I've been running on and off for the past 16 years. In my experience, I do not get as wet while running in the rain as I would just standing in it.
I think there must be a missing variable, such as excess water whisking off more quickly, greater evaporation due to heat transfer or maybe something else.
My point is that reducing your exposure time is basically altering a different variable in the equation.
If you control that variable by not running to a place where the exposure to rain stops, it becomes clear that by running you will get more wet than if you were simply walking.
And yes I understand that practically, running to a dry spot is the whole point.
The running is reducing your exposure time, and that reduce is enough to get you less wet.
Um, the "exposure time" variable is exactly that. The act of running causes you to increase your rain exposure, so unless I'm missing something, at some point the "exposure time" will become long enough that the act of running is rendered ineffective, and then actually becomes worse. (For example, if you ran around in a circle for a set time, instead of from point to point).
Like I said, I do get that by that point it may not functionally matter, and that if you ran from your car to the store you will not be as wet as if you walked, but it is important to understand the subtleties in order to properly understand why.
Nope, I give up. It seems to me that what you're saying is either trivially true and therefore completely pointless, or simply wrong. I can't believe you're as clueless as my parsing/reading seems to make you, so I guess we're just talking past each other.
Maybe others will understand you and gain something from it, but I doubt there's much to be gained by you continuing to explain to me, and me trying to understand.
I've spent a lot of time learning math (have a CS degree, which required lots of math). But sadly, I'm not comfortable enough with differential equations to come up with a solution like the first part. It makes sense once someone else has done it, but I wouldn't have gotten that far.
Perhaps I just need more practice. Practice makes perfect with math like everything else?
You don't really need much math to understand this. Imagine that a person is a perfect cube. The amount of rain hitting the top of this cube is constant-- does not depend on the speed of the cube. The amount of rain hitting the front of the cube is proportional to how fast the cube is moving. From this insight, everything else is algebra.
I wonder if the multivariate nature of this problem is throwing you off more than the differential equation aspect of it. If you know multivariable calculus you can think about this problem at a higher level of abstraction (vector fields and flux). The integral you see is the output of the thinking at that higher level of abstraction.
I bet with proper background and practice you could set things like this up rather easily. You just need to learn to think about the problems at the proper abstraction level and then develop some intuition by actually doing lots of problems.
Your CS degree required "math", but not much calculus or analysis. If your degree was in, say, mechanical engineering instead (or anything in the family of applied physics), you'd be much more comfortable with the differential equations. But then, you'd probably have a harder time with discrete stuff like statistics, and the number theory behind RSA would completely baffle you.
I think there is a simpler way to picture this. Imagine a volume of water suspended in the air - the height and width is the person's cross section, and the length is distance to be travelled. All of that water is going to get onto you regardless of how fast you travel. So speed is not relevant there. But for the water hitting the top of the cube, it gets wet only with respect to time, and not to speed.
Conclusion: if the rain is falling straight down, it always makes sense to run.
Interesting rule, however I disagree with the extent of the assumptions taken from the experiment in the wiki, because:
Blasting the second group with a less painful noise AFTER a more painful noise will result in a sense of relief when the less painful noise occurs. I believe this relief has a big impact on what people remember.
Also, I believe the second group would insist on increased unpleasantness if the less painful noise preceded the more painful noise.
Nonetheless, I believe there is some truth to the rule.
I, like you, try to optimize a different thing than the article: I want the time at which my wetness level is normal to be as soon as possible. As such, it makes sense for me to run to shelter if only because I will get to start drying off sooner.
Oddly enough, all three optimizations lead to the same conclusion: that the best thing to do in any case is to run until you escape the rain.
Nice. A fun/rational way to look at what is at heart an emotional decision. :)
Another angle on this is that running spreads the wetness over more surface area (less on top, more on front). If you're wearing a hat, you might choose to walk, etc.
I won't argue the conclusion, just introduce an anecdotal observation.
When it is spitting or raining very lightly, sit in a stopped car and watch the rain on the window.
Now, speed that car up to about 80km and see what happens. Disregarding spray from other vehicles, odds are that there will be more rain on the windshield in the same amount of time.
Of course, because you've substantially reduced your exposure time. But the act of increasing your speed itself actually causes you to come in contact with more raindrops, not less.
This question is the reason I went into engineering.
I learned calculus by correspondence in high school. Solving this problem transformed calculus in my mind from just some abstract problems to solve into something useful. It was a big turning point for me, and focused my interests in areas of applied math.
