Piston Theory-A New Aerodynamic Tool for the Aeroelastician

TLDR: In this paper, a point-function relationship between the local pressure on the surface of a wing and the normal component of fluid velocity produced by the wing's motion is predicted, and the computation of generalized forces in aeroelastic equations, such as the flutter determinant, is then reduced to elementary integrations of assumed modes of motion.

Abstract: Representative applications are described which illustrate the extent to which simplifications in the solutions of high-speed unsteady aeroelastic problems can be achieved through the use of certain aerodynamic techniques known collectively as "piston theory." Based on a physical model originally proposed by Hayes and Lighthill, piston theor}^ for airfoils and finite wings has been systematically developed by Landahl, utilizing expansions in powers of the thickness ratio 8 and the inverse of the flight Mach Number M. When contributions of orders 8/M and 8/M are negligible, the theory predicts a point-function relationship between the local pressure on the surface of a wing and the normal component of fluid velocity produced by the wing's motion. The computation of generalized forces in aeroelastic equations, such as the flutter determinant, is then always reduced to elementary integrations of the assumed modes of motion.