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 fine-scale kinematics and estimate the hydrodynamics of routine and energetically expensive swimming modes at the largest scale.

Automated summary

The study reveals that mass-specific thrust in baleen whales increases with swimming speed and body size, while Froude efficiency decreases with body size but increases with swimming speed. This differs from smaller animals where Froude efficiency typically increases with body size. The dynamics of oscillatory swimming in baleen whales exhibit high Froude efficiency despite higher drag compared to a simple gliding model.