Is It Better to Run or Walk in the Rain?

[Pikkugnome]

TL;DR Summary

Should you run or walk in the rain to become least wet. You should go as quickly as possible.

I have seen running or walking in the rain puzzle many times. I have not seen a quick answer to the question yet. I was provoked, when a newspaper claimed a professor had been studying it a bit and came up an answer. Honestly I doubt anyone has studied.

My answer is that one should go as quickly as possible. One can imagine two perpendicular cross sections of a body. One is along the horizontal direction of motion and another vertical. The horizontal part scoops water droplets between the start and the end positions. Since the density of water droplets in the air is constant in place and time, the amount one scoops is constant. The vertical cross section scoops as long as one is in the rain, so one should minimize the duration.

Did I get this right?

 

[phinds]

Honestly I doubt anyone has studied.

Really? Why? Of all the billions of people in the world, you are confident that NOT ONE of them has studied this problem (which, by the way, has been around decades if not longer). I am impressed by your hubris.

Aside from that, I agree that moving quickly is likely the best answer. I find that thinking about the extremes in such cases is helpful. In this case, the extremes are moving incredibly slowly or incredibly quickly. If you walk 100 yards at a pace so slow that it takes you an hour to get there, you are going to accumulate a LOT of water on your head and shoulders. If you run so fast that it takes you 10 seconds to get there you'll get pretty wet on your entire front, but nowhere near as much water accumulation as in the slow case.

 

[Pikkugnome]

Really? Why? Of all the billions of people in the world, you are confident that NOT ONE of them has studied this problem (which, by the way, has been around decades if not longer). I am impressed by your hubris.

Aside from that, I agree that moving quickly is likely the best answer. I find that thinking about the extremes in such cases is helpful. In this case, the extremes are moving incredibly slower or incredibly quickly. If you walk 100 yards at a pace so slow that it takes you an hour to get there, you are going to accumulate a LOT of water on your head and shoulders. If you run so fast that it takes you 10 seconds to get there you'll get pretty wet on your entire front, but nowhere near as much water accumulation as in the slow case.

And faster one moves more the situation resembles scooping all the water droplets at once, since the duration is reduced.

 

[phinds]

And faster one moves more the situation resembles scooping all the water droplets at once, since the duration is reduced.

I do not see that as a pertinent argument. That is, it is true, but so what?

Given that the accumulation area of your head and shoulders is considerably less than that of your front, I think there is likely an optimum speed BETWEEN a very long time and a very short time. That is, moving quickly IS likely to be better but moving as fast as possible may well NOT be the optimum solution.

 

[Pikkugnome]

If one goes to the limit, then one scoops all the water along the way and nothing else. How can one do any better, because one would have to skip some water droplets to manage that.

 

[phinds]

If one goes to the limit, then one scoops all the water along the way and nothing else. How can one do any better, because one would have to skip some water droplets to manage that.

You don't seem to understand the difference between top of head plus shoulders on the one hand and full front on the other hand.

 

[Pikkugnome]

You don't seem to understand the difference between top of head plus shoulders on the one hand and full front on the other hand.

Anyways that was my idea, I am not upset when it doesn't work.

 

[jedishrfu]

One could compute the volume of water by making some simple assumptions:

1) Imagine the raindrops as being of equal size equally spaced in space at say 1 cm spacing and stationary in space.

2) You walk at an even pace 1 cm per second

3) You have a cross-section of 1 sq meter (# raindrops = 100^2)

4) You walk for 60 seconds (# raindrops to hit you 60 * 100^2)

5) water contained in the volume 60*100^2*(ml in each raindrop)

You can do a similar analysis for just standing in the rain as it falls for the same time. You will have a smaller cross-section of shoulders and head.

When you combine the two, compare a fast walk to a slow one over the same distance. It would seem that walking fast reduces the amount of water that will strike you, ignoring any puddles you might splash through.

 

[JT Smith]

TL;DR Summary: Should you run or walk in the rain to become least wet. You should go as quickly as possible.

I have seen running or walking in the rain puzzle many times. I have not seen a quick answer to the question yet. I was provoked, when a newspaper claimed a professor had been studying it a bit and came up an answer. Honestly I doubt anyone has studied.

