Geometric perfection of da Vinci's design

by Photo: Terje S. Johansen

Five hundred years after he conceived it for the ruler of the Ottoman Empire, Leonardo’s ingenious arch graces a quiet suburb of Oslo, Norway. The geometric perfection of da Vinci’s design is demonstrated in the explanatory graphics, produced by engineers who worked on the Norwegian project. 1. A simple cylinder with concave wings is cross-cut with a horizontal plane.
2. The cut figure is now a crude arch.
3. The arch’s concave wings are then cut away, producing parabolic curves.
4. The arch is now a structurally sound bridge: wide at its feet, and narrow at its middle.
5. The geometric model is now almost identical to Leonardo’s 1502 drawing (below).

It was like falling in love,” says Norwegian artist Vebjorn Sand. “I just couldn’t get it out of my mind.” Six years ago, while visiting an exhibit of the works of Leonardo da Vinci, Sand became captivated by a model of a bridge that, in 1502, da Vinci had proposed building for Sultan Bajazet II, ruler of the Ottoman Empire. The Sultan wished to span the Golden Horn, an inlet between the Turkish cities of Pera and Constantinople (known today as Istanbul). At that time, it would have been one of the world’s largest bridges. But to the astonishment of the Ottoman court, the proposed design took the form of a giant arch. After conferring with advisers, the sultan responded with what seemed like common sense — an arch that big would collapse in the middle. He declined the proposal.

But the moment Sand saw the model, he says, he knew it would work. “After all,” he thought, “we’re dealing with Leonardo.” Sand lost no time in approaching the Norwegian Public Road Administration with a proposal to build
it. Economics required that the bridge be scaled down: Instead of a stone structure some 787 feet long as proposed by Leonardo, the Norwegians funded a 328-foot bridge made of laminated pine in the Oslo suburb of As. On Oct. 31, Norway’s Queen Sonja unveiled the finished construction.

What is perhaps most striking about the bridge is its modern — some even say futuristic — appearance. The reason for this, says Sand, is the design’s mathematical basis. “Math and geometry transcend time,” he says, “as does nearly everything Leonardo conceived.” But on close inspection, one can’t help sympathizing with the Ottomans: How is it possible for an arch to span even the lesser distance? The answer lies in its “pressed-bow” construction (see drawings above). The bridge is much wider at its feet, or bases, which produce a counterforce from the ground that supports it. The double-arch construction makes the bridge resistant to powerful side-gusts of wind.

Despite worldwide praise, Sand isn’t finished yet. He wants to build new and grander versions of the bridge in other parts of the world. “Perhaps,” he said repeatedly during a recent visit to the United States, “we might build one here.”