Undulatory locomotion of flexible foils as biomimetic models for understanding fish propulsion.

An undulatory pattern of body bending in which waves pass along the body from head to tail is a major mechanism of creating thrust in many fish species during steady locomotion. Analyses of live fish swimming have provided the foundation of our current understanding of undulatory locomotion, but our inability to experimentally manipulate key variables such as body length, flexural stiffness and tailbeat frequency in freely swimming fish has limited our ability to investigate a number of important features of undulatory propulsion. In this paper we use a mechanical flapping apparatus to create an undulatory wave in swimming flexible foils driven with a heave motion at their leading edge, and compare this motion with body bending patterns of bluegill sunfish (Lepomis macrochirus) and clown knifefish (Notopterus chitala). We found similar swimming speeds, Reynolds and Strouhal numbers, and patterns of curvature and shape between these fish and foils, suggesting that flexible foils provide a useful model for understanding fish undulatory locomotion. We swam foils with different lengths, stiffnesses and heave frequencies while measuring forces, torques and hydrodynamics. From measured forces and torques we calculated thrust and power coefficients, work and cost of transport for each foil. We found that increasing frequency and stiffness produced faster swimming speeds and more thrust. Increasing length had minimal impact on swimming speed, but had a large impact on Strouhal number, thrust coefficient and cost of transport. Foils that were both stiff and long had the lowest cost of transport (in mJ m(-1) g(-1)) at low cycle frequencies, and the ability to reach the highest speed at high cycle frequencies.

Performance variation due to stiffness in a tuna-inspired flexible foil model.

Tuna are fast, economical swimmers in part due to their stiff, high aspect ratio caudal fins and streamlined bodies. Previous studies using passive caudal fin models have suggested that while high aspect ratio tail shapes such as a tuna's generally perform well, tail performance cannot be determined from shape alone. In this study, we analyzed the swimming performance of tuna-tail-shaped hydrofoils of a wide range of stiffnesses, heave amplitudes, and frequencies to determine how stiffness and kinematics affect multiple swimming performance parameters for a single foil shape. We then compared the foil models' kinematics with published data from a live swimming tuna to determine how well the hydrofoil models could mimic fish kinematics. Foil kinematics over a wide range of motion programs generally showed a minimum lateral displacement at the narrowest part of the foil, and, immediately anterior to that, a local area of large lateral body displacement. These two kinematic patterns may enhance thrust in foils of intermediate stiffness. Stiffness and kinematics exhibited subtle interacting effects on hydrodynamic efficiency, with no one stiffness maximizing both thrust and efficiency. Foils of intermediate stiffnesses typically had the greatest coefficients of thrust at the highest heave amplitudes and frequencies. The comparison of foil kinematics with tuna kinematics showed that tuna motion is better approximated by a zero angle of attack foil motion program than by programs that do not incorporate pitch. These results indicate that open questions in biomechanics may be well served by foil models, given appropriate choice of model characteristics and control programs. Accurate replication of biological movements will require refinement of motion control programs and physical models, including the creation of models of variable stiffness.

Hydrodynamic function of biomimetic shark skin: effect of denticle pattern and spacing.

The structure of shark skin has been the subject of numerous studies and recently biomimetic shark skin has been fabricated with rigid denticles (scales) on a flexible substrate. This artificial skin can bend and generate thrust when attached to a mechanical controller. The ability to control the manufacture of biomimetic shark skin facilitates manipulation of surface parameters and understanding the effects of changing denticle patterns on locomotion. In this paper we investigate the effect of changing the spacing and arrangement of denticles on the surface of biomimetic shark skin on both static and dynamic locomotor performance. We designed 3D-printed flexible membranes with different denticle patterns and spacings: (1) staggered-overlapped, (2) linear-overlapped, and (3) linear-non-overlapped, and compared these to a 3D-printed smooth-surfaced control. These 3D printed shark skin models were then tested in a flow tank with a mechanical flapping device that allowed us to either hold the models in a stationary position or move them dynamically. We swam the membranes at a frequency of 1 Hz with different heave amplitudes (from ±1 cm to ±3 cm) while measuring forces, torques, self-propelled swimming speed, and cost of transport (COT). Static tests revealed drag reduction of denticle patterns compared to a smooth control at low speeds, but increased drag at speeds above 25 cm s(-1). However, during dynamic (swimming) tests, the staggered-overlapped pattern produced the fastest swimming speeds with no significant increase in the COT at lower heave values. For instance, at a heave frequency of 1 Hz and amplitude of ±1 cm, swimming speed of the staggered-overlapped pattern increased by 25.2% over the smooth control. At higher heave amplitudes, significantly faster self-propelled swimming speeds were achieved by the staggered-overlapped pattern, but with higher COT. Only the staggered-overlapped pattern provides a significant swimming performance advantage over the smooth control and the other two denticle patterns. Quantitative hydrodynamic comparisons among skin models where control over manufacture allows alteration of design parameters provides a useful experimental tool for future work on the considerable natural diversity of shark skin denticles both among species and on different body locations.

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

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 (5.5 × 10(-5) Nm(2)) and low (1.9 × 10(-5) Nm(2)) 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 0° 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 0° 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.