Drip… drip… drip…

This morning's downpour got me thinking about a physics professor I had in high school who argued you get just as wet running through the rain as you would at a comfortable walk, except that the former might cause you to get out of breath and/or look silly running around in the rain. Here's how the theory goes, if I remember it correctly.

Consider two people, Walker and Runner, who both have to travel 100 meters through a rain shower falling at a constant rate all along the course. Runner sets out at a dead-on sprint, while Walker takes his time. If the rain is falling at a constant rate it should be thought of as an aqueous medium (i.e. x number of drops per cubic meter) rather than as individual drops. Even though Runner passes through the medium more quickly, he will still pass through the same amount of water as Walker will. Thus, neither of them is "wetter" than the other when they reach their destination.

If you're having trouble keeping up, think of it as driving in the rain on the highway vs. your residential street. You need your wipers on "high" at 60 mph, but only on "intermittent" in your neighborhood, right? Even though the rain is falling at the same rate, you encounter more drops-per-second at higher speeds. Similarly, if you are sprinting through the rain you will run into just as much rain (maybe even more?) as you will if you would just walk.

So far, so good.

However, you may have noticed that when you come in out of the rain your hair is wet, along with the front of your body. The afore mentioned theory accounts for all of the rain you run into, but not that which lands on the top of your head. Even if you're standing still, the raindrops will continue to amass on top of your head at a constant rate.

So, if we really want to know how wet Walker and Runner get, we need to know how long their heads were in the rain.

Let's assume that each of our travelers passes through a gallon of water (for the sake of round numbers) between point A and point B, regardless of their speed. Let's also assume that the rain is falling at a rate of .1 gallons per second per square foot of vertically exposed surface area (i.e. the top of your head). If it takes Runner 10 seconds to get there, he will have received one gallon of rain on top of his head, for a total of 2 gallons on his person. If Walker takes his time and clocks in at 50 seconds, 5 gallons of rain will have fallen on top of his head. Add that to the gallon he "ran into" and his total is 6 gallons of rain.

Since 6 is more than 2, we can conclude that a person does in fact get more wet by walking through the rain than running. Of course, it is worth mentioning that you can reach a point at which you are as "soaked" as you're going to get. In cases such as this, my advice would be to bring along an umbrella.