Everyone’s favorite “planet” killer had a spare hour because COSMOS was pre-empted Sunday by the Coca Cola 600. Astrophysicist Neil deGrasse Tyson edified us with some “NASCAR physics”.
There were 43 drivers who had no problem taking the corners at more than 165 mph without skidding into the “embankment” and a couple million viewers who knew instinctively that these were not correct statements.
Some basic physics. A car going around a racetrack in a circle is no different from a ball on a string being swung in a circle. In both cases, the reason the object makes a circle is because there is a force that point toward the center of the circle at all times. For the ball, it’s the string. For the car, the tires generate that force through friction between the tires and the track. The car tries to slide away from the center and the tires keep it from doing that.
The amount of force the tires generate is proportional to the force pushing down on the car. If you slide a tire across a parking lot, it takes you a certain amount of force. If someone sits on the tire, you need more force to pull it. The force the tires generate is given by:
There are two forces pushing down on a racecar: the weight of the car (which provides mechanical grip) and the aerodynamic downforce (which provides aero-grip). Let’s ignore the downforce for a moment because it gives car more turning power and lets it reach higher speeds, so it only helps the argument.
If you look at a flat track, all of the frictional force is in the direction you want it to go – toward the center of the turn.
I’m showing three forces: The track exerts a force on the car equal to the car’s weight. The frictional force is toward the center of the turn, as required.
In most situations, the coefficient of static friction (the μs) is less than one, which means that you get less frictional force than the weight of the car. For regular tires on asphalt, for example, you only get 70-80% of the force pushing down. On ice, you get maybe 10-20% of the force. Racing tires are different. They take advantage of some really interesting physics, which is that of adhesive friction (versus abrasive friction, which is what we all learn about in school). Rubber is a truly amazing material. While the actual coefficients of friction for specific race tires are closely guarded, you can use 1.2-1.3 as a good approximation. The 165 mph number Tyson came up with is a result, I believe, of having used the coefficient of friction for regular tires, not race tires.
Now throw in banking.
The directions of the forces change. Except gravity, which (on Earth) always points straight down.
The track always pushes perpendicular to its surface, so now part of the force from the track is pushing up and part is pushing toward the center – the banking helps the car turn. The higher the banking, the more help you get turning. If the track had a banking angle of 45 degrees, half the track force would be pushing up and half would be helping the car turn.
If you’re paying attention, you’ll notice that the frictional force (which always acts parallel to the track surface) also changes direction. In fact, the amount of frictional force in the direction you need to turn actually decreases a little; however, you get such an advantage from the banking that it compensates for the loss due to the frictional force. (Of course – otherwise, no one would bank tracks.)
The calculations (without aero) are pretty straightforward and standard in many intro physics courses. Hyperphysics is my go-to reference for basic physics when I don’t have a textbook handy. You can follow them through the whole calculation to get the equation that shows the maximum velocity is determined by the radius of the track (r), the static coefficient of friction between the track and the tires (μs), and the banking angle of the track, θ and the acceleration due to gravity (g).
The parameters are easy to look up. g has a value of 32.2 feet per second per second (ft/s2), the turn radii at Charlotte vary (
At Charlotte, the turn radii are 685 feet (turns 1/2) and 625 feet (turns 3/4) and the banking angle is 24 °. Hyperphysics even gives you boxes and lets you plug numbers in on their site, so you can play around to see how the maximum velocity changes with the parameters.
The important thing here is the difference in friction between race car tires and regular tires. Race car tires are made of a different composition of rubber. They get much hotter than passenger car tires and the surface layer of the tire actually melts a little bit. Rubber gives additional grip in a way I like to describe as what happens if you step on a piece of chewing gum on a hot day. The chewing gum sticks to your foot and prevents you from moving – a slightly different type of friction.
Physics classes rarely teach students about materials that aren’t pretty well-behaved solids. Stretchy, squishy materials like rubber or any type of liquid introduces a lot of complications. I had been teaching physics for 15 years before I learned you could have a coefficient of friction greater than one. So it’s not too surprising Tyson didn’t know it either.
However, as my friend James Riordan points out, theory always has to be checked against experiment. And that’s part of what’s so annoying about this. All you had to do was watch the race to know this upper limit was incorrect. A huge number of media outlets re-tweeted these ‘facts’, or featured the tweets as they exclaimed how wonderful it was that an astrophysicist was explaining NASCAR to its fans. Sorry folks – NASCAR fans are smarter than they are given credit for. There’s a level of complication and sophistication to the sport that people who have never paid attention to it simply don’t appreciate. Sure, NASCAR isn’t F1 – but there aren’t many of the high-level teams that don’t have at least a few Ph.D. level aerodynamicists and mechnical or chemial engineers on the payroll. It’s a must if you want to be competitive.
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Hi Diandra. It’s been many years since college physics but this was fun. We had a similar project with maximum acceleration/top speed in a quarter mile. Prof had “book learnin'” drag enthusiasts had observation. He was not amused with our challenge! Regarding the example above, if calculating actual maximum speed wouldn’t tire camber be a factor?
Hi Gary: Slip angle, aerodynamic downforce, line taken… there are a lot of factors. One of the most important things in science — and one of the hardest to teach — is what to neglect and what not to. Using the wrong coefficient of friction was a 10-20% error. The others I suspect are much lower percentages – but you are right, if you want to be accurate, you would need to consider all of it. Thanks for reading!
I’d also bet he had no allowance in his calcs for aero downforce. With enough downforce you can run a race car on the roof of a tunnel around a corner. These cars create a “ton” of downforce – if not more. Not enough for the roof of a tunnel example (leave that to F1…), but certainly enough to outweigh any potential CoF error. The higher the areo downforce, combined with stiffer springs, all adds up to the more downward pressure into the asphalt, which not only makes simple friction work harder for you, but it also accentuates the “stretchy and squishy” (your words…LOL) factor, where the rubber will actually mold to the surface – creating a massively higher contact area between the tire and the pavement. Nothing either about asphalt compound, asphalt age, ambient temp, sunny, cloudy, or a myriad of other factors that affect traction.
Don’t forget to take into consideration Mark Donahue’s “circe of traction” as the cars are accelerating while in the corner. The attitude of the car changes in different parts of the corner. That is what race driver’s asses are designed to factor.