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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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bobh
climber
Bishop, California
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Jan 25, 2007 - 12:34pm PT
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The potential for minor-axis loading of the power point biner in the anchor pictured above is something that should really be avoided. As pictured, this is a bad rig. Additionally, both this anchor and the mooselette anchor reduce extension at the expense of putting some 'american-triangle' type force amplification on the lateral anchor points. Something to consider when tabulating the pros and cons of each system.
Interesting discussion. Love your anchor books, John.
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Ksolem
Trad climber
LA, Ca
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Jan 25, 2007 - 01:03pm PT
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This is an interesting discussion with some good examples as well. But, practical application in the field is another story. So I have a question or two for all of you anchor scientists.
First, how often, when you set an anchor system at the end of a pitch, do you really think there is a possibility that one or more of your pieces might pull if loaded?
Also, given the fact that there is a limit to how much stuff one wants or is able to carry up a hard pitch, what would you rather have when you arrive at the belay - 20 ft. of 7mm cord and 6 or 8 extra carabiners, or a couple extra cams and nuts to choose from.. ?
Not to say that equalization is not important, especially if you are in the unfortunate position of having a dicey anchor. But I usually look at the multiple pieces in an anchor as backups. I use the rope to clip in, usually in series without any slack between. Of course I am usually swinging leads, not guiding, so this is not inconvenient. And with only 35 years of this under my belt I guess I am due to get chopped any day now anyway... :-)
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rgold
Trad climber
Poughkeepsie, NY
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Jan 25, 2007 - 02:07pm PT
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Ksolem, I do something similar much of the time, and it wouldn't be surprising to find JL did too. I've never had a piece pop on a loaded anchor, but I do know people who have and have read about others.
But regardless of whether or not it seems likely that gear will fail, perhaps you might change over to something that didn't load your anchor pieces sequentially with the full load if the new method was almost as quick and easy as your series of clove hitches and didn't eat up a good part of your rack for two belays.
Moreover, for better or worse, climbing is heading in the direction of "foolproof" systems that enable people who have not acquired experience through a long apprenticeship to participate. Direct rope tie-ins were replaced by swami belts which where, in turn, replaced by harnesses, which have now been replaced by harness with buckles that don't need to be back-threaded. Belay devices have been followed by autolocking belay devices, nuts by cams, and so on.
Traditionalists scream "foul" when innovations appear, but then, after a sufficient period of abstinence, embrace them. Gear that make things safer for novices typically has found favor with experts. The same thing will happen with rigging systems, if we can together come up with better ways of doing it.
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Ksolem
Trad climber
LA, Ca
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Jan 25, 2007 - 02:25pm PT
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RGold - I don't disagree, and I am not one to cry foul over new innovations.
How about the second question..?
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murcy
climber
San Fran Cisco
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Jan 25, 2007 - 03:16pm PT
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given that the alternative is a bunch of biners and too much fussing, why not have a special piece of gear, a "powerpoint biner", with a main locking compartment for the load and three little closed compartments (maybe with pulleys on them like those dmm revolver biners) for cordalette loops. keep a single, continuous cordalette loop running through all three pulley compartments. clip the three resulting loops of it to your pieces (shortening the cordalette with a butterfly if you like). that's as good equalization as you're going to get and it's instantaneous to set up because you'd keep it pre-tied.
for limiting extension have a bundle of three short "backup" cords with a figure 8 on a bight tied at their mutual end; the bight is kept clipped to (or tied through another special compartment of) the "powerpoint biner". tie the cords off loosely to each piece based on how much extension you want to tolerate.
one big specialty biner, one cordalette that can be a bit shorter than usual (no huge figure 8), one bundle of three cords that's about half a cordalette total in weight. compared to the old cordalette method, a bit heavier, but just about as easy to set up.
i don't know how important this stuff is compared to solid placements and just not screwing up etc., but it is a fun brain teaser.
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 25, 2007 - 03:35pm PT
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maybe I can answer as a scientist...
This is an interesting discussion with some good examples as well. But, practical application in the field is another story. So I have a question or two for all of you anchor scientists.
Practical applications is what we all are trying to get at, if the problem is susceptable to meaningful analysis, then that is a good place to start as it will make the principals important to a successful application apparent.
