Silly Calculations Related to Driving


A few weeks ago I mentioned that I had a long car trip. Whenever I have to drive a lot, I find myself thinking of the same silly questions, but I never care enough when I stop driving to do the calculation. Here they are:

Motivation: If you’re driving 69 mph on the highway (65 mph speed limit), you will probably never get pulled over. I’m not advocating breaking the law. I’m just stating a pretty well-known fact. If you go 71 mph, you’re flirting with getting a ticket. I always wonder just how much time I would save by going those 2 mph faster.

I warned you this would be silly. You can probably even do this one in your head. Suppose my trip is about 500 miles long. Going 69 mph would take a little less than 7 hours 15 minutes. Going 71 mph would take a little over 7 hours. So you’d only save about 10 minutes on a trip that is over 7 hours. Considering the significant increased risk for a ticket, this doesn’t seem worth it to me. On short trips of an hour or less, the difference in time can’t even be detected.

Motivation: No one drives perfectly straight. You always have to make little adjustments back and forth to stay in the lane. You also probably change lanes on the highway. I always wonder just how much distance those little adjustments add. Do they add up over a long trip, or does it remain insignificant?

Wikipedia tells us a highway lane is 12 feet wide. Let’s do an underestimate that doesn’t factor in lane changes and say you swerve from one end to the other of the lane twice every mile:

Now use the Pythagorean theorem, and you’ll find that the diagonal line isn’t even a full foot longer than if you didn’t swerve. In fact, the 4 diagonal lines don’t even add up to an extra foot over that mile. That means this swerving estimate produced less than 500 feet extra travel distance over 500 miles. It’s not even a quarter of a mile!

Even if you try to modify the estimate to be way over, factoring in lane changes and everything, as long as you keep the numbers realistic, you probably can’t even get it to be more than a mile or two. This means that these little adjustments do not add up, even over a very long drive. So swerve away!

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