Running at altitude: the 100-m dash.

Abstract

Theoretical 100-m performance times (t100-m) of a top athlete at Mexico-City (2250m a.s.l.), Alto-Irpavi (Bolivia) (3340m a.s.l.) and in a science-fiction scenario "in vacuo" were estimated assuming that at the onset of the run: (i) the velocity (v) increases exponentially with time; hence (ii) the forward acceleration (af) decreases linearly with v, iii) its time constant (τ) being the ratio between vmax (for af= 0) and af max (for v = 0). The overall forward force per unit of mass (Ftot), sum of af and of the air resistance (Fa=k v2, where k = 0.0037 J·s2·kg-1·m-3), was estimated from the relationship between af and v during Usain Bolt's extant world record. Assuming that Ftot is unchanged since the decrease of k at altitude is known, the relationships between af and v were obtained subtracting the appropriate Fa values from Ftot, thus allowing us to estimate in the three conditions considered vmax, τ, and t100-m. These were also obtained from the relationship between mechanical power and speed, assuming an unchanged mechanical power at the end of the run (when af≈0), regardless of altitude. The resulting t100-m amounted to 9.515, 9.474, and 9.114s, and to 9.474, 9.410, and 8.981s, respectively, as compared to 9.612s at sea level. Neglecting science-fiction scenarios, t100-m of a world-class athlete can be expected to undergo a reduction of 1.01 to 1.44% at Mexico-City and of 1.44 to 2.10%, at Alto-Irpavi.