First of all, I should just say that you have to feel for Neil DeGrasse Tyson. He's a brilliant man, and he makes one mistake and we're all over him like flies on a rib roast. But that's okay — mistakes are useful for smart-making, and we called in our own captive physicist to explain exactly what went wrong.
Before we go into why Neil DeGrasse Tyson was wrong, we should be clear that he, in fact, was wrong. Here's some speed data from NASCAR for that banked turn:
Rk Turn 1 Finish MPH
1. Jimmie Johnson 1 184.004
2. Matt Kenseth 3 183.976
3. Joey Logano 12 183.917
4. Aric Almirola 11 183.775
5. Jamie McMurray 5 183.685
So, it looks like Tyson's claim that you'd fly off the track if you went over 165 just isn't true. Here's why according to physicist Stephen Granade - JT.
I'm always cautious about disagreeing with Neil deGrasse Tyson. He's a smart guy who knows a lot about science. But one big rule of science is that when your measurements contradict your theory, you've got to take a second look at what's going on.
If this were one of my experiments, I'd look at the theory I was testing, double-check my measurement setup, and go through the math again. Unfortunately we can't double-check NASCAR's measurements, and Tyson didn't have enough room in 140 characters to show all of his math. So let's do some math of our own, see if we get in the neighborhood of what Tyson got, and then ask what we might be missing.
The basic physics of a car going around a corner involves three things: centripetal force, friction, and how much a turn is banked by.
When you're turning in a circle, you've got to have a force pulling you towards the center of that circle or else you'll keep going straight. That's Newton's first law of motion: if you don't have a force acting on you, then you'll keep going in a straight line and at the same speed. The force that bends your path from a line into a circle is called the centripetal force. Ever been on a turning merry-go-round? You've got to hold on tight to the bars to keep from flying off. Your arms are providing the centripetal force towards the center to keep you going in a circle instead of falling off the merry-go-round and cracking open your head.
The faster you go, the more centripetal force you need to make the turn. If we figure out what provides the centripetal force and how much that force would be, then we can figure out the maximum speed a car can have and not fly off of the turn.
When you're driving on a flat road and turn a corner, then that centripetal force has to come from your tires' friction with the road. But if we tilt the road so that it's higher on the outside of the turn, then the road pushes the car towards the center of the circle and provides some of the needed centripetal force.
There's a surprise lurking in all of this: it doesn't matter how much the car weighs! The needed centripetal force depends on the car's mass, which is related to its weight. The more mass your car has, the more centripetal force you need. But the more mass your car has, the more friction you get, and the more the banked road pushes you towards the center! All of those mass terms cancel out, and you end up with equations that don't depend on the car's mass. That makes life a lot simpler.
Wikipedia has a straight-forward derivation of the equations for the maximum speed a car can have when taking a banked turn. We just need to know three things: the angle of the bank, the radius of the turn, and the coefficient of friction between the tires and the asphalt.
We can get two of the three from the Charlotte Motor Speedway's track facts page. As Tyson tweeted, the turns have a 24-degree bank. There are actually two radii for the track's turns: 685 feet at one end, and 625 feet at the other. I'll use both, since I don't know which Tyson might have used.
That leaves the coefficient of static friction between tires and asphalt. Here's where we're going to have to wave our hands hard enough to start flying. The coefficient of friction isn't something we can calculate, it's something we have to measure. And it varies depending on how smooth the tires are, what exactly they're made of, what the track is made of, even the humidity. Data's hard for NASCAR laymen like me to come by, so I'll take this source's value of 0.9 for rubber on asphalt and round it up to 1.
Plugging all of those values into the equations, I get a maximum speed of 156 MPH around one turn and 163 MPH around the other. That's close enough to Tyson's results to tell me I'm in the ballpark, or at least the racetrack.
So why can cars go around those curves faster than 163 MPH? The results are sensitive to the coefficient of friction: raising it from 1 to 1.1 raises the maximum speed to 176 MPH. That's the first assumption I'd challenge. The second thing I'd challenge is my model of tire friction, which is really simplistic. I'm ignoring the cornering force from tire deformation, for example. Real tire friction is a complex thing.
The next thing I'd look at is aerodynamics. NASCAR cars have a spoiler on them, which are like the opposite of an airplane wing. An airplane flies because, as it moves forward and wind rushes over the wings, the wings throw air down. By throwing air down they generate lift that keeps the airplane in the air. Car spoilers do the opposite: they throw air up to push the car's rear down. That could make the car push down on the track with more than just its weight and increase the friction force. But spoilers exist to counteract the natural lift that race cars experience, which decrease friction. Without wind tunnel data, I can't tell you if the spoiler makes the friction force be more than I've estimated, or if the friction force would actually be less than I've estimated, even with the spoiler.
I think this is a neat example of how basic physics can teach you some things about a real-world situation, like how the mass of the car doesn't matter all that much and how much the coefficient of friction matters. It helps explain why cornering gets so much harder on wet pavement, when the coefficient of friction can drop by half or more. But it's not good enough to get you your final answer. And when the real world contradicts your theory, well, the real world wins.