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Gear ratings - a physics question 26-Nov-2007 At 4:42:26 PM anthonyk

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all these F=mgqprX^2 equations are far too simplistic. they're ok for maximum forces on a carabiner and how far people are going to fall, but they assume for example that ALL the energy gets transferred from PE to KE to strain energy, but in reality energy also gets converted to heat through friction eg between strands. Heat would be removing energy that doesn't need to be taken as strain but it also potentially changes the properties of the strands of the rope.

In addition forces in particular parts of a rope can be greater than in other parts, and there's a lot of assumptions being made. Eg if you are assuming that a rope can hold a static force of say 20kN you are really saying that there are say 20 strands and each can hold a force of 1kN, so you are _assuming_ that the force is being evenly distributed between the strands (within a certain degree of variation). Knots are a classic example of the effect of this, as are ropes being bent over carabiners or edges.

Nice equations cancel out a lot of competing factors. But you have to remember that they only cancel each other out in particular conditions. A lot of equations really specify the average effect, which can be different from how the effect is distributed, and they miss out a lot of difficult to calculate factors like friction and heat.

The only practical information you can use is experimental, eg by dropping things onto ropes and seeing where they break. In a lot of ways the critical question isn't what happens in a perfect system, its how imperfect your system is, ie how far it deviates from the perfect model. Scrabbling equations to try and prove something is safe is an exercise in self-delusion.

[edit] oh wait the question was about force on a climber or carabiner, ok thats reasonable to calculate, but once you get into how much a rope is going to take it gets a lot messier