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Phi -Bonacci Butterfly Stroke Numbers to Assess Self-Similarity in Elite Swimmers

Author

Listed:
  • Cristiano Maria Verrelli

    (Department of the Electronic Engineering, University of Rome Tor Vergata, via del Politecnico 1, 00133 Rome, Italy)

  • Cristian Romagnoli

    (Department for Life Quality Studies, University of Bologna, 47900 Rimini, Italy
    Sport Engineering Lab, Department of Industrial Engineering, University of Rome Tor Vergata, 00133 Rome, Italy)

  • Roxanne Jackson

    (Institute of Automation Technology, Otto-von-Guericke University Magdeburg, 39106 Magdeburg, Germany)

  • Ivo Ferretti

    (Biomechanical and Video-Analysis Area for the National Teams of Federazione Italiana Nuoto (FIN), 00100 Rome, Italy)

  • Giuseppe Annino

    (Sport Engineering Lab, Department of Industrial Engineering, University of Rome Tor Vergata, 00133 Rome, Italy
    Department of Medicine Systems, University of Rome Tor Vergata, 00133 Rome, Italy
    Centro di Biomedicina Spaziale, University of Rome Tor Vergata, 00133 Rome, Italy)

  • Vincenzo Bonaiuto

    (Sport Engineering Lab, Department of Industrial Engineering, University of Rome Tor Vergata, 00133 Rome, Italy)

Abstract

A harmonically self-similar temporal partition, which turns out to be subtly exhibited by elite swimmers at middle distance pace, is formally defined for one of the most technically advanced swimming strokes—the butterfly. This partition relies on the generalized Fibonacci sequence and the golden ratio. Quantitative indices, named ϕ -bonacci butterfly stroke numbers, are proposed to assess such an aforementioned hidden time-harmonic and self-similar structure. An experimental validation on seven international-level swimmers and two national-level swimmers was included. The results of this paper accordingly extend the previous findings in the literature regarding human walking and running at a comfortable speed and front crawl swimming strokes at a middle/long distance pace.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1545-:d:586803
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    References listed on IDEAS

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    1. 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.
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