Applications of actuator disk theory to membrane flapping wings

This study addresses the aerodynamics of elastic membrane flapping wings. Several applications of the actuator disk theory to the flapping wings of insects and birds are reviewed. In previous studies, to account for spatial and temporal variance in the wake behind the flapping wings, empirical corrections were proposed for the induced velocity and power. In the present paper, a new procedure for determination of the correction factor is proposed, using membrane-type flapping-wing devices. Wind-tunnel experiments were conducted and the stroke-averaged propulsive thrust was measured on 25-cm-wingspan (flat and 9% camber) and 74-cm-wingspan flapping-wing models. Either flapping frequency or input power was held constant during the tests. Obtained thrust forces were compared to theoretical values predicted by the actuator disk theory. Empirical correction factors to the actuator disk theory were determined, providing a best fit to the experimental data when the flapping axis aligned with freestream velocity. It is noteworthy that the numerical value for the correction factor for the 25 cm cambered wing agrees with the results obtained on large insects. The theoretical corrections for angle of attack of the flapping wing give satisfactory agreements with the experimental data only for relatively low forward speeds.

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