Energetics of optimal undulatory swimming organisms

Abstract

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.

Diving into a simple anguilliform swimmer's sensitivity

“…Recently, much emphasis has been placed on designing optimal undulatory swimmers [40,71,78,30,56,41,79,59]. In general these studies attemptded to optimize either shape, kinematics, or both in regards to swimming speed and either efficiency or cost of transport.…”

“…These ideas could help inform the design of faster, more efficient, more maneuverable underwater vehicles [80,81,82]. Optimal morphologies and kinematics were different depending on whether maximal speed, maximal efficiency, or lowest cost of transport were desired [40,56,41,78,59]. Optimization studies by Tokić and Yue [78,59] suggest that swimming speed and cost of transport are the main drivers of evolution, rather than locomotion efficiency.…”

“…Optimal morphologies and kinematics were different depending on whether maximal speed, maximal efficiency, or lowest cost of transport were desired [40,56,41,78,59]. Optimization studies by Tokić and Yue [78,59] suggest that swimming speed and cost of transport are the main drivers of evolution, rather than locomotion efficiency. However, the studies above assumed high Re settings; only the studies by Gazzola et al 2012 [71], Van Rees et al 2013 [56], and Van Rees et al 2015 [41] explored designs within the intermediate Re space -in particular, one specific Re, Re = 550.…”

“…This data is provided in Figures S3 and S4 in the Supplemental Materials. Lastly, a Pareto-like optimal front is identified when plotting the non-dimensional cost of transport (COT ) against the non-dimensional swimming speed (1/St) [30,31,58,32,59], see Figure 8a. This is referred to as Pareto-like simply because minimal COT is desired for maximal 1/St, thus both metrics are not being maximized as is standard in traditional Pareto optimization.…”

Hopscotching Jellyfish: combining different duty cycle kinematics can lead to enhanced swimming performance

“…To that extent, bioinspired computational studies are invaluable in this process as they allow scientists to more easily probe either biological or theoretical parameter spaces, in a much reduced cost-efficient and time-efficient manner. For example, widespread morphological and/or varying kinematic studies can find parameter combinations that lead to optimal swimming for a given performance metric [30,31,32]. Ultimately, performance (speed and cost of transport) are observed to be highly sensitive to kinematic variations.…”