Sir James Lighthill proposed a method for estimating the hydrodynamic forces generated by slender fish, and his analysis made clear the mechanism of fish swimming. His method is based on slender body theory, and the hydrodynamic forces produced by fish are explained by their kinematics and the added mass of the body sections. More recently, numerical techniques for estimating hydrodynamic forces are making progress, but Lighthill's method is still very important and useful because it contributes to our understanding of the physics of fish swimming. We propose a new method for estimating the aerodynamic forces generated by flapping wings: the forces are explained by the added mass of vortex wake sheets. In concept, it is similar to the momentum theory for fixed wings, which was developed by Prandtl. So, when the forward velocity is large, the method agrees with the momentum theory for a fixed wing. For hovering flight, where vortex sheets are generated continuously, this method agrees with the Rankine–Froude momentum theory of propellers. Like Lighthill's method for swimming, this newly developed method provides useful insight into the physics of flapping wings.
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Sunada et al. (2001) studied this question.