Because you are generally taller than your surface area from above, running forwards will sweep a path collecting all the rain falling in an area matching your frontal area.
Walking slowly, you just pick up the rain that would be falling onto your head and shoulders, the surface area from above.
There’s a lot more variations on this, angle of the rain, how much, how fast you are going to be moving (eg standing still isn’t going to be smart)
Mythbusters did a test on this with people wearing paper suits that were weighed afterwards to see how much rain they soaked up.
When you’re walking, most of the rain falls on your head and shoulders and some by walking into it. When you’re running the rain falls on your head, shoulders, but you’re also running into the rain ahead of you. Since you’re running faster than you’re walking, you’re going to absorb a lot more rain by running into it even though the overall time spent in the rain is reduced.
[Here’s the Mythbusters episode](https://www.youtube.com/watch?v=HtbJbi6Sswg) that /u/AverageNeither682 was referencing.
Consider a thought experiment where it’s a steady drizzle that is falling **perfectly straight down**. The rain you collect is based on the surface area of your head (*collecting rain from above*) and the surface area of your front (*as you move forward into the drops falling in mid air*).
**Your front will collect the same amount of rain no matter what your speed is**. If your speed is zero, your front collects no rain, but you make no progress. If your speed in infinite, you collect every drop suspended in the air between you and your destination, Your moving forward is just integrating the average volume of rain between you and your destination.
But the rain that falls straight onto your head varies by how long you spend in the rain. That you can control.
Since you can’t control for the rain you will collide with in front of you (*your speed will not matter*), but you can control how long you are there for the top of your head to have drops fall on to it, **you should go as fast as you can**.
Edit to add tl;dr
tl;dr There is always about the same amount of rain in the volume of space between where you start and your destination. **You will eventually pass through all that space**. You will always collect the same amount of water in the front, no matter what your speed. But you can control the amount of rain on your head. Run.
https://www.sciencefocus.com/planet-earth/do-you-get-wetter-if-you-run-or-walk-in-the-rain/
> Whether you walk or run, you’re going to get wet, but there is an optimal speed to avoid the worst of it.
> People still argue about this question, even though Harvard mathematician David Bell worked out the answer back in 1976. His answer was that if the rain is falling vertically, or there is a wind blowing in your face, you should run – and the faster you run, the less wet you will get over the same distance. If the wind is blowing from behind, you should still run, but now there is an optimum speed at which you will get least wet – the speed of the wind
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