Meeting Abstract
18.5 Thursday, Jan. 3 A Hydroelastic Model for the Scaling of Steady Swimming in Cetaceans ENGEL, Virginia L*; MCLELLAN, William; PABST, Ann; FISH, Frank; LONG, John; Vassar College; University of North Carolina Wilmington; University of North Carolina Wilmington; West Chester University; Vassar College viengel@vassar.edu
Cetaceans range in length from 1.5 to 30 m, scaling isometrically over this order of magnitude, with body mass increasing in proportion to the cube of body length. However, deviations from isometry are seen in a few species. Our goal was to understand how both allometric deviations and isometric changes might impact the biomechanics of steady swimming. For example, why do large cetaceans beat their tails more slowly than small cetaceans? Or, if a species deviates from geometric similarity, how, if at all, does that different shape alter swimming performance? We derived a simple model from first principles that treats cetaceans as oscillating elastic beams driven by fluke-generated lift. We simplified the solution of the resulting Newtonian equation of motion to allow us to predict the oscillatory frequency of a whale�s propulsive motion from the body�s stiffness, size, and shape, from the fluke�s size and shape, and from swimming kinematics. This hydroelastic model served as our fundamental hypothesis, which we tested by comparing its predicted frequencies with those measured in small cetaceans swimming in the lab and with those measured in larger cetaceans swimming in the wild. For seven small cetacean species, the model provided an excellent prediction of the actual median frequencies of each species, with the regression slope approaching unity. For the 17 species measured in the wild, regression yielded a slope less than one. While the match is close for the largest cetaceans, we are uncertain why smaller cetaceans in the wild show much greater discrepancies than they do in the laboratory. In both cases, our hydroelastic model predicts more than half of the variance in the actual frequencies.
