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On technical considerations of velodrome track design

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Abstract

A novel approach to velodrome track design is presented. The mathematical model uses differential geometry to form a three-dimensional ruled surface. The surface accounts for the safety zone, blue band, and track region, the latter of which is comprised of three segments: straight lines, the arcs of circles, and connecting transition curves. Following a first-principles approach, the general expressions are derived from the Frenet–Serret relations, as a function of the banking and curvature profiles, lengths of curve segments, and turn radius of the bends. Particular solutions to the design problem are obtained using a least-squares minimization of an objective function, within the framework of numerical optimization. Symmetric and asymmetric designs are presented to demonstrate the versatility of the approach. The resulting formulation may be used to design velodrome tracks of any UCI Category and track geometry specification.

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Notes

  1. We detail the pertinent regulations that restrict the velodrome surface design; the complete list of technical specifications are listed in [17, Chapter VI].

  2. For readers intersted in model-based optimization strategies, we recommend the textbooks of [26,27,28].

  3. For instance, although we do not consider such features in this article, the banking profile could be designed to have portions with constant inclination angle.

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Acknowledgements

I wish to acknowledge the following professors, without whom this article would not be possible: Michael A. Slawinski, for his unwavering mentorship and for fostering an enthusiasm for mathematical modelling; Len Bos, for sharing his mathematical rigour, to which I strive continually to emulate; and Ivan Booth, for sparking an interest in differential geometry and its infinite applications. In addition, I would be remiss not to acknowledge the reviewers of this article, whose insightful comments enhanced greatly the practicality of the formulation.

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  1. Department of Earth Sciences, Memorial University of Newfoundland, 40 Arctic Avenue, St. John’s, NL, A1B 3X7, Canada

    Theodore Stanoev

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12283_2023_425_MOESM1_ESM.pdf

Supplementary file 1 Online supplementary material accompanies this article: Online Resource A quantifies the curvature along curves of constant ruling; Online Resource B demonstrates that parameterizing the inclination along a curve of constant ruling leads to inconsistent angles (pdf 203 KB)

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Stanoev, T. On technical considerations of velodrome track design. Sports Eng 26, 36 (2023). https://doi.org/10.1007/s12283-023-00425-5

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