The Mathematical Bridge

Public summary: 

Self supporting bridges using only wooden poles.

How can a bridge stay up without bolts?
Useful information
Kit List: 

10 long poles
5 short poles
Optional pick up sticks

Packing Away: 

Tie poles together with some rope. Lose in the van.

Frequency of use: 

The Mathematical Bridge at Queens' College in Cambridge, legend has it, was built by Isaac Newton without using bolts.
The present bridge has bolts, thanks to some curious students who disassembled the bridge to study it, but failed to replicate Newton's genius.

Of course, this story is entirely false - the bridge was built just over 20 years after Newton's death by James Essex to a design by William Etheridge.
As with arch bridges, it derives its strength from the material's response under compression - wooden beams are strong in this manner and their tangential nature to the curve of the bridge helps ensure they are not bent.

However, a similar design of bridge, entirely self-supporting, was invented by Leonardo da Vinci (and such designs may have been known to Eastern cultures for a long time before that).

It is very hard to make this bridge on your own - you ideally need a small team of people who can help support bits.
It should be built with care as it is quite unstable.
This has been achieved however with a scout group who didn't appear to speak any English, so it is quite possible!

To make the bridge, first get four long poles. Prop them up at an angle, two facing one way separated by a bit less than the length of the short poles, and two the other way, such that they cross over ~ 2/3 of the way up. Now introduce the short poles as cross beams, slotting in between the protruding ends and the pole it crosses.
Gently adjust (lower) the structure until it settles at a point that the poles interlock: one of the slanted poles leans on the cross beam, which leans on the poles slanted the other way, which lean on the other cross beam in the pair, which leans on the original pole.
This means you can look at it two equivalent ways - where the poles cross there is an x shape: the cross beams mean that each pole rests on the other and neither moves.
Alternatively, from above, you should be able to trace two squares of each one laying on another.
(Note that if the angle between the slanted poles is too great, too much of their force is pushing the cross beams outwards - the angle needs to be small enough that the friction can overcome this - this could be a good angle for a plus event [though I haven't thought it through enough!] - how does the angle required relate to the material and its coefficient of friction? [I think it should be tan theta = mu, for angle 2 theta between poles]).

In summary, the downwards force causes members to interlock due to sheer and bending.

Now you've done this once, you can place a cross beam under one of the ends on the ground, carefully use it to lift the structure, and build the same arrangement again - you can keep iterating to build a bigger and bigger bridge!

How could we make it more stable?
We could add notches to the poles - this would stop them rolling or sliding.

Risk Assessment
Date risk assesment last checked: 
Sun, 05/01/2020
Risk assesment checked by: 
Andrew Sellek
Date risk assesment double checked: 
Mon, 20/01/2020
Risk assesment double-checked by: 
Beatrix Huissoon
Risk Assessment: 
Hazard Risk Affected Person(s) Likelihood Severity Overall Mitigation Likelihood Severity Overall
Sticks People use them as swords/lightsabers/maces/etc - may injury someone through deliberate or accidental contact All 4 3 12 Keep close eye on children, firm warnings if they try anything, suspend experiment if they persist 2 3 6
Bridge Not weight bearing, people may stand on it and it collapse, could topple sideways onto someone All 4 3 12 Make sure bridge held by demonstrator, warn people not to stand on it, don't use in high wind. 2 2 4
Entrapment Catching fingers between poles when assembling bridge All 3 2 6 Demonstrator to warn people about their fingers and where not to put them. Make sure no weight put on bridge. 2 2 4
Splinters Potential for splinters from the wood All 3 2 6 Demonstrator to visually inspect poles at the start. In case of injury call first aider. 2 2 4