If you run in the rain, you get exposed to rain for a smaller interval of time than walking, however you also maximize the body surface that directly comes into contact with the rain droplets. Bocci take on the issue comes with a twist as he used simplified geometrical bodies, when previous attempts assumed people to be thin sheets or upright, rectangular boxes.
From his paper, which you can read here in its entirety, complete with equations and thorough statements, the author derived these conclusions:
- “For rain falling vertically, the best strategy is to run as quickly as possible. The same is also true for motion into the wind.”
- “For motion downwind, there may be an optimal speed, which equals the component along the direction of motion of the wind velocity. This happens only if the ratio between the cross-section of the body perpendicular to the motion and the horizontal one is large enough; otherwise, the best choice is again to run at the maximum speed one can reach.”
In short, the answer depends on the shape and orientation of the moving bod, as well as the wind direction and intensity. You can say that in the majority of cases, when rain is joined by little to no wind, it is better to run if your intentions are of staying as dry as possible.
Bocci’s paper was published in the journal European Journal of Physics.
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