Propulsion by heaving strips

The propulsive and control surfaces of swimming and flying organisms are flexible and variously shaped. These physical characteristics affect how such structures interact with the surrounding fluid, and therefore have an impact on swimming performance. Plastic strips (h = 6.9 cm) of various stiffness and length (l = 0.5 – 30 cm) were flapped in a flume by a robot mounted on air-bearings. This made it possible to measure the self-propelled speed of each strip, which was then used as a metric of swimming performance. The strips were mounted in the streamwise direction and actuated at the leading edge in heave only (i.e. the transverse direction). Swimming speeds ranged from 15 to 50 cm/s with Reynolds numbers between 26,000 and 870,000. The motion of the flapping strips was captured by high-speed video and digitized.

Stiffness and strip length had significant effects on swimming performance. Most interestingly, strips of particular stiffnesses exhibited multiple maxima and minima in self-propelled speed at different lengths, suggestive of a resonant mechanism with harmonics. However, the wave forms observed in the strips did not match standing-wave patterns calculated from the strip wave speeds and lengths (assuming even partial reflection of the strip wave). For a given strip stiffness the average wave amplitude over the entire strip

and self-propelled speed rose and fell together as strip length was increased. These findings are evidence of a fluid-structure interaction that is strongly affected by the length and stiffness of the strip. Further analysis has shown us that the maxima occur where the amplitude of the trailing edge is greatest. This phenomenon may be an important factor in understanding the functional morphology of flexible propulsors.

Alben, S., Witt, C., Baker, T. V., Anderson, E. and Lauder, G. V. (2012). Dynamics of freely swimming flexible foils. Phys. Fluids. 24, 051901; doi: 10.1063/1.4709477.

Lauder, G., Lim, J., Shelton, R., Witt, C., Anderson, E. and Tangorra, J. L. (2011). Robotic models for studying undulatory locomotion. Mar. Tech. Soc. J. 45 (4), 41-55.

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