How High Could the Fastest Man Jump?

================= (A-ROLL)

How would you build the best pole vaulter possible? You’d probably take what makes the best great and combine them to make something… perfect.

Now, I want you to think of an elite pole vaulter. What attributes do they have that made them successful?

And what happens if we take those attributes and turn them up to the max?
Just how high could a human vault?

(B-ROLL)(Mondo Duplantis footage at the olympics with announcers talking about his attributes)

Witness: Mondo Duplantis, the Olympic Champion. What makes him so special?

He’s not the tallest in the field.He’s not the strongest in the weight room.

And at the first glance of the lineup, several other athletes appear to outmuscle him. (Lineup, show Guttormsen, Nilsen, Lisek, big muscular vaulters)

How does Duplantis outperform bigger, stronger athletes? (A-ROLL)

The answer: Mondo is fast. Really fast. So what happens if the fastest man in the world had the best pole vault technique? Just how high would he jump?

================= end intro Body: Whiteboard Start with physics equations showing KE relationship with velocity, explain why the horizontal impulse forces the linear relationship seen in the study.

Now this is the equation you’ve probably seen.
Vaulter runs with some velocity V.

Kinetic energy of this run is then converted into potential energy as the pole bends.
This potential energy is converted into kinetic energy as the vaulter releases the pole and shoots upwards.

(Speed up the unnecessary part)

You’ll have some efficiency factor 1 here and some efficiency factor 2 here.
Now, when you solve this energy conversion, you get h = beta * v^2

If you’re curious, beta = efficiency factor 1 efficiency factor 2 / 2 g
This is not so important what is important is that height is proportional to velocity squared

Now what this is saying is that for a small increase in velocity, a large increase in height will occur.

Most people stop here and say they’ve explained the pole vault.

But this isn’t what actually happens.

When you plant the pole, this dot represents your grip and this line the pole.
You plant with some angle theta. It bends in here, and then it’s released… By the time you move it to

vertical, the angle will be 90 degrees.
There is work required, it takes energy to move the pole from theta to 90 degrees. If you don’t

move the pole to 90 degrees, you will land in the box or be shot out back onto the runway.
So work required to move the pole to vertical equals force times distance.

And force is mass times acceleration which is vfinal - vinitial over tfinal - tinitial

In a succesful vault, the vfinal equals 0 as theta equals 90 degrees, placing you right over the bar,

and tinitial will be taken at the start of the plant, which will be 0.
Therefore, we can rewrite force as -vt

And work as -vtd, where v is the initial velocity, t is the time from the plant to the completion of the jump, and d is the
distance that the pole moves.
The negative sign makes sense here, because it takes work from outside the system to move the pole to vertical.

Now, let’s think about what happens when you run at a higher velocity and increase your grip accordingly.

The distance from your grip to the box increases, and therefore the distance that the pole has to travel to get to

vertical increases.
The work, -vtd, becomes more negative, and thus takes energy away from your jump proportional to velocity.
Now, you might ask why don’t you just stay at the same grip and increase pole stiffness?
And this is absolutely right. When you have an athlete go up a pole, you increase
pole stiffness before you raise grip. But this only works once.
When you increase stiffness too much without raising grip, you change the

flight path of the vault.
You need the vault to follow this flight path in order to make a vertical bar.

Lowering grip increases the speed of the pole. We call this ‘rolling over’.
If the pole rolls over too fast, you either miss your swing or your flight path
becomes like so. And remember, we want to clear a vertical bar, so excessive

horizontal distance does us no favors.
Yes, you can maintain more energy in the pole by raising stiffness not grip,

But at a certain point, you have to raise grip in order to maintain the proper flight path.

Okay, let’s take what we’ve learned and write a final equation.
Kinetic energy(height) = Kinetic energy(run) + Work(vertical)

= Bv^2 - vtd

Now there’s still more factors in this equation, so if you’re interested in learning more, I’ll link the study in the description.
But from this equation here, we can see that there are retardant factors proportional to velocity that balance out the
quadratic nature of the energy equation, leaving us with a linear relationship.

height is directly proportional to velocity

Calculate Usain Bolt’s vault performance using c calculated from Mondo’s stats and m from the study. Return 6.61m prediction. According to a 2012 study, pole vault performance has a linear relationship with run-up velocity.


Start here:

(whiteboard scripting)

KE = 1/2 * m * v^2

PE = m * g * h = KE *F

h = 1/2 * v^2 * F / g
From this equation, height is proportional to the square of velocity.
But we know this is not true, due to this study.

Height is really linearly proportional to velocity.

The math is simple: more speed, more kinetic energy

Alright so let’s answer this question: if the fastest man in the history of the world had perfect pole vault technique