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Danger Area Below Cliff Rescue 31-May-2012 At 3:06:27 PM Olbert

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On 31/05/2012 kieranl wrote:
>Here's one for the physicists/engineers among you.
>One of the big risks with a cliff rescue at Arapiles is of people on the
>ground getting hit by rocks dislodged by the stretcher or rescuers on the
>cliff. Most rope-rescues at Arapiles involve lowering to the ground and
>the tendency is for personnel to get close to where the stretcher is going
>to come down so they can get into things straight away.
>One thing we have to do is try to keep people back at a "safe" distance
>until the stretcher is down.
>My question is, how do we work out a "safe" distance.
>In my experience from cleaning climbs, people generally underestimate
>the area affected by a falling rock when it hits the ground, in particular
>the distance that fragments can shoot out laterally really stuns people
>(in some cases literally).
>My rule of thumb, which has no basis except that it seems better than
>ignoring the issue, is that people need to be at least as far from the
>cliff as a rock
>can fall. So, if it's a 30 metre high cliff, people should stay 30 metres
>away from the fall-line.
>What does the physics say?
>Let's try one example : If a 9Kg rock free-falls 30 metres, and splits
>into 3 equal fragments when it hits flat ground, how far laterally do the
>3 pieces fly?

Not that I'm that good on the physics of breaking rocks but I think I can safely say that there is no theoretical/analytical answer to that question. With a few assumptions and simplifications you could probably get some fairly useless maximum speeds and such but in a real situation a billion and one slightly different things could happen which would significantly effect the result.

I'll have a go at solving this one scenario which is a bit simpler though as an illustration of what could happen:

10% of the energy gained during the fall was then transferred perfectly into only one of the three fragments, in the form of kinetic energy.

Energy gained during the fall: E = mgh = 9 * 9.8 * 30 ~ 3000J

Energy transfered to one of the three fragmets E_fragment = 0.1 * E = 300J

Kinetic energy: E_k = 1/2 * mv²

So velocity of the fragment: v_fragment = the square root of (2 * E_k / m) = sqrt (2 * 300 / 3) ~ 14m/s

If this was shot up at an angle of 45 degrees (worst case scenario) and assuming that there is zero air resistance (bad assumption but I definitely couldn't be bothered doing the more realistic calculations) then after a bit more maths of which I couldn't be assed writing up, then it would travel 30m.

Buuuuuuut that calculation relies on some pretty unsafe assumptions - for one, if the rock breaks into smaller fragments then the same amount of energy makes them go faster and further. Then again those small fragments are much more effected by air resistance (imagine dropping a brick and a pebble out of a plane, the brick is less affected by the air resistance).

In reality it comes down to experience and rules of thumb. If your rule of thumb is that people have to be as far away as you are high works then go with that. If people still get occasionally injured, then go further. Beware of creep - if you continually shrink the distance you keep people away by insignificant amounts then eventually people will be close enough to get hurt.