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Ed Hartouni
Trad climber
Livermore, CA
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Topic Author's Original Post - Mar 19, 2006 - 12:51am PT
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I was a bit frustrated at not finding the Young's modulus of commonly used climbing slingage for a recent calculation. It is not hard to find this information for climbing ropes, a lot of discussion by the rope manufacturers centers on the spring constant K,
F = Y*A*(dL/L)
where F is the force elongating the rope, Y is the Young's Modulus, A the cross sectional area, dL the extension of the rope and L is the length of the rope. Usually the constant K is defined as K = Y*A, it has units of Newtons or kiloNewtons...
Rope manufactures will often give the "static extension" of the rope under an 80 kg mass, it is easy to calculate K from this:
K = mg/(dL/L)
where mg = 784 N,
dL/L is the manufacturer's number, 7% is typical for dynamic ropes, that gives:
K = 785 N/0.07 = 11,208 N. See the Beal Ropes web page for some of this information.
The K can change depending on the load (the ropes do not have a linear response). The question I had was what is the K for slings. Usually the manufacturer will only quote the breaking strength. That isn't was I needed as I was interested in the dynamic response of the slingage under loading, far from it's breaking strength.
So I went out and got a bunch of slingage and hung some weights on it to measure the extension... This is what I found:
For nylon tube webbing (I got 1", 3/4" and 9/16") the extension is about 3%, which gives a K ~ 24,000 N within about 30%. Good enough for my work.
For a 7mm perlon cord the extension is about 2.7% with K~30,000 N (also to about 30%).
For 5mm spectra cord the extension is about 0.7% with K~109,000 N.
So the extension for "nylon" webbing and utility cord seems to be about half that of a lead rope, and for spectra, about a tenth of the extension.
Anyone else ever think about this?
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WBraun
climber
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Mar 19, 2006 - 01:01am PT
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Ed
We've discussed this here at Yosar. For rescue rigging a lot of this stuff will be analyzed for the dynamics and forces exerted on the anchor systems.
I believe Dill loves this stuff too, he went to MIT as physics major.
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rgold
Trad climber
Poughkeepsie, NY
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Mar 19, 2006 - 01:21am PT
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I've wondered about this too. Given that the response is not precisely linear, one might want to calculate it at loads approximating the loads one is interested in. Climbing ropes are engineered to stretch as little as possible at low loads, so it might be better to calculate the spring constant K from the published UIAA impact force rating. This turns out to be
[K = F(F-1.568)/1.396] Edit: should be F(F-1.568)/2.792
where F is the UIAA impact force in kN. The other numbers come from the standard formula for impact force, the fact that the falling weight is 80 kg, and the fall factor is 1.78.
This is the calculation I've used, but I've never compared it to the static elongation figure to see if there is any discrepancy.
I do remember a test reported in a UIAA journal that the UIAA impact force for a sewn nylon sling (don't recall the width) was 18 kN or about twice the impact force of a climbing rope. There are no engineers trying to reduce the elongation of slings under low loads, so the calculation there might be more accurate.
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Ed Hartouni
Trad climber
Livermore, CA
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Topic Author's Reply - Mar 19, 2006 - 01:22am PT
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Werner - sort of what I was doing, calculating the loads on various anchor systems (cordelette, sliding-x) from the long discussion on rc.com. John Long is updating the Climbing Anchors book, and has had various anchor setups tested.. with some very interesting results.
I was just trying to see if I could calculate some of these in idealized settings and reproduce the general features of the tests, which I think I was able to do. I had to estimate the properties for cord, I guessed about a factor of 2 stiffer than the lead rope. Glad that my tests today verified that.
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Ed Hartouni
Trad climber
Livermore, CA
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Topic Author's Reply - Mar 19, 2006 - 01:28am PT
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rgold - thanks for the non-linear formula! The slings are "quadratic" at low load to, but the other way, the stretch more under small loads and stiffen as the load increases (at least according to my data, and one other plot that I saw on this). I can refit the data, but it is probably not relevant (as it occurs at very small loads).
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WBraun
climber
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Mar 19, 2006 - 01:37am PT
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The elongation of spectra as you've confirmed is very small and presents a real danger for daisy chains made from this material.
I can really phuck you up royal if one takes a wipper onto it. I believe we've had one rescue on El cap attributed to this.
Take note big wall aid climbers.
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Ed Hartouni
Trad climber
Livermore, CA
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Topic Author's Reply - Mar 19, 2006 - 02:04am PT
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Richard,
If I fit Beal's curve (see link above) I get something more like this:
K = F*[F - 1.570]/2.78
K in Newtons, F in kN. Which is smaller than your formula...
