December 10th, 2009

Froude number

Road corrugations

Dr. Science!

Can you tell me why packed snow (and graded dirt roads) often end up with a series of small ripples/ridges after heavy traffic tamps down the snow?

Still Curious

I can!

Washboarding, as it's called, is one of those phenomena that people come up with complicated explanations for (even The Straight Dope gets it wrong, blaming car suspensions) when it's actually just very straightforward physics.

So you've got a wheel going over sand or dirt or snow. If it's going fast enough, when it hits an irregularity, it's going to do a little hop. And when it lands, it's going to make a little bit of a crater. That dip forms another irregularity for the next wheel that comes along, which does the same little hop on the first bump, deepens the dip a bit, and does another little hop as it comes out of the dip. Repeat over and over and you get a whole series of corrugations.

A key factor is speed. How far the wheel hops depends on how fast it's going. (If it's going slow enough, it won't hop at all.) If every wheel that came through was going a different speed, the resulting dips would be all spread out and would cancel one another out. But most cars passing along a certain section of road are going to be travelling at roughly the same speed, so they all have roughly the same spacing on their hops and you get lovely washboards.

This is all shown by an experiment done by Keith Mather and published in Scientific American in 1963, which you can read about here: