This is why light cars with low CG's corner better then heavy cars with a high CG. So, if you corner hard and transfer and extra 50% load to the outer tyres their grip does not increase by 50%. You also need to know that the CF of a tyre typically drops off as load increases.
I have seen numbers greater than 1.7 for modern racing tyres probably higher. I think I am right in saying that the Dunlop Historic race tyres that I have on my Formula Ford have a CF around 1.3. I don't know specific numbers but a good road tyre probably has a CF around 1.0. No, tyre adhesion doesn't follow classic physics.
Unfortunately, there appears to be no consensus regarding the appropriate value or measurement technique for the tire-road coefficient of friction used to estimate critical speed. Overwhelmingly, the literature indicates that the coefficient of friction is the function of many variables and that it is the most ubiquitous factor affecting speed estimates when the critical speed formula is used. Important dynamic factors are listed and the connection between longitudinal and lateral friction is discussed. Influential factors such as tire characteristics, tire inflation pressure, road conditions, and dynamic factors are reviewed.
Common coefficient of friction field measuring techniques are described, including the skid-to-stop test and drag sled. The primary components of tire-road friction, adhesion and hysteresis, are discussed along with minor effects such as tearing, wear, waves, and roll formation. Background information is presented covering general definitions and the connection between the basic critical speed formulas and the coefficient of friction. A literature review of tire-road friction studies was conducted to identify the primary factors effecting the tire-road coefficient of friction. This paper covers briefly the theory of tire-road friction, coefficient of friction measurement techniques, and the vagaries of tire-road friction as they relate to critical speed estimation.
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