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## Circular motion and centripetal acceleration

Current time:0:00Total duration:6:25

# Optimal turns at Indianapolis Motor Speedway with JR Hildebrand

## 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.