Tailoring the Bending Pattern of Non-Uniformly Flexible Pitching Propulsors Enhances Propulsive Efficiency

Aquatic animals swim rapidly and efficiently by using flexible propulsors. It has been observed that bio-propulsors typically have non-uniform flexibility with increasing flexibility towards the trailing edge. However, most previous research has examined the effect of uniform flexibility on bio-propulsion. Here, we conduct experiments on three-dimensional propulsors with non-uniform chordwise flexibility. We used a simple step function distribution where there is a rigid leading-edge section and a finite flexibility trailing-edge section. This piecewise distribution is defined by the flexion ratio, that is, the ratio of the rigid section length to the chord length. The forces and moments are measured for purely pitching propulsors with various flexion ratios and effective flexibilities. Peak efficiencies for these purely pitching propulsors reach as high as $56\%$ and occur above the first resonant frequency of the system. Additionally, a scaling relation for the resonant frequency of non-uniformly flexible propulsors is determined. This work highlights the result that not only is the resonance condition important for high efficiency performance, but also the bending pattern of a propulsor.