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When it's raining, would you get less wet if you run or more wet?

I think you will get less wet, because rain is coming down in a constant volume and if you run you will have a shorter amount of time you will get less volume

I'm not too sure though, some people say when you run you are running into a more volume of rain because rain is not all coming up to down, it will hit you more horizontally

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If you want to minimize the volume of water you absorb per unit time, you should better stay still (more precisely be at rest with respect to the horizontal components of the raindrops' velocity). However, people usually run because they have a place to hide. The faster they run, the earlier they can hide. If you multiply the water per unit time by the actual time you need to hide somewhere, be sure that it's a rational idea for people to run! ;-) For speeds much greater than the (total) speed of rain, it doesn't matter much whether you speed up even more. –  Luboš Motl Jan 15 '12 at 8:37
    
    
The question physics.stackexchange.com/q/61643 has been marked as a duplicate, but IMO it's not. This question is asking about the case where you want to get hit by the minimum amount of rain before getting to your destination. The other question is asking only about how to minimize the rate at which rain hits you. These are completely different questions with qualitatively different answers. –  Ben Crowell Apr 20 '13 at 16:10
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A funny but correct version of the answer is given by minutephyosics: youtube.com/watch?v=3MqYE2UuN24 –  Dimensio1n0 Jun 21 '13 at 15:30

5 Answers 5

Consider the frame of reference in which the rain is stationary; in this frame, you are moving upward (assuming no wind) at the rain's terminal velocity along with any horizontal motion you make. In this frame, the raindrop at a given point wets you iff you, at some point along your path, occupied that point; the amount of rain that hits you is proportional to the volume of the union of your entire path.

Therefore, you wish to minimize that volume. Since the path must reach from your origin to your destination — let's assume you're moving only horizontally — and has a height equal to the rain's velocity × your travel time, the volume is bigger the slower you move; all else being equal, you are better off running faster.

Another way to reduce the volume is to reduce its cross-section, by turning — i.e. leaning forward, for taller-than-wide bodies — so as to present the smallest area to the rain (mathematically, minimize the area of the projection of your volume in the direction of the rain, in your reference frame). However, for human bodies this is probably of little benefit compared to adopting a posture for faster and safer running.

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If you stand still you get infinitely wet. I think we can safely say that running is better than standing still. If you run at nearly the speed of light, then each drop of rain is effectively frozen in time, and you "carve out" an amount of rain equal to your body's cross-sectional area times the distance you travelled times the density of rain. If you walk at some speed between zero and the speed of light, you not only "carve out" the same volume as if you run at near the speed of light, but you also get "rained on", with a factor that is equal to the density of rain times your (vertical) cross-sectional area times the rate of rain times the time spent in the rain. The answer is that you should run.

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The only situation where running as fast as you can might not minimize the total amount of rain that falls on you is when the wind is from behind you. In that case, if the wind is strong enough, the optimal strategy might be to run only as fast as the raindrops are moving horizontally (if you can!).

Specifically, using the "box approximation" (that is, that a person is shaped approximately like a box) from Qmechanic's link, we can show that running as fast as you can is suboptimal if and only if all the following condition hold:

  • The wind is blowing no more than 90° away from the direction you want to go.
  • When standing still (and facing your destination), more rain hits you from behind than from above and from the side together.
  • You're able to run fast enough that, when running, the rain only hits you from above and/or from the side.

If all these conditions are satisfied, the optimal strategy is to run only as fast as required to satisfy the third condition.

Of course, this analysis assumes not only that you're approximately box-shaped, but also that you don't care on which side of your body the rain falls on. In practice, depending on what you're wearing, you may well prefer rain on your back (or on your head, if you're wearing a hat) over rain on your face, which will affect the optimal strategy (and may well favor slower speeds in some cases).

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Okay, so this is probably not a proper scientific study but the Mythbusters tried this on two separate occasions and found that you are drier when you run.

http://mythbustersresults.com/episode38 http://dsc.discovery.com/videos/mythbusters-running-in-the-rain-minimyth.html

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I expected the mythbusters answer. Accorded to their results, it depends on the direction of the wind. If the wind blows forward, you should run as fast as the rain. But if the rain gkes towards you, you're getting more rain by running. Of course, if the rain blows in every direction, I would say run! The optimal answer would be to follow the wind vector in the horizontal axis so that it becomes equivalent to standing in a perfectly downward rain.

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