Research Article: Measurement of time-varying kinematics of a dolphin in burst accelerating swimming

Date Published: January 30, 2019

Publisher: Public Library of Science

Author(s): Hiroto Tanaka, Gen Li, Yusuke Uchida, Masashi Nakamura, Teruaki Ikeda, Hao Liu, Roi Gurka.


Dolphins are well known as excellent swimmers for being capable of efficient cruising and sharp acceleration. While studies of the thrust production and power consumption of dolphin swimming have been the main subject for decades, time-varying acceleration process during successive fluke beats still remains poorly understood. In this study, we quantified the time-varying kinematics of a dolphin (Lagenorhynchus obliquidens) by directly recording its burst-accelerating swimming before vertical jump in an aquarium with two synchronized high-speed video cameras. We tracked the three-dimensional trajectories of its beak, body sides, and fluke. We found that dolphin could quickly accelerate from 5.0 m s-1 to 8.7 m s-1 merely by 5 strokes (i.e. 2.5 fluke beats) in 0.7 seconds. During the strokes, it was further found that the dolphin demonstrated a great acceleration in downstroke but less acceleration or even a slight deceleration in upstroke. Hydrodynamic forces and thrust power for each stroke were further estimated based on the equation of body motion and a static hydrodynamic model. The drag coefficient of the dolphin was estimated through computational fluid dynamics (CFD) modeling of the steady flows around a realistic geometric model based on 3-D scan data. The thrust and thrust power were then calculated by combining the body kinematics and the drag coefficient, resulting in a maximum stroke-averaged thrust and power-to-mass ratio of 1.3 × 103 N and 90 W kg-1 at downstroke, and 3.3 × 102 N and 19 W kg-1 at upstroke, respectively. Our results point out the importance of asymmetric kinematics in burst acceleration of dolphin, which may be a useful mechanism for biomimetic design of high-performance underwater robots.

Partial Text

Dolphins are well known for their excellent swimming ability, as demonstrated by high-speed swimming, porpoising, acrobatic jumping, and tail standing. In particular, dolphins demonstrate remarkably rapid acceleration from low speed to top speed. The hydrodynamics and energetics behind their high-speed swimming performance has attracted broad attention of both scientists and the public over decades. The famous “Gray’s paradox” was proposed in 1936, in which Sir James Gray calculated that the power output per kilogram of muscle of a dolphin during high-speed swimming was 7 times larger than that of a human [1]. Based on this result, Gray also suggested that the boundary layer around the dolphin may feature laminar instead of turbulent flow, thus reducing fluid drag. Gray’s paradox led to numerous follow-up studies in an attempt to elucidate the hydrodynamics of dolphin swimming [2–12]. To date, however, no evidence of the laminarization of a boundary layer or other special mechanism reducing fluid drag has been found, according to thorough reviews by Fish and Rohr (1999) [13] and Fish (2006) [14]. In fact, Gray’s calculation was flawed due to his underestimation of human power output. Gray calculated the thrust of the dolphin using the observed speed of 10.1 m s-1 for a 7 s sprint, whereas the power output of oarsmen during 3–5 min of sustained exercise was his reference for human performance. Since the power output of muscle decreases with time, the power output of a human for less than 10 s of exercise must be greater than Gray’s estimate based on 3–5 min of sustained exercise. Moreover, Gray used the power per unit kg mass of muscle as an index for comparison; however, the muscle mass and mechanics between muscle activity and locomotive movement are challenging to evaluate.

The experimental procedure was approved by Yokohama Hakkeijima Sea Paradise, the National Museum of Nature and Science, and Animal Experiment Committee of Chiba University. No dolphin was harmed during any part of the study. The animal welfare and housing condition details of the dolphin are provided in S1 Appendix.




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