## On the performance of Usain Bolt in the 100 metre sprint

**J.J. Hernández Gómez, V. Marquina, R.W. Gómez**

A theoretical model of the performance of the 100 m world record sprint of Usain Bolt during the 2009 World Championships at Berlin is developed, assuming a drag force proportional to $v$ and to $v^2$. The resulting equation of motion is solved and fitted to the experimental data obtained from the International Amateur of Athletics Federations that recorded Bolt’s position with a LAVEG (laser velocity guard) device. It is worth to note that our model works only for short sprints.

Read more: http://arxiv.org/pdf/1305.3947v1.pdf

Figure 3 shows the effective power (ie rate of useful work generated per unit time). But since Bolt has to overcome the drag as well as perform useful work, his actual power exerted is much higher! Pexerted is just Force times velocity, which is F0=815N multiplied by the velocity in equation 5. Using this, I calculate that his exerted power goes to a whopping 10kW, or 13.4 horsepower, for the last 5 seconds of the race. Isn’t this 13.4 hp statistic a more meaningful and impressive one than the 3.51 hp quoted in the article? Or maybe they should add another line that shows the exerted power next to the effective power, illustrating the regimes of aerodynamic drag and mass acceleration.

Bob LansdorpJuly 27, 2013 at 1:23 am