How do you calculate how many kN are generated in a fall?


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May 10, 2012 - 12:33am PT
lol ^^^^

Trad climber
The pitch of Bagalaar above you
May 10, 2012 - 12:34am PT



Trad climber
May 10, 2012 - 03:07am PT
Lab results can and do provide very important information.

Lab results can provide a lot of information on "how to use gear to get the most it can provide". Those kNs and other numerical stuff are intermediate outcome. It's more for comparison and development the best strategies than for direct in-field usage.

Anyway belay is just a belay. It's not a lifesaver. No guaranties. It's the last frontier - if belay actuate you definitely did several mistakes one-by-one and allowed the situation gets out of control when your (and your buddy!) health and life depends on kN, wires, materials elasticity/braking strength and other technical stuff not on your skills. It's a defeat.

It doesn't mean we should not make a belay in mountains - it's a chance and we can develop our skills and modern gear is good enough (e.g., ref. thread) so the chance would really count.

Nowdays we have excellent gyms where we can fall on a perfect belay many times each day to learn and push our limits. But in mountains belay is just a belay - the last frontier without any guaranties.

Trad climber
The Windiest Mountain, Wyoming
May 10, 2012 - 04:12am PT
It's actually very easy to measure the force if you use a car as the top anchor. Simply attach the rope to the car by wrapping it several dozen times around the driveshaft (this is easy to do if you jack up the wheels and run the engine a bit).

Now, place the vehicle in neutral and start climbing. When you fall, you'll hear the car 'peel out'. Measure the length and thickness of the strip of black rubber and you'll very easily be able to determine the force vs time.


Trad climber
May 10, 2012 - 04:34am PT
Now, place the vehicle in neutral and start climbing. When you fall, you'll hear the car 'peel out'. Measure the length and thickness of the strip of black rubber and you'll very easily be able to determine the force vs time.

And don't forget to put on your Da Brim - skin cancer is able to wait.

Mountain climber
San Diego
May 10, 2012 - 08:26am PT

Thanks for your last post.

Social climber
Hercules, CA
May 10, 2012 - 10:10am PT
All models are wrong!

Some are useful.

Trad climber
Poughkeepsie, NY
May 10, 2012 - 10:58am PT
But with an actual belayer instead of a tied off tree stump it'll be different. These models don't address that difference.

The statement is at least sometimes true but the implied conclusion may not be. I say "sometimes" because friction in the system often contributes enough so that no rope slips through the belay, which is the primary mechanism for load reduction at the top anchor.

As for implied conclusions, when experiments are done with real belayers and climbers (as has been done extensively by the Italian Alpine Club), the performance of the system shows so much variation that almost no useful conclusions can be made about the effects of individual elements in the belay chain. The way in which various choices affect the loads is overwhelmed by the extreme variability in belayer performance, even when everything else is kept exactly the same. (We don't like to think our belaying is subject to wide variation but, apparently, it is.)

This is one of many applied situations in which a good mathematical model is almost a necessity if one wants to study the effects of various elements. (For an example of such a study, more than about 20 cm of lift for the belayer contributes nothing further to peak load reduction on the top anchor.)

The standard equation mentioned is the first stage of a modeling process which has to be extended considerably to get something that gives consistent good agreement with real-life performance; as I said above the standard equation tends to overestimate the loads. There are several far more sophisticated models (involving more computation but almost nothing new in terms of the basic ideas), including one by the CAI, that correlate far better with results obtained with real belayers and leaders.

All models are wrong!

Some are useful.

Absolutely! One of the things that seems to confuse people is that being "wrong" is part of what makes a model a model. If you don't ignore some of the details of the system you are modeling, then you don't have a model, you have an exact replica of the system. Of course, the devil is in the details you chose to ignore...

May 10, 2012 - 11:21am PT
No one has mentioned in this complexityfest whether the rope has just previously held an earlier fall. And whether it is fresh out of the bag and further did not spend years on the shelf. Years ago when I needed to know the peak force that would be exerted on these nut things, I went out and measured it,

(Oh yes, some tests I did in the nuclear reactor at the National Bureau of Standards revealed that the catalyst used in the manufacture of nylon remains in the nylon. I am not surprised that nylon has a shelf life.)

The numbers were surprising.

