Effects of non-uniform stiffness on the swimming performance of a passively-flexing, fish-like foil model

Abstract

Simple mechanical models emulating fish have been used recently to enable targeted study of individual factors contributing to swimming locomotion without the confounding complexity of the whole fish body. Yet, unlike these uniform models, the fish body is notable for its non-uniform material properties. In particular, flexural stiffness decreases along the fish’s anterior-posterior axis. To identify the role of non-uniform bending stiffness during fish-like propulsion, we studied four foil model configurations made by adhering layers of plastic sheets to produce discrete regions of high (5.5x10-5 Nm2) and low (1.9x10-5 Nm2) flexural stiffness of biologically-relevant magnitudes. This resulted in two uniform control foils and two foils with anterior regions of high stiffness and posterior regions of low stiffness. With a mechanical flapping foil controller, we measured forces and torques in three directions and quantified swimming performance under both heaving (no pitch) and constant 0o angle of attack programs. Foils self-propelled at Reynolds number 21,000-115,000 and Strouhal number ~0.20-0.25, values characteristic of fish locomotion. Although previous models have emphasized uniform distributions and heaving motions, the combination of non-uniform stiffness distributions and 0o angle of attack pitching program was better able to reproduce the kinematics of freely-swimming fish. This combination was likewise crucial in maximizing swimming performance and resulted in high self-propelled speeds at low costs of transport and large thrust coefficients at relatively high efficiency. Because these metrics were not all maximized together, selection of the “best” stiffness distribution will depend on actuation constraints and performance goals. These improved models enable more detailed, accurate analyses of fish-like swimming.