Q: If I alight from the bus and it is raining, I tend to run for my door, in the belief that I will arrive home less wet than if I walk. However, I have heard that the same number of rain drops will strike me whether I run or walk. Is this really the case?
A: The volume of space swept by the body between bus and door is identical. Therefore, assuming a constant rate of deluge, the number of falling rain drops (below the crown of the head) swept is the same. However, the number of raindrops falling directly on to the top of your head is proportional to the time spent exposed to the rain, so running reduces this component.
But running will deposit all the swept component in a shorter time. This will produce greater apparent wetting since normal evaporative drying has less time to work. So for light showers, with small swept and falling components, walking is probably preferable. We make this complex decision completely unconsciously, while also taking into account the likelihood of the rain becoming harder or lighter, the distance we have to travel, and our ability to run.
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It would be interesting to confirm this theory by filming pedestrians, recording the rate of rainfall, and relating the latter to the point at which the former begins to run.
A: If the walker is in the Lake District, where horizontal rain is common (and always opposes the direction of travel), then it is recommended that they move as quickly as possible because the volume of drops swept out through the rain is now determined by the relative velocity of rain and walker multiplied by the time taken on the journey.
Indeed, if the rain is moving over the ground at speed vr (opposing travel) then the walker, moving at speed vp, will be 1 + vr/vp wetter than in vertical rain by the time they reach shelter. By running to keep up with the rain (defined as vp = 鈭抳r) it is theoretically possible to stay dry.
A: The following (from memory) is attributed to one D. Brown of York:
When caught in the rain without mac,
Walk as fast as the wind at your back,
But when the wind鈥檚 in your face
The optimal pace
Is as fast as your legs can make track.