Pole Vaulting - Momentum vs. Force

[nautica]

Before jumping into my post, allow me to give a bit of background. I was a vaulter for the 91-92 Arkansas Razorbacks (2 of the 38 National Championship years - and no they did'nt need me to win). Presently, I help a couple of high school vaulters.

I would like to have a discussion about momentum vs. force as it relates to the vault and MOST IMPORTANTLY would like to have as much imput from you guys as possible. I really do not have a particular question as of yet, but after the discussion begins, I might.

For those of you who are not familiar with the vault, I will give myself as an example so you will know what kind of numbers we are dealing with. And what I would like to do is figure out a perfect formula for speed vs. acceleration in the vault.

In college these were my stats:

5'11"
179 lbs
4.35 - 40 yard time
held 15'6" on the pole but the box droped 8" into the ground so 14'10"
Clearance was 17'
my reach is approximately 7'6", so when the pole was planted my hand was 7'6" off the ground. Obviously the higher the reach the better the angle and the easier it is to accomplish the vault - but I am a shorty.
My center of gravity is half of my hieght and was elevated to 17'

I guess it would have been easier to convert to metric. But anyway, I am not sure the numbers are all that important anyway, just thought it might make it a bit easier to understand what is happening.

Anyway, it is obvious that what a vaulter must over come is gravity or acceleration. So, it would stand to reason that it is extremely important for a vaulter to be accelerating through the last step of the vault while jumping off the ground. Now, here is the tricky part (at least for me). There is a trade off. The faster a vaulter is running (higher speed or large momentum) the slower the acceleration or small force and v/v.

So, what vaulters do or at least what coaches attempt to get their vaulters to do is to NOT reach maximum speed so that one can accelerate not decelerte through the vault.

So what should I, as a coach, be trying to get my vaulter to do. Which is more important speed or acceleration, momentum or force. Is there possibly a magic ratio. Is it possible that a slower vaulter could obtain a greater acceleration and have the potential of vaulting higher.

I see so many vaulters, some even world class that appear to only be striving to reach a top speed and maintain that speed through the vault. But, it looks to me like even though speed is obviously important that the emphasis should be more on the acceleration?

Any thoughts or comments would be greatly appreciated. Even if you do not understand the vault, you can relate it to a couple of cars in a head on collision (actually, this would be much much simpler to discuss). We could discuss one car travel at an extremely high speed and the other traveling at a fast speed but a higher acceleration. Who wins, where is the "magic" number or calculation here?

Thanks
Nautica

 

[PhysicsFan]

I found a video clip on the web of Stacy Dragila, one of the first great women's pole vaulters. The clip may enhance the description in the message above. Her run up to the bar is captured well, although the camera view of her planting the pole (and the subsequent bending of the pole) don't show up that well, in my opinion. First, go to:

http://www.azcentral.com/sports/azetc/04olympics/04olymulti.html

Then, in the column with the heading "SPOTLIGHT VIDEO," you have to go down a good bit to find the heading "Gold medalist pole-vaulter Stacy Dragila...," which you should click on.

I have also located some web documents on the physics of pole vaulting:

American Institute of Physics
http://www.aip.org/png/html/polevault.html

"How Stuff Works"
http://health.howstuffworks.com/pole-vault3.htm
(scroll down a bit, once the page appears)

American Physical Society
http://www.aps.org/apsnews/1100/110009.cfm

Physics and the Olympics
http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/Daniel_Lenord/vault.html

Kimo Morris
http://pukashell.net/kimo/polevault/physics.html

NeoVault
http://www.neovault.com/articles_physics_of_pole_vaulting.asp

Only a Game
http://www.onlyagame.org/shows/2004/03/20040306_14.asp

 

[krab]

I don't know what you mean by "accelerate through the vault". Once your feet have left the ground, you cannot accelerate. So you accelerate up to that point. But this acceleration is of no subsequent importance. You need the highest speed possible to load up the pole with potential energy. So what counts is the speed you have when you plant the pole.
Look up the links in post 2. You will see they all calculate height from speed. It's a pretty simple calculation too.

 

[rcgldr]

Pole vaulters get a significant portion of their height by doing work after their feet have left the ground, so it's not just the speed.

