This question occurred to me while driving on the freeway today.
In a freely moving flow of traffic consisting of a mix of vehicles from motorcycles all the way up to tractor-trailers, it seems that the smaller the vehicle, the easier to advance through the traffic, so car, motorcycles, and regular size trucks can move in and out of traffic, and brake/accelerate to pass with ease. The larger box-vans and cargo trucks can move in and out and pass, but with less ease as they are less nimble, accelerate more slowly and need a larger space to fit into and more stopping time and distance. Tractor-trailers can only pass when a space large enough for them to fit into is available, and tend to maintain a steady speed and not do a lot of maneuvering since they are the least nimble and take the most time to accelerate and to stop. All of this made me think of granular convection or the “brazil nut effect” and I am curious to know if in physics what I saw on the road was in fact granular convection on a large scale, or something else. I tried to find information on google and so far the typical results(regardless of search terms, for me they all lead to traffic jams or this) don’t really seem to have to do with motor-vehicle traffic really much at all that I can tell (some of those results are pretty dense with the math and sciencese).
For starters, could you tell us, in some detail, exactly what you saw happening on the road? Did you see one of those thousand-car pile-ups in a tule fog, where all the big rigs ended up on top of the pile?
There are plenty of traffic engineering texts and reports which observe that we can legitimately treat flowing traffic pretty similar to a partly compressible fluid. It’s not a good model for a traffic collision or the immediate aftermath, but once the wreckage quits moving the flow of the remaining traffic around the newly-created obstacle is also fairly well modeled as turbulent flow of a viscous fluid.
There are a lot of differences between traffic and true viscid flow, but at the arm-waving amateur level they’ve got a lot in common too. See Traffic flow - Wikipedia for more.
As such I’d agree that granular convection is a *mostly *valid model for traffic behavior vs. vehicle size.
The one area it gets pretty metaphorical is that granular convection relies on a fixed force vector, gravity, to drive it. That’s not relevant to traffic.
In the case of mixed traffic the corresponding force is the impatience of the individual drivers. Which *may *tend towards greater impatience in crotch-rocket riders & BMW drivers, and greater patience in delivery van and truck drivers. But that’s not a fact of physics, it’s a psycho-social correlation.
Yes, a crotch-rocket *can *accelerate and maneuver more aggressively than an 18-wheeler can. But it doesn’t *have *to.
Of course with motorcycles there’s the issue that everywhere in North America except California we accept the legal fiction that they take up just as much room on the road as a car. In virtually every other country in the world (and California) they’re allowed to filter between cars in congested traffic, so in the mixed nut analogy they’d maybe be crumbs or bits of salt that zip to the bottom of the dish and stay there.
Yes, this right here is part of what was messing me up. People driving on a road have volition, where nuts, or other granular mixes do not appear to have intelligence and are motivated by an exterior force, such as gravity, instead of “I want to”.
Also its hard not to get tripped up on the term “fluid dynamics” when contemplating the big rig next to you at 70 mph
Oh and Senegoid, nothing, just driving along the freeway observing normal, freely moving traffic.
I would guess not. What makes granular flow so much different from ordinary fluid flow is that the forces are very short-ranged and very strong – more or less, there is no force between the particles until they touch, and then it is extremely strong (because the particles cannot penetrate each other). These sort of “excluded volume” forces tend to produce quite different statistical mechanics than the softer forces that are also important in ordinary fluid flow.
In the case of traffic, you are presumably tempted to equate the interacting particles (the cars etc) as granular because they look “hard” – with definite edges and such. But what’s important from the point of view of the flow is what the forces are between them, or rather, in this case, what the effective forces are that are caused by each driver’s desire to (1) get where he’s going as fast as possible but (2) remain alive, and with a car undented.
In fact, these effective forces are very far from being short-range hard “excluded volume” forces. They have much more in common with soft long-range forces like the Coulumb force. Typically, a driver is gently repelled by another car at quite a large distance, and effective force of repulsion (staying away) increases as the distance gets lower, and increases faster as the distance gets lower.
It’s because of these softer long-range forces that traffic is more often modeled as a compressable fluid. Phenomenologically, it behaves that way because it clearly supports sound waves. (Well, not literal sound waves, but waves that you could “hear” if you had a 5km eardrum that responded to the force exerted on it by waves of cars crashing into it.) There are also shock waves around obstacles, and loads of other typical compressible fluid features. But these are all indications that traffic is not like granular flow, which is on the other side of the spectrum, as far from compressable fluid as you can get.
I agree with Carl Pham’s characterization of long-range soft forces versus short-range hard forces.
An interesting feature of traffic is that as density increases from very light the fluid changes from mostly long/soft forces to, in bumper-to-bumper conditions, almost exactly and entirely short/hard forces.
This has some gross similarity to subsonic vice supersonic flow. It’s easy to carry this metaphor too far. Sonic flow has an abrupt discontinuous transition, whereas increasing traffic density behaves more like increasing viscosity with non-linear, but still continuous, changes in behavior.
Here’s another metaphor:
Imagine a homogenously mixed fluid composed of, say, 5 kinds of molecules each with very different sizes and densities. In our mixture by design the largest molecules are the densest and vice versa. Now fill a beaker with a sample of this mixture. Assume thermal equilibrium and no stirring.
Over time we’ll see gravity drive fractionation; the big dense stuff will settle to the bottom and the small light stuff will float to the top.
That’s a model that captures both “granular convection” effects (at least at the arm-waving level) as well as viscid fluid behavior. And it probably conforms fairly closely to the OP’s ideas. The only hard part is seeing the behavior of the individual molecules as they collectively fractionate.