In reply to kermit_uk:
> To dumb it down lots, if a 50kg climber would exert 5kn would I at 90kg exert 9kn or does it multiply up or down. Assuming same ropes and gear etc and that the gear holds and doesn't rip through the rock etc
Ok. In the same spirit, a similarly dumbed-down answer to try to get a vague theoretical answer at least...
I think less. More force than the lighter climber, but not *that* much more, here's why:
If the 90kg climber falls the same distance that the 50kg climber falls before the rope comes tight, and then also decelerates to a stop over the same distance afterwards, then yes - 5kN for the one will mean 9kN for the other. But this doesn't happen, because the rope stretches further.
Just for a moment, lets take away the rope and drop both climbers onto a perfectly elastic bungee. I've just convinced myself that the peak impact force, and also the distance travelled between the rope/bungee pulling tight and the climber coming to a stop (before beginning to bounce back up) will increase with the square root of the climber's weight. (So a monster 200kg climber will exert twice the force of the 50kg climber, whilst also travelling twice as far - the thing that defines a perfectly elastic spring/bungee/whatever is that they're kind of the same thing, the force is proportional to the extension.)
In this case 5kN for the 50kg climber will mean 6.7kN for the 90kg climber.
(Because the square root of 9/5 = 1.34 meaning 34% more impact force, and also 34% further distance travelled whilst decelerating to a stop.)
Ok, now lets put them both on a via ferrata instead, with one of those screamer type via ferrata lanyards. The 50kg climber falls, stitching rips at 5kN, and after he stops the climber see's he's ripped 5cm of stitching out. When the 90kg climber falls his stitching will also rip at 5kN, but after he's stopped he'll notice that 9cm of stitching ripped.
Post edited at 22:43