> So, if you are crossing an open space that is 50 feet wide and it is raining steadily, will you get more water on you if you walk across or if you run?

The answer is there's no easy answer. Is the rain falling straight down, or at an angle? How much rain per square inch of ground per second is falling? What are your measurements? There are two separate problems here.

If rain is falling straight down, you get the least amount of rain per second by standing still. Of course, if you're standing still, you're not getting across the open space. The faster you move, the more rain you'll hit, because you're still getting the same amount of rain falling on you from above, but now you're also getting the rain you run into from the side. (This is why your measurements are important -- you need to know what the area of exposure on top is, and you need to know what the area of exposure is to the rain you're running into from the side -- which is NOT a measure of your visible surface area from the horizontal but rather at some angle elevated along the vertical, the angle being closer to the horizontal the faster you go. [The logical extreme is when you are running infinitely fast and hit ONLY rain from the side and NONE from the top, in which case your area visible from the horizontal is what you want to measure.]) I suspect solving the problem requires some sort of limit, where you find out what the minimal value of a ratio is, in which you trade off added rain that hits you from speeding with the lesser time you take *in* the rain by moving fast.

If the rain falls at an angle, you do NOT get rained in minimally by standing still. If the rain is angled such that it hits your back, the way you can get the least rained on is by moving at some speed forward (the exact speed being determined by the angle of rainfall and your measurements). Consider the extreme case -- rain falling horizontally, from directly behind you. You can minimize the rain that hits you to nothing if you run at the speed of the rainfall. And, since there is no vertical movement of the rain AT ALL, you can even go faster than the speed of the rainfall without getting any extra rainfall from running into rain from the side. When there is an angle to the rainfall that is neither wholly vertical or wholly horizontal, there's a set speed that minimizes how wet you get, and you couldn't go slower or faster without getting more wet.

This is NOT to say, however, that this is necessarily the speed you should walk. That set speed only determines how wet you get PER SECOND. The speed you travel to get across the open space while getting minimally wet would be greater than or equal to this speed, because moving faster means you spend less time in the rain.

My hunch is that the more angled the rain behind you, the faster you want to walk. I also think if the rain is angled *toward* you, you'd want to walk faster than if it were falling straight down. Consider the extreme. If the rain is falling horizontally toward you from the front, the amount of rain you hit depends entirely on how long you're in it. If you run infinitely fast, you'll get less wet than if you run any slower. But to stay minimally wet per second in such rain, you'd have to run backwards, and that doesn't help you get where you're going.

I'll let gremlinn take it from here.