Question

Mental exercise I've been pondering: Write a model for the amount of water a car windshield accumulates while driving in the rain.

Answer 1

Begin by identifying relevant variables and necessary assumptions. I've thought a good bit about this, but I'll let you guys have a go at it before I say anything.

Answer 2

Now that is some exercise there! I'm wondering if car speed and the adhesiveness of water are related... You would need to know the shape and material of the windshield and the amount of water that hits it as well.

Answer 3

Definitely a lot of variables involved.

Answer 4

I would use some dif eq I think, with some limit on the max amount

Answer 5

Coefficient of drag, Reynold's number would also apply I think.

Answer 6

Diff eq? Meaning you think the accumulation of water depends on the amount of water already present?

Answer 7

some rate at wich water collects and then come up with some equation with the peramaters needed

Answer 8

would need a limiting factor im thinking

Answer 9

and then I'll learn to spell

Answer 10

List me some variables, fellas.

Answer 11

How about the angle at which the rain hits the windshield. The assumptions you would make would depend on how complicated you want your model to be so. That would be up to you!

Answer 12

Windshield angle definitely.

Answer 13

I would assume the size and shape of each droplet to be the same. Temperature, air density and pressure should be assumed constant as well.
My brain! I looked at the Surface Tension wiki article and that itself is complicated enough!

Answer 14

Ahaha.
Oh, IceCream. You're thinking about this a lot more in depth than I was thinking of it. I was thinking of taking more assumptions and simpler variables.

Like, instead of dealing with individual rain droplets, I was thinking more of treating rain as just a single variable, more like flowrate.
Liters/m^2/second in a directly downward direction, or something like that.

I wasn't getting into surface tension at all.. that scares the hell out of me.

Answer 15

How to handle different angles of the windshield and different speeds is what's really got me a little baffled...
Even if you assume it's perfectly flat, rectangular windshield.

Answer 16

But my list of variables that you have to account for, even in the simplest model would be:
rainflow
windshield size
windshield angle
car speed

Answer 17

Well, if you consider the windshield to be parallel to the rain then that would be an easier thought process to start with. Keep speed constant and rate of flow constant. Consider how much water accumulate in that case. I come across the problem of the bonnet/hood affecting the accumulation now...