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ptlong
May 22, 2009, 8:16 PM
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On Monday, May 18, 2009, jt512 wrote: Edit: I have derived an equation for maximum impact force that incorporates the effect of friction at the top anchor, and will post it soon. Jay
Well?
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jt512
May 22, 2009, 8:43 PM
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ptlong wrote: On Monday, May 18, 2009, jt512 wrote: Edit: I have derived an equation for maximum impact force that incorporates the effect of friction at the top anchor, and will post it soon. Jay Well?
I finished a first draft of the write-up yesterday. I need to proof read it today. I may ask rgold if he'd be willing to look it over, too.
Jay
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rocknice2
May 22, 2009, 9:25 PM
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I have always assumed the max impact force of a rope is measured at the climber.
Is this the case or is it measured at the top anchor?
Another thing about the load cell response times.
If the cell takes a reading every 1/1000 sec, how long does it take to get it's data.
Analogy: if I take pictures with my camera in rapid fire mode, I can take pics @ 3 frames/sec and a shutter speed of 1/500 of a sec.
It make s a world of difference if the load cell takes data @ 1000/sec but has a measurement window of 1/1001 of a second.
A third note;
The discrepancy of the analog reading may be due to the momentum of the needle.
This shouldn't be much but I don't recall if the discrepancy difference was posted.
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rgold
May 22, 2009, 10:05 PM
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Been too busy to contribute recently. Used my disposable time for climbing rather than typing!
It is worth noting that Attaway's account in Rope System Analysis includes a good analytical account of friction at the top piece.
http://lamountaineers.org/xRopes.pdf
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JimTitt
May 25, 2009, 7:19 AM
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For rope tests the maximum force is effectively measured at the climber. For other tests you measure where you need the information- at the belayer or top piece for example.
Maybe you should look at how load cells work, they are reading continuously and as fast as the electrons (or rather the electromagnetic wave) can move through the system which is near enough the speed of light. This signal is then sampled by the strain gauge, most sytems running at 15,000 to 500,000 per second. This is usally way too much information so this is then reduced for example to your 1,000 per second to be usable on any reasonable computer, as in your camera analogy the problem is not how fast you can read the information but how fast you can write it on the storage medium.
For a digital display that has to be read directly, such as on a crane scale this is going to be filtered down to 10 per second or less because crane drivers brains cannot read any faster.
The analog description with a needle was a simile to make the concept easier to understand. Rather than sampling the original signal the data acquisition system "looks" at the load cell signal and stores the highest and/or lowest value, again at effectively the speed of light.
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rocknice2
May 25, 2009, 3:38 PM
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Thanks Jim that was very helpful and clear
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ptlong
May 27, 2009, 6:20 PM
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rgold wrote: Been too busy to contribute recently. Used my disposable time for climbing rather than typing! It is worth noting that Attaway's account in Rope System Analysis includes a good analytical account of friction at the top piece. http://lamountaineers.org/xRopes.pdf
Attaway makes an approximation in his expression for the strain energy which he doesn't justify (or even mention). Does this matter? Maybe not since by ignoring belayer dynamics the resulting (somewhat complicated) equation isn't likely to represent real world forces anyways. And without the approximation I'm not sure there is an analytic solution... which is why I was interested to see the tack that Jay took.
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jt512
May 27, 2009, 7:38 PM
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ptlong wrote: rgold wrote: Been too busy to contribute recently. Used my disposable time for climbing rather than typing! It is worth noting that Attaway's account in Rope System Analysis includes a good analytical account of friction at the top piece. http://lamountaineers.org/xRopes.pdfAttaway makes an approximation in his expression for the strain energy which he doesn't justify (or even mention). Does this matter? Maybe not since by ignoring belayer dynamics the resulting (somewhat complicated) equation isn't likely to represent real world forces anyways. And without the approximation I'm not sure there is an analytic solution... which is why I was interested to see the tack that Jay took.
I follow his approach through his Equation 29, but I think he made a mistake in Equation 30 that leads him to the erroneous conclusion that the effect of friction is greatest when the fall factor is high. I come to the opposite conclusion.
