JOHN OCHSENDORF remembers the first time he stood on top of the domed vault of the chapel at King鈥檚 College, Cambridge. 鈥淵ou鈥檙e standing 80 feet off the ground on a thin piece of stone,鈥� he recalls. 鈥淵ou can even feel small vibrations. And you can鈥檛 help thinking, 鈥楾he nerve of these people!'鈥�
Ochsendorf is a structural engineer at the Massachusetts Institute of Technology and a historian of architecture and construction, and 鈥渢hese people鈥� are the long-dead members of England鈥檚 masonry guilds who built the chapel roof around 1510. It is not hard to see why he is so impressed with their engineering skills. The chapel鈥檚 roof spans nearly 15 metres, yet it is only 10 centimetres thick, which is similar to an eggshell in terms of its radius to thickness ratio.
Along with his graduate student Axel Kilian, Ochsendorf is adapting a computer graphics tool to help unlock the elusive secrets behind the arches and domes of Gothic cathedrals. Eventually he hopes to provide designers with a technique that could lead to revolutionary architectural designs and environmentally friendly buildings.
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Today we build almost exclusively with steel and reinforced concrete, materials that are good at withstanding the forces of both tension and compression. However, many modern buildings have a severe impact on the environment. Steel corrodes with time and the manufacture of concrete produces huge quantities of greenhouse gases.
Five centuries ago, Gothic builders had to figure out how to turn stones into stable structures held together only by the forces of compression, like a stack of children鈥檚 building blocks. This is how the stone tiles on the vault of King鈥檚 College chapel are held in place.
The oldest cathedrals have stood for a thousand years, so medieval masons clearly knew a thing or two about stability. 鈥淭hese people developed a very real science of construction to attain a high degree of stability,鈥� says Ochsendorf. 鈥淚鈥檓 simply in awe of the fact that we haven鈥檛 surpassed it yet.鈥�
Much of that secret knowledge has been lost, but there are clues. Architects and engineers have long known that a chain suspended from two points will always come to rest in a state of pure tension: tension is the only force between consecutive links, and that force inevitably acts parallel to the chain at every point along it. Inverting the resulting shape 鈥� called a catenary, from catenarius, the Latin word for chain 鈥� into an arch reverses it into one of pure compression. Masonry and concrete break relatively easily under tension but can withstand huge compressive forces. The inverted catenary shape can therefore be used to form structures like domes or arches that span a considerable horizontal distance. The 17th-century English scientist Robert Hooke phrased it best: 鈥淎s hangs the flexible chain, so but inverted will stand the rigid arch.鈥�
Architects have devised all manner of methods for discovering the best possible structural forms. A century ago, the Spanish architect Antoni Gaud铆 devised a 鈥渉anging model鈥� to calculate the loads on the arches he incorporated into his building designs. It was an elaborate system of threads, representing the columns, arches, walls and vaults of any given design, from which he suspended sachets filled with lead shot to mimic the weight of building components. He used this method to design a chapel for the Col貌nia G眉ell neighbourhood on the outskirts of Barcelona.
Contemporary Swiss architect Heinz Isler creates what he calls reversed 鈥渉anging membranes鈥� to design the delicate, thin-shelled dome structures for which he is famous. After pouring liquid plastic onto a cloth resting on a flat, solid surface, he lowers the surface, leaving the plastic-covered cloth to hang in pure tension, suspended from its corners. The plastic hardens, freezing that position. Once it has dried, Isler turns the solid shell model upside down, and that form becomes the basis for his design.
Ochsendorf鈥檚 method works in much the same way, but it does so virtually. It is based on a computer graphics technique called particle spring modelling, in which virtual masses at the various 鈥渘odes鈥� of a design are connected by virtual springs. These bounce around until they find equilibrium and are able to support the requisite loads, just like Gaud铆鈥檚 hanging chain. CGI (computer-generated imagery) animation already uses such particle spring models to recreate the movement of fabrics and hair.
Ochsendorf and Kilian realised that there were parallels between the fabrics that CGI animators model and Isler鈥檚 hanging membrane. A length of cloth is strong under tension, but if you push on it, it simply crumples. What Ochsendorf needed was something with precisely opposite properties, so he worked out a way to turn the fabric model round. This allowed him to model architectural structures, specifically, Gothic cathedrals.
When it comes to analysing arches, Ochsendorf鈥檚 prototype program has already scored some successes. He used it to demonstrate that the domes of the new Pines Calyx conference centre near Dover on the south coast of England, would stay in compression under all possible loadings, thereby satisfying stringent safety regulations. Due to open next month, the centre is topped by domes made from clay tiles glued together edge to edge. The domes span 15 metres, yet the tiles are only 15 centimetres thick, and required no supporting framework during construction.
鈥淲ithout Ochsendorf鈥檚 program these remarkable thin-shelled shallow domes would not have been allowed to be built,鈥� says Alistair Gould, a member of Helionix Designs, the firm based in Kent that designed the building. Ochsendorf鈥檚 team also helped to design domes built from tiles for a new visitors鈥� centre at Mapungubwe National Park in South Africa, in conjunction with architect Peter Rich, a principal partner of Lerotholi Rich Associates. Both buildings are designed to last and use local materials rather than polluting concrete.
In Dover, for instance, clay dug from local hillsides is used to form the walls, and the tiles are made from waste clay. Everything comes from within 8 kilometres of the site.
The environmental rewards could be even greater when Ochsendorf has refined his computer software. Already it has shown that certain buildings could have been built with much less material. Take for example MIT鈥檚 Kresge Auditorium, designed by Eero Saarinen in 1955. It has a domed roof made of concrete 15 centimetres thick. After analysing the geometry of the dome and feeding the measurements into his hanging chain model, Ochsendorf reckons that it could have been built with half the thickness of concrete.
Similarly, MIT鈥檚 new computer science building, designed by Frank Gehry, features columns leaning in every direction. The structure uses roughly 30 per cent more material than would have been needed if the program had been used to find where the lines of force naturally fall, Ochsendorf says.
The master builders of old may be long dead, yet they are still teaching us a thing or two about architecture from beyond the grave.
