Fall Force calculator


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Trad climber
Topic Author's Original Post - Jan 29, 2010 - 07:14pm PT
I tried to find a fall force calculator online a while back (I believe Petzl used to have one), but I could not. So I did a bit of reading and made my own. Its real ugly and probably not very accurate (considering the holes in the literature).


Its at least kind of fun to see what kind of falls are necessary to start breaking biners!

Most of the force dynamics of a fall are fairly well known (ropes mostly obey Hooke's law, rope stretch is well measured, etc). However, the interaction between the rope and the top carabiner doesn't seem to be well documented. From what I can tell, Petzl and others have simply reduced this interaction down to single number, which in all likelihood they measured empiracally. Probably a decent estimation, but it would be more satisfying to seem some theory and some experimental results. Anybody know of such things? (See the references on the above page for the best theory I could find).

Additionally, it would be nice to calculate and also measure the effects of a dynamic belay. This one would be pretty easy, but I haven't seen anything on the topic.

Does anybody have better references? It would be fun to write a full software model of a fall.



Trad climber
Poughkeepsie, NY
Jan 29, 2010 - 09:03pm PT
You might have a look at these (two are in your references, and another one or two are in the Custer powerpoint you refer to. The most extensive model, which includes rope slipping through the belayer's hands, is the Italian one. I'm missing the more precise reference at the moment.

Even if you are just using the Wexler equation, I'd be concerned about trying to calculate the rope modulus from the so-called static elongation. You'd be better off using the manufacturer's impact force and converting that.

There is, by the way, some absolute garbage out there:

I'd suggest not putting up a calculator without an accompanying account of how it arrives at its results.

Attaway, s. W.
Rope Systems Analysis
International Technical Rescue Symposium
Albuquerque, NM (1996)

The Mechanics of Friction in Rope Rescue
International Technical Rescue Symposium
Fort Collins, CO (1999)

Attaway and Weber, C.
Predicting rope impact forces using a non-linear force deflection.
International Technical Rescue Symposium
Denver, CO (2002)

Attaway and Beverly, J.M.
Measurement of dynamic rope system stiffnes in a sequential failure of lead climbing falls.

Bedogni, V.
Computer mathematical models in belaying techniques.
Nylon and Ropes for Mountaineering and Caving
Torino, Italy, (2002)

Bramley, A., Philips, A., and Vogwell, J.,
Forces Generated in a Climbing Rope During a Fall
The Engineering of Sport 6

Custer, D.
An estimation of the load rate imparted to a climbing anchor during fall arrest.
Engineering of Sport, 6th International Conference
Vol I pp 45--50 (2006).

Powerpoint version

Leonard, R.M., Wexler, A.,
Belaying the leader
Sierra Club Bulletin 31 (7) (1946)

Manin, L., Richard, M., Brabant, J.-D., and Bissuel, M.
Modeling the climber fall arrest dynamics
ASME International Design Engineering Technical Conferences and Information in Engineering Conference,
IDETC-IEC 2005, pp 1077--1084,
Long Beach, CA (2005)

Manin, L., Richard, M., Brabant, J.-D., and Bissuel, M.
Rock climbing belay device analysis, experiments and modeling,
The Engineering of Sport 6, Vol 1 pp 69--74, Springer (2006)

Pavier, M.
Experimental and theoretical simulations of climbing falls
Sports Engineering 1 (2) pp 79--91 (1998)

Derivation of a rope behavior model for the analysis of forces developed during a rock climbing leader fall, The Engineering of Sport 1. (1996)


Jan 30, 2010 - 03:23pm PT
As rgold says, using the static elongation is going to throw things off a bit because at low loads the rope elongation isnt proportional to load.
Normally youd expect to see around 30% elongation at the full impact, most companies give this information but if in doubt 3-4% is nearish.
The karabiner factor is certainly complicated, it is possible to create a model using various fall factors and rope velocity but you need to do a lot of testing to get it accurate. (Ive got a model but it is not for publication). At the moment the best you can do is work on a factor of about .3 for small falls (less than FF0.4) and 0.65 for big ones (over FF1) and 0.5 for the rest. Unfortunately fall distance also plays a role so if its a big long one then some adjustment is needed but this is going to be complicated.
For an empirical solution the Bedogni is your man!
As it stands your calculator is underestimating the belayer loads by ca 40% and over-estimating the runner load by about 20% depending on what I input, even without allowing for belay slip which makes quite a difference to the end result. If you put in a more realistic elongation factor and fudge a bit with the belaying factor you start to get nearer the values we see experimentally.
The biggest problem with this sort of calculation or model is that there are many more dynamic effects in the system which are not generally identified correctly, the most common being the hysterises in the frictional effects (belay device and karabiner) which make some pretty drastic differences to some of the numbers.

Trad climber
Topic Author's Reply - Jan 30, 2010 - 05:50pm PT
Thanks guys, that is exactly what I was hoping for. I will bookmark those links in case I ever get motivated to write some code....


Jan 30, 2010 - 05:54pm PT
My math sucks so I use an inline Tractel load cell with a peak hold function to determine loads on my systems. It makes explanations to OSH engineers way simpler.


Jan 31, 2010 - 04:24am PT
One thing you might have overlooked is that you are working with climber weight (to give real world forces) but the rope test figures are with a solid weight. This 80kg weight represents the forces typically generated by a ca 90kg climber so you want to correct for this when you work out the elasticity of the rope.
Also Id pull the reference in Gear Strengths to the maximum theoretical force being only 9kN, there are plenty of test results which show whatever theory was used is wrong!
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