When it's cold out and you didn't dress for the weather and you're far from shelter, you
have a crucial decision to make: should you run (or ski) to try to warm up, or go slow
and avoid the cooling effects of wind? When it's cold out and you're not moving,
the heat you lose goes to heating up the air around you, forming a slightly warmer protective
layer so you don't cool off as quickly. But if you're moving (or if it's windy), you’re
being exposed to some amount of fresh, new, cold air – more of it the faster you go.
You’re literally running away from the air you warmed and so you cool off faster than
if you stayed put. Though once you're going fast enough, the
protective layer of air will be pretty much entirely gone and you'll basically lose heat
at the same rate regardless of how fast you're running.
Now, when humans run, we also generate a fair amount of heat inside our bodies. In fact,
we produce a roughly constant amount of heat per kilometer traveled, so the faster you
go, the more heat you generate any given minute. Because the heat generated by running has
a steady increase, while your protective layer of warm air goes away quickly at low speeds,
it turns out that there's a kind of "forbidden range" of speeds where it's not worth walking,
or even running slowly, since you’d lose less heat standing still.
So what's the minimum speed where the heat you generate running finally balances out
the additional heat you lose due to air movement? Well, using some estimations for the surface
area and energy generation of an adult human running naked and the effects of wind on heat
loss, I found that when it's freezing outside , you need to be able to run roughly a 5 minute
mile to be better off moving than staying put. And faster, if it’s colder out. And
this wouldn’t even mean you're not losing heat – it's just the point at which you
lose less heat running than you do standing still.
Now if that sounds like a challenge, don't worry. All you need to do is put on some clothing
– like, enough that you're only losing half as much heat as a naked person – and a
15 minute mile (basically a brisk walk), will do just fine.
So, either stay put, or wear appropriate winter clothing, or run naked very very fast through
the snow.