David Bell published an analysis in The Mathematical Gazette in 1976, nearly 50 years ago. His conclusion was that running kept you drier provided there was no wind. If there was wind at your back it was better to run at the speed of the wind but no faster.

Ehrmann and Blachowicz published "Walking or running in the rain—a simple derivation of a general solution" in the European Journal of Physics in 2011. They came to the same conclusion as Bell.

Both of these analyses are simple in that they model humans as sponges of unlimited absorption potential traveling through a steady, concentrated, homogeneous rain. How well does that map to reality?

Mythbusters famously tested the question by exposing participants dressed in cotton jumpsuits to an artificial rain while they either walked or ran. They found that running didn't keep you drier; in fact the jumpsuits were slightly heavier with water after running as compared to walking. They later revisited the question using natural rain and got the opposite result. I haven't read of any explanation for why running results in less wetting in natural rain versus an artificial rain. If it's really true it would point to the problem being more complex than the simple models suggest. Could the distribution of droplet sizes affect absorption? If what Mythbusters found is false it might mean that the difference was due to measurement error and the difference between running and walking isn't very large under normal circumstances.


Personally I've tried both approaches when caught in the rain without rain gear and found that in either case I got pretty wet. One time I was at a hotel that had an adjoining bottle shop. I was thirsty for some beer but there was a gap of about 8 meters between the hotel door and the bottle shop entrance. It was bucketing and even though I sprinted like an athlete I got soaked. On the way back I walked those 8m.

 

[DaveC426913]

Mythbusters famously tested the question by exposing participants dressed in cotton jumpsuits to an artificial rain while they either walked or ran. They found that running didn't keep you drier; in fact the jumpsuits were slightly heavier with water after running as compared to walking. They later revisited the question using natural rain and got the opposite result. I haven't read of any explanation for why running results in less wetting in natural rain versus an artificial rain.

I expect running introduces a host of confounding factors, one of which is surely that water won't pool while the material is in a state of vigorous shaking. Water can't pool in creases, and any rivulets running down will get flung off.

Basically, it's like when you take off your coat and shake it to get the rain off it - but without taking it off, and with shaking it constantly.



It seems to me, the answer is quite plain by looking at the extreme case: traveling outrageously fast will effectively be like running through rain drops that aren't falling at all. You encouter the least possible number of rain drops this way. But short of that outrageous edge condition, it's still true that the least rain will be encountered by minimizing the time spent in it.

 

[phinds]

it's still true that the least rain will be encountered by minimizing the time spent in it.

I disagree. See posts #4 and #6

 

[DaveC426913]

I disagree. See posts #4 and #6

I did read them; I didn't see any convincing arguments.

I am not convinced that you can reduce the rain falling on your front by walking slower. It may seem that way at first, but I don't think it pans out.

If you only look at a single freeze-frame instant, sure, fewer drops will encounter your front, but that's made up for by having more instants.

There has got to be a way of graphing this in a 3D space, height width and time as axes.

I imagine an ideal rectangle moving along the time axis, tracing out a 3D ... uh ... parallelohedron*?, with a grid of raindrops, and simply counting the number of drops in the long parallelohedron versus the short parallelohedron, thus:

It's not finished of course.

But the point is that the area of the plane on the front of the walking man is larger in the slow walk (blue diagram, right) than the fast walk (red diagram, left), which means, overall, the slow walk will intercept more rain drops.

I may have to do this in Blender, so I can plot the intercept points in 3D and count them.

* I guess, technically, it's a parallelogramic prism.

 

[jedishrfu]

Theres some other realities to consider as well.

If you run or take big strides you risk slipping on a slippery section of ground.

Depending on the distanced walked or run and the heaviness of rain you will get soaked and then wont matter how much rain will strike you.

If you get pneumonia then all bets are off and youll rue the day decided to conduct this experiment.

Lastly, its more fun to just go Singing in the Rain.

 

[DaveC426913]

Theres some other realities to consider as well.

If you run or take big strides you risk slipping on a slippery section of ground.

Depending on the distanced walked or run and the heaviness of rain you will get soaked and then wont matter how much rain will strike you.