First, during the early part of a vault, the vaulter swings forwards producing a centripetal reaction. During this time, the pole vaulter raises his center of gravity, mostly by whipping his legs and using his stoumach muscles. Then, because the legs are pulled in, decreasing angular momentum, the vaulter continues to rotate backwards until the vaulter is approaching an inverted position. At this point, the vaulter straigthens out and pushes against the pole, both adding even more to the overall height.

It's not the fastest guys that get the best height. It's the guys with the best technique, and that swing motion that takes a vaulter from under his grip point to above his grip point is the key part of this technique.

It would seem to me that if a vaulter could manage jumping and then "diving" so his center of gravity was higher and further back at the point in time that the pole plants, that this could provide even more of a swing which would translate into more height.

 

[rcgldr]

For a good visual exmaple of just how much energy can be produced during a swinging motion, here's a video of a guy doing a quadruple back flip on swinging rings. In just two swings, the guy is even with a bar over 20 feet high in the air. What happening here is that the center of mass is moved away from the bar when at the ends of the swing where g forces are almost zero, and the movement more horizontal, so little negative work is done, followed by moving the center of mass towads the bar during the middle of the swing where g forces are high (a bit over 3 at the bottom), and the direction more upwards so a lot of positive work is done.

If you stream this video, press ALT-2 to see it regular size, as windows movie player uses a smaller view when streaming (some sort of bug).

http://jeffareid.net/cgi-bin/quad.wmv

 

[rcgldr]

From what I've now read, the swing, pull, push, technique is good for an additional 3 feet or so above what is converted from the speed of the run.

 

[pervect]

Any thoughts or comments would be greatly appreciated. Even if you do not understand the vault, you can relate it to a couple of cars in a head on collision (actually, this would be much much simpler to discuss). We could discuss one car travel at an extremely high speed and the other traveling at a fast speed but a higher acceleration. Who wins, where is the "magic" number or calculation here?

Thanks
Nautica

If two cars collide, there's no question - the important thing is the speed they are going when they collide. The length of the collision is so short that the acceleration capability of the car just isn't going to matter.

Pole vaulting is a bit more complex, though. The way I would look at it is this. If you get up a good speed, but your feet/body is still pointing downwards when you reach the bar, all that speed is not going to help you because your feet are going to hit the bar and knock it down.

So you need to get your body into a horizontal position when you are crossing the bar as an absolute miniumum. Actually I think there is even more sophisticated technique involved - I think I read somewher that a good pole vaulter can get his body over the bar even though his center of gravity is always lower than the bar via the proper contortions. This is only a matter of inches - but those inches can spell the difference between winning and losing.

The "leap" at the end you describe would certainly help one get one's body into the proper position to cross the bar. So I would say the idea is to run as fast as you can BUT still be able to get your body into position.

 

[rcgldr]

I think the term "acclerate" may be misleading here. What would help is a slight forwards lean as you plant the pole to increase that swing effect I mentioned. Leaning forwards would also increase the forward speed of a vaulters center of mass for a brief period.

 

[rcgldr]

Kimo's website mentions what I've posted about above:

"By getting completely inverted and pushing off the top of the pole, a vaulter can actually "pull" and then "push" their center of mass higher as the pole uncoils (unbends). See my UCI picture from 1994 to get a visual idea of this. Really good vaulters can push their hips (center of mass) up as much as 4' beyond their top hand grip."

So it's not just the speed at the time the pole is planted.

 

[nautica]

I appreciate all of the responses. But, I understand the physics of vaulting. I have trained with many olympic athletes and was hoping to be one myself before an injury forced me to stop competing at the beginning of my sophmore year.

I am not concerned with what happens after the vaulter leaves the ground and I realize that speed is what is important.

But, a runner can not maintain a maximum speed except for a split second. The acceleration, which I am speaking of is the brief split second just before taking off. It is a combination of jumping and running.

I know my original question was confusing. But, I guess what I am asking is how much difference it would make if the vaulter was not completely at full speed until that last step and how much better would it be for the last step to be an acceleration to the top speed or if it is the speed alone that contributes to converting the kinetic energy to potential and then back to kinetic?

Or v/v. If the vautler reached top speed just before taking off and the last step was a deceleration. This should hinder the vault. Right? Or is it speed alone?

