For road races, we will first discuss the number of jerseys in grand tours [1]: why do we have
three different jerseys (leader, sprinter, climber) in Giro, Vuelta and Tour de France ? We will then
consider more precise questions such as the impact of wind on the cycling speed and propose a
scenario for the origin of echelon formation. Finally, we will show that the optimization of descents
is a variational problem which admits a geometrical solution.

For track races where bikes have no gears, we will focus on the optimal gear ratio and
discuss its dependance on the athlete physiology and on the race distance.

[1] C. Cohen and E. Brunet and J. Roy & C. Clanet, J. Fluid Mech. 914, A38 (2021)