The Complex Physics of Olympic Pole-Vaulting

The level of athleticism and skill required for a successful vault is overwhelming. Pole-vaulting, a Track and Field event, was introduced to the Olympics in 1896 (The Physics of Pole Vaulting, 2009). The goal of this event is to get over a bar that is set at a certain height using a vaulting pole for a boost. The athlete has three attempts to get over each height; once they have failed the three attempts, they are out of the competition. Athletes that are able to get over the height within the three attempts move on to the next height, which usually increase by 3 to 6 inch increments. Although the vaulting pole is crucial in pole-vaulting, there is more to it then that, all of which play a huge role in how high you get.

When pole-vaulting

was first invented, people used poles made out of steel or bamboo; these are called rigid poles. Because these poles were not flexible, the energy that goes into the plant does not transfer and is essentially lost. This makes it very difficult for the vaulter to move into a vertical position (upward motion), and prevents them from reaching heights higher then the pole itself (McCormick, 2015). Poles are not made up of fibreglass and carbonfibre. While energy is more easily lost during the plant and jump in rigid poles, the flexible poles are able to minimize the amount lost. Theses poles are very similar to a spring and can bend over 120 degrees without breaking (Linthorn, 2000). Although, when bent past the 120 degree angle, it is more likely that the force during its spring back into natural length will not be as great because of its elastic limit (Bloomfield, 1997). Other advantages of the poles used today include the angle during the plant is smaller and the height at which you grip your hands on the pole are higher then the rigid poles, which all helps increase the height of your vault (Linthorn, 2000).
Because the poles closely resemble a “one-dimensional” spring (Linthorn, 2000), they also can only endure so much force before it breaks. Each pole has a rating, which are based off of weights instead of force. The larger the weight, the stiffer the pole (Morris, 2008). Based on Hooker’s Law, the stiffer the pole is, the more force needs to be implemented on the pole, but the harder the pole will snap back into its original shape (Bloomfield, 1997), which in turn sends the vaulter up higher. In other words, the stiffer the pole, the more force needed exerted onto the pole, and the larger the deflection will be on the vaulter; also meaning that the energy loss will be greater (Linthorn, 2000).
A crucial part of pole-vaulting high is being able to run fast. When on the runway, the vaulter holds the pole in position so that the dominate hand is holding the pole near the hips while the other hand is holding the pole in front of the body, so that the elbow is at a 90 degree angle. When running down the runway, the vaulter increases the kinetic energy; the faster you can run, the more kinetic energy you will have and the higher you will go (Nice, 2015)). As Nicholas P. Linthorne says in his article Energy Loss in the Pole Vault Take-off and the Advantage of the Flexible Pole, to reach your full height potential, running at full speed right before the plant will increase the kinetic energy. This is because your peak height is mostly determined on your speed right before your plant. Therefore, you need to obtain as much kinetic energy as you can right before the plant, which is transferred into the pole and converted into potential energy (Linthron, 2000; Nice, 2015). Poles used today weigh less then the rigid poles and therefore help the vaulter run a little faster (Nice, 2015). How fast you run also depends on the altitude, or air resistance. The higher the altitude is the less dense the air is which reduces air resistance, making it easier for the vaulter to run faster on the runway (The Physics of Pole Vaulting, 2009). Height also factors in on how fast the vaulter needs to go. A shorter vaulter will have a smaller angle between the pole and end of the box during the plant and will be farther away from the box. The taller vaulter who is holding the pole at the same height is the complete opposite: larger angle but closer to the box. This means that the shorter vaulter will have to run faster in order to posses more kinetic energy in order to increase their center of mass before planting. An easier way to look at this is if you are farther away from the box during your plant, you will have a farther distance to travel during your vault, and therefor will need more energy (Morris, 2008).
During the sprint down the runway the pole is at an equilibrium position.

Once we plant by pushing the pole to the back of the box in the ground, the pole begins to bend, and like a spring will eventually return to its normal shape. During this period of time, the pole is in a stable equilibrium (Bloomfield, 1997). Right before the vaulter plants, they should be going in a forward and upward motion (Linthorn, 2000). During the plant, the pole begins to bend as you are putting force on it and absorbs the kinetic energy that is transferred from the vaulter. Like a spring though, the kinetic energy that was absorbed is transferred into elastic potential energy. The pole is bent because of the energy, force, and momentum from the vaulter. Once the pole hits the end of the box, there will be some energy lost. In order to minimize as much energy loss as possible, you would have to perfect the planting technique (The Physics of Pole Vaulting, 2009). This is a hard mission to accomplish, for most of the energy is lost in the plant is determined on the angle of your arms and position of your body (Linthorn, 2000). For instance, when you plant the pole and your arms are flimsy or bent with the planter foot pointing to an angle other than straight in front,, your body will move in that direction and you risk hitting the crossbars that hold the bar up. In order to lose less energy and control where your body goes, the vaulters arms need to be strong and straight while pushing on the pole as you jump in the air during the plant. Your body and planter foot also need to be pointing straight ahead, pointing at the pole. Although, at some point the force the pole has on the vaulter will be to strong and the arms and torso will push back; this helps the vaulter then pull on the pole as they try to rotate into an upside down position (Linthorn,

2000).
Right after the vaulter plants the pole into the box, the potential energy that was transferred and stored in the pole is needed (Nice, 2015) for when the vautler rotates his shoulders to the vertical position (Linthorn, 2000). While in the air at the peak of the vault, horizontal velocity is needed in order to get over the bar. This velocity comes from the kinetic energy that is being transferred from the pole back to the vaulter (The Physics of Pole Vaulting, 2009). In other words, at the peak of the vault, the pole has already sprang back into its natural shape (Nice, 2015), transferring the energy from the pole back into the vautler; kinetic energy. If the vaulter was unable to put enough force into the pole to bend it, the force the pole would have on the vaulter would not be as high, making it harder for the vaulter to rotate the shoulders and body into a vertical position (Linthorn, 2000).
Pole-vaulting, although fun, is a very complicated sport to master, but knowing the physics behind it is a good start. It’s important to understand just how crucial the run right before the plant is: possessing as much kinetic energy as possible in the run makes it much easier when it is transferred to the pole, wich is then used as gravitational potential energy during the vault (Linthorn, 2000). The kinetic energy in the run also determines how high you can grip on the pole. The higher you grip, the longer the vaulter has to rotate into an upside down position (Morris, 2008). This is why the higher grip has become the main advantage to the new flexible poles (Linthorn, 2000). At the peak of the vault, after rotation, the hips are bent, making the vaulter in the shape of a “V”. Bending the hips, so that they are higher then the bar causes the center of mass to be right under the bar, while you are above it (The Physics of Pole Vaulting, 2009). In the end, the vault would not be possible without the right pole, fast run, perfect plant, and the energy that goes into it all.