Potential Energy and the Vault

[willrieffer]

Vault Physics – The Vertical Line and Potential Energy Curves

My name is William E Rieffer. I vaulted at Ohio State and while there studied physics.

I find what I call the “folk” physics of the pole vault to be littered with problems. I took me six years of studying the system to hopefully rectify that. The vault is dominated by potential energy concerns and curves.

I'm going to start with an argument to illuminate our situation followed by two tangible scientific demonstrations that only take a stubby and a roll of athletic tape to make my point.

Argument

Facts – Flex poles lose some amount of energy as heat. The amount is small, usually around 2% or so. Still, this is energy not recouped as max potential energy or height. Straight poles, because they don't take on significant energy as flex, don't lose significant energy.

The argument then follows. IF flex poles lose energy and straight poles don't then we should use straight poles to jump higher because they don't lose energy.

The facts in this argument are true. The logic is sound. Yet the resultant claim is one that any vault coach knows isn't the case! Why? Because of all the science left out of the argument. There are many arguments made about the vault that are faulty in this way because of what they leave out. And most of that is because they do not consider potential energy changes and curves per the vault.

1)Potential Energy and the Vertical Line

Take the roll of tape and the stubby. Roll out one or two feet of tape and leave it attached to the roll. Attach the tape to one end of the stubby. Place the stubby at an angle modeling the pole takeoff angle. The tape and roll act to model our vaulter with the roll approximating the center of mass of the vaulter. The roll should settle into hanging straight down in accord with the vertical line of gravity. This is the resting state equilibrium where energy and potential energy are at their minimum. Now slowly rotate the pole forward as with the vault. Notice that we have to push the pole because we're changing the potential energy of the system by moving the roll of tape, our center of mass, up. Now even though the pole angle has changed the resting state equilibrium still presents the roll hanging right under it's attachment to the pole (the vaulters “top hand”).

Now stabilize the stubby and push forward on the roll of tape. Since we have constructed a pendulum to displace the roll as center of mass we have to push energy into the system as the roll in it's pendulum motion is curving up to a higher potential energy state.

This analysis holds true if the energy is coming in the form of the kinetic energy of the vault approach.

In the immediate post takeoff there are three energy states. The residual kinetic energy state per velocity and mass. The energy now in the bending pole. And the changing potential energy as the vaulters center of mass rises. These three values extend from the initial kinetic energy at takeoff and cannot be immediately changed. In order to generate energy through force you need to have something to push on. Later, the vaulter can push the pole against the ground and increase energy, here there's nothing to push against to add energy.

So we are looking at a three variable problem that can't exceed the starting kinetic energy total. Thus if the vaulters center of mass moves up, there's less energy in either kinetic energy, or pole elastic energy, or both. Thus if the vaulter keeps their mass under the top hand they will have more pole energy and/or more kinetic energy/velocity.

The most important line in vault is the vertical line of gravity through the top hand.

Rocket Science or “Wobble”

2)Let's go back to the stubby. Balance the stubby on your palm. Now push up vertically on stubby. One of two things will happen. A) The stubby's center of mass will be closely lined up with gravity through your palm where you are exerting vertical thrust. If so then the stubby will fly skyward like a rocket. Or, B) The stubby's center off mass will be off from the vertical line of gravity through your palm and the stubby will “tumble” or rotate as you push up and will gain very little altitude. Thus, what makes a vaulter finish well is lining up their center of mass on the vertical line of gravity through the top hand.

And like the beginning we again see that the most important line in vault is the vertical line of gravity through the top hand.

To take it a step further the further the vaulters center of mass is displaced from this line over time(almost always forward of it), the harder the vault becomes. Or, nothing good happens in front of our line.

Answering the Questions

Using this framework we can easily and concisely address many questions about technique and other issues.

Getting “Stuck in the Bucket”

As newer vaulters find out nothing good happens when they get their hips and thus center of mass forward. Gravity is pulling down on the hips. If they haven't set up a good swing or lack strength they get stuck. This is compounded by the fact that if their hips were back under the top hand gravity would be providing a vertical compression force on the pole. Since they are forward and there's less compression on the pole the pole will go into recoil earlier and faster. And the vaults over.

Launder and Gormley once emphatically pointed out to me Bubka's highest rotational rate as measured by the IAAF. But they then couldn't tell me why it was good. Now I've explained it. He spent less time out in the “bad zone” in front of the line of gravity. The vault is a game of wait and hurry up.

The Leading Hand

So what does the leading hand do? Well it's in the unique position to be in front of the vaulter and vertical line so that it can be used to keep the center of mass back closer to being under the top hand. If punched or locked at plant it can be used to keep the center of mass back. I should mention that this is a very brief moment of impulse force right at plant/takeoff. I routinely see people pointing out much later in the vault the nature of the arm. Well, as soon as the vaulters legs start to rise they are now lifting their mass against gravity and generally the arms will be “pulled” straight. This is significantly after the point where the left arm can influence the center of mass placement.

Remember our three variable problem? When the hips are kept back closer to the vertical line it flattens the initial potential energy curve meaning there is more energy for the pole and residual kinetic velocity. Effective use of the leading arm results in more energy being directed into the pole at the TOP hand. These things are mutually beneficial. More energy into the pole is more bend and more energy to recoup later as vertical thrust. More velocity means more penetration.

Premature Rowing

Premature Rowing is bad simply because its forcing the center of mass up and forward prematurely. It impacts the potential energy curve negatively. Less energy goes into the pole and it slows faster. The athlete doesn't want to engage the shoulders before they have swung through and are lifting their center of mass. Wait and hurry up.

Other Considerations

The vault is dominated by potential energy concerns. Rotational dynamics is dwarfed by potential energy considerations.

Let's imagine we have a spaceman in a rotating space capsule. Outside on the capsule is a very very long pole pointed such that if the spaceman climbs it, he will lengthen the his distance from the axis of rotation changing the moment of inertia of the system causing it's rotational speed to slow. However, he is neither adding nor detracting from the systems energy state. Friction-less, it will keep rotating forever. If we add a plane of the crossbar to this system the spaceman will ALWAYS reach the plane.

What does effect and slow the vault system is the change and rate of change of the potential energy value. Vault is a bit like going up a hill in a car. Unless you step on the gas and add energy the car will stop. Most fail vaults, stalls, are for the reason that the athlete turned the potential energy curve up to fast, or likewise wasn't able to hold it down well enough, and like a car without gas they slow and stop.

The invention of the flex pole, while we can say it changed the rotational dynamics of the system, what it actually did was that bending poles allow a lower potential energy curve. The athlete stays closer to the ground with the benefits brought forth before. Lower potential energy value, higher residual velocity and/or pole energy state.

Parabolas

Any unpowered and liftless object is going to have its flight path conform to a parabola. This applies to vaulters when they leave the pole. Now there are low flat parabolas and high skinny parabolas. It should be obvious that vaulters want, in the end, high skinny parabolas that conform to the crossbar or has it's peak on or very near the crossbar. This is again a potential energy trajectory the one the vaulter needs to steer themselves and their center of mass towards. A parabola is mirrored. The vault isn't completely mirrored as a parabola until exit from the pole. A high skinny parabola is going to be closer to the plane of the crossbar. Thus the need for “penetration”. Again we're back to the three variable problem.

An interesting video showing this is Joe Dial's 5.96m jump in Norman. Joe enters at around 18' and clears easily landing well into the coaches box. Next, ~18' 6' and again he lands well into the coaches box. But at 5.96m he knows he needs to “skinny up” his parabola. He clears and lands in front of the coaches box just off the bevel.

Do I Dare?

When I started coaching I read everything I could get my hands on. What I found were just glaring physics mistakes.

The Petrov Bubka model

I would read that unless you used the free takeoff and jumped like Bubka you would “lose energy into the plant box”. This is, per the laws of physics and thermodynamics, wrong. The box doesn't move, therefore it can't take on kinetic energy. Is there some heat buildup with tip strike and friction? Yes, but the amount is certainly so small as to be insignificant particularly in a focus on mitigation. There were other things. Bubka admitting he “did not get the free takeoff today”, and yet still jumping high. At '93 Worlds I don't think he gets the free of either of the two bombs he launched there.

Of course now we have Mondo who doesn't get on the pole like Bubka, Mondo not doing the FTO and being routinely under. He doesn't swing like Bubka. And he doesn't exit the pole like Bubka. What he is is faster than Bubka and can take a big pole, drive it forward, and get his center of mass lined with his top hand and the vertical line of gravity.

Lavillenie had excellent form per my analysis. Punch the left. Keep the hips back. He also dropped the right leg lowering his center of mass, while also reaching his left far behind moving his center of mass, you guess it, towards our line.

One last thing. The “pole chord”. Well, if someone is talking about the pole chord they're wasting their breath. It doesn't mean anything. IF the swing isn't regulated by the hands the vector engagement that pulls the pole forward happens at around 45 degrees from the vertical which will extraneously coincide with the chord at some point as the athlete swings through. Likewise I've seen comments that Bubka's famous “negative invert”, 'lined up some part of his body with the pole chord'. That's mere coincidence. What it does is puts his center of mass in line with the vertical line of gravity through the top hand.

I've been a coach at Eureka HS Missouri for a decade. I've had kids the MO state meet every year but the first one when I transferred to Eureka from Grandview Hillsboro where I had multiple All State Vaulters. I coached many notable vaulters at Pole Vault STL until I retired from there as it got too painful on my body.

William E Rieffer

[willrieffer]

A few things...

Vectors in x and y.

https://en.wikipedia.org/wiki/Vector_(m ... nd_physics)

We're primarily concerned with vector spaces. In this case our vector spaced is defined by x and y for horizontal and vertical and is oriented with the everyday world where x is horizontal distance and y is vertical height. This became important study with the advent of artillery. Galileo was one of the first to study parabolic trajectory.

