Circumferences

So after Christmas Eve dinner at my brother’s house, my brother poses a mathematical conundrum. He’s worked out an answer and he wants to hear mine and compare notes.

Very well! I like mathematical conundrums!

In a nutshell, he wants to know how tire wear will specifically affect his mileage.

Brand new tires on his vehicle have circumferences of 92 inches.

Since there are 5,280 feet in a mile and 12 inches in a foot, there are 63,360 inches in a mile. Divide that figure by 92 and you get about 688.7. Every mile, my brother’s tires go through 688.7 revolutions. Some gear thingy inside the motor knows this, and that’s how the odometer knows how to calculate mileage, or distance traveled.

Now say the tires wear to the point where the circumference is now 90 inches.

Divide 63,360 by 90 and you get 704. The tire needs to spin 704 times to travel a mile.

But that gear thingy doesn’t know this. It doesn’t know wear and tear. All it knows is how to count revolutions and convert that into distance.

When the worn tire spins 688.7 times, it only goes 61,983 inches, or 5,165.25 feet, or 97.8 percent of a mile. Everything decreases in efficiency by 2.2 percent. The odometer will be off, the speedometer will be off, fuel economy will be off.

So when he’s going down to Florida to Disneyworld, and Mapquest says it’ll be 1,122 miles, his tripometer will read 1146. Where did those 24 extra miles come from?

Instead of spending $135 on gas filling up on the way down, he’ll spend $138. Thus is the terrible cost of worn tires.

Actually, though, doesn’t seem all that bad.

In fact, makes me question my math …

Or the last time I actually, er, slept …