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The
But of
course, those bubbles hardly skittered there of their own free will. Creating
this frothy confection took a lot of steel, a lot of manpower, and not least, a
lot of fancy mathematics.
The
motivating idea for the building was that it would express the spirit of water.
Its designers first thought of liquid water, vapor, or ice, but finally settled
on foam. The bubbles, they decided, really would be bubbles: pillows made of a
transparent plastic called ethylene tetrafluoroethylene (or ETFE ) filled with
air, attached to a steel framework outlining the edge of each bubble.
A basic
challenge was that they wanted the foam to look random and organic. But for the
engineering to be practical, it had to have some underlying order. So Tristram
Carfrae, an engineer at Arup, the Australian engineering firm on the project,
looked into the mathematics of foam.
The trail
led all the way back to an idea from the 1880s. The physicist Lord Kelvin
decided that the ether, the mysterious substance then believed to fill the
universe and transmit light waves, must consist of foam.
George
Darwin (Charles’ son) declared the idea “utterly frothy,” but Kelvin was
undeterred. He set out to understand the shape that ether-foam must have. The
fundamental thing keeping bubbles together, he realized, is surface tension,
which tends to pull bubbles into a shape with the least surface area for the
volume. That’s why a single bubble forms a sphere. The same principle
determines the complicated shapes bubbles form when they are packed together.
He also
figured that the individual bubbles in the ether were probably all of the same
(very small) size. So the structure of the ether-foam would be one with equal
cell size and minimal surface area. But what bubble shape created those
properties?
It turned
out that Kelvin was asking a hard question indeed — so much so that it’s still
unsolved and has been dubbed the “Kelvin problem.” But Kelvin didn’t know that,
and he set to work in the most straightforward way possible: he started blowing
bubbles with soapy water. Before long, his experimentation paid off with a
candidate shape he dubbed the “tetrakaidecahedra.” It’s a modified octahedron,
with each sharp point sliced off and the edges and faces slightly curved.
Kelvin guessed, but couldn’t prove, that by packing these shapes together, he
had created the foam with least surface area for a particular bubble size — and
hence, perhaps, found the structure of the ether.
He was
wrong about the ether — not because it wasn’t foam, but because it didn’t exist
at all. But when Carfrae read about this, he figured it was just what he needed
to solve his engineering problem: a systematic way to build foam.
Carfrae
created a large block of Kelvin’s foam on a computer and tried slicing it up,
cutting at various angles to produce a flat surface he could use for his walls.
The result, however, didn’t look right. When he cut at some angles, the bubbles
were too regular. Other angles produced too many rectangular bubbles, which
just didn’t look real.
Kelvin’s
work did not solve Carfrae’s problem. Kelvin’s work did inspire an entire
branch of mathematics that Carfrae could mine for ideas. Mathematicians were
stuck on the small fact that Kelvin hadn’t proven
his structure was the single best. Could some other foam structure be lurking
out there with even lower surface area?
It took
more than a century, but finally two physicists, Denis Weaire and Robert Phelan
of
Unlike
Kelvin’s structure, the Weaire-Phelan foam was built from two different shapes.
One was a slightly curved dodecahedron and the other was a 14-sided shape with
two opposite hexagonal faces and 12 pentagonal faces. Despite the different
shapes, Weaire made sure all the bubbles had the same volume. The resulting
surface area was a whopping 0.3 percent less than that of Kelvin’s foam.
Weaire and
Phelan are convinced that their solution is the best one, but, just like
Kelvin, they haven’t been able to prove it. Weaire says that at this point, a
proof would be extraordinarily difficult. “I’m not holding my breath.”
Carfrae
didn’t need a proof, though. He just needed the foam. He tried his same slicing
method using the Weaire-Phelan foam. This time, by cutting at an angle of about
111 degrees, he found a pattern that looked entirely natural. In fact, the
pattern actually repeated in ways that were very hard for the eye to detect.
That repetition was key, because it meant the building would be far easier to
construct.
The
Weaire-Phelan foam provided not just a pretty surface for the walls, but the
building’s very structure. Imagine an enormous block of the foam, with steel
beams outlining the edge of each bubble. Now carve out the center to form a
building with 12-foot-thick walls and 24-foot thick ceilings. This is the
weight-bearing structure of the Water Cube.
The result
is so strong, the engineers say, that the entire building could be turned on
its side without collapsing. Furthermore, the remarkable effect is that they’ve
designed a building without triangles. Ordinarily, buildings rely on triangles
to provide stiffness, since a triangle is the only two-dimensional shape that
can’t be deformed without changing the length of its sides. The engineers say
that this lack of triangles will make the building more flexible and hence more
able to withstand earthquakes.
To form the
outside of the walls and ceiling, the designers placed ETFE pillows in the
polygonal openings created by the steel beams. This created the
three-dimensional, bubbly surface they were looking for. They did the same
thing for the interior walls. The empty chamber between the interior and
exterior walls provides solar heating and cooling.
Weaire
learned of the building only after the design was complete, and he visited the
building during construction. He has two words to describe it: “It’s
spectacular.”
Found in: Numbers and Science & Society
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