Kinematics of Driving: Some 'Real' Traffic Considerations

July 2000

Does Tailgating Pay?

When the car in front of us is traveling slower than we want to go, most of us subconciously get closer than we should. The loss of critical stopping distance and reaction time makes this very unsafe. Also, the shorter time forces us to react more strongly to everything the car in front does, making the drive much harder on our nerves and on our car. Can we justify all this by getting to our destination faster?

Compare the cases of keeping 2 seconds or 1 second between you and the car in front. You are keeping a constant separation in both cases, hence your speed is the same as the car in front in both cases. (You both travel the same distance in any given amount of time and {speed} = {distance traveled}/{time interval}.) One way to look at it: no matter what you are doing behind it the car will still pass any given location at the same time and you will then pass the same location either 1 or 2 seconds after it. So the most benefit you can expect from tailgating is to save 1 second on your trip. If you really care about every second, you can get the same 1 second saving by traveling a safe stress-free distance for most of the trip, then closing the gap by speeding up in the last few seconds of the trip.

In the case of heavy traffic, tailgating can actually slow you down. When traveling in heavy rush hour traffic I mentally tag a few cars desparately tailgating and weaving. After half an hour they are usually still easy to see, within a few seconds of where I am and often behind me. Why does this happen? This is similar to the traffic light simulation above. By tailgating you are forced to slow down and even stop when the car in front slows down to turn. The time taken to get back up to speed means that there is a larger gap in front of you than if you had been keeping a safe distance. In heavy traffic a gap is quickly filled, so the tailgating causes you to end up with more cars in front because there is more space available after the car in front turns.

It is often the case that "real" considerations produce different answers than the idealized problems we give to teach the principles of physics. One example of this is that a person will probably believe that by speeding -though they risk a ticket and/or an accident- they will get to their destination faster. Often this is true, but real traffic can do things you aren't expecting. Bill Beaty's article Traffic Waves, Physics for bored commuters shows how people who speed and weave in and out of traffic are themselves the source of the very things that they are trying to avoid. In the following article I'll consider what can happen when trying to beat the traffic lights.

Timing of traffic lights is usually set to try and ease the flow of traffic - especially on major routes. One common approach permits a person to drive along a street at the speed limit and get every light green - or at least every light green after one red light (since you are now on the green sequence the others should be green). So what happens when you try to beat the system?

The animation at the top of this page shows two cars driving down such a street. The light blue minivan is traveling at the speed limit, the little red sports car is in a hurry and hits the gas hard when the light turns green. The minivan has an easy drive hitting every light green. The sports car leaves a lot of rubber on the road, wears a bit a the brakes at every stop, gives the transmission a good workout... in general the trip is not kind to the car. Both drivers take the same trip in the same time (within a few seconds), but while the minivan driver arrives relaxed the sports car driver walks into the room cursing his luck "You won't believe my bad luck, every single traffic light was red!!!".

I'm not going to try and convince you of anything with kinematic equations... those are useful of course, but I'm dealing with something which is also very useful and not given nearly enough credit - gut feeling physics. No matter what your test scores might say, your ability to look at something and just have a feeling what will happen is one of the key indicators of how much physics you really understand. So study the animation above and you should be able to figure out what is going on. The challenge is to see whether this contrived animation has much bearing on real traffic situations. Around where I live it does! Many a time I've been "in a hurry" but have had to admit that the same cars as I passed 15 blocks ago keep closing the gap at "red light" after "red light" (green for them). So your challenge is to watch the traffic around you and see if the same pattern is true where you live. Your watching of cars speeding up and slowing down at intersections will also be good for your gut feeling of kinematics.

Something else to consider is who creates problems in heavy traffic?. Suppose the sports car in the animation is being followed by a bunch of minivans. The one immediately behind it would have to slow down a bit at the intersection because otherwise it might hit the sports car while it gets back up to speed. That causes the next minivan to also slow down, which causes the next to also slow down... hence there will be some minivans that should have made it through the intersection, but the sports car's "hurry" has left behind it congestion that keeps some of them from making it. And the sports car generates these problems at intersection after intersection, creating the very problems that he hopes not to meet himself.

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