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rgold
Trad climber
Poughkeepsie, NY
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"I don't get it. If it took energy to yank the piece out, that energy is not going to create force on the remaining pieces. Imagine that it took nearly all the energy of the fall to yank the first piece; the falling climber would be slowed to nearly a stop, and the remaining pieces would have very little to hold. Of course, the rope might not be able to absorb too much more energy, but hey, it was going to have to absorb it all anyway."
It doesn't take energy to yank a piece out. It takes force. (A very small amount of energy may be consumed by moving the piece a short distance and by generating some heat, but I believe this is negligible compared to the fall energy to be absorbed.)
The so-called "energy absorbed by extracting a piece" is the work done in stretching the rope until the rope tension (force) is enough to break or extract the piece. If that rope tension is not released, and I'm suggesting it won't be with fixed arm rigging, the force, i.e. the stretched rope, will simply be transferred to the remaining piece(s). Further stretching will occur to arrest the fall, at which point the total amount of stretch in the rope will be exactly the same as if the piece hadn't pulled, but now that load is applied to fewer pieces.
If you stretch a 2" rubber band by an additional 1", it doesn't matter how many times you stop while you're doing it. The total energy absorbed will be the energy it takes to stretch the rubber band by 50%, and the tension in the rubber band at the end will be...the tension in a 2" rubber band stretched to 3".
In the case you describe, I'm saying that although the additional rope stretch that occurs on the remaining pieces may be very little, the fact that there has been no release of rope tension means that the remaining pieces will still be subjected to the entire maximum force involved in arresting the fall.
Let's say there is only one other piece and the first piece held while most of the rope stretch was happening. Then the good piece experiences half the total load up until the failure of the bad piece, at which point the load on the good piece nearly instantaneously doubles. Isn't this what people mean by shock loading?
Now on the other hand, if the tension in the rope is released by a small extension in the anchor, then stretching and the build-up of rope tension (= force on remaining pieces) only has to absorb the fall energy remaining, with the ideal result that the remaining pieces experience lower load than they would have with the non-extending anchor.
It's all hypothetical, of course, but it seems quite plausible to me, unless of course I've missed something. I hope someone can test this.
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GOclimb
Trad climber
Boston, MA
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Murcy, that's correct. I said in an earlier post here, as well as in a response to CharlesJMM on the original rc.com thread that the CHJMM anchor only really equalizes between all the pieces within a narrow range, and for exactly the reason you stated so elegantly.
In reality, an elipse is close enough to a circle that within a range, the equalization of the CHJMM is pretty good. It's slightly better than the equalette, in which you immediately unweight one of three pieces completely as soon as you move the centerpoint at all. And of course it's far better than the cordelette, which really only ever weights one piece at a time as soon as you get off center.
This is exactly why the CHJMM anchor was not on the top of my list of anchors, despite its simplicity.
RG wrote: I don't have the time now to check, but one does wonder whether limiting knots in some of the other three-anchor rigs may also impose geometric constraints on equalization.
The Mooselette, multi crossed-sling, and Gordolette do not suffer from this drawback. However the Gordolette has a rather limited range and is awkward to set up.
GO
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GOclimb
Trad climber
Boston, MA
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RG wrote: Next, consider what happens when a piece fails and there is a small extension. During the instant of extension, rope tension drops to zero.
No it doesn't. It drops to the tension of stretching the rope X feet minus the number of inches of extension.
Removing for the moment a falling belayer from the equation (not unreasonable, since in many cases the belayer is on a stance) the force that then comes onto anchor should be very slightly less than the exact force at which the piece pulled out. What is key, however, is that in a two piece anchor that force is *shared* across the two remaining pieces in a dynamically equalizing rig, but is all on one piece in a cordelette.
To put it in simple terms: because it doesn't equalize, a cordelette makes it more likely that
1 - The first piece will rip, because in some cases it feels almost all the load.
2 - If the first piece rips, that the other pieces will rip, because they each feel more force than they would if they were sharing the load.
GO
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rgold
Trad climber
Poughkeepsie, NY
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""During the instant of extension, rope tension drops to zero."
How do you justify this assumption? Is Hooke's Law being thrown out? Or are you saying that the elongated rope shrinks back to its (near) original length during anchor extension? If the rope elongation is large compared to the anchor extension then how can this be? "
Hooke's law is still in operation. I'm saying the elongated rope shrinks some. Tension going to zero is an idealization, although I'm not quite sure how to think about a non-zero the tension in an unloaded rope. The small extension combined with the fact that the rope and climber are falling will limit the amount of recovery before the rest of the pieces engage. A shock-wave calculation made by Ken Cline some years ago on rec.climbing suggested that recovery occurs in extremely short time intervals.
