Talk:Fall factor/Archive 1

Description of equation wrong
mg can no be the mass of the climber as the result is a force, not a mass. I assume, m is the mass of the climber and g is the acceleration due to gravity (9.81 m/s2 near the surface of the earth). — Preceding unsigned comment added by 131.152.143.41 (talk) 14:20, 27 November 2013 (UTC)

Irrelevant for most sports climbing scenarios
It should be mentioned somewhere that all considerations here are relevant only if the belayer is considered fixed - which is not the case in ALMOST ALL sports climbing scenarios, i.e. 1 pitch routes. And even in multi-pitch routes the belayer has at least some distance to the anchor which softens the impact acceleration considerably compared to what is calculated here!

--Felix Tritschler (talk) 17:51, 30 October 2013 (UTC)

What is the original source for the fall factor of 2?
How did people first calculate that a fall factor of 2 is as much as the human body can withstand? I've heard at least one rumor on this issue which is described in this mail I tried to send to snopes.com (but their submission form is broken):


 * I'd like to submit a rumor on the origins of the climbing fall factor. The fall factor is the amount of force due to de-acceleration that a human being can tolerate. See e.g. this Wikipedia article on the matter:


 * http://en.wikipedia.org/wiki/Fall_factor


 * The rumor that I've heard several times in climbing circles is that the original source for what the human body can tolerate in these circumstances are medical experiments performed by the Third Reich in Germany during World War 2.


 * However I haven't found anything online supporting this assertion, one paper which I've found which discusses fall factors located here:


 * http://www.rockclimbing.com/cgi-bin/forum/gforum.cgi?do=post_attachment;postatt_id=746


 * States in its acknowledgements section that:


 * "Calculations like these have been published many times over. As best as I can tell, their origin goes back to Belaying the Leader, Richard M. Leonard and Arnold Wexler, Sierra Club Bulletin 31 (1946)"


 * It would be interesting if you guys could debunk this and find out what is the original source for how much de-acceleration a human body can tolerate. Did someone do practical experiments on this (like the rumored Third Reich) or is the source derived from calculating how much stress the human skeleton can take or something else entirely?

The sources cited in this article don't give a definite answer to this question, it would be interesting if someone could add them. --Ævar Arnfjörð Bjarmason 16:34, 11 December 2009 (UTC)

92.14.248.136 (talk) 19:50, 8 February 2011 (UTC)

Since the Fall Factor is defined as the length of the fall divided by the length of the rope, a climber can only climb up to the length of rope above an anchor point. Hence the total length of the fall can be up to twice the length of the rope, hence the limiting value of Fall factor two as the text says under the section on Lead Climbing. It has nothing to do with the amount of de acceleration that the human body can tolerate. For information on that topic, see http://www.hse.gov.uk/research/hsl_pdf/2003/hsl03-09.pdf.

Units of variables needed
Please provide the units for the variables used in the equations (F, k, U, m, R, g). A diagram or two would also be useful. —Preceding unsigned comment added by 174.25.59.149 (talk) 06:37, 28 October 2010 (UTC)

Arguments for the new version of December 4, 2010
The last version contained several errors, unclear passages, and uncommon use of variables and expressions: --Iratheclimber (talk) 10:36, 4 December 2010 (UTC)
 * 1) Formula for maximum impact force F1: With the spring constant k as it is used in physics, the dependency on the rope length is not correct (when k is defined as Elasticity modulus the dependency on the rope’s cross section is missing).
 * 2) The calculation of k with parameters of the UIAA standard fall conditions is not transparent and not correct with respect to the dimensions. A more transparent formula is given with an explanation for its use.
 * 3) Used variables such as r for length of rope and l for fall height are uncommon in physics and were replaced. The variable k as modulus of elasticity is not correctly used (see point 1.)
 * 4) “Maximum impact force” is usually only called “impact force” by rope manufacturers.
 * 5) A section on the deficiencies of the undamped harmonic oscillator model for describing a climbing rope has been added.
 * 6) The formula of the impact force when the rope is clipped into several carabiners is cancelled, because 1. no reference is given (the cited reference does not show it), and 2. the situation is not described correctly, e.g. the angles between rope and carabiners for the dry friction are not considered (for the same number of carabiners a zig-zag clipping leads to more dry friction than a straight line clipping).
 * 7) The order of chapters has been changed: theory at the beginning, applications at the end.
 * 8) The references have been classified according to true references and external links.
 * 9) “Category” has been expanded to include physics

