Do You get Wetter if You Run or Walk in the Rain?

there is a common sense semi scientific view here puzzles. One website demonstrates convincingly that you are better off running in the rain, that the effect of the reduced time outweighs the effect of the speed.

wow! thanks for that answer, anon66902! A student asked me this question in class and I felt unable to answer. Your explanation is much clearer to me than the article bit. I still contend, as I did in class, that rate of impact probably has more to do with how wet one will get. however, my student wanted to know about total number of raindrops met, which perhaps is a slightly different question.

interesting. a surprisingly complicated question after all!

anon66902 has given this way more consideration than it deserves.

Who cares? If I go out for a run, I'm going to sweat more than it is raining, so it doesn't matter.

I'll have to take a look at that magazine article. But in the meantime, let's just examine the case of zero winds peed, and let's model a person as a rectangular prism (a tall box) that moves in a direction perpendicular to one of its vertical surfaces.

There are two ways that a person gets wet in this model: from the top, and from the surface facing the direction of motion (the front).

1. From the top. Wetness from the top is directly proportional to time of exposure, which is inversely proportional to velocity. So, someone standing still in the rain (velocity=0) will get infinitely wet on their top surface.

And someone who zooms for cover faster than a lightning bolt (velocity=infinite) will not get wet at all on top. In between these two boundary cases, the function is monotonic (how do we know that?), meaning that it is always the case that the faster you travel, the less wet you'll become on top.

2. From the front. This is where the result might be surprising: If you're moving at all, the front face will accumulate the same wetness regardless of your speed. This is trickier to demonstrate.

First, the front face of the rectangular prism, in motion in a straight line from starting point to shelter, itself describes a long rectangular prism: its four horizontal edges are the length of the distance from origin to shelter, and its end faces are the same as the person-model's front face.

(You might imagine holding up a rectangle of cardboard, moving it from one place to another, perpendicularly to its face, and then considering how you just traced a three-dimensional box through the air. That's the rectangular prism we're talking about now.)

Anyway, this prism contains a certain amount of water, namely, Volume x Density_of_rain. This quantity of water is constant over time: when rain falls through the bottom of the prism, rain enters the top at the same rate.

Now, the amount of water in this prism is precisely the water you'll encounter on your front face as you move to shelter. If you move infinitely fast, you'll obviously encounter all the water in an instant. But because the density of the water in this prism is constant, it actually doesn't matter how fast you move.

All that matters is that you're moving through a constant density over a given distance. You will encounter the same amount of material regardless of speed. (So, the statement in the official answer above, that, "The walker might benefit slightly from not running into the raindrops ahead of her/him" is actually incorrect.

If you're moving slowly, you encounter *fewer* raindrops on your front face, but not *none*. Then multiply that by how much longer it takes to reach shelter, and you've encountered the same amount of rain on your front face as if you'd bolted.)

Conclusion. Now, let's put the top and the front faces together. As we saw, the front face encounters the same amount of water regardless of speed. And the top face accumulates monotonically less water the less time you spend in the rain. So the answer is, run as fast as you can, because the more slowly you go, the wetter you'll become.

Assumptions and Limitations.

1. As we said earlier, this analysis is only for zero windspeed.

2. We only examined the case of running for shelter in a straight line. (I doubt the general case would be much different, but doubt is much different than proof!)

3. Rain was modeled as density. This implicitly assumes that that the water is evenly distributed throughout a given volume. Mist comes close to this ideal, but raindrops are further off.

In the extreme case, say one raindrop per cubic meter, you could run around dodging the individual raindrops, defying this entire analysis. But in the normal case of rain, at most the effect on this analysis would be that it makes our smooth functions a bit bumpy.

For instance, the relationship between wetness on top and time spent in the rain would not be a perfect line, but rather a bumpy curve that is very close to linear. So that assumption is not much of a problem.

4. Finally, this model does not account for airflow. If you drive down the highway while it's snowing, you'll notice that little snow lands on your car. That's because the movement of air around the car carries the light snowflakes with it.

Raindrops are often heavy enough to make the effect negligible, but that might not be the case for a fine mist. However, such an effect would only enhance the benefit of moving quickly, so it would not change our conclusion here.

When one brings in wind speed, what really is happening is that the distance one travels in relation to the column of rain changes. If you move at the same speed as the rain, you can travel across country, but you are traveling zero distance through the rain.

I love this question. I have thought about it and worked on understanding it for years on-and-off. The most interesting thing about this problem is that if you pose it to your friends and family, they look at you like you are crazy because the answer is "obviously" to run. However, when you begin to point out the subtleties of the problem, they very quickly get a confused look on their faces.

One thing the analysis above does not take into account is wind speed. In November 1973 in Mathematics Magazine, they take wind speed into account and this really shakes the problem up.

In summary, if you can run the speed of the wind, you will get the least wet. However, if you can run faster than the wind, do it because you will get less wet.

I hope I summarized the conclusion of that paper correctly. .. it is not as straight forward as one would think.