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**

Where,

*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**

Where,

*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**

SLR = 0.96 x R, How do you generate 0.96

This is an approximation, to be more precise

SLR = R – (thread depth)

did you mean tread depth instead of thread depth???

yes

how to calculate tread from tire cure lay out

hey tell us roll center position

Interesting solution given by you. Thanks for sharing.