Unsteady lift of flapping membrane wings: Connecting theory to experiments

The aerodynamic performance of flapping membrane wings has been studied both theoretically and experimentally to understand the remarkable maneuverability of bats and other flying mammals. These wings passively deform during flight due to the coupling between the membrane profile and the surrounding flow. The complex physics of this problem often necessitates simplifying assumptions, such as using a 2D airfoil, inviscid flow, and small membrane deformations, to achieve an analytical solution. However, these assumptions are typically not sustained in realistic experimental studies. In this work, we aim to connect the unsteady aerodynamic theory of membrane wings with experimental results. We demonstrate how a simplified theoretical model can predict the unsteady lift of a flapping membrane wing based solely on measurements of membrane deformation. To that end, we extend the unsteady aerodynamic theory of flexible membrane airfoils to include effects of the unsteady freestream velocity encountered by the wing and compare the theoretical predictions with experimental measurements of a robotic flapping wing in hover. Our results show good agreement between the theoretical and measured values of the unsteady lift due to membrane oscillations obtained for moderate to high pitch angles, in which the flow remains mostly attached.