I get:
K = F(F - 2mg)/(f 2mg)
where m is the mass, g is the gravitational constant and f is the fall factor.
For 80kg: 2mg ~ 1.57kN,
for a factor 1.77 fall, f2mg ~ 2.77kN
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rgold
Trad climber
Poughkeepsie, NY
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Mar 19, 2006 - 02:41am PT
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Ed, you're right. We have the same symbolic formula. I didn't multiply my denominator by 2 when I posted. (Edit: see correction on original post.]
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Fingerlocks
Trad climber
where the climbin's good
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Mar 19, 2006 - 12:43pm PT
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Ed,
You looked at the Spectra cord, but how about Spectra webbing? Does being woven give it a bit more give?
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Ed Hartouni
Trad climber
Livermore, CA
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Topic Author's Reply - Mar 19, 2006 - 04:41pm PT
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I only tested what I could get from my local shop, Sunrise...
...I will probably order some more varieties from Mountain Gear to check. But I actually have most of what I want now...
It doesn't pay to try to be too precise as the variations in the products are rather large. My guess is that the breaking strength stats are extremely conservative, as they should be. But in terms of calculating what happens to anchors, a la the rc.com discussion, getting the modulus to 30% is sufficient.
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roy
Social climber
New Zealand -> Santa Barbara
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Mar 19, 2006 - 05:46pm PT
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Hi,
There's also a trend towards using presewn spectra on cams and draws. Exactly where I would like to see a bit of elongation for shock absorption. One reslinging service uses Spectra Ultratape; very high breaking strength, but does anyone know the Young's modulus for this?
Cheers,
Roy
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Wheatus
Social climber
CA
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Mar 19, 2006 - 08:37pm PT
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Ed,
I posted this web link last year on testing of various cord materials. This link does not address your question but it illuminates many interesting considerations other than static elongation.
http://www.xmission.com/~tmoyer/testing/High_Strength_Cord.pdf#search='Technora%20fibers,%20Tech%20Cord
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Ed Hartouni
Trad climber
Livermore, CA
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Topic Author's Reply - Mar 19, 2006 - 09:34pm PT
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Wheatus, thanks for the link, I checked it out in my research on the modulus for sling material. It is a nice paper on the breaking strengths and the effects of "bending" on the strength (as well as other things).
The breaking strength may be an important parameter in some applications, but it is not important for calculating the dynamic response of the material to loading. That was what I was interested in.
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Rags
Trad climber
Sierra foothills, CA
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Mar 19, 2006 - 10:56pm PT
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Quote: "The elongation of spectra as you've confirmed is very small and presents a real danger for daisy chains made from this material.
I can really phuck you up royal if one takes a wipper onto it. I believe we've had one rescue on El cap attributed to this.
Take note big wall aid climbers."
Werner, are you suggesting that taking a daisy fall on spectra chains is not a good idea (half kidding). It was someting I considered in the past, but was unaware that the difference to nylon was so significant.
Ed,We are not dealing with a lot of material here. What exactly are the force differences in application?
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Ed Bannister
Mountain climber
Victorville, CA
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Mar 20, 2006 - 11:52am PT
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Why do you guys think that two or three feet of spectra, or half inch wire cable for that matter, has any significant effect on a system with 20, or 180 feet of dynamic rope in it? A daisy chain affecting impact force? You might as well try to measure which rock your fall was "absorbed" by!
Sure, if you were to fall 20 feet on a spectra rope, it would cut you in half if you could get the knot to hold, but that would not be done either. All your spectra products are only half, or less spectra, the stuff by itself will not hold a knot.
Ed (Bannister, not Hartouni : )
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lazide
Big Wall climber
Bay Area, CA
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Mar 20, 2006 - 12:16pm PT
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Werner: what makes it worse is that it is almost impossible to buy nylon daisy chains in many stores (REI, etc) any more. I pity the folks taking daisy chain falls on them! (I only use traditional daisies for gear organization at bivies any more)
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Ed Bannister
Mountain climber
Victorville, CA
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Mar 20, 2006 - 02:47pm PT
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My daisy is 36 inches long. Ed, what force is exerted by a 72 inch freefall of 80 kg??
A bar tack sewn with 42 stitches yields roughly these results per thread size:
#138 nylon thread 750 - 800 lbs.
#92 nylon thread 450 lbs.
#69 nylon thread 350 lbs.
