How fast should you run when it is raining?

Currently the gray days of autumn seem to be right around the corner and the water pouring from the sky is much too cold to be enjoyable. So most people just want to get through the rain to some dry place. Our instinct tells us to run as fast as we can to avoid getting wet. But is this intuition correct? Do you really get less wet if you run at your maximum speed?

The short answer is no. But as always the long answer is more complicated and while this might not be cutting edge research in physics it presents a useful training problem for undergraduates and has thus been discussed in the literature. So naturally different answers can be found depending on the assumptions the authors made.

The first assumption one has to make is the shape of the body that is moving in the rain. While it is usually assumed that this does not influence the general answer a recent paper showed that it actually does [1]. Borrowing methods from electrodynamics more complex body shapes could be addressed in this paper and the value of the optimal velocity was compared. That is if an optimal velocity even exists, i.e. it is not the best strategy to run as fast as you can.

Not surprisingly the answer does not only depend on the shape of the body but also on the direction from which the rain is coming. If the rain is coming straight from the back, for example, an optimal velocity always exists and its value does not even dependent on the body shape. For other direction the answers vary and no general rules seem to exist.

Another restriction that may apply is the assumption of a rigid body motion. While it is convenient to calculate a rigid cylinder floating effortlessly through the rain humans are not rigid, especially while running. No attempt has so far been made to include this into the models.

So if the rain is not coming straight from the back you might need to do some further calculations to figure out what the best speed is for your body shape and running style. But as a final tip make sure that you do the calculation in a nice and dry place and only then venture out into the rain. If the weather catches you off guard, just take your chances and run to the next cover.

Stephan Koehler

Read more:

[1] F. Bocci, Whether or not to run in the rain , Eur. J. Phys. 33 (2012) 1321–1332