Walking in the rain

Factual Questions
1

I remember this question from back in my school days. I can’t remember if it was a trick question, or if there really was a definitive answer.

Let’s say you are walking in a parking lot heading to a store, you are 20 meters from the store entrance. It begins to rain. The rain is steady and can be defined by 200 drops of 10 ml each, equally spaced, in each 1 cubic meter of air. You are fully clothed and wearing a hat, all of your clothes are “super absorbent”, that is, each drop of rain that hits your body will be absorbed by your clothes. Your head, back and front is 1 square meter of area (for this problem, you can be thought of being a box walking erect, where the top of the box has 1/10th the area of the rest of your body).

Now, is there an optimal speed you can walk to get the least amount of rain on your clothes?

2

walk or even better, run as fast as you can.

Which will keep you drier, running through the rain or walking? - answered by cecil adams.

3

I should have known this problem was esoteric enough for the master. :slight_smile:

4

Not to belabor the point, but the answer is pretty easy to get with no calculation or experimentation at all. If you want to consider the drops which hit you in the chest as you move forward, simply imagine the drops are frozen in place, suspended in the air. As you move from start to finish, you sweep up a certain volume of space (your frontal area times the length of your path) basically creating a tunnel through these suspended drops. It doesn’t matter how fast you move; you sweep out the same volume either way. That tells you that the number of drops hitting you in the chest is independent of your speed (to a first-order approximation at least), so you just need to count the drops hitting your head, and the solution to that versus your speed is pretty obvious (slower speed = more time exposed to drops).

5

Mythbusters did a similar experiment, down to wearing rubber suits under the clothes so that perspiration would not add to the weight of the outerwear and found that the running guy got wetter than the walker.

6

That doesn’t sound right. Lets say the walker walked really slowly, so slowly that it takes a week to get there. He’s going to get saturated. If he sprints, he’s going to a scattering of drops over him. The slower he goes, the more time is spent in the rain and the wetter he gets.

7

Well, of course it was a very specific setup, and it was not an especially long distance. I think the deal was that when you’re walking, mostly just the top of you gets wet. But if you’re running, you get wet on the front and back, too, not to mention splashes on your feet and legs. IMHO had it been a rather long distance, then your scenario would affect the outcome.

8

I saw that episode. To say it was less-than-scientific is an understatement. I don’t buy it a bit.

I have always explained to people very similarly to what micco posted.

Now, if you add in wind or some such, then you have something difficult to figure out. No wind: run fast.

9

The Discovery/TLC show “Mythbusters” also tackled the Walk V Run in the Rain question. As I recall, they stated after all of their tests (which if you’ve seen the show, you know is exhaustive) running gave a slight advantage.