Scaling of oscillatory kinematics and Froude efficiency in baleen whales

High efficiency lunate-tail swimming with high-aspect-ratio lifting
surfaces has evolved in many vertebrate lineages, from fish to
cetaceans. Baleen whales (Mysticeti) are the largest swimming
animals that exhibit this locomotor strategy, and present an ideal study
system to examine how morphology and the kinematics of swimming
scale to the largest body sizes. We used data from whale-borne inertial
sensors coupled with morphometric measurements from aerial drones
to calculate the hydrodynamic performance of oscillatory swimming in
six baleen whale species ranging in body length from 5 to 25 m (fin
whale, Balaenoptera physalus; Bryde’s whale, Balaenoptera edeni; sei
whale, Balaenoptera borealis; Antarctic minke whale, Balaenoptera
bonaerensis; humpback whale, Megaptera novaeangliae; and blue
whale, Balaenoptera musculus). We found that mass-specific thrust
increased with both swimming speed and body size. Froude efficiency,
defined as the ratio of useful power output to the rate of energy input
(Sloop, 1978), generally increased with swimming speed but decreased
on average with increasing body size. This finding is contrary to previous
results in smaller animals, where Froude efficiency increased with body
size. Although our empirically parameterized estimates for swimming
baleen whale drag were higher than those of a simple gliding model,
oscillatory locomotion at this scale exhibits generally high Froude
efficiency as in other adept swimmers. Our results quantify the finescale
kinematics and estimate the hydrodynamics of routine and
energetically expensive swimming modes at the largest scale.