On Gravity Glue

The importance of equilibrium

Michael Grab is an artist with a website called Gravity Glue. I think its a great title, which describes perfectly his stone balancing art work. It’s also a really good description for the concept of equilibrium, which is probably the most important principle in structural engineering. For unless there is equilibrium none of the other concepts much matter.

If you have not come across stone balancing before it is worth looking at Gravity Glue. The essential idea is to stack a pile of rocks one on top of the other without them toppling. The key is to find stones of different shapes and sizes and to join them in a way that intuitively seems unstable. There is nothing holding the stack of rocks together other than gravity acting on their weight and pushing them together; hence the term gravity glue. Finding precisely the right position and angle to stack each rock is tricky. It takes experience and patience to find the point of balance.

I don’t just like Michael Grab’s stone balancing, because of the engineering parallel, but also because the arrangements he creates are attractive in their own right. Some of this is attributable to the visual backdrops, but it is also more than that. His arrangements are clever and visually interesting. I too could balance some rocks on top of each other, but I don’t think the result would come close to what Grab achieves. He manages to surprise our innate sense of balance and to challenge our perception of what ought to be stable. I think it is these qualities, which provide the visual interest.

Equilibrium is simply the term that engineers use to describe a structure that is balanced. In order for balance to be achieved two criteria must be satisfied. Firstly, the magnitude and direction of all the forces acting on and within the structure must add up to zero i.e. for every force acting upwards there must be one of equal magnitude acting downwards. Similarly, for every force acting left there must be one of equal magnitude acting right. If this condition is not satisfied the structure will not be stable and will move in the direction of the unbalanced force. For example, if the force acting to the left is greater than that acting to the right then the structure will move to the left.

The second condition of equilibrium is that the moments resulting from the forces acting on a structure must also add up to zero. Moment is a turning action, which is the product of a force and its distance from the point of rotation. For this reason a small force acting at a large distance can generate the same moment, as a large force acting at a short distance. This abstract concept is easily illustrated by considering an adult and a child on a see-saw. To find the point of balance the adult must move closer to the fulcrum of the see-saw than the child. Conversely, if the adult sits too close to the end of the see-saw the child will be propelled upwards and the adult downwards. It follows that if the forces acting on a structure are balanced, but the moments are not, then the structure will topple in the direction of the unbalanced moment.

Applying these principles to stone balancing the forces acting on a stack of rocks are the self weights of the stones due to gravity. The first of the two equilibrium conditions is satisfied  by default. Since the stack is supported on the ground the ground will push back on the stones with an equal an opposite force. If it did not then the rocks would either sink into the ground or they would take off. The tricky bit is therefore balancing the moments.

Since the rocks are of different sizes and have unusual shapes their centre of gravity [the axis through which their weight acts] does not act through the point where the rock above is in contact with the rock below. An overturning moment is therefore generated. To balance the overturning moment the rock above must be rotated to move its centre of gravity towards the point of contact or the next rock up must be placed such that it generates a restoring moment in the other direction. As long as one of these two options are selected then the stack will be in equilibrium and will remain stable.

That said, if the weather were to turn and a strong wind were to blow then an additional external overturning moment would be generated. If this moment exceeds the effect of the stones self weight then the stones will topple. This thought introduces an interesting subtlety to the concept of equilibrium.

A structure can be in a state of equilibrium, however if that equilibrium is vulnerable to disturbance by an external action, particularly a small disturbance, then it is said to be in a state of unstable equilibrium. This is precisely the reason why stone balancing is difficult and requires such patience. The arrangements are invariably in a state of unstable equilibrium and in many cases the stability of the lower stones relies on the presence of the upper stones. I imagine that it must require octopus-like qualities to hold the lower stones in precisely the right place while the upper ones are added.

It is precisely this unstable form of equilibrium, which makes Michael Grab’s creations so visually interesting. Much like trying to stand a pencil on its end it does not seem possible to find the ‘Goldilocks point’ were there is neither too much over-turning moment in one direction nor in the other. Herein lies the patients and the skill.

Of course, while it creates an interesting work of art, unstable equilibrium is not at all desirable in buildings and bridges. It is self-evident that you want such structures to be resilient to disturbance so that they do not easily become unstable. Indeed this is a key structural design principle.

This does not stop an engineer from appreciating Michael Grab’s gravity glue. I would suggest it enhances your appreciation of his art.