Optimal shape and motion of undulatory swimming organisms

Abstract

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, fishlike body shapes and motion indeed emerge when U and COT are optimized. Inherent boundary-layerdependent 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.

Viscoelastic properties of the nematode Caenorhabditis elegans , a self-similar, shear-thinning worm

“…To gain deeper insight, This article is a PNAS Direct Submission. 1 To whom correspondence should be addressed. E-mail: dalnoki@mcmaster.ca.…”

“…biomechanics | viscoelasticity T he undulatory motion of snakes and fish as they crawl or swim through a medium is considered a superior form of locomotion in terms of its adoption across a broad range of length scales and efficiency (1). Several attempts have been made to achieve the same level of performance artificially (2), but the agility seen in nature is far from being reproduced in manmade systems.…”

Effect of aspect ratio in free-swimming plunging flexible plates

“…Li, et al [21] investigated the thrust performance of rigid three-dimensional plates with a non-rectangular geometry that represented a forked tail fin and found that forked fins are more efficient than rectangular fins. Other studies sought to optimize the fin shape using both Lighthill's theory [22,23] and viscous flow simulations with fully prescribed kinematics [24]. Each of these studies produced optimal shapes that roughly resembled a real fish -a streamlined body with a caudal fin appendage -but differ between studies.…”

Gait and speed selection in slender inertial swimmers

“…The hydrodynamics of swimming has been the subject of a variety of studies for more than half a century from experimental (3-6), theoretical (7)(8)(9)(10)(11), and computational (12)(13)(14)(15)(16)(17)(18)(19) perspectives. Recently there has been growing interest in integrating these physical approaches with neurobiological models using coupled neuromechanical simulations (20) and biomimetic devices (21,22) to study developmental and evolutionary aspects of the problem.…”