# Chart of the Day: Flow Rate v. Density (on Freeways)

This chart comes from Philip Ball’s interesting book Critical Mass, which describes complex non-linear dynamics using real world examples. There’s one fascinating chapter on traffic jams, and I’m going to post a few of the charts from it.

For example, the overall volume of a freeway is a combination of speed + density, something that is here called “flow rate.” (I.e. 100 cars per hour can equal 100 tightly packed cars traveling at 30 mph or 100 loosely spaced cars traveling at 60 mph.)

As density increases, the flow rate increases as well until you reach a critical point, whereby the slightest perturbation in the system will cause a dramatic decrease in speeds to cascade through the system, average speeds to plummet, and the overall flow rate to decrease into a second kind of “basin of attraction.”  This is a classic example of non-linear dynamics, and is one of the things that makes traffic jams so predictably unpredictable and therefore fascinating.

(Stay tuned for more next week…)

Bill Lindeke has been blogging about sidewalks and cities since 2005, ever since he read Jane Jacobs. He has a PhD in geography from the University of Minnesota, teaches geography around town, and has written for Minnpost, the Park Bugle, and Growler Magazine, among others. He was born in Minneapolis, but has spent most of his time in St Paul. Check out Twitter @BillLindeke or on Facebook.

## 4 thoughts on “Chart of the Day: Flow Rate v. Density (on Freeways)”

1. Andy

I’m not sure if this works but I always compare traffic to water flow in a pipe. If one chooses a pipe too large in diameter, the lack of pressure can actually cause more problems (like having too many lanes on a road). I didn’t study dynamics but, does this analogy fit? Like, are roads basically 2-d pipes running water? Seems that this critical point concept holds for both models. Also seems like this is the greatest argument against adding lanes. If the volume and capacity don’t match, jams could end up being worse?

2. Stacy

Andy – In short, no. Extra lanes would not cause worse jams. If anything, extra lanes would be an inefficient use of land and pavement, but they do not slow cars.

Flow rate is not the same as speed. The speed label on this chart is misleading.