where "mg" is the climber's weight, "h" is the fall height and "k" is the spring constant of the rope. Using the elastic modulus "E" = "k L/q" which is a material constant, the impact force depends only on the fall factor "f", i.e. on the ratio "h/L", the cross section "q" of the rope, and the climber’s weight. The more rope is available, the softer the rope becomes which is just compensating the higher fall energy. The maximum force on the climber is "Fmax" reduced by the climber’s weight "mg". The above formula can be easily obtained by the law of conservation of energy at the time of maximum tension resp. maximum elongation "xmax" of the rope: