Air density in cycling: how much altitude, heat and pressure change your speed

At equal power, thinner air makes you faster: at 300 W and CdA 0.24 m², a flat 40 km time trial takes 55.4 minutes at sea level and 15 °C, and 51.3 minutes at 2000 m. But at 2000 m the rider cannot hold 300 W, and the real gain shrinks to a little under 2 minutes.

What does air density depend on?

Density (ρ) is the mass of air per cubic metre. It rises with pressure and falls with temperature: ρ = p / (R·T), with pressure in pascals, temperature in kelvin and R = 287 J/(kg·K) for dry air. Humidity lowers it only slightly, because water vapour is lighter than dry air. In practice two factors dominate:

• Altitude, which lowers pressure: about 11 % less pressure every 1000 m in the lower atmosphere.
• Temperature: going from 15 to 30 °C at sea level lowers density by 5 %, from 1.225 to 1.164 kg/m³.

Because the aerodynamic term of the power equation is ½·ρ·CdA·v³, 5 % less density is equivalent to 5 % less CdA. That is the same gain as a good skinsuit, just from the weather^1,5.

How much faster do you go at altitude?

The dashed line is the purely physical effect: about 2 minutes less per 1000 m. The solid line adds physiology: maximal oxygen uptake falls almost linearly with altitude in endurance athletes, by around 6 % per 1000 m⁴. The two forces partly cancel, and beyond a certain altitude the gain stops growing.

This trade-off is exactly why so many hour record attempts have been made on velodromes at moderate altitude, and why going much higher does not always pay³. We develop it in the article on how much power the hour record takes.

What about a hot day?

Heat has the same physical effect as altitude on a smaller scale: at 30 °C the example 40 km time trial is almost 1 minute faster than at 15 °C at equal power. But heat also reduces sustainable power, and in long events the physiological hit can outweigh the aerodynamic gain. That is why it pays to plan with the temperature at the actual time of passage, not at the start (see wind and weather by ETA).

How to use it when planning

• Calculate ρ for the time and place of the race, using forecast pressure and temperature. A 0.05 kg/m³ difference between two days changes the expected time as much as an equipment change.
• Compare performances in air density, not in kilometres per hour. Two identical time trials on two different days are not comparable if density changed by 5 %.
• When measuring CdA, record the density. A CdA calculated with the wrong density is off by the same proportion.

Rule of thumb: every 1 % less density is equivalent to 1 % less CdA. At equal power on the flat, that is roughly 0.3 % less time.

What is known and what is not

The physical effect of density is well established, and models that include it accurately predict power measured on the road^1,2. What varies most between individuals is the power loss at altitude: 6 % per 1000 m is an average, and some athletes lose much more or much less, especially without acclimatisation⁴.

Frequently asked questions

Do you ride faster at altitude?

At equal power, yes: the air drags less. But the body produces less power at altitude, so the real gain is smaller than physics alone suggests.

How much does air density change with temperature?

About 0.35 % per degree. Going from 15 to 30 °C lowers it by 5 %.