Towards a general theory of accelerating foils in the attached-flow regime

Closed-form expressions for aerodynamic force on an accelerating aerofoil were presented in the 1930s, relating instantaneous force to geometric and kinematic parameters under the following assumptions: a thin aerofoil, small-amplitude motions, planar wake development, and a flow that is inviscid, incompressible and two-dimensional. The present work is a step towards analogous closed-form expressions for large-amplitude motions of thick foils when the flow remains attached and boundary-layer thickness approaches (but does not equal) zero. A mathematical framework is derived from vortical flow theory to highlight the finite degrees of freedom that must be solved or predicted in order to yield a predictive aerodynamic model under the stated conditions. The special case of periodic motion is further considered, and an equation is derived to calculate mean forces from known or assumed time histories of circulation, vorticity-weighted mean wake convection velocity and trailing-edge velocity.