The scale dependence of locomotor factors has long been studied in comparative biomechanics, but remains poorly understood for animals at the upper extremes of body size. Rorqual baleen whales include the largest animals, but we lack basic kinematic data about their movements and behavior below the ocean surface. Here, we combined morphometrics from aerial drone photogrammetry, whale-borne inertial sensing tag data and hydrodynamic modeling to study the locomotion of five rorqual species. We quantified changes in tail oscillatory frequency and cruising speed for individual whales spanning a threefold variation in body length, corresponding to an order of magnitude variation in estimated body mass. Our results showed that oscillatory frequency decreases with body length (proportional to length(-0.5)(3)) while cruising speed remains roughly invariant (proportional to length(0.08)) at 2 m s(-1). We compared these measured results for oscillatory frequency against simplified models of an oscillating cantilever beam (proportional to length(-1)) and an optimized oscillating Strouhal vortex generator (proportional to length(-1)). The difference between our length-scaling exponent and the simplified models suggests that animals are often swimming non-optimally in order to feed or perform other routine behaviors. Cruising speed aligned more closely with an estimate of the optimal speed required to minimize the energetic cost of swimming (proportional to length(-1)). Our results are among the first to elucidate the relationships between both oscillatory frequency and cruising speed and body size for free-swimming animals at the largest scale
