Matt Zusy

BTW updated figures in question.

Cornering force is a lateral force on the wheel through the contact patch. The cornering force is perpendicular to the wheel rolling direction and parallel to the wheel axle. It's the force that changes the velocity direction of the wheel and car.

@Chuck The most important difference in our opinions is the location of vertical axis rotation. I say the only way for a wheel to create a lateral force is after it rotates on a vertical axis within its contact patch. You believe the axis of the wheel’s travelling rotation is at the turn center. My experiments reveal that idea ignores the physics of a rolling wheel.

Cornering wheels create a side force. Can they do that without first rotating on a vertical axis?

But that is a reaction to the force you applied.

Can a rolling wheel create a side force without first rotating on a vertical axis?

Look at the cornering mechanism in the video. It's simple and it explains everything.

If the tire was steel it wouldn't deform and it would slide. Now at what degree of elasticity of the steel tire is required before it no longer needs to slide when it corners? It's not about deforming. Geometry reveals they all slide when cornering. New tread elements enter the contact patch in a perpendicular direction to the axle.

The tire then has the next connected tread elements to be placed on to the road without lifting off the road as your foot can. You can’t change the direction without the tread sliding. It’s impossible.

The tire rotates. It’s part of the “system”. The four wheeled car. Thanks. We all see what we see.

@Chuck Look at 40 seconds into the video link below. In there is the empirical proof that cornering wheels are always rotating on a vertical axis, always turning while cornering. The video then provides the explanation showing a simple mechanism that all cornering vehicles experience when you aim wheels, rudders, etc. a different direction. youtube.com/watch?v=fvTBDdW-T-Q

@Chuck Another thing about letting the steering wheel go. Imagine the front wheels were replaced by skates. When you let the steering wheel go, the skates are biased to slide the direction they point and will continue in a straight path (let’s go with no Ackermann to keep it simple). At some point the rear wheels are rolling that direction and car is traveling straight. If we do not let go, the skates are forced by a torque to rotate on a vertical axis, continually changing direction and leaving a circular/curved path behind. The same goes for the rear wheels. The torque occurs at each.

About releasing the steering wheel: Figs 2b – 2c show a force applied to the tire that creates a rotating torque. I don’t address it, but the friction at the contact patch resists that rotation. So while a car corners, the front wheels experience a constant torque that changes the wheel’s travel direction. When you let go of the steering wheel there is no more vertical axis torque applied to the wheels (like in Fig 2d but without the lean). The wheel then continues in the direction it points. This is why wheels straighten out when you let go of a steering.

About constraints: We have to look at what creates the constraints and that would be the wheels. The wheels guide the car along the circular path and wheels only change the direction they travel when they are rotated on a vertical axis. They are not proceeding by way of the rule of rotational motion. They individually create their own path. I am proposing a completely different way to look at this and it starts with what a single wheel does.

@Chuck Thanks. You are correct that you can point to an instantaneous velocity direction at each wheel of a car that is perpendicular to the turn center. The problem is when you roll the car forward where each wheel is biased to travel straight. The rotation of a wheel around its circumference, around its axle, results in only linear motion on the plane of the surface it rolls along. What you describe is angular motion and forward for a wheel is only linear motion.

@GlenH7 Just reviewed this question and nowhere do I see the word “slide”. Also reviewed the question that is deleted and nowhere do I see a reference on when and how the cornering force is created. Can you undelete that question that deals with a different aspect (sliding) of the same subject? Thanks!

@GlenH7 Actually, that question deals with the geometry of the contact patch of the cornering wheel and how it must slide on the road which is contrary to what we think occurs with the slip angle concept. This question deals with how the cornering force is created. Same cornering subject, but NOT the same question.

What I think happens: The straight path rolling wheel rotates on a vertical axis and then the cornering force occurs. The frequency makes it appear to be a smooth and circular path. What they think happens: The wheel rolls around a turn center along a circular path and the cornering force is constant without the cause demonstrated in Figs 1 and 2. The wheel’s travel is thought to be angular even though a wheel can only roll in a straight path. These are two distinctly different descriptions of cornering wheels.

@Kamran Roll a cylinder and it only rolls along a straight path. If you want it to change the direction it rolls/travels you must rotate it on a vertical axis. A torque must be applied to make it do that. A car wheel has the same rolling properties of the cylinder. Put the car wheel or cylinder on a car and we think it no longer needs to rotate on a vertical axis to change direction. Not true. The car wheel/cylinder must rotate first and the cornering force will then follow.

