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cintune
climber
Penn's Woods
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Jan 25, 2007 - 10:01pm PT
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Well, JL, that will deserve a fresh page, so let me do the honors of filling this one out.
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john hansen
climber
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Jan 25, 2007 - 11:03pm PT
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I brought up the idea before for a more springy cordellete that would stretch more and distribute the load. As the first anchor point began to come under load, it would only take a small percentage of the total load before the second piece started sharing the load. As both these "arms" stretched further the third anchor point would also start to come under load.
I know this is more of a force 'distribution' rather then true equalization.
Does this idea make any sense Ed ,and all you other number crunchers on the topo.
And here is another probably stupid idea. Imagine a V shaped piece of fabric about two feet tall and eighteen inces across the top made out of something like they use for trampolines.
At the bottom of the V would be the power point. On top of the 'V' would be a 'W' of three adjustable clip ins. This way as the power point was loaded it would have the same affect as the system above, only greatly enhanced.
Imagine a one pound wieght,connected by three wire cables to three nails driven into the wall so the cables are as close to equal as the eye could see. You drop the wieght ,and one of the anchors will be 'shock loaded' with the full force generaterd by the fall. What would a scale measure that force as...
Now , imagine the same set up only with rubber bands instead of cables. As one slowly comes under load the other points would gradually take a share of the force generated.
Does this make any sense or am I just full of Stienlager?
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 26, 2007 - 12:43am PT
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the impact force grows, at worst, with the square root of the spring constant... for falls that generate much more force than the weight of the climber.
So if you reduce the spring constant by a factor of 4, you will get, at most, a factor of 2 reduction of the force.
If you look at the ST Forum topic physical properties of ropes and slings I reported on several types of ropes and slings:
K = 11.2 kN for a Beal dynamic rope,
K = 24 kN for nylon webbing
K = 30 kN for a 7mm perlon cord
K = 109 kN for a 5mm spectra cord
Using a 7mm perlon cord would provide a smaller impact force than a 5mm spectra cord... by a factor of 1.9 (nearly 2), depending on the magnitude of the fall. For small falls the difference will be smaller.
In my analysis higher up on this thread, the spring constant K of the slingage is a part of the calculation.
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rgold
Trad climber
Poughkeepsie, NY
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Jan 26, 2007 - 10:36am PT
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I brought up the idea before for a more springy cordellete that would stretch more and distribute the load. ...I know this is more of a force 'distribution' rather then true equalization. Does this idea make any sense Ed ,and all you other number crunchers on the topo.
How stretchy do you have in mind? The belayer might be a bit miffed if it turns out he's in for a day of bungee jumping.
More seriously, there appear to be two obstructions to load equalization. One comes from the inevitable practical failure to have the arms exactly the correct length in knotted rigging. Wootles' results illustrate that the resulting inequities can be quite significant. It has been hypothesized that stretchier material will offset unequal arm tensions in this situation. Just how elastic the rigging needs to be before one sees a significant equalizing effect is unknown.
The second obstruction to load equalization comes from unequal arm length. Changing the stretchiness of the rigging might reduce the total load but can make no difference at all in inequities of distribution in this case, so stretchier rigging material cannot provide a comprehensive solution to the equalization challenge.
I don't think one ought to view the anchor rigging itself as part of the fall energy absorbing system, and I don't think one is likely to get much contribution from any standard rigging. Part of the reason is the load is supported not by one strand of the material in a cordelette rig but rather by six, so the anchor is going to be a relatively rigid component of the system.
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Largo
Sport climber
Venice, Ca
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Jan 26, 2007 - 10:48am PT
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Rich wrote: "I don't think one ought to view the anchor rigging itself as part of the fall energy absorbing system, and I don't think one is likely to get much contribution from any standard rigging. Part of the reason is the load is supported not by one strand of the material in a cordelette rig but rather by six, so the anchor is going to be a relatively rigid component of the system."
I suspect that a workable soultion is kind of polymer biner, or doughnut, that we can attatch and tie into at the power point (backed up by a sling, of course). Modern polymers are remarbably strong, and the relative stretch can be controlled in fabrication. This is a possibility worth investigating. A four inch polymer "power ring" that might stretch to, say six or eight inches under extreme loading might bear some interesting results providing it's light and sufficiently durable.