Nautica

 

[rcgldr]

From what I've seen on TV and read at various sites, most sprinters can maintain their maximum speed for 10 to 15 yards (some even more), more than enough for a situation like a pole vault.

Again, the only other thing a vaulter can do is jump or lean into the pole just as he/she plants the pole.

I think there has to be a comprimise between what's idea and what's controllable. The ideal situation might be a take off like a long jump with a bit of a diving position where the pole is planted at the moment the jumper reaches peak height of center of mass. You might sacrifice a bit of speed, but the swing and leg whip which help propel a vaulter upwards would improve, and the starting center of mass would be much higher.

 

[nautica]

So, what you are saying is that it is irrelevant if you are accelerating vs. running at a constant rate of speed through the plant?

And as far as the take off, I didn't want to get into the mechanics of the actual vault, but the vaulter tries to lead through vault with his chest at a 45 degree angle. 15 or 20 years ago vaulters actually tried to push with their lower arm in order to store more potential in the pole, but after 1000s of broken poles, they found out that was not needed.

As far as your analysis of the take off, it is pretty well in line. Obviously the higher intitial center of mass has less distance to travel in order to reach a certain hieght.

There are 2 major concerns of a vaulter after leaving the ground. The first being linear movement in order to land on the mat and the second being verticle movement in order to reach the desired hieght.

The running, jumping off the ground and the drive of the lead knee carries the vaulter to the mat. The swing leg is only used to allow the vaulter to rotate upside down and bascially behind the pole, so that the when the potential energy of the pole is release, it along with the kinetic energy carry the vaulter up, the the vaulter can pull, turn and and eventually push off the top of the pole.

But, none of this is really relavant to my original question. This is why I tried to keep it extremely simple, such as with the two cars. So, allow me to try to simplify my question again.

2 cars traveling to a head on collision. Both cars are traveling exactly the same speed upon impact. BUT, one car is accelerating and the other car is deccelerating. BUT, at the point of impact the speeds are exactly the same. WHAT HAPPENS?

Nuatica

 

[Astronuc]

So, what you are saying is that it is irrelevant if you are accelerating vs. running at a constant rate of speed through the plant?

I wouldn't necessarily use term 'irrelevant'.

Perhaps it is a matter of optimizing where in the process one applies the effort. If one where to accelerate to maximum, perhaps one would achieve at maximum performance prematurely with respect to the take-off, and therefore the takeoff would be less effective - point at which fatigue (possibly wrong term) in arms and legs begins to set in. {Question - Would anerobic metabolism be involved here?}

There is also the mechanics of the vaulting pole which stores mechanical energy due to the bowing, as well as pivoting. Going too fast may not allow one to respond effectively to the dynamics of the pole.

 

[rcgldr]

In the case of the cars, the accleration versus deceleration doesn't matter, except the accelerating car's bumper will be higher than the decelerating car's bumper.

Getting back on topic, one of the goals of a vaulter is to put as much energy into the pole as possible. Even after the initial plant, if the vaulter can continue running forwards and apply a force to the pole to further store energy into the pole, this will result in more height. Perhaps this is what you mean by accelerate into the vault. By leaning forwards (for balance) and continuing to run forwards at the time of the plant, a vaulter will be able to apply additional force into the pole.

I think this is one aspect being ignored by the speed only based estimates. In addition to a vaulter's speed, a vaulter can also continue to apply force to the pole while bending it until his/her feet are pulled off the ground, perhaps one or two steps.

So there is a trade off of sheer speed, or maybe planting at a slightly slower speed, but being able to apply more leg force during the initial bend of the pole.

It's also possible that a good jump near the time of the plant would also help.

Regarding bending the pole using pressure through the arms, aren't the poles with carbon-fiber strong enough now to handle this without breaking, or is the weight penalty for more strenth at the vaulters end of the pole not worth it?

 

[rcgldr]

Lastly, as a saftey measure, why aren't there crash pads in front of the bar, on either side of where the pole is planted? With a death rate around 3 per year, seems like this would help some.

