On Snow & Ice

Engineers are supposed to be numbers people who thrive on logic, objectivity and data. Engineers are not supposed to appreciate subjectivity; and we’re definitely not supposed to like art. At least that’s the theory. The truth is that art isn’t always as subjective as you might think and engineers can and do like art.

Fillippo Brunelleschi is most famous for designing the dome of Florence Cathedral. It is a spectacular structure designed and built using an exceedingly novel method of construction. Both architects and engineers claim Brunelleschi as one of their own, yet his apprenticeship was served in the Arte Delle Seta, where he became a master goldsmith and sculptor. That is how it was in the Renaissance, master builders and designers learned about material and form in the artist’s studio.

One of my favourite modern artists is Andy Goldsworthy. I wouldn’t remotely consider myself an art critic nor would I claim to know what Mr Goldsworthy was thinking when he conceived a particular piece, but I am going to speculate that he has developed a keen sense of material and form through hours of trial and error in the artist’s studio.

I have made this speculation, because he succeeds in combining natural materials with shapes and forms that make complete sense from a structural perspective. He appears to understand exactly what he is doing.

Perhaps my favourite examples of Goldsworthy’s work are those which he creates from snow and ice. I like them for several reasons. The first is because snow and ice illustrate particularly well that material properties can and do vary. For example ice remains solid when cold, but melts when warm.

Just as important, but perhaps more subtle, snow can be squashed and moulded into different shapes while ice is hard and brittle. It would rather fracture than bend.

Both materials have a dislike for tension; though they express their dislike in different ways. Snow will disintegrate and crumble, while ice will crack and fracture. Conversely both snow and ice will quite happily resist compression without difficulty.

It turns out that materials, like people, have temperaments that must be understood to get the most out of them. This Goldsworthy achieves exceedingly well.

If we consider, for example, the ice sculpture shown below. It consists of eight storeys each resembling the columns and entablature of a greek temple or if you prefer the sarsens at stone henge.

 

Just like the designers of those ancient structures, Goldsworthy has realised that tension is the enemy he must subdue. By placing the ice columns close together he prevents the lintels from developing excess tension on their soffits. For a similar reason the columns have been carefully aligned so that load can travel from top to bottom in direct bearing.

Further examples of matching form to material are shown in the sculptures below. One shows an arch constructed from thin wedges of ice and the other from stone and snow. Both resemble the classical form of a traditional masonry arch. 

It is of course well known that arches are compression structures and are therefore inherently suited to materials that dislike tension. With an ample supply of stone, and a primitive form of concrete, it is unsurprising that Roman architecture features arches so prominently.

That said, it is Goldsworthy’s decision to construct his arches in the traditional way using wedges that is interesting, particularly the one made of ice. This choice allows us to get a deeper sense of how arches work.

After finding ourselves unintentionally seated on the ground, everyone has undoubtably discovered that ice is slippery. Knowing this to be true why don’t the pictured ice wedges at the crown of the arch simply slip past each other, under the action of their own self-weight, thus causing the arch to collapse? This is not a trivial question.

In 1695 the Frenchman Philippe de la Hire was the first to compose a theory of masonry arches using mathematics. He began by assuming that the wedge shaped stones (voussoirs) from which arches were formed have infinitely slippery surfaces i.e. the joints between them are frictionless. He then set about tackling the question, how heavy [and by inference how thick] should the voussoirs be to keep an arch stable?

In this most slippery of scenarios it is, by definition, impossible for forces to develop parallel to the joints between voussoirs. The weight of the arch must therefore thrust exactly perpendicular to the joints.

It can be seen from the photos above that the wedges of ice [and thus the joints between them] are vertically aligned at the crown of the arch and therefore at this point the weight of the arch must act horizontally i.e. perpendicular to the joints.

Moving away from the centre of the arch the inclination of the ice becomes steadily flatter. Since, the weight of the arch must still act perpendicular to the joints it is bent around the curve of the arch. 

This is where the problem starts to get interesting. If the arch is built on a flat base, as shown in the image above, La Hire discovered that the weight acting at its base must be infinite or the arch will be unstable, which is obviously wrong.

La Hire rightly concluded that friction must therefore be present between the voussoirs [even if they are made of ice] though it was left for others to account for it in subsequent theories. It is this frictional force that stops the wedges of ice slipping from the arch’s crown.

In some ways it would be satisfactory to end here, but we are not quite ready to finish. There is something else that turns out to be important, which we have not yet discussed. Thus far we have been taking about wedges or voussoirs and the analogy holds reasonably well in the instance of the Goldsworthy’s snow arch.

In the case of his ice arch the analogy is a little imperfect, because the shards of ice are in fact flat and not really wedge shaped al all. We would normally think of a wedge as having a fat and a thin end.

This doesn’t at all undermine what we have said thus far; all of that still holds. What is interesting is that without a fat and thin end the shards of ice are in contact on the inside of the arch, but gaps necessarily open up at the outside edge. The thicker the arch the more pronounced would be the gaps.

The significance of this is the contact area between the shards of ice is only a fraction of their surface areas. Since the ice does not fracture we may infer that the stress in the arch must be quite low and would certainly be in no danger of crushing its component parts. 

This principle was demonstrated in 1846 by Barlow at the Institution of Civil Engineers in London. He built a model arch with six voussoirs using slender prices of wood en lieu of mortar. In progressively withdrew the slips of wood in three locations to show the stability of arch would be maintained.

Taken together the thoughts we have outlined illustrate the key principles of masonry arch design. Namely, friction must be present between the stones; the strength of the stone is of little importance; and finally the stability of an arch relies entirely on its geometry and weight. Since weight is a function of geometry and friction is a function of weight we might just as easily say the stability of an arch is a function of its geometry.

I have no idea whether or not Andy Goldsworthy’s thinking has extended this far, nevertheless the question was worth addressing, because the answer surely enhances our appreciation of his art.

Now I realise in reaching this point that some may be thinking that I have, in discussing geometry and forces, undermined the original premise of this post. You might say that I have turned art into science.

I beg to differ. 

Isn’t the point of modern art it’s subjectivity? Isn’t it supposed to make us think individually about what it represents and then decide how that makes each of us feel? Well, in my subjective view this is what I think it represents. It satisfies my curiosity and that makes me feel happy.