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cintune
climber
Penn's Woods
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Jan 26, 2007 - 06:11pm PT
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Werner, wouldn't prapati be more appropriate to this discussion?
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WBraun
climber
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Jan 26, 2007 - 06:20pm PT
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Gene
I would say real world anchor failures are a rarity. But when they do fail there is usually catastrophic results, duh.
Duane Raleigh as I remember had one total failure on the rappel and still lived, of course since he's still with us today. His number was not up.
Another example of the opposite. Some rescue instructor in the SF Bay Area some years ago had just finished setting up the main and belay anchors for a rescue rigging seminar. He was going to demonstrate to his class how if the main anchor system failed the belay system will back up and save the day.
He then took a knife I believe it was, and cut the main line to provide a real world, real time example in action.
Cut he did and immediately the load was transferred to the belay line in which the anchor immediately failed and he fell to his death to the witnessed shocked onlookers. Huh? His number was up.
Yes folks, strange tales from the past annals of life.
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rgold
Trad climber
Poughkeepsie, NY
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Jan 26, 2007 - 08:01pm 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.
God has made the desire to understand one of the central defining characteristics of the human race. Did God do this in order to have subjects for practical jokes?
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WBraun
climber
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Jan 26, 2007 - 08:09pm PT
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God has made the desire .....
No no ..... you have made the desire.
This world is created by OUR desire NOT God's desire.
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 26, 2007 - 08:42pm PT
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don't know how to calculate god... leave that for Werner...
as for the plot, it has two cases, one damped, one undamped.
d2x/dt2 is the acceleration
dx/dt is the velocity
 is the position.
the "primed" constant, e.g. x' is for the damped case.
In the differential equation, we have the three terms:
a*d2x/dt2 + b*dx/dt + c
which has the velocity dependent part of the model, which is the damping due to the rope.
jstan and rgold both pointed out that the rest of the anchor system has a significant effect in dissipating the energy of the fall. The analysis in my plot is for a factor 2 fall with the forces borne by the anchor, no slipping, etc.
This is not a realistic representation of a fall, but represents the extreme. It could happen if you were soloing, having tied off your anchor, and ran it out...
The point was to see what a ball park value of the "b" coefficient would be, given our fall experience is that we don't bounce on the rope. I wanted to know how much damping was required.
The constant is the "specific" constant, independent of the rope dimesions.
Maybe too much for the forum.
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cintune
climber
Penn's Woods
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Jan 26, 2007 - 09:09pm PT
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No one appreciates Sanskrit humor anymore. I don't get no sammāna, no sammāna at all, I tell ya.
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 26, 2007 - 10:25pm PT
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The model that the Italian Alpine Club reported has the details for the simulation, but their results are only graphical... the constants determined by their fitting to the experimental data was not provided.
Playing around with some spread sheet program you can match the graphical results at least qualitatively.
Anyway, those of you so inclined could have a bit of fun...(some of us think this sort of thing is fun).
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 26, 2007 - 11:27pm PT
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1 bhakti f. distribution , partition , separation RV. Ta1n2d2Br. &c. (cf. %{kSetra-} , %{bhaGgI-bh-}) ; a division , portion , share AitBr. ; a division of a Sa1man (also called %{vidhi} , of which 7 or 5 are enumerated) La1t2y. [743,2] Sam2k. ; division by streaks or lines Ragh. ; a streak , line , variegated decoration Hariv. Ka1v. ; a row , series , succession , order (%{-tyA} and %{-ti-tas} ind. in succession) RPra1t. ; (ifc.) the being a part of (%{ajbhakteH} , `" on the part of the vowels "') , belonging to Siddh. &c. ; that which belongs to or is contained in anything else , an attribute Nir. Pra1t. ; predisposition (of body to any disease) Car. ; attachment , devotion , fondness for , devotion to (with loc. , gen. or ifc.) , trust , homage , worship , piety , faith or love or devotion (as a religious principle or means of salvation , together with %{karman} , `" works "' , and %{jJAna} , `" spiritual knowledge "' ; cf. IW. 326 RTL. 97) S3vetUp. Bhag. Ka1v. Pur. &c. ; (ifc.) assumption of the form of Megh. 61 ; often w.r. for %{bhaGgi} or %{bhukti} ; (%{-tyA}) ind. not in the regular sense , figuratively S3am2k.
