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An unsteady lifting line theory of flapping wings with application to the forward flight of birds

A lifting line theory of flapping wings in steady forward flight is presented in which the unsteady features of the flow are modelled. A detailed three-dimensional model of the vortex wake is used to evaluate the unsteadiness to first order. The method gives satisfactory agreement with well-known limiting cases. Relationships between the geometric and the kinematic parameters, and the forces and the power are predicted which are compatible with the limited experimental evidence. The theory is applied to the calculation of the power curve of specific birds. Important similarities and differences are observed between the present results and those of Pennycuick (1975) and Rayner (1979c).