Sunday, November 04, 2007

Text Savvy: Odometer and Speedometer Errors with Winter Studded Tires

Text Savvy
An odometer records the number of kilometers a car travels. Assume that the odometer gives the correct distance when the overall diameter of the wheel plus tire is 50 cm. If several months later, 6.8 mm of the tread was worn evenly from the tire, what percentage more or less than the actual distance traveled will the odometer reading give?
Yesterday I wrote about the odometer error on cars when a tire becomes worn. The effect is that your actual mileage is greater than the odometer reads. Is the inverse true? If you increase your tire size, is your actual mileage less than what the odometer reads? Even more important, for me: could a speedometer error with winter studded tires on the car cause me to be stopped for speeding?

You know those numbers on your tires? I learned what they are all about. I won’t detail their meaning here. You can go to the Burke paper to learn about them. But in order to figure out my questions about my studs, I took a tape measure and found that from side to side, my tires measured 24.5 inches. This seemed an odd number to me, and I wondered what their diameter should actually be. I was with four other teachers at an in-service day when I was solving this. We all went outside to read the numbers on my wheels, and they read 195/65R15. I learned from Burke’s paper that I can calculate the diameter with the formula he gives:

Diameter = 15 + (195 • 65) ÷ 1270 = 24.98, which would be 25 inches diameter.

(What happened to the rest of the rubber on the tires? That is a lot of rubber to lose on each tire. Does it evaporate? Remain on the road? How much pollution is this causing for the environment? (Perhaps one of you knows.))

Odometer Errors
One other teacher used to drive studs before she got her truck. She and I calculated that studs are one-quarter inch long, which increases the diameter of the tire by one-half of an inch. (I will verify this next week when my tires are put on.) That would give a new diameter of 25.5 inches on new studded tires, versus 25 inches on new tires. Using Burke’s ratio, the odometer error would be 25.5 inches ÷ 25 inches, or 1.02. Therefore, when my odometer clicks 1 mile, I have actually traveled 1.02 miles, or twenty miles more for every 1,000 miles traveled.

Speedometer Errors
According to Burke, the formula for speedometer errors is:

Actual speed = (speedometer reading • new tire diameter) ÷ original tire diameter

The speed limit on the state roads in Vermont is 50 mph (unless you are in a village, where speed limits vary). I assume that my car is calibrated so that with 25-inch tires my speedometer will read the correct speed of the car. Therefore:

Actual speed = (50 mph • 25.5 inches) ÷ 25 inches = 1275 ÷ 25 = 51 mph

That isn’t enough to cause me to be pulled over. That’s a relief!

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