Effects of ceratotrichia diameter and packing density on chimaera pectoral fin kinematics

Abstract Chimaeras – a group of cartilaginous fishes – swim using a distinctive locomotory mode, termed flapping flight. Dorsoventral oscillation of the flexible pectoral fins is driven by muscles at the base of the fin. This motion induces an undulatory wave which travels from the leading edge to the trailing edge of the fin. It is thought that this undulatory wave is passively induced, and hence, the kinematic waveform is largely influenced by the fin’s structure. Recent work focusing on bony fishes and models of their fins has shown that fin models with internal structure (fin rays) show different kinematic waveforms than models made of a single material, but our understanding of which structural parameters of fin rays are most influential on kinematics is still developing. Our goal was to understand the significance of internal structure for the swimming kinematics of chimaeras. We designed a physical modeling system based on the kinematic patterns of real chimaeras and examined artificial fins of varying fin ray diameter and packing density to investigate how internal anatomy influences pectoral fin tip amplitude, leading-edge curvature, and undulatory waves. As diameter and packing density increased, fin tip amplitude and leading-edge curvature decreased. Diameter had a much larger effect on fin tip amplitude than packing density over the tested ranges. Surprisingly, undulatory wave speed was greatest in the most flexible fin models rather than the stiffest. Empirical evidence and the mathematical equations stating that wave speed increases with stiffness run counter to this last result, suggesting our findings align with a more nuanced relationship between fin stiffness and wave kinematics described by a mathematical fluid flow model. Our work provides new insights into the anatomical parameters that could influence the evolution of chimaera flapping flight and pectoral fin locomotion more broadly and provides direction for possible biomimetic applications.