Physics of Mountaineering

Climbing is a fascinating sport with very complex requirements to psyche and constitution. Aside from practicing this sport, there are several topics which are interesting from a theoretical point of view. 

For instance, using methods of physics we can model climbing ropes or the force a climber feels in taking a fall. The very interesting topic of grade systems in free climbing comes from psychophysics. 

In addition we focus on multi-pitch climbing routes and provide theoretical answers to practical questions, such as what are the empirical values of a team’s climbing speed as a function of the climbing grade. 

We hope that the topics here may be useful to climbers, and perhaps even interesting to other people at the periphery of mountaineering and climbing.

Physics of Climbing Ropes, Part 1

Viscoelastic theory of climbing ropes: The popular undamped oscillator model which describes the characteristics of climbing ropes cannot explain fundamental phenomena, such as energy dissipation and the lack of oscillations under force. A viscoelastic model removes these shortcomings and can explain the empirical parameters of various manufacturers’ climbing ropes, such as impact force and static and dynamic elongation.


Physics of Climbing Ropes, Part 2

Impact forces, fall factors and rope drag: For all kinds of climbing situations, the impact force and the maximum elongation of a climbing rope are calculated by taking into account both internal viscous friction and dry friction between the rope and the protection points. The climbing situations can include an arbitrary number and placement of protection points. In addition, we calculate the rope drag that a climber has to overcome in order to move forward.


Physics of Climbing Ropes, Part 3

Viscous and dry friction combined, rope control and experiments: The full equations of motion for a fall in a climbing rope are set up and solved when both internal viscous friction and external dry friction between the rope and one anchor point are taken into account. An essential part of the work is to discuss how the belayer can control the fall by adjusting the rope slip in the belay device. The theory can fully explain measurements of the maximum impact force, the force on the belayer and on the anchor point with and without rope control.


Physics of Climbing Ropes

The dynamic failure process of a fiber bundle: an explanation of the fracture of a climbing rope: The fracture of a climbing rope is explained by means of a fiber bundle model in a dynamic loading situation. First, a general system of equations for the resulting forces and elongations together with a fracture criterion is established. After presenting several exact solvable cases for different fiber breaking probabilities, a nonlinear model with a mixture of different fiber types is applied to the fracture process of a climbing rope. Good agreement with norm fall experiments is achieved.



Grade Systems for Free Climbing

Difficult Difficulties in Free Climbing: About Objective, Subjective, Maximum, Mandatory and Overall Climbing Grades (still in German): What is the relationship between the free climbing grade system which is a subjective perception and the underlying, not directly observable, objective difficulty? Do we need the French global grade system (IFAS), if the maximum and the mandatory difficulties of a climbing route are known?


Climbing Speed of Teams

Climbing speed of teams on alpine-style, multi-pitch routes (in German): We give a rule of thumb for the average climbing speed of two climber teams as a function of the average difficulty of the climb.



Mountain Hiking

About walking uphill: time required, energy consumption and the zigzag transition: A physical model for walking uphill is introduced. It is based on simple principles like the conservation of energy and a force dependent efficiency coefficient. Excellent agreement with experimental data was achieved.