Pendulums

Most are probably familiar with pendulums. Probably seen a video, or a desktop decoration, or swung one on a playground swingset. Pendulums have as their cause of motion a relationship between kinetic energy and potential energy. As the body swings up it slows, stops, and reverses.

https://en.wikipedia.org/wiki/Pendulum_(mechanics)

On the wiki we are most interested in the energy derivation and examples. The examples are of rigid rod pendulums. IF they were rope pendulums their behavior would be most different. IF you've been on the playground swing and got up to around 90 degrees what happens is that the tension in the swings ropes or chains is a little bit of elastic energy and at 90 degrees there's no longer any vertical compression on the system. So the rider gets "pulled back" towards the pivot, inside the circular curve of the swing pendulum, and enters into a bit of free fall before their trajectory intersects again with the circle defined by the rope length. I mention this because at 90 degrees there's no vertical compressive force on the pendulums pivot. It starts at 100% of gravity as it hangs straight down and reaches 0% at 90 degrees. Think about how that applies to the vault.

As kids we used to run and belly flop into the swing and ride it like that. This is much the way the vault works.

Inertia

Inertia is quickly and sparsely defined as, objects in motion tend to say in motion in a straight line unless acted upon by an outside force. For the vault this means that when the vaulter first encounters the pole plant with the pole their center of mass, usually found around the waist, is going to want to continue forward. But now we have at one end of the vaulters body as pendulum the top hand meeting the pole braking force. There are two general options.

1) The Pendulum. The pole will immediately cause the vaulter to swing up and forward. With straight poles there is very little forgiveness here. This is why straight pole vaulters leaped high to try and reduce or "get over" the pole braking force as its value is set by the angle of the pole. Higher angles have reduced horizontal braking according to trigonometric values. Here we refer back to Wikipedia on Pendulums and the energy derivation. Swinging forward and up has a cost in potential energy. In the vault doing so reduces the energy for either the pole elastic energy, the residual kinetic energy/velocity, or both.

2) The Sail. Imagine you have two boats. One boat is perfectly normal. The other has a damaged mast so that while it remains anchored to the deck it is also able to pivot. Our "pivot" boat the effect is quite like a pendulum, and the top of the mast pivots in a hemisphere with the radius of the mast. Now the wind blows on our pivot boat, and the mast is blown around the pivot, and the boat doesn't move. Normal boat is using the mast to transfer the force of the wind into the hull and it starts moving forward almost immediately. Now the captain of the pivot boat is trying to figure out a solution to keep the sail upright and so it can transfer wind energy into the hull. Well he comes up with two ideas. Ropes to hold the mast steady. And a brace of lumber at the base. This is our analogy for the lead arm in vault. It's the brace to stop the pendulum "pivot" and direct the inertial energy not into swinging up but into the pole. Again, the "brace" of the lead arm puts more pressure on the top hand because the vaulter isn't swinging forward and up changing their potential energy value.

The Chord and The Swing

When I was club coaching we had a rolling high bar and a swing up rack. So I did an experiment. IF I pushed horizontally on the bar by walking forward simulating the plant, the bar would swing to about 45 degrees before the high bar would start rolling. This is more vector analysis.

At the plant take off with the "free swing" pivot model we have a similar situation. The vaulters energy is horizontal kinetic energy. What happens is that without bracing the pendulum motion starts. And it doesn't hit equilibrium with gravity until about 45 degrees. Initially you have a very small force working horizontally at the top hand. I've looked at thousands of videos of this. The top hand will for some vaulters drastically slow down its horizontal movement. They'll swing out forward, this changes the angle and vectors. Imagine a pendulum with a spring scale at the top. You attach a rope at the bottom of the pendulum and start pulling horizontally. Where do you think the scale will balance with the pulling force? Well, not until you've pulled the pendulum through 90 degrees and you're pulling the whole system horizontally. The scale will start with small readings as you start pulling and the value will increase as you increase the degrees. Well the pole is the spring in the vault system. And so IF you're a pivot/free swing vaulter you're not going to generate enough top hand force until you are at a swing degree that generates enough force value to "move the pole" or start its compression. But IF your using your top hand as the "brace" it starts moving immediately, putting energy into the pole faster.

The pole chords meaning is found in it's x and y components. That's it. There's nothing else. You find those by triangulating it in x and y where y is the height and thus potential energy value.

Centrifugal Force vs Raising the Center of Mass.

For big swingers like Bubka it is the case that they are generating centrifugal force in the vault. The question, and I'd be happy to hear answers, at what value.

So I have to go back into potential energy. When the typical vaulters trail leg foot reaches the bottom of the arc of its swing, and this is btw perpendicular to the ground and not the athletes body, the process of lifting the body of the athlete starts effecting the pole. So you will see a secondary bend moment in the pole as they do this. We can do a thought experiment. Imagine with have a pole a we mount it horizontally. How is not important. Let's imagine its just magically affixed in the sky by the tip. Now you put a vaulter on the other end and have them swing up. What do you think happens? Muscular work against the force of gravity is going to bend that pole. So is it really some force/centrifugal force coming down the chord or is it just the effect of the vaulter now using the pole, putting force into it and through to the ground, that's causing this secondary bend? I say its the latter.

I know people believe this, "pole chord is everything". I know they believe that the chord is magic and attach all kinds of pattern recognition with it. But I think that's all it is, faulty pattern recognition, not science.

IF only he had comments turned on...if you know you know.