## Robin Hood - a catapult stunt

Note: these articles have been published in InfoChem, the supliment to Education in Chemistry produced by The Royal Society of Chemistry.

In the 1991 version of Robin Hood, staring Kevin Costner [1], there is a scene where Robin and a friend are safely catapulted over castle battlements landing onto a large haystack the other side! It looks great but really how feasible is this stunt?

In the film the catapult looks a strange device consisting of a tensioned string connected somehow to the platform that the two are sitting on, rather like a giant crossbow. It looks like it would be better at firing a giant arrow or bolt horizontally, rather than flinging two heavy bodies upward. Way back in antiquity though there have been catapults and trebuchets capable of flinging heavy objects great distances. Such a mechanism can develop its power by winding up tension on a rope and unleashing the stored energy like a giant spring. There is a legend that the best fibres were made of maidens hair: bundles of long hairs cut from several woman's heads and plated into a rope.

Hair is composed of the protein keratin which itself is made up of rope-like filaments. It is very strong and has a natural elasticity which is good for storing energy [2]. The strength of the human hair is far greater than many appreciate. There are circus acts that suspend people from their hair [3]. A typical hair is very fine of course, about 0.1mm in diameter. By hanging weights I found that a typical hair could take 50g but hair strength varies from person to person and with ethnicity [2]. We need to estimate the forces on the catapult rope to see if it would be possible to make such a thing from hair.

Let's say the men are each 50kg giving a total mass of 100kg. If the walls are 10m high we get a potential energy E(p) = mgh = 100 x 10 x 10 = 10,000 J. This is equal to the initial kinetic energy they need at lift-off which is E(k) = ½mv² so we get 10,000 = ½ x 100 x v² and so v = √ (2 x 10,000 / 100) = √ 200 = which gives a lift-off velocity of about 14 m/s.

Let's also say the catapult seat imparts its force over a short period of time e.g. T=1/4 sec say. An estimate of the force would be: F = ma = m (change in seat velocity/Time) = 100 x 14 x 4 ~ 100 x 50 = 5000N = 500 kg i.e about ½ tonne of force. The catapult is essentially a lever so the rope would need to have much greater force wound up in it, say 10 times this. The hair rope would therefore need to take the equivalent of ca. 10 x 500 = 5000 kg = 5,000,000 g.

If each hair can take 50g we would need 5,000,000 / 50 = 100,000 hairs - about the number of hairs on a typical head. This amounts to a bundle of about 330 x 330 hairs cross section which would only be a few cm in diameter - so not unfeasible. The serious issue though is not so much the catapults ability to lift the load but the accuracy of its trajectory. Even if it could throw them up how would you make sure it didn't smash them onto the walls or simply toss them in the wrong direction – it would be the end of our merry men!

References and Links
[1] Robin Hood, Prince of thieves, Warner Bros., 1991.
[2] Hair entry on wikipedia
[3] wiki hair hang page

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THE CREATIVE SCIENCE CENTRE

Dr Jonathan Hare, The University of Sussex
Brighton, East Sussex. BN1 9QJ.