It has been a matter of debate for years whether any real recovery actually happens. In addition to how much recovery might happen in the time interval of an anchor extension, there are the mitigating factors of rope stiffening (we know this happens) and the additional effects of the belayer falling.
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GOclimb
Trad climber
Boston, MA
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RG wrote: Let's say there is only one other piece and the first piece held while most of the rope stretch was happening. Then the good piece experiences half the total load up until the failure of the bad piece, at which point the load on the good piece nearly instantaneously doubles. Isn't this what people mean by shock loading?
Now on the other hand, if the tension in the rope is released by a small extension in the anchor, then stretching and the build-up of rope tension (= force on remaining pieces) only has to absorb the fall energy remaining, with the ideal result that the remaining pieces experience lower load than they would have with the non-extending anchor.
It's all hypothetical, of course, but it seems quite plausible to me, unless of course I've missed something.
I don't know whether you missed it, but it sure sounds like it:
If you have a 20 foot rubber band and stretch it 6 feet, you'll get tension X. Lower the top end 6 inches, and you'll get a tension of X minus a very little bit.
So in your scenario two, the remaining piece feels nearly double the force that extracted the first one.
Of course, that's assuming that the belayer doesn't fall directly onto the anchor. If she does, the anchor may feel significantly *more* force in scenario two than in scenario one.
By the way, if it's an equalizing three piece anchor instead of two piece anchor, when that first piece fails, the other two feel only 50% more force than the first one did, rather than double the force.
GO
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GOclimb
Trad climber
Boston, MA
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RG wrote: Tension going to zero is an idealization
Why? Take a rubber band stretched 50%, and reduce the stretch to 48%, and you say the ideal calculation of the tension in the rubber band is zero?
GO
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rgold
Trad climber
Poughkeepsie, NY
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"If you have a 20 foot rubber band and stretch it 6 feet, you'll get tension X. Lower the top end 6 inches, and you'll get a tension of X minus a very little bit.
Good points. I was thinking of the tension in the belayer's tie-in. What if I have a two-foot tie-in that stretches 8" and an 8" extension in the anchor?
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Largo
Sport climber
Venice, Ca
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I'm fiddling with the CHJMM right now. Once again, the devil is the limiter knots--the "geometric limitation" Rich mentioned. The CHJMM is an elegant idea but it doesn't work as well as hoped because once the limiter knots are set, it dynamically equalizes (within a limited but acceptable range) only in a vertical orientation. Meaning, so long as you are pulling straight down, you're okay within the given range. On the horizontal plane (meaning when you lean out on the rigging, as usually happens on all but hanging belays), the middle piece goes slack.
I'll have to start fiddling with the Moosealette and other two and see if there's not some way to simplify these ideas.
GO, can you be bothered to sketch out those other rigs as well. Thanks,
JL
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cintune
climber
Penn's Woods
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This is getting really interesting. I think this has been posted before in another thread, but here's some stuff that might possibly be useful to test out some of these ideas:
http://www.squid-labs.com/projects/erope/
"Squid Labs has developed an Electronically Sensed Rope - a rope or webbing with integral sensing capability which can be monitored electronically. Our technology can be used to sense wear and load conditions in rope and webbing. We currently work with customers to develop commercial and end-user solutions using our technology, including appropriate sensing elecronics integrated to the application."
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the Fet
Knackered climber
A bivy sack in the secret campground
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Murcy, that's correct. I said in an earlier post here, as well as in a response to CharlesJMM on the original rc.com thread that the CHJMM anchor only really equalizes between all the pieces within a narrow range, and for exactly the reason you stated so elegantly.
I missed this version of the CharlesJMM Anchor (Chuckolette?) on the rc.com thread and thought you (GO) were referring to one of his earlier designs. I played with it a little and it seems like if it's tied like this photo, with extra slack given to the strand with the twist, then it DOES load share good over a good range (if the strand with the twist is only weighted in one piece failure mode). It don't think it "equalizes" since the middle arm looks like it puts 2X the force of the outside arms (25/50/25) but that's ok, if it does everything else good. It equalizes 50/50 if one of the pieces fails.
The main issues I see are: if an outer piece fails a limiter knot pulls through the powerpoint biner, it's a little tricky and time consuming to tie (but not bad).
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WBraun
climber
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So ah mmmmmmmmm
What's behind the blue door?
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GOclimb
Trad climber
Boston, MA
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JL: Not sure how you're setting up your rig - it should make no difference whether you're pivoting around a vertical or horizontal axis.
GO, can you be bothered to sketch out those other rigs as well. Thanks,
Sure, if I have time, will do so tomorrow.
