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SAL KHAN: This is Sal here
with famous Indy car driver--

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smiling when I said
famous-- JR Hildebrand.

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And since you're
here, I thought I

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would ask a question that's
always been on my mind.

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JR HILDEBRAND: Yeah.

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SAL KHAN: We have a picture
here of the Indianapolis Motor

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Speedway.

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And I've always
wondered how you--

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it seems like turning is a
very important part of the--

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JR HILDEBRAND: It's
absolutely an important part

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of what we're doing.

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SAL KHAN: --of the race.

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JR HILDEBRAND:
People get fixated

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on the car going straight.

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But the turning part
is pretty important.

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SAL KHAN: Turning seems
to be the part where

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a lot of the skill
comes into it.

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And I've always wondered,
what is optimal?

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Do y'all try to minimize your
distance and kind of take

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the turn as quickly or as in
short of a distance as possible

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by really hugging the
corner, by going like that?

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But when you do that,
you have to turn more.

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There's more g-forces.

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There's more kind
of centripetal force

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that your tires
have to deal with,

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the human has to deal with.

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Versus taking the
outside where you

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have to cover more distance, but
the centripetal acceleration,

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the g-forces aren't
going to be as dramatic.

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So how do you think about that?

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JR HILDEBRAND: Well,
every track ends up

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being a little bit different.

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But when we take Indianapolis
here as the example,

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if you're already
on the inside--

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it's like the 800 meter
runner's kind of path.

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It's the shortest distance.

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You can kind of get
from point A to point

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B. The lap is the same every
time, so it doesn't actually

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depend on you running a
specific distance or not.

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For us, in this example, the
car actually just won't do that.

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If you think about being
all the way on the inside,

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being all the way on the
inside through the corner,

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and then exiting all
the way on the inside,

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it's having to do the most
work to follow that path.

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And in Indianapolis,
we're approaching

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turn one at upwards
of 240 miles per hour.

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And that turn one is
not-- it's hardly banked.

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It looks quite flat in person.

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So as opposed to NASCAR running
at Talladega or Daytona,

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these big, giant
super speedways,

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the car is having to
do quite a lot of work

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to get through the corner here.

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SAL KHAN: So how do you--?

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Do you take the outside or--?

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JR HILDEBRAND: So
then you look at that.

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And I think if you
noted the radius--

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if you drew a full circle
out of each of those arcs--

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SAL KHAN: Let's do that.

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So let's say that this is
the shortest distance path.

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This is kind of a circle that
looks something like this.

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Let me scroll over
a little bit so we

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can see a little bit better.

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So this would be
a circle like this

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if you were to keep that arc.

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It would be a circle that
looks something like this.

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JR HILDEBRAND: So that's
a pretty small circle

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in the grand scheme
of things here, yeah.

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SAL KHAN: That's a small circle.

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And for the larger
one, the circle

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would look something like this.

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So you have a larger radius,
a larger turning radius.

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So you would have to have
less centripetal acceleration,

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inward acceleration,
and fewer g-forces

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on this outside one, the
larger the circle is.

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JR HILDEBRAND: Right.

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And a different
way to look at it,

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if you looked at the car trying
to just go around these two

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different circles,
and it's going

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to be going the same
speed on either one,

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it's doing a lot less work to
get around this outside circle.

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And therefore the speed that
you could carry around that,

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that sort of goes up.

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The car has a limited ability
to stick to the racetrack.

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So opening that up definitely
makes a difference.

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SAL KHAN: But that's
an important point.

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At least in Indianapolis, you're
full throttle the entire way.

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I mean, obviously, if
you hit the brakes,

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the car could do a very
small turning radius.

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But you're at full throttle.

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You're not going to have any
chance if you at all let off

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the gas.

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JR HILDEBRAND: That's right.

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When you qualify
at Indianapolis,

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you've got to put in four
laps, four of your best laps

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of the season, of your career
in Indianapolis to qualify.

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And that you are
absolutely flat trap

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all the way around
the racetrack.

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There's no lifting.

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There's no braking.

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SAL KHAN: And so
that's why you're

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saying the car just
wouldn't do that.

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If you're going all
out, the car just

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wouldn't even be able
to make this path.

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JR HILDEBRAND: Exactly.

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That's a good point.

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From the driver's
perspective, you

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have to stay flat out if
you're going to go fast.

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If you're going to set a
lap time that's relevant,

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you have to be able
to stay flat out.

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And so at that point,
you're searching

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for the line around
the race track

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that you can do that
most efficiently.

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And so then, in this
example, increasing

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that radius by going
from our green circle

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out to the purple circle
does that rather effectively.

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SAL KHAN: I see.

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We're going for the
purple to the green back

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to-- so you're saying like this.

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JR HILDEBRAND: Well, yeah.

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And so then to find the actual
optimal line, what we end up

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doing is starting out on
the outside of the track,

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then bending the car into
the inside of the track,

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and going back to the
outside of the track,

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really using all of the
road that's available to us.

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SAL KHAN: Right.

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So that's interesting.

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So when I posed the
question, it was

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kind of like my brain was just
looking at these two circles.

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But you realize there's a bigger
circle that you could fit here,

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that there's an arc like this.

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And this would be,
if you imagine,

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this would be a part
of a circle that's

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way huger than even that purple
circle that we're drawing.

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So that center of that circle
is like here or something.

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So you have a lot less
centripetal acceleration

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that you have to place,
inward acceleration

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that you have to
place on the car.

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JR HILDEBRAND: Exactly.

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And therefore, the
car is able to carry

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a massively increased level
of speed through the corner.

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And that's really what
we're looking for.

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And you consider, I think
it's a very interesting-- when

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I think about what I'm
doing as the driver,

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I don't think I
really am consciously

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thinking that much about
the mathematics that

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go into finding this
optimal racing line.

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You sort of instinctually
just gravitate

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towards what the car
feels like it wants to do.

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But when we look at it
from this perspective,

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you've got the car going
down the straight away here.

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It's at 240 miles per hour.

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That's almost as fast as
the car is going to go.

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So it's just this sort
of terminal velocity.

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The drag of the
air hitting the car

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won't allow it to go
much faster than that.

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SAL KHAN: The engine's
giving all the power it can.

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JR HILDEBRAND: Yeah.

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You're absolutely flat out.

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SAL KHAN: And that's just
offsetting the drag of that,

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so that you can't accelerate
to that top speed.

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JR HILDEBRAND: Exactly.

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It's almost like you're hitting
a wall of air at that point.

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You're not going to be able
to accelerate any faster.

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And so what you're
really trying to do

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is you're trying to-- in
order to set that fastest lap

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time, which ends up
equating to the highest

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average speed around the
lap, that's what's the lowest

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number in terms of lap time
perspective-- you're trying

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to get the car to
most efficiently get

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through the corners so that you
can allow it to accelerate down

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the straights as
much as you can.

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You're getting it to diverge
from this intended course that

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is going on here as
efficiently as you can.

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And so by creating the largest
radius around the corner,

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that's how we end up
finding that optimal line.

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SAL KHAN: That's fascinating.

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