Unsteady lifting line theory using the Wagner function

A method is presented to model the incompressible, attached, unsteady lift and moment acting on a thin three-dimensional wing in the time domain. The model is based on the combination of Wagner theory and lifting line theory trough the unsteady Kutta-Joukowsky theorem. The result is a set of closed form linear ordinary di erential equations that can be solved analytically or using a Runge-Kutta-Fehlberg algorithm. The method is validated against numerical predictions from an unsteady Vortex Lattice method for rectangular and tapered wings undergoing step or oscillatory changes in plunge or pitch. As the aerodynamic loads are written in state space form in the proposed method, they can be easily included in aeroelastic and flight dynamic calculations.