s4wood

I just shudder at coefficients of friction...differential equations...etc.

yuck.

Chris C

Me fail english? Unpossible. :-)

s4wood

And that is saying a lot at University of California Santa Barbara.

I loved taking the upper division Advanced Techniques of Volleyball class. :-)

Partaaaaaaaay

LCP

...I noticed that the stock cars would get down to about 160mph in the corners at Texas Motor Speedway; of course coming in faster and exiting faster. So to test our formula for how much degrees of banking increases maximum permissible cornering G's, first let's start with the formula:

G = (cos(a) + sin(a))/(1-sin(a))

Now, what do we know about Texas Motor Speedway. Well, it has 24º of banking on its 750' radius corners. Plugging 24º into the above equation and solving for G gives 2.225. So on these banked corners, a car that could otherwise pull 1g on a corner can pull 2.225g's (ignoring of course, factors like decreasing tire grip with load, aerodynamic downforce, etc.).

The formula for determining lateral G's given velocity in mph and turn radius in feet is below:

G = ((v*5280/3600)²)/r)/32.1

Using 160mph for v and 750' for r yields 2.287g's using this formula.

But can't a stock car corner at more than 1g on flat ground? Per this <a href="http://popmech.popularmechanics.com/automotive/motor_sports/2002/11/two_chevys/index3.phtml">Popular Mechanics article</a>, a Winston Cup NASCAR stock car can corner at 1.12g around a 200' diameter skidpad. So yes it can, and if you could just multiply 1.12 by 2.287, then the NASCAR stock car should be pulling 2.56g on these 24º corners, but you can't just multiply when the increase in g's is that high because, among other things, the coefficient of friction of the tires is going to decrease as the load on them more than doubles. Add in a little more grip from aerodynamic downforce, and then discount the coefficient of friction generated by the tires, and it seems that generating 2.287g's at 160mph on a 24º banked 750' radius corner is just about right.

For what it's worth, I could see 120-125mph in this corner running TMS's ALMS roadcourse configuration in my S4 (on K03's with the stock chip on street tires). That works out to 1.3-1.4g's. Another 10mph would have been easy if I'd had the horsepower to get up to it -- that could have been 1.5-1.6g's. Beyond that, who knows. Stickier tires and a stiffer suspension would have been needed for sure.