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Largo
Sport climber
Venice, Ca
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Apr 15, 2008 - 11:56am PT
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Per Ed's note, the fact that the anchor tie in biner can slide at the master point makes all the difference, but said biner is also prone to bind (the so-called "clitch" effect) on the sliings if things are not set up correctrly. Testing showed that an anodized, pear-shaped biner laregly overcame any binding.
JL
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rgold
Trad climber
Poughkeepsie, NY
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Apr 15, 2008 - 01:43pm PT
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Ed's calculations are basically the same as ones I posted several years ago on rc.com, back when people still thought a cordelette would genuinely equalize if you could just tie it right. In particular, I mentioned, as the ultimate test case for equalizing, the three-point anchor with all three pieces in a vertical line, and that example eventually made its way into Largo's book.
As for systems with more than two arms being just combinations of the two-arm system, well, yes and no. Starting with three arms, the system becomes, in engineering terms, "statically indeterminate," which means, in the case of three arms, that there are three unknown tensions but only two equations relating them derived from force decomposition, meaning that there are infinitely many different solutions. Of course, the physical system doesn't have all those solutions, because there are additional constraining equations that come from Hooke's Law. (The engineers are usually more interested in beams, in which case they can get additional equations from the necessary equilibrium of torques.)
So it turns out that the elongation of the strands, which can be ignored when there are two arms of equal length, becomes essential to the solution when there are more than two arms, and of course then calculations become quite a bit harder.
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the Fet
Knackered climber
A bivy sack in the secret campground
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Apr 15, 2008 - 02:21pm PT
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Ed, thanks for the diagrams, they really help clarify what's going on.
I think Raymond's point is that as the angle of the arms to a vertical line above the power point increases the force on the piece increases. (e.g. if the piece is 60 degrees off vertical then that piece is getting a force equal to the total load at the powepoint).
I just saw this for this first time, good stuff:
http://www.caves.org/section/vertical/nh/51/Multi-point%20pre-equal%20anchors.pdf
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Chiloe
Trad climber
Lee, NH
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Apr 15, 2008 - 05:01pm PT
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I should be doing something more constructive, but instead ... for your edification, here's a different view of some key findings from Jim E's original test data, which involved 2-anchor rigs with either equal-length or unequal-length arms.
Two findings are that (1) well-tied cordelettes don't seem to equalize forces at all, if both arms are not the same length (or even if they are the same length); (2) the sliding-X does better than a cordelette but in the unequal-length case, due to binding, the short arm still feels significantly more force.
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Ed Hartouni
Trad climber
Livermore, CA
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Apr 16, 2008 - 12:17am PT
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Port
Trad climber
San Diego
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Apr 16, 2008 - 12:37am PT
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Thanks Ed, great info.
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raymond phule
climber
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Apr 16, 2008 - 03:13am PT
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"Two findings are that (1) well-tied cordelettes don't seem to equalize forces at all, if both arms are not the same length (or even if they are the same length); (2) the sliding-X does better than a cordelette but in the unequal-length case, due to binding, the short arm still feels significantly more force."
The point I tried to make is that the two tested cases are very special, atleast the vertical one, and I dont believe we can draw some of the conclusions that people have drawn because of that.
Unequal arm lengths might in theory result in ok equalisation in some cases. See my example above.
The testing was done in two different configurations, no angle (vertical) and an angle between the slings. I believe that a large part of the test results are a result of this instead of only a result from the difference in arm lengths.
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Ed Hartouni
Trad climber
Livermore, CA
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Apr 17, 2008 - 01:16am PT
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