Physics Question: Raindrops and getting wet!

c0y0te

So - its raining (a constant ) and joeshmoe has the option of either walking to his car or running to his car. The car is 30m away. There are no obstacles in the way.

From a physics perspective - which option will result in joe getting wetter? Vote for your answer and then post your reasons for same, quoting realistic / valid physics principles to prove your answer.

c0y0te

[edit] Damn - the post screwed up on me before I could set the poll in motion, so how about you just post your answers and your justification. Thanks in advance [/edit]

ApeXaviour

Walking he'll get wetter

Say he walks at 1m/s and runs at 3m/s.
Raindrop velocity is in the order of 20m/s. The greater surface area (while running) on yer man that the rain can fall on, caused by the extra-angle is negligible when compared with the fact that he will only spend one third of the time getting rained on.

It can be worked out pretty easily, but I don't think there is much need for that as it is pretty obvious when you take the above into account.

Bass.exe

ApeXaviour wrote:

Walking he'll get wetter

Say he walks at 1m/s and runs at 3m/s.
Raindrop velocity is in the order of 20m/s. The greater surface area (while running) on yer man that the rain can fall on, caused by the extra-angle is negligible when compared with the fact that he will only spend one third of the time getting rained on.

It can be worked out pretty easily, but I don't think there is much need for that as it is pretty obvious when you take the above into account.

Unless it's horizontal rain, falling (flying?) at exactly 1 m/s in the same direction the man is walking!!

Ali Cat

I concur, though I note that this may not be as straight forward as it appears: is the rain falling at an angle?

ApeXaviour

Oh right, yeah I assumed the rain was falling vertically. Actually thought it said that in the question .
It should have n anyway, otherwise there is not enough info to go on and ali is right, it depends...

Capt'n Midnight

the did this in New Scientist a while back, the consensus seemed to be that you lean when running so only the top gets wet, the angle depends on the vector between the falling rain and your speed.

the top will get wet no matter what - but you might save your front or back getting wet too.

Sev

Ok, maybe im conceptually mistaken, but here's how I see it. I kind of enjoyed putting this together actually...

I've modelled a person as being a crude box like thing as shown in the diagram.



We want to get an expression for the total amount of rain landing on a person (a box) for any arbitrary distance x, and minimise it over Vm, the velocity of the man.

The amount of rain landing on the man per second is equal to the amount of rain falling directly down on top of him, and the amount hitting his side facing the oncoming rain.

The amount of rain that lands vertically down on any given amount of area per second would be given by Area x Rc. Where Rc is the "rain constant".

And the amount of rain landing obliquely on the side of the object in the diagram will be equal to the amount of rain landing per second in the Region D.

The Area of region D = wn

And n = h(Vm/Vr)

Where Vm = Velocity of the man, and Vr is the velocity of the rain.

So, the total amount of rain landing on the object per second = Φ = Rc[w² + wh(Vm/Vr)]

The total amount of rain landing on the object in the time taken to traverse an arbitrary distance x in time t is..

φ = Φt = Φ(x/Vm)

= (x/Vm)Rc[w² + wh(Vm/Vr)]

= Rc(w²x/Vm + whx/Vr)

φ is a function of the distance x, and the velocity of the man Vm, and from this expression we can see that at least Rc(whx/Vr) amount of rain will land on the man no matter what speed he runs at. But there is an additional quantity Rc(w²x/Vm) which in order to minimise, we need to maximise Vm.

In conclusion the man will get less wet if he runs fast.

Bass.exe

Excellent work, but it does not take into account the fact that the faster one moves, the farther one leans over(thus altering surface area available for the rain to hit).

Also, if a person is running, he is hitting more rain already present in the air in front of him that he wouldn't be hitting if he were walking...

I'm actually for the theory that "more velocity" = "less time in rain" = "drier person" but I felt I had to balance this up a little...

Sev

Well, im happy with my running box for the moment, im not gonna go too crazy. I'd imagine a full analysis of it would approximate to something similar.

I dunno what you mean by if he's running that he'd hit more rain thats already in the air in front of him.. I thought I took that into account, with the picture and the idea of region D.

Sev

Actually, just looking at that expression I got again. This is kind of interesting.

φ = Rc(w²x/Vm + whx/Vr)
= Rc(w²)(x/Vm) + Rc(whx/Vr)

The part thats dependent on the speed of the man is Rc(w²)(x/Vm) = Rc(w²)t which is just the total of all the rain that lands on the top of the box in the time taken to cross the distance x.

The other part of the sum, Rc(whx/Vr), then has to be the total of all the rain which hits the side of the box facing the rain. And we cant do anything about that, it turns out to be the same no matter how fast you go and is only dependent on the speed of the rain, the distance travelled, the height of the box, and of course our "rain constant".

ApeXaviour

Sev wrote:

Ok, maybe im conceptually mistaken, but here's how I see it. I kind of enjoyed putting this together actually...

I've modelled a person as being a crude box like thing as shown in the diagram.

Well done Sev, ya that's pretty much what I described (the conceptualised box was a clever step!) but I was far too lazy to work it out. Bloody SS and your free time..

Hows your project goin n anyway? You in the dept or abroad or what? I've been exchanging emails with the evil one in Culham.. you hear about his "discovery"?

By the way bass, the leaning forward IMO is a bit pointless, it's totally subjective. If your gonna start taking that into account then what about how high they raise their legs, whether they extend their arms, how big their head is etc.?

Sev

Im not SS, Im SF.. evil one? project? discovery? I've no idea what youre on about

Ali Cat

Φ
The flux density of the rain,I like it!

Being too lazy to work it out for myself I thought I'd just throw this out there in the hope that some one else will do it and satisfy my curiosity:
Is there an angle of rain fall at which point walking and running would get the subject equally wet?

ApeXaviour

Sev wrote:

Im not SS, Im SF.. evil one? project? discovery? I've no idea what youre on about

Meh.. me had a few drinks earlier and totally got you mixed up with someone else (chump). I'm kind of name dyslexic. pity really

Sev

Ali Cat wrote:

Φ
The flux density of the rain,I like it!

Ive awful difficulty these days trying to come up with symbols to represent different quantities, theyre always taken by other things that they could be confused with, or just weak letters that look crappy, so I decided to go greek this time. Phi! I tells ya.

Ali Cat

Well at this point so much of the greek alphabet--both upper and lower case--has been used to represent things that I say it's about time that we sought out another non-latin script from which to hijack letters..

ApeXaviour

How about katakana? It's pretty simple, not like the others (あなたは　日本語　有賀と etc.)

The quantum magnetic flux of a semi-conductor: マ　（ma)

etc: 　リ　(ri)

etc: 　フ (fu)


Hopefully you can read that, if you can't just install eastern languages..

Ali Cat

Perfect...now let us go forth and spred this new notation amongst our fellow nerds..

ApeXaviour

Lol, and the the good thing is there's like 70 of them, so it'll take a while to run out..
ア エ イ オ ウ
カ ケ キ コ ク
ガ ゲ ギ ゴ グ
ハ ヘ ヒ ホ フ
バ ベ ビ ボ ブ
パ ペ ピ ポ プ
ナ ニ ネ ノ ヌ
マ ミ メ モ ム
タ チ テ ト ツ
ダ ヂ デ ド ヅ
サ シ セ ソ ス
ザ ジ ゼ ゾ ズ
ラ リ レ ロ ル
ヴ ヲ ヤ ヨ ユ ん
After that I'm afraid it looks like we'll have to start using egyption hieroglyphics..

Ali Cat

ApeXaviour wrote:

After that I'm afraid it looks like we'll have to start using egyption hieroglyphics..

works for me...