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TGT
Social climber
So Cal
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Jan 19, 2007 - 11:40pm PT
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The answer to all your equalization problems
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 19, 2007 - 11:54pm PT
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I did an analysis of the Cordelette and the Sliding X which end up being extremes in the physical model of a 2-anchor system. I'd be happy to send it anyone...
...in this model I correctly calculated the different performance of the test results.
You all may think this is obvious, but, the way the Cordelette works, each arm works in parallel. This means that when you try to extend the "master point" the stiffness will be determined by the stiffest arm, which is the shortest arm. That means that much more force will be on the short arm then the long one.
The Sliding-X works with both arms effectively in series, so the entire sling extends, reducing the force and equalizing it, except for the friction at the "master point" (the 'biner "pulley"). This is also possible to calculate to get the differential force on the arms.
Here are the details of the calculation... rgold might like to comment on whether or not this makes any sense... I am notorious for goofing up on this stuff...
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GOclimb
Trad climber
Boston, MA
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Jan 20, 2007 - 12:29pm PT
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Tito - that's right - that's why Wootles' test results typically show a 25% difference in peak load between the two arms of the uneven crossed sling.
I simply don't know how large a factor the friction over biners would be for the mooselette in the case of a hard fall. Yes, the cord has to run around three biners - the power point and two out of the three protection biners. But at least it has the potential to equalize pretty well over all three (or more) points.
Compare that to the CharlesJMM anchor, which only has full (potential) equalization within a narrow range of angles, or if all three pieces are within the same plane, or the equalette, which pretty much only equalizes on any two pieces at a time, except within a narrow range of angles where it can equalize over three or more strands.
GO
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ghand
Sport climber
Golden,Colorado
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Jan 20, 2007 - 01:04pm PT
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This guy seems to have forgotten his mooselette!
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Largo
Sport climber
Venice, Ca
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Jan 20, 2007 - 05:42pm PT
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Hey, Ed, if you were to try and break those figures down for us who never got past Cal.2 (and didn't want to even go that far), what would it all mean?
Thanks,
JL
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 20, 2007 - 06:07pm PT
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boy I guess I take up the mantel of "buzz kill" from Roger...
OK, simple...
The stiffness of the arms depends on their length and their "Young's Modulus" which is a constant property of the material (so it is the same independent of what the size of a sling, or the diameter of the rope, etc).
If an arm is shorter, it is stiffer, which means that you need more force to pull it a distance x.
When you tie a cordelette with arms at two different lengths, you are making the shorter one stiffer than the longer one.
When you apply force at the "master point", you are pulling both arms the same distance x, but the force on the short arm is higher than the force on the long arm, thus, the forces are not equalized. This is what the test found.
For the sliding-x, you are applying the force at the 'biner, which is free to slide. The entire sling extends, it is less stiff than either of the cordelette arms because it is longer. When you extend the master point it takes less force to move it x than in the case of the cordelette, and the force is equal in each arm, the 'biner allows the sling to slip around and equalize the forces as long as you neglect the friction of the 'biner sliding at the master point. The test saw this too.
The analysis of these two systems also agree quantitatively with the test, which gives me confidence that the analysis.
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Mighty Hiker
Social climber
Vancouver, B.C.
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Jan 20, 2007 - 08:12pm PT
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Another angle on this subject, so to speak, is the subjective side. Over half of mountain and climbing fatalities in western Canada are due to snow avalanches. A few years ago, 29 died in one winter. (The average is something like ten.) Partly due to that, the various governments decided to put some funding into looking at the subject.
There were already lots of introductory and refresher and intermediate and advanced and professional avalanche courses. Most backcountry skiers were taking them and practising the various skills they learned. Less so snowmobilers, and those being guided - though the latter usually got at least some introductory training.
I'm no expert, but used to teach introductory avalanche (and rock) courses, have been backcountry skiing for decades, and have lost ten or more friends. I've attended various programs on what has been learned, and it may be relevant to this discussion, as far as I understand it.
They've done a great deal of analysis, and looked hard at what's done in Europe and elsewhere. Some of what they've learned, which is being translated into tools for the recreational user, is objective. That is, create tools that can be easily learned and applied to assess risk and make decisions.
