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This section is dedicated to present selected papers discussing themes related directly to the climbing Physics. There are papers written by Brazilian climbers and by authors from other countries. Some are cited in the Brazilian papers so that some information can be verified at the origin. As Brazilian papers are translated into English, they will be published on this page as well, for the English-speaking readers to have access to the technical discussion about specific Brazilian issues. The optimistically expected production rate is one new paper in English per month. The site welcomes any comments, critics or questions from people that, although outside the country, are still interested in the Brazilian climbing environment. Whenever possible, new pages in English will be available. A warning about downloading, this provider for an unknown reason mix the files' names when you download, so rename them to know what they are.

The Special Formula of the Maximum Impact Force
P. P. de Lima-e-Silva (2019)

The classic formula of the maximum impact force (FMAX) on a falling climber is improved. It is special because it is restricted to free fall. The Experimental Model 1, or EM1, is a semi-empiric and more realistic model for it takes into account factors ignored by the classic model, the dynamic belay (DB) and the friction on the last carabiner (LCF). Besides, the EM1 introduces a formula for the maximum force on the last anchor (FBOLT). The study has sought to explain the apparent paradox between estimated FBOLT values supposedly higher than the P-bolts resistance in Brazil. The methodology included a historical summary, literature review, facts from experience, and sensitivity analyses. The comparison between FMAX and FBOLT estimated with the EM1 and classic model revealed striking differences and may explain the absence of accidents in Brazil due to P‑bolt failure. The EM1 produces FMAX and FBOLT values remarkably lower and more realistic, allowing better estimates of the risks.

Physics of climbing ropes: impact forces, fall factors and rope drag
Ulrich Leuthäusser (2016)

One result of this paper was that viscous friction can be approximately neglected until the force maximum and irrespective of nonlinear forces a harmonic oscillator model is a good approximation. On this basis it is shown in the following how a climbing rope behaves in the case of one or more protection points (usually bolts with quickdraws) between leader and belayer taking into account the so-called dry friction between rope and the protection points. It turns out that dry friction leads to the same form of equations and thus the same expressions for dynamic elongation and impact force as in the case without dry friction, if the elastic modulus is redefined properly. Furthermore the rope drag is calculated depending on the number of protection points and the angle deviations of the rope at these points.

The omnipresent impact force formula for a climbing rope
Ulrich Leuthäusser (2016)

This work demonstrates the omnipresence of the known impact force formula. Although originally derived only for the straight fall with a linear elastic rope, it applies almost unchanged for many other, more complex fall models and situations. In the following we will derive the well-known impact force formula as simply as possible and show its importance for more complex fall models and situations. It turns out that the same form of the impact force formula can also describe falls with internal and external friction, with slack rope and under an oblique fall angle. It even appears in its original form in modeling rope brakes of belay devices.

Rope Behavior
Dave Custer (2006)

Custer develops a series of calculations and equations about the forces coming into play in rock climbing sport. This is not a paper, it is a collection of aspects into the climber fall phenomenum, that together reinforces the rationale around the issue. Custer has helped ceu‑ in the development of paper no.2, “The General Formula of the Maximum Impact Force” (“A Fórmula Geral da Força Máxima de Impacto”), and stays connected as a support from our ideas and dedication to develop in Brazil a climbing physics literature acceessible to non English-speaking climbers. The above text is a quick view, a tiny window from his sketchs about this hobby of us, the wonder of climbing mountains.

Bergsteigen und Klettern – was sagt die Physik dazu?
Tina Czermin, Peter Dullnig, Leopold Mathelitsch, Werner B. Schneider (2007)

Climbing has experienced a significant upswing (...) enhanced by the availability of artificial climbing facilities. These additional options (...) ​​including climbing in the school sports program. (...) For example, e.g. a school firmly anchored in Bavaria climbing is in the context of the differentiated physical education. (...) More and more schools are being equipped with climbing walls, both in sports halls and in the pubs. (...) But it should not be forgotten that physical laws set limits or framework conditions when climbing. On the other hand, technical developments help to approach these limits more and more or to provide the athlete with greater security within the limits. In this text, these physical aspects of climbing and mountaineering will be illustrated with some examples.

Incorporating Friction Into The Standard Equation For Impact Force
Jay Tanzman (2009)

This is kind of a technical report concerning a specific issue, the change in the apparent rope modulus during a climbing fall. Tanzman developed an equation to adjust the fall factor in order to account for this change. On his words: (...) the standard model makes simplifying assumptions. It assumes that there is no slippage of rope through the belay device, that the belayer remains motionless and his body does not absorb any of the energy of the fall, that there is no friction in the system, etc. While many of these factors differ unpredictably (...), and hence are dificult to incorporate (...) friction between the rope and the top anchor, is nearly always present. (...)This frictional force is conventionally assumed to be equal to (1/3)·T1. Since its effect is signicant and present in almost every fall, it would be useful to have a model which incorporates it.

Rope System Analysis
Stephen W. Attaway (1996)

This paper presents an analysis of the loads in a typical climbing rope system subjected to a dynamic loading from a fall. Several examples are illustrated to show how to calculate the force on ropes and anchors subjected to dynamic loads that are experienced by a falling rock climber. The force in a rope that is generated when a falling weight is arrested depends on how fast the weight is stopped. We will use the energy method to solve for the maximum strain energy in the rope. The effects of friction, dynamic rope modulus, and rope condition will also be considered. We developed some rules of thumb to help a lead climber place fall protection and understand the limitations. The amount of ‘safe’ lead out depended on the amount of rope that is between the belayer and the climber, the type and condition of the belay rope, and the type of anchor used.


Comment:      A Austrian Physicist with a lot of very good papers about climbing physics.

Comment:      An interview with nice President of Australian Climbing Association at Queensland Dave Reeve.

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