The Calculus Diaries - Jennifer Ouellette [85]
Ochsendorf and Kilian realized there were parallels between the fabrics that CGI animators model and Isler’s hanging membranes. A length of cloth is strong under tension, but if you push on it (compression), it simply crumples. What Ochsendorf needed was something with precisely opposite properties, so he worked out a way to turn the fabric model around. This allowed him to model architectural structures, specifically Gothic cathedrals.
He’s already scored some successes with his prototype program. Ochsendorf used it to demonstrate that the domes of the Pines Calyx conference center near Dover, England, would stay in compression under all possible loadings, thereby satisfying stringent safety regulations. Open for business since 2008, the center is topped by domes made from clay tiles glued together edge to edge. Those domes span 15 meters, yet the tiles are only 15 centimeters thick and required no supporting framework during construction. “Without Ochsendorf’ s program these remarkable thin-shelled shallow domes would not have been allowed to be built,” Alistair Gould told me. Gould is a member of Helionix Designs, a firm based in Kent that designed the building.
Eventually Ochsendorf hopes to provide designers with a technique that could lead to revolutionary architectural designs and more environmentally friendly buildings. Many modern buildings have a severe impact on the environment. Steel corrodes with time, and the manufacture of concrete produces quantities of greenhouse gases. Ochsendorf ’s software program has already demonstrated that certain buildings could have been built with much less material. In essence, the program finds the solution to an optimization problem for the materials.
Take MIT’s Kresge Auditorium, designed by Saarinen in 1955. It has a domed roof made of concrete 15 centimeters thick. After analyzing the geometry of the dome and feeding the measurements into his hanging-chain model, Ochsendorf reckoned that it could have been built with half the thickness of concrete, resulting in significant savings in building costs and reduced environmental impact—without sacrificing the artistry. He made similar findings about MIT’s new computer science building, designed by Frank Gehry. The building features columns leaning in every direction, and the structure used roughly 30 percent more material than would have been needed if his program had been used to find where the lines of force naturally fall, Ochsendorf insists.
THE QUEEN’S GAMBIT
One of the most famous optimization problems can be found in Virgil’s Aeneid. A Phoenician woman named Dido was forced to flee her homeland after a tyrannical brother murdered her rich husband and tried to seize her wealth. Dido didn’t exactly travel light: She “fled” via several boats filled with her belongings (including her late husband’s stash of gold) and numerous attendants, eventually landing on the coast of Africa, where she hoped to start a new life. Her reception by the natives was frosty at first—perhaps they’d encountered would-be colonists before—but she struck a shrewd bargain with their king, offering a substantial sum of money in return for as much land as she could mark out with the hide of an ox upon which to build her own city.
It may be that the king bought into the stereotype that women aren’t inherently good at math; figuring he was getting the best of the deal, he agreed. Dido promptly took her oxhide