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A mathematical analysis of the motion of an in-flight soccer ball

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Abstract

In this paper, an analytical and numerical study of the three-dimensional equations describing the motion through the air of a spinning ball is presented. The initial analysis involves constant drag coefficients, but is later extended to involve drag varying with the spin ratio. Excellent agreement is demonstrated between numerical, analytical and experimental results. The analytical solution shows explicitly how the ball’s motion depends on parameters such as ball roughness, velocity and atmospheric conditions. The importance of applying three-dimensional models, rather than two-dimensional approximations, is demonstrated.

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Acknowledgments

The research of TGM was supported by the Marie Curie International Reintegration Grant Industrial applications of moving boundary problems, Grant No. FP7-256417 and Ministerio de Ciencia e Innovación Grant MTM2010-17162. SLM acknowledges the support of the Mathematics Applications Consortium for Science and Industry (MACSI, http://www.macsi.ul.ie) funded by the Science Foundation Ireland Mathematics Initiative Grant 06/MI/005.

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Authors and Affiliations

  1. Centre de Recerca Matemática, Campus de Bellaterra, Edifici C, Bellaterra, 08193, Barcelona, Spain

    T. G. Myers

  2. MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland

    S. L. Mitchell

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  1. T. G. Myers
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  2. S. L. Mitchell
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Correspondence to S. L. Mitchell.

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Myers, T.G., Mitchell, S.L. A mathematical analysis of the motion of an in-flight soccer ball. Sports Eng 16, 29–41 (2013). https://doi.org/10.1007/s12283-012-0105-8

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  • DOI: https://doi.org/10.1007/s12283-012-0105-8

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