@Kamran Thanks Kamran. The question is, can anyone see this error? I show how the way we describe and calculate the cornering wheel and the force created is inconsistent with the laws of motion and geometry. I then say it can only be described one way and create a force one way (by rotating on vertical axis). I ask, can you see this? This is another way of saying, am I wrong?, which is a common question on this site. People present what they believe to true, because they see that it’s described another way.

Oops. Must have accidentally clicked on the accept check button. Unchecked now.

I also don’t address if the car and bike are cornering on a hill or if it’s snowing out. I think I clearly state enough information to consider the question.

Not talking about leaning. If it helps, think of the bike having wide cylinder shaped wheels.

Hi Solar Mike. Yes. Questions about the same subject, cornering vehicles, was asked by me, but not about the how the cornering force is created. Previous questions disappear because of this site’s voting rules. I previously addressed the geometry of the cornering contact patch and the motion of the cornering vehicle. All involve different areas of the same subject. Hopefully this question has a longer life. It has sound reasoning as far as I can tell, although I also thought that about the other ones.

Yaw motion, yaw velocity, angular momentum, rotation, etc. whatever term that is used, is not an influence on why the car corners and travels a circular path. That disagrees with what we believe.

When the car corners, the 4000 pound part of the cars stays in one orientation because of its inertia and the vertical bearing. The car still travels the circular path when the front wheels are turned. Now is the angular momentum of the one pound chassis changing the travel direction of the wheels and entire 4001 pounds? I don’t think so.

Going back to your point that the vehicle orientation can be fixed and still travel a circular path, consider this. Imagine a car with a very light chassis attached by a vertical bearing to the rest of the car. The chassis is a simple light frame with wheels and only weighs one pound while the rest of the car on top of the chassis weighs 4000 pounds.

They say it must yaw to change the direction it is pointing. They even say the needed yaw changes the heading. I interpret yaw to mean a vertical axis rotation and I interpret heading to mean the travel direction of the vehicle. This couldn’t be more clear that they need vertical axis rotation to make the cornering vehicle change direction and travel the arc/circular path.

Here’s another quote. This is from the-contact-patch.com “The centripetal force is applied to the car through the four contact patches. But the car needs more than centripetal force: it must yaw as well. This means changing the heading – the horizontal direction in which it is pointing.” the-contact-patch.com/book/road/c0415-cornering-basics

I don’t think that is the issue. This is only about our knowledge of physics and how the current vehicle dynamics of cornering vehicles is not aligned with what we know about the laws of motion. What makes a wheel change its travel direction? Certainly not a rotation around the turn center or CoM.

I’m sorry but I see no other way to interpret “yaw angular inertia tends to keep the direction the car is pointing changing” than meaning the angular momentum of the car keeps changing its travel direction. They are saying that vertical axis rotation of the moving car results in a circular travel path because its pointing direction is changing. You might be thinking that there is a rotation about the turn center ICP, but that is never the case.

They claim the need for yaw rotation to change the vehicle direction. I brought slip angle into the conversation but it doesn’t need to be considered. What is important is the location of the rotational axis and how the friction at the wheels prevents the rotation from changing the wheel’s travel direction.

“The yaw angular inertia tends to keep the direction the car is pointing changing at a constant rate.” Doesn’t this state that vertical axis rotation of the vehicle is changing its travel direction?

Consider what they claim is the reason a cornering vehicle travels a circular path. The front wheels are turned which results in a lateral frictional force on the wheel. The wheel then travels in a direction defined by the slip angle. At the next instant the wheel is pointing and traveling in a different direction. Slip angle phenomena provides no explanation for the change in wheel travel direction. This is where they need the vertical axis rotation to explain the change in wheel travel direction. It is not clearly stated how this happens, just that it is necessary.

The cornering car is rotating on a vertical axis. We should be able to point to the location of that axis. The location is at the center of mass. The car proceeds with forward motion and rotates around its center of mass. The rotation cannot change a wheels direction because of friction. The wheels do change direction but not by this rotation.

@Sammy Thanks Sammy. Here is what I attempted to ask but in a more direct way. Current vehicle dynamics claims the vertical axis rotation changes the cornering vehicles direction. I tried to show through simple reasoning that this is false. My question is whether my reasoning was correct.

@Bill N This is actually a simple look at the cornering car vertical axis rotation and how the car wheel friction prevents the rotation. With that simple fact, what we currently believe is not true.

@Sammy - Not a rant. I’m asking if anyone can see that vertical axis rotational motion of the vehicle has no influence on why the vehicle keeps turning. We currently believe it is necessary but these things I point out show that rotation does not change the direction of the cornering vehicle.