The Hour Record at Altitude
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. In a recent paper by P. D. Heil the author gives a nice overview about
this topic, for details look
at his paper at:
Heil,
D. P. European Journal of Applied Physiology, Vol.
93, 56, 547  554

The density of air varies with barometric pressure and
temperature, both of
which decrease with an increase in altitude (Olds et al. 1995b).
r = 1.225 ×
(P_{B} / 760) × (288.15/T)
The pressure P_{B} follows the well known "barometric altitude
equation":
P_{B}=exp(6.632680.112 × H 
0.00149 × H^{2})
where P_{B} 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 ^{o} C, 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:
K_{A} = (100.35  4.073 × H  1.434
× H^{2} + 0.178 × H^{3} 0.35)/100
where K_{A} is the VO_{2max} expressed as a percentage of
VO_{2max}
at sea level (Basset et al. 1999), see figure on the right. So for example at 4
km altitude the athletes VO_{2max} 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: P_{Air }= F_{Air}×v
= 0.5 ×cwA×r×v³
with different values for r at different
altitudes,
the power output of the athlete P_{Rider } 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. 

References:
Basset et al. 1999: Med Sci Sports Exerc 31:16651676
Olds et al. 1995: J Appl Physiol 78:15961611
West 1996: J Apll Physiol 81:18501854 
