Pole Stiffness and Angle of Attack
Technique, pole composition, and pole stiffness have all improved over the years. Each factor helped to increase the greatest height a vaulter can clear. This got to the point where vaulters were able to double the height jumped over the sports lifetime; Sergey Bubka of Ukraine is the current world-record holder with a jump of 6.1 m, or about 20 ft (The record height before fiber poles was a mere 10.5 ft.). Vaulters now use either carbon-fiber or fiberglass poles, which allow for extreme bending (up to 110º) without any irreversible physical consequences. (It is polite to not step on poles with spikes/shoes, as it causes scratches or cracks in the pole — greatly increasing the likelihood of a pole break.) In the past, vaulters used either stiff bamboo or aluminum poles.
This advancement changed the entire dynamic of the sport. Vaulters were now able to run at maximum speeds into the box and experience smaller impulse forces due to the stiffness of the pole as the end of the pole is fixed into the box. An easy way to spot a pole that is too stiff for a vaulter’s strength/momentum, is whether the vaulter’s arms collapse on the take-off.
Poles are rated by the greatest mass of the vaulter allowed while holding a few inches from the top, with stiffer poles (for heavier vaulters) having larger radii and fiber thicknesses. If a vaulter chooses a pole that is too stiff for their given momentum, hand placement, and/or take-off angle, the vaulter will essentially be “denied” at their attempt. The .gif shown below is a good example of this “denial”:
As you can see, the vaulter is holding the pole at a position about 1 foot from the top of the pole and does not extend his arms straight up as he takes off. Holding lower on the pole essentially shortens it, and thus, without changing any other characteristics, the pole’s stiffness will increase. Extending your arms during the take-off increases the angle of attack, or take-off angle, of the pole by increasing the sine value. This not only decreases the initial resistance of the pole acting on the vaulter in the x-direction, it increases the take-off height. This is also explains why taller vaulters have an advantage.
Another pole vaulter is able to explain this a bit better than I:
Thus, poles have the capacity to bend and act just like a spring. Poles are built with a variety of resistances depending on the amount of fiberglass in the pole, and thus each pole can withstand a certain amount of force applied to them depending on their rating. If you are a vaulter, this is not new to you. You are aware that all poles have a “weight” ascribed to them. However, from a physics stand point, this assigned weight is more or less arbitrary. Remember: we are concerned with FORCE, which is a function of MASS and ACCELERATION. However, pole vault manufacturers do not put a force rating on a pole because normal human beings don’t think in terms of force. Rather, we think about the two variables that result in force, namely how much you weigh (mass) and how fast you run (without getting too technical, your speed, or velocity, is factored in to get acceleration which is the change in velocity over time). Since the variation in the speed of vaulters is less than the variation in the weight of vaulters, it is reasonable that poles are rated by weight. You should therefore pay close attention to the weight marked on a pole. You should use that mark as a starting point to figure out what pole to start with. But since you are all physics wizzes, you all know that speed is an equally important variable. Assuming your weight does not change much, then as you run faster and faster, you will continue to produce a greater force at the plant, imparting a greater load on the pole. The solution is then to use a pole with a greater weight rating. The result, since your weight does not change in flight, is that you will be whipped off the top of the pole with a greater force. Think about it in terms of a spring. The stronger the spring, the more force is required to load it, but at the same time, that stronger spring will throw a light object with greater force, provided that the lighter object (that would be you, the vaulter) is capable of loading the stiffer spring. Thus, as you get better, you will actually start using poles that are rated higher than your weight. For comparison, when I was in the prime of my vaulting career, I weighed 124 lbs, but the pole I used was rated at 155lbs, 31lbs over my weight! The only way I could achieve this was to produce the same amount of force at the plant as an average 155lb vaulter would on the same pole. Remember f = ma? I achieved this by running faster.
-Kimo Morris http://pukashell.net/kimo/polevault/physics.html
If a vaulter comes in with too much momentum for the stiffness of the pole, the amount of resistance that the pole can exert on the vaulter will not be enough to convert all of their kinetic energy into potential energy. In this extreme case, the vaulter will bend the pole past the 110º cut-off (for most poles) and break the pole at its weakest point(s). These points will be the ones experiencing the most torque will deform, and thus bend the most. So, assuming there are no inconsistencies in the structure of the pole along its length, the pole should break halfway between the fixed end of the pole and the average force (due to vaulter) position. In addition, poles are not completely straight. When you hold up one end of the pole off the ground, it has an equilibrium position in which the heaviest part of the pole (the longer side – as you’ll see) is on the underside. If you look at it from the side, it should look like it is a not-completely-taught rope slung over the shoulder of the vaulter. When the vaulter adjusts their hand position, they must arrange their hands so that the longer side of the pole (bottom of saggy-rope) will face away from the vaulter as they take-off. This allows for an orientation where the pole will be able to bend with a smaller resistive force. If the pole was rotated 180º about its longitudinal axis, the opposite would be true. The fiber will not bend properly, and the amount of force generated by the vaulter required to break the pole diminishes. An example of a case where the pole undergoes these excessive torque forces is shown below:
Here are two diagrams that explain two variables of the jump: