The propulsive performance of airbreathing pulse detonation engines at selected flight conditions is evaluated by means of a combined analytical/numerical analysis. The work treats the conservation equations in axisymmetric coordinates and takes into account finite-rate chemistry and variable thermophysical properties for a stoichiometric hydrogen/air mixture. In addition, an analytical model accounting for the state changes of the working fluid in pulse detonation engine operation is established to predict the engine performance in an idealized situation. The system under consideration includes a supersonic inlet, an air manifold, a valve, a detonation tube, and a convergent-divergent nozzle. Both internal and external modes of valve operation are implemented. Detailed flow evolution is explored, and various performance loss mechanisms are identified and quantified. The influences of all known effects (such as valve operation timing, filling fraction of reactants, nozzle configuration, and flight condition) on the engine propulsive performance are investigated systematically. A performance map is established over the flight Mach number of 1.2-3.5. Results indicate that the pulse detonation engine outperforms ramjet engines for all the flight conditions considered herein. The benefits of pulse detonation engines are significant at low-supersonic conditions, but gradually decrease with increasing flight Mach number.