Wheel rolling radius or static loaded radius is taken as input for tire rolling circumference calculation.
The rolling circumference (RC), in turns, is further considered as input in various vehicle dynamics calculation like traction force calculation and grade ability calculation.
The formula used here is quite simple,
RC = 2 x ∏ x SLR……………….eq.1
SLR = static loaded radius for the wheel or wheel rolling radius
Now, when the wheel is not fitted with the vehicle then it remains at its circular shape and
SLR = R
R = Tire outer radius
But, as soon as the tire is fitted with the vehicle (and loaded) it makes a flat contact with ground and thus its outer radius got reduced. In this condition, roughly,
SLR = 0.96 x R
So, the eq.1 turns to
RC = 2 x ∏ x 0.96 x R ………….eq.2
Pretty simple, right?
But how to know the outer radius (R) of a tire? For that you should note down your tire spec code and you must know how to decode it. The below example will clarify it further.
How to Read a Tire Specification Code?
Take the example of the below tire. And refer the below picture before proceeding further. It has the spec code starting with P215/65R15.
Image source: wiki
As you can understand from the above picture that, the width of the tire is 215 mm.
And, the depth (height) of the tire is 65% of 215 that is 215 x 0.65 = 139.75 mm
The rim outer diameter for the wheel can be obtained from the “Rim diameter code”, which is 15 inch or 381 mm.
So, the rim outer radius = 0.5 x 381 = 190.5 mm.
Hence, the outer radius of the wheel,
R = Depth of the tire + Rim outer radius = 139.75 + 190.5 = 330.25 mm
Further by using the eq.2, the rolling circumference for this example is
RC = 2 x ∏ x 0.96 x R = 2 x 3.14 x 0.96 x 330.25 = 1991.01 mm