Acrobatic skills as engineering structures – study

Acrobatic skills as engineering structures – study

Acrobatic gymnastics is a sport that I formerly took part in, and now coach. The idea is that gymnasts compete in groups of two, three or four, in a routine consisting of individual, dance and – most iconicly – partner skills.

Partner skills, in general, are split into two groups: static (balance) skills, and dynamic (moving) skills. Interestingly, both can be looked at from an engineering perspective – and human bodies are a particularly versatile structural ‘material’, since tension, compression and shape can be cleverly controlled through knowledge and practice.

To investigate further, I want to combine engineering and gymnastics knowledge to investigate the limitations of some specific acrobatic skills. I’ve noticed that typical skills are used time and time again – there is of course variation, but it often comes down to the same basic shapes and skills – rarely does someone just ‘invent’ something entirely new.

Skill Study 1: ‘Teepee’

  • Number of gymnasts involved: 3 (a women’s group)
  • Type of skill: static
  • Description: Two gymnasts (the bases) form a handstand triangle, facing each other, with one base’s feet resting on top of the other’s. The top is balancing on her hands on the feet of one base, in an optional position – here I’ve sketched a straddle hold, but sometimes a handstand, ‘Mexican’ or a combination of skills will be used.
  • Diagram:

Q: What is the minimum coefficient of friction between the ground and bases’ hands for the structure to be stable?

To answer the question, there are a number of assumptions to be made:

  • Both bases are the same height and weight. Here, I will take the height as 1.65m and weight (W) as 60.g (mass = 60kg).
  • The top’s weight (w) is 40.g (mass = 40kg)
  • The centre of mass of each base occurs at 1/3 of their height from the fingertips.
  • The whole position forms an equilateral triangle
  • The structure is in equilibrium

Simplified base position – ie an equilateral triangle with sides of length 1.65m.

A diagram of the forces acting on Base 1: namely the weight of the top, the push from Base 2, her own weight, the normal reaction and friction with the floor.

Trigonometry shows the push from Base 2 (P) can be divided into vertical and horizontal components (see right diagram).

If we put all the vertical and horizontal forces on Base 1 into one diagram, we can see that, since she is in equilibrium, they must equal zero. Therefore:

R + root3/2 (P) = W + w [Eq A]

F = P/2, so 2F = P [Eq B]

Now, taking moments about the feet, at X (so that the force of Base 2 and the top can be ignored):

1.1(Wcos60) + 1.65(Fsin60) = Rcos60

So 0.55W + root3/2(1.65)F = R/2 [Eq C]

Now for some rearranging. If we substitute equation B into A, we get:

R = 100g – root3(F)

Then, equation C becomes:

F (33.root3/40 + root3/2) = 17.g

Making F, the frictional force = 72.7 N

Lastly, this F value is the minimum frictional force – it assumes the base is on the point of sliding.

72.7 < μR, and we know that R = 100g – root3.F from previous notes.

Finally, we obtain μ > 0.085 as the minimum coefficient of friction for a base at 60 degrees in the assumed situation.

That is quite a small value!! I think it is a good show of the advantages of a triangular (truss) structure in both acrobatics engineering, and why they can be quite so sturdy.

Skill Study 2: the rig

The rig is a type of mechanical harness used by tops during training. It is used to learn somersaulting (dynamic) skills and consists of a harness and ropes on either side that reach to the ceiling in a triangle. They lead back down on one side, where a coach pulls on the ropes at the appropriate time to control the height and speed of the gymnast.

  • Number of gymnasts involved: 1 harnessed, plus 1-2 bases on ground
  • Type of skill: dynamic
  • Description: A jumping movement straight into the air, that usually leads to a somersault.
  • Diagram: