R.P.M.

Calculating Revolutions Per Mile is usually not a necessary item of concern for most people. However, it can be an issue for someone that is changing tire sizes or the profile of the tires that are on a vehicle. Changing tire sizes obviously changes the outside dimensions of a tire, which changes revolutions required to drive any distance, which in turn changes the speedometer reading. Drastic changes require attention, especially for commercial vehicles. 

While it may seem simple to some to calculate these numbers, it isn't as easy as it seems. First, we must remember, that we need to know how many turns per mile the tire makes while under a loaded condition. So simply measuring the outside of a tire with a tape ruler will not be accurate. We must therefore make adjustments for this and for tread depths.

First we will start with a brand new tire. We will use a Michelin XZA3 steer tire in an 11R22.5 size.

We need 2 pieces of information which can be obtained from either measurement or a Manufacturers Data book. If you have the MFG data book you probably don't need to calculate RPM because it should be contained in the book.

The 2 pieces of information we need are the diameter of the tire when unloaded and the Static Load Radius. Overall Diameter (O.D.) can be obtained by measuring the tire from top to bottom making sure to pass over the center of the tire or if the tire is on the vehicle you can measure from the hub center to the top of the tire (radius) and multiply by 2.

Static Load Radius (SLR) is obtained by measuring the tire on a loaded vehicle that is not on any jack, lift, or stands and is stationary on a flat surface. The measurement is taken from the center of the hub to the ground

Warning: Upon investigating and testing these formulas with various manufacturer data books it was found that the RPM data contained in some books is VERY inaccurate. I have confirmed that some RPM data statistics are off by hundreds of RPM's. Some are off by 30% or more. Reasons for this are unknown but it is assumed that these are editing errors.

Once we have these 2 measurements, we just need to plug them into a formula to get our answer.

Our formulas are as follows:

First we determine what is called deflection.

   Deflection = O.D. / 2 - SLR    i.e. (Overall Diameter / 2) - Static Load Radius

Now we plug all of our numbers into the following formula.

          R.P.M. = 20,168  /  ((O.D. - ( .8 x deflection)))

                   63,360 / PI     These numbers are always the same

   As stated we will use the XZA3 11R22.5 as an example below.

          Deflection = (41.3 / 2) - 19.3  answer: 1.35

          R.P.M. = 20,168 / ((41.3 - ( .8 x 1.35)))  answer:  501.44 RPM

The Michelin Data Book lists 502 RPM for this tire. That is because most RPM data is based on average observation during testing in development. Various factors affect these tests including pavement conditions, route, etc. This formula however will result in an accuracy of 1.5% and in general, it seems to come within a 1-3 RPM of actual road testing.

For used tires, you can use actual measurements or you can measure the current tread depth and start w/figures obtained from a new tire data book for the current design and size tire you are looking at.

To calculate the RPM on a used tire by using data from a new tire data book you must do the following:

  1. Measure tread depth in 3 areas on the tire and average them out

  2. Subtract the remaining tread depth from the amount on the tire when it was new

  3.  Take the answer from above (we'll use 10/32") and convert it to a decimal by dividing 10/32. The answer here is .31. Round this to .30.

   4. Subtract .30 from the O.D. for the equations above and subtract half of this number from the SLR. (This would be .15)

   5. Plug these new numbers into the formulas above as follows:

       Deflection --- (41.0 / 2) - 19.15 = 1.35

       RPM ---  20,168  / ((41.0 - ( .8 x 1.35 ))) = 505.21 RPM

As you can see, there is a difference between RPM on a new tire and a used one. Sometimes this can make a difference that is significant, especially if fuel mileage is a consideration. But, understand that there are many factors involved in fuel mileage including the fact that as a tire is worn down, it requires less energy to move it due to it's loss in weight as the tread wears down.