Neil deGrasse Tyson Gives Us A Detailed Breakdown Of NASCAR Physics

Back in May, astrophysicist and science educator Neil deGrasse Tyson found his show was bumped due to a NASCAR race. Undeterred, he took to Twitter to explain some of the physics of racing. We're fans, but we thought his math was a little off. So Dr. Tyson just showed up in the comments to explain it all.

Our bone of contention was that Dr. Tyson's assertion that the maximum cornering speed at the track was 165 miles per hour, while we had regularly seen race cars exceed that velocity by a significant amount.

The 140-character limit of Twitter doesn't exactly lend itself to a display of one's work, however, so we gave Dr. Tyson the benefit of the doubt and invited him into the comments just in case he wanted to expand upon his original claims. We also had our own captive physicist, Stephen Granade, write his own post to explain everything, and carried on our merry way.

I personally figured that that was that, as Dr. Tyson's a pretty busy guy, between his scientific research, his excellent podcast, and his TV show, Cosmos, explaining the ways of the universe to everyone. Surely he wouldn't have the time to answer every little question about race car physics thrown his way.

This time, I was the one who was wrong.

Not only did Dr. Tyson pop in to teach us further, he showed his work, too:

Neil deGrasse Tyson > Michael Ballaban

Yesterday 6:26pm

Sorry for the delay in my jumping into this conversation. The universe has been keeping me quite busy lately, but I'm always happy to see long threads that debate applications of the laws of physics. A sure sign that science is trending in the world.

I stand by my calculation. — sorry that Twitter does not allow one to "show all work," but I thank Mr. Ballaban for creating this space for me to explain my steps.

1) I state here, flatly, in case some of you don't know, that the maximum acceleration a car can achieve, when the coefficient of frction between its tires and the road is 1, is the acceleration of gravity for the planetary object you are racing on — unless, of course, you strap on rockets. On Earth, that acceleration is 32 feet per second, per second. Or in more common language: 22 miles per hour per second. Or in even more common language: Zero to 60 mph in 2.8 seconds. This is true no matter the mass of the car or the nature of its suspension or construction. That's why all the most expensive production sports cars come in around 3 seconds for 0-60 mph. This is simply a cool fact of physics. On the planet Jupiter, if it had a surface to drive on, the higher force of gravity would allow a car to accelerate from 0 to 60 mph in 0.6 seconds.

2) Most materials on most materials have a coefficient of friction of less that 1. But rubber on asphalt makes an awesome match for transportation, and routinely registers a coefficient of friction within 5% of 1.0. If you manage to increase the coefficient of friction above 1.0 you can accelerate horizontally even faster than gravity would accelerate you falling vertically. Hot, gummy, sticky tires on asphalt do just that, as drag racers well know. Spoilers at high speeds offer a similar advantage — but in this case increasing the weight of the car without increasing its mass. This helps the friction do its job even better.

3) A banked track allows a car to turn at a faster speed than is otherwise possible on a straight track because you're invoking the track itself to assist your turn. In this way, the friction between the tires and the road need not bear the entire load of the turn. But for every track angle and tightness of turn ("radius of curvature"), there is a speed above which the friction cannot hold the car, as the countless scratch marks can attest on the outer embankment of every racetrack and every clover-leaf offramp to a highway.

4) For my calculation, I used the published radius of curvature and bank angle for Charlotte Motor speedway. Assuming a coefficient of friction of 1.0, I derived 165 mph. I then monitored the CocaCola 600 race for the intermittently displayed speed bubbles over cars of interest. Every car they showed, when in the peak curvature of its turn, had slowed to about 165 mph. The range was between 163 and 167 mph. I presumed that what I saw was not unusual, which indicated that whatever benefit the warm NASCAR tires offered their drivers, it did not provide significantly more than a coefficient of friction of 1.0 with the track.

5) Of course, entering the turn, cars must slow down from near-200 mph to 165. So I'm guessing that the 180 mph speeds reported in this thread were drawn from those transitional parts of the curved speedway. Note further that the car spends hardly any time at 165 mph, so you can fully expect the average speed to be much higher than 165 mph after all laps are taken.

I deeply appreciate the attention you have all given to my Cosmos-Interruptus NASCAR tweets. And, as some of you may already know, I have a lead essay in the upcoming annual "Speed" issue of Car & Driver.

Respectfully Submitted — Neil deGrasse Tyson, New York City (writing from Paris)

So there you have it. It wasn't so much a gross error of physics, but rather an explanation based on various assumptions like friction and a lack of downforce.

Despite all my studying in the ensuing six weeks, I have yet to receive a degree in physics, and am still naught but a humble journalist. A lot of things sound right to me here, but I can't be 100% certain. If you care to check Dr. Tyson's work one more time, let us know in the comments below!

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