Abstract
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.
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Acknowledgements
Financial support of the Lions Club, Udine Duomo, Italy, is gratefully acknowledged.
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PEdP and CO analysed the data and wrote the initial version of the manuscript, the final version of which was edited, revised and approved by all authors. JBM, JS, GP, and PS had previously shown that, during a 100 m sprint, forward acceleration and velocity of the centre of mass are linearly related, thus setting the stage on which the present study is grounded.
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Communicated by Jean -Rene Lacour.
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di Prampero, P.E., Osgnach, C., Morin, JB. et al. Running at altitude: the 100-m dash. Eur J Appl Physiol 121, 2837–2848 (2021). https://doi.org/10.1007/s00421-021-04752-y
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DOI: https://doi.org/10.1007/s00421-021-04752-y