posted
Most of my serious Cousin Hobbes topics have turned into Hobbesians (which, I did stop there for a bit, but I’ve got to I’ve working on now which I should get up decently soon). So now I’m willing to turn silly stuff into Cousin Hobbes, and this one I’ve put some work into so I don’t feel bad about it.
The question is, when it’s raining out, you will stay the driest (hit the least number of rain drops) by moving fast or slow?
OK, first we start off with you’re path, you’re going from one point to another via some means that leaves you open to the rain. An example of a random path between two points is displayed here (we’ll assume direction doesn’t matter). It doesn’t matter what the specific path is, this is just an example drawing.
Now I feel the best way to visualize this problem to reach a solution, is to divide the route up. To see what I mean, I drew an illustration, each little red box is a section of you’re path, equal to the surface are you’ll be filling as you walk it (to visualize this we’re assuming you’re both two dimensional and a box, how’s that working out for you by the way? ).
Now of course we keep making the boxes smaller and smaller down to infinity until they perfectly represent you’re path, but this visualization is good enough for now, and I don’t want to get into calculus for this.
OK, so we have the boxes that, when summed together, equal you’re travel area, let’s make them 3D so it’s easier to visualize. Each box, at any one point during the raining will be filled with water that’s currently falling through the box. Since you have to travel through that box on your travel (we’ve already defined your travel path as including that box) you have to hit all of the water in that box, this is a base amount.
To see an illustration, go here. This is interesting because it tells us that no matter what, you will always get wet going through the rain, fast or slow, you have to go through the boxes. But now, how does speed effect this? Well for that, let’s turn to picture four.
You’re speed will determine how long you’re in the box, the slower you are, the longer you will be in that box. Now no matter how long you’re in there, the base amount wont change, you don’t occupy more or less volume based on you’re speed (assuming non-relativistic speeds of course), what changes is that red box on top (it should be on a side as well, but I left it our for clarity, we’ll assume zero wind). The red box represents the rain that will fall into the box while you are there. There’s a constant amount of rain falling at a constant rate (since we’re dividing the time infinitely), so the longer you stay there, the more rain will get in. This makes intuitive sense, the rain has time t to get from where it is above you, into you’re box. Time t is the amount of time you’ll be in that box, and the longer you’re there, the bigger time t, and thus, the easier it is to enter the box (it can come from farther away). And since speed is directly proportional to time spent in the box, we can thus see that the lower the speed, the more rain will fall in the box while you’re in it.
Which leads to the final conclusion that the faster you go, the drier you’ll be by the end. If you go infinitely fast, you will have been hit by the base number of rain drops (the amount of rain drops that you have to hit to traverse your path through the boxes), infinitely slowly (not moving) and you’ll have an infinitely high red box above you of rain to come into you’re original box, and thus get infinitely wet.
So next time you have to get through the rain, remember, the faster the better.
posted
Unless, of course, you go fast enough to splash. Or -- worse yet -- to slip and fall in a puddle.
Posts: 32919 | Registered: Mar 2003
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posted
hobbes, i'm guessing your a philosophy major?
and I have to say, that was pretty interesting, do you think about stuff like that often?
something else to ponder: A pair of identical twins are seperated at birth. Each is in an isolated room with no human contact. Everything else they need is provided, including food, recorded voices for learning, and the finest schooling materials. Their controlled enviroment is identical. So is their DNA. When the twins are old enough, each is asked to write an essay. Would their writings be identical?
Posts: 208 | Registered: Aug 2004
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posted
I imagine if you were traveling infinitely fast and hit something as large and heavy as a raindrop, you might get more than wet. Posts: 5957 | Registered: Oct 2001
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posted
Close, Civil Engineering. Yes, I guess I do, what else is there to do durring class?
You're question will give an easy answer for just about anyone who belongs to a religion (as almost any religion includes the beleif in something unique, often reffered to as a soul). So my answer is, as I am religious, yes, they would be. But creating identical conditions is almost impossible anyways, including in the mother's womb, and the way in which the cells reproduce and all that, just moving to one side or another in the bassenet due to coming out 3 seconds later (I know, all you mothers of twins are going "I wish!" at the three seconds ) would cause changes in devlopment, large or not. And things like subtle air movements outside of the controlled enviroment, or just differences in gravitational pulls would make changes in the exact make up of the human, not to mention the differences in the enviroments themselves, something of that size could never be made twice exactly the same. How big any of these differences would make is up to chance really, but I would guess that over that much time it would be enough.
If we assume that it's an abstract world and the molecular make-up of the people at the time their told to write an essay is identical then the question comes down to if you believe there is a soul (or soul like "thing"), and that's that.
quote:I imagine if you were traveling infinitely fast and hit something as large and heavy as a raindrop, you might get more than wet.
Well techincally if you were traveling infinitely fast you'd be going backwards through time, which would be way more interesting than getting wet, but since we assume non-realtivistic speeds that goes away, and it was just a demonstration of the limit of speed -> infinity, the faster you go the closer to the base amount of water you'll hit.
posted
Though actually, since water is a discrete element (quantum physics aside), really infinitly fast isn't required to reach that base amount of water, only a very high speed and the right conditions (no rain-rops periously close to the box's top border). Of course for any significant length of time spent traversing you're path (as in more than portions of a second) that speed is more than high enough to be out of anyone's real speed.
