Uh, I can't afford to ask a question :D...

Very interesting discussion, I blistered two tires at my last trackday.

As you say impossible. Since a tires grips is partially a result of the elasticity of the tread compound.

Slip angle isn't necessarily a bad thing, just something that happens and is lived w/. It's component from the twist in the carcass can certainly be minimized by using lower profiles and stiffer cord sidewall materials, but the component from the tread compound is part of where the grip comes from, part of the 'feel' a tire translates to the driver, You do want some slip angle, and you do want it to be linear and predictable in application and release.

You have to keep in mind that there is no such thing as a perfectly rigid object, nor is one desireable in many situations

Lots of really good and accurate answers here. The "third grade" part is what's missing. I have found that a simple description of what a tire goes through will make it so anyone can understand slip angles and what the dynamics involved really mean.

Lets start with a question: How much distortion does a tire have when it is unloaded? Pretty easy to answer: None!
Second question: If you push (apply force) sideways on a tire will it distort? Another easy answer: Yes!

Let's put these two bits of 'obvious' info together.
As a tire rotates and the tread comes down towards the ground how distorted will that portion of the tire be? There is no force applied yet so of course the tire is undistorted. Right when the tire touches the road it is still relaxed so it can't be distorted. So the leading edge of the contact patch is always undistorted.

We are going to be applying force so we know that it will be distorting at some point. If we look at our 'example point' on the tire we know it won't move around on the ground because the tire is adhering to the road. If you track how this point passes from the relaxed leading edge backwards the quantity of distortion has to increase and it will be in a straight line because it isn't going to be moving around on the asphalt. (If you want to get really picky it isn't really a straight line. It will be an arc with a radius equal to the radius of the corner you are turning. It is negligible so we calculate it as a straight line so you get your 'slip angle'.)

It starts to get a bit complicated at the rear of the contact patch. We described the distortion as a straight line. It takes a lot of force to distort a tire and as we get near the rear of the contact patch the downward force will start to lessen as the tread gets close to leaving contact with the ground. Say you have a tire with a coefficient of friction (CF) of 1.0 that is capable of 1 lateral G. As we watch our 'example point' get near the rear, when the quantity of downward force is reduced to the point where it no longer exceeds the force of the lateral force the tire will break loose and start to undistort. As a more simple answer: If the side force is 100lbs on each sqr inch, the tire will break free when the vertical load goes below 100psi in our 1G example.

http://forums.pelicanparts.com/uploa...1172989332.jpg

As you can see at the bottom of the contact patch on the example above, the rubber is snapping back to its undistorted shape.

If you think about it you should be able to visualize why if a tire is pushed past its 'optimal' slip angle you are only going to have more of the tire slipping and trying to snap back towards its relaxed form. Because of this when you have exceeded the optimal slip angle you aren't distorting as much of the tire and that is why the steering wheel feedback force gets lighter. If you look at it in another way the angled distortion amounts to a twisting of the contact patch and that is where we get the self centering torque on the steering wheel. (Yeah, the caster angle supplies some of it but the tire distortion is the biggie here.)

If you look back at the phrase, "when the quantity of downward force is reduced to the point where it no longer exceeds the force of the lateral force" you will see that a tire doesn't have a fixed 'optimal slip angle'. The more weight (force) you have pushing down on a tire the more it will distort before the sideways force exceeds the downwards force. If a tire is stiffer it will distort less at the same force level as a more flexible tire.

BTW - Slip angle isn't really a good description for what we are measuring here. Distortion angle would be more accurate because the tread isn't slipping in the part of the contact patch that we are measuring.

Another fun fact to run through your noggin...
If the tire goes out of contact with the ground all of it will relax. It the tire is undistorted it can't be pushing sideways to generate cornering force. Once it comes back in contact with the ground it has to travel a bit so the leading edge can move towards the rear and become distorted enough to apply force to the car. This means you really need to keep the tires continuously stuck to the ground. (Reduce that unsprung weight so the tire can follow the variations in the ground!) Just imagine what is happening under the tire on a washboarded road! That is why all of your cornering force goes away. The tire is spending all of its time building and rebuilding its distortion/slipangle.

To be more specific then Bill. The higher a slip angle that a tire has the more gradually the force levels rise and fall as you come up to your 'optimal slip angle' and then surpass it. This makes the tire forgiving. The 'warning' comes from the increasingly large part of the tail end of the contact patch that has broken free and the resulting reduction in self-aligning torque (steering wheel feedback). With your theoretical 'zero slip angle' tire there is no trailing edge 'breakaway zone' so it would just break loose instantly with no warning. Just imagine the pucker factor of driving something that didn't tell you that it was about to break free, and then the fun that you can have after the instant reduction in traction when it starts sliding! Want to give it a try? :p

To clarify: Most of the tire isn't slipping. Only the small trailing edge of the contact patch slips but it is negligible unless you are really over cooking the tire.

If you take a coat hanger and bend it back and forth real fast the part that is bending will heat up enough that you can almost burn yourself with it. (Give it a try!) Almost all of the heat in a tire (that is being used correctly) is generated by the flexing of the rubber.

If you keep trying harder even when you have exceeded the tire's ability to supply cornering force, you will start to actually slide a noticeable percentage of the contact patch and the act of tearing the surface of the tread off in little bits if rubber will generate lots and lots of heat. This is why you can chase someone who is very neat and careful with their tires, and when you start trying 'a little bit harder' you will reduce your grip with to large a slip angle and then over heat the tire further reducing your grip. (At this point frustration can cause people to really over do it and completely roast their tires as they watch someone easily walk away from them!)

If you are on a skidpad, and you increase your speed until the front end starts to push, cranking the wheel past the optimum slip angle will not make the front end turn in, because it will interfere with the rotation of the tire, and the tire will start to scrub. you cannot exceed the limits of grip, only introduce scrub, which we all know will start to slow the car down, because it is interfering with the wheels ability to turn.

When you are saying that the tire grips better at the optimum slip angle, I do not know if this is true, I only know that the slip angle is the vector of the way you want the car to go vs. the way the car wants to go. The tire can only reach full Gs when it is fully loaded whether you are breaking, accelerating or cornering. The tire will distort under any of these circumstances. Slip angle is the distortion that occurs during cornering, and it is a vector force. You cannot avoid the distortion and achieve maximum grip. Since the tire is at an angle to the cornering force, it will twist.

Third grade explanation: too much slip angle is scrub. Scrub is loosing the ability to turn the wheel by transfering steering grip to braking grip. Hope that helps.