New look at unsteady supersonic potential flow aerodynamics and piston theory
Piston theory is an inherently quasi-steady theory, in that higher powers of frequency do not appear, as well as a local theory in that the pressure at a point on the airfoil only depends on the downwash at the same point. In the extension to piston theory developed here, the pressure is expressed as a power series in frequency, and the dependence on downwash involves only the local value and simple quadratures of the downwash. The first term in this series is the classical piston theory, and the next term in the series is the correction or the extension to the classical piston theory. The success of the expansion in powers of the inverse Mach number squared, but with an assumption of small reduced frequency to obtain the final result, suggests that an expansion in terms of reduced frequency for an arbitrary Mach number may be useful.
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