I agree with your answer, and i think that if one day in the future we could conduct the experiment we should, although we actually shouldnt because of humanitarian issues. I dont know. Maybe a similar experiment with mice, se how much the little differences you mentioned count.
Posts: 208 | Registered: Aug 2004
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posted
not to bring up an old topic, but the myth busters came to the oposite conclusion, by a person running, then walking, and taking the weight of the clothes.
Posts: 7 | Registered: Sep 2004
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In particular, studies on this topic -- and there HAVE been studies on this topic -- have found that rain is almost never perfectly vertical.
Posts: 37449 | Registered: May 1999
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quote:not to bring up an old topic, but the myth busters came to the oposite conclusion, by a person running, then walking, and taking the weight of the clothes.
This is a pretty faulty test for the answer I was giving. Total amount of rain you hit is very different than the amount absorbed by your clothes. For one, if you go faster you'll probably be hitting the rain harder, making absorbtion more likely. The rain will have less time to run off your clothes before being hit with more, meaning that if you assume that the run-off speed isn't linerarlly praportional to the rate of spray (and though I can't proove it, this is likely the case) then the water will form pools and significantly increase absorbtion rate. And then there's the fact that if you go very quickly, really anything above a swift walking pace, your clothes will billow out and drastically increase surface area to the direction of rain fall, as well as create less direct run-off paths by increasing their horizontal compenent.
quote:I would think there might be interesting behavior around the point where your speed is close to the average speed of the raindrops.
That would be interesting. I'm assuming you mean horizontal speed, unless you're going really far down somewhere? Unfortunatly my method would have to be adapted as I assume pure vertical rain fall.
quote:In particular, studies on this topic -- and there HAVE been studies on this topic -- have found that rain is almost never perfectly vertical.
Though it does change my "proof", I would think that a few degrees off vertical should make no noticable impact on my findings. A lot of what I used can be used in conjuction with non-vertical rain-fall, we simply draw the red box a little crocked and cover a few of the sides. The problem is then we have to take into account direction of motion realtive to rainfall, instead of just speed, and that makes it much more compilcated.
posted
Your solution does not explain why my front side is always wetter than my back side when I've ridden my bicycle in the rain.
Posts: 12591 | Registered: Jan 2000
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posted
Rabbit, you must have a guard over your back tire. I didn't in college and can tell you my backside was always much wetter.
Hobbes, what if, as you ran, you could squat at the same velocity as the falling rain? As you moved on, wouldn't the boxes become smaller and smaller (shorter and shorter) thereby presenting less water? Maybe people should not only run fast, but be running like a duck by the time they get to where they're going.
Posts: 4625 | Registered: Jul 2002
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posted
Actually Georgia Tech did a study on this very topic and discovered that it doesn't really matter if you run or walk. Because by running, you actually run into raindrops that you would have missed had you been walking where as when you are running you only get the rain drops that can get to the upward facing surfaces or you... Or something like that. It is hard to explain in writing.
But the purpose of this post was to state that there has been an indepth study into the matter and it was decided that you could run or walk and still get just as wet. Sorry
Of course I have fenders. No regular bike communter would ride without fenders. If you don't have fenders, not only do you end up with a stripe of muddy water up your back but you soak your feet and get the lower part of your pants filthy. The rain that is still falling from the sky is much cleaner than the stuff that sprays up off the ground.
Posts: 12591 | Registered: Jan 2000
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posted
Alas Rabbit, that is not one of the things they told incoming freshman. That had to be learned through experience.
And realizing that, as an 18-yr old male, you looked like a bigger dork with a streak up your back than you did with a fender.
Posts: 4625 | Registered: Jul 2002
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posted
No, that one is pretty straight forward. All you need is an efficiency curve for the engine vs. rpm, the gear ratios and a curve for the wind resistance as a function of speed.
Posts: 12591 | Registered: Jan 2000
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posted
The problem with the conclusion that the speed doesn't matter or the conclusion that slower is better is that they are clearly wrong. Both those conclusions imply that if you stand still (zero velocity) you will get no wetter than if you move. However, if you don't move it will take an infinite length of time to get from one building to the other and so you will pick up an infinite number of rain drops. Clearly, speed matters and as your speed approaches zero, you will get wetter and wetter.
In this light, there are only two conclusions that could make sense. 1. The faster you go the dryer you stay or
2. There is an optimum speed, if you move either faster of slower than this speed you stay dryer.
[ September 07, 2004, 05:44 PM: Message edited by: The Rabbit ]
Posts: 12591 | Registered: Jan 2000
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posted
Or there's more than one optimum speed. The equations could have multiple peaks (or valleys, depending on if you plot dryness or wetness).
Posts: 26071 | Registered: Oct 2003
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posted
H, do you have all your Cousin Hobbes threads bookmarked? I think they're worth saving, maybe even to a separate read-only forum like the landmark forum -- they're damn well-written and cover quite a few interesting subjects.
In any case, if you have the URLs handy (but don't go digging on my account), could you post them? I'd love to browse through them at my leisure.
Posts: 3293 | Registered: Jul 2002
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Yes, I guess I do, what else is there to do durring class? ![[Taunt]](graemlins/taunt.gif)
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Thanks Lalo! Always nice to have someone who appreciates your work. ![[Embarrassed]](redface.gif)
