I think there is a simpler way to picture this. Imagine a volume of water suspended in the air - the height and width is the person's cross section, and the len

I think there is a simpler way to picture this. Imagine a volume of water suspended in the air - the height and width is the person's cross section, and the length is distance to be travelled. All of that water is going to get onto you regardless of how fast you travel. So speed is not relevant there. But for the water hitting the top of the cube, it gets wet only with respect to time, and not to speed. Conclusion: if the rain is falling straight down, it always makes sense to run.