Should You Run or Walk Under the Rain?

Which of them is the optimal strategy? Scientifics say run. Mythbusters say walk.

There will be always an experimental case in which walking is the best option, and also the contrary. This is because there is not an optimal behaviour adapted to all the cases, as the amount of water that reaches your body depends in a huge amount of factors: your complexion, the raindrop size, wind-speed, the angle between your path and the wind direction, the fact that you make splashes in your way home... each one of the infinite combinations of these factors lead to a different optimal solution, and therefore there is not an absolute conclusion. However, it has been demonstrated that in most of the cases, the faster is the better, and this is the solution that we will prove here theoretically.

Assuming the most basic situation, a straight path without stops, the answer is simple. If you put yourself out of the range of a drop, you are simultaneously entering into the range of the next one, and therefore we can assume that the flux of water over your body can be considered constant, no matter your velocity. To better understand this, you can imagine a field of permanent water drops, and the floor and yourself moving upwards along the rain. The figure that your body would describe in its movement along the rain can be approximated as the volume of a parallelepiped.

As its volume does not depend on the inclination, it does not matter the velocity at which you are moving. Of course, if you do not move at all, there will be no rain affecting towards you, but this strategy will not help you to get to your house. Then, assuming that you have to make a displacement, it does not matter the velocity at which it happens. A good everyday example, we can take a snow plow, that removes the same amount of snow from the road(per unit area), no matter its velocity. The total amount of water that affects you can be computed as the amount of water over you by the time spent over the rain, plus the amount of water per meter that you are surpassing multiplied by the number of meters that you cross. This calculation does not take into account the speed at which you move, and for a fixed path, we can only reduce the quantity by reducing the amount of time spent under the rain. Therefore, you must scape the rain as fast as possible!