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.

Optimal shape and motion of undulatory swimming organisms.

Undulatory swimming animals exhibit diverse ranges of body shapes and motion patterns and are often considered as having superior locomotory performance. The extent to which morphological traits of swimming animals have evolved owing to primarily locomotion considerations is, however, not clear. To shed some light on that question, we present here the optimal shape and motion of undulatory swimming organisms obtained by optimizing locomotive performance measures within the framework of a combined hydrodynamical, structural and novel muscular model. We develop a muscular model for periodic muscle contraction which provides relevant kinematic and energetic quantities required to describe swimming. Using an evolutionary algorithm, we performed a multi-objective optimization for achieving maximum sustained swimming speed U and minimum cost of transport (COT)--two conflicting locomotive performance measures that have been conjectured as likely to increase fitness for survival. Starting from an initial population of random characteristics, our results show that, for a range of size scales, fish-like body shapes and motion indeed emerge when U and COT are optimized. Inherent boundary-layer-dependent allometric scaling between body mass and kinematic and energetic quantities of the optimal populations is observed. The trade-off between U and COT affects the geometry, kinematics and energetics of swimming organisms. Our results are corroborated by empirical data from swimming animals over nine orders of magnitude in size, supporting the notion that optimizing U and COT could be the driving force of evolution in many species.