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The Mathematical Bridge of Cambridge

The Mathematical Bridge is a wooden footbridge across the River Cam, connecting the old and new parts of Queens' College in Cambridge. The bridge is much admired because of its intriguing design—it is constructed entirely out of straight timbers, but has an arched shape.

In The History of the University of Cambridge, author Edmund Carter praises the bridge as “one of the most curious pieces of carpentry of this kind in England”. The timbers of the bridge are “curiously joined together, and supported on abutments of rustic stone-work, between which is a passage for the Cam, 40 foot in the clear, and of such height, that the waters in a common flood cannot reach the lowest timbers thereof.”

Mathematical Bridge

Mathematical Bridge. Image credit: Michael Jefferies/Flickr

The Mathematical Bridge is constructed out of interlocking pieces of timber. Each rib of the superstructure are set at tangents to the circle describing the underside of the arch of the bridge. In the arch itself, each member is under compression with little or no lateral force that could cause bending. Where the main members cross, the wood joint transmits the compressive stress from one member to the next, with a bolt serving to hold the joint together laterally, rather than itself carrying any stress. There are also radial members which both support the top rail and lock all the overlapping tangents into a rigid truss. The load bearing deck is supported by horizontal cross-beams attached to the bottom of the radials, close to the junction of two tangents. When a load is applied the vertical forces get distributed along the tangents as compression opposite to the compressive forces from the tangents, thus balancing each other.

Mathematical Bridge

The tangent and radial trussing of the Mathematical Bridge in Queens' College, Cambridge, with its tangential members highlighted. Image credit: Cmglee/Wikimedia Commons

The bridge was built in 1749 based on a design by architect William Etheridge, who had designed a similar but much bigger Old Walton Bridge over the Thames. However, the design for the Mathematical Bridge was not Etheridge’s original idea.

In 1737, James King, the master carpenter at Westminster Bridge, proposed a similar design using tangent-and-radial trussing for a wooden Westminster Bridge. Unfortunately, when the Thames froze over in the winter of 1739–40, some preparatory structures broke and the design was abandoned. When the stonework for the Westminster Bridge was being laid, a few years later, James King was appointed again to erect the wooden centers on which the stone arches would be laid. He used the same system of tangent and radial trussing he employed in his earlier design of the failed wooden bridge. This design permitted ships to pass under the arches while they were being erected.

Old Walton Bridge (1754)

Old Walton Bridge (1754) by Canaletto

William Etheridge was a foreman to James King, and after the latter’s death in 1744, Etheridge took over the work at Westminster. It’s possible that Etheridge was inspired or even borrowed the system of tangent-and-radial trussing designed by James King when he drew the plans for the Mathematical Bridge at Cambridge.

James King himself might have been inspired by a craftsman and engineer of far greater caliber—Leonardo da Vinci.

In Leonardo da Vinci’s notebook, which is preserved at the British Library, there is a suspiciously similar design for a bridge built using interlocking pieces of timber. Da Vinci used no nails or fasteners as the structure was self supporting. Not surprisingly, the popular myth about the Mathematical Bridge is that it was originally built without using nails, but as the story goes, when students of the University took the bridge apart to see how it worked, they were unable to put it back together again, and had to hold the structure together using nuts and bolts.

Leonardo da Vinci’s bridge.

Leonardo da Vinci’s self supporting bridge.

Another curious myth associated with the bridge was that it was designed by Isaac Newton. There is no evidence of this, and in any case, Newton could not have been directly involved since he died in 1727, twenty-two years before the bridge was constructed.

Similar bridges inspired by da Vinci’s design have appeared in various parts of the world, such as this footbridge in Morsø in northern Denmark.

footbridge in Morsø in northern Denmark.

Wooden footbridge in Morsø in northern Denmark. Image credit: Core77

Mathematical Bridge

Mathematical Bridge. Image credit: Michael Brace/Flickr

Mathematical Bridge

Mathematical Bridge. Image credit: Steve James/Flickr

Mathematical Bridge

Mathematical Bridge. Image credit: Jocelyn Erskine-Kellie/Flickr

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