Nonlinear unsteady aerodynmiac modeling by Volterra variational approach

The aerodynamics at high-angle-of-attack is an unsteady and nonlinear phenomena in time. In this paper, we present a phenomenological and mathematically rigorous approach to nonlinear modeling of the unsteady aerodynamics based on Volterra variational equations. The model consists of differential equations of internal states corresponding to different kernels of the Volterra series. The model structure is generic as the number of states can be chosen contingent on available wind tunnel test data and fidelity of the model desired. Model parameters are estimated using forced oscillation wind tunnel test data. We present modeling of the normal force coefficient of a delta-wing aircraft. We find that two-states are sufficient for accurate modeling of the normal force coefficient in small and large amplitude oscillations in pitch at different frequencies. We show that the model is consistent with various experimental observations reported in literature. In the end we compare it with other models proposed in literature.