Heterocercal tail function in leopard sharks: A three-dimensional kinematic analysis of two models

Two different models have been proposed to explain the function of the heterocercal tail in shark locomotion. The classical model proposes that, as a result of lift generated by the tail as it beats, the net force acting on the tail is directed dorsally and anteriorly. In contrast, Thomson's model suggests that the tail generates a net force directed through the shark's center of gravity, i.e. ventrally and anteriorly. In this study, we evaluate these two models by describing the three-dimensional kinematics of the heterocercal tail in the leopard shark Triakis semifasciata during swimming. Lateral and posterior views of the tail were examined from four individuals swimming in a flow tank at 1.2L s^-1 (where L is total length) using two high-speed video cameras filming simultaneously at 250 fields s^-1. These two simultaneous views allowed eight landmarks on the tail to be followed in three dimensions through time. These landmarks allowed the tail to be divided into separate surfaces whose orientation over time was calculated. Points located anteriorly on the tail go through significantly smaller excursions and reach their maximum lateral excursion significantly earlier in the beat cycle than points on the trailing edge of the tail. Three-dimensional angle calculations show that the terminal lobe leads the ventral lobe through a beat, as predicted by the classical model. Dye-stream visualizations confirmed that this pattern of movement deflects water ventrally and posteriorly to the moving tail, providing strong support for the classical model. Additionally, our results show that a three-dimensional analysis is critical to understanding the function of the heterocercal tail.