From Piston Theory to a Unified Hypersonic-Supersonic Lifting Surface Method

A unified hypersonic - supersonic lifting surface method has been developed, where the concept of piston theory is generalized and suitably integrated with the aerodynamic influence coefficient (AIC) matrix due to linear theory. Thus, this unified method can account for the effects of wing thickness and/or flow incidence, upstream influence, and three dimensionality for an arbitrary lifting surface system in an unsteady flow, whereas piston theory fails to account for the latter effects. In particular, the present composite series renders the AIC matrix uniformly valid for all supersonic-hypersonic Mach numbers, thus extending the method applicability to cover both the Ackeret limit at the low supersonic end and the Newtonian limit at the hypersonic end. From various cases studied it is concluded that the present method makes a substantial improvement over the linear lifting surface theory and piston theory in terms of unsteady pressures, stability derivatives, and flutter speeds. Among other theories it also predicts the most conservative flutter boundary and it confirms that the supersonic thickness effect is to reduce the flutter speed.