Large Angle Unsteady Aerodynamic Theory of a Flat Plate

A purely analytical approach is taken for the evaluation of the unsteady loads on a flat plate. This allows for an extremely low cost theoretical prediction of the plate loads in the style of Wagner and Theodorsen, without making the assumption of small angle of attack or small disturbance flow. The forces and moments are evaluated using the time rate of change of fluid momentum, expressed as an integral of the vorticity field. The flow is taken as inviscid and incompressible with isolated vorticity bound to the plate and in the shed wake. The bound vorticity distribution on the plate is solved exactly using conformal mapping of the plate to a cylinder. In keeping with the original assumption of Wagner, the wake vorticity is assumed to remain stationary in an inertial reference frame and convection is disregarded. Formulation in this manner allows for a closed form solution of Wagner's problem valid at all angles of attack. Separation from the leading edge of the plate can also be included to further increase the fidelity of the model at high angles.