Vehicle Dynamics Problem: Cornering wheels must slide on the road

Can anyone see this geometric fact that cornering wheels must slide on the road? What I mean is that the tread within the contact patch of the rolling wheel, which is travelling along a curved/circular path, will slide on the road because the wheel is changing rolling direction - rotating on a vertical axis.

Slip angle concept and all its phenomena rely on the tire tread staying in place on the road while the wheel corners and travels around the turn center. Geometry reveals this to be impossible.

As a wheel travels around the turn center it also rotates on a vertical axis at the same angular rate. Whether the turn is very tight with a small radius or very wide with a large radius, the wheel rotates on a vertical axis relative to the road.

The tread deformation that defines a slip angle occurs over a distance of wheel travel and that travel is only along a straight path. We must look at the next instant where the wheel has rotated on a vertical axis and over that period the travel path is curved. Slip angle does not address this reality and only describes straight path travel of a rolling wheel experiencing a side force.

A cornering wheel does experience a continual side force and tread deflection, but the slip angle concept provides no explanation for why the tread deflecting side force from the road changes direction - always toward a turn center. The actual reason is because the wheel rotates on a vertical axis and, because of the reality of its geometry, the tread must slide on the road which then means a slip angle defining tread deflection cannot be created and or maintained.

The rolling exercise ball Fig 4 shows how a cornering/turning contact patch can be created that doesn’t slide/skid. But when the ball is constrained with an axle Fig 5 such as a wheel on a car, the contact patch must slide on the floor when the rolling/travelling direction changes. An experiment we can try at home.

When your car has a flat tire, roll the spare along the ground and see that it only rolls along a straight path. When you try to make it turn you will see it, hear it, slide at its contact patch. We currently believe that when we put that wheel on our car it magically inherits a different principle of physics where it no longer needs to slide when it turns. Not the case. Cornering wheels slide/skid on the road because nature says so.

Can anyone else see this?

• – Solar Mike Nov 25 at 14:44
• Nope. This is about geometry and the wheel. You are correct that it also relates to cars, but please look more carefully. Thanks! – Matt Zusy Nov 25 at 14:47
• No paradox. The same elasticity that admits the formation of a contact patch also admits a degree of compliance when turning. For equal lateral forces, there will be more scrubbing during a turn than on a sideslope going straight ahead. So there are differences due to the differing shear field over the contact patch. But as long as most of the tire patch is operating in a linear range of strain, the slip angle should be pretty much the same. Weight transfer and alignment are probably more important issues to account for. – Phil Sweet Nov 25 at 16:33
• @PhilSweet Are you saying the tread deforms into a curved shape that aligns with the circular path the cornering wheel travels? One side stretches and the other side compresses and this allows the tread within the contact patch to stick to the road and not slide? Doesn’t slip angle deformation of the tread define the travel direction of the wheel? If the tread deforms to align with the curved path, how would we define a slip angle? – Matt Zusy Nov 25 at 21:47
• What about it? Why do you think that "vehicle dynamics" implies that there is no slipping? You have not defined vehicle dynamics, so you are arguing with yourself. Does your definition of "vehicle dynamics" only cover the motion of general bodies or does it explain everything down to the individual atom? You are arguing that an undefined term doesn't explain every single phenomenon. Does it matter if a small patch slides if the whole tire does not slide? Your diagram shows that some patches don't slide, so the whole tire is not sliding. – hazzey Nov 29 at 0:42