Trigonometry, 3rd Edition

How does an odometer or speedometer on an automobile work? The transmission counts how many times the tires rotate (how many full revolutions take place) per second. A computer then calculates how far the car has traveled in that second by multiplying the number of revolutions by the tire circumference. Distance is given by the odometer, and the speedometer takes the distance per second and converts to miles per hour (or km/h). Realize that the computer chip is programmed to the tire designed for the vehicle. If a person were to change the tire size (smaller or larger than the original specifications), then the odometer and speedometer would need to be adjusted.

Suppose you bought a Ford Expedition Eddie Bauer Edition, which comes standard with 17-inch rims (corresponding to a tire with 25.7-inch diameter), and you decide to later upgrade these tires for 19-inch rims (corresponding to a tire with 28.2-inch diameter). If the onboard computer is not adjusted, is the actual speed faster or slower than the speedometer indicator?*

In this case, the speedometer would read 9.6% too low. For example, if your speedometer read 60 mph, your actual speed would be 65.8 mph. In this chapter, you will see how the angular speed (rotations of tires per second), radius (of the tires), and linear ...