# Running in the Rain

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To stay driest, is it better to walk or run in the rain? The conventional wisdom was conveyed in a limerick by Matthew Wright in *New Scientist* magazine in 1995: "When caught in the rain without mac, walk as fast as the wind at your back. But when the wind's in your face, the optimal pace is as fast as your legs will make track." But this advice is only partially correct. Yes, in the absence of a tail-wind, running flat out is best. But "as fast as the wind at your back" is misleading. It is the best pace for box-shaped travelers provided the tail-wind is sufficiently strong. But if the tail-wind is too weak, or if you are a more well-rounded individual (in appearance, at least), then your optimal pace *exceeds* that of the tail wind.

Contributed by: Bruce Torrence (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The "dimensions of traveler" controls set the lengths of the semi-axes of an ellipsoidal traveler, and half the lengths of the sides of a rectangular-solid traveler. The area of the front face of a rectangular-solid traveler is therefore , while the corresponding projection for an ellipsoidal traveler is . If the traveler moves one unit forward at super-speed, the rain region approaches a horizontal cylinder whose volume approaches these values. Hence total wetness is asymptotic to the red line shown.

Complete derivations of the wetness functions can be found here:

D. Kalman and B. Torrence, "Keeping Dry: The Mathematics of Running in the Rain," *Mathematics Magazine*, 82(4), 2009.

Wright's limerick was first published here:

M. Wright, "Letter to the Editor," *New Scientist*, 1960, 1995 p. 57.

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