## Die Hard

Can you survive a hose pipe fall?

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

The scene we are going to investigate is in Die Hard where Bruce Willis makes an escape by jumping off the top of a tower with only a fire hose wrapped around his waist to break his fall! [1] It's so 'Bruce Willis' that in what follows I am not even going to call him by his film character name. To help us discover what might happen to him we need to consider the material properties of the hose pipe, but first we need to do some calculations to work out the forces on Bruce.

Looking at the clip it looks like he free falls about 2 or 3 floors, say 10m before the hose brings him to a stop. Now from basic physics equations we can estimate how long it will take from standstill to fall this distance (f). We have that the fall f = ½gt² which on rearranging gives t = √(2 x f/g) = √(2 x 10 / 10) = √2 ~ so t is about 1.5 seconds (g is the acceleration due to gravity g = 10m/s²).

Using this we can work out how fast (v) he will be going just before the hose stops him. From v = g x t we get v = 10 x 1.5 = 15 m/s. Now if Bruce's body mass (m) is say 70kg we can work out his energy from E = ½mv² = ½ x 70 x (15)² = 7900 J (Joules) – the sort of energy liberated when a very large firework goes off!

As he is brought to a standstill all this energy has to be dissipated in the hose or in him. If this happens only at the very end of his fall he will experience a much greater force than if he is brought to a stop over a longer braking distance. Now energy = force x distance (E = F x d) which we can use to calculate the forces on Bruce by rearranging we get F = E / d (where d is the braking distance).

Let us start by being kind to Bruce Willis. Just for now let us say that instead of a fire hose, he uses a 5m bungee rope, and that this stretches another 5m to bring him to a nice gentle stop 10m below. Now bungee ropes are made of many latex strands bundled together. Because of the elasticity of the strands they can absorb a great deal of the energy of a fall making bungee jumps relatively safe. Using the formula we get a force on Bruce of F = E / d = 7900 / 5 = 1580 N (Newton), equivalent to a weight of 158kg i.e. about 2 x the weight of Bruce Willis - like the force on your feet when you give someone a piggy back - so as we see that's not so bad.

But he is not using a bungee rope he is using a fire hose. Fire hose are made of woven nylon a masterpiece of chemical engineering. They can withstand pressures of up to 80 atmospheres (80 bar), pressures which, if the hose splits, can brake brick walls. I tried putting a bin full of water onto a 1m piece of fire hose hanging from a tree. It barely stretched a mm before the branch eventually broke under the weight. So in the Die Hard fall its unlikely to stretch very much. Lets say in Bruce's jump a 10m fire hose stretches 1% i.e. 0.1m. Our force formula now becomes F = 7900 / 0.1 = 79000 N ... equivalent to the weight of about 100 Bruce Willis!

So what would happen to our action hero? Talking through all this one day with the actor and presenter Robert Llewellyn he quite rightly reflected "I think there would be a Bruce and somewhere else a Willis!"

[1] Die Hard, Twentieth Century Fox, 1988

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THE CREATIVE SCIENCE CENTRE

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