Running at altitude: the 100-m dash

Purpose Theoretical 100-m performance times (t(100-m)) of a top athlete at Mexico-City (2250 m a.s.l.), Alto-Irpavi (Bolivia) (3340 m 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 (a(f)) decreases linearly with v, iii) its time constant (tau) being the ratio between v(max) (for a(f) = 0) and a(f)(max) (for v = 0). Methods The overall forward force per unit of mass (F-tot), sum of a(f) and of the air resistance (F-a = k v(2), where k = 0.0037 J center dot s(2)center dot kg(-1)center dot m(-3)), was estimated from the relationship between a(f) and v during Usain Bolt's extant world record. Assuming that F-tot is unchanged since the decrease of k at altitude is known, the relationships between a(f) and v were obtained subtracting the appropriate F-a values from F-tot, thus allowing us to estimate in the three conditions considered v(max), tau, and t(100-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 a(f) approximate to 0), regardless of altitude. Results The resulting t(100-m) amounted to 9.515, 9.474, and 9.114 s, and to 9.474, 9.410, and 8.981 s, respectively, as compared to 9.612 s at sea level. Conclusions Neglecting science-fiction scenarios, t(100-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.