Scaling laws for the thrust production of flexible pitching panels

Abstract We present experimental results on the role of flexibility and aspect ratio in bio-inspired aquatic propulsion. Direct thrust and power measurements are used to determine the propulsive efficiency of flexible panels undergoing a leading-edge pitching motion. We find that flexible panels can give a significant amplification of thrust production of $\mathscr{O}(100{\unicode{x2013}} 200\hspace{0.167em} \% )$ and propulsive efficiency of $\mathscr{O}(100\hspace{0.167em} \% )$ when compared to rigid panels. The data highlight that the global maximum in propulsive efficiency across a range of panel flexibilities is achieved when two conditions are simultaneously satisfied: (i) the oscillation of the panel yields a Strouhal number in the optimal range ( $0. 25\lt \mathit{St}\lt 0. 35$ ) predicted by Triantafyllou, Triantafyllou & Grosenbaugh (J. Fluid Struct., vol. 7, 1993, pp. 205–224); and (ii) this frequency of motion is tuned to the structural resonant frequency of the panel. In addition, new scaling laws for the thrust production and power input to the fluid are derived for the rigid and flexible panels. It is found that the dominant forces are the characteristic elastic force and the characteristic fluid force. In the flexible regime the data scale using the characteristic elastic force and in the rigid limit the data scale using the characteristic fluid force.