Approximate Performance of PeriodicHypersonic Cruise Trajectories

This paper develops the analytical framework to compare the approximate performance of periodic hypersonic cruise trajectories with previously proposed hypersonic trajectory pro-les for global reach. Speciically, range, V and payload carrying capacity are evaluated for various trajectory types to illustrate the enhanced performance achieved by ying periodic hypersonic cruise trajectories with existing hypersonic vehicle aerodynamic, propulsion, and structures technology. Analytical results reveal that periodic hypersonic cruise trajectories achieve better fuel consumption savings over long distances (20,000 km) than other trajec-tory types proposed for high-speed ight. A 20+% improvement in fuel consumption savings is possible for a Mach 10 vehicle with a modest L/D=4, and a curve-tted rocket-based combined cycle engine model. g = Gravity h = height h scale = Atmospheric scale height I sp = Speciic Impulse I sp e = EEective speciic impulse L = Lift m = mass m e = mass of engine m f = mass of fuel m p = mass of payload m s = mass of structure MF = Vehicle fuel mass fraction MR = Mass fraction n = Number of periods R = Range R e = Radius of the earth s = Length t = Time T = Thrust vector V = Velocity 2 ^ v = Velocity unit vector V = Dimensionless velocity C L = Ballistic coeecient = Fuel weight fraction = Flight path angle = Natural number = Nondimensional range = Density f = Reference density subscripts a = Aerodynamic A = Aerodynamic en = Entrance ex = Exit f = Final i = Initial I = Impulsive o = Conditions after powered ight