With a steel framework of seemingly random polyhedrons covered in soft plastic pillows, the centre, known as the Water Cube and home to the swimming and diving events at the Olympics beginning this week, “really looks like nothing else in the world”, said Tristram Carfrae, the structural engineer who designed it. “It’s a box made of bubbles.”
That’s an appropriate image, for the inspiration for Carfrae’s design originated with a problem about aggregations of bubbles—in other words, foams—posed by the great British physicist William Thomson, Lord Kelvin.
Lord Kelvin studied foams to try to understand the “ether”, the medium through which he and others thought light propagated. In his work, he wondered what would be the most efficient foam—how space could be partitioned into cells of equal volume that would have the least surface area. True bubbles were not the answer, of course, because there would be gaps between the spheres. Lord Kelvin’s answer used 14-sided polyhedrons.
Ready for the plunge: An external view of the Beijing National Aquatics Center, also called the Water Cube, which will host swimming and diving events of the 2008 Olympics in China.
Lord Kelvin conjectured that his solution was the best possible one, although he offered no mathematical proof. And for more than a century, physicists and mathematicians tried without success to devise a solution using polyhedrons of less surface area.
Then in 1993, Denis Weaire and Robert Phelan, physicists at University College, Dublin, answered the problem using two polyhedrons, one of 14 sides and one of 12, that nest together in groups of eight. Their computations showed that it had about 0.3% less surface area than Lord Kelvin’s solution—the physicist’s equivalent of beating him by a mile.
It is this Weaire-Phelan structure that Carfrae used as the basis for the Water Cube. But it is not as if Carfrae had dabbled in foam physics and had been aware of the Kelvin problem.
“I knew nothing of this area at all,” confessed Carfrae, a principal with the firm Arup. “But from an architectural perspective we were very keen to end up with a building that had some connection with water.” So, in the course of researching waves, icebergs, mists and the like, he came across foams and, ultimately, Weaire and Phelan’s work.
“It was not like anything I’d seen before in the world of structural engineering,” Carfrae said. There was no guarantee that it would make a good structure for a building, though, so it took much computer analysis to determine how it would work. And it took the labour-intensive Chinese construction industry to fabricate the structure from more than 22,000 steel beams.
Cut through the froth
And the Weaire-Phelan solution is doing just fine in Carfrae’s building. It turns out that the structure is very flexible and thus efficient at absorbing seismic energy, which is good given China’s history of earthquakes. Carfrae’s major modification was to use a diagonal section through the Weaire-Phelan structure, as if cutting through a block of foam at a 60-degree angle, rather than adopting the structure straight on. It is that decision that most impressed Weaire, now an emeritus professor at the university. “That’s what gives it its random appearance,” he said. “Only if you look carefully do you see that it’s a repeating pattern.”
Inside the cube.
“That was just the masterstroke,” he added. “I’d love to think that I suggested that to him, but he did that entirely on his own.”
©2008/ The New York Times
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Cluster of coincidence
Just as Carfrae was not specifically looking for the Weaire-Phelan structure when he found it, Weaire and Phelan were not looking to solve the Kelvin problem when they did, said Weaire. Rather, they were “playing around on the fringes” of the problem, looking at alternative structures as part of what for Weaire was a career-long investigation into the science of foams.
In their work they were aware of clathrates, naturally occurring cage-like clusters of atoms that trap other atoms within them. So, using what was then new software developed by Kenneth A. Brakke at Susquehanna University, they decided to evaluate clathrate structures in relation to the Lord Kelvin problem, Weaire said. They were stunned to discover that one particular structure, when translated into polyhedrons and run through the software, had lower surface area than Lord Kelvin’s solution. “It was a bit like a hole in one in golf,” Weaire said. “From a crystallographer’s point of view this structure wasn’t new,” he added. But using it to beat Kelvin’s solution was.
©2008/The New York Times