I am currently pondering the physics of banked curves in roadways. Everyone even slightly aware of roadways and cars has encountered turns in which the road is tilted up sideways so that one has to go uphill to take the turn. This is especially apparent in car racing tracks where the banking angle is quite steep to compensate for the high speeds of the race cars. But why are the turns tilted, while the straightaways are flat? It has to do with Newton's law of NASCAR: F = ma. And Newton's law of gravity as well. The force that keeps the car on the road when it is making a turn is the friction of the tires pushing the car towards the center of its curved turn (as if it were going around in a circle, rather than just taking a turn). The faster the car is going, the more the inertia of the car wants to just fly off the road in a straight line rather than keep turning. Hence the noise of tires and the excitement as a speeding car takes a turn. But there is a way to help the cars stay on the road: let gravity do some of it. The banked turn adds the force of gravity, at least a portion of it, to the anti-skid friction force of the tires. If the car skids, it has to skid uphill. But at the same time, as one of my Friendly Scientists has informed me, the incline also takes away some of the force holding down the car (the "normal" force) so that the drivers still have to be careful to calculate just how much speed they can have going into the turn. There are always mistakes to be made on the high-speed turns.

On the notorious Washington Capitol Beltway, there is a stretch near Bethesda and Silver Spring in Maryland, which takes three or four rather sharp turns, at least for a major highway. If you drive (as I have done countless times) on this stretch during one of the less trafficky hours of the day, you come into this segment at speed and take those turns like a race driver. Each of these curves has a very noticeable tilt, to help the Beltway bashers keep their vehicles on the road. I call this section the "Bethesda Speedway."

The section is anything but a speedway at evening rush hour times (which last from 3 PM until 8 PM in the DC-Metro area). The cars are packed in there for miles, halted by roadwork, accidents, or just plain "volume," as the traffic radio announcers euphemistically say. I have inched along with the hapless drivers in this dreary stream many a time. When they get to the inclined curves which were designed to be taken at 50 MPH or more, they are going about 5 MPH. So the speed is not compensating for the tilt, and the drivers and passengers just sit there on an incline, oozing downward toward the left-side doors of their speedless conveyance.

There is, though, one especially sharp curve at Silver Spring, where no matter how dense or slow the traffic is, things speed up. I never fail to hope, when I am about to enter this curve where things are moving, that this is the end of the backup and I will be in the clear to drive freely. I see the cars speeding up in front of me. I see space between them. They are taking this banked turn with adequate speed. Free at last! But no, after the curve, out of my sight, the cars back up again, and the slow line of traffic continues as it did before. There must be some sort of physics which explains why the traffic speeds up only for this few hundred yards of curve, and then stops again. Is it the incline? Is it because drivers coming up on it can't see beyond it? What mysterious force liberates the flow just for that moment and then bottles it up again? I have a name for this Beltway curve, which is so full of physics and disappointment. I call it the Curve of Lost Illusions, where brief hope is quickly crushed under a multitude of slowly turning wheels.

Posted at 3:30 am | link