Finding Miles Per Hour

Date: 03/06/2002 at 20:21:44
From: joshua
Subject: RPM (How to find mph)

Let's say I'm going 64.2 rpm. How many mph am I going? How do you 
solve it?

Date: 03/06/2002 at 21:26:21
From: Doctor Twe
Subject: Re: RPM (How to find mph)

Hi Joshua - thanks for writing to Dr. Math.

That depends on the size of your wheel(s). Suppose your tire is 28" in 
diameter. Then the circumference is 28*pi inches, or about 88".

Assuming that there is no slippage, that means that the wheel is 
moving 88" every time it makes one complete revolution. At 60 rpm, 
that equals 60 * 88" = 5280" every minute.

Now we must convert inches per minute to miles per hour. There are 60 
minutes per hour so:

     5280 in.   60 min.   316,800 in.
     -------- * ------- = -----------
      1 min.     1 hr.       1 hr.

There are 12 inches per foot, so:

     316,800 in.    1 ft.   26,400 ft.
     ----------- * ------ = ----------
        1 hr.      12 in.      1 hr.

And finally, there are 5280 feet per mile, so:

     26,400 ft.     1 mi.    5 mi.
     ---------- * -------- = -----
        1 hr.     5280 ft.   1 hr.

So with a 26" diameter wheel (and no slippage), 60 rpm = 5 mph.

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.com/dr.math/