Impact force

This article covers the importance in climbing. For the hunting meaning see impact force (hunting) .

Impact force is a term used in sport climbing and mountaineering and describes the maximum force on the rope at the rope point if the climber falls. The climber feels this force as a jolt when the fall is stopped from the rope. The German version of the relevant standard EN 892 uses the somewhat more precise term impact force , but the shorter term impact force is used in climbing literature and is retained in the following.

To keep the impact force low, climbing ropes have a so-called fall elongation of up to 40 percent of their own length. The further a rope can stretch, the slower and less jerky the potential energy released by the climber during a fall can be transferred to the rope and the better the forces acting on the climber and the entire safety chain can be reduced. According to the Euro 892 standard, all climbing ropes must be able to withstand at least 5 standard falls (i.e. number of falls ≥ 5). Nevertheless, for safety reasons, a rope should be sorted out after a hard fall. However, with normal sport climbing falls, only fall factors <1 are achieved, which damage the rope significantly less than a hard fall (fall factor> 1) or even a standard fall (fall factor around 1.7).

In a rope team between two climbing partners, the weight factor is also a determining factor in the amount of the impact force. If the belayer is significantly heavier than the climber, a higher impact force occurs under otherwise identical fall conditions, which is perceived by the falling climber as a harder fall. If, on the other hand, the belayer is significantly lighter than the climber, in the event of a fall the belayer is pulled more strongly in the direction of the first intermediate belay or rope deflection, which can lead to the climber reflexively letting out the safety rope when hitting the climbing wall and consequently the climber falling into the ground. The DAV recommends taking additional safety measures if the climber is more than 10 kg heavier than the belayer. The previously specified weight factor has been dispensed with.

Standard fall

The impact force is measured in the event of a standard fall and must not exceed the values ​​specified by the EN or UIAA standard:

• Single ropes in a single strand: max. 12 kN
• Half ropes in a single strand: max. 8 kN
• Twin ropes in double strand: max. 12 kN

In practice, the impact force is smaller than with a UIAA standard fall, since the fall factor is smaller than the standard fall factor as soon as the rope runs through several securing points. As a result, the available rope length is greater, the rope can absorb more energy and the fall becomes "softer" with the same height of fall. At the same time, the friction between the rope and the securing points causes the rope to become effectively stiffer, which in turn increases the impact force. These two opposing effects can be described mathematically.

Physical considerations

The impact force for a dynamic climbing rope can be approximately easily calculated for the common HO rope model. Here the force on the rope is approximated using Hooke's law . This describes the elastic behavior of solids, the elastic deformation of which is linearly proportional to the applied voltage . The proportionality constant is the modulus of elasticity E, a material constant that is independent of the rope length and the rope cross section. ${\displaystyle \varepsilon }$ ${\displaystyle \sigma }$

Impact force depending on the fall factor with E q = 33.3 [kN]

${\displaystyle E={\frac {\rm {Spannung}}{\rm {Dehnung}}}={\frac {\sigma }{\varepsilon }}={\frac {F/q}{x/l}}}$

F: force, q: cross-sectional area, x: expansion (= Δl change in length), l: length of the rope.
From this follows the well-known relationship between force and elongation.

${\displaystyle F={\frac {E\cdot q}{l}}\,x}$

E · q / l = D is the usual spring constant , which depends on the length l.

In order to calculate the energy that is in the rope when the rope is stretched x, one has to integrate the force along the path from 0 to x.

${\displaystyle {\rm {{Energie}=\int _{0}^{x}{F\,dx}={\frac {E\cdot q}{2\,l}}\,x^{2}}}}$

For the maximum rope elongation x _max after a fall height h, the potential energy mg (h + x _max ) is set equal to the elongation energy. At the lower turning point, the entire potential energy has been converted into strain energy.

${\displaystyle {\frac {E\cdot q}{2\,l}}\,x_{\rm {max}}^{2}=mg\,(h+x_{\rm {max}})}$

Solving for the maximum rope elongation x _max gives:

${\displaystyle x_{\rm {max}}={\frac {mg\,l}{E\cdot q}}+{\sqrt {\left({\frac {mg\,l}{E\cdot q}}\right)^{2}+{\frac {2\,mg\,lh}{E\cdot q}}}}}$

The impact force F _max = (E q / l) x _max then results after inserting x _max :

${\displaystyle F_{\rm {max}}=mg+{\sqrt {(mg)^{2}+2\,mg\,E\cdot q{\frac {h}{l}}}}}$

The impact force depends on the fall factor f = h / l, as well as on the material constant E, the rope cross-section q and the weight of the climber. Typical experimental values ​​for E · q of single ropes are in a range from 30 to 50 [kN]. The more rope is spent, the softer the rope becomes, which just compensates for the higher fall energy. The maximum force on the climber is F _max reduced by the weight of the climber mg.

In the case of a secondary fall without a slack rope, i.e. fall factor h / l = 0, the impact force F _max  = 2 mg; d. H. a load with twice the body weight.

However, this simple, undamped HO model of a climbing rope cannot adequately describe the behavior of real ropes for the entire fall process. This can be explained if the undamped HO is supplemented by a nonlinear term up to the impact force, and then, close to the maximum force in the rope, an internal friction is added in the rope, which ensures that the rope relaxes quickly into its rest position.

As soon as the rope runs through several carabiners, an additional type of friction must be taken into account, the so-called dry friction between the rope and the carabiners. The last clipped carabiner is particularly important in the event of a fall, as the deflection angle for the rope is a maximum, i.e. H. Becomes 180 °. Dry friction results in an effective rope length that is less than the "spent rope length" (that is, the rope length between the climber and the belayer in an unstretched state), which increases the impact force. Dry friction is also responsible for the rope pull , which always occurs when the rope runs over bumps in the rock or through several securing points that are not in line. This rope pull can be described by an effective weight of the rope, which is always greater than or equal to the actual rope weight. It depends exponentially on the sum of the angles that arise when hanging in the securing points.

See also

• Knot strength
• HMS backup

Individual evidence

1. ↑ DIN EN 892: 2012-11, Mountaineering equipment - Dynamic mountain ropes - Safety requirements and test methods ; German version EN 892: 2012
2. ^ German Alpine Association: Sport climbing: belaying with weight difference. 2017, accessed February 7, 2018 (eng). 
3. ↑ ^{a b} Leuthäusser, Ulrich: Physics of climbing ropes: fall factors, impact forces and rope drag. (pdf; 195 kB) 2011, accessed on January 18, 2011 (eng). 
4. ^ Leuthäusser, Ulrich: The physics of a climbing rope under a heavy dynamic load. In: Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology. doi : 10.1177 / 1754337116651184
5. ↑ Physics of a climbing rope. 2015, accessed June 28, 2016 . 

literature

• Pit Schubert, Pepi Stückl: Alpine curriculum , vol. 5 (safety on the mountain, equipment, safety). Munich: BLV, 2003. ISBN 3-405-16632-2