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Front crawl stroke in swimming: Phase durations and self-similarity
C M Verrelli1, C Romagnoli2, R R Jackson3
1Electronic Engineering Department of the University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy.
Journal of Biomechanics
|February 11, 2021
Summary
The golden ratio, a mathematical pattern, is found in human walking and running. This study reveals its presence in front crawl swimming, particularly at middle/long distances, indicating enhanced self-similarity in elite swimmers.
Area of Science:
- Biomechanics
- Human Movement Analysis
- Sports Science
Background:
- Human locomotion, including walking and running, exhibits rhythmic patterns with underlying time-harmonic structures.
- The golden ratio has been observed in the sub-phase durations of comfortable-paced walking and running gaits.
- Preliminary evidence suggests front crawl swimming may also display similar golden ratio-based harmonic structures.
Purpose of the Study:
- To mathematically demonstrate the existence of a connection between the golden ratio and front crawl swimming strokes.
- To identify the specific swimming pace analogous to a 'comfortable speed' in terrestrial locomotion.
- To analyze the self-similarity of front crawl strokes and its relation to swimming performance.
Main Methods:
- Application of generalized Fibonacci sequences to analyze the durations of aggregated front crawl swimming stroke phases.
- Characterization of simple and enhanced (stronger) self-similarity in swimming strokes.
- Analysis of experimental data from front crawl swimmers to validate theoretical findings.
Main Results:
- A mathematical link between the golden ratio and front crawl swimming has been established.
- The middle/long-distance pace functions as the 'comfortable speed' in swimming, analogous to walking and running.
- Increased swimming technique correlates with higher levels of self-similarity; enhanced self-similarity is linked to top-level swimmers.
Conclusions:
- The golden ratio is a fundamental pattern in front crawl swimming, particularly at middle/long distances.
- Swimming technique and performance are associated with the degree of stroke self-similarity.
- Enhanced self-similarity in front crawl swimming is a marker of elite athletic performance.
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