Generalized formulation and review of piston theory for airfoils

Abstract

The present work presents a brief review of some of the notable contributions to piston theory and of its theoretical basis. A generalized formulation of piston theory is given, applicable to both local and classical piston theory. A consistent generalized formulation of the downwash equation is given, accounting for arbitrary motion in the plane of the airfoil. The formulation reduces to established downwash equations through appropriate definition of the cylinder orientation. The theoretical range of validity of Lighthill’s classical piston theory is examined, and the relative accuracy of a number of approximate theories encapsulated by the formulation as applied to a planar wedge is considered. The relative importance of higher-order terms in piston theory is examined, with the significance of recent literature extending the fidelity of the firstorder term highlighted. It is subsequently suggested that current implementations of local piston theory may be improved through the use of a first-order term of suitable accuracy.