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Common KNs in real world falls
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jt512


Feb 8, 2010, 4:38 PM
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Re: [Jo_Rock] Common KNs in real world falls [In reply to]
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Jo_Rock wrote:
Friction in the rope system can increase fall forces significantly when you are further out on the pitch, right?

Fundamentally, it's not a question of where you are on the pitch, but rather, what the "nominal" fall factor is. What friction does is to increase the fall factor, producing an "effective" fall factor. But the effective fall factor still can't exceed the maximum theoretical value of two.¹ In the UIAA test, the fall factor (1.78) is close to 2, so there's not much "room" for friction to have an effect.

However, if the nominal fall factor is lower—as it normally would be further from the belay, with more running pro placed—then friction can cause a larger effect. In principle, with enough friction, you could turn a harmless 0.15-factor fall into a horrendous fall approaching fall factor 2. But, qualitatively, the results are the same, regardless of the nominal fall factor: friction will increase the force on the climber, and decrease it on the belayer and the top anchor. See the discussion in my paper.

Jay

¹ Can we, for once, agree to leave via ferratas and other weirdnesses that can result in fall factors greater than 2 out of the discussion?


(This post was edited by jt512 on Feb 8, 2010, 4:43 PM)


Jo_Rock


Feb 8, 2010, 4:45 PM
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Re: [Jo_Rock] Common KNs in real world falls [In reply to]
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I realize my problem now. I am not mathematically gifted so I was trying to simplify the model and went with 10m to first piece, 10m above that piece, 20m fall, 20m rope out = FF1. This is a lot easier than the math in the UIAA drop test, it just gives different results. If there is no friction you get rope stretch equal to 20m of rope. If friction reduces the force on the belayer to 1/2 of the force on the climber the rope on the belayer side will stretch 1/2 as much as the rope on the climbers side meaning that the climber is decelerated in a shorter distance/time and increase the total force on the anchor, right? This is effectively the same as you would get with a FF 1.5 with no friction, right?

If this is true. (??????) and if that increase in force applied to a UIAA drop test (now even I realize that it doesn't) then you would have results that are the opposite of the what the table shows.

Recommendation: Save a link to this page so the next time I post something stupid in the middle of the night you all can just remind me of where it will lead.

Thanks for helping me figure this out as I could never make it through the math to understand all of this on my own.


Jo_Rock


Feb 8, 2010, 4:52 PM
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Re: [jt512] Common KNs in real world falls [In reply to]
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jt512 wrote:
Jo_Rock wrote:
Friction in the rope system can increase fall forces significantly when you are further out on the pitch, right?

Fundamentally, it's not a question of where you are on the pitch, but rather, what the "nominal" fall factor is. What friction does is to increase the fall factor, producing an "effective" fall factor. But the effective fall factor still can't exceed the maximum theoretical value of two.¹ In the UIAA test, the fall factor (1.78) is close to 2, so there's not much "room" for friction to have an effect.

However, if the nominal fall factor is lower—as it normally would be further from the belay, with more running pro placed—then friction can cause a larger effect. In principle, with enough friction, you could turn a harmless 0.15-factor fall into a horrendous fall approaching fall factor 2. But, qualitatively, the results are the same, regardless of the nominal fall factor: friction will increase the force on the climber, and decrease it on the belayer and the top anchor.


Pretty much what I was trying to say, I think, while we were simul-posting. As for referencing the linked paper, those bits in early cuneiform scare me!

Thanks to you especially for helping me remove my head, it was getting stuffy in there.


Jo_Rock


Feb 8, 2010, 5:12 PM
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Re: [Jo_Rock] Common KNs in real world falls [In reply to]
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I had actually hoped that my original post would lead to more discussion of the validity of their assessment of the needed strength of pro and if there are other similar independent studies that reach similar results. The erroneous error catching was just supposed to be an aside, but I guess around here at under 2 pages it is pretty insignificant.

edit: ok, under 3. My second post actually and that still didn't really come out clear at all.


(This post was edited by Jo_Rock on Feb 8, 2010, 5:16 PM)


brenta


Feb 9, 2010, 6:23 AM
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Re: [jt512] Common KNs in real world falls [In reply to]
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jt512 wrote:
The methodology for these calculations is explained here.
Thanks for posting that article.

Attaway seems to make an incorrect assumption, but maybe it is correct in a way that is too subtle for me. I'll use your notation to describe it.

If we say that T2=k*y2/L2, we assume that the length L2 of rope, once stretched, is under tension T2. However, the distance between the belay end of the rope and the top anchor is fixed (L2), and whatever rope moves to the climber's side of the biner is actually under tension T1.

The way I've seen similar problems modeled is to use the length of unstretched rope that moves to the climber's side of the biner as basic variable--let's call it s2 and then say that T2=k*s2/(L2-s2). That is, a rope of length L2-s2 stretches until its length is L2. On the other side, we have now L1+s2 unstretched rope, which stretches according to T1=k*y/(L1+s2), where y is the total amount by which the entire rope lengthens.

The rest of the derivation would follows the usual lines; that is, one would still set up an energy balance equation, though the expression for the elastic energy obviously would change as well.


