The effects of wind and altitude in the 400-m sprint

In this paper I use a mathematical model to simulate the effect of wind and altitude on men's and women's 400-m race performances. Both wind speed and direction were altered to calculate the effect on the velocity profile and the final time of the sprinter. The simulation shows that for a constant wind velocity, changing the wind direction can produce a large variation in the race time and velocity profile. A wind of velocity 2 m?·?s^?1 is generally a disadvantage to the 400-m runner but this is not so for all wind directions. Constant winds blowing from some directions can provide favourable conditions for the one-lap runner. Differences between the running lanes can be reduced or exaggerated depending on the wind direction. For example, a wind blowing behind the runner in the back straight increases the advantage of lane 8 over lane 1. Wind conditions can change the velocity profile and in some circumstances produce a maximum velocity much later than is evident in windless conditions. Lower air density at altitude produces a time advantage of around 0.06 s for men (0.07 s for women) for each 500-m increase in elevation.