What is the approximation that you are referring to?
Jay
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ptlong
May 27, 2009, 8:47 PM
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jt512 wrote: I follow his approach through his Equation 29, but I think he made a mistake in Equation 30 that leads him to the erroneous conclusion that the effect of friction is greatest when the fall factor is high. I come to the opposite conclusion. What is the approximation that you are referring to? Jay
Yes, there are mistakes. As well as a lack of parentheses in places, he inverts L1/L2 in (30), then simplifies the expression as if it were written correctly but maintains the inversion in the quadratic (31). I took this to mean that he copied it incorrectly but did the actual calculations properly. I don't have the patience to crunch the numbers to verify this. It will be interesting to see what you've come up with.
The approximation he makes is to treat the L1 and L2 portions of the system as independent springs. In fact the extension of the L1 portion is not at the same tension as the rest of the L1 portion since it has slipped over the carabiner to the other side. It is at the higher tension of the L2 side. His expression for the tension F2 in (20) ignores this (instead of L2 it should be L2 + delta2 delta1). The result is that he underestimates the strain energy.
(This post was edited by ptlong on May 27, 2009, 8:54 PM)
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jt512
May 27, 2009, 11:14 PM
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ptlong wrote: jt512 wrote: I follow his approach through his Equation 29, but I think he made a mistake in Equation 30 that leads him to the erroneous conclusion that the effect of friction is greatest when the fall factor is high. I come to the opposite conclusion. What is the approximation that you are referring to? Jay Yes, there are mistakes. As well as a lack of parentheses in places, he inverts L1/L2 in (30), then simplifies the expression as if it were written correctly but maintains the inversion in the quadratic (31). I took this to mean that he copied it incorrectly but did the actual calculations properly. I don't have the patience to crunch the numbers to verify this. It will be interesting to see what you've come up with. The approximation he makes is to treat the L1 and L2 portions of the system as independent springs. In fact the extension of the L1 portion is not at the same tension as the rest of the L1 portion since it has slipped over the carabiner to the other side. It is at the higher tension of the L2 side. His expression for the tension F2 in (20) ignores this (instead of L2 it should be L2 + delta2 delta1). The result is that he underestimates the strain energy.
And the underestimation of the strain energy is not accounted for by the frictional work?
Jay
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ptlong
May 28, 2009, 1:41 AM
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jt512 wrote: ptlong wrote: The approximation he makes is to treat the L1 and L2 portions of the system as independent springs. In fact the extension of the L1 portion is not at the same tension as the rest of the L1 portion since it has slipped over the carabiner to the other side. It is at the higher tension of the L2 side. His expression for the tension F2 in (20) ignores this (instead of L2 it should be L2 + delta2 delta1). The result is that he underestimates the strain energy. And the underestimation of the strain energy is not accounted for by the frictional work? Jay
I don't believe so.
Attaway treats both sides of the problem like two seperate springs. But what really happens is that a length of rope slips over the carabiner and adds to the length of the other side while effectively shortening the spring on the belayer side. Attaway's expression for the strain energy doesn't include this.
It may not matter. Afterall Attaway began by first deriving the no friction case and then commenting that everybody knows this is "nonsense". So including friction, even with admitted approximations, is a step in the right direction. It could be that it's a relatively small correction in a model that fails to predict real life results for other reasons.
[edited to remove any trace of mathematics]
(This post was edited by ptlong on May 29, 2009, 1:35 AM)
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cintune
May 28, 2009, 10:13 PM
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Not to interrupt this number crunching too much, but there is a fairly germane discussion of some of these issues in a PDF at http://www.hse.gov.uk/...df/2003/hsl03-09.pdf
The focus is on industrial falls, but it makes for interesting reading anyway.
Carry on.
(This post was edited by cintune on May 28, 2009, 10:13 PM)
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ptlong
May 29, 2009, 1:36 AM
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cintune wrote: Not to interrupt this number crunching too much, but there is a fairly germane discussion of some of these issues in a PDF at http://www.hse.gov.uk/...df/2003/hsl03-09.pdf The focus is on industrial falls, but it makes for interesting reading anyway. Carry on.