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cintune
climber
Penn's Woods
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Jan 26, 2007 - 11:40pm PT
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Prapati: To throw oneself down.
Get it? I'll be here all week.
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Largo
Sport climber
Venice, Ca
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Jan 27, 2007 - 12:06am PT
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Much as it might be a blast for numbers gurus to crunch the figures, try this one on for size. It's guaranteed to tax your gray matter.
Get a 20-30 foot piece of thin cordage (a big piece of rope makes it easier to see the process and noodle possible solutions). Get three faux anchor points (like weights or a hooks on a wall) and try and devise a rigging system that won't extend too horribly, that uses minimal biners, equalizes the three anchors (perhaps not perfectly but offers substantial load sharing) and can withstand, within practical reason, multi-axis loading. And, is easy and fast to rig.
I've gotten reasonably close but the no-extension part reduces or eliminates the active pully action (the rope self-adjusting when weighted) I sense is required for dynamic self-equalization. It's easy with two points, but the third causes one arm to go slack on anything but a pure downward pull.
A hint: I suspect, but certainly don't know, that the middle strand will have to be a loop, while the two side can more easily be single strands.
This one is a real puzzle, boys . . .
JL
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WBraun
climber
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Jan 27, 2007 - 12:22am PT
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multi-axis loading?
Can't you guys for the life of us just sit still in one place long enough for the damn anchor to hold? WTF are people doing down below?
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rgold
Trad climber
Poughkeepsie, NY
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Jan 27, 2007 - 01:57am PT
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multi-axis loading? Can't you guys for the life of us just sit still in one place long enough for the damn anchor to hold? WTF are people doing down below?
One of those vertical dance routines?
I tried explaining this earlier in the thread. I hope I do better this time. Suppose the leader falls onto the belayer with no intermediate pro in yet. It is possible that the leader will fall from a point directly above the anchor, but it is more likely that she will be on one side or the other.
When the rope comes tight, the leader will pendulum underneath the belayer. At the instant the rope comes tight, the rope forces the leader's directly downward fall path to change direction. This requires force (sharpen your pencils, lads) and I suspect, without having done any calculation, that depending how much rope is out and how far to the side the leader falls, the the force need not be insignificant.
The result would be that the first impact on the belayer will be off the vertical axis, and the subsequent pendulum will load the anchor in a range of directions. If the anchor is rigged with fixed arms, then it is most likely (depending on the configuration) that that initial off-axis load will be applied entirely to one arm---usually an outer arm, and so to just one of the anchor pieces. If an outer arm's anchor piece blows, then most fixed-arm rigging will transfer the entire load to the middle piece, so in this case the pieces will get the full load one at a time without any load sharing---the cascade failure.
Another scenario, involving a "leader fall" from below, is the Tahquitz accident. (I mean this as a scenario; we do not know whether or not there was a catastrophic failure of a belay anchor. The S&R team concluded the climbers fell off the top while the belayer was walking with a cordelette and three pieces tied to the climbing rope which was tied to his harness.)
The accident to the rescue instructor that Werner mentions is a good but tragic example of the fact that even experts are not always able to judge the holding power of their anchors. (If the load and belay anchors were not in a vertical line, there would be a chance for the type of failure described above.) The point of equalization is to maximize our chance of surviving if and when one of our misjudgements---and make no mistake, we all make them---is tested, perhaps in a way (like off-axis loading) that we did not anticipate.
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WBraun
climber
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Jan 27, 2007 - 02:08am PT
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That was beautiful rgold.
