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layton

rope drag and fall factor quandry?

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ok, so I'm no engineer so here's a possibly dumb question.

 

I've got two competing ideas when it comes to rope drag and fall factor on the climber (not the belayer) in a scenario of bad rope drag.

 

Climber is 40 meters out with plenty of good pro in, but a shit load of rope drag.

 

1. Climber falls and forces are huge on top piece since rope drag effectively makes his rope shorter...i.e. it's like a factor 1-2 fall.

 

2.Climber falls and forces are lowered because the force of the fall is absorbed by all the friction.

 

So which is it? Is friction good because it absorbs energy of a fall, or bad because it creates a higher fall factor.

 

I had never ever considered the 1st as an option, but the more I thought about it, the more I realized that the length of the rope out becomes "shorter" since the drag on the rope doesn't transmit the force through the whole rope (i.e. only a smaller part of the rope stretches).

 

Would a frictionless system create lower loads on the top piece (even though the belay would now get more of a jolt), or is there a "perfect" amount of friction that absorbs some energy, but allows forces to transmit the entire length of rope out?

 

Finally, what does this mean in reality. Would a rack of DMM revolvers, half ropes, and fully extended slings be a great idea on sketchy gear and soft rock?

 

Food for thought. hope that made sense. I'm out for a couple days, but will check to see what the response is.

 

 

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Hey Mike:

 

I think Option 1 is better than Option 2. I know that in rigging arbor systems, a block (pulley) is prefered to drapping over a limb (no pulley) in part because it reduces the impact force and overall stress on the anchor (the tree top).

 

I think you're getting at it with this:

 

"allows forces to transmit the entire length of rope out"

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If I understand your language in option 2, then I think it is incorrect. Are you saying the force on the falling climber is less than without rope drag? The total amount of force onto falling climber is the same regardless of rope drag. There is a total kenetic energy that must be "absorbed" by the rope system. The rope system spreads out that total energy to minimize impact force onto both protection and climber. With the rope drag, there is less rope to stretch therefore less time to slow down, therefore higher impact forces onto everything, except the belayer. (like what you said)

 

Assuming a frictionless top piece of protection, then the force on the pro piece would be double the force of the falling climber

 

Now if you are saying that the belayer feels less force in your option 2, then you are correct but who cares if that person is feeling less force.

 

The way I see it, friction is bad because it increases the forces imparted onto both protection and climber. Friction would be good if you were concerned about the rope stretching to much and hitting a ledge or something.

 

good question Mike.

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The difference in fall force felt by the climber would be negligible. For anything but a tiny fall, the friction forces are be small compared to the other forces in the system. The rope would still stretch over its entire length, the friction will not "shorten" the length of rope.

 

I am an engineer, so I would know.

 

You could test this with a weight, fish scale and a bungee cord. Let us know what you find.

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Hmmm. In general, I always try to sling things well to minimize rope drag and when that looks like it isn't going to be possible I switch to half ropes (though it can be hard to find belayers competent with halfs - more of an east coast deal).

 

I also have climbed above a lot of marginal pro over the years and have [successfully] fallen on quite a bit of it. In most cases I've used screamers on placements I thought were real borderline and had that pay off as well.

 

IMHO I'd say sling to minimize drag as much as possible and deal with marginal pro independent of that. Oh, and when I've been runout over marginal gear I've never wanted my belayer to fuck around with attempting a 'soft catch', but rather just lock that puppy up and either my gear holds or it doesn't.

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The difference in fall force felt by the climber would be negligible. For anything but a tiny fall, the friction forces are be small compared to the other forces in the system. The rope would still stretch over its entire length, the friction will not "shorten" the length of rope.

 

Agreed.

 

The only way you'd effectively shorten your rope is if you have it truly jammed in a constriction, and even then it's likely that a bunch of the core can still pull through and stretch over the entire ropelength. Correct my if I'm wrong, but the core is about 80% of the strength of the rope.

