By
Brian Peterson
Last Updated May 31, 2000
Table of
Contents
1. Introduction
2. Hypothesis
3. The Grip
4. The Run
6. The Swing
7. The Pull-up
10. Pulley Apparatus
11. Raw Data
12. Analysis
14. Works Cited
15. Conclusions
16. Links
On July 31, 1994, Sergei Bubka set a world record in the polevault at 20’ 1-3/4". He was able to attain that height by working hard in multiple areas and having the right equipment. "There are eleven components to the polevault program: strength, power, speed, endurance, flexibility, technique, orientation, coordination, recovery, mental preparation, and diet"(Ed Jacob, Bob Fraley 1996).
The actual polevault itself is comprised of about six stages; "(1) The grip, (2) the run, (3) the plant and take-off, (4) the swing, (5) the pull-up, and (6) clearing the bar"(The World Book Encyclopedia 1995). By improving himself in every one of these areas, Sergei Bubka was able to keep "skying" higher and higher. These are important components but equally important, if not more important, is also the pole which you select.
Poles are built with three specific measurements: first the length, second the body weight, and third the flex number (the lower the flex number, the harder to bend the pole. This just measures the natural bend of the pole, or it’s stiffness value) which we won’t worry about. Usually, people most commonly denote poles by stating first the length, then the weight. For example: a thirteen foot pole made for a one-hundred forty pound person is denoted as: 13’ 140 – most commonly read as, "a thirteen forty." It is very important to have the right pole and to be comfortable with it.
"Success in the polevault really depends on the action between the vaulter and the pole"(Jim Santos and Ken Shannon 1991). "The more experienced you are with the pole, and the better the pole is for your particular build and vaulting experience, the better your performance will be and the higher you will vault." Poles today are made of strong, but light fiberglass. Poles are made in many different ways and it’s important to use a pole that is made for you. "Poles today are usually made of spun fiberglass (and the newest ones are laced with carbon to make them stronger and lighter). Different manufacturers make them slightly different. Catapole make their poles by using a triangular piece of fabric and spinning the fiberglass on as the fabric is rolled up. This makes the pole thicker in the middle and thinner on the ends. Pacer makes their poles a little bit differently. They use three pieces of fabric and then spin on the fiberglass. The middle piece is triangular with two more rectangular pieces on the top and bottom ends. This allows pacer to make a ‘Faster response poll,’"(USAPVA 1999). By having three different focal bending points, basically means that the pole is able to transfer and contain more energy. We call this process of transferring energy into the pole "loading." If you load the pole well, at the end of your vault, the pole will give the energy back to your body and throw you up over the bar. Good vaulters can jump two, or possibly three feet higher then their handhold. That truly is incredible. Of course, all of this is with the assumption that you have the strength and technique in the six stages of the vault listed above to jump that way.
"Perhaps the most important factor behind the polevaulters success is his/her ability to run fast and generate a lot of speed on the takeoff. Running speed allows you to transfer energy into the pole when you plant it at the end of the approach: the energy is returned to you when the pole straightens as you finish your vault"(1991).
"As soon as an athlete leaves the ground, because of gravity he/she begins to fall back to earth. Therefore, the higher the hip due to either body stature or running technique, the greater the potential for a higher jump. A high center of mass means the athlete will remain airborne longer"(1995). The higher your center of mass, the higher you jump. The higher you jump, the more energy you will safely transfer into a pole.
It’s important to look at all the different stages of the polevault because most of them help create energy, which will be stored in the pole at one point or another. It should be possible, using physics, to calculate the amount of energy every stage of the vault has. That was the purpose of this experiment; to find how much energy a 13’ 140 lb. pole can store, and hopefully make a formula that shows how much energy the pole has at any one point in time. This is useful because the greater an understanding you have on polevaulting, in any area, the more helpful it is to you and the higher you will go. You can make your vault better by knowing exactly what the pole is doing and how to use the pole for you. I’m hypothesizing that the pole will contain the most energy when it is bent the most.
To try to tackle this project, I tried to think in terms of writing a formula. I figured that there had to be a formula out there somewhere that related energy and how much of it a pole could store. I went about my research primarily on the Internet and came to a very quick conclusion that such a site didn’t exist, at least not in English. So I decided that I would try to create a formula. This was challenging because the polevault is all one continuous motion; it never stops. This makes it hard, even nearly impossible, to form a formula. What I tried to do is break the vault down into the six stages and try to formulate a formula for each stage. This way I could try to combine the formulas together after I’ve come up with one for each part of the vault. Like making a puzzle.
Steps of the polevault (To Top)
If you remember before, "The actual polevault itself is comprised of about six stages; "(1) The grip, (2) the run, (3) the plant and take-off, (4) the swing, (5) the pull-up, and (6) clearing the bar"(The World Book Encyclopedia 1995).