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murcy
climber
San Fran Cisco
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Jan 27, 2007 - 02:38am PT
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not to ... well yes, to ...
AHEM! my COMPLETELY IGNORED :-) gizmo solution above equalizes three pieces "perfectly" and allows you to limit extension however you please.
sure it uses a so-far nonexistent device, but hell, belay anchors are kind of important.
plz send royalty checks c/o murcy, sf, ca. thanks.
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Ed Hartouni
Trad climber
Livermore, CA
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Jan 27, 2007 - 03:11am PT
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murcy,
you could do it with three carabiners in series, cords through each also... not sure about the friction though...
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jstan
climber
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Jan 27, 2007 - 05:49am PT
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I too am enjoying this and appreciate Richard's,Ed's, and everyone's ideas. Now where did I leave my damn pencil?
When we used hemp ropes during haying you heard a veritable chorus of complaints as a rope was loaded. During my own tensile machine days I was struck by how noisy a heavily loaded sling can be, and how hard it gets. This leads me to a slipping model for dissipation analogous to a rope running over a biner. Perhaps a rope is composed of structures above and beyond the core and sheath. Might we presume two of these structures have relative motion after the rope has been heavily loaded so there is, if you will, internal sliding friction? (Don't ask me how to fabricate such a structure.) Frictional force would be proportional to normal force and that would be proportional to the instantaneous loading. I would be nervous were I to hold onto our friend,Hooke's Law, at this early stage so I can't claim the frictional force is also proportional to extension. If by some strange chance there is anything to this, the rope itself would have to be modelled on two components. I can't respond right now to Richard's suggestion that the fall factor theory assumes no significant dissipation. So I won't try.
My first year of climbing while in a secure sitting position at the cliff edge, I caught from above one of those pendulum falls of which Richard speaks. The force was comparable to that of a serious leader fall. After it was over I looked around and found someone had untied my anchor. After that I made it a rule not to load my anchors if there was any way at all it could be avoided.
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Largo
Sport climber
Venice, Ca
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Jan 27, 2007 - 11:35am PT
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Murcy Me,
The fun (to me) of this particular challenge is to try and drum up a solution with just the one long piece of cord and no gizmos, do-dads and/or horsefeathers. If we started fudging the criteria I imagine there would be more than a few options. But I do think your "speciality biner" might be a good idea in some cases.
JL
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rgold
Trad climber
Poughkeepsie, NY
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Jan 27, 2007 - 01:19pm PT
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Murcy,
I, for one, rather like your gizmo, especially if the little holes are equipped with rollers, because friction and binding are the two things that seem to defeat the tantalizing cave-man solutions (y'know, nothing that can't be made with the ten essentials and a dead goat) we we are striving to find here.
Unfortunately, it doesn't address the small-extension requirement and so isn't quite ready for prime time just yet.
When it is, make sure it doesn't weigh more than two locking belay biners (needed, for example, for the equalette) and you will soon be the filthy-rich CEO of Equalizers Are Us.
Just remember where you got your start.
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rgold
Trad climber
Poughkeepsie, NY
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Jan 27, 2007 - 01:31pm PT
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After that I made it a rule not to load my anchors if there was any way at all it could be avoided.
Agreed! But fashion is heading in another direction. I regularly see climbers setting up virtual hanging belays on ledges that they could sit down on fully braced. Based on some discussions I've had, I think one of the reasons for this is that newcomers spend a day with a guide to learn about constructing belay anchors and then replicate the set-up they were taught---hanging back on the rope, stacking the slack on the tie-in, belay device on the anchor or belay redirected through the anchor---in every location regardless of its bracing potential.
The fact that fewer and fewer climbers interpose anything between the belay load and the anchor makes it more important than perhaps it used to be to find absolutely optimal anchor rigging techniques.
The Italians whose work I referenced above seem to think that belaying the leader directly off the anchor is a good idea too.
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