Did you download Adobe Acrobat recently? You usually just post a jpeg.
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jt512
May 29, 2009, 1:50 AM
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ptlong wrote: [edited to remove any trace of mathematics]
Wasn't this the post where you derived an expression for tension as a function of fall height and length of the rope segments, continuing from Attaway's results? Did you find a mistake in your algebra? I had plugged numbers into your equation and mine, and came up with different results, and I was wondering if I could be sure that the discrepancy was due to differences in Attaway's derivation and mine.
Jay
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ptlong
May 29, 2009, 1:55 AM
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jt512 wrote: ptlong wrote: [edited to remove any trace of mathematics] Wasn't this the post where you derived an expression for tension as a function of fall height and length of the rope segments, continuing from Attaway's results? Did you find a mistake in your algebra? I had plugged numbers into your equation and mine, and came up with different results, and I was wondering if I could be sure that the discrepancy was due to differences in Attaway's derivation and mine. Jay
I thought you'd grown bored with the whole thing and that the staleness of the thread was attracting a buzzard. So I removed the carrion.
But as long as you copied what I'd posted there's no real harm done.
I really wish rgold would stop working and climbing in his spare time and come back here. He's got this stuff nailed whereas I just dabble.
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jt512
May 29, 2009, 2:14 AM
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ptlong wrote: jt512 wrote: ptlong wrote: [edited to remove any trace of mathematics] Wasn't this the post where you derived an expression for tension as a function of fall height and length of the rope segments, continuing from Attaway's results? Did you find a mistake in your algebra? I had plugged numbers into your equation and mine, and came up with different results, and I was wondering if I could be sure that the discrepancy was due to differences in Attaway's derivation and mine. Jay I thought you'd grown bored with the whole thing and that the staleness of the thread was attracting a buzzard. So I removed the carrion. But as long as you copied what I'd posted there's no real harm done.
But are you confident in your algebra, because tension calculated with your/Attaway's equation differs from mine. So, my question is, can I conclude that that is a difference between Attaway's derivation and mine, rather than an error in your algebra.
In reply to: I really wish rgold would stop working and climbing in his spare time and come back here.
I know. After all, I have.
Jay
(This post was edited by jt512 on May 29, 2009, 2:14 AM)
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ptlong
May 29, 2009, 2:52 AM
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jt512 wrote: But are you confident in your algebra, because tension calculated with your/Attaway's equation differs from mine. So, my question is, can I conclude that that is a difference between Attaway's derivation and mine, rather than an error in your algebra.
I haven't checked the algebra so a mistake is certainly possible. On the other hand I plugged in the numbers that Attaway used and got the same values. So I'm reasonably confident.
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hafilax
May 29, 2009, 6:37 PM
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cintune wrote: Not to interrupt this number crunching too much, but there is a fairly germane discussion of some of these issues in a PDF at http://www.hse.gov.uk/...df/2003/hsl03-09.pdf The focus is on industrial falls, but it makes for interesting reading anyway. Carry on.
http://www.theuiaa.org/...ar_need_to_be(0).pdf
It goes through the estimates of fall forces used in determining the strength standards and procedures in the UIAA tests.
With a dynamic belay, a tube style device and friction they give an upper bound of 7kN for typical forces on running belays. This is supported by field experiments in the 80s on the open strength of biners. There was a sudden decrease in the break rate in going from 6kN open gate strength to 7kN. Experiments indicate that the maximum brake force of a tube style device is between 2 and 4kN and usually on the lower end of that.
The maximum impact force of a rope of 12kN implies that the max force on an anchor from a fall similar to the drop test will be 20kN with a rigid belay and the biner pulley effect with friction. Typical impact forces for modern ropes are more like 9kN so this number will be smaller.
My hypothesis is that 7kN would be kind of the 95th percentile figure for falls on a piece in the middle of a pitch with average forces being at around 5kN and rare events hitting above 7kN.