If the force was huge... wouldn't the tacks rip and absorb energy long before the loop failed?
Daisys properly sewn are in a loop with six tacks at the anchor and normally three tacks between incremental loops.
Most narrow web is rated north of 3,000 lbs. and, lest we forget, daisys are loops, so the number must be doubled for a realistic failure number. Spectra is yet stronger and more resistant to cutting than nylon.
Who broke one, where, when, and Who was the maker?
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hobo
climber
PDX
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Mar 20, 2006 - 04:32pm PT
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For Werner:
I know dill has compiled quite a lot of information, and arganized it well, on this subject and more. Is it possible to put some of this on the web? Calculations and all? Thanks for any help.
alex
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Rags
Trad climber
Sierra foothills, CA
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Mar 20, 2006 - 06:51pm PT
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Thanx for the link Del, I hadn't seen that before.
I think the last of the article is sage advice.
"Lastly, many of us have just been dodging the bullet. Time to change our ways. After witnessing carabiners, slings and daisy chains explode in what I previously considered minor falls, I’m rethinking the way I aid-climb: instead of clipping a daisy chain to a placement and keeping it clipped in until after I’ve climbed above the piece, I’m going to clip the rope to that piece and unclip the daisy before I climb past it. Then, if I fall, I can ride on down the easy way."
That more or less answers my earlier questions..
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Russ Walling
Social climber
Same place as you, man...... (WB)
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Mar 20, 2006 - 09:01pm PT
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Alps wrote:
**A bar tack sewn with 42 stitches yields roughly these results per thread size:
#138 nylon thread 750 - 800 lbs.
#92 nylon thread 450 lbs.
#69 nylon thread 350 lbs. **
on the pure math thing I use the following: (bst = breaking strength of thread) 13lbs. with #92.
bst X 2 X 42 with bs being 13 and then minus 10% for heat. So, 13 (bst) x 2 (top and bottom thread) = 26 x 42 (stitches in cycle) = 982 +/- per tack. In a loop, these numbers are verified by testing to failure.
If the force was huge... wouldn't the tacks rip and absorb energy long before the loop failed?
Seems true to me. Over a long daisy there a a lot of tacks to break. We have something like 9 pockets with 3 tacks each. 27 tacks is some sort of "lab type ripper"™™™ that probably does not exist in the real world.
Daisys properly sewn are in a loop with six tacks at the anchor and normally three tacks between incremental loops.
True
Most narrow web is rated north of 3,000 lbs. and, lest we forget, daisys are loops, so the number must be doubled for a realistic failure number.
True, more or less.
Spectra is yet stronger and more resistant to cutting than nylon.
So they say.
Who broke one, where, when, and Who was the maker?
Unknown, unknown, unknown, and wasn't me!!!
Here are some pics of a test I just did a few minutes ago, since it was beer thirty and all:
Web is 11/16" tubular nylon, thread is either #69 or #92 and has a BS of about 13lbs. Bartack has 42 stitches per cycle.
The clip of DEATH™™™ will get you killed.
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Ed Hartouni
Trad climber
Livermore, CA
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Topic Author's Reply - Mar 20, 2006 - 11:53pm PT
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So let me say on the out set that I am not an engineer, just a physicist, and my interest is in estimating the forces, not in calculating the limits of gear. But that being said...
the impact force for a fall is:
F = mg + mg sqrt[1+(2fK/mg)]
where mg is the product of mass and the gravitational constant (g = 9.807 m/s^2),
f is the fall factor, K is the product of the modulus and the cross sectional area.
For a factor 2 fall of an 80 kg climber and a sling material K= 30000 N (nylon sling)...
F = 10.5 kN
if K = 109,000 N, F = 19.3 kN
A breaking strength of 3000 lbs is 13.4 kN so your nylon sling is ok if the sewing doesn't blow.
Depending on the spectra you get, the breaking strength is about 3000 to 4500 lbs, or
from 13.4 to 20.0 kN. It looks like you don't want the daisy made out of spectra.
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WBraun
climber
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Mar 21, 2006 - 12:08am PT
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WOW!
Nice test Russ, clip of death, ........ coooool!
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Ed Hartouni
Trad climber
Livermore, CA
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Topic Author's Reply - Mar 21, 2006 - 12:55am PT
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I am not so sure about doubling the strength... if you have the sling looped through a 'biner, then think about the tension in the sling at the 'biner... there is only one thickness of sling, and it sees a tension equal to the impact force.