The Fet: I agree with everything you said regarding the CHJMM. I do not know if there is a more efficient way to break it down and build it again, as I have not used it much in the field. From my limited experience, the Mooselette seems much easier, since I just leave the two limiter knots in it. Then all that's required is to clip it into the three pieces, adjust the limiter knots, and I'm good to go.
Werner: What's behind the blue door?
Ah, but Werner, can't you guess? Another anchor, and another blue door, of course!
GO
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raymond phule
climber
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"A great link, thanks for it. But no useful data on factor-2 falls reported there, unfortunately"
The most important info was that you cant put a large force on a rope using an ordinary belay device. This is also true in a class 2 fall. The force on the anchor cant be high except in some special cases. The rope cant slip through the belay device, the climber falling on the belayer, the belayer falls an loads the anchor. Any more possibilities?
"Here I think you are wrong. As you say, peopel make misstakes, even in the presence of knowledge of the problems. They are sometimes wrong about which piece is good. The best strategies are those that minimize potential load to all pieces, are tolerant of off-axis loading, and redistribute the load to remaining pieces if one fails."
I agree
"These are the only available means of coping with the uncertainties that are part of real life."
I disagree about this. Assume that most belayas that fail is due to one problems mention above, rope cant slip, climber falls on the belayer and belyer fall and loads the anchor ( a rigid connection is very bad here). Then are a perfectly equalised anchor better than a non equalised but it might not be enough. Pointing out the main problem is important because it can make people more carefull.
"But it is also the case that very few experienced climbers have ever had their anchor judgements subjected to a real test, much less a statistically significant sequence of tests. This means that most climbers really have no basis in reality for judging the strength of their anchors. The tragedy described by Werner earlier in this thread indicates that these claims are not simply hypothetical."
I agree, but this make it important to try to analyze what actually happens.
"Once again, in the face of this really quite massive uncertainty, equalization is the best strategy, if it can be achieved."
Yes, but the problem is to achieve it. I am also afraid of the load from the belayer due to extension.
"It seems to me that a relatively small group of climbers is interested in the intellectual challenge involved"
It sure can be fun.
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raymond phule
climber
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Interesting thoughts rgold.
The reason for the result is that the maximum force happens when the fallen climber velocity is zero(or there about) because the rope elongation and thus the force is maximum at that time.
My quess though is that the rope is not going to be able to recover fast enough. Isn't a rope very stiff right after a fall? It sure is longer.
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GOclimb
Trad climber
Boston, MA
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JL: GO, can you be bothered to sketch out those other rigs as well. Thanks,
First, the 2 crossed-slings. I don't think you need a sketch, but I just want to reiterate that I think this is an excellent method for distributing the force over three pieces (note, I say distributing rather than equalizing).
Looks like this:
Of course if you wanted to use two anodized big biners at the power-point, you'd get the full non-binding characteristics of the equalette.
-*-*-*-*
To make the mooselette:
1 - Put two overhand knots in the cordelette. These should incorporate the section of line with the joining knot, so as to keep it out of the way. You can do this on the ground. These knots never need to come out.
2 - Place three pieces of gear, and put a loop of the cord through each biner, and pull the centers down to a powerpoint like if you were going to make a standard cordelette. Put the strand with the knots on the middle piece.
3 - Adjust the two limiter knots so that one is down near the powerpoint, and the other is up near the top.
4 - On each side, clip one biner (or draw, if it needs to be longer) between either of the outside strands, and either of the inside strands. Doesn't matter which one, but in the middle, clip it above the upper limiter knot.
That's it.
When I have time, I'll come back and add the Gordolette.
GO
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Degaine
climber
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Thanks for the sketches, goclimb.
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GOclimb
Trad climber
Boston, MA
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Here's the Gordolette. It's pretty cool, but a little too finicky for me. Still perhaps someone with some free time can refine the basic idea.
It's been a while since I've made one, and I drew this up from memory. If I have time this weekend I'll build the real thing and make sure it matches up with my sketch.
GO
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rgold
Trad climber
Poughkeepsie, NY
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Here is an anchoring solution I had sewn up for me recently. Sorry not to have pictures of it in use in the field (I've been out with it for several days of climbing, none with a camera in tow so far). All I have at the moment are the following indoor shots.
The idea is based on something I called the chopolette in the massive rc.com sliding X thread. It generated little interest there, in part because of a biner that had many sliding strands and the feeling that binding of strands would almost certainly destroy its effectiveness in equalizing.
In honor of its gimmicky nature (a source of embarrassment to me and a deal-breaker for Largo and others who believe in the primacy of simple tools) I've dubbed it the Geekqualizer, and admit, with regret, my passage to the Dark Side of gadget worship.
It consists of a commercialy available equalizing module with no crossing strands, and three arms that extend from the equalizing module and are clove-hitched to the protection. Here's what the whole unit looks like:
here's a closeup of the equalizing module and its connection to the arms:
and here is a view of a possible set-up for three pieces at different distances from the power point.
