On Gothic Cathedrals

How tracery works

When it comes to gothic cathedrals most people tend to think of flying buttresses. There is of course no doubt that flying buttresses were a tremendous invention and are indeed an important part of gothic architecture.

Nevertheless, while flying buttresses are rather clever devices that provide a clear load-path, the thing that always leaves me astonished is how gothic tracery works. Even when you know its secret the slenderness of gothic tracery still appears to defy the laws of physics. Perhaps, one of the best examples is to be found at Gloucester Cathedral.

The stained glass window at the end of the Chancel is reported to be the size of a tennis court, and it fills almost the entire gable. The stonework seems impossibly thin, how on earth do the mullions manage to span from floor to roof? 

Before we answer that question we are first going to take a diversion into my childhood. Every year, after Christmas, one of the things that we liked to do as a family was settle down in from of the television to watch the World’s Strongest Man competition, which back then was televised on the BBC. We would cheer on Geoff Capes, who won the competition on several occasions, and was always in with a chance.

One of the delights of the competition, which has been lost in its modern incarnation, was the nature of the games in which the competitors were required to compete. While truck pulling and car lifting has been retained, but back then there was arm wrestling, bending iron bars behind the neck, balancing weights on your head and other such fun. Another of the lost games was brick lifting. If you have never seen brick lifting before its not as straightforward as it sounds. The bricks are laid out horizontally on table and are lifted by stretching out the arms and grabbing the stack at either end. It is self evident that simply holding the two end bricks and lifting would not work. There is nothing joining the bricks together and therefore gravity will keep them firmly planted on the table. To lift the bricks it is first necessary to apply axial pressure to the stack in order to generate friction between the bricks. The magnitude of the frictional force must exceed the force of gravity in order that the strongman can lift the stack without the bricks falling out. 

It is also important to maintain the axial force directly through the centre of the bricks to prevent an unstable hinge from forming. This is harder to do than it might seem because while the arms are clamping they are also required to be lifting. You can see in the image below Geoff Capes’ right arm has moved slightly forward and a hinge has already started to form. It will not be long before the bricks experience a rapid increase in their entropy!

 This may have seemed like an odd digression from gothic cathedrals, however it is nonetheless a relevant digression, because it illustrates the principle of prestress that is at work in window tracery. In the case of brick lifting the prestress, which is applied to the bricks before they can be lifted, is provided by the strongman. It is a far greater test of his strength than the actual weight of the bricks themselves. For as long as he maintains compressive force in the stack of bricks it will continue to bridge between his two hands. Since the dominant behaviour is compression the load-path he has created is actually that of a flat arch.

We can apply the same principle to window tracery by turning the problem on its side. But before we do this let us considered the case without prestress. If we imagine the stone mullions as a tall stacks of bricks spanning between the floor and roof it would be rather easy for the wind to simple blow them over. The reason for this is because masonry can resist compression, but not tension. When the wind blows on the window load is transferred from the glass into the stone. The stone begins to bend causing it to take up a curved profile. The windward side of the curve is squashed and is therefore in compression, while the leeward side is stretched and is in tension. Of course masonry cannot resist tension and therefore the masonry fails. 

It follows that the purpose of compressive prestress in window tracery is to overcome the tensile forces that wish to cause bending in the stonework. Providing the compressive stress in the mullions exceed the tensile stresses generated by the wind they will remain stable and can arch from top to bottom. The obvious next question is where the prestress comes from? 

The answer is both simple and clever. Medieval masons simply built some rather heavy masonry above tracery windows demonstrating that they understood exactly what the load-path was. In the example above at Gloucester Cathedral the head of the primary mullions have cleverly been bent to the form of pointed arches and are actually supporting part of the roof, as well as masonry above.

This load path does of course have an important implication that is not necessarily evident straight away. Arches produce lateral thrusts, which must be resisted or they will collapse.

In the example above there is one large arch, which spans the chancel and two subordinate arches that fall within the larger arch. It is also possible to divide the larger arch into three parts; a central arch bridging the two internal mullions with buttresses either side, which transfer load into the two outer mullions. In reality the complete load-path is a combination of the two descriptions and it ensures that there is sufficient compressive load in each mullion.

If we begin with the two subordinate arches it is clear that the thrusts, which push towards the middle of the window are balanced against each other. It is no accident that the heaviest transom in the window extends from the base of each arch and joins them together.

It is also not an accident that the outward thrust from the large arch and the subordinate arches occur in the same place, though the method of resistance is not obvious from inside the chancel.

The key is of course the use of heavy buttresses on the outside of the chancel and that brings us back nicely to where we started, the humble buttress and its more elaborate cousin the flying buttress, which we will tackle in a different post.

Notwithstanding all of the above the ability of gothic tracery to resist all that nature can throw at it still amazes me!