We use modeling and simulations guided by initial experiments to study thin foils which are oscillated at the leading edge and are free to move unidirectionally under the resulting fluid forces. We find resonant-like peaks in the swimming speed as a function of foil length and rigidity. We find good agreement between the inviscid model and the experiment in the foil motions (particularly the wavelengths of their shapes), the dependences of their swimming speeds on foil length and rigidity, and the corresponding flows. The model predicts that the foil speed is proportional to foil length to the −1/3 power and foil rigidity to the 2/15 power. These scalings give a good collapse of the experimental data.

Fish are a potentially rich source of inspiration for the design of smart materials. Fish exemplify the use of flexible materials to generate forces during locomotion, and a hallmark of fish functional design is the use of body and fin deformation to power propulsion and maneuvering. As a result of nearly 500 million years of evolutionary experimentation, fish design has a number of interesting features of note to materials engineers. In this paper we first provide a brief general overview of some key features of the mechanical design of fish, and then focus on two key properties of fish: the bilaminar mechanical design of bony fish fin rays that allows active muscular control of curvature, and the role of body flexibility in propulsion. After describing the anatomy of bony fish fin rays, we provide new data on their mechanical properties. Three-point bending tests and measurement of force inputs to and outputs from the fin rays show that these fin rays are effective displacement transducers. Fin rays in different regions of the fin differ considerably in their material properties, and in the curvature produced by displacement of one of the two fin ray halves. The mean modulus for the proximal (basal) region of the fin rays was 1.34 GPa, but this varied from 0.24 to 3.7 GPa for different fin rays. The distal fin region was less stiff, and moduli for the different fin rays measured varied from 0.11 to 0.67 GPa. These data are similar to those for human tendons (modulus around 0.5 GPa). Analysis of propulsion using flexible foils controlled using a robotic flapping device allows investigation of the effect of altering flexural stiffness on swimming speed. Flexible foils with the leading edge moved in a heave show a distinct peak in propulsive performance, while the addition of pitch input produces a broad plateau where the swimming speed is relatively unaffected by the flexural stiffness. Our understanding of the material design of fish and the control of tissue stiffness is still in its infancy, and the development of smart materials to assist in investigating the active control of stiffness and in the construction of robotic fish-like devices is a key challenge for the near future.

In fishes the shape of the body and the swimming mode generally are correlated. Slender-bodied fishes such as eels, lampreys, and many sharks tend to swim in the anguilliform mode, in which much of the body undulates at high amplitude. Fishes with broad tails and a narrow caudal peduncle, in contrast, tend to swim in the carangiform mode, in which the tail undulates at high amplitude. Such fishes also tend to have different wake structures. Carangiform swimmers generally produce two staggered vortices per tail beat and a strong downstream jet, while anguilliform swimmers produce a more complex wake, containing at least two pairs of vortices per tail beat and relatively little downstream flow. Are these differences a result of the different swimming modes or of the different body shapes, or both? Disentangling the functional roles requires a multipronged approach, using experiments on live fishes as well as computational simulations and physical models. We present experimental results from swimming eels (anguilliform), bluegill sunfish (carangiform), and rainbow trout (subcarangiform) that demonstrate differences in the wakes and in swimming performance. The swimming of mackerel and lamprey was also simulated computationally with realistic body shapes and both swimming modes: the normal carangiform mackerel and anguilliform lamprey, then an anguilliform mackerel and carangiform lamprey. The gross structure of simulated wakes (single versus double vortex row) depended strongly on Strouhal number, while body shape influenced the complexity of the vortex row, and the swimming mode had the weakest effect. Performance was affected even by small differences in the wakes: both experimental and computational results indicate that anguilliform swimmers are more efficient at lower swimming speeds, while carangiform swimmers are more efficient at high speed. At high Reynolds number, the lamprey-shaped swimmer produced a more complex wake than the mackerel-shaped swimmer, similar to the experimental results. Finally, we show results from a simple physical model of a flapping fin, using fins of different flexural stiffness. When actuated in the same way, fins of different stiffnesses propel themselves at different speeds with different kinematics. Future experimental and computational work will need to consider the mechanisms underlying production of the anguilliform and carangiform swimming modes, because anguilliform swimmers tend to be less stiff, in general, than are carangiform swimmers.