# Fall factor

Fall factor

In climbing, the fall factor is derived from the length of the fall, divided by the length of the rope from faller to the fixed point, whether belayer or anchor. It represents the amount of force generated by a fall given the shock absorption of dynamic rope. The fall factor is mathematically given by:

:$f = frac\left\{l\right\}\left\{r\right\}$

where

f = fall factor l = length of fall r = total length of rope out

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

:$E=mgl=int_0^\left\{Delta\right\} dr F approx Delta F_\left\{ m max\right\}$

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 $F_\left\{ m max\right\}$

:$frac\left\{Delta\right\}\left\{r\right\}propto F_\left\{ m max\right\}$.

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

:$F_\left\{ m max\right\}propto sqrt\left\{l/r\right\} = sqrt\left\{f\right\}$

References

*cite web
last = Busch
first = Wayne
coauthors =
title = Climbing Physics - Understanding Fall Factors
work =
publisher =
date =
url = http://www.southeastclimbing.com/faq/faq_fall_factor.htm
format =
doi =
accessdate = 2008-06-14

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