(This post was edited by brenta on Feb 9, 2010, 6:24 AM)


JimTitt


Feb 9, 2010, 7:42 AM
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Re: [brenta] Common KNs in real world falls [In reply to]
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However the thorny problem still arises in that one is assuming that the rope is moving from the T2 to the T1 side at a constant rate (or a least with a constant decceleration) but this is not what occurs. The frictional constants used in most papers are a simple fudge factor which gives reasonable results on a larger time scale but when we look at higher speed traces of the forces it is apparent that friction and the T1/T2 issue are not following the rules.
Depending on the fall rate and the way the rope is braked it is clear that at some times the rope will actually go backwards through the karabiner which is going to make a unified theory of everything a bit difficult!
It´s also apparent that µ (if we extract it from T2/T1) varies between 0.35 and 0 with negative values when T1 becomes greater than T2 (and in some applications we are getting up to 0.6 but these are not concerned with falls).

For most practical purposes jt´s model gives a good match to an experimental force curve when it has been considerably smoothed out but the short term peaks are massively higher than one predicts (and the corresponding troughs naturally). The damping of the rope smooths a lot of these out but you would still be suprised to see some of the forces that are appearing, though they don´t seem to be breaking things so perhaps the make it unbreakable concept is still the way to go for gear designers!


hafilax


Feb 9, 2010, 8:21 AM
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Re: [JimTitt] Common KNs in real world falls [In reply to]
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JimTitt wrote:
However the thorny problem still arises in that one is assuming that the rope is moving from the T2 to the T1 side at a constant rate (or a least with a constant decceleration) but this is not what occurs. The frictional constants used in most papers are a simple fudge factor which gives reasonable results on a larger time scale but when we look at higher speed traces of the forces it is apparent that friction and the T1/T2 issue are not following the rules.
Depending on the fall rate and the way the rope is braked it is clear that at some times the rope will actually go backwards through the karabiner which is going to make a unified theory of everything a bit difficult!
It´s also apparent that µ (if we extract it from T2/T1) varies between 0.35 and 0 with negative values when T1 becomes greater than T2 (and in some applications we are getting up to 0.6 but these are not concerned with falls).

For most practical purposes jt´s model gives a good match to an experimental force curve when it has been considerably smoothed out but the short term peaks are massively higher than one predicts (and the corresponding troughs naturally). The damping of the rope smooths a lot of these out but you would still be suprised to see some of the forces that are appearing, though they don´t seem to be breaking things so perhaps the make it unbreakable concept is still the way to go for gear designers!
I think that the analytic approach has been pushed as far as is reasonable but do you think a numerical dynamics simulation could push things further?


JimTitt


Feb 9, 2010, 11:04 AM
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Trouble is I´m not that much of a mathematician to know where to start!
The wave forms we are seeing on the braking side of the system give quite a lot of concern (at least in what I´m doing) and to work out the damping effects further up the chain is going to need something much more powerful than simple analysis is capable of. (One problem is that these waves were discussed and theorised as inertial effects a few years back, subsequently we can see that this was a false turning and that other factors were at work but no one seems to have got to grips with this yet). In many ways Pavier showed the way with fluid theory but I guess we need something better, glad you volounteered!
If one could develop a truly dynamic simulation then a lot of the gear designers work would be simpified, currently it is still a bit of "suck and see" but the pressure for ever lighter and ever better is pushing this approach a bit, at least in the development time required.
One major area of concern is the increasing trend to autolocking and autoblocking belay devices on fixed belays where it´s clear the loads are becoming much higher than is generally realised especially with lower factor falls. A lot of this is to do with the unrestrained nature of the locking mechanisms on Grigri´s and such (which is another theme) but even with guide plates the forces are considerably higher than one likes to see without the benefit of a fatty belayer as a shock absorber.

Obviously the desirable situation would be a dynamic simulation where we can change parameters to reduce the loads so we know where to look, then either belayers can change their habits, other kinds of belay device be developed or the rope manufacturers can alter the rope dynamics. Other uses are to save the empirical correlation between pull tests (which are cheap and easy) to drop tests, at the moment we make a good guess based on pulls and then have to drop test, particularly a pain in the neck with rope access gear which have specified maximum forces.

Hmmm, we need an industry sponsor and a couple of brilliant mathemeticians, I´ll make the coffee and fetch the beer! (Talking of beer it´s 8pm, prost!)


jt512


Feb 9, 2010, 1:26 PM
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Re: [brenta] Common KNs in real world falls [In reply to]
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brenta wrote:
jt512 wrote:
The methodology for these calculations is explained here.
Thanks for posting that article.

Attaway seems to make an incorrect assumption, but maybe it is correct in a way that is too subtle for me. I'll use your notation to describe it.

If we say that T2=k*y2/L2, we assume that the length L2 of rope, once stretched, is under tension T2. However, the distance between the belay end of the rope and the top anchor is fixed (L2), and whatever rope moves to the climber's side of the biner is actually under tension T1.