First I tied a loop in 8mm perlon but put a drilled out cylinder of plastic on one leg of the rope, fixed to the sling on one end by pushing a finishing nail through the perlon. There was another nail pushed through the perlon such that when the perlon stretched it would push a brass slider along the plastic cylinder. By measuring its position after the fall you could estimate the peak force to which the perlon had been exposed. I calibrated the rig using using static loads applied by a tensile machine. (We had a tensile machine at work so we could test to see whether our work on shooting down missiles with high powered lasers was getting anywhere. Apparently we weren't.)

I need to set the scene. The McCarthy wall is a good place so I went there, Just to the right of Something Interesting. There is a prominent overhang( surprise surprise) about 70 -80 feet up. I put in a piece of protection so that if I hauled 165 pounds of shale in an army duffle bag up to the ceiling and dropped it, it would free fall around forty feet. It was tied in with a waist loop and came to rest ten or fifteen feet up, i would guess. Almost a ground fall.

As an aside I also did an experiment with a really poor nut and stayed right at the placement during the test. The bag went winging past me but the nut followed so swiftly I never saw the manner in which it failed. I had backed the whole system up to an old piton. The old piton also followed directly leaving a cloud of rust in the air. As I was well up the wall I was spared having my friends detecting my embarrassment. They were more interested in all of the excitement, I suspect.

Now the surprise. When I just anchored the belay rope to a big tree trunk we got a peak force of 1000 pounds. When I belayed the fall with me anchored to the same tree I was whipped up into the air. In that case the peak force was about 500 pounds. This is why I keep railing against belays directly off anchors. Doing so makes one imperturbable, but you are not doing good things for the leader.

Using the generated forces to accelerate a second massive object is a really good idea. Go to accounts of poorly protected leads on gritstone to see how shrewdly the Brits use the idea of a second massive object. A natural shock absorber.

My main concern was not in modelling to allow a calculation to approximate the measurements. When I held the belay I successfully showed myself the fall was a doosey. We know ropes and carabiners are very hot after a big fall and there was a lot of lateral whipping in the system that would extend the peak force application over time. The dynamics of the system have to play a role.

I had what I sought. When my hydraulic system put 3000 pounds on a nut during later experiments

I knew I was in the ball park.

Someone above mentioned wishing they could predict when a nut will fail (and how). I published an approach to that back in 1971 based on shear modulus. I have repeated it endlessly since

to no apparent result.

Suffice it to say I have had only one nut fail on me and that was a small brass RP

in Eldorado. I concluded falling in Eldorado is probably

not a good idea.

Sandstone. Well metamorphosized

but still.........


It will groove.

Trad climber
Poughkeepsie, NY
May 10, 2012 - 11:23am PT
Climbing safety is an experiential thing, testing in the lab is of little consequence.

Well, yes and no. For example, how you place your favorite single blue Camelot belay anchor of course influences how effective it will be, but the fact that you have such a device at all and the fact that it responds in ways that are capable of correlating with "experience" is because of the sophisticated engineering thinking (logarithmic spiral cam outline) and testing (appropriate cam angle) that went into it. The fact that all this work is hidden as your experienced eyes seek out and find the ideal placement and you slide that cam in should not be mistaken as the primacy of experience over "testing."

And frankly, climbing experience is a wonderful thing, but still has very substantial deficits as a way of understanding what practices are best.

The fact of the matter is that our decisions are never subjected to robust testing and sometimes are not subjected to any testing whatsoever (consider the tiny fraction of climbing anchors that have been subjected to a factor-2 fall, and compare that to the number of climbers who are certain they have built a "bombproof" anchor, in spite of the fact that not one of their anchors has ever been subjected to a worst-case scenario test).

In this regard I'm reminded of some tests conducted, I think, by the DAV that found, unsurprisingly, that very experienced climbers had no ability to judge the worth of fixed protection. The same is surely true of bolting, where only a substantial testing program can ever tell us what best practice should be.

Trad climber
Poughkeepsie, NY
May 10, 2012 - 03:43pm PT
I would like to add that, even if many people were unaware of it, that John's tests played a hugely significant role in climbers accepting the use of small nuts and so in the transition away from pitons.

At the time, it was commonly assumed that smallish wired nuts were aid pieces. John went out and did his tests and realized they could be used for protection. More than that, he developed an excellent sense of how far one could climb above such things. Then he put his money where his mouth was and did scores of ground-breaking ascents with those small nuts, ascents which don't see a whole lot of traffic from today's climbers.

I really believe that John's knowledge, obtained from testing and then refined by experience, spread from him to the rest of country. His partners learned to use and trust small gear from him, and as they traveled, they spread John's knowledge. (Of course, there were people in other areas who placed small gear, but unlike John, they generally did not have a good idea of what kinds of loads the gear would or would not take. John knew.)