First, how often, when you set an anchor system at the end of a pitch, do you really think there is a possibility that one or more of your pieces might pull if loaded?
You never know, and experience isn't necessarily the answer. There is a finite probability that your anchors will blow. We do not know what that probability is, however, you cannot calculate a meaningful answer by taking the number of anchors you've set and saying "less than one in N" as this implies that the chance of failure goes down everytime you set an anchor that doesn't fail.
This is the "Challenger" mind set that NASA had, they couldn't calculate the probability of catastrophic failure that made sense, so they set a limit on the number of flights. The reason the calcuation didn't make sense is that they hadn't had a failure in the time they would expect, 1/200 flights... Now we know that is about the correct failure rate.
Same thing with anchors, you don't know if a particular anchor you set would or would not have failed, you never tested it. You don't know how close you've gotten to disaster 'cause the disaster never occured.
Also, given the fact that there is a limit to how much stuff one wants or is able to carry up a hard pitch, what would you rather have when you arrive at the belay - 20 ft. of 7mm cord and 6 or 8 extra carabiners, or a couple extra cams and nuts to choose from.. ?
I think that the initial "concept demonstration" is where we'd like to get to first, then the technology can be refined from there. The cordelette's appeal was the simplicity of setting it up. The cordelette replaced numerous slings, etc, in systems that equalized. If there is a solution to the problem, I'd think it unlikely that the first thing proposed is the ultimate thing we use.
Not to say that equalization is not important, especially if you are in the unfortunate position of having a dicey anchor. But I usually look at the multiple pieces in an anchor as backups. I use the rope to clip in, usually in series without any slack between. Of course I am usually swinging leads, not guiding, so this is not inconvenient. And with only 35 years of this under my belt I guess I am due to get chopped any day now anyway... :-)
We know that equalization is desirable, and we know that it works because it has been used in aid placements as well as to protect leaders, in both cases where a single piece may not hold. The anchor system works best when the load is as distributed over as many pieces as practical, thus no one component is stressed. This is a simple engineering design rule, stay far from the failure point as possible in a multiply redundant system where any one of the redundancies would accomplish the goal of the system.
As for when you will get the chop, the probability of it happening is probably no differnt today as it was 30 years ago... at least not in terms of the knowledge you bring to the table.
Sometimes you roll the dice and you win... fortunately the dice is loaded in your favor, but it is still possible that the dice roll could go against you. We all should keep trying to load them even more in our favor.
That's what this conversation is all about.
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GOclimb
Trad climber
Boston, MA
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Jan 25, 2007 - 03:59pm PT
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Ksolem - the only reason to be concerned with any of this is if there is a possibility of the leader falling onto the belay. For normal lead falls and for bringing up a second I've been perfectly happy with just wedging my fat ass in a crevice, or backing up my two good legs with one really good nut. For that purpose - sure, a few good cloved pieces is perfect.
But this is really all to answer the question of what happens when the leader falls with no gear in.
Or to put it another way - how many of your clove-hitched-in-sequence anchors would you have been comfortable with catching a leader with no gear on the pitch?
Leader is 10 feet up, falls to 10 feet below you, your bottom piece is weighted with a pretty high force - depending on the type of device you're using, perhaps 10-15kN. Can that one bottom piece hold all that force? What if it pops? Then the next piece in sequence feels approximately the same force. You get the idea.
GO
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rgold
Trad climber
Poughkeepsie, NY
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Jan 25, 2007 - 05:04pm PT
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How about the second question..?
I think that an appropriate anchoring system would make it a false dichotomy. But I also agree with you that systems that eat up too much gear are not going to be useful to many climbers.
On the other hand, climbers have, over time, shown almost limitless willingness to carry more gear. The common rack I see nowadays has at least twice as many pieces on it as the rack of nuts we used 30 years ago, and the pieces, cams, are heavier too. I could go on about the other "necessities" climbers now have on their harness that add weight to the enterprise, starting, I suppose, with the harness itself.
So an alternate answer to your question is, if the rigging system is effective enough, climbers will carry it and the extra gear they think they need even if the load is heavier.
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the Fet
Knackered climber
A bivy sack in the secret campground
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Jan 25, 2007 - 05:51pm PT
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In my limited knowledge, I understand the dynamic properties of the rope should limit the max force(in a factor 2 fall) to not more than 12kN, and is about 9kN.