 

Modern dynamic ropes are pretty amazing.

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I would just add to the discussion that there are two coefficients of friction in any sliding contact system: the static coefficient, which applies when transitioning from not moving to moving, and the dynamic coefficient, which applies to any sliding system already in motion. Typically, the static coefficient is much larger than the dynamic one. A climber on lead will move rope through the system in small increments - repeatedly having to overcome the static friction as the rope stops and starts. This constitutes the bulk of "rope drag" - the energy required to get the system moving. In a fall, the static friction only needs to be overcome once, and then the lower dynamic value applies until the system comes to rest. Once set in motion, energy dissipation through friction between the rope and protection placements, if the route does not wander or zig-zag, is likely to be small in comparison to the energy dissipated through the belay and the rope deformation as the fall is arrested.

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The difference in fall force felt by the climber would be negligible. For anything but a tiny fall, the friction forces are be small compared to the other forces in the system. The rope would still stretch over its entire length, the friction will not "shorten" the length of rope.

 

Agreed.

 

The only way you'd effectively shorten your rope is if you have it truly jammed in a constriction, and even then it's likely that a bunch of the core can still pull through and stretch over the entire ropelength. Correct my if I'm wrong, but the core is about 80% of the strength of the rope.

 

Modern dynamic ropes are pretty amazing.

 

http://www.beal-planet.com/sport/anglais/facteurdechute.php

 

thearetical versus actual

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Rope drag caused by rock is bad. Friction generates heat, which polymers in tension really hate.

 

Rope drag caused by gear would put more rope in the system.

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Interesting thread.....

 

Things I have read so for make sense in my brain for the most part. An element I don't think that has been brought up yet is that of the friction reducing the overall speed generated in an accelerating fall.

 

Sean wrote some good stuff to consider about friction, and stated...

 

"Once set in motion, energy dissipation through friction between the rope and protection placements, if the route does not wander or zig-zag, is likely to be small in comparison to the energy dissipated through the belay and the rope deformation as the fall is arrested."

 

I have FELT THIS. When I have fallen without much friction in the system, I have fallen FAST, and I knew it (after it was over). I have also had several falls where I was way out, with lots of drag (friction) and the falls felt like they were in SLOW MOTION. It's still all about the dissipation of energy, but shouldn't a slower fall with a lower maximum speed, caused by friction, spread out the energy on several pieces and release less energy on the top piece of gear?? Thoughts??

 

Come to think of it...I like SLOOOOOOOW falls better anyway. Bring on the drag!

 

I

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I have FELT THIS. When I have fallen without much friction in the system, I have fallen FAST, and I knew it (after it was over). I have also had several falls where I was way out, with lots of drag (friction) and the falls felt like they were in SLOW MOTION. It's still all about the dissipation of energy, but shouldn't a slower fall with a lower maximum speed, caused by friction, spread out the energy on several pieces and release less energy on the top piece of gear?? Thoughts??

 

Come to think of it...I like SLOOOOOOOW falls better anyway. Bring on the drag!

 

I

I think you may want to rethink this. I don't think the speed of your fall is affected by the rope at all until you begin to weight your last piece. Once you begin to weight the last piece it seems like the friction would spread the force of the fall over a longer period of time - a good thing unless the extra drag is what caused you to peel in the first place.

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The info in the link that chriss posted was telling. I didn't address friction between the rope and the rock at all, and if that exists it is going to be significantly greater than the friction through a carabiner at a point of protection. Also, even if you disregard that, the problem is not really predictable - the linked site shows an example with alternating 160 degree angles - that's about as likely as a straight shot through perfectly placed pro from the belay to the lead so that only the top piece is loaded - that is to say a very small but non-zero probability. An illustrative example, though feel free to place your pro with laser alignment if you want ;-)

 

Getting back to the OP, obviously there is a continuum of possible friction conditions. More friction in the rope system means more energy dissipation there, and consequently more force on the loaded protection. In that case, the theoretical fall factor is greater as explained in the link. However, the additional friction will lessen the braking load on the belayer, which may make it easier to bring a leader fall under control in a dynamic fashion. Exposure permitting, taking some time/distance to arrest a fall lowers the theoretical fall factor due to the increased length of rope.

