Study of the thrust--drag balance with a swimming robotic fish

A robotic fish is used to test the validity of a simplification made in the context of fish locomotion. With this artificial aquatic swimmer, we verify that the momentum equation results from a simple balance between a thrust and a drag that can be treated independently in the small amplitude regime. The thrust produced by the flexible robot is proportional to A^2 f^2, where A and f are the respective tail-beat amplitude and oscillation frequency, irrespective of whether or not f coincides with the resonant frequency of the fish. The drag is proportional to U^2, where U is the swimming velocity. These three physical quantities set the value of the Strouhal number in this regime. For larger amplitudes, we found that the drag coefficient is not constant, but increases quadratically with the fin amplitude. As a consequence of this correction, the Strouhal number becomes an increasing function of the fin amplitude as well.