However, if you are using a re-direct at the belay which acts as a pulley you could almost double that force on the biner/anchor to 18kN.
A camalot is rated for 8 - 14 kN.
A closed biner is rated for about 24 kN.
Personally, I think that it's calling it close to fully rely on an anchor without any form of equalization. Say you have a 9kN leader fall on a 14kN camalot, that's a saftey factor of about 1.5 (14kN / 9 kN). And it gets worse if you use a small camalot or a redirect where you could break a piece, or pop it.
Equalizing 2 pieces (with a sliding X with limiter knots, or an equalette) should do a pretty good job at sharing the force. So your almost cutting the force on each piece in half and doubling your safety factor, very easily. So an approximate 50% reduction on the force compared to just 1 piece.
Equalizing 3 pieces is more difficult, time consuming, and probably requires more gear, and you're only getting another possible 17% reduction of force on each piece. (i.e. instead of 50/50 you get 33/33/33. So there's a diminishing return the more pieces you equalize.
For the average trad anchor where the pieces appear solid, I think splitting the force among 2 pieces is probably going to do the job fine (with a 3rd as a backup as needed). You would probably only need to equalize 3 pieces if they weren't solid placements. Then you would probably be an advanced climber and have more options in your bag of tricks for that situation.
So as a replacement for the cordelette, and as the anchor 90% of climbers could use 90% of the time, I think something that equalizes two pieces, simply, with little gear is the way to go.
I'm not giving up on a solution to something simple, that will equalize 3 pieces with minimum gear, but I don't think it's really necessary for most people and situations. And due to the complexity I don't know if there is a simple solution.
A couple points (that have been addressed before but the numbers above reinforce):
*Always tie in with the rope
*A belay redirect should be used judiciously
*Trusting one piece with your life ain't a good idea
*Place a piece above the belay asap
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Mighty Hiker
Social climber
Vancouver, B.C.
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Jan 25, 2007 - 06:19pm PT
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A fascinating discussion, with lots of interesting stuff. I know just enough physics to get the idea, though analysis of dynamic systems is pretty complex.
I'm still not sure what the objective is, or more accurately how equalizing anchors will contribute to it. If the goal is to better understand belay system dynamics, so that climbers learn to build stronger/safer belays, that's good. I suspect that there are other factors that have a greater influence on this, including equipment and environment limitations, and the subjective elements - skill, experience, circumstances.
Looking at it another way, an analysis of climbing accidents may show belay failure well down the list, and that when it does occur, it's more commonly due to inadequate or poorly placed gear, poor rock, and/or the subjective factors. Should we perhaps be looking at those?
More worrisome, a discussion like this can easily lead to some concluding that the solution is fixed anchors - bolts - at all belays. Which in turn can lead to greater evils, such as the grid bolting found in some places, even though the rock offers good natural protection. Those who think that climbing can or should be completely safe are an ever-present risk.
Somewhere I once heard or read that the human body in a sit harness will likely suffer internal injuries or worse if subject to forces of over 12 kN. Hence gear being designed to take roughly twice that force.
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NoRushNoMore
climber
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Jan 25, 2007 - 08:12pm PT
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Assumptions about FF2 load of 12-18kN on the anchor are unrealistic. Even gri-gri slips at about 4.5kN giving max force in the case of belay thru the anchor of about 7.2 kN
And that is only in if you are anchored down. Otherwise you will be sucked into power point and in to the same load position as if you belaying of the hardness: 4.5kN max load on the anchor.
With these numbers in hand whole discussion about load balancing is a waste, all you need is redundancy (any other belay device will give you even lesser numbers to worry about)
Of course there is a case of human funk device but that much you can control instead of overbuilding anchor
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Largo
Sport climber
Venice, Ca
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Jan 25, 2007 - 09:20pm PT
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Ya' all:
Don't want to speak too soon but I will anyhow. Im perilously close to figuring out the equalized 3-point anchor set up (rigged on one standard piece of thin cordage with no shenanagans or gizmos). Gotta few bugs to work out so it may take a few more hours but I'm hoping . . .
This is fun because I always enjoyed physical puzzles.
JL
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