The bridge that Newton didn't build

The Mathematical Bridge in Cambridge is famously (and incorrectly) said to have been built by Isaac Newton. But the structure itself is of interest to engineers, like Graham McShane, as it has very useful properties for things like bike helmets. First, Rutherford's punter Max Thompson tells Chris Smith about Queens' college.

Max - At the moment we’re at the mill pond area as you mentioned. It is one of the major hotspots for punters to have their tours begin. But we’re also next to Darwin College just over there. One of the newer colleges on the river, of course named after Charles Darwin. And then to my right hand side we have the old Anchor pub as well, formerly known as the Jazz Club and it was actually where a small band you may have heard of, Pink Floyd, played their very first gigs back in the 1960s when Syd Barrett was the lead singer.

Chris - We’re now going under the bridge. This is the bridge next to the pub. Which road is above us now Max?

Max - It’s Silver Street. This will be Silver Street Bridge, hence the association. This will often be where most tourists will be standing to view the Mathematical Bridge. And also to watch the most punts crash into one another because this is a turning point for most chauffeurs to go down to the other side of the river. And so they’ll be bumping into self-hires and everyone bumps into one another so it gets a little bit chaotic shall we say. We’re now arriving at Queen’s College here founded back in 1448, in part, by one Margaret d’Anjou, the wife of King Henry VI who founded King’s College which we’ll see later on. We’ve just gone underneath the Mathematical Bridge here designed back in 1749 by a student of Isaac Newton’s called William Etheridge and build by David Essex. So if anyone tells you it was designed by Isaac Newton, they’re lying. We’re about to pick up our first guest so I’m going to find ourselves a nice spot to park up and get him on here safely.

Chris - We’re just maneuvering into the side here. And there is teetering on the bank above us our first passenger. Welcome aboard.

Graham - It’s a long way down.

Chris - It’s a very long way down.

Georgia - Welcome to our studio.

Graham - Thank you. My name’s Graham McShane. I’m a Fellow in Engineering at Queen’s College. And I’m an academic in the Engineering Department so I lecture and do research in topics in engineering materials.

Georgia - We’ve just travelled under the very famous or infamous Mathematical Bridge that Max was just telling us about. Unlike most of the bridges which are kind of solid, this one is like a crosshatch kind of design with lots of wood and poles. Loads of geometric shapes. They look like sort of folded up like a duplex kind of structure. So why is the bridge, apart from looking great, why is it special?

Graham - It’s very unusual amongst the bridges that you see behind the colleges on the river. As you mentioned, all the other bridges are solid stone arches, but the mathematical bridge, is made out of wood. It’s the first thing to notice about it. and the reason you can get away with making it out of wood is that it’s a totally different kind of bridge. It’s what’s known as a “truss structure.” A truss structure is made up of a whole series of bars which are linked together and they transmit the forces very efficiently to the supports. And so by using a truss structure, you can create a structure which isn’t necessarily as strong as a solid stone arch but it uses little material. It uses the material very efficiently, and so it transmits the forces to the supports very efficiently so you have a very lightweight structure.

Georgia - This is why it can be not so solid as all the others?

Graham - That’s right, that’s right. And what’s also unusual about the Mathematical Bridge is not that it’s just a truss structure but it’s an arched truss structure. You very often see trusses used to build things like railway bridge. In those cases, it’s a flat truss structure that goes straight across the river, but the Queen’s Mathematical Bridge is an arched truss structure and that’s quite difficult to achieve. And so the bridge uses a very distinctive way of arranging the bars called “radius and tangent trussing,” and that’s a way of achieving this curve to truss shape.

Georgia - Ah, oh. Being attacked by another punt. We’re trying to have an interview here.

Chris - We’re going to be boarded in a minute.

Georgia - Do you get punt pirates? Is that a thing? It’s a very impressive structure and it seems like it’s a great idea if you want to save material. You’re an engineer, do you use this structure in your work?

Graham - Well, truss structures are obviously of interest for efficient lightweight structures. And saving weight is very important in mechanical engineering design because people want lighter aircraft, lighter cars, lighter trains and so there’s a whole area of research looking at how you can create materials using the same concepts. If you imagine taking a truss structure like the Mathematical Bridge and miniaturising it down until the bars are a few millimetres in length and you’ve got a material that’s called a “lattice material.” A lattice material’s a type of material where it’s made up of an array of bars distributed to transmit forces very efficiently through the structure. And so this allows you to create very stiff, very lightweight materials that are very good for lightweight engineering design. They also have other interesting properties, so when you crush these lattice structures they absorb energy very efficiently. So they can also find uses in things like crash protection and also in helmets.

Georgia - Ah. Another Cambridge favourite - cycling then?

Graham - Absolutely. People want lightweight, efficient helmets for sports and for cycling and all kinds of other applications, and so we’re very interested in using lattice materials to create the next generation of protective equipment and helmets. Maybe in future you might see a helmet that when you cut it open it looks like the Mathematical Bridge inside.

Chris - Graham, do you see the same sort of structures cropping up in nature? Has nature engineered its own solution using the same physics?

Graham - Absolutely. If you look at the structure of the bones in bird’s wings for example, those are very stiff, very lightweight structures where they’ve got a complex network of bones within the bone. You’ve got this truss like structure that give you that stiffness and lightweight, so you do see it evolved in nature in any application where you want to save weight but still has to be stiff and strong at the same time.

Georgia - Max eluded to the fact that there’s an often heard rumour that Newton built this bridge. What is that rumour and why do we know it’s not true?

Graham - Well, it’s a good story but, unfortunately, it doesn’t have any basis in fact. The main reason why it can’t be true is that the bridge was designed and built long after Newton died so he couldn’t have had anything to do with it, unfortunately.

Georgia - He was clever but he wasn't that clever.

Graham - He wasn’t that clever, that’s right. There’s also stories that it was designed by a student of Newton, but that’s not true either.