I read the ratings of different gear, such as cams and such, but I did not really understand what the ratings mean in terms of comparison with an actual fall. I did the analysis below. I am assuming a worst case 10 m fall. This would be climbing climbing to a height of 10 m, and then falling back 5 m back to the site of the anchor, then 5 m back down to the starting point. Basically falling the entire length of the rope. As expected, this calculation holds whether the fall is 20 m or 100 m, in the end, it depends only on the mass of the climber and the elongation of the rope.
There is a little error in this in that the climber would hit the ground before the rope would grab hold of the climber and start stretching and bringing things to a stop. But lets assume there is no floor, and the climber falls past the start; and then the rope starts holding and stretching.
Mass of Climber: M=80 kg
Acceleration due to gravity: g=9.8 m/s^2
Distance of fall: d= 10 m
Length of rope: x= d= 10 m
Dynamic elongation of rope: E= 30%
Duration of free fall: t= SQRT(2*d/g)= 1.4 sec
Velocity at the end of free fall: v= g*t= 14 m/s
Length of rope stretch: xs= x*E= 3 m
Duration of arrested fall: ta= xs/v= 0.2 sec
Acceleration back to rest: a= v/ta= 65 m/s^2= 6.7 g
Force of arrested fall: f=M*a= 5.2 kN
General equation: f(E,M)= 2*M*g/E, where E is dynamic elongation in %, M is mass in kg, and g is 9.807 m/s^2
Is this correct?