Suppose you’re walking home on a bright day and suddenly get caught off guard by a downpour of rain. You quickly rummage through what little you brought in search of an umbrella or raincoat, but you’re out of luck. And, so, you're left with a dilemma—should you walk or run in the rain to stay as dry as possible until you reach a safe, shaded space? If you walk, you’ll spend more time in the downpour; on the other hand, if you sprint to safety, it seems like you will run into more raindrops from the side.
For the sake of simplicity, we will be assuming that other variables—such as rainfall duration, total amount of rainfall, and rainfall intensity—are kept constant. The rain your body receives consists of both the droplets that will fall on top of you and the ones you’ll run into. As you move and avoid one falling raindrop, you also move into the path of another raindrop. This means that how fast you walk or run through the rain will not affect the number of raindrops landing on you since you run into another raindrop for every raindrop you move away from. In other words, the amount of rain your top receives per unit of time is constant.
However, we need to consider the number of raindrops that your body runs into when you walk or run through the rain. It seems evident that you reduce the expected number of raindrops you’ll run into per unit of time by standing still. Nevertheless, if you stand still, you’ll spend more time in the rain. So, how do these two variables relate to each other?
We can see that per unit of time, running or walking through the rain will soak you more than just standing would. After all, if you stay still in the rain, the only raindrops that will come into contact with you are the ones that fall onto your top; on the other hand, if you walk or run, you will also have to deal with droplets that you run into. However, walking or running to a specific place does not change the total amount of rain you run into from the side. To make it easier to understand, try imagining a snow plow plowing a snowy road with a set length; regardless of its driving speed, it will plow through the same amount of snow.
Therefore, if you have an end destination in mind, since the expected number of droplets you’ll run into—as well as the expected amount of overhead rain per unit of time—are constant regardless of your speed, we can conclude that you will run into fewer raindrops in total if you run. After all, you’ll be spending less time in the rain, which means less overhead rain.
Thus, over a given time, approximately the same amount of rain will fall onto your top regardless of your speed; moreover, over a given distance, your speed will not affect the amount of rain you’ll run into. Thus, how wet you’ll be can be calculated with the following equation:
Total Wetness = Wetness per second (the amount of rain falling on you) X Time spent in the rain + Wetness per meter (the amount of rain you run into) X Meters traveled.
Although it is impossible to shorten the distance you would have to travel to a given destination without actually moving, walking, or running—you can lessen the amount of time spent in the rain by simply running as fast as you can to your destination. Of course, make sure not to slip since falling onto a wet floor would get you more soaked. To add, you will be able to minimize the amount of rain falling on you by slanting your body in a way that is parallel to how the rain falls.
Therefore, we can conclude that the best way to stay as dry as you can is to run to your destination as fast as possible while keeping the slant of your body parallel to the rain.
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