A Fluid/Solid Model for Predicting Slender Body Deflection in a Moving Fluid

An analytical solution is presented for the steady-periodic shape variation of a thin elastic beam subject to fluid mechanic forces and driven by the motion imposed on its ends. The general solution is applicable to such problems as swim fins and aerodynamic flutter, with the proper choice of boundary conditions. The general results are exemplified here by using specific boundary conditions that mimic the motion of swim fins. The calculated instantaneous shape, position, slopes, and lateral velocities of the fin are compared with corresponding measurements taken from underwater video of fins worn by divers swimming at a controlled speed. The analysis revealed new swim technique parameters that characterize the heel slope and its phase with respect to the heel motion. The calculated power, thrust, and Froude efficiency are presented in terms of these parameters.