Some is what we call subjective. Crudely, that people sometimes do stupid things, often for environmental reasons. They include things like fatigue, poor conditions, lack of nourishment, group dynamics, and even composition of the party. (A party comprised of both males and females is more likely to get into trouble, especially if they're in the 15 - 30 age range. The males almost always end up in the decision making roles, and make poorer decisions.)
This seems to apply to anchors also. A lot depends on the objective factors - how strong and reliable is the gear, how strong is the rock, how well is the gear placed, is it well connected? And the SERENE stuff. And, how well people have learned about both the technical side, and the judgment and experience needed to apply it.
Failing belays aren't exactly common - there was one on the DNB of Middle Cathedral a few years ago, but fatalities are more common for other reasons. Some of it is the influx of new climbers, who're sometimes perplexed by a stance that doesn't have a fixed belay. (I've seen some who couldn't figure out that a healthy large tree in a forest abutting the top of the cliff was a perfectly good anchor.) Perhaps some is how they learn, given that so many now learn in courses.
In terms of constructing belays, we shouldn't forget the non-technical side. That is, are other subjective factors such as those mentioned relevant, and should be climbers learn to be aware of them? After all, how often do we simply think "We're in a hurry/it's getting dark/I'm hungry or thirsty/I need to look like I know what I'm doing so that chick will be impressed/I know what I'm doing even if that old fart says I don't"? Worse still, be affected by these things, but not be aware that we're being affected?
An example is commonly referred to on ST. The novice, setting up a toprope belay. Who may not be receptive to help or suggestion, for pride or similar reasons. (Interestingly, the typical adolescent male may be more receptive to such suggestions from females than males, AOTBE.)
Anyway, just some thoughts.
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TGT
Social climber
So Cal
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Jan 20, 2007 - 10:17pm PT
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All my preceeding posts have been jokes, but have kind of obtusely been generated by this point of view.
1. You can't teach mechanical aptitude.
2. The abillity to visualize the forces involved is not all that common.
3. No rule set can cover every or even a small fraction of belay anchor possibilities, or lack thereof.
Sometimes a good bucket to place your butt in really is good enough.
Sometimes the most complex multi piece anchor isn't.
knowing the difference, is more of a talent and or product of experience than a science project.
Now go forth and analyze the physics for another 170 posts. I'm not doubting the value of the analysis or that we all might learn something, just its practicality,
If you don't have the judgement and eye for the practical application all the theory in the world won't do you any good.
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knudeNoggin
climber
Falls Church, VA
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Jan 21, 2007 - 12:36am PT
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> How much wottle
> Would a Wootler wot
> If a Wootler would wot wottles?
ootles!
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 21, 2007 - 01:59am PT
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TGT - working out the physics taught me something important about setting up ALL anchors. I am probably still not explaining this very well, or maybe it isn't as important to someone else as to me...
...but the trying to understand the tests that were done allows me to generalize the lessons contained in the results.
The lesson? only the sliding-x equalizes a two point anchor. The problem is the extension on a blown anchor. The tests also show that in some situations, the extension of the sliding-x onto one anchor doesn't load as much as feared.
I sometimes use a sliding-x and tie in with the rope on the third anchor. Seems redundant and secure.
A cordelette has real problems when the arm lengths are very different, especially if you have poor anchors. There may be a situation where a cordelette is fine to use, however, especially with nearly equal arm lengths (I know wootles doesn't think so, but here I would probably believe the analysis).
The physical analysis of the two rigs, compared to the test results, allows for a general understanding which is useful, at least to me.
I have to admit, I was completely surprised that the cordelette was so poor in unequal arm anchors. That is worth a lot.
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Chiloe
Trad climber
Lee, NH
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Jan 21, 2007 - 08:51am PT
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The lesson? only the sliding-x equalizes a two point anchor.
I'd qualify that by saying that the sliding-X equalizes better than a cordelette. In the tests, friction proved to be a significant complication for the sliding-X, resulting in a median absolute difference of 1kN between arms in the unequal-length setup (compared with 3kN for the cordelette, but only 0.3kN for the "equalette"). That was the second unexpected result of the tests.
These comparisons, not all of them included in Wootles' data table, are visualized in the graphic that he posted earlier (from John's book):
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GOclimb
Trad climber
Boston, MA
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Jan 21, 2007 - 02:33pm PT
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Chiloe, I have a question about methodology. It relates the the chart in your post, and I'll get to that later.
