LONG, JR., J H; ETNIER, S; PABST, D A; JOHNSON, M; MCLELLAN, W A; Vassar College; Butler University; University of North Carolina, Wilmington; Vassar College; University of North Carolina, Wilmington: Swimming Cetaceans: Hydrodynamics, Body Stiffness, and the Scaling of Performance
Our goal is to integrate external and internal forces in a model that offers a first approximation of the mechanics of steady swimming in cetaceans. One challenge is to produce a model that is robust enough to account for hydrodynamic and body-elastic forces across a wide range of body sizes. Another is to produce a model that is testable given the paucity of reliable data. We focused on predicting tail-beat frequency, since it varies greatly with body size and is a reliable, oft-measured feature of swimming kinematics. We combined steady-state lifting theory for forces on the flukes with the Newtonian equation of motion for elastic-inertial forces of the body. The combined hydro-elastic model requires information about body size, mass distribution, fluke shape, fluke motion, swimming speed, and the body’s flexural stiffness. We used published values when available. Since no published data are available for flexural stiffness, we performed body bending tests on late-juvenille bottlenosed dolphin, Tursiops truncatus. We derived an apparent material stiffness and applied it to all cetaceans; flexural stiffness was varied by adjusting the second moment of area. We held the fluke’s pitch angle constant at a value chosen in the physiological range to adjust the slope between actual and predicted values of tail-beat frequency to one. Using data from controlled experiments in captivity (eight odontocete species swimming over a range of speeds) for comparison, the hydro-elastic model predicts the actual tail-beat frequency with a coefficient of determination above 0.70, a value independent of the fluke’s pitch angle. Thus this hydro-elastic model provides a means to explore the mechanical interactions of hydrodynamic forces, internal elasticity, body size and shape, and swimming speed.
