Question

A bicycle computer or cyclometer uses a magnet counter that records each wheel rotation to calculate the bike’s total distance traveled. To set up the computer, you select a calibration constant for the bike’s wheel size. The computer multiplies this constant times the number of tire rotations to find the total distance in miles. Enter a function for the distance d in miles if the calibration number is 0.00125. If the function is incorrect and your tire is actually slightly smaller, how should the function change?

Answer 1

The simplest and probably the best way to understand this problem is to make up a problem that obeys what you have been given. It doesn't have to be realistic. It just has to obey the conditions. Let us suppose that you thought the diameter of the tire is 1 yard. That would mean the circumfrence is pi * d

C = 3.14 * 1

That would mean that the circumference is 3.14 yards. It would also mean that you would have to have the wheel turn 1760 yards / /3.14 yards / revolution which is about 561 revolutions / mile. So the way I have set up the problem, my equation is d = 561 * R where R is the number of revolutions.

Now let's see what happens when you say "O my Goodness, the wheel diameter is really 32 inches" which 0.8888888 yards  what happens now?

Now you still have to go 1760 yards How many revolutions is that?

C = pi * d

C = 3.14 * 0.88888888

C = 2.79111 yards

How many revolutions does it take to 1760 yards.

R = 1760 // 2.78111 yards / revolution

R = 631 revolutions / mile. What happened?

Your constant goes up if the wheel diameter goes down. Think about this. Do you ride a bicycle? I do. It makes perfect sense to me that if the wheel is small, it will have to turn more often to go a mile. No matter where that 0.00125 comes from or how it was derived, the constant will have to go up if the wheel gets smaller.