# Tire engineering - are "free rolling" and "slip ratio" defined with respect to a specific tire/road material pair?

Pacjeka states the following on his introduction to tire characteristics:

The upright wheel rolling freely, that is without applying a driving torque, over a flat level road surface along a straight line at zero side slip, may be defined as the starting situation with all components of slip equal to zero. A relatively small pulling force is needed to overcome the tyre rolling resistance and a side force and (self) aligning torque may occur as a result of the not completely symmetric structure of the tyre. When the wheel motion deviates from this by definition zero slip condition, wheel slip occurs that is accompanied by a build-up of additional tyre deformation and possibly partial sliding in the contact patch.

The following is my understanding, and I'd like input on if it is correct:

• "Free rolling" is defined as the state at which a wheel rotates without any driving/braking torques acting upon it, not as the state at which a wheel rotates with a driving torque that balances the tire rolling resistance. As a consequence, a freely rolling tire is actually experiencing deceleration.
• The "slip ratio" is defined to be zero at the free rolling state.
• In this sense, the slip ratio doesn't directly relate the absolute value of the relative motion between tire and road (what is commonly understood as "slipping"). In addition, the exact relative motion experienced by a wheel in free rolling is dependent on the tire/road pair, e.g. inflated vs. deflated, pavement vs. snow, and so on, even though the free rolling condition for all of those will by definition lead to a slip ratio of 0.
• if this is true wheel rotates without any driving/braking torques, then how can this be true? ... tire is actually experiencing deceleration Aug 25, 2022 at 21:00
• @jsotola I meant "braking torque" to be a torque other than the one developed due to rolling resistance.
– jvf
Aug 26, 2022 at 0:33
• The above para says that free rolling means zero slip. It's just a wheel that isn't turning and the wheel speed = road speed. Aug 29, 2022 at 4:26

You are right, the free-rolling on a flat surface is decelerating, albeit relatively slowly.

As to the road conditions again free-rolling means no skid/slip.

If we ignore air friction the source of friction in free-rolling is the elastic deformation of the tire which is two parts: designed deformation for traction and self-alignment and incidental deformation. both are very complex.

• >As to the road conditions again free-rolling means no skid/slip. By definition, there is no slipping in the "slip ratio" sense, but that doesn't necessarily mean there isn't any rubber sliding against the road, right?
– jvf
Aug 26, 2022 at 0:34

If the tire is decelerating, there is a transfer of momentum. If there is a transfer or momentum, there is a force, and where there is a force, there is slip.

If what you are looking for is the state of zero slip, 'free rolling' means powered enough to overcome rolling resistance.

It's not just theoretical: if you want to prevent tire skidding in a low-friction situation, you must provide enough power to overcome rolling resistance.

In some other context, 'free rolling' may have some other meaning.