Running in the Rain

shape of traveler

rectangular solid

ellipsoid

dimensions of traveler

x

0.5

y

1

z

3

components of rain velocity

tail wind SubscriptBox[\(w\), \(\(\)\(t\)\)]

5

cross wind

w

c

0

vertical speed of rain

12

the traveler	optimal pace shown in green (if finite)

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.

This Demonstration calculates total wetness for box-shaped and ellipsoidal travelers moving in a straight line in prescribed rain conditions. The wetness measure is simply the volume of the rain region, the region in space containing all the drops that will strike the traveler as he moves a distance of one unit in the positive

x

direction (his direction of travel is indicated by the large arrow in the left frame). Total wetness is graphed in the right panel as a function of the traveler's speed, and the optimal speed of travel is shown in green provided that it is finite.

It is interesting to note that for ellipsoidal travelers, the optimal pace is very sensitive to changes in the

x

dimension of the traveler. Chubby travelers seem better served by running faster. For rectangular travelers, minor perturbations in the

x

dimension make no difference whatever.