In the last picture, the left arm has been clipped to a far away piece with the loop sewn into its end, while the other two arms have been clove hitched to their biners, after which the end loop has been dropped into the biner as a backup to clove-hitch slippage.
Here is a closeup of the clove hitch and loop backup:
For those increasingly ubiquitous two-bolt anchors, the arms can be dropped and the equalizing module clipped directly to the anchors. The overhand knot at the right shortens the webbing and thereby decreases the extension if one of the bolts fails:
Four-piece anchors can be accomodated by adding a carabiner. The off-axis range is smaller for this set-up and of course there is more friction in the system.
The Geekqualizer wraps up into a small package somewhat smaller than a 7mm cordelette: Wrap-up is very simple and the time is about the same as for a cordelette. Installation time is the time it takes to make three clove hitches.
Advantages:
1. Adaptable to all anchor configurations with consistent installation. Regardless of the placement of the pieces, you rig it up the same way, with no choices or special adjustments. It is easily adapted to two- and four-piece riggings. (I think most of the other methods are tailored to a single fixed number of anchor points.)
2. Zero carabiner cost for two and three anchor points. Other than the always essential biners on the pieces and the power point biner, no other biners are required. Two Geekqualizer anchors consume the minimum of eight biners, whereas two equalette anchors (for three points) require ten biners and two mooselette anchors require twelve biners.
For the occasional four-point anchor, the Geekqualizer requires a total of seven biners, chained equalettes require ten biners, and the mooselette is, I think, out of the running.
3. A consequence of the zero carabiner cost is that there are no biners in the system that might be compromised by unanticipated cross-loading or gate opening. (The sliding X is especially susceptible to a very dangerous configuration if one of the pieces fails.)
4. Very fast installation for all configurations---no limiter knots to tie, adjust, and wrestle with when they become wet, tight, and cold, no potential need to readjust anything as there is with the cordelette, no special circumstances that the system doesn't work for. You clove (or clip) the arms, clip into the power point and you're on.
5. Equalization potential as good and perhaps better than other equalizing methods because of the lack of multiple crossing strands on a biner somewhere. Extension if one piece fails is about four inches.
6. Responds to off-axis loads and redistributes load if a piece fails (as do most equalizing systems).
Disadvantages:
1. Yet another special-purpose item. Although it can be used in other ways in an emergency, it isn't remotely as versatile as a cordelette.
2. Sewn webbing must be inspected and retired when appropriate.
3. Low-stretch material provides little energy-absorbing utility. Tying in to power point with rope is essential for the belayer. Followers who clip in, even temporarily, with a daisy should keep it tight and stay below the anchor. (On the other hand, low-stretch material might behave better when it comes to friction over the various pulley points.)
4. Potential for clove-hitch slippage may be a concern. There are some tests (private communication) that indicate this isn't a problem. Even so, one should be careful to tie the clove hitches without twists in the webbing and should make sure that the hitches are oriented so that the load-bearing part of the knot is close to the spine. (The clove hitch can often be backed up by half hitches around the arm before clipping the end loop to the biner.)
5. Friction. Friction is the reality death-knell of any equalizing system, and this is no exception. I think the elimination of crossing strands should prove to be an advantage (but know of no tests to address this question). There is still friction around all the rings. The worst case is when the strands all make full 180 turns around the rings---three pieces in a vertical crack. If systems such as this have a future, it lies in finding components that will reduce the friction. For example, it would be interesting to know how much difference roller biners on the protection points would make.
Remember, however, that the standards for acceptibility aren't very high, now that we are learning how bad the cordelette is, even with just two equal length arms. My guess is that even with their current levels of friction, the Geequalizer (and many of the other methods) provide equalization on average better than the cordelette provides, together with the advantages of off-axis load adaptibility and redistribution of the load to the remaining pieces if one piece fails.
6. No doubt perspicacious readers will come up with a slew more disadvantages in short order.
What I like about the Geekqualizer so far is that it is fast enough and simple enough for me to use automatically on every anchor. It costs me nothing in time, effort, and gear to use it rather than a more traditional method. The value in this corresponds to my feeling that something terrible is just as likely to happen in mundane casual circumstances as in the midst of some epic, and the instant you need the advantages of equalization, if such a time should come, may not be a moment that you can anticipate and so make special preparations for.
Test results post:
http://www.supertopo.com/climbing/thread.html?topic_id=307091&tn=308
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Ed Hartouni
Trad climber
Livermore, CA
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did you get Wootles to test it?
I'll think about friction later tonight...
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murcy
climber
San Fran Cisco
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nice, rgold!
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