JL
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 26, 2007 - 11:08am PT
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one way to play this game is to take the extremes,
the stretchiest material will have a K = 0 kN,
then the impact force will be: F = 2 mg
twice the weight of the climber.
If the K -> very big,
F ~ mg*sqrt(2*f*K/(mg))
where f is the fall factor = h/L the distance of the fall h divided by the length of rope L.
Now here's a thought and a jump into complexity... you could have multiple polymer rings, each with a different K, in colors, and build a cordelette anchor attached through the rings to the anchors. For short arms you'd put a strechier ring, for long arms a stiffer ring (or no ring).
That would equalize the force...
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cintune
climber
Penn's Woods
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Jan 26, 2007 - 11:55am PT
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The problem I see is that whatever stretches will bounce back, and the bigger the load, the more often, and the bigger potential variation in the angle of pull. This repeated loading and unloading of a "bungeelette" might defeat the purpose with sketchy anchors by walking them right out of their placements. Although I'm starting to sound like a broken record by now, this is the beauty of the screamer. Peak load is limited to ~2Kn, and there's no rebound to add to the uncertainty.
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Brian in SLC
Social climber
Salt Lake City, UT
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Jan 26, 2007 - 12:24pm PT
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I suspect that a workable soultion is kind of polymer biner, or doughnut, that we can attatch and tie into at the power point (backed up by a sling, of course). Modern polymers are remarbably strong, and the relative stretch can be controlled in fabrication. This is a possibility worth investigating. A four inch polymer "power ring" that might stretch to, say six or eight inches under extreme loading might bear some interesting results providing it's light and sufficiently durable.
Hmmm, like a dog chew toy (or the donut ring and chew toy that some folks use to train hand strength with).
Interesting...heck, this might be KISS off the shelf easily available...
Someone oughta go to the pet or grocery store, pick one up and load test it...high loading rate, see the peak load graph type thing.
-Brian in SLC
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rgold
Trad climber
Poughkeepsie, NY
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Jan 26, 2007 - 12:31pm PT
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A screamer only limits the load to 2 kN if the fall energy is completely absorbed by the time it reaches full extension. In general, I think the approximate effect of a fully extended screamer on the subsequent anchor impact is that the anchor load will be that of a five foot shorter fall.
It would follow that screamers can have a significant impact for short falls of a given fall factor, but would probably contribute little to force reduction for long falls of the same fall factor.
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Largo
Sport climber
Venice, Ca
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Jan 26, 2007 - 12:57pm PT
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The "Bungeelette" has a nice ring, but I don't see it like a spring that will vault a belayer to the moon via recoil. The "dog chew" toy is closer to it but I'm just guessing.
I'm just going to have to track down something and start fiddling. The 3-point simple sling perfect equalizing plan I was so high on isn't panning out as I'd hoped. A sliding power point--in practice--works great for two points but add a third point and an change in loading invariably results in one arm going slack. This is caused by the limiter knots, without which we're looking at huge extension if one placement blows. It might be doable but after fiddling with slings for hours last night I'm starting to wonder if it isn't physically impossible to have a self-adjusting system that spans three placements. The odd number--"3"--is the bugaboo.
JL
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 26, 2007 - 01:27pm PT
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ropes are designed not to bounce back...
a ring could also be... note that the ring could be a sling made of a synthetic material designed with a particular K value... doesn't have to be solid plastic...
A sceamer is an "irreversible" example of this sort of thing. I'm thinking more like a special "dog-bone"
where are the material guys?
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 26, 2007 - 01:37pm PT
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here's something!
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jstan
climber
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Jan 26, 2007 - 01:38pm PT
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This observation may/may not be useful. Slings and ropes are not perfectly elastic. Some energy is dissipated in the rope and leads to a rise in its temperature. Do we know how dissipative rope is? If we suppose it were perfectly dissipative the anchor question changes markedly. In that case if one anchor fails the remaining anchor(s) should only have to deal with the portion of the fall remaining. Serial failure of anchors then may be less less problematic.
We know rope is pretty dissipative. I know of no case where the falling climber rebounded to the height from which the fall originally occurred.
Edit:
Ed's graphic apparently tied the system up enough so did not see his suggestion similar to mine. What this does is change markedly the time evolution of the forces in the overall solution to the dynamical problem. It almost looks worthwhile, now, to do the dynamical problem if inelasticity can be incorporated.
