Approximate Performance Comparison ofPeriodic Hypersonic Cruise Trajectories

This paper develops the analytical framework to compare the approximate performance of periodic hypersonic cruise trajectories with previously proposed hypersonic trajectory prooles for global reach. Speciically, range, V and payload carrying capacity are evaluated for various trajectory types to illustrate the enhanced performance achieved by y-ing periodic hypersonic cruise trajectories with existing hypersonic vehicle aerodynamic, propulsion, and structures technology. The use of approximate analytical performance measures eliminates the need for case speciic mission data. Analytical results reveal that periodic hypersonic cruise trajec-tories achieve better performance over long distances (20,000 km) than other trajectory types proposed for high-speed ight. A = Vector term c = Exhaust velocity C D = Drag coeecient C L = Lift coeecient D = Drag E = Range/Mass parameter F = Force vector 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 Graduate Research Assistant, Student Member AIAA. 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 ^ v = Velocity unit vector V = Dimensionless velocity C L = Ballistic coeecient = Flight path angle = Natural number = Nondimensional range = Density f = Reference density subscripts a = Aerodynamic