Unsteady aerodynamics of membrane wings

The ability of membrane wings to adapt their shape passively in unsteady flow conditions enables several aerodynamic advantages over rigid wings. In pursuit of a theoretical model for evaluating these benefits, a theoretical framework is developed to predict the two-dimensional membrane wing response to unsteady flow conditions in an inviscid flow. An extensible membrane of small camber is assumed, with a constant tension along its length, encountered by a vertical gust. The aerodynamic load on the airfoil is obtained using unsteady thin airfoil theory, where special consideration is given to the modeling of the wake vortices. The dynamic response and unsteady lift of the membrane wing due to arbitrarily-shaped gusts are analyzed for various values of membrane mass and tension to highlight their role in the membrane wing aeroelastic performance. The indicial lift responses are compared with known analytical functions available for rigid airfoils (e.g., Sears and Küssner functions) to assess the effect of membrane flexibility on the unsteady lift response.