SUMMARY As a result of years of research on the comparative biomechanics and physiology of moving through water, biologists and engineers have made considerable progress in understanding how animals moving underwater use their muscles to power movement, in describing body and appendage motion during propulsion, and in conducting experimental and computational analyses of fluid movement and attendant forces. But it is clear that substantial future progress in understanding aquatic propulsion will require new lines of attack. Recent years have seen the advent of one such new avenue that promises to greatly broaden the scope of intellectual opportunity available to researchers: the use of biorobotic models. In this paper we discuss, using aquatic propulsion in fishes as our focal example, how using robotic models can lead to new insights in the study of aquatic propulsion. We use two examples: (1) pectoral fin function, and (2) hydrodynamic interactions between dorsal and caudal fins. Pectoral fin function is characterized by considerable deformation of individual fin rays, as well as spanwise (along the length) and chordwise (across the fin) deformation and area change. The pectoral fin can generate thrust on both the outstroke and instroke. A robotic model of the pectoral fin replicates this result, and demonstrates the effect of altering stroke kinematics on the pattern of force production. The soft dorsal fin of fishes sheds a distinct vortex wake that dramatically alters incoming flow to the tail: the dorsal fin and caudal fin act as dual flapping foils in series. This design can be replicated with a dual-foil flapping robotic device that demonstrates this phenomenon and allows examination of regions of the flapping performance space not available to fishes. We show how the robotic flapping foil device can also be used to better understand the significance of flexible propulsive surfaces for locomotor performance. Finally we emphasize the utility of self-propelled robotic devices as a means of understanding how locomotor forces are generated, and review different conceptual designs for robotic models of aquatic propulsion.

SUMMARY Although various hydrodynamic models have been used in past analyses of squid jet propulsion, no previous investigations have definitively determined the fluid structure of the jets of steadily swimming squid. In addition, few accurate measurements of jet velocity and other jet parameters in squid have been reported. We used digital particle imaging velocimetry (DPIV) to visualize the jet flow of adult long-finned squid Loligo pealei(mantle length, Lm=27.1±3.0 cm, mean ± s.d.) swimming in a flume over a wide range of speeds(10.1-59.3 cm s-1, i.e. 0.33-2.06 Lms-1). Qualitatively, squid jets were periodic, steady, and prolonged emissions of fluid that exhibited an elongated core of high speed flow. The development of a leading vortex ring common to jets emitted from pipes into still water often appeared to be diminished and delayed. We were able to mimic this effect in jets produced by a piston and pipe arrangement aligned with a uniform background flow. As in continuous jets, squid jets showed evidence of the growth of instability waves in the jet shear layer followed by the breakup of the jet into packets of vorticity of varying degrees of coherence. These ranged from apparent chains of short-lived vortex rings to turbulent plumes. There was some evidence of the complete roll-up of a handful of shorter jets into single vortex rings, but steady propulsion by individual vortex ring puffs was never observed. Quantitatively, the length of the jet structure in the visualized field of view, Lj, was observed to be 7.2-25.6 cm, and jet plug lengths, L, were estimated to be 4.4-49.4 cm using average jet velocity and jet period. These lengths and an average jet orifice diameter, D, of 0.8 cm were used to calculate the ratios Lj/D and L/D, which ranged from 9.0 to 32.0 and 5.5 to 61.8, respectively. Jets emitted from pipes in the presence of a background flow suggested that the ratio between the background flow velocity and the jet velocity was more important than L/D to predict jet structure. Average jet velocities in steadily swimming squid ranged from 19.9 to 85.8 cm s-1 (0.90-2.98 Lm s-1) and were always greater in magnitude than swimming speed. Maximum instantaneous fluid speeds within squid jets ranged from 25.6 to 136.4 cm s-1. Average jet thrust determined both from jet velocity and from three-dimensional approximations of momentum change in successive jet visualizations showed some differences and ranged from 0.009 to 0.045 N over the range of swimming speeds observed. The fraction by which the average jet velocity exceeded the swimming speed, or `slip',decreased with increasing swimming speed, which reveals higher jet propulsive efficiency at higher swimming speeds. Jet angle, subtended from the horizontal, decreased from approximately 29° to 7° with increasing swimming speed. Jet frequency ranged from 0.6 to 1.3 Hz in the majority of swimming sequences, and the data suggest higher frequencies at the lowest and highest speeds. Jet velocity, angle, period and frequency exhibited increased variability at speeds between 0.6 and 1.4 Lms-1. This suggests that at medium speeds squid enjoy an increased flexibility in the locomotive strategies they use to control their dynamic balance.

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.

A B S T R A C TMany fish swim using body undulations to generate thrust and maneuver in three dimensions. The pattern of body bending during steady rectilinear locomotion has similar general characteristics in many fishes and involves a wave of increasing amplitude passing from the head region toward the tail. While great progress has been made in understanding the mechanics of undulatory propulsion in fishes, the inability to control and precisely alter individual parameters such as oscillation frequency, body shape, and body stiffness, and the difficulty of measuring forces on freely swimming fishes have greatly hampered our ability to understand the fundamental mechanics of the undulatory mode of locomotion in aquatic systems. In this paper, we present the use of a robotic flapping foil apparatus that allows these parameters to be individually altered and forces measured on self-propelling flapping flexible foils that produce a wave-like motion very similar to that of freely swimming fishes. We use this robotic device to explore the effects of changing swimming speed, foil length, and foil-trailing edge shape on locomotor hydrodynamics, the cost of transport, and the shape of the undulating foil during locomotion. We also examine the passive swimming capabilities of a freshly dead fish body. Finally, we model fin-fin interactions in fishes using dual-flapping foils and show that thrust can be enhanced under correct conditions of foil phasing and spacing as a result of the downstream foil making use of vortical energy released by the upstream foil.