So that is actually a prediction. Russ, if you just pull on a loop of webbing where does the webbing fail? I'd guess at one or the other 'biners.
Anyway, I'm sure that manufacturers test this stuff, or that the UIAA or some climbing organization... but I am also a true believer in nylon sling... I tie many of my own slings, I re-sling my cams with tied nylon sling, most of my utility cord is nylon sling (and the stuff I have slung with spectra I'm probably going to resling with nylon).
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Russ Walling
Social climber
Same place as you, man...... (WB)
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Mar 21, 2006 - 01:29am PT
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Ed with the big brain sez: (not that the other Ed has a small brain or anything... you know what I mean...)
So that is actually a prediction. Russ, if you just pull on a loop of webbing where does the webbing fail? I'd guess at one or the other 'biners.
The webbing or cable or anything really will fail at the pulling points, be it a biner, a 10mm pin or whatever. Provided that the stitching or swage or whatever you are testing is full strength of the particular material or better.
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rgold
Trad climber
Poughkeepsie, NY
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Mar 21, 2006 - 01:44pm PT
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I am not so sure about doubling the strength... if you have the sling looped through a 'biner, then think about the tension in the sling at the 'biner... there is only one thickness of sling, and it sees a tension equal to the impact force.
As a mathematician, and not at all an applied one, I'm even further removed from the realities of equipment failure than physicist Ed, but...
I've certainly read practical pull tests confirming that the breaking strength of loops is approximately double the strength of the sling material. For example, here is Chris Harmston, quoted on Russ's Tech Weenie pages:
"Most people would assume that the strength of a loop is twice the strength
of the single strand breaking strength. What I have found is that this is
not correct for two reasons. First is that the tack does factor in. It
is not always easy to ensure that the tack is stronger than the webbing.
So take off 5%. Second is that the single strand strength is obtained by
testing over large radii. Loops are tested over 10 mm pins. The pins
weaken the loop as you should expect. So remove another 5%. What I find
is that the loop strength is about 10% weaker than 2 times the single
strand rating. This is plus or minus 5% or there abouts."
Although the sling material may be weakened in the bend over the carabiner, I don't think the "one thickness of sling" argument is persuasive. If the carabiner acted as an ideal pulley, then the tension in the sling would be the same everywhere, including at the pulley wheel, "single thickness" or not. To the extent that the carabiner is not an ideal pulley, friction around the biner might prevent the equidistribution of tension, and so it seems plausible that the tension in the part that bends around the biner might be somewhat higher. There are also probably materials-level effects relating to the fact that slings have a thickness and so not all strands bend with the same radius. These effects would account for slings braking at the biner when tested, but according to Harmston these effects are in the 5% range, and so loops are ideally twice the strength of the material, and in practice are still roughly twice that strength.
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rgold
Trad climber
Poughkeepsie, NY
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Mar 21, 2006 - 03:49pm PT
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Before we go too far piling on poor ol' spectra, it is worth remembering that both spectra and nylon slings are not meant to absorb fall energy, that's the rope's job. I don't think one has to worry about spectra runners and draws used for protection, because the rope does the energy absorbtion, imparting in the absolute worst (and very rare) cases perhaps 13 kN to the draw or runner, which can handle loads around twice that much without breaking.
The problems happen when a nylon or spectra sling is required to be the sole agent absorbing fall energy, for example if an aid fall is arrested by a daisy. Then potentially catastrophic tensions are a possibility. In such cases, you may be better off with nylon, but you ain't in good shape no matter what textile you're relying on.
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Ed Bannister
Mountain climber
Victorville, CA
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Mar 21, 2006 - 11:55pm PT
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Thanks for the laugh Russ.
my brain might be smaller, but I use both halves!
The web breaks at the radius around a biner, Russ is right again...
and what happens to the pro is in fact more important than the sling in most cases...
In product development, I have broken a lot of biners, and a lot more web.
I use nylon runners sewn by me, or Russ, or Phil.
Russ you would like the fact that i used to pull stuff apart at the Russ Anderson developed pull tester in the Sierra Madre fire station. not too great for data though, the best came from the Edelrid test tower while Bernt Prause was there.
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Russ Walling
Social climber
Same place as you, man...... (WB)
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Mar 22, 2006 - 12:37am PT
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I remember the OLD Russ in Sierra Madre.... he still living??? (I know I'm not)
Breaking things is fun. Knowing what they break at is even funner.
