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  #1  
Unread 04-27-2006, 03:04 AM
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Exclamation The theoretical fall factor Vs the actual fall factor (April 27th 2006)

The theoretical fall factor Vs the actual fall factor


The theoretical fall factor

The fall factor determines the hardness of a fall: the higher it is, the harder the fall. Its value, lies between 0 and 2 in climbing conditions, and is calculated by dividing the height of the fall by the length of rope deployed.
The hardness of a fall is not a function of its length but of this ratio, because the longer the rope, the more it can stretch to cushion the fall.

This theoretical fall factor assumes that there is no friction between the belayer and the highest runner to allow all the rope in play to absorb energy equally.


Height of fall
f =
length of rope
Examples:

The actual fall factor

Friction in karabiners or against rock limits propagation of the force generated by a fall back along the rope. Thus only the length of rope between the penultimate and the ultimate runner will be fully loaded, with each length between the previous runners successively less loaded.
As a result the energy absorbing capacity of the rope is not deployed fully all along its length and thus the actual fall factor is much greater than the theoretical fall factor.

In practice, on the highest runner
It is commonly argued that in practice fall factors are low and that dynamic belaying places a low limit on impact forces. One can thus conclude that the maximum impact force figure for the rope has little influence on the forces developed on runners (and the climber).
This is totally false.
The Italian Alpine Club has conducted numerous practical tests, has filmed them, and has measured the loads all along the security chain.
On the basis of these results Dr. Bedogni has established a mathematical model allowing the calculation of the loads developed along the security chain in all configurations. Notably, it allows the calculation of the load placed on the last runner as a function of the maximum impact force of the rope.

Maximum impact force: When a climber falls, the energy must be absorbed by the belaying system and in particular by the rope. If the rope is a good energy absorber, it will reduce the impact on the climber. The force sustained by the climber as a fall is arrested is what we call the impact force.
Its value depends on the fall factor, the climber’s weight, and the capacity of the rope to absorb the energy of the fall.
Maximum rope impact force: All mountaineering ropes are characterised by their maximum impact force, measured in the laboratory under extreme conditions which may never be encountered when climbing using a metal mass, fixed anchor, and rope lock.
In these conditions all the energy of the fall is absorbed by the rope, none of it by friction, the harness, or deformation of the human body.
It thus concerns the maximum obtainable impact force in the rope.
Note: In climbing, with successive falls, the dynamic capacity of the rope reduces and thus the impact force increases.


Dr. Bedogni’s results show very clearly that the loads on the top runner are very different depending on whether the rope in use has low maximum impact force or a high maximum impact force.
Example 1: Clipping in line with no rubbing points below the top runner. Fall of 8 m.
Example 2: Clipping 5 slightly off-line runners in 19 m of ascent, with no rubbing against the rock. Fall of 8 m.
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Unread 04-27-2006, 03:05 AM
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continued.....

Example 3: Clipping 5 slightly off-line runners in 19 m of ascent, with some rub-points. Fall of 8 m.
Example 4: Overhanging passage with a rub-point on the roof lip - Fall of 8 m.
The Pulley Effect:

During a fall, the highest runner sustains both the impact force generated by the climber, and the force held by the belayer. These two forces add together. This is what we call the pulley effect. The force held by the belayer is lower than the impact force on the climber because of friction in the karabiner. That’s why, in total, the force exerted on the highest runner is around 1.6 times the force on the climber!
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Unread 04-27-2006, 01:34 PM
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You really went all out making those animations!
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Unread 04-28-2006, 01:10 AM
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Quote:
Originally Posted by Pedro de Pacas
You really went all out making those animations!

No expense is spared for you guys (cut and paste )
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