Pietro E di Prampero1,2, Cristian Osgnach3, Jean-Benoît Morin4, Jean Slawinski5, Gaspare Pavei6, Pierre Samozino7. 1. Department of Sport Science, Exelio SRL, Udine, Italy. 2. Emeritus Professor of Physiology, University of Udine, Udine, Italy. 3. Department of Sport Science, Exelio SRL, Udine, Italy. cristian.osgnach@gmail.com. 4. Laboratoire Interuniversitaire de Biologie de La Motricité, Univ Lyon, UJM-Saint-Etienne, 7424, F-42023, Saint-Etienne, EA, France. 5. French Institute of Sport (INSEP), Laboratory Sport, Expertise and Performance, 7370, Paris, EA, France. 6. Department of Pathophysiology and Transplantation, University of Milan, Milano, Italy. 7. Laboratoire Interuniversitaire de Biologie de La Motricité, Univ Savoie Mont Blanc, 7424, F-73000, Chambéry, EA, France.
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.
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.