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Optimal turns at Indianapolis Motor Speedway with JR Hildebrand

Created by Sal Khan.

Video transcript

SAL KHAN: This is Sal here with famous Indy car driver-- smiling when I said famous-- JR Hildebrand. And since you're here, I thought I would ask a question that's always been on my mind. JR HILDEBRAND: Yeah. SAL KHAN: We have a picture here of the Indianapolis Motor Speedway. And I've always wondered how you-- it seems like turning is a very important part of the-- JR HILDEBRAND: It's absolutely an important part of what we're doing. SAL KHAN: --of the race. JR HILDEBRAND: People get fixated on the car going straight. But the turning part is pretty important. SAL KHAN: Turning seems to be the part where a lot of the skill comes into it. And I've always wondered, what is optimal? Do y'all try to minimize your distance and kind of take the turn as quickly or as in short of a distance as possible by really hugging the corner, by going like that? But when you do that, you have to turn more. There's more g-forces. There's more kind of centripetal force that your tires have to deal with, the human has to deal with. Versus taking the outside where you have to cover more distance, but the centripetal acceleration, the g-forces aren't going to be as dramatic. So how do you think about that? JR HILDEBRAND: Well, every track ends up being a little bit different. But when we take Indianapolis here as the example, if you're already on the inside-- it's like the 800 meter runner's kind of path. It's the shortest distance. You can kind of get from point A to point B. The lap is the same every time, so it doesn't actually depend on you running a specific distance or not. For us, in this example, the car actually just won't do that. If you think about being all the way on the inside, being all the way on the inside through the corner, and then exiting all the way on the inside, it's having to do the most work to follow that path. And in Indianapolis, we're approaching turn one at upwards of 240 miles per hour. And that turn one is not-- it's hardly banked. It looks quite flat in person. So as opposed to NASCAR running at Talladega or Daytona, these big, giant super speedways, the car is having to do quite a lot of work to get through the corner here. SAL KHAN: So how do you--? Do you take the outside or--? JR HILDEBRAND: So then you look at that. And I think if you noted the radius-- if you drew a full circle out of each of those arcs-- SAL KHAN: Let's do that. So let's say that this is the shortest distance path. This is kind of a circle that looks something like this. Let me scroll over a little bit so we can see a little bit better. So this would be a circle like this if you were to keep that arc. It would be a circle that looks something like this. JR HILDEBRAND: So that's a pretty small circle in the grand scheme of things here, yeah. SAL KHAN: That's a small circle. And for the larger one, the circle would look something like this. So you have a larger radius, a larger turning radius. So you would have to have less centripetal acceleration, inward acceleration, and fewer g-forces on this outside one, the larger the circle is. JR HILDEBRAND: Right. And a different way to look at it, if you looked at the car trying to just go around these two different circles, and it's going to be going the same speed on either one, it's doing a lot less work to get around this outside circle. And therefore the speed that you could carry around that, that sort of goes up. The car has a limited ability to stick to the racetrack. So opening that up definitely makes a difference. SAL KHAN: But that's an important point. At least in Indianapolis, you're full throttle the entire way. I mean, obviously, if you hit the brakes, the car could do a very small turning radius. But you're at full throttle. You're not going to have any chance if you at all let off the gas. JR HILDEBRAND: That's right. When you qualify at Indianapolis, you've got to put in four laps, four of your best laps of the season, of your career in Indianapolis to qualify. And that you are absolutely flat trap all the way around the racetrack. There's no lifting. There's no braking. SAL KHAN: And so that's why you're saying the car just wouldn't do that. If you're going all out, the car just wouldn't even be able to make this path. JR HILDEBRAND: Exactly. That's a good point. From the driver's perspective, you have to stay flat out if you're going to go fast. If you're going to set a lap time that's relevant, you have to be able to stay flat out. And so at that point, you're searching for the line around the race track that you can do that most efficiently. And so then, in this example, increasing that radius by going from our green circle out to the purple circle does that rather effectively. SAL KHAN: I see. We're going for the purple to the green back to-- so you're saying like this. JR HILDEBRAND: Well, yeah. And so then to find the actual optimal line, what we end up doing is starting out on the outside of the track, then bending the car into the inside of the track, and going back to the outside of the track, really using all of the road that's available to us. SAL KHAN: Right. So that's interesting. So when I posed the question, it was kind of like my brain was just looking at these two circles. But you realize there's a bigger circle that you could fit here, that there's an arc like this. And this would be, if you imagine, this would be a part of a circle that's way huger than even that purple circle that we're drawing. So that center of that circle is like here or something. So you have a lot less centripetal acceleration that you have to place, inward acceleration that you have to place on the car. JR HILDEBRAND: Exactly. And therefore, the car is able to carry a massively increased level of speed through the corner. And that's really what we're looking for. And you consider, I think it's a very interesting-- when I think about what I'm doing as the driver, I don't think I really am consciously thinking that much about the mathematics that go into finding this optimal racing line. You sort of instinctually just gravitate towards what the car feels like it wants to do. But when we look at it from this perspective, you've got the car going down the straight away here. It's at 240 miles per hour. That's almost as fast as the car is going to go. So it's just this sort of terminal velocity. The drag of the air hitting the car won't allow it to go much faster than that. SAL KHAN: The engine's giving all the power it can. JR HILDEBRAND: Yeah. You're absolutely flat out. SAL KHAN: And that's just offsetting the drag of that, so that you can't accelerate to that top speed. JR HILDEBRAND: Exactly. It's almost like you're hitting a wall of air at that point. You're not going to be able to accelerate any faster. And so what you're really trying to do is you're trying to-- in order to set that fastest lap time, which ends up equating to the highest average speed around the lap, that's what's the lowest number in terms of lap time perspective-- you're trying to get the car to most efficiently get through the corners so that you can allow it to accelerate down the straights as much as you can. You're getting it to diverge from this intended course that is going on here as efficiently as you can. And so by creating the largest radius around the corner, that's how we end up finding that optimal line. SAL KHAN: That's fascinating.