The effect of advance ratio on the aerodynamics of revolving wings

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Abstract
Recent studies have demonstrated that a quasi-steady model closely matches the instantaneous force produced by an insect wing during hovering flight. It is not clear, however, if such methods extend to forward flight. In this study we use a dynamically scaled robotic model of the fruit fly Drosophila melanogaster to investigate the forces produced by a wing revolving at constant angular velocity while simultaneously translating at velocities appropriate for forward flight. Because the forward and angular velocities were constant wing inertia was negligible, and the measured forces can be attributed to fluid dynamic phenomena. The combined forward and revolving motions of the wing produce a time-dependent free-stream velocity profile, which suggests that added mass forces make a contribution to the measured forces. We find that the forces due added mass make a small, but measurable, component of the total force and are in excellent agreement with theoretical values. Lift and drag coefficients are calculated from the force traces after subtracting the contributions due to added mass. The lift and drag coefficients, for fixed angle of attack, are not constant for non-zero advance ratios, but rather vary in magnitude throughout the stroke. This observation implies that modifications of the quasi-steady model are required in order to predict accurately the instantaneous forces produced during forward flight. We show that the dependence of the lift and drag coefficients upon advance ratio and stroke position can be characterized effectively in terms of the tip velocity ratio – the ratio of the chordwise components of flow velocity at the wing tip due to translation and revolution. On this basis we develop a modified quasi-steady model that can account for the varying magnitudes of the lift and drag coefficients. Our model may also resolve discrepancies in past measurements of wing performance based on translational and revolving motion.