As a result, a conflict emerges: if the cyclist breaks away too soon then they risk fatigue effects kicking in before the finish line and being caught by the peloton. However, the cyclist will not be able to sustain this extra force indefinitely, with fatigue effects coming into play. In doing so, the rider must provide an additional pedal force to offset the effects of air resistance that would otherwise be mitigated by riding in the peloton. However, if a cyclist wishes to win a race or a Tour stage then they must decide on when to make a break. With energy savings of up to around a third when cycling in the peloton compared with riding solo , it is energetically favourable to stick with the main field for the majority of the race. The main reason for this behaviour is that cycling in a group reduces the air resistance that is experienced by a cyclist. Long-distance cycle races, such as a stage of the Tour de France, typically follow a prescribed pattern: riders cycle together as a main group, or peloton, for the majority of the race before a solo rider or small group of riders makes a break from the peloton, usually relatively close to the finish line. In addition, mathematics can provide a fundamental underpinning for the race dynamics and strategy, to complement the results of more sophisticated analyses such as computational fluid dynamics simulations.

Improvements in performance typically require the combined expertise of a wide range of specialists, including sports scientists, engineers, and dieticians. For example, the 2018 Tour de France was won by a margin of less than one minute for a total race time of more than 86 h . 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.Ĭycling science is a lucrative and competitive industry, in which small advantages are often the difference between winning and losing. 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. On the other hand, if the rider breaks away too late then they will not maximize their time advantage over the main field. 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. 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. A common method to achieve such reductions is for the riders to cycle in one large group, known as the peloton.

In long-distance competitive cycling, efforts to mitigate the effects of air resistance can significantly reduce the energy expended by the cyclist.

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