Running at altitude: the 100-m dash

Eur J Appl Physiol. 2021 Oct;121(10):2837-2848. doi: 10.1007/s00421-021-04752-y. Epub 2021 Jun 26.


Purpose: Theoretical 100-m performance times (t100-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 (af) decreases linearly with v, iii) its time constant (τ) being the ratio between vmax (for af = 0) and af max (for v = 0).

Methods: 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.

Results: The resulting t100-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, 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.

Keywords: Acceleration; Air resistance; Altitude; Mechanical power; Sprint.

MeSH terms

  • Acceleration
  • Altitude*
  • Athletes
  • Athletic Performance / physiology*
  • Energy Metabolism / physiology*
  • Gravitation
  • Humans
  • Running / physiology*