Okay. COSMOS was pre-empted Sunday in favor of the Coca Cola 600 and COSMOS host, astrophysicist Neil deGrasse Tyson, decided to edify us with some NASCAR physics.
I bet 90% of NASCAR fans immediately know there’s something wrong here. In fact, all you had to do was watch the broadcast. I’ll write a longer post, but here it is in brief.
The calculation for a car rounding a banked track with friction is pretty straightforward. There are a lot of angles in it, but if you work through it, it does make sense. Check out hyperphysics for the details. The important thing here is that the maximum velocity is determined by the radius of the track, the coefficient of friction between the track and the tires, and the banking of the track.
where r is the radius of the track, θ is the banking angle and μs is the coefficient of static friction. I know, it looks complicated, but stay with me. The next paragraph is just the important stuff.
At Charlotte, the turn radii are 685/625 feet (the two turns are different, depending on whether you’re going into the dogleg or the backstretch) and the banking angle is 24 °. Hyperphysics even lets you plug in numbers on their site, so I could very quickly determine that 165 mph is what you would get if you assumed a normal coefficient of friction between a regular tire and an asphalt track (around 0.75). The reality is that NASCAR tires have a much higher coefficient of friction, which is why they easily exceed 165 mph and have no problem staying away from the “embankment” – whatever the heck that is.
Details to follow, but I wanted to get this up because I’m getting flooded with questions.