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Running in the Rain simplified equations

By: RTSplayer , 3:01 AM GMT on December 30, 2012

Quoting wxchaser97:

Basically, if it is raining outside and I am standing outside of a store looking to get to my car I would run. I would get to my car faster thus spending less time in the rain.


Spending less time in the rain doesn't guarantee you get less wet.

That's what some are failing to understand.

The terminal velocity of a 6-millimeter raindrop was found to be approximately 10 m/s. This value has been found to vary between 9 m/s and 13 m/s when measurements were taken on different days. The variance has been contributed to different air temperatures and pressures. In comparison, a human being falling to the surface of the Earth experiences a drastically larger terminal velocity of approximately 56 m/s.

http://hypertextbook.com/facts/2007/EvanKaplan.sh tml

Ok, so something as simple as changes in temperature and pressure changed the rate of a rain drop's terminal velocity by a factor of about plus/minus 2m/s.

If you consider a human sprint, which is not a world class sprinter, and is a straight shot, not a shuttle run with turns, would also be about 9 or 10m/s.

If the front of your body is thrice as big as the top of your body, then exposures are:

T = 1 (standard metric for area of top of body)
F = 3T (area of front of body)*
r = rate
x = time
E = x *(rT + rF) total exposure

* I picked a round number that seems close. I doubt it's exactly this ratio.

For terminal velocity: 9m/s
Walk: 5m/s
Trot: 7m/s
Run: 10m/s
Distance: 50m


rT = 0.8746*T (sin 61)
rF = 0.4856*3*T = 1.4568T (3*sin 29)

x = 10s

E = 23.314 arbitrary units water.


rT = 0.7894*T (Sin 52.12)
rF = 0.6139*3*T (Sin 37.88)

x = 7.15285s

E = 18.8199 units water


rT = 0.6691*T (sin 42)
rF = 0.7431*3*T (3*sin 48)

x = 5s

E = 14.492 units water*


13m/s terminal velocity:


rT = 0.9333*T
rF = 0.3590*3*T

x = 10s

E = 20.103 units water


rT = 0.7926*T
rF = 0.6097*3*T

x = 5s

E = 13.1085 units water

Ok, so I guess I've proven myself wrong, not sure though, because I don't know if the 3 to 1 ratio of front body surface area to top of the body surface area that I used was high enough. The higher this ratio the more it favors walking.

This also still doesn't account for dynamic motion of the body, and still only incorrectly treats the body as a prism...but what the heck, he wanted to see some math...

The 9m/s terminal velocity calculation actually has exposure rate ratio of just 1.24, which means the Build team runners actually got much wetter (compared to walking,) than THIS attempt to solve the problem suggests they should have, because the actual ratio was 1.6.

The 13m/s terminal velocity ironically causes the person to get less wet, whether walking or running. I guess a faster falling drop is more likely to fall out of the way before you run into it. Additionally, the ratio of exposure rates is higher.

So what happened on Jamie and Adam's experiment, and why did it work for both of them, with and without wind?

Below terminal velocity 5m/s:

rT = 0.7071*T
rF = 0.7071*3*T

x = 10s

E = 28.284 units water


rT = 0.4472*T
rF = 0.8944*3*T

x = 5s

E = 15.652 units water

Simplified explanation still doesn't replicate Jamie and Adam's results, and it under estimates how wet the runner got. It under estimated the ratio of rate of exposure for the runner in the build team's experiment by 40%.


I actually think the scales in at least one of the experiments was screwed up. Remember, in one part of the build team's tests, they got the outrageous conclusion that Torre ended up having lighter clothes after running in the rain than before he started, which they threw that out because it was obviously wrong, but what about the not-so-obviously wrong results?! If this is the case, then the margin of error on the scales is too large to even do the experiment properly.

The views of the author are his/her own and do not necessarily represent the position of The Weather Company or its parent, IBM.

Reader Comments

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7. WunderAlertBot (Admin)
5:16 PM GMT on December 30, 2012
RTSplayer has created a new entry.
6. RTSplayer
4:24 AM GMT on December 30, 2012
The video on page 2 was wrong. It makes an error in dimensional analysis.

It does not agree with either of the experiments done by the mythbusters, because in both sets of experiments the runner got wet much faster compared to the walker than what would be predicted if that video's explanation had been true.

At the 1,00 mark, the speaker claims the total amount of rain you run into from the side while en route has nothing to do with how fast you are going. This is definitely false, as anyone who knows how to do vector sums or reference frame conversions would know.

In the real experiment with the build team, the runner got 60% more wet per second than the walker. This contradicts the video's claims about how/why the runner should get less wet, because he claimed that you'd get the same rate regardless of speed, and that only the duration matters. He was most certainly wrong. If he had been right, then the ratio of water would have been identical to the ratio of time spent in travel, which it wasn't.

Angle of incidence influences how much bounce and absorption you get, just as with light on the Earth, though it's not identical.

Additionally, he incorrectly uses a solid, static prism to model the body, when our bodies are rounded and are not solids, and are not static.

I'm not done with this yet, because there are other variables involved.

Plus it's more complicated still.

If you run into a heavy sheet of rain, your front is much larger and you will get hit across a much larger surface area compared to if you had been walking or standing still.
Member Since: December 31, 1969 Posts: Comments:
5. WxGeekVA
4:09 AM GMT on December 30, 2012
My brain won't let me do this over winter break. I'll contemplate once school starts again.
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4. Barefootontherocks
3:51 AM GMT on December 30, 2012
Well, that was a fun discussion while it lasted. I enjoyed reading it anyway.

I did not see a response to my morning response to your response last night to the first posting of the physics video, but that's okay. It was just a poem and I think you understood what it meant. Variables. Different ways of viewing a problem, i.e. a scientific question.

The most important variable to me is if I'm walking hand in hand with the one I love... you know, when the rain starts falling. Not making fun of anyone here, just, this is a variable that I did not see mentioned in the discussion elsewhere and it could be pertinent to the quantum study and the PDEs.

From this rain question, I don't think you can remove the human element involved. Well, you can, and maybe that's the only way to run it. With stuffed animals or something.

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3. TropicalAnalystwx13
3:22 AM GMT on December 30, 2012
You're thinking too much into it RTS.

It's simple logic, really. The less time you spend in the rain, the less wet you will be, at least compared to your total wetness while walking.
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2. wxchaser97
3:21 AM GMT on December 30, 2012
Running is better than walking, and why does my comment have to be turned into a whole blog? I fully support TomTaylor.
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1. Astrometeor
3:16 AM GMT on December 30, 2012
running is better than walking, I support Tom and TA's argument.

I do not understand how you can get less wet by being out longer?
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