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

Abstract

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

“…Three-point bending tests were conducted in order to obtain values for the flexural stiffness of each material, which are recorded in table 1 along with the naming and color foil identification scheme used throughout this study. (Quinn et al 2014a, b;Shelton et al 2014;Feilich and Lauder 2015;Lucas et al 2015). Briefly, each foil was screwed into a flat shaft at the leading edge, with an ATI-Nano17 six-axis force-torque transducer (ATI Industrial Automation, Apex, NC, USA) fitted to the top of the shaft.…”

“…High-speed videos of the swimming foils were taken using selected motion programs to (Shelton et al 2014, Lucas et al 2015. To facilitate comparison between these models and the tuna kinematics, the corresponding region of the tuna's body needed to be identified.…”

“…For example, we would expect that the stiffest foil, S6, would generate the greatest thrust based on studies such as Shelton et al (2014). Theoretically, the stiffer foils should be able to exert greater force on the surrounding fluid during undulatory motion.…”

“…1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 We hypothesized that the stiffest foils would generate the most thrust based on the results of Shelton et al (2014) and Katz and Weihs (1978), which show that stiffer foils studied consistently had a higher coefficient of thrust than more flexible foils, although the Katz and Weihs (1978) foils were high aspect ratio compared to those used here. Further, based on Shelton et al (2014), we hypothesized that the most flexible foils would generally be the most efficient. Finally, following the results of Lucas et al (2015), we hypothesized that a zero-degree angle of attack motion program (described below) that constantly adjusts foil leading edge pitch during swimming would mimic live tuna motion more accurately than programs without any pitch.…”

Hydrodynamic function of dorsal fins in spiny dogfish and bamboo sharks during steady swimming

“…Fluid flow patterns were calculated from video recordings using standard multiple-pass PIV algorithms (Willert and Gharib, 1991) performed using DaVis software (v7.2.2, LaVision GmbH), which divides the image into a grid and performs cross-correlation within two consecutive frames to compute a matrix of velocity vectors, as in our previous research (e.g. Shelton et al, 2014;Nauwelaerts et al, 2007;Quinn et al, 2014).…”