It is well known that the air density decreases with an increase in altitude, which reduces the aerodynamic drag but also reduces the athletes power output.
r = 1.225 – (PB / 760) – (288.15/T)
The pressure PB follows the well known „barometric altitude equation“:
PB=exp(6.63268-0.112 – H – 0.00149 – H2
where PB is the barometric pressure in mmHg and H is the altitude in km (West 1996), which is shown in the figure on the right. If we assume that cycling records will be attempted at a temperature around 20 oC, the air density is just a function fo the altitude: So it is obvious to go as high as possible, isn’t it?
It’s not so easy, since the athlete’s ability to consume oxygen is comprised with an increase in altitude:
KA = (100.35 – 4.073 – H – 1.434 – H2 + 0.178 – H3 -0.35)/100
where KA is the VO2max expressed as a percentage of VO2max
at sea level (Basset et al. 1999), see figure on the right. So for example at 4 km altitude the athletes VO2max has decreased to about 70% compared to sea level.
Now we just have to modify our basic equations from the
Motion of a cyclist page
PAir = FAir – v = 0.5 -cwA-r-v3
with different values for r at different altitudes, the power output of the athlete PRider has to be reduced in parallel.
The result is the predicted hour record as a function of the altitude. The effect is clearly to see: If one takes the hour record at sea level of ca. 56 km/h, with increasing altitude the speed increases more an more, until a maximum of about 60 km/h is reached for an altitude of about 3700 m. At higher altitudes the velocity decreases again. Similar results (optimal altitude around 3000 m – 3500 m) were found also by other authors. So in principle the velodrome in La Paz (Bolivia) at 3400 m should be perfect. Its interesting that the Mexico City velodrome at 2230 m should already give an advantage of about 3 km/h!
For the UCI hour record the results are comparable, Chris Boardman’s attempt of 49.4 km/h would be around 52 km/h at Mexico City or even around 53 km/h at 3800 m. So, comparing Eddy Merckx at Mexico City and Chris Boardman or Ondrej Sosenka at sea level, this makes their records even more impressive.
Basset et al. 1999: Med Sci Sports Exerc 31:1665-1676
Olds et al. 1995: J Appl Physiol 78:1596-1611
West 1996: J Apll Physiol 81:1850-1854
Taken from http://www.wolfgang-menn.de/altitude.htm