Years after John's tutelage, I still found myself climbing with climbers, some quite prominent, who didn't trust small gear and didn't even want to bring it on our climbs, and so were still carrying pitons. I once did a long climb in which my partner placed a piton on every pitch he lead and I never had to place a single one, because John had taught me about the use of small gear.

What happened here is that John's tests turned into what others, who may not even have known about those tests, viewed as experience.


May 10, 2012 - 04:28pm PT
It was a very exciting time.

Everyone was learning.

It is a very sad thing when people try not to learn.
Jay Wood

Trad climber
Land of God-less fools
May 10, 2012 - 05:03pm PT
If the question behind the question is whether micro nuts are worth carrying on a trad rack,

I would say yes. As Tornado said- light, and fit where nothing else will. I have used them even for anchors when nothing else worked. It's not only about maximum strength. Sometimes I bring a few small cams and some micros when using someone else's rack, for back up.


Trad climber
Poughkeepsie, NY
May 10, 2012 - 05:50pm PT
Del, the CAI found tremendous variation in results when human belayers were involved. That point had nothing to do with belaying off tree stumps, and I did not mean to suggest that human belayers were equivalent to static belays.

On the other hand, if I recall another paper I read, belayers who jump backwards, as they sometimes do to try to prevent a leader decking, or belayers who mis-time a jump dynamic belay, can achieve anchor loads in the same range as a tied-off anchor. In other words, within the range of human behavior are, albeit very occasionally, loads of the sort you might get from a gri-gri on a tree stump.

As for preferences, I take the human harness belay any day when climbing. But if I want to understand the effect of lifting the belayer, then a sophisticated mathematical model will probably be much better.

Trad climber
Poughkeepsie, NY
May 10, 2012 - 06:20pm PT
Yeah...brevity is not a virtue I have ever acquired.

(Just for fun I tried it here.)

May 10, 2012 - 09:17pm PT
The following youtube seems almost comedic till you think about what it is showing.

The kinetic energy of the falling climber is transformed directly into raising the belayer. This extends the time interval during which the force is applied to the top anchor. We are working in integrals here. If you integrate over a very short time the peak forces have to become much increased.

OK a real example. When I freed To Have and To Have not (just some aid climb - nothing to lose your blob over) there was only one nut in the system. A number three stopper. I had no idea what problems lay ahead meaning I had to plan on a forty footer on that one nut. So I had my 110 pound wife belay me unanchored, I judged she still felt I was a halfway useful guy and would hold onto the rope. I had her stand out from the base of the cliff. That way as she was dragged into the cliff the initial transient in the force would be limited and would increase substantially only as she would be shot up into the air. I think it is really important to avoid very sudden shocks to protection. Doing an integration when you have a singular argument causes all kinds of difficulty. Go ahead - ask Hartouni. Those residues are something awful. It was a steep descent but I was not into the Steepest Descent Method(Copson).

And oh yes. There was a subsequent divorce.


May 10, 2012 - 09:25pm PT
Tell me about it!

I would have asked Bragg to belay me, even at his larger weight and higher peak force, but he was off somewhere putting in Gravity's Rainbow. Kids! They never stick around.
Ed Hartouni

Trad climber
Livermore, CA
May 11, 2012 - 12:32am PT
Doing an integration when you have a singular argument causes all kinds of difficulty. Go ahead - ask Hartouni. Those residues are something awful.

If the integrand you desired
Near an analytic function required
To find the closed path in the complex plane
Corresponding to your real interval's a pain
Ask Richard Goldstone for some advice
His teaching experience will suffice

Trad climber
Poughkeepsie, NY
May 11, 2012 - 01:47am PT
A physicist name of jstan
had a bold and unusual plan.
But from the crux pitching
he heard his wife bitching,
"I need to be tied to a van!"

A climber named Stannard one day
had to make sure a nut would just stay.
So he roped up his wife
and caused marital strife
when she flew up the cliff on belay.

A climber who might have seemed callous
had a need to stay out of the talus.
So his wife he employed
as a counterweight droid
which she took as a sign of some malice.

It turned out to be Stannard's lot
to free the climb Have or Have Not,
To keep a nut tight
his belayer was light
and up in the air she was shot.

D Fred

Trad climber
san francisco, ca
May 19, 2012 - 02:15pm PT
i'll be damned, you're right...

BD #6 stopper rated at 10kN is the same size as BD C3 00 cam which is rated to only 6kN

go nuts!
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