Tires, traction and the physics behind it
 

Was looking at the thread about vehicle dynamics (this one: http://forums.pelicanparts.com/off-topic-discussions/329482-vehicle-handling-dynamics.html ) and it got me thinking back to a discussion years ago with my high school physics teacher. We were discussing the implications of Coulomb equation with respect vehicle tires. For those who forget, the equation is this:

http://forums.pelicanparts.com/uploa...1171112185.jpg

His position (and it makes sense, even if it's a bit simplistic) was that the size (width) of tires on a car had no bearing whatsoever on how "grippy" they would be, since the Ff (force due to friction) was a function of the coefficient of friction between the two surfaces (tire composition & pavement surface) and the "N" value ("normal force" - basically the weight of the vehicle). So a thin, skinny tire should in theory grip just as well on a drag strip as a wider, fatter one. His claim was that wide tires were largely a marketing ploy because they "looked cool", but actually did nothing to make the car grip better under acceleration and a powerful car would break the tires loose just as easily on a fat-tire-equipped rear end as a skinny-tire-equipped one.

Of course we all know this isn't entirely true in practice and there are other physical principles that must come into play here, but does anyone on here know exactly which ones they are and how these principles avoid conflicting with the Coulomb equation? Curious to know if anyone has thought about it. . .

The other implications of the formula make sense - heavier vehicles will "stick" better (and by Newton's Second Law, be slower to accelerate), tire composition determines frictional coefficent, which is very important (and can change with temperature, of course), etc. . . Just wondering about this one aspect where observed behavior seems to conflict with predicted behavior.

Drag slicks are usually quite 'tall' compared to other tires and of course they are running much lower pressures than street tires to enable more square inches of that very sticky tread surface to meet the pavement.

Wide tires allow more lateral friction to get all that 'road hugging weight' to go around corners.

Les

Yea, no doubt they help in cornering - we discussed that - but I'm wondering about a straight-line dragstrip scenario. . . We've all seen top fuel dragsters and stuff and know they run very tall (and wide) tires on the drive wheels but why? According to this equation, it shouldn't matter for straight-line performance. . .

Don't know about the math end of it, but actual results always trump theories. I suspect in a perfect world where both surfaces are perfectly flat and true and in constant perfect contact......pavement and rubber tires don't fit that description.

The tires on a top fueler run low pressures and by design distort under initial acceleration, causing the contact patch to grow into a sort of heart-shaped affair for the launch; as speed increases (rapidly), centrifical force caused the tires to grow in diameter which changes the final drive ratio.

Your physics teacher was obviously no idiot or he wouldn't have been teaching physics, but it sounds like he was trying to apply simple theory and ideal behavior to the real world. In some ways that makes him an idiot. I had a physics teacher try to do the same with me in HS. He told me that all driveshafts were solid because it takes less energy to rotate a solid object than a hollow one. He was right about the last part, but the drive shaft in my '65 impala was most definitely hollow.

Part of the issue is that tire rubber can only withstand so much force before the rubber starts to shred and tear. By spreading the Frictional force over more rubber that reduces the force acting on each small area of rubber. Also heat is an issue and larger tires will not get as hot as smaller tires. Excess heat is bad for tire rubber.

Also, there's more to the friction that a tire makes than just the adhesion between the two materials. There's a great book on this of which the internet has a couple of really good excerpts. I'll find it and post.

Here, check this out
http://insideracingtechnology.com/booktiredescrptn.htm

lots of good info including some physics stuff.

The size and shape of a tire helps to determine the shape of the contact patch and the way the tire works as a whole system. We all know that tires are more than just a static square contact patch that exhibits friction. Sports car tires, to maximize cornering want a contact patch that runs mostly side to side. Dragster tires need to accelerate, so their contact patch needs to be longer from front to back. Also, the sidewalls of a dragster tire are designed to be soft, allow the bead of the tire to rotate in relation to the tread surface, and be a part of the whole traction system. It's more than just where the rubber meets the road. Tires and traction are part of a whole system.

Dragsters run tires that have a highly variable diameter, it's part of their gearing, short to get off the line transitioning to tall for top end.

A tires contact patch area is strictly determined by tire air pressure, weight of the vehicle at the tire, and sidewall compliance.

the shape of the patch is determined by the tire aspect ratio, lower aspect ratio gives a short wide patch, higher aspect ratio a long narrow one.

for acceleration the short wide one is desireable, it's not pure classic friction at the interface you also have chemical bonding of the tire to the road, that's one reason they do burnouts.

the hot sticky tires w/ soft rubber insinuates itself into all the little nooks and crannies of the surface and glues itself down, traction comes from breaking all of the chemical bonds

THis sublink of the link I posted above goes very in depth into this stuff.
http://insideracingtechnology.com/tirebkexerpt1.htm