Pole vaulting is an incredible sport to watch. The vaulter's technique can be so fluid and graceful -- the result of a highly studied technique designed to optimize energy conversion.
In this article, we will learn a little bit about the history of pole vaulting, and then we will explore the physics of pole vaulting.
History of Pole Vaulting
In the late 1800s, colleges started competing in the pole vault. Originally the vaulters used bamboo poles with a sharp point at the bottom. They competed on grass, planting the point in the grass (because holes were not allowed back then), vaulting over a pole and landing back on the grass. In the 1896 Olympics, the record, set with a bamboo pole, was 10 ft 6 in (about 3.2 m).
As heights started to increase because of improvements in technique and materials, mats started to be used for landing. Now the modern pole vault takes place on an all-weather track surface, with a box for planting the pole in, and plenty of padding in the landing pit. Modern poles are made of advanced composite materials like carbon fiber.
Today, the world-record pole vault is over 20 feet (6.1 meters).
The vaulting pole is a very advanced piece of equipment. It is constructed from carbon fiber and fiberglass composite materials in several layers. The pole must be able to absorb all of the vaulter's energy while bending, and then return all of that energy as it straightens out. These advanced composite materials waste very little energy when they bend, and have a good strength-to-weight ratio.
A 200-lb (90.72 kg) pole vaulter needs to put about twice as much energy into the vaulting pole as a 100-lb (45.35 kg) vaulter. But the vaulting pole has to bend about the same amount, this means that the heavier vaulter needs a stiffer vaulting pole than the lighter vaulter. So, the stiffness of the vaulting pole must be carefully tuned to match the weight of the vaulter.
Anything that helps the vaulter run faster on his approach will help him go higher. Reducing the weight of the vaulting pole is an obvious way to help the runner go faster. The carbon fiber poles used today are much lighter than the wood, bamboo or metal vaulting poles sometimes used in the past.
Physics of Pole Vaulting
If you read the article How Force, Power, Torque and Energy Work, you learned all about potential energy (PE) and kinetic energy (KE). Let's try to figure out how high a pole vaulter could vault if he had absolutely perfect technique. If he ran as fast as anyone in the world, and his vaulting motion was so perfect that he wasted no energy.
First, we'll figure out his kinetic energy when he is running at full speed, and then we'll calculate how high he could vault if he used all of that KE to increase his height and, therefore, his potential energy (PE) without wasting any of it. If he converted all of his KE to PE, then we can solve the equation by setting them equal to each other:
1/2 m v2 = m g h
Since mass is on both sides of the equation, we can eliminate this term. This makes sense because both KE and PE increase with increasing mass, so if the runner is heavier, his PE and KE both increase. So we'll eliminate the mass term and rearrange things a little to solve for h:
1/2 v2 / g = h
Let's say our pole vaulter can run as fast as anyone in the world. Right now, the world record for running 100 m is just under 10 seconds. That gives a velocity of 10 m/s. We also know that the acceleration due to gravity is 9.8 m/s2. So now we can solve for the height:
1/2 x (102 / 9.8) = 5.1 m
So 5.1 meters is the height that a pole vaulter could raise his center of mass if he converted all of his KE into PE. But his center of mass is not on the ground; it is in the middle of his body, about 3 ft (1 m) off the ground. So the best height a pole vaulter could achieve is in fact about 20 ft (6.1 m). He may be able to gain a little more height by using special techniques, like pushing off from the top of the pole, or getting a really good jump before takeoff.
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Click "Play" to watch the pole vault.
In the animation above, you can see how the pole vaulter's energy changes as he makes the vault. When he starts out, both his potential and kinetic energy are zero. As he starts to run, he increases his kinetic energy. Then, as he plants the pole and starts his vault, he trades his kinetic energy for potential energy. As the pole bends, it absorbs a lot of his kinetic energy, just like compressing a spring. He then uses the potential energy stored in the pole to raise his body over the bar. At the top of his vault, he has converted most of his kinetic energy into potential energy.
Our calculation compares pretty well with the current outdoor world record of 20 ft 1-3/4 in (6.15 m), set by Sergey Bubka in 1994.
Now that we've done this calculation, let's look at what a vaulter can do to try to break the record. They have two main ways to increase the height of his vault. One is to increase his running speed, which increases the amount of kinetic energy he can use. The other is to make more efficient use of the energy, perfecting his technique so that absolutely no energy is wasted.
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