The Grip is just where you hold the pole. It isn’t going to affect anything too much unless you hold down a pole more than a foot and a half from the top. We’ll just say we’re holding as high as we can. (To Top)
The Run: probably the most important part of building up energy for the pole. I (To Top)
Believe that this is where the most energy is made for the pole. Force is energy. So using the following formulas:
F = ma, m = w/g, a = (v-u)/t
I was able to create one formula for the run: F = (w(v-u))/(gt)
The Plant and Take-off: This is the point where Ek is transferred into the pole, being stored up as Ep. As the vaulter jumps, gravity pulls him down, but his momentum bends the pole. (To Top)
Using the formulas below;
W + Ek + Ep = W + Ek +
Ep
W = Fd cos q – keeping in mind that F is the total force and q is approximately 21°
Ek = 1/2mv2
Ep = mgh
I found that: Fd cos q + 1/2mv2 + mgh = Fd cos q + 1/2mv2 + mgh
The Swing. The swing is where the pole bends the most. (To Top)
W + Ek + Ep = W + Ek +
Ep
W = Fd cos q – keeping in mind that F is the total force, now the pole is pulling you at an average angle of about 45°
Ek = 1/2mv2
Ep = mgh
Fd cos q + 1/2mv2 + mgh = Fd cos q + 1/2mv2 + mgh
The pull-up. This is part in the vault where you begin to receive the Ek from the pole (To Top)
W + Ek + Ep = W + Ek +
Ep
W = Fd cos q – keeping in mind that F is the total force and is still about 45°
Ek = 1/2mv2
Ep = mgh
Fd cos q + 1/2mv2 + mgh = Fd cos q + 1/2mv2 + mgh
Clearing the bar: The final part of the vault. (To Top)
The last part of the vault, you push off the pole. And all energy is out of the pole into you.
W + Ek + Ep = W + Ek +
Ep
W = Fd cos q – keeping in mind that F is the total force, and knowing that q becomes 0°
Ek = 1/2mv2
Ep = mgh
Fd cos q + 1/2mv2 + mgh = Fd cos q + 1/2mv2 + mgh
Basically, I set the kinetic energy plus potential energy plus work before the action, equal to after the action. So, using the formulas and having enough of the variables, you can find out how much energy the pole is storing in each stage of the pole by solving for the potential energy. I wasn’t actually able to create a formula for any point in the vault. Actually I just used the formula, W + Ek + Ep = W + Ek + Ep, over and over again.
Using the formula, I hypothesized that the pole would have the most energy when it was bent the most. This occurs in the pole vault during the "swing" stage. So I decided to try to test out my hypothesis.
To do this, first I had to think of possible ways to bend a pole. With a little help from my physics teacher, Mr. Murray, I was able to devise and create a piece of apparatus to bend a pole.
The box; was primarily a padded wooden box with a long wooden base that had some more padding on the end. I reinforced it with a lot of wood and nails to keep the top from ripping off. I did this because my original hypothesis was that it would take three to four hundred pounds to bend the pole. I got this number by using the formula; F = ma. Now my mistakes were that I used weight instead of mass, and I used an acceleration of 2. To get the mass of 140 lb. person, I used the formula; w = mg. 140/9.8 = 14.285. I got 14.29 kg instead of 140 lb. Having the incorrect acceleration, I used the formula; v = u + at to get the correct acceleration. Knowing that the starting velocity of a polevaulter will always be 0, and that the final is around 2 m/s. I also knew that it would only take about five seconds to run down the runway. So, I ended up with an acceleration of .4 m/s/s, a much more realistic number. Then going back and using the formula F= ma, I got the force to be 5.716 kg. This seemed awfully low, but I tested it with the box.
Now an interesting thing happened when I used the box, the polevault pole bent in only one place. This place was the spot, right on the front pad. The pole did begin to bend at approximately 6 kg, but it only bent in one place, and not even that much. So I concluded that the 5.716 kg. was a sort of starting or activation force to get the pole to bend. After that the pole would stay bent, but wouldn’t bend any more. Being afraid that the pole was going to break, I stopped, and counted the box method as a failure. But not entirely, I had still made some steps towards my goals.
Next I remembered what my polevault coach, Rick Baggett, had said about testing poles and how he wanted to make a pole-bending machine. Also I remembered Mr. Murray mumbling something about a pulley. So I decided to construct a huge pulley system. It looked like below.
