Do you get less wet if you run in the rain?

[Jarrod Cook]

It's a question that's been around for a long time. Now, someone has tried to prove using calculus what you should do that will get you less wet. The link is here: http://news.bbc.co.uk/1/hi/magazine/4562132.stm

I thought it was an interesting article. The equations he came up with suggest that you get less wet if you don't run in the rain, unless there is a nearby shelter - in which case you should run to it. The author of this makes several "assumptions" which aren't ideal. But it's an interesting article anyways.

 

[Dan Cook]

They did this on Mythbusters and found out you get wetter if you run.

 

[Jarrod Cook]

Yeah, that's what the calculations say if you look at it. Either walk if you aren't close to a shelter, or run straight to one if it is nearby.

 

[Skip Talbot]

So what is the ideal speed? If you get less wet when you walk then it seems that the slower you travel the less wet you get... so why not just stand still in the rain?

 

[David Wolfson]

That's true. You get least wet standing (or, precisely, moving at the same horizontal velocity as the wind is driving the rain) for a period of time than you do running for the same period of time.

 

[Jeff Snyder]

Originally posted by David Wolfson
That's true. You get least wet standing (or, precisely, moving at the same horizontal velocity as the wind is driving the rain) for a period of time than you do running for the same period of time.

Not true. If your body "advected" with the rain, then you'd only be as wet as the amount of water you displaced. However, rain has a vertical component of motion (i.e. rain falls)... Since people do not tend to fall, there is a net flux of rainwater onto your body even if you move with the wind. Thus the result that, if you stand in the rain, you'll get soaked.

You'd really have to sit down and do some math to come up with an ideal walking speed. If you walk very slowly, the fact that rain falls means that you'll get soaked from the top. If you run very quickly, your wetness will come less from rain falling on your head and shoulders and more from you "running into" raindrops from the front.

I would guess that it just comes down to the wind speed (or your walking wind-relative speed) relative to the raindrop fall speed. If it's very windy, you can run at the same speed of the wind and likely not get very wet since the time you spent in the rain lessens... Since the amount of water that falls on you is relative to the time you spend in the rain, less time in the rain means less rain falling on you. On the other hand, if you walk in a very windy environment (assume you walk with the wind), you'll actually get more wet since you'll have an increased time in the rain (so the rain falls on you longer) AND you'll have a horizontal component of rain flux since the wind drives the rain into your back.

 

[David Wolfson]

Jeff, I'm pretty sure that moving at the same horizontal velocity as the rain results in the rain falling normally with respect to the body's cross-section. The assumption is that rain hitting you vertically wets you less because the body's cross-section is least from that aspect. I'm intending to use the term velocity precisely, whereby the rain has both vertical and horizontal components of velocity, a vector of direction and speed.

I said (or meant) least wet -- not un-wet!

Also not the important qualifier, "for a period of time." Which is heavier? A pound of feathers, or a pound of lead? :wink:

 

[Jarrod Cook]

In the formula, the author used a variable for the front of the body and a variable for the top of the body (head/shoulders). So the formula is valid for even standing in the rain. Sure, it you won't get as wet.

 

[Jeff Snyder]

David,

I think I understand where we differ... You're talking about this relative to a fixed period of time (or per some unit of time). For example, 1 minute in the rain moving with wind vs. 1 minute in the rain running as fast as you can. I was thinking about this in terms of moving some fixed distance (in which case the speed you move affects the time you spend in the rain). For example, if you want to considering running from the parking lot to the store... In this case, if you run, you spend less time in the rain; if you walk very slowly, you spend a lot of time in the rain to get to the store. So, given a very windy day (arbitrarily with the wind direction in the same direction as it is from the parking lot to the store), you will be better off running to the store than you would be walking to the store. If it's a calm-wind day, then walking may indeed keep you drier than running.

 

[Andrew Khan]

I normally just walk in the rain...sometimes run, if needed.

When I was a little kid, about 5 or 6 years old, I had this theory/idea, that I could literally "Dodge" the rain drops in rain. I would demonstrate by hopping around and saying I wad dodging them...I thought it worked, LOL...but I actually just got wetter, by putting myself in the path of other rain drops that would normally miss me otherwise.

 

[David Wolfson]

Well, the vertical component of wettining is a function of the terminal velocity of the rain (a function of drop size), the density of the rain, and the vertical cross-section of the human subject. The horizontal component of wettining is a function of the relative horizontal velocity of the rain (delta of rain velocity and human velocity), the terminal velocity of the rain, the density of the rain, and the normalized horizontal cross-section of the human subject. At least I think that's how it works.

Each component is summed over the time interval to get total wetness, where the time interval is the distance to shelter divided by the speed of the human toward the shelter.

Assuming a 1:5 vertical:horizontal cross-section ratio and a relative horizontal velocity of about 15 mph for a typical (non-Olympic conditioning :? ) sprinting human in a 5 mph opposing wind, the horizontal component of wettining would be of around five times the vertical component of wettining. The speed of destination approach would be around 10 mph. This assumes a terminal velocity of 15 mph for the rain.

For a relative horizontal velocity of about 7.5 mph for a typical walking human in a 5 mph opposing wind, the horizontal component of wettining would be on the order of two and one-half times the magnitude of the vertical component. The speed of destination approach would be around 2.5 mph. Thus it takes four times as long walking as running to the destination in the rain. Under these assumptions running wetness is ~6w and walking wetness is ~14w, i.e. a bit over twice the wetness.

At least I think this is how it figures out under a reasonable set of assumptions. Note that the result is independent of the rain density.

 

[Shane Adams]

I just carry an umbrella