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adatesman
May 29, 2009, 6:49 PM
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vivalargo
Jan 12, 2010, 7:02 AM
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Hafilax wrote: My hypothesis is that 7kN would be kind of the 95th percentile figure for falls on a piece in the middle of a pitch with average forces being at around 5kN and rare events hitting above 7kN.
----------
That's pretty much my take on it as well.
JL
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Jo_Rock
Feb 8, 2010, 10:56 AM
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I don't know if I should be trying to resuscitate a dead horse here....
Did you notice that in the document you linked to they have force on the runner dropping as friction in the pro biner increases? (table 1 p7) They seem to be assuming that the 12 kN in the UIAA drop test is a law of physics. I think they are assuming that if you change the test jig to increase the friction that the rope will get stretchier in order to still pass at 12 kN.
I also noted that they mentioned that their idea of producing screws of greater strength because the 10 or 15 kN standard is just a minimum, but I don't know if this is a good idea if you are just incresing the strength of the screw and not of the placement, as this might just create a false sense of security. I am assuming that screws are not actually tested in ice or an analog, but in a jig.
Their stuff about typical pro forces is really interesting and seems to fit my real world experiences much better than assuming a static belay, steel masses and figuring from there. I wish they had more of their raw data and methodology in there or some better sources.
edit: link to relevant document http://www.theuiaa.org/...ar_need_to_be(0).pdf
(This post was edited by Jo_Rock on Feb 8, 2010, 11:04 AM)
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Jo_Rock
Feb 8, 2010, 11:16 AM
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Agree with you, the paper, and Vivalargo that most of the common falls are gonna max out around 7 kN [edit: force on pro] as my personal experience is that I've always avoided (so far) the really high impact force situations and never broken (or seen one break) a 10 kN nut with a fair number of falls on them, but.... all of the esoteric discussion of the improbables does wonders for ones ability to spot the dangerous situations and avoid being that "freak" accident.
(This post was edited by Jo_Rock on Feb 8, 2010, 11:18 AM)
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jt512
Feb 8, 2010, 7:32 PM
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Jo_Rock wrote: Did you notice that in the document you linked to they have force on the runner dropping as friction in the pro biner increases? (table 1 p7) They seem to be assuming that the 12 kN in the UIAA drop test is a law of physics.
They're not assuming that it's a law of physics. They're assuming it's the highest force achievable. They spend half of page 6 explaining their rationale for, and the limitations of, this assumption.
In reply to: I think they are assuming that if you change the test jig to increase the friction that the rope will get stretchier in order to still pass at 12 kN.
That would be a ridiculous assumption, and they're not making it. The fact that friction with the top biner reduces the force on the biner is evident from elementary physics. The force on the biner is the sum of the tensions in the belayer-side and climber-side ropes. If the biner were frictionless, then these tensions would be equal, and therefore the force on the biner would be twice the force on the climber side. However, if the biner is not frictionless, then the tension on the climber side must be balanced by the sum of the frictional force and the tension in the belayer-side rope. Thus, the greater the friction, the less the tension in the belayer-side rope, and hence the less the total force on the biner.
Jay
(This post was edited by jt512 on Feb 8, 2010, 9:22 PM)
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Jo_Rock
Feb 8, 2010, 7:53 PM
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I may be missing something or just be an idiot and I could have been clearer, but...
Run the rope through the test stand (assume a polished surface on the redirect that simulates a biner) with a rope that passes at 12 kN. Now, sand and scuff the redirect to simulate a manky biner that increases friction and what happens to the forces? Up right? I think they are making the assumption that the rope must still pass the same 12 kN standard, but it either gets tested with a polished surface or a rough and passes and then it goes into the real world where circumstances change and the rope properties do not.
I may just be following logic that made perfect sense at 4am but now the rut is carved in my brain.
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Jo_Rock
Feb 8, 2010, 8:00 PM
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Just to preempt: I am not saying that the real world does not change rope properties, just that that is not what we are talking about here.
Also I am not trying to imply that it [edit: the erroneous assumption if it is erroneous] effects the conclusions they reach as there [are] other things that come into play as they point out that normally limit the forces to well below theoretical maximums.
(This post was edited by Jo_Rock on Feb 8, 2010, 8:02 PM)
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