If you get pneumonia then all bets are off and youll rue the day decided to conduct this experiment.

Lastly, its more fun to just go Singing in the Rain.

I was going to pedantically object that these are all subjective and don't contribute to the answer, until I checked the thread title and saw that it says "better" and not "more efficient". Your contributions definitely factor into a "better" experience.

 

[pines-demon]

MinutePhysics gots this covered:

Also it was tested twice by MythBusters if I remember correctly (1st time they concluded the opposite but got the right result when revisited).

 

[KingGambit]

Really? Why? Of all the billions of people in the world, you are confident that NOT ONE of them has studied this problem (which, by the way, has been around decades if not longer). I am impressed by your hubris.

Aside from that, I agree that moving quickly is likely the best answer. I find that thinking about the extremes in such cases is helpful. In this case, the extremes are moving incredibly slowly or incredibly quickly. If you walk 100 yards at a pace so slow that it takes you an hour to get there, you are going to accumulate a LOT of water on your head and shoulders. If you run so fast that it takes you 10 seconds to get there you'll get pretty wet on your entire front, but nowhere near as much water accumulation as in the slow case.

Sure, there are people who study it.
I remember many years ago, I watch a video about it in MinutePhysics

Walk in rain

 

[KingGambit]

MinutePhysics gots this covered:

Also it was tested twice by MythBusters if I remember correctly (1st time they concluded the opposite but got the right result when revisited).

Whatt,
I should have scrolllll.

[Add:]
I watched @phinds reply and then search the video, that I remember I watched years ago and post the answer. Didn't see @pines-demon 's coming.

 

[JT Smith]

I imagine an ideal rectangle moving along the time axis, tracing out a 3D ... uh ... parallelohedron*?, with a grid of raindrops, and simply counting the number of drops in the long parallelohedron versus the short parallelohedron, thus:
View attachment 353361
It's not finished of course.

You could save effort and simply look up the work of other people. This analysis has been done more than once and the result isn't too surprising. I don't think you have to go through the math to see that in this simplified model the result is to "run" -- actually translate the rectangular object -- as quickly as possible.

Ehrmann and Blachowicz considered a slightly more complicated model. They chose to represent a human as a cylinder instead:

They also included wind speed and rain speed. The result for the case of zero wind speed is the same: run as fast as you can. But when you include a non-zero tailwind the optimal speed is equal to the wind speed, most of the time. In the graph below the dark squares are the zero wind speed case and the other symbols represent different tail winds. For wind speeds above a critical speed there is a minimum in the wetting that represents the optimal speed:

They also varied the radius of the "human". All else being equal, humans with larger radii should always run as fast as they can. But for smaller radius humans there may be a lesser optimal speed. In the graph below the radius is largest with the top line (circles) and progressively smaller below that:

They did not consider other factors however. For example, the degree to which one can be wetted is not constant given differences in clothing and hair. What if you wear a big hat? How much water can be absorbed or adhere will vary over time with exposure to rain. If it's raining hard enough and the distance is large enough running or walking will produce the same result: saturated clothing and shoes filled with water. The size of the water droplets and the rate of rainfall will also affect how much rain bounces or drips off rather than wets the person. Also the dimensions of a human are not fixed. The horizontal and vertical surfaces of a body change as one walks or runs, and not in identical ways. Splashing and evaporation are additional factors.

All that said, in the extreme cases of running at the near the speed of light versus walking one femtometer per century it's clear the speed wins. But in the more practical realm of 1-10m/s the quantitative difference is important. And even if it's true that running leaves you drier overall the distribution of wetness may not be in a way that is more comfortable.

 

[DaveC426913]

You could save effort and simply look up the work of other people. This analysis has been done more than once and the result isn't too surprising.

Yes. thanks for finding that.

And even if it's true that running leaves you drier overall the distribution of wetness may not be in a way that is more comfortable.

Very true. I do find one consequence that has a major effect on wet/dry result: when you run you tend to splash a lot of puddle water onto your shoes/ankles and legs - much more than you might get sprinkled on you by rainfall.