 

[nautica]

I think you have a misconception about the job of the pole or the storing of energy into the pole. The goal of a vaulter is to put as little stress on the pole as possible. A vaulter essentially wants to jump over the pole (over his handhold) and put absolutely no stress on the pole (obviously this is not completely possible). His goal is not to load energy into the pole, he is trying to jump as high as he possibly can with very little stress on the pole. The higher he can hold on the stiffest pole possible, the better off he is. He is not simply running down the run way with the intension of planting the pole and bending as much as possible and then waiting on the pole to spring back with the stored energy and throw him over the cross bar.

He runs fast and jumps high so that he can reach a certain hieght. Obviously the taller the pole the better and of course the stronger the pole the better. If a pole is too soft it will just bend and move forward to quickly instead of aiding the vaulter in going verticle.

Now back to my original question, which I believe you have now answered. Although, I am confused about the answer. You said in the case of the two cars it does not matter (lets forget about the bumber hieght). All things being equal, are you saying that force is irrelvant and only momentum matters?

So, at the point of any impact acceleration/decceleration does not matter. All that matters is actual speed? I just don't see how that is possible. I am not disagreeing with you it just seems like a car accelerating to a speed at impact would cause more damage than one that is decelerating. Obviously, it would have a greater "force" but what you are saying is that force does not matter. If that is the case what is the purpose in studying forces, when all that matters is momentum or speed?

"Regarding bending the pole using pressure through the arms, aren't the poles with carbon-fiber strong enough now to handle this without breaking, or is the weight penalty for more strenth at the vaulters end of the pole not worth it?"

Yes, the expensive poles use carbon, but they can still break. But, like I said the goal is not to bend the pole. What did you mean by the weight penalty for more strength?

You also mentioned that jumping may help the vaulter. Yes, a vaulter must be jumping. He essentially leaves the ground in the same manner that a long jumper does. At a 45.

Thanks
Nautica

 

[nautica]

Lastly, as a saftey measure, why aren't there crash pads in front of the bar, on either side of where the pole is planted? With a death rate around 3 per year, seems like this would help some.

As far as crash pads in front of the cross bar. There are. The deaths occur from the vaulters going straight up and coming straight down into the metal box, where the pole is planted. A vaulter can go straight up and complete a vault and loose where they are. They will go up and come down thinking they are going to land on the pad but land in the box. Or, they can go up and stall out and come down head first into the box, breaking their neck or busting their head open.

There is actually as many pads around the box as can be possible. Helmets should be required, but that will not keep vaulters from breaking their necks.

Most vaulting accidents can be taken care of by coaching and putting safety first, but accidents do happen, even with expert vaulters.

Nautica

 

[pervect]

Now back to my original question, which I believe you have now answered. Although, I am confused about the answer. You said in the case of the two cars it does not matter (lets forget about the bumber hieght). All things being equal, are you saying that force is irrelvant and only momentum matters?

What is important is the total momentum of the car at the moment of impact. The reason for this is fairly simple - collisions happen very quickly. So, if you were somehow able to accelerate at 1g throughout a collision (or deccelerate, for that matter), the total amount of momentum you would lose is acceleration * time

If you run into something going, say 30 mph, and you have a "crumple distance" of 2 ft, the total amount of time the collision process will take is appoximatly (2 ft)/(30 mph), which is .045 seconds.

Accelerating/deccelerating at 1g (that's a very hefty rate, approximating the best possible acceerlation/decceleration you can get with the very best tires - this is the same rate at which a body falls when you drop it) would mean that you change your speed due to to the acceleration by 1 mi/hour during this .045 seconds time interval (.045 seconds) of the collision.

(The unit changes here are somewhat involved, which is why I used

google calculator

to take care of the unit conversions.

Thus you can see acceleration is a very minor effect. We are not saying the effect is zero, just that a very small speed change (1 mi/hr) is at least as important than a very large acceleration (1 g, 32ft/sec^2, or 9.8 m/s^2), and that the reason for this relative lack of importance is that collisions happen very rapidly.

This is the same reason as why seatbelts are necessary for restraint in an automobile accident, and why you can't stop yourself by "bracing" with your hands, arms, or legs. The amount of acceleration / force that you can supply by bracing yourself is not going to matter (much) during the very short time that the impact takes. You just won't be able to stop yourself by "bracing" - you are not strong enough.