I visited a company in Auckland yesterday, which involved negotiating the famous Auckland traffic. Now, I have to say that arriving in Auckland after the rush hour proved a very smart move, and we cruised to our destination without any fuss, but it got me thinking about traffic flow and physics.

In **some** ways, the flow of traffic along a road is similar to the flow of water in a pipe, or flow of blood cells through the body, or electrical charge through an electrical circuit. For example, when you get to an intersection, if there are no delays, the flow of traffic leftwards, plus the flow of traffic rightwards, must equal the flow arriving at the intersection. Same with water; when a pipe splits, the number of litres per minute flowing left, plus the number of litres per minute flowing right, equals the number of litres per minute arriving. In traffic flow, however, jams can form, for example if the flow of cars leaving an intersection is lower than the flow arriving. In this case there must be a build-up of cars at the intersection. This effect also arises in other areas of physics (e.g. heat flow) and can be described by the continuity equation.

But traffic flow can show really odd effects. With water, if you increase the pressure, the flow rate increases. But that’s not necessarily true with traffic. If you pack more cars onto the road, you don’t necessarily get more flowing per minute; instead they can grind to a halt and you get less flow. These ‘non-linear’ effects are difficult to work out, but there are many physicists who are dedicated to studying traffic flow in order to make it go more smoothly. (Example.) Although you might not like them, on-ramp traffic lights and variable speed limits (yet to hit New Zealand, but anyone who’s driven on the M25 around London will know them), have been designed partly by physicists and do actually work. Physics doing something useful, again.

The same kind of analyses can also be used for people traffic, too.