Sunday, 12 September 2010

deriving in the rain

If you are caught in the rain, will you get wetter running to shelter, walking, or standing still?

This is the sort of thing I think about for the half-second it takes me to gear up for the dash to shelter when I'm caught in the open by one of Toronto's sudden downpours.

Standing still, I present a relatively small surface area to the falling rain -- in a vertical downpour, just my head and shoulders. When I move through the vertical rain, I collide with water droplets that would otherwise have passed me by -- but the same amount of water should strike my top surfaces (I move out of the paths of some droplets, but into the paths of others). Standing still wins in the first approximation.

On the other hand, I'll be in the downpour for a shorter period of time, so fewer droplets will strike my head after all. Running wins in the second approximation.

Jesse, of The Virtuosi derives mathematical support for the running side of things, concluding that "if you are Usain Bolt, you can reduce how wet you get by almost a factor of two by going from a meander to a sprint!"


Anonymous said...

I'm going to be overthinking the next time it rains. I suspect I'll find a solution after I get totally drenched and the sun peeks through the clouds.

Anonymous said...

This is way late but the Mythbusters tackled this one twice. Once they created an artificial rain environment and found that walking was superior for a brief distance, but they re-visited it with more runs spread out over lots of random natural showers over months and found running superior. Some scientists had previously found running to be superior based on a single trial (I believe that is published).

Probably for most scenarios running is superior but it may be that certain special cases make walking superior.