Shape, lift, and vibrations of highly compliant membrane wings

Abstract

Membrane wings are common in flying animals such as bats, lemurs, flying squirrels, and pterosaurs, as well as in low Reynolds number Micro Air Vehicles. Vortices shed from the sharp leading and trailing edges and wingtips of membrane wings, and the vortex interactions with the membrane play an important role in the wing’s performance. With compliant membrane wings that are initially tension-free at rest, there are two issues to consider: (a) the static relationship between the net aerodynamic forces and the bulk wing deformation, and (b) the interaction between the membrane dynamics and unsteady flow structures. We present a simple model of the finite deformation and natural frequency of an initially tension-free membrane wing, which depends only on an aeroelastic parameter. We extend our theory with a computer model that accounts for nonuniform chordwise load. We conduct experiments on low aspect ratio membrane wings with different support structures and thicknesses, over a broad range of freestream velocities and angles of attack. We measure wing shape and dynamics, aerodynamic force, and the wake, and find good agreement between the experimental results, the computer model, and our theoretical model. Membrane deformation affects the membrane vibration modes, which in turn affects the coupling between the membrane and vortex shedding. Wings with different wingtip support, but similar stiffness show similar static behavior, but exhibit markedly different dynamic behavior.