Much less is known about the energetics of swimming than about its kinematics due to the inherent complexity of measuring energetic quantities in swimming animals. This remained a long-standing controversy, but has finally been found as flawed. The problem was brought to the forefront by Gray’s paradox -the notion that dolphin’s muscles should produce seven times more power per unit mass than other types of mammalian muscles. Our conclusions explain and unify existing observations and are supported by our computational data covering nine orders of magnitude in body size.įrom the very beginning of the study of animal swimming, the problem of swimming energetics has generated a lot of interest. For all these different modes of locomotion, it is COT that always decreases with body mass, and it is optimizing for COT (and not efficiency) that provides evolutionary drive for greater body sizes.

These efficiencies are found to decrease with the size of the swimmer, in surprising contrast to runners or fliers who are generally more efficient with increasing body size. We find that maximizing swimming speed or minimizing cost of transport COT (energy consumed per body mass per distance traveled) do not, in general, correspond to optimal muscle or total efficiency (power produced as a fraction of power consumed). Using theoretical considerations from first principles coupled with a novel muscle-hydrodynamic model, and extensive computations, we answer a number of outstanding controversies regarding swimming energetics. Our conclusions explain and unify many existing observations and are supported by computational data covering nine orders of magnitude in body size.įish-like undulating swimming exhibits remarkable speeds, efficiencies and versatility over many orders of magnitude in body size. We also provide further evidence that the use of tendons in caudal regions is beneficial from an energetic perspective. Our results lead to three main conclusions: (1) in contrast to previous hypotheses, achieving optimal values of U and COT is independent of producing maximal power or efficiency (2) muscle efficiency in swimming, in contrast to that in flying or running, decreases with increasing body size, consistent with muscle contraction characteristics (3) the long-standing problem of two disparate patterns of longitudinal power output distributions in swimming fish can be reconciled by relating the two patterns to U-optimal or COT-optimal swimmers, respectively.

Based on a comprehensive theoretical framework that incorporates cyclic muscle behavior, structural dynamics and swimming hydrodynamics, we perform extensive computational simulations and show that many of the outstanding problems in swimming energetics can be explained by considering the coupling between hydrodynamics and muscle contraction characteristics, as well as the trade-offs between the conflicting performance goals of sustained swimming speed U and cost of transport COT. In swimming locomotion, a number of questions related to swimming energetics of an organism and how the energetic quantities scale with body size remain open, largely due to the difficulties with modeling and measuring the power production and consumption. Energy consumption is one of the primary considerations in animal locomotion.

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