Cited by 994Biomimetic flight and propulsion mechanismsFluid Dynamics and Vibration AnalysisFluid dynamics and aerodynamics studies

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

Taylor, Graham K., Nudds, Robert L., Thomas, Adrian L. R.·2003·Nature

DOI 10.1038/nature02000

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Abstract

Dimensionless numbers are important in biomechanics because their constancy can imply dynamic similarity between systems, despite possible differences in medium or scale. A dimensionless parameter that describes the tail or wing kinematics of swimming and flying animals is the Strouhal number, St = fA/U, which divides stroke frequency (f) and amplitude (A) by forward speed (U). St is known to govern a well-defined series of vortex growth and shedding regimes for airfoils undergoing pitching and heaving motions. Propulsive efficiency is high over a narrow range of St and usually peaks within the interval 0.2 < St < 0.4 (refs 3-8). Because natural selection is likely to tune animals for high propulsive efficiency, we expect it to constrain the range of St that animals use. This seems to be true for dolphins, sharks and bony fish, which swim at 0.2 < St < 0.4. Here we show that birds, bats and insects also converge on the same narrow range of St, but only when cruising. Tuning cruise kinematics to optimize St therefore seems to be a general principle of oscillatory lift-based propulsion.

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Authors: Taylor, G. K., Nudds, R. L., & Thomas, A. L. R.
Affiliations: University of Oxford (GB)
University of Leeds (GB)
Corresponding author: Taylor, Graham K.
ORCID: Taylor, Graham K.
Nudds, Robert L.
Thomas, Adrian L. R.
Venue: Nature
Publisher: Springer Science and Business Media LLC
Published: 2003-10
Volume: 425
Issue: 6959
Pages: 707-711
ISSN: 0028-0836 (ISSN-L)
1476-4687
DOI: 10.1038/nature02000
OpenAlex: W2003172346
Cited by: 994
References: 42
Citations by year: 2026: 53 · 2025: 45 · 2024: 71 · 2023: 56 · 2022: 43 · 2021: 70 · 2020: 69 · 2019: 50 · 2018: 50 · 2017: 56 · 2016: 55 · 2015: 51 · 2014: 43 · 2013: 44 · 2012: 32
FWCI: 40.63
Type: journal article
Language: en
Open access: closed
Licence: www.springer.com/tdm (tdm)
Locations: Nature (publishedVersion)
PubMed (publishedVersion)
RePEc: Research Papers in Economics (submittedVersion)
Research Explorer (The University of Manchester) (submittedVersion)
Topics: Physical Sciences › Engineering › Aerospace Engineering › Biomimetic flight and propulsion mechanisms
Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Vibration Analysis
Physical Sciences › Engineering › Computational Mechanics › Fluid dynamics and aerodynamics studies
Keywords: Strouhal number, propulsive efficiency, vortex shedding, birds, bats, insects, flying animals, dynamic similarity, natural selection
MeSH terms: Animals, Biomechanical Phenomena, Birds, Chiroptera, Flight, Animal, Insecta, Models, Biological, Monte Carlo Method, Swimming, Wings, Animal

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

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