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

Adrian Bejan, James H. Marden

Research output: Contribution to journalArticle

156 Scopus citations

Abstract

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 Mb-1/6, 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.

Original languageEnglish (US)
Pages (from-to)238-248
Number of pages11
JournalJournal of Experimental Biology
Volume209
Issue number2
DOIs
StatePublished - Jan 1 2006

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All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics
  • Physiology
  • Aquatic Science
  • Animal Science and Zoology
  • Molecular Biology
  • Insect Science

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