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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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