The Iron Cross – or: Why is Gymnastics so Darn Difficult?

I know the olympics are basically over. Really, I should have posted this earlier. Anyway, the gymnastics feat that always impresses me is the Iron Cross (I think that is what it is called). I know you have seen this, but here is a picture from wikipedia:

![Example 2ofironcross](http://blog.dotphys.net/wp-content/uploads/2008/08/example-2ofironcross.jpg)

(http://en.wikipedia.org/wiki/Rings_(gymnastics))

Why is this so impressive? Why is this so difficult? Let me start with something completely different that is exactly the same (in some ways).


Here is a heavy box hung from a rope that has horizontal attachment points. (assume the mass of the rope is negligible compared to the box)
![Hanging box](http://blog.dotphys.net/wp-content/uploads/2008/08/hanging-box.jpg)

Now, let me draw a free body diagram for the box. (A free body diagram is a graphical representation of the forces as vectors on the object)
![free body 1](http://blog.dotphys.net/wp-content/uploads/2008/08/free-body-1.jpg)

Since the box is in equilibrium, all the forces should add up to zero (because of Newton’s second law). When dealing with vectors graphically, I can move them around as long as I keep the direction and length the same. To add vectors, place them tip to tail like so:

![free body 2](http://blog.dotphys.net/wp-content/uploads/2008/08/free-body-2.jpg)
Notice that the result of these three vectors is indeed the zero vector (they form a triangle). Great. What if I increase the tension in the rope? The one thing that doesn’t change is the length of the weight vector. The lengths of the tension vectors must be longer – but they must STILL add up to zero. What if I JUST increase the length of the two tension vectors?

![free body 2](http://blog.dotphys.net/wp-content/uploads/2008/08/free-body-21.jpg)
Notice that they don’t add up to the zero vector. But if I change the angles, I can make it work:

![free body 3](http://blog.dotphys.net/wp-content/uploads/2008/08/free-body-3.jpg)
But now the angle of the forces changed. Ropes and cables have this weird property in that they can only pull in the direction of the rope. This means the rope would look like this:

![hanging box 2](http://blog.dotphys.net/wp-content/uploads/2008/08/hanging-box-2.jpg)
Maybe you can start to see my point, but maybe not. Is it possible to have the tension high enough so that the cable is completely horizontal? The answer is “no”. Here is one last example of that with the tension at “super-high” level.

![free body 4](http://blog.dotphys.net/wp-content/uploads/2008/08/free-body-4.jpg)
So, no matter what the tension, the forces will STILL have to have some vertical component to compensate for the weight of the box. The more horizontal you want the rope to be, the greater the tension you would need in the rope.

So, what does this have to do with the iron cross? Pretend like the box above is the body of the gymnast and the ropes are the arms. If you want to have your arms nearly horizontal, there needs to be very high forces involved. Also note that most gymnasts look something like this:

![gymnast 1](http://blog.dotphys.net/wp-content/uploads/2008/08/gymnast-1.jpg) where the forces are pushing up rather that hanging – but the same idea applies.

But WAIT! I said that you could never be horizontal and you are sure you saw a chinese gymnast in what appeared to be a horizontal iron cross. Well, this is because the arm is not a single rope, but there are several “attachment points” for the arm. (it’s complicated). Either way, hopefully you will see that this is a difficult feat and one that I will likely never accomplish.

2 thoughts on “The Iron Cross – or: Why is Gymnastics so Darn Difficult?

  1. He’s got the mechanics of the human body all wrong. The gymnast isn’t supported like that by pulling along the length of his arms, but by pulling the arm down with his lats. These run from near the end of the upper arm to the spine. Since they attach so close to the shoulder, they don’t have much leverage.

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