You can't count on the material guys. They all just want to have fun.
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rgold
Trad climber
Poughkeepsie, NY
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Jan 26, 2007 - 02:24pm PT
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Slings and ropes are not perfectly elastic. Some energy is dissipated in the rope and leads to a rise in its temperature. Do we know how dissipative rope is? If we suppose it were perfectly dissipative the anchor question changes markedly.
So would all the calculations, which so far appear to agree decently with test results. These calculations assume energy dissipated is negligible. If energy dissipation is a significant mechanism, the concept of fall factor, which is an artifact of elasticity, would probably be out the window.
In that case if one anchor fails the remaining anchor(s) should only have to deal with the portion of the fall remaining. Serial failure of anchors then may be less less problematic.
This would render moot the long-standing internet debate about whether, when a piece blows, the rope recovers significantly before it is stressed again by loading the next piece.
We know rope is pretty dissipative. I know of no case where the falling climber rebounded to the height from which the fall originally occurred.
Right, but that isn't necessarily an indication of dissipation. A more accurate mathematical model for the rope than the simple spring is probably the damped spring---critical damping would result in no recovery from maximal extension without any dissipation of energy and no beneficial effects for sequential loading. However, I have never seen an argument that, in principle, indicates why the rope should behave like a damped harmonic oscillator. Such an explanation, if there is one, might have to refer to the behavior of the polymer molecules themselves under elongation and contraction, rather than the more obvious case of internal friction, which would probably support John's idea better than the damping concept.
The Italian Alpine Club (CAI) has a sophisticated mathematical model for the entire belay chain, modeled in just this way as a system of damped harmonic oscillators.
http://www.caimateriali.org/Eventi/Torino/computermodel.html
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the Fet
Knackered climber
A bivy sack in the secret campground
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Jan 26, 2007 - 04:43pm PT
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For those of you who are interested and missed it on the rc.com slidingX thread, here is an anchor design I came up with that equalizes evenly among 3 pieces (neglecting friction, binding, etc.)(note: center piece gets the same force due to 2:1 pulley effect), limits extension, and uses just a couple extra biners.
Some problems are:
If one pieces fails then the force isn't distributed 50/50 on the remaining pieces.
Not very simple.
Biners placed in the limiter knots are untested.
Friction will limit the equalization.
But maybe this will help inspire some more ideas.
I never adopted it into my anchors beyond trying it a couple times because I think equalizing on two good pieces (with a 3rd as backup) is probably good enough, and if I did need to equalize 3 pieces I would use a slidingW and back it up with the rope or something.
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 26, 2007 - 05:05pm PT
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One of the problems with the Italian Alpine Club link posted is that the physical value of the dissipation term is not given. They determined it by fitting to the accelerometer data, but didn't report the fit values.
The model is a spring and a "dash-pot," which has a term proportional to the velocity, do dissipate the energy.
I played around with this a lot to come up with the value of 600M/(m/s) for that constant, this gives a fall trajectory that seems reasonable:
x'(t) is "over" damped, x(t) is undamped
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jstan
climber
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Jan 26, 2007 - 05:42pm PT
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Now why did TIG have to go and kick all this off by mentioning bounce?
When fall factor is less than 2 the biner at the top piece also provides dissipation. For a 180 degree bend at a biner I think a 30% diminution of the force is typically assumed. If you measured the temperature rise in such biner you could get an averaged caloric value for force diminution. Biners get really hot.
If ever there was a problem that cries out for use of the Method of Steepest Descent - this is it. (Just kidding.)
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WBraun
climber
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Jan 26, 2007 - 05:45pm PT
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Just see ..... the Supertopo mathematical science lab in action trying to calculated the external energy of god. At any particular time he can send the results both negative and positive outside the established rules to maintain his supremacy over all those trying to understand him without bhakti submission.
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Gene
climber
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Jan 26, 2007 - 05:59pm PT
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Lots of good stuff, both theoretical and practical.
How common/how many catastrophic anchor failures occur in climbing situations? I can remember fatalities on DNB and on a desert spire over the last 5 to 10 years. Stipulated that there are many others I don’t know about and one is too many, how often do anchors fail in the real world?
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healyje
Trad climber
Portland, Oregon
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Jan 26, 2007 - 06:06pm PT
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ED, WTF? It's pretty and all, could you interpret for us neanderthals...?
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Let us know!