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tire diameter and drive ratio
Math in the Round by Summitracing.com
Tuesday, November 18, 2003
What could be better than spending an afternoon in the garage, quaffing your favorite beverage and doing—math? This isn’t the stuff that numbed your mind in high school, but fun gearhead math. We’re gonna show you formulas to help determine the effect of tire diameter on your Mustang’s performance.
Why is this important? Tire diameter changes the final drive ratio, or rear axle gearing, which in turn affects performance. A Mustang that has decent acceleration with a set of 26 inch tall tires and 3.55 rear axle gears becomes a dog with 29 inch tall tires and the same gearing. By calculating tire height, comparing final drive ratios with different height tires, and determining proper axle gearing, you can find the right size tires and appropriate gears for your application before buying your rollers.
You will need three figures to do all this: the vehicle’s present rear axle gearing, the diameter of your existing tires, and the diameter of the tires you want to use. Let’s break out the calculator and start figuring!
Determining Tire Diameter
There are two ways of determining tire diameter. One is to call your friendly tire dealer and ask for it—easy, but not always available. The second is to use the following formulas and figure things out yourself. Please note that these formulas are for metric-rated passenger and light truck tires. Slicks, large off-road, and some larger, Pro Street style tires are already rated by diameter, so you don’t have to do any calculating for them.
We will be using a P235/60R-15 tire as our example: 235 is the section width, 60 the aspect ratio, and 15 the required wheel rim diameter. Here is the basic formula, where TD is tire diameter, SW is section width, AS is aspect ratio, and RD is rim diameter:
TD = (2 x SW)/25.4 x AS/100 + RD
When you plug in the values from our sample tire, the formula looks like this:
TD = (2 x 235)/25.4 x 60/100 + 15
Now, let’s do the calculations:
TD = 2 x 9.25 x .60 + 15
TD = 2 x 5.55 + 15
TD = 26.1 inches
So, the effective tire diameter for our example is 26 inches.
Calculating Effective Drive Ratio
Once you determine the diameter of your old tires and potential replacements, you can compare the effect of new tires on the final drive ratio. For example, you have 26 inch tall tires with a 3.55 gear, and you want to go to 28 inch tall tires. To calculate the effective drive ratio with the new tires, divide the old tire diameter by the new diameter, then multiply that figure by the gear ratio:
26/28 = .92857142857
.92857142857 x 3.55 = 3.2964 or 3.30
As you can see, the larger tires reduce your final drive ratio to 3.30—a measurable difference. You can also do this to determine the effect of smaller tires on the final drive ratio.
Calculating Equivalent Drive Ratio
Now that you know that 28 inch tall tires reduce your final drive ratio, you can calculate the gearing needed to match the performance of your original 26 inch tire/3.55 gear combination. First, divide the new tire diameter by the original tire diameter, then multiply that figure by the original (3.55) gear ratio:
28/26 = 1.0769230769
1.0769230769 x 3.55 = 3.82
With 28 inch tires, you would need a 3.82 rear axle gear to match vehicle performance with 26 inch tires and 3.55 gears. Since a 3.82 gear is not offered for most rear axles, you will need to choose a gear between 3.73 and 3.90 to get close to the optimum. See, was that so hard?