For me, splashing in puddles is actually the dominant factor in how fast I move - more so than how hard it's raining. A wet shirt and head I can live with - they'll dry. Soaked shoes, socks and pant-hems are a serious bummer.

 

[JT Smith]

I think it really begs for experimental testing. Other than the Mythbusters the only other experiment I was able to find was by a couple of meteorologists (Trevor Wallis and Thomas Peterson). They also found that running left you drier in reasonable agreement with the simple models.

Someone actually wrote an online calculator: Is it Worth Running in the Rain?

 

[anuttarasammyak]

All that said, in the extreme cases of running at the near the speed of light versus walking one femtometer per century it's clear the speed wins.

It would be tough thing to get bombardment of almost light speed droplets.

 

[JT Smith]

It would be tough thing to get bombardment of almost light speed droplets.

Not in the world of simple models. The droplets are incident upon the rectangular object and are thereby counted.

Actually, in these models there are no particles, no rain drops. The "rain" is treated as a uniform field of wetness.

 

[pines-demon]

Not in the world of simple models. The droplets are incident upon the rectangular object and are thereby counted.

Incident with relativistic energy, there might be more matter after collision.

 

[JT Smith]

With relativistic energy.

So what? The rectangular human has infinite strength because of previously drinking milk from a spherical cow.

 

[pines-demon]

So what? The rectangular human has infinite strength because of previously drinking milk from a spherical cow.

My problem is not with the human, I edited my post. My problem is with each droplet nuking the atmosphere and modifying the rainy weather.

 

[anuttarasammyak]

It would be tough thing to get bombardment of almost light speed droplets

A merit. The runner can make time to feel unpleasant in the rain as short as he like, e.g., much shorter than time window of skin sensor, or time that nerve signals from skin reach his brain, though his body might be heavily damaged.
In this exagerated and absurd sense OP could be interpreted : which is better living with unpleasantness or going to be dead with no unpleasantness ? To be, or not to be, that is the question.

 

[JT Smith]

My problem is not with the human, I edited my post. My problem is with each droplet nuking the atmosphere and modifying the rainy weather.

The models don't include an atmosphere.

 

[pines-demon]

The models don't include an atmosphere.

Ok. Secondary worry: Does water even wet at those speeds? Or it transitions to metallic ice phase upon collision? Neutron matter? Quark-gluon plasma maybe?

 

[JT Smith]

You're just looking for a stray hair in a model that has no hair.

But if it would make you sleep easier replace "near the speed of light" with "100 miles per hour". The point is that at the limits the simplified problem is easily understood.

 

[WWGD]

Ok. Full body rain coat and boots it is, at least when you know in advance. At least nice, sturdy rain/Winter boots.

 

[jbriggs444]

Just pretend that you do not care whether it is raining. If you pretend anything long enough and well enough, it ceases to be a pretense.

 

[Hornbein]

One can see right away that wetness will be roughly inversely proportional to speed of the walker. 1/s. This decreases rapidly with increases in s. The incidence of rain on the side of the walker increases with the sine of the arc tangent of s/r, with r the speed of vertically falling drops. This increases rapidly but not nearly as fast as 1/s decreases. So moving as fast as one can wins.

 

[jbriggs444]

I like modelling the body as a right rectangular prism (a cuboid). In the absence of wind, the rain will only ever strike the front and top faces. The front face sweeps out a fixed amount of rain regardless of walking speed. The top face is rained on at a constant rate regardless of walking speed. The best strategy is to walk fast so that less time is spent getting the top wet.

No calculations involved.

 

[A.T.]

I like modelling the body as a right rectangular prism (a cuboid)...No calculations involved.

And I don't think replacing the coboid with a cylinder makes it much more realistic.

If nowadays someone wants to seriously improve on that, he should simulate an animated shape of a actual running human und use collision detection for different rain / wind conditions. This would also provide useful data on which parts are hit by the rain, as they are usually not equaly protected.

 

[jbriggs444]

And I don't think replacing the coboid with a cylinder makes it much more realistic.

I believe that such a replacement is an exact equivalence.

The amount of rain swept out by the forward facing half of the cylinder would be the same as for a cuboid of the same frontal cross-section.