zero lift angle of attack, deg A = denotes an increment y = flight-path angle, deg 4> = fuel-to-air equivalence ratio