On thrust estimates for flapping foils

The average thrust developed by flapping foils seen among the birds and fast swimming marine animals is often estimated experimentally from the time-averaged velocity profile in the wake. We present a parametric investigation of the error due to neglect of the unsteady terms, under the assumption of two-dimensional ideal flow. A numerical simuation algorithm allows comparison of exact average thrust and mean-flow momentum flux in the wake, and two simple models for the wake, based on linear foil theory and the Karman vortex street, provide further insight into the problem. The main observation is that mean-flow wake surveys tend to overestimate the thrust force, most severely for high reduced frequencies and low values of the proportional feathering parameter. We also find that a thrust estimate based on the Karman vortex street model yields surprisingly accurate results over the entire range of tested parameters. The linear theory predicts thrust well for all but the highest Strouhal number. (C) 1998 Academic Press Limited.