The pulley system is 15 ft. long track connected to an 8 ft. tall pulley system. It worked, by having a pole holder on wheels (as seen above right) connected to a light steal cable. The cable went through the pulleys and was connected to a weight. The weight pulled the cable through the pulleys, pulling the pole holder in the above picture from right to left. This caused the pole to bend outward, and I was semi-successful at bending a pole. The reason I was semi-successful was that the pole wouldn’t actually bend by itself. I thought that the more weight you put on a pole, the more it would bend, but this actually didn’t happen. I put on 44 kg. and the pole only became taught, it didn't really bend. But I grabbed the pole and pulled it, thus bending it. I tried to make measurements on the ratio between bend and weight. What I was able to do to measure these ratios, was to pull the pole out as far as it would bend, then let it go and let it settle. When it was not moving anymore, I took off 1 kg at a time, and found how much it dropped. It dropped at an average of 1.413 inches. To get that average I subtracted the second term from the first, and added that to the subtraction of the second term minus the third term etc. then divided by the total number of measurements. What I discovered was that for approximately every 11 kg, the pole would bend an approximate 18 in. So after 22 kg. the pole was bent about 36 in. or 3 ft. I was never able to bend it any more than about that much due to a weak apparatus, fear of hurting myself, money, and time. But I was able to prove my hypothesis; The more the pole bent, the more weight it could sustain and the more energy it held.
To view the raw data taken in 1 kg measurements click here To Data or on raw data.
I originally thought that the reason the poles weren’t bending was because the poles didn’t have a velocity affecting them. However, the velocity doesn’t bend a pole, it’s just what causes the pole to move. So when you plant (stick the pole in the hole in the ground; named the box), then the end of the pole (not in the box) moves in an arc. We call how fast the pole moves on this arc, the pole-speed. So, it wasn’t a lack of velocity. I had forgotten something else. I had forgotten that when you plant a pole, you plant it as high as possible. You don’t plant the pole on the ground, but about two or three feet over your head. If you don’t plant high then the pole has no way to compress and bend. This is an excellent example of why it’s imperative to have a high plant. So in order to truly bend a pull, I would need to create a new apparatus with a track that moves in an arc-like motion, where it starts at about seven to nine feet off the ground.
Other Pole Discoveries (To Top)
Another interesting discovery linked to the pole and how it stores energy is how it bends. Polevault poles don’t bend uniformly. I noticed that where the pole bent the most it had the smallest diameter, and that where the pole bent the least, it had the greatest diameter. I believe this has to due with how the pole was constructed. Because the poles are cloth wrapped and spun with fiberglass, I believe the top is thinner so when the pole bends it bends more up near the top. However, the pole not only bends but compresses. It compresses all along the pole. The most energy is stored where the pole is bent the most, and that would be where the pole compresses the most. Possibly one reason why the poles bend less near the bottom and more near the top is because there is less fiberglass near the top. On the other hand, if you’re using a Spirit pole, which is wrapped with a triangular sail piece and two rectangular sail pieces, it bends in three different focal points. This can be advantageous if you want a quick pole that releases its energy differently. I think that Spirit probably makes their poles by using a thinner amount of fiberglass on each of its sail pieces. They do this and are able to obtain, in my opinion, better overall results on the amount of energy one of their poles can contain because the fiberglass overlaps. Since the fiberglass overlaps, it creates three thin areas in the middle of the pieces where they bend. It’s interesting to use one of these poles because you can actually see the three different bend points and watch them unbend in order, giving different amounts of energy at different times. I find that Spirit poles are a lot quicker and I have an easier time receiving more energy from them. However, it all depends on the length, weight flex number of a pole, and experience you have vaulting with the pole. There are still many variables.
One form of pole construction.
Spirit pole construction.
World Book Encyclopedia
Chicago;, 1996, pg. 818 619
World Book Inc.
Santos, Jim, and Ken Shannon. Sports
Illustrated Track the Field Events.
New York: Time Incorporated, 1995
Jacoby, Ed, Bob Fraley. Complete Book of Jumps. United States:
Ed Jacoby and Bob Fraley, 1995
Douglas C. Physics Principles with Applications. New Jersey;
Douglas C Gianeoli, 1991
"USAPVA" Poles 1999
<http://www.speed-fitness.com/uspva/pobs.htm>
Conclusion (To Top)
Though my experiments might not have been complete successes, I was able to gather some data, and make some conclusions. However, not all the conclusions may be 100% accurate. My diagrams for how the poles might be constructed are only guesses. I don’t know the exact shapes of the sails. Any information or comments you would like to submit would be appreciated very much. Just email me at Bcpeterson@yahoo.com
http://www.polevault.com/ A well constructed website about polevaulting with regularly updated information. Primarily focusing on recent events.
http://www.speed-fitness.com/uspva/index.html A great web site with many ideas and drills, which show the basic motions of polevaulting. And contains many other links to other websites.
http://hometown.aol.com/polevaults/Page1.html Advantage Athletics Pole Vault: Has drills that a lot of Pole Vault Sites lack. It's a fantastic site!
http://www.vaultworld.com/tips/tips.html A great site with detailed steps on the polevault.
http://www.gloryroad.net/~vaulth/ A site full of more polevaulting links.
Last Updated May 31, 2000