Fin Ray Stiffness and Fin Morphology Control Ribbon-Fin-Based Propulsion

Ribbon-fin-based propulsion has rich locomotor capabilities that can enhance the mobility and performance of underwater vehicles navigating in complex environments. Bony fishes using this type of propulsion send one or multiple traveling waves along an elongated fin with the actuation of highly flexible rays that are interconnected by an elastic membrane. In this work, we study how the use of flexible rays and different morphology can affect the performance of ribbon-fin propulsion. We developed a physical model composed of 15 rays that are interconnected with an elastic membrane. We tested four different ray flexural stiffness and four aspect ratios. The robotic model was tested in a low-turbulence flume under two flow conditions (U infinity = [0, 1: 1] wavelength/s). In two experimental sets, we measured fin kinematics, net surge forces, and power consumption. Using these data, we perform a thrust and power analysis of the undulating fin. We present the thrust coefficient, power coefficient, and propulsive efficiency. We find that the thrust generation was linear with the enclosed area swept by the fin, and square of the relative velocity between the incoming flow and traveling wave. The thrust coefficient levels off around 0.5. In addition, for our parameter range, we find that the power consumption scales by the cube of the effective tangential velocity of the rays (Aw)(3) (A is the amplitude of the ray oscillating motion, and w is the angular velocity). We show that a decay in stiffness decreases both thrust production and power consumption. However, for rays with high flexural stiffness, the difference in thrust compared with rigid rays is minimal. Moreover, our results show that flexible rays can improve the propulsive efficiency compared with a rigid counterpart. Finally, we find that the morphology of ribbon fin affects its propulsive efficiency. For the aspect ratio considered in our experiments, AR = 0.317 was the most efficient compared with AR = [ 0.199, 0.424]. Our results suggest that there could be an optimal morphology for a given ribbon fin kinematics. Therefore, both natural swimmers and underwater vehicles using ribbon-fin-based propulsion can take advantage of flexible rays and optimal aspect ratio to improve propulsive performance.