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Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency

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  • Graham K. Taylor

    (University of Oxford)

  • Robert L. Nudds

    (University of Oxford
    University of Leeds)

  • Adrian L. R. Thomas

Abstract

Dimensionless numbers are important in biomechanics because their constancy can imply dynamic similarity between systems, despite possible differences in medium or scale1. A dimensionless parameter that describes the tail or wing kinematics of swimming and flying animals is the Strouhal number1, St = fA/U, which divides stroke frequency (f) and amplitude (A) by forward speed (U)2,3,4,5,6,7,8. St is known to govern a well-defined series of vortex growth and shedding regimes for airfoils undergoing pitching and heaving motions6,8. Propulsive efficiency is high over a narrow range of St and usually peaks within the interval 0.2

Suggested Citation

  • Graham K. Taylor & Robert L. Nudds & Adrian L. R. Thomas, 2003. "Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency," Nature, Nature, vol. 425(6959), pages 707-711, October.
    • Handle: RePEc:nat:nature:v:425:y:2003:i:6959:d:10.1038_nature02000
    DOI: 10.1038/nature02000
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    Cited by:

    1. Xiaotian Zhang & Noel Naughton & Tejaswin Parthasarathy & Mattia Gazzola, 2021. "Friction modulation in limbless, three-dimensional gaits and heterogeneous terrains," Nature Communications, Nature, vol. 12(1), pages 1-8, December.
    2. Emanuel Camacho & Fernando Neves & André Silva & Jorge Barata, 2020. "Numerical Investigation of Frequency and Amplitude Influence on a Plunging NACA0012," Energies, MDPI, vol. 13(8), pages 1-13, April.
    3. Li, Weizhong & Wang, Wen-Quan & Yan, Yan, 2020. "The effects of outline of the symmetrical flapping hydrofoil on energy harvesting performance," Renewable Energy, Elsevier, vol. 162(C), pages 624-638.
    4. Cristiano Maria Verrelli & Cristian Romagnoli & Roxanne Jackson & Ivo Ferretti & Giuseppe Annino & Vincenzo Bonaiuto, 2021. "Phi -Bonacci Butterfly Stroke Numbers to Assess Self-Similarity in Elite Swimmers," Mathematics, MDPI, vol. 9(13), pages 1-12, July.
    5. Joel W. Newbolt & Nickolas Lewis & Mathilde Bleu & Jiajie Wu & Christiana Mavroyiakoumou & Sophie Ramananarivo & Leif Ristroph, 2024. "Flow interactions lead to self-organized flight formations disrupted by self-amplifying waves," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    6. Ding, Rui & Zhang, Xiaoke & Chen, Minmin & Lian, Yuxi & Yu, Daoping, 2023. "Vorticity preference of the Yangtze finless porpoise (Neophocaena asiaeorientalis) during the dry season at the Wanhe River Estuary confluence," Ecological Modelling, Elsevier, vol. 485(C).
    7. Paweł Piskur & Piotr Szymak & Michał Przybylski & Krzysztof Naus & Krzysztof Jaskólski & Mariusz Żokowski, 2021. "Innovative Energy-Saving Propulsion System for Low-Speed Biomimetic Underwater Vehicles," Energies, MDPI, vol. 14(24), pages 1-15, December.
    8. Brendan Hoover & Richard S. Middleton & Sean Yaw, 2019. "CostMAP: An open-source software package for developing cost surfaces," Papers 1906.08872, arXiv.org.
    9. Trivellato, F. & Raciti Castelli, M., 2015. "Appraisal of Strouhal number in wind turbine engineering," Renewable and Sustainable Energy Reviews, Elsevier, vol. 49(C), pages 795-804.

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