-- I am not happy with the current formulation of the page. While I appreciate the original research of Ulrich Leuthäusser, published on his website, this is a classic case of Original Research that is not suitable for the Wikipedia. My main complaint is that this is not "Fall Factor" as understood in the climbing community, but instead is a considerably more thorough examination of rope physics - and thoroughly confuses the matter. I suggest that the article would be MUCH BETTER if it was based on Goldstone's article (published in the prestigious journal Rockclimbing.com) and the other 'External Sources'. Not sure how many people are following this article... please pipe in with an opinion. Thanks. Ratagonia (talk) 21:12, 18 July 2013 (UTC)


 * 'My main complaint is that this is not "Fall Factor" as understood in the climbing community, but instead is a considerably more thorough examination of rope physics.' I think you're confusing the definition of the fall factor with the physical justification for using it, which involves relating it to the maximum force.--75.83.76.23 (talk) 14:30, 15 August 2013 (UTC)

Worse, the final formula (for Fmax) cannot possibly be right, because it doesn't depend on h, the supposed height of the fall. (Clearly a fall of one metre vs one millimetre will result in very difference forces, even if the fall factor is the same.) Sadly, I don't know enough physics to fix it. — Preceding unsigned comment added by 92.28.129.66 (talk) 20:54, 9 August 2013 (UTC)


 * "the final formula (for Fmax) cannot possibly be right, because it doesn't depend on h, the supposed height of the fall" It depends on f, which depends on h. I haven't checked the derivation, but the result for the maximum force is not obviously wrong.--75.83.76.23 (talk) 14:30, 15 August 2013 (UTC)


 * I'm puzzled by that formula. If it's right, why does Fmax tend to 2mg (two gravities) when f tends to zero? Why doesn't a fall of 0m result in an Fmax of just one gravity, as when at rest? Munrogue (talk) 15:42, 26 August 2013 (UTC)
 * Oops. Answering my own question, it's because a fall of factor 0 is still a fall (onto a slack rope, tensioning it). The average tension over time will be mg, as when hanging on the rope, so under the harmonic oscillation model the tension will cycle between 0 and 2mg.
 * It's true that "a fall of one metre vs one millimetre will result in very difference forces, even if the fall factor is the same," but that's because elasticity elsewhere in the system (eg the climber's body) isn't being modelled. (Admittedly, the description is wrong(?) because h doesn't appear in the formula. (Correct this?))
 * To answer Ratagonia, fall factors are used in work-at-height regulations, so they're not just about climbing. Munrogue (talk) 08:09, 27 August 2013 (UTC)


 * I'm not sure I made my point well. I am not disputing Iratheclimber's formulation, I am disputing its use as a Reliable Source on the wiki. I am also disputing that it represents the concept "Fall Factor" as used in the climbing community. I think the article would be better if it discussed the simpler model which I know as "Fall Factor", rather than this more complex model. Would anyone like to address these points? Ratagonia (talk) 01:39, 28 August 2013 (UTC)


 * Could you be more precise about "the simpler model which I know as Fall Factor?" If you mean the undamped harmonic oscillator, I would oppose reverting to that because high viscosity is a design goal of dynamic rope manufacture, without which impact forces would be much higher (viscosity-induced friction acts as a braking force throughout the stretch; elastic braking is concentrated at the end by its quadratic charateristic (see Hooke's Law).
 * I don't like the way this article brow-beats the reader with physics almost immediatly, but if Ira's list of criticisms is right, the previous version was far worse (especially the howler of conflating UIAA impact force with maximum impact force, the breaking strain of the rope).
 * If there's a problem with WP:OR a more suitable source should be found, but there's such a thing as letting the best be the enemy of the good: a bad article on this subject could literally kill someone! On that point, my opinion is that the opening paragraph should make clear that fall factors are NOT proportional to impact forces under ANY model. I've heard several climbers (including sales staff in outdoor shops) blithely assert that halving the FF halves the impact. It does not (VERY roughly, in practice it lops about a quarter off).
 * The article should also record that the UIAA test half-ropes with 55kg loads, not 80kgs, and their impact forces (circa 5-6kN, vs. 8-9kN) reflect that. Munrogue (talk) 11:04, 30 August 2013 (UTC)