Should you walk or run in the rain?

Question

Rain is falling straight down at a steady rate and you must cross a stretch of open ground of fixed length. You are roughly box-shaped: a flat top (your head and shoulders) and a flat front. Should you walk or run to minimise the total amount of rain that hits you? Analyse the top and the front separately, then combine. What changes if the rain is blowing towards you, or from behind?

Accepted Answer

Run. In vertical rain, the rain on your head shrinks the faster you go, and the rain on your front does not change. Rain on top. Your top catches rain at a fixed rate per second while you are outside. The total is that rate times the time outside, and the time is distance divided by speed. So the faster you go, the less lands on your head. This part says run. Rain on your front. Picture the rain frozen in the air as a cloud of droplets. As you move forward, your front sweeps out a box of air whose volume is your frontal area times the distance travelled, and you collect every droplet in that …

Should you walk or run in the rain?

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