Unifying constructal theory for scale effects in running, swimming and flying

Abstract

SUMMARY Biologists have treated the view that fundamental differences exist between running, flying and swimming as evident, because the forms of locomotion and the animals are so different: limbs and wings vs body undulations,neutrally buoyant vs weighted bodies, etc. Here we show that all forms of locomotion can be described by a single physics theory. The theory is an invocation of the principle that flow systems evolve in such a way that they destroy minimum useful energy (exergy, food). This optimization approach delivers in surprisingly direct fashion the observed relations between speed and body mass (Mb) raised to 1/6, and between frequency(stride, flapping) and \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(M_{\mathrm{b}}^{-1{/}6}\) \end{document}, and shows why these relations hold for running, flying and swimming. Animal locomotion is an optimized two-step intermittency: an optimal balance is achieved between the vertical loss of useful energy (lifting the body weight,which later drops), and the horizontal loss caused by friction against the surrounding medium. The theory predicts additional features of animal design:the Strouhal number constant, which holds for running as well as flying and swimming, the proportionality between force output and mass in animal motors,and the fact that undulating swimming and flapping flight occur only if the body Reynolds number exceeds approximately 30. This theory, and the general body of work known as constructal theory, together now show that animal movement (running, flying, swimming) and fluid eddy movement (turbulent structure) are both forms of optimized intermittent movement.

The constructal-law physics of why swimmers must spread their fingers and toes

“…In brief, bigger and taller means faster, and this trend coincides not only with the mass-speed scaling of all animals with locomotion (swimmers, runner and flies; cf. Bejan and Marden, 2006) but also with the measurable evolution of the sport of speed running. The scientific contribution that sport evolution makes is that it provides a laboratory in which we can observe the phenomenon of evolution in our life time.…”

“…Speed in sports comes from this principle (Charles and Bejan, 2009), and this holds for all swimming animals as well (Bejan and Marden, 2006). Lifting a larger weight requires a larger downward force, and this is why larger paddles (spread fingers and toes, with web or without) is a common design in evolutionary biology.…”

Addressing Grand Challenges In Organismal Biology: The Need For Synthesis

“…For the development of predictive models and methods necessary to identify general patterns and overarching principles, we need to define and articulate the limits of biological questions such that appropriate modeling techniques can be applied. Examples include the emergence of a metabolic theory of ecology (Brown et al 2004) and the application of thermodynamics to the configuration of organs (Reis et al 2004), organisms (Miguel 2006), and animal movement (Bejan and Marden 2006).…”

A simple game-theoretic model for upstream fish migration

“…Such models have recently been a basis of a generalized biological theory for the physiological energy minimization principle (Papadopoulos 2009(Papadopoulos , 2013. Some authors assumed that a migrating animal selects a path that minimizes the total resistance force (Bejan and Marden 2006;Lindberg et al 2015;McElroy et al 2012). Stöcker and Weihs (2001) analyzed a conceptual optimization model based on Weihs (1974) for energy-saving conceptual burst swimming of fishes.…”