One of the things that many people ask about and sometimes talk about without really understanding the science or math behind it is Fall Factors.
Fall Factors are a calculation of the risk / forces that impact a person when they fall from a specific location with or without pro.
Petzel has created a great article on it and I’ll share it with you:
Fall factor and impact force - theory
Fall factor and impact force are two important concepts in the physics of climbing falls. To understand a climbing fall, it is important to recall a basic law of physics: when an object falls, it stores energy.
Impact force
During fall arrest, this energy is dissipated by elongation of the rope, displacement of the belayer, the climber's body... Energy is transmitted to the belay chain in the form of force. This is the impact force. For the climber, it's the impact experienced during fall arrest.
We are often interested in the impact force transmitted to the climber, the belayer, and the redirect point.
This value relates to all of the important factors in energy absorption: rope elongation, belayer displacement, the climber's body, rope sliding through the device...
The impact force indicated on a rope corresponds to the maximum force measured on a metal mass (a climber) in the standard test conditions (see Impact force-standards).
Theoretical fall factor
The fall factor is often used to quantify the severity of a climbing fall.
It can have a value between 0 and 2 in climbing.
Fth =
Fall lengthRope length
Fth = theoretical fall factor
Fall length = length of the climber's fall
Rope length = length of rope between belayer and climber
The fall factor is the ratio of fall length to rope length.
In climbing the severity of the fall dœs not depend on the fall length, as the longer the rope, the more energy it can absorb.
In these two cases, the severity of the fall increases. The free fall length is the same. There is the same amount of energy to absorb, but the system is less dynamic.
Case 1
rope length = 10 m, fall length = 4 m so fall factor = 4/10 = 0.4.
The rope length is significant, so the absorption capacity is significant. The severity is low, so the impact force is low.
Case 2
rope length = 2 m, fall length = 4 m so fall factor = 4/2 = 2.
The rope length is short, so the absorption capacity is low. The severity is significant.
To learn more
In theory, the higher the fall factor, the higher the forces generated. The concept of severity as a function of fall factor is useful only with a dynamic rope. The longer the rope, the more energy it can absorb. The fall factor model is rather simplistic, as it dœs not take into account important factors such as rope drag, type of belay device, belayer displacement... In the following chapters, we will see the impact of some of these factors.
Actual fall factor
The theoretical fall factor dœs not take into account the rope friction against the rock and in quickdraws. This friction prevents the rope from stretching over its entire length. Thus, only a part of the rope (solid line) will absorb the energy of the fall: this is called effective rope length. It is therefore useful to talk about the actual fall factor. It is clear that if a climber dœs not take the necessary steps to avoid rope drag, the actual fall factor can quickly increase. In this case, the fall will be more severe for the climber.
Fr =
Fall lengthEffective rope length
Fa = actual fall factor
Fall length = length of the climber's fall
Effective rope length = actual length of rope in play