Efficient cruising for swimming and flying animals is dictated by fluid drag

Daniel Floryan, Tyler Van Buren, and Alexander J. Smits
PNAS August 7, 2018 115 (32) 8116-8118; published ahead of print June 18, 2018 https://doi.org/10.1073/pnas.1805941115

  1. Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved May 29, 2018 (received for review April 05, 2018)

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Significance

Almost 30 y ago, researchers discovered that a great variety of efficient swimmers cruise in a narrow range of Strouhal numbers, a dimensionless number describing the kinematics of swimming. Almost 15 y later, separate researchers discovered that fliers (bats, birds, and insects) also cruise in the same narrow range of Strouhal numbers. Attendant experiments on flapping airfoils have shown that this narrow range of Strouhal numbers gives rise to the most efficient kinematics. Here, we explain why this range of Strouhal numbers is the most efficient.

Abstract

Many swimming and flying animals are observed to cruise in a narrow range of Strouhal numbers, where the Strouhal number St=2fA/U is a dimensionless parameter that relates stroke frequency f, amplitude A, and forward speed U. Dolphins, sharks, bony fish, birds, bats, and insects typically cruise in the range 0.2<St<0.4, which coincides with the Strouhal number range for maximum efficiency as found by experiments on heaving and pitching airfoils. It has therefore been postulated that natural selection has tuned animals to use this range of Strouhal numbers because it confers high efficiency, but the reason why this is so is still unclear. Here, by using simple scaling arguments, we argue that the Strouhal number for peak efficiency is largely determined by fluid drag on the fins and wings.

Footnotes

  • ↵1To whom correspondence should be addressed. Email: dfloryan{at}princeton.edu.

  • Author contributions: D.F. and T.V.B. designed research; D.F. and T.V.B. performed research; D.F. and T.V.B. analyzed data; and D.F. and A.J.S. wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission.

  • See Commentary on page 8063.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1805941115/-/DCSupplemental.

Published under the PNAS license.

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Efficient cruising for swimming and flying animals is dictated by fluid drag
Daniel Floryan, Tyler Van Buren, Alexander J. Smits
Proceedings of the National Academy of Sciences Aug 2018, 115 (32) 8116-8118; DOI: 10.1073/pnas.1805941115
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