1 - In the chart Wootles posted (the one where I circled several of the data points) each item got three drop tests, each with increasing values. The average absolute values vary a good bit from test to test.
2 - Wootles mentioned that in later tests, he used a rope that gave pretty consistent force values, and mentioned that the equalette drops were done on that rope.
So my question - were the numbers in your chart taken from those two different sets of drops? The reason why I ask is that for the percentage difference between arms, it seems to make very little difference how much force the anchor felt, so the methodology doesn't matter, but your chart shows delta in absolute value, not percentage value. So the different methodology could produce very different results.
If my point isn't clear, I could give examples.
GO
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rgold
Trad climber
Poughkeepsie, NY
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Jan 21, 2007 - 09:58pm PT
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if you were to try and break those figures down for us...what would it all mean?
I think the simplified answer is the one I gave a few years ago in a thread on rc.com BSX (before the sliding x thread):
In a fixed-arm system, arm tension is inversely proportional to arm length.
So if one arm is double the length of a second arm, the tension in the first arm will be half the tension in the second arm. These results are extremely simple consequences of the assumption that the rigging material obeys, at least approximately, Hooke's Law, but are strictly valid only for the situation when all anchor pieces are in a single vertical line.
Ed's calculations are considerably more complex because he wants to predict the anchor loads from the fall data. I was only interested in the way the anchor load, whatever it might be, will be distributed.
Now predictions based on idealized behavior may or may not be observed in practice. In the field, it is the climber who ties the arm lengths, which of course can never be perfect, and even if they were, the way in which small amounts of slack may or may not be released by the knot is unknown. Moreover, neither my simplistic formulation nor Ed's calculations nor Wootle's drop tests consider the effects of arms radiating from the power point at various angles.
The unequal arms in Wootles' posted chart were of lengths 100 (+/-) 3 cm and 45 (+/-) 3 cm, so the long arm is about twice the length of the short arm. Ideally then, the load measured at the long arm should be about half the load measured at the short arm. In the first two columns of Wootles' chart, this ratio is roughly apparent in about half the trials, rows 4,5,6,9,11,12, and 15, but way off in the other half. The lack of exactitude isn't suprising when one looks at the discrepancies from 15% to 35% in the equal-armed cordelette, which indicate just how hard it is to actually tie functionally equal arms.
What I get from the combined theoretical and experimental results is that equalization is unobtainable in principle when the arm lengths are unequal, but in any case the climber's best efforts to tie a correctly proportioned fixed-arm rig will nonetheless lead to unpredictable and perhaps significant inequities in load distribution. I think that in that post I mentioned above, I also said (and have since repeated) that for fixed arm rigging, you should probably assume that each piece will get the full load in turn. This turned out to be far more appropriate than I imagined, with 6 of 15 attempts at fixed unequal-arm rigging ending up with more than 80% of the load on one piece.
It has often been proposed that stretchier rigging materials would help to compensate for the inevitable small deviations from perfection made when tying fixed-arm rigging. I see little evidence for this in the data; spectra doesn't fare significantly worse in percentage difference in the equal-arm tests than stretchier materials like 7mm cord. The 6 mm cord does seem to provide a levelling effect, I'm not sure whether that cord it is spectra or nylon. The equalizing performance of webbing and cord might also be affected by differences in the way knots in the two emit or retain additional slack.
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cintune
climber
Penn's Woods
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Jan 21, 2007 - 11:05pm PT
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Wouldn't stored elastic energy introduce a whole new variable to deal with?
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rgold
Trad climber
Poughkeepsie, NY
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Jan 21, 2007 - 11:43pm PT
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You mean energy absorbed by stretching the rigging itself? In principle, yes, and I think Ed does this. In the case of a belayed leader fall, my guess is that the climbing rope and belayer tie-in would absorb most of the fall energy, and that neglecting the contribution of the anchor rigging itself would not be a source of substantial error. But this is just a hunch based on having tried once or twice to include such factors in a model only to discover that they made little difference
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Chiloe
Trad climber
Lee, NH
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Jan 22, 2007 - 09:33am PT
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GOclimb:
your chart shows delta in absolute value, not percentage value. So the different methodology could produce very different results.
Within these data, our general conclusions seemed reasonably stable. For example, percentage differences show the same ordinal pattern as absolute differences.
