This will be the fifth and last installment in my "connections" series, because, frankly, I have run out of ideas after this.
If you haven't followed the series thus far, here are the links to my first Mathematics, Biology, and Philosophy peices, as well as a special on the draft.
Mathematics can be linked directly to wrestling, like I have shown before, as not only are there mechanical connections within wrestling itself, but other processes within the business are also heavily influenced by mathematics.
In this article, I will aim to consider and solve two frequently discussed issues within pro wresting and the WWE.
Landing in the middle of the ring
The mathematics behind this section is pretty sound, and although a bypass of the meaning of the key equation is omitted in the middle, it is a fairly accurate proof of my statement.
It is known by many in the wrestling world that the middle of the ring is the best place to land, but why?
The first concept that needs to be addressed in understanding this problem is how a wrestling ring works in general.
The way that a fall is “cushioned” is to increase the time that an opposing force is applied to a wrestler’s body. A given momentum has to be stopped by applying a specific total force, so if you apply it over a longer time the force at any given moment can be reduced.
Consider how a bungee rope works. If you were to jump off a bridge with a bungee cord attached you would begin to feel the rope pull at you from only a few seconds into the jump, right up until the moment you stopped.
No harm would be done as a small force would be applied over a long period of time.
Whereas if you had no ropes attached you would hit the ground. The same force could be applied by the ground to stop you, but it would all occur within a fraction of a second.
A large force would be applied to the body, and it is easy to imagine what the result would be.
So with that concept in mind, why does the middle of the ring provide a better cushion than the edge?
One mechanism that applies aptly in this instance is the workings of a spring.
A spring applies an opposing force on an object proportional to the distance of the displacement from its equilibrium position, and to an individual spring constant.
In vector form F = - k X (where underlining indicates a vector, F is the opposing force, k is the spring constant, and X is the displacement on the mat by the wrestler).
In this instance the spring constant in any given wrestling ring should be roughly equal across the entire mat.
As wrestlers only really apply force downwards when falling, I will be considering only the upward force produced by the mat.
This equation may look confusing, but all it is basically saying is that the bigger the force you apply to the mat, the harder it will push back.
The question I want to solve, using this equation, is while considering a specific displacement to the mat, where in the ring will the least force be felt?
The area that provides the smallest force for a given displacement will be also be the area that will allow the most time in contact with the mat. From my explanation above, this will be the best place to land in the ring.
I will consider movements of a distance “x” away from the centre of the ring for a given displacement downwards “a”, and try to determine if this increases or decreases the overall force applied.
After many hours spent doing calculations, re-ordering equations, and re-examining the problem several times, I came up with a solution.
Using the equation for a spring above, and some use of trigonometry, this is the formula I derived for the force experienced for a given displacement:
F=-k(((√((10+x)^2)-a^2)-(10+x))sin(arctan(a/(10+x)))+ ((√((10-x)^2)-a^2)-(10-x))sin(arctan(a/(10-x))))
This equation is quite complex, and I don’t expect anyone to have an idea what it means, but I can show you graphically what happens.
The picture for my article shows how the force varies with x. The horizontal axis represents position away from the centre, and the vertical axis shows the force experienced.
If you find it difficult to see what is happening in the picture, then follow the instructions at the end of the article.
You can see that the force is minimal at 0, i.e. the centre of the ring, and the further out you get the higher it becomes.
The areas close to the centre provide roughly the same the centre itself, so landing close to the middle is relatively safe too.
It is only when you approach the edge of the ring that the force applied back to your body becomes larger, as you can see from the graph.
I hope the way in which I have shown this was understandable, regardless of the complexity of the equation. It was hard to go about due to the nature of the mathematics, but I hope you can all see the implications.
Although some assumptions have been made, this strictly proves that the best place for a wrestler to land is the middle of the ring.
40 Comments
Loading more comments...
This comment and all replies have been deleted This comment has been deleted Undo delete