We can model a dynamic rope as a
spring with constant k proportional to 1/L,
where L is the length of the rope.
The force is then:
If the climber is a height h/2 above the last
anchor, then he will fall a distance h till the
rope starts to stretch.
From this and mechanical energy conservation we
get:
Solving the equation gives us:
So the maximum force in the system is:
This gives us the surprising result that the
maximum force (with a given rope and climber) is
dependent only on h/L.
This is defined as the "Fall Factor".
