# Effective radius of a tire and rolling resistance based on information on velocity and tire pressure

I need to make an nonlinear observer of a system and need to know how the charactaristics of a tire are to get the final conclusion.

I really need some good articles about how the effective radius of a tire will vary depending on velocity and pressure. I would appreciate any articles about rolling resistance too.

I would appreciate if someone could give me a hint.

• Read this answer : engineering.stackexchange.com/questions/5670/… Sep 6 '17 at 20:28
• Have you tried searching google scholar? Dec 8 '17 at 0:07
• A lot Ms Katarina, I found a magic formula for Adam tire model. it is however too complicated and includes variables that are not available at this moment in my project Dec 29 '17 at 17:59
• Here's an article with loads of handy info, as well as what you're looking for: the-contact-patch.com/book/road/c2020-the-contact-patch. Also cited here
– ChP
Mar 5 '18 at 12:52

## 2 Answers

Measure the effective circumference to calculate the diameter. To do this mark the tire, and the ground with paint or a soapstone. Move the vehicle until the mark on the tire contacts the ground again, and mark the ground. Then measure the distance between the marks on the ground. This distance is the effective circumference. C = 2 * pi * r. Solve for r. r = C / (2 * pi).

• A good start but not the answer, the effective radius is not constant; it gets smaller when driving faster.
– Bart
Apr 4 '18 at 17:58
• Oh course. This is an approximation used in by the Society of Automotive Engineers. Without, turning this into a multi-physics problem with elastic materials. What is your solution, Bart? May 30 '18 at 0:05
• @Derkooh . Thanks but that not the the answer Im looking for. What you propose is a radius of a perfect circle that is a totally unloaded tire. Jun 10 '18 at 19:45
• @Payam30. On the contrary this can be used for loaded tires. It is an industry standard I’ve used with heavy equipment. Check out SAE J2204. Jun 11 '18 at 20:24

Rough estimate:

If the car is not moving fast- Let's call the flat contact surface of tire A, and forget about the bending flexure resistance of the side-walls and the leading and trailing edges of this surface. $$A*air\ pressure \ = tire\ load$$

So $$A = \frac{tire\ load }{air\ pressure}$$

And from there having the section dimensions of the tire we can calculate the effective radius, which is the distance from a circle section A to its center.

However this can hardly be a good estimate when the car is accelerating and the torque from the wheel is warping the walls of the tire, pinching and wrinkling the attack edge of the flat surface, or the tire is hot after lengthy trip.