Energetics of optimal undulatory swimming organisms

Energy consumption is one of the primary considerations in animal locomotion. 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. 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. 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. We also provide further evidence that the use of tendons in caudal regions is beneficial from an energetic perspective. Our conclusions explain and unify many existing observations and are supported by computational data covering nine orders of magnitude in body size.