Fall factor

In climbing, (specifically in lead climbing), the fall factor roughly represents the amount of force generated by a fall given the shock absorption of dynamic rope. It is computed by taking the length of the fall before the rope becomes taught and dividing by the total length of the rope that is out between the belayer and climber. Mathematically, the fall factor is defined as:

$FF={\frac {l}{r}}$,

where

FF = fall factor
, l = length of fall before rope becomes taught
, and r = total length of rope out
.

Traditional Climbing

A fall factor of 2 is the maximum that should be possible in a lead climbing fall (traditional or sport), since the length of an arrested fall can't exceed two times the length of the rope. Normally, a factor 2 fall can occur only when a lead climber who has placed no protection falls past the belayer (two times the distance of the rope length between them), or the anchor if it's a solo climb. As soon as protection is placed, the distance of the potential fall as a function of rope length is lessened, and the fall factor drops below 2.

A fall of 20 feet is much more severe (exerts more force on the climber and climbing equipment) if it occurs with 10 feet of rope out (i.e. the climber has placed no protection and falls from 10 feet above the belayer to 10 feet below--a factor 2 fall) than if it occurs 100 feet above the belayer (a fall factor of 0.2), in which case the stretch of the rope more effectively cushions the fall.

Via Ferrata

In falls occurring in a via ferrata, fall factors can be much higher. This is possible because the length of rope between harness and carabiner is short and fixed, while the distance the climber can fall depends on the gaps between anchor points of the safety cable.

Force

The severity of a fall (the force generated in the system) is proportional to the square root of the fall factor, so that a factor 2 fall is considerably more serious than a factor 1 one. This can be seen by noting that the maximal force can be estimated by

$E=mgl=\int _{0}^{\Delta }drF\approx \Delta F_{\rm {max}}$

where $\Delta$ is the distance over which the fall is stopped. The distance $\Delta$ can be estimated by stating that the relative expansion of the rope is proportional to the force $F_{\rm {max}}$

${\frac {\Delta }{r}}\propto F_{\rm {max}}$.

Solving this equation for $\Delta$ and inserting it into the above expression one arrives at

$F_{\rm {max}}\propto {\sqrt {l/r}}={\sqrt {f}}$

References

• Busch, Wayne. "Climbing Physics - Understanding Fall Factors". Retrieved 2008-06-14. {{cite web}}: Cite has empty unknown parameter: |coauthors= (help)