# Staying warm while cycling

With the current cold weather, I got curious — how should you stay warm while cycling?

Clearly, cycling faster requires more energy, heating you up. On the other hand, it also increases heat losses: the air flows around you faster, cooling you down. How does this scale? Does doubling your cycling speed increase or decrease your temperature over time?

It turns out the answer is easy. Let’s consider ourselves as a sphere. The Reynolds number, a dimensionless number estimating the degree to which a flow is turbulent, around a sphere with a particular radius, can be expressed as

We can make some rough approximations here. η is about 10⁻⁵ kg/m/s. ρ is about 1 kg/m³. We can assume v is about 5 m/s (so 18 km/h). The diameter d of a human is a bit questionable, but let’s say it’s about 0.8 meters. At that point, the Reynolds number is about 400.000 — pretty huge!

To actually calculate the heat loss, we can use a Nusselt correlation. We assume Re is large (which seems accurate) so that the constant term is irrelevant — it’s usually <10. Pr (Prandtl — always impossible to type) isn’t a function of the velocity. Therefore, heat losses scale as a function of Reynolds to α, which is 0.5 for a sphere.