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 edition of How Stuff
Works 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 The pole vault originated in Europe,
where men used the pole to cross canals filled with water. The
goal of this type of vaulting was distance rather than height.

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. The world record today is over 20 feet!

Vaulting Pole 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 v^{2} = 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 v^{2} / 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/s^{2}. So now we can solve for the
height:

1/2 x (10^{2} / 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.

Figure 1. Animation of
pole vault

In Figure 1, 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.