The way I've seen similar problems modeled is to use the length of unstretched rope that moves to the climber's side of the biner as basic variable--let's call it s2 and then say that T2=k*s2/(L2-s2). That is, a rope of length L2-s2 stretches until its length is L2. On the other side, we have now L1+s2 unstretched rope, which stretches according to T1=k*y/(L1+s2), where y is the total amount by which the entire rope lengthens.

I need to think about it more, but, IIRC, ptlong has raised a similar objection.

Jay


brenta


Feb 14, 2010, 1:02 PM
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Re: [brenta] Common KNs in real world falls [In reply to]
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brenta wrote:
y is the total amount by which the entire rope lengthens.
I finally got to play a bit more with this problem. The above quote is (rather obviously) incorrect. The total stretch is s2+y: s2 on the belayer's side and y on the climber's side. With octave's help, I got the following graph for the force at the top anchor as a function of the fall factor:



It is not terribly different from those based on Attaway's formulation, but it does show crossings. Reassuringly, for mu=0 my solution coincides with Wexler's. The graph was obtained for k=20 kN.

Of course, the assumption that a rope behaves like an ideal spring is rather crude and masks some interesting effects.


(This post was edited by brenta on Feb 14, 2010, 7:31 PM)


patto


Apr 19, 2010, 7:07 AM
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Incident Report of a Factor 2 Fall

From http://www.chockstone.org/...mp;Replies=4#newpost

PATW
In reply to:
19/04/2010
Thought I'd share a recent experience of a "Factor 2" fall with the hope that anyone interested may learn from it:

My gf and I were on "Lamplighter" at araps. It was her lead on the second pitch – her first on a multi pitch route, having not led much on trad before. As she left the belay I encouraged her to put in a piece early, or clip the top piece of the anchor on the way past. I was a bit surprised when she charged up a couple of metres without slotting anything but wasn’t concerned because she had been completely solid on lead for the whole trip and it looked like there were good slots for gear just above. It was a bit of an awkward stance – slabby, but without a customary grade 14 bucket to hang off – and after trying to place a nut or two, it was clear that those slots weren’t so good after all. She had skipped the fixed pin with my encouragement (“not really trustworthy”).

At this point she started getting a little flustered and poked in a small cam (a yellow WC Zero). It wasn’t aligned with the direction of the fall so I got her to move it, but apparently that made the cam lobes go crooked and offset and it looked dodgey so she moved it back. After all this frigging around she was getting pumped and stressed and suddenly the delicate moves in an increasingly airy position got a bit hard. She tried the next move but half fell, half retreated to rest on the cam. The cam ripped out and she went for the big plummet. Thankfully she sailed right out over the belay ledge, over the slab below and the ropes pulled her up on the steeper section below that.

She came up pretty much without a scratch, very fortunate given that she’d just taken a factor two fall which probably ended up being greater than six metres from top to bottom. It was by far the nastiest fall I’ve seen. She heroically got back up, and after a brief pause to check all limbs were intact, she charged on and led the pitch (one of the best pitches ever, though some of the gloss was probably taken off for both of us). This time she headed off with a bomber nut placed just above the anchors and also clipping the fixed pin above that.

Unfortunately I didn’t come off quite so well. I was sitting on the edge of the big comfy belay ledge, and as she sailed past the ropes ran over my leg. As the ropes came up tight, my leg got squished between the ropes and lip of the ledge. At first I thought my leg just had a deep, juicy bruise but it turns out that I had torn my hamstring as well. My guide hand (on the climber’s side of the belay device) got smashed into the rock. Just as predicted in the manuals, some rope slipped through the device and gave me some minor rope burn. I may also have damaged my sciatic nerve, possibly from the impact being transferred through my harness and into my lower back. My physio and I are still working out the exact nature of the damage to my leg and back, but whatever, it’s bloody painful and I may be out of action for a while.

Interestingly, it seemed that the anchor had taken very little of the impact. All the pieces popped out easily (two nuts and a hex) when I cleaned the anchor. The knot in my cordelette may have tightened up, but only a fraction. I was clove hitched into the ‘power point’ of the anchor with both strands of our double ropes and there wasn’t any slack. It appeared that most of the energy from the fall was transferred elsewhere in the system, a lot of it into my body – possibly an example of just how effective the old-school method of hip belaying from a good stance could be?

Anyway, the message is: Don’t be a muppet! Learn from our mistakes and remember...

- Factor two falls are bad for your health and bad for your belayer too.

- On multi pitch, place that gear as soon as possible off the belay, even if it is while you are standing right there next to your belayer on that cosy ledge. If the anchor is bomber (we could have towed away the Pharos with ours), consider clipping one of the pieces.

- Small cams need to be placed with care and with and good understanding of their limitations if you are to trust them. They may not be the best tool for beginner trad leaders.

- If climbing with an inexperienced partner make sure they understand the concept of fall factors before setting off on that multi pitch classic, even if you expect it to be a cruise.

- Learn all you can about building good anchors, and make sure they are up to taking a factor 2. You never know when you might need it so save the bacon of you and your climbing buddy.

My 2cents:

Factor 2 falls are bad. They are not good for the climber of the belayer. I'd be far less worried about dodgy anchors and moosalette/equallette equalisation issues. And more about actually getting the catch done.

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