What determines whether or not snow sticks to my windshield?

[Ori Vandewalle]

It snowed last week and I noticed that, when my car was stationary, snow built up on the windshield, but above about 10 mph (4.5 m/s, if SI units are required here), the snow didn't stick. I'm wondering what accounts for the difference.

My first thought was that the extra kinetic energy of my car's motion would be enough to sublimate falling snowflakes. After a few mathematical missteps, however, I determined that my car would have to be going about a thousand times faster than I was willing to drive it to get the required amount of energy. That is to say, this was too little energy by a factor of about a million.

Which leaves me at somewhat of a loss. I wouldn't be at all surprised if the temperature of my windshield plays a role, but I can't see how my car moving forward would affect that equation.

The only other thought that comes to mind is that the air my car pushes through might exert some pressure on an incoming snowflake, such that the snowflake isn't able to land. But the physics I've taken was a little light on fluid mechanics, so I'm not sure how to proceed from there.

Any help you folks can provide would be greatly appreciated. I don't even require anyone to spell out the answer for me; if I can be pointed in the right direction, I'll try to work out the problem myself.

Some relevant factoids: Wiki says a typical snowflake is 10¹⁹ water molecules, which would give it a mass of about 3x10^-7 kg, and I estimated that a snowflake's terminal velocity is somewhere around 1 m/s from this paper.

Thanks.

 

[I like Serena]

Welcome to PF, Ori Vandewalle!

Snow sticks due to friction.
When you drive at speed, the air exerts a force (drag).
When the force of the air is greater that the required friction to stick, the snow flakes will slide off.

 

[Ori Vandewalle]

Heh. The physics I've taken certainly wasn't light on objects sliding along inclined planes. I really should have guessed that myself. Thanks!

There is a wrinkle, though, which is that finding the coefficient of friction between snow and glass is not exactly easy. What I can do is accept your hypothesis as true, guess that my 10 mph estimate is accurate, and see if a reasonable μ pops out of the force equation. Doing that, I've got friction and weight pulling the snowflake down the windshield, and drag pushing it up.

With an esimate of 3x10^-7 kg for the snow, the drag coefficient of a sphere for the snowflake (.1), a circular snowflake with a diameter of 1 cm, and a 40° angle for my windshield, I get a μ_k of .53. Looking around at other coefficients of friction for snow, I bet this is a little high, which means the critical speed is lower (likely) and/or my rough estimate of the shape and size of a snowflake is wrong (very likely).

But hey, at least the results aren't entirely unreasonable.

 

[I like Serena]

I wouldn't know what the drag coefficient of a snowflake is.
It's not really spherical.

And I wouldn't know what the coefficient of friction is either.
It's not really a nicely defined mass with more or less smooth edges.

I guess the best way to find out is by trying it out.
And I suspect that different types of snow flakes exhibit significantly different behavior.