BAN #122: What causes those ripples in dirt roads?

[Saturn image credit: NASA / JPL / Space Science Institute / Gordan Ugarkovic]

A Bit o’ Science

The entirety of science is too much for one sitting. Here’s a morsel for you.

I live in the country, so I have to drive over lots of dirt roads. My biggest pet peeve with them is how they form ripples over time, making the drive over them bumpy and jarring.

I’m a curious person, and I’ve always wondered what causes those ripples. The best idea I could come up with is that a small bump in the road causes the wheel to move upward, lessening its impact on the dirt. Then it comes back down due to gravity, creating a trough. However, it seems that the car suspension would play a role, as well as wheel size, weight, distance between front and back wheel, and so on. Every car and truck would have a different track, which should suppress ripples, not create them. So what gives?

Well. One day I posted a jokey tweet about wheel marks in my driveway:

[Click through to see the whole thread]

YosemiteSteve then replied, saying it reminded him of ripples in dirt roads, and I replied to him wondering if anyone has studied how those are made. I wouldn’t even know a scientist friend who might know, though!

But I do know someone who is not only wickedly smart, he has the ability to make connections with all his knowledge, making him a genius. That man is my friend Randall Munroe, the creator of xkcd. So I asked him, and cosmos bless him, he found an article about it Science Daily, which led to this paper published in Physical Review E in 2009!

The authors did experiments to create ripples in sand using both a heavy wheel and a plow blade. Both could be adjusted for weight, and the blade could also be tipped and rotated to different angles. What they found is as amazing as it is complicated.

First, and most importantly, the creation of ripples — called washboarding — does NOT depend on the suspension of the vehicle! They carefully crafted the experiment to avoid anything like a car suspension and ripples formed anyway. So right away, wow. Cool.

The size and shape of the grains of sand didn’t matter either. What does matter is density of the grains. That’s because a vehicle exerts a force downward due to gravity that is balanced by the sand pushing up, and the density of the grains in the ground affects that. Again, cool.

Then things get complicated. Think of it this way. A wheel sitting on sand is applying a force, but it’s static. The sand dissipates this force via friction with the grains to balance it. The depth the sand compacts — the penetration depth ­— doesn’t depend on speed (because the wheel is motionless). They call this the static depth.

But if a small bump in the road causes the wheel to move up, it comes back down with more force, and penetrates deeper. This is the dynamic depth, because it depends on velocity. What they found is that a speed increases, the dynamic depth decreases; the faster the vehicle the smaller the effect. But the static depth remains the same, so at some point there’s a transition between the two. At that critical speed the wheel moves up and down ballistically (only due to gravity), and this periodic force is what creates the ripples.

That critical speed depends on a few things, like gravity, the mass of the wheel (or plow blade), the density of the sand, and, weirdly, the width of the wheel/plow blade.

The suspension can play into this but only at a very minor level. Those other factors are what are important.

This is where things got complicated. Dividing the physical equations that determine the two depths (static and dynamic) gives what’s called a dimensionless number, a number with no units — for example, dividing 6 meters by 3 meters gives you 2, with no units). Numbers like this are useful in many ways, and in this case it allows you to find the velocity where ripples start to form. Slower than that and the sand dissipates the force, faster than that and the wheel jumping up creates ripples.

This is similar to what’s called the Froude number, which I had to look up. It relates to the wave made by a boat in water. If the boat moves slowly the water flows easily around it, but at a critical speed the water becomes turbulent. The Froude number defines that velocity, and it depends on the some characteristics of the boat itself and the speed of the water.

What’s interesting to me is that they found this ratio (2.58, if you care) for the plow, but for the wheel it’s a lot more complicated. A non-rolling wheel is like a plow, and their equations worked fine. But let the wheel actually turn, and things went wonky. The force of a rolling wheel on the sand changes, and the equations don’t work any more. The authors said they would be continuing this work with more detailed experimental setups; I found this paper which does that but I need to read it more carefully; the physics is a bit daunting (in fact, searching on the authors’ names yields many papers related to the topic).

OK, so what do we conclude from this? Well, the bottom line is that washboarding will occur if people drive above a critical speed on dirt roads, and that speed depends on the road itself. It’s different for gravel than it would be for sand or dirt, due to the different densities. Worse, there’s no practical way to stop it! If the critical speed is really slow, like 20 kilometers per hour, there’s no hope of getting people to stick below that. It’s gonna ripple.

The only way to stop rippling is to have a non-deformable surface… aka paving. That’s expensive. If it were that easy then every dirt road would get paved and we’d be done.

I wonder though. If you use some type of grain that interlocks with other grains such that deformation is minimized then this might help. What you need is for the road to be non-deformable enough for typical driving speeds on that road.

But hey, I’m just an astronomer and science communicator, not a civil engineer. I’m guessing this sort of thing is studied by them, so maybe this is nothing new. But if you’re reading this and you are a civil engineer, then take a look at those papers. If you wind up solving this problem, I want a cut of your Nobel Prize. And a small percentage ownership of your road-grain manufacturing and installation company.

P.S. Randall has a new book coming out in September called How to: Absurd Scientific Advice for Real-World Problems” and seriously d you need to know anything about it except Randall wrote it? Pre-order it now! (associate link)

Et alia

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