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Ed Hartouni
Trad climber
Livermore, CA
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Topic Author's Reply - Mar 22, 2006 - 01:47am PT
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If I pull a single strand with a force on each end which is equal, the tension is twice the force when the strand is not moving (equal and opposite forces). This is the situation when you have a frictionaless pulley. If the tension exceeds the breaking strength of the sling then it will break. This is not at twice the single strand breaking strength. The impact force will pretty much distribute evenly on both sides of the strand. When the impact force exceeds the sling breaking strength the loop will break.
The frictional forces of cord wrapped around a spindle are exponential in the wrap angle. We all know that to get more friction from a rope you increase the amount the rope is wrapped around something.
The force that you have to pull to keep the rope from moving is:
F = F0 exp(-mu*theta)
where theta is the angle around which the rope is wrapped, mu is the coefficient of friction and F0 is the force on the rope.
For the case of a sling wrapped around the 'biner, half the force is on one leg of the sling, and half on the other. The tension of the sling at the "top" of the 'biner can be calculated by considering theta=pi/2...
I don't have the coefficient of nylon sling on aluminum, but plastic on aluminum has a mu ~ 0.4 (same for cardboard) then
Tension: T = 2*(F/2)exp(-0.4 * pi/2) = 0.53*F
The "strength" of the loop is increased about 1.9 times that of the the single strand.
Note that this calculation assumes that the sling material has the same properties throughout its bulk. This is very much not what is observed... but friction around the 'biner does seem to play an important roll in the effective strength of the sling.
Also, if the coefficient of friction is smaller the force increases, for instance take teflon, which would have a COF of about 0.04, T = 0.94*F.
This is complicated in the case of a kernmantel constructed cord as the mantel-to-sheath COF and the sheath-to-aluminum COF may all be different, and with very different performance. If the mantel is essential free to move around in the sheath, the effective breaking strength is much reduced.
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mike hartley
climber
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Mar 22, 2006 - 10:43am PT
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For some practical experience on spectra falls; I did take about a 3' spectra daisy fall years ago. With my belly and aid rack that probably amounted to ~190 lbs. I ripped one pocket out but the 1" cam in Navajo sandstone held. I felt pretty lucky.
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lazide
Big Wall climber
Bay Area, CA
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Mar 22, 2006 - 11:01am PT
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One thing to keep in mind about that mag test (if I remember correctly) - they used a 80 kg steel weight for that 3' drop, right?
My guess would be that if you used a steel cable in the same test (rated to the same strength) it would break as well when the nylon wouldn't.
A steel weight does NOT duplicate the forces of a 3' fall by a human in this scenario - I would guess that if they did that same 3' drop with a haulbag full of loose sand or water (with the same mass), it wouldn't of broken.
That said, I still think using spectra daisy chains for anything that could catch a fall is a really bad idea - but not because of the spectra breaking, but because *I* don't want to break. (I would consider myself lucky if the gear pulled!)
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rgold
Trad climber
Poughkeepsie, NY
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Mar 22, 2006 - 12:09pm PT
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Ed Hartouni
Trad climber
Livermore, CA
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Topic Author's Reply - Mar 22, 2006 - 05:54pm PT
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ugh, my brain hurts...
if I have one strand and hang a weight off of it the tension is just mg
if I have two strands, the total tension is just mg, each strand has a tension of half that
if I join the two strands together around a frictionaless pulley, what is the tension of the strand at the top of the pulley? isn't it just mg?
anyway.. I'll work this out over beer on my week long trip without contact to the cyber world.. post more later tonight...
keep it real
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rgold
Trad climber
Poughkeepsie, NY
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Mar 22, 2006 - 09:57pm PT
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if I join the two strands together around a frictionaless pulley, what is the tension of the strand at the top of the pulley? isn't it just mg?
The tension is still mg/2; tensions don't add inside the strand. The tension at any point, as Del X said, is the force either strand exerts on the other at that point, given that the point is in equilibrium. The point at the top of a (frictionless) pulley enjoys no special privileges in this regard.
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Ed Hartouni
Trad climber
Livermore, CA
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Topic Author's Reply - Mar 23, 2006 - 02:58am PT
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ok,ok, classical mechanics was not my thing... that's why I became a particle physicist...
I'll rethink the friction analysis also, probably do some tests once I get back from the desert. A week of climbing.
You all had better figure this stuff out by the time I return!
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hobo
climber
PDX
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Mar 23, 2006 - 10:48am PT
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Hey dudes. Im kinda lost as to what exactly yout trying to figure out, but i just got on spring break and maybe i have some time do some tests. So, what are you tryin to figure out?
alex
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