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**

### Shibashis Ghosh

Disclaimer: I work for Altair. mechGuru.com is my personal blog. Although i have tried to put my neutral opinion while writing about different competitor's technologies, still i would like you to read the articles by keeping my background in mind.

#### Latest posts by Shibashis Ghosh (see all)

- How to Make Line Follower Robot without Using Microcontroller - September 15, 2018
- Design for Additive Manufacturing Worksheet - July 7, 2018
- 3D Printing Simulation Software – Are They Capable Enough? - July 16, 2017

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