Calculate Fall Factor & Impact Force
On all ropes you will find information on impact force and rope elongation. Modern ropes are so stable, that under normal conditions and with careful use they cannot break. But this does not mean, that you can't be injured in a fall. This is because, although ropes can withstand forces of several kilonewtons (kN) relatively problem free, people have substantial problems with these loads.
In the following information, we want to clarify for you how these forces arise and what the numbers on the ropes mean.
When a fall is stopped, the body of the climber absorbs the energy that is generated from the rope being stretched and the movement of the belayer. The force generated at the moment of maximum rope elongation, is known as impact force. This impact force is a quality feature of a dynamic rope. The lower the value, the lower the impact during fall arrest held and the smaller the force on the climber.
The maximum force which arises in a fall is:
Here m signifies the mass of the climber, g gravity, E the elasticity modulus (a value dependent on the material), A the rope diameter and f is the so-called fall factor. This in turn arises from the ratio of the fall height h to the length of the paid out rope L:
If you want to minimise the stopping force, there is only one option. You must minimise the fall factor, since the other values are set.
The fall factor is a measure of the "force" of the fall. This makes sense, when you think about the numbers. When the payout rope is four metres, a fall of two metres is more uncomfortable than a fall of one metre.
The same applies when shortening the payout rope. A shorter rope at the same fall height is more uncomfortable than a longer one.
It is interesting to note that the fall factor does not change when the fall height and payout rope are changed in the same proportion. So a fall of 3 metres with 9 metres of payout rope has the same fall factor as a fall of one metre with three metres of payout rope.
The fall is therefore just as "hard" However this only applies the force, that impacts on the rope. When you consider the energy generated (and not loads), then a fall of three metres is more dangerous, since you would have more kinetic energy at the end of the fall and that means that you can smash into the rock face at a higher speed!
To soften a fall, you should therefore only reduce the fall height while keeping the rope payout as long as possible. This is of course easier said than done. That's because we can't actually choose the fall height, since we don't usually choose when we fall. The rope payout can be varied. But it can also only be made smaller, after all you have to stick to the fixed protection points, and the position of the belayer comes from their layout. What's more, you should try to avoid slack, since this usually increases the fall height. But more on that later.
The formula comes from a relatively simple theoretical model of a fall. In reality several different factors play a role in influencing the maximum force. We will go into some of these aspects in the following section, and investigate their influence, so that you can better evaluate the risk of a fall on the cliff face.
At the protection points, that is where the rope goes through the carabiners etc, there is friction between the rope and metal. If the rope is straighter as it passes through the hangers, the friction at this point will be lower. But if the rope zigzags through the hangers, the friction on this point is relatively high. This prevents the rope from stretching in case of a fall. In our comparison this means that the payout rope length must be replaced by an effective payout rope length, which is always smaller than the actual rope length. So the fall factor will be larger, the less straight the rope line is.
The belayer hangs on the rock face and is free moving. If the climbing partner falls, they can also be pulled up a bit. This has the result that some of the energy generated in the fall, is released onto the belayer and the person falling "loses energy". They slow down. In our formula the displacement of the belay partner has the effect of a reduced mass. This means the mass, which is relevant for the impact force, will be reduced by the movement of the belayer.
At the same time it is important to note, that the movement of the belayer can also be dangerous. In falls with a high fall factor the belayer will really be jerked upwards. This can in some cases lead to injuries. The only way to prevent this is by ensuring that you have enough manoeuvrability, which means that the belay position is ideally a few metres under the first protection point, so that the belayer can be hoisted a large distance.
If the rope is allowed to sag a little, the fall height and the rope length increase equally. This can have both a positive as well as a negative effect on the fall factor. For f<1 the fall factor increases and the fall becomes harder. Therefore slack should be avoided. In falls with fall factor f≥1 the fall factor becomes smaller with slack. The impact of the fall will therefore be reduced. It is also important to make sure that the increased fall height of the climber does not lead to a higher risk of accidents, for example collision with the rock face, the ground or even the belayer, if the fall height is longer than the payout rope!
Dynamic rope elongation describes how much the rope can stretch in the case of fall, which means how elastic the rope is. The more elastic the rope, the softer the fall. It is important to note here that the rope should not stretch so far that you will crash into the ground. There is an EN certification for this which designates that the dynamic elongation should not be more than 40%. Typical values lie between 28% and 35%.
Static rope elongation indicates how the rope stretches under static loads. So for example when you are top roping and attached to the rope or pulling equipment behind you. The value should be as small as possible, since you have to climb back up the stretched distance, or rather the equipment has to stretch by the proportion, that the rope has stretched by.
Fortunately, the tensile strength which a climbing rope must have is standardised. Every rope must therefore withstand at lease five UIAA falls and cannot exceed the determined threshold values for the impact force and static elongation. The threshold values themselves are different for single ropes, half ropes and twin ropes. UIAA fall standards have been conceived so that the resulting forces can in practice only be reached in absolutely exceptional cases (e.g. load over a sharp edge) – so in reality a climbing rope can is virtually unbreakable.