Optimizing the breakaway position in cycle races using mathematical modelling
In long-distance competitive cycling, efforts to mitigate the effects of air resistance can significantly reduce the energy expended by the cyclist. A common method to achieve such reductions is for the riders to cycle in one large group, known as the peloton. However, to win a race a cyclist must b...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer London
2018
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| Online Access: | http://hdl.handle.net/1721.1/119427 |
| _version_ | 1811078076759539712 |
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| author | Gaul, L. H. Griffiths, I. M. Thomson, Stuart |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Gaul, L. H. Griffiths, I. M. Thomson, Stuart |
| author_sort | Gaul, L. H. |
| collection | MIT |
| description | In long-distance competitive cycling, efforts to mitigate the effects of air resistance can significantly reduce the energy expended by the cyclist. A common method to achieve such reductions is for the riders to cycle in one large group, known as the peloton. However, to win a race a cyclist must break away from the peloton, losing the advantage of drag reduction and riding solo to cross the finish line ahead of the other riders. If the rider breaks away too soon then fatigue effects due to the extra pedal force required to overcome the additional drag will result in them being caught by the peloton. On the other hand, if the rider breaks away too late then they will not maximize their time advantage over the main field. In this paper, we derive a mathematical model for the motion of the peloton and breakaway rider and use asymptotic analysis techniques to derive analytical solutions for their behaviour. The results are used to predict the optimum time for a rider to break away that maximizes the finish time ahead of the peloton for a given course profile and rider statistics. Keywords: Mathematical model, Air resistance, Asymptotic analysis, Optimization |
| first_indexed | 2024-09-23T10:53:01Z |
| format | Article |
| id | mit-1721.1/119427 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:53:01Z |
| publishDate | 2018 |
| publisher | Springer London |
| record_format | dspace |
| spelling | mit-1721.1/1194272022-09-27T15:43:59Z Optimizing the breakaway position in cycle races using mathematical modelling Gaul, L. H. Griffiths, I. M. Thomson, Stuart Massachusetts Institute of Technology. Department of Mathematics Thomson, Stuart In long-distance competitive cycling, efforts to mitigate the effects of air resistance can significantly reduce the energy expended by the cyclist. A common method to achieve such reductions is for the riders to cycle in one large group, known as the peloton. However, to win a race a cyclist must break away from the peloton, losing the advantage of drag reduction and riding solo to cross the finish line ahead of the other riders. If the rider breaks away too soon then fatigue effects due to the extra pedal force required to overcome the additional drag will result in them being caught by the peloton. On the other hand, if the rider breaks away too late then they will not maximize their time advantage over the main field. In this paper, we derive a mathematical model for the motion of the peloton and breakaway rider and use asymptotic analysis techniques to derive analytical solutions for their behaviour. The results are used to predict the optimum time for a rider to break away that maximizes the finish time ahead of the peloton for a given course profile and rider statistics. Keywords: Mathematical model, Air resistance, Asymptotic analysis, Optimization 2018-12-04T18:45:28Z 2018-12-04T18:45:28Z 2018-05 2018-11-30T04:38:44Z Article http://purl.org/eprint/type/JournalArticle 1369-7072 1460-2687 http://hdl.handle.net/1721.1/119427 Gaul, L. H., S. J. Thomson, and I. M. Griffiths. “Optimizing the Breakaway Position in Cycle Races Using Mathematical Modelling.” Sports Engineering 21, no. 4 (May 10, 2018): 297–310. en https://doi.org/10.1007/s12283-018-0270-5 Sports Engineering Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer London Springer London |
| spellingShingle | Gaul, L. H. Griffiths, I. M. Thomson, Stuart Optimizing the breakaway position in cycle races using mathematical modelling |
| title | Optimizing the breakaway position in cycle races using mathematical modelling |
| title_full | Optimizing the breakaway position in cycle races using mathematical modelling |
| title_fullStr | Optimizing the breakaway position in cycle races using mathematical modelling |
| title_full_unstemmed | Optimizing the breakaway position in cycle races using mathematical modelling |
| title_short | Optimizing the breakaway position in cycle races using mathematical modelling |
| title_sort | optimizing the breakaway position in cycle races using mathematical modelling |
| url | http://hdl.handle.net/1721.1/119427 |
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