This Tuesday, I rolled out of bed at 8:50 a.m. for a 9 a.m. class, forgot to look out the window, and found myself on the sidewalk in front of my apartment in the pouring rain, knowing that I was going to look like I had swum to Schaffer Hall. I thought about sprinting across the quad, but had nowhere near enough sleep or breakfast to seriously consider the option. Would running have kept me drier in the rain? A surprising amount of scientific debate exists on this topic.
In pursuit of a definitive answer to the question, people have gone out in the rain in water-absorbent clothes and weighed the water they soaked up, or covered themselves in construction paper and counted the number of raindrops that landed on the pages.
In an episode that aired in 2005, the MythBusters tackled the issue by setting up a rain corridor with a controllable level of “rain,” put on pre-weighed clothes and wetsuits, running back and forth in the corridor, and then weighing their clothes again.
They concluded that if you’re only travelling a hundred yards, you do stay drier by walking. But by that logic, should you plod through the rain, or, going to the extreme, stand still as soon as you feel drops hit?
We can reasonably assume that how wet you get is proportional to the heaviness of the rainfall and the speed at which you’re travelling. (What matters here is your speed relative to the rain’s speed — if you’re standing still and a strong wind is blowing rain towards you, you’ll get wetter than if the rain is falling straight down.)
In fact, according a column for BBC News written by Nick Allen, the rate at which you get wet is equal to the integral of the density of the rain multiplied by your speed relative to the rain, taken over your body’s surface area.
However, it’s pretty difficult to figure out the surface area of a human body. In order to simplify the equation enough to find a solution, we need to make a few less reasonable, but more useful, assumptions.
Let’s assume that raindrops fall straight downwards and that you’re walking or running perpendicular to the direction they’re falling. Let’s also assume that the human body is shaped like a rectangular box, sort of like SpongeBob if he didn’t have any limbs. This makes it very easy to calculate the surface area.
The amount of water your head, or the top side of the rectangle, collects is equal to the speed the rain is falling down multiplied by the top side’s area. The amount of water your chest, or the front side of the rectangle, collects is equal to the speed you’re travelling through the rain multiplied by the front side’s area.
The total amount of water you (or limbless SpongeBob) collect during a journey is then equal to the sum of the water your head and chest collect multiplied by the rain’s density and the time your spend in the rain.
Out of all these variables, the one you probably have the most control over is the speed you’re travelling through the rain. The faster you run, the wetter you get because you’re going through a greater distance and collecting more water. By decreasing your speed, you decrease the amount of water your chest collects and your total wetness.
However, the math only applies if you spend the same amount of time running as you would walking. In other words, if you find yourself in a rainstorm with no shelter in sight, you’re better off standing still than moving at all.
But if you are heading towards someplace warm and dry, your instincts to book it are right. If your choice is between running and walking the same distance, you’re considerally better off running as fast as you can. In the above equation, the time you spend in the rain will be replaced by the distance you’re traveling divided by your speed. This fraction gets smaller the when your speed increases.
To summarize, if you’re stuck in the middle of nowhere with no shelter or umbrella, you’re better off standing still and waiting for the storm to pass. If you’re heading towards shelter, you’ll be drier the faster you run.
Of course, if neither walking nor running in the rain seem like appealling options, you could always try singing.