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 22, 2007 - 10:46am PT
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The elastic nature of the material is incorporated into the calculations above. The parameter "K" is the spring constant which defined by the product of the cross sectional area and the Young's modulus Y of the material:
K = Y*A
The force required to increase a sling of length L the distance x is then given by Hooke's law:
F = K * x/L
Where we can use the very good approximation that the material obeys Hooke's law. The agreement of the calculation with the data seem to support this assumption.
The idea of all these calculations is to equate the energy of a falling mass into the work done to "pull the spring."
This calculation is based on an idealization of the anchor system. I think it shows that to first order (which is good to probably 30% to 50%) that the major aspects of the anchor can be understood in this simple way.
That is impressive. Most "real world" situations are usually not well represented by such idealizations. Anyway, you can take it or leave it... I think the rgold has a wonderful way of expressing the essential features of the analysis. His conclusions are right on.
This physics helps us understand why something behaves the way it does. It's not intended to lead to a solution of the "anchor problem." In fact, it points the way to the likely conclusion that the "anchor problem" cannot be solved, that is, unextendable, equalizing anchor systems may not exist.
If that is true, then we start looking for other solutions for anchor systems.
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rgold
Trad climber
Poughkeepsie, NY
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Jan 25, 2007 - 12:07am PT
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Before asking such questions, it is important to check the sliding x thread on rc.com, where many rigging proposals have been made. I'm fairly sure your set-up hasn't been suggested, and it has a very nice way of dealing with extension in case a piece fails. Nonetheless, I don't think it is likely to be of much interest, for at least the following reasons.
1. It is for two anchors, and the equalette already does a good job with less complexity and more adaptability.
2. The two anchors have to be at the same level. If they aren't, one of the side rope pieces has to be retied. This makes the set-up impractical for many gear anchors.
3. When loaded off the vertical axis, one of the arms can slip down over the gate of the central biner. You'd be well advised to use two biners with the gates reversed there. But now your rigging uses twice the non-power point biners that the equalette needs.
Forget two-anchor rigging. The standard trad anchor is a three-piece anchor. The challenge is to find rigging for this that equalizes effectively, has a small extension if a piece fails and re-equalizes the load if this happens, can adjust to different directions of load, is quick and foolproof to set up regardless of the anchor configuration, and does not require excessive depletion of the party's carabiner supply.
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Largo
Sport climber
Venice, Ca
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Jan 25, 2007 - 10:47am PT
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Rich wrote: "Forget two-anchor rigging. The standard trad anchor is a three-piece anchor. The challenge is to find rigging for this that equalizes effectively, has a small extension if a piece fails and re-equalizes the load if this happens, can adjust to different directions of load, is quick and foolproof to set up regardless of the anchor configuration, and does not require excessive depletion of the party's carabiner supply."
That's exactly right. The solution is looming out there somewhere.
The interesting things about all of this is, to me, not all the number crunching (which guides the results, as it must), but in looking at this as a kind of riddle (which is currently is) waiting to be solved. The criteria has been stated--now meet it.
One thought: The sticking point so far is that with a two-point anchor, both arms of an equalette (or variation thereof) go to a sliding powerpointthat to some extent can shift and redistribute some of the loading once weighted. When strung to three placements, one or the other of the two arms is connected to two placements, while the other arm secures one placement, resulting in unequal loading across the three placements.
The first part of the riddle to figure out is how to rig something that A) still has a sliding powerpoint, and B) distriburtes equal loading to 3 placements.
In other words, how do rig a three-armed system that still has a sliding power point? I'm thinking the bottom of the loops between the three arms (the two "U" sections at the bottom of the sling between the three placements)have to be divided into two unequal strands (and left tied that way), with one strand of each "U" extended down a bit and drapped over the other and clipped off like a regular equalette. Can you picture that??
JL
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 25, 2007 - 11:30am PT
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From what I understand of the equalette, it is functionally in between the cordelette and the slinding-x..
The idealized sliding-x is one long piece of sling which is free to distribute the load over the entire sling.
The cordelette can be thought of as individual slings connected to a single master point, each sling undergoes an identical elongation (thus unequal forces for unequal sling lengths).
I assume the equaletted is in the new edition of the Anchors book, I'll try to find a copy and take a look. Perhaps rgold can describe it functionally here.
My guess is that there may be no ideal way of solving the problem, that every solution will have limitations that will need to be understood... the problem might be more complex than to admit a simple solution.
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