Math for Tailgaters

I had a bunch of stuff to mail, so I drove to the post office to drop them off, in my once or twice per month driving outing. When I thought to myself, the driver in front of me is going kind of slow, I thought that must mean I'm improving health-wise. Of course, I didn't do anything stupid, like the driver who ended up behind me a little while later.

I found myself behind a motorcyclist on the freeway, so I decided to leave about 50 feet of clearance. Not only because my sister's young friend was recently killed in a motorcycle accident, but because that is always the common sense thing to do. 50 feet to me is a rather normal spacing between cars on a freeway. For motorcyclists I leave more, because I ask what if he slips, because they do.

The driver behind me thought it would be cool to tell me that I'm doing some great wrongdoing to him, by first honking and then passing on the left and practically driving through the front of my car (at least that's how it looks from the driver's seat) right before he exited the freeway. And the point is...?

Sometimes it's tempting to make a bigger gap or drive slower when being honked at by a tailgater. But that's almost resorting to similar stupid behavior.

First of all, when going any speed anywhere, it doesn't matter if there's 5, 10, 20, or 100 feet of space in front of your car or the car in front of you. You're still going the same speed, and won't get anywhere any faster! (in any relevant units of time)

A Wily Blog recently posted how math is useful for pill poppers. Here is an even simpler math problem of everyday life:

If I were to have ridden on the motorcyclist's butt, leaving a mere 10 feet instead of 50 feet of space, and the cars on the freeway are moving at 50 mph, how much sooner would the tailgater on my butt get to his destination?

(50 - 10 ft) / (5280 ft/mi) / (50 mi/hr) * (3600 s/hr) = 0.54 s

It would save half a second. This doesn't change no matter how long the tailgater is riding on my butt, if other cars and especially cars in front of me are going the same speed. Unless you think you can drive through cars, which apparently he did try to do.

According to the three-second rule mentioned in drivers' ed, how much space should I leave between cars, when traveling at 50 mph?

(3 s) / (3600 s/hr) * (50 mi/hr) * (5280 ft/mi) = 220 ft

I would also argue that if drivers in general didn't tailgate as much, traffic would actually move faster, because driving too close causes more stop-and-go which slows everything down, if you notice the delay time domino effect between acceleration of a line of cars.