 

The theoretically ideal situation would be to have the energy of a fall absorbed solely through a combination of rope elongation and controlled belay slack over as great a distance as possible (i.e. brake the rope at a constant acceleration to arrest the fall just before the leader hits the ground), while miraculously managing to distribute the rope loads on all pieces of protection evenly across them in proportion to the strength of the placement. (i.e. your bomber slings are off-route and take much load, while your sketchy screws in rotten ice happen to be perfectly in-line and unloaded).

 

There is so much variability that the problem only really exists as an academic exercise. It does, however, support the idea of spacing your protection placements evenly, versus running out a long way on lead in comparison to the distance between your last couple of placements.

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Here is a more technical answer from the Definition of Fall factor.

 

Quote from the end of the first section:

When the rope is clipped into several carabiners between the climber and the belayer, an additional type of friction occurs, the so called dry friction between the rope and particularly the last clipped carabiner. Dry friction leads to an effective rope length smaller than the available length L and thus increases the impact force.[2] Dry friction is also responsible for the rope drag a climber has to overcome in order to move forward. It can be expressed by an effective mass of the rope that the climber has to pull which is always larger than the rope mass itself. It depends exponentially on the sum of the angles of the direction changes the climber has made.[2]

 

 

It references This paper if you want the full scientific analysis

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Ok I guess I understand the OP's question now, does the effective shortening of the rope from the friction raise the forces on the last piece more than the lessening of forces due to the impact being drawn out over a slightly longer period of time. Hopefully some college kid can get his masters degree figuring this thing out for us.

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It's often easiest to start with an oversimplified model and work from there.

 

To begin with, imagine the zero friction case where all of the energy is converted into heat in the rope. The fall factor is then the fall distance over the length of rope between the belayer and the climber.

 

In the second case imagine infinite friction. Only the rope between the climber and the last piece will stretch during the fall. The fall factor would therefore be very close to 2. This would maximize the impact force on the top piece for the given fall distance.

 

To generalize this to intermediate cases it seems reasonable to assume that rope friction between the belayer and the top piece increases the impact force on the top piece.

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The post to the Beal site by Chriss is the most interesting because it has actual experimental data. However, lets put this data in perspective. The difference in max fall force is 1-3KN on a 7-14KN fall (using the autolock data). To put that in perspective, for a 200lb man, 1KN is approximately 1G (the Beal data doesn't include the weight they tested with). A fall force of about 50-75KN is what it takes to kill a man.

 

So, the question is, is this significant? Regardless, its an interesting question to think about while waiting for the crags to dry out.

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It's often easiest to start with an oversimplified model and work from there.

 

To begin with, imagine the zero friction case where all of the energy is converted into heat in the rope. The fall factor is then the fall distance over the length of rope between the belayer and the climber.

 

In the second case imagine infinite friction. Only the rope between the climber and the last piece will stretch during the fall. The fall factor would therefore be very close to 2. This would maximize the impact force on the top piece for the given fall distance.

 

To generalize this to intermediate cases it seems reasonable to assume that rope friction between the belayer and the top piece increases the impact force on the top piece.

 

Yup.

 

Conservation of energy: the kinetic energy of your fall will either be converted to the fiber to fiber frictional heat along the length of the rope (rope stretch), point frictional heat at the points of rope drag, or some combination of the two.

 

More of the former will obviously reduce your fall factor.

 

If you used pulleys instead of biners to clip the rope into on lead, you'd fall a bit further and experience the equivalent lower fall factor.

 

Edited by tvashtarkatena

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A fall force of about 50-75KN is what it takes to kill a man.

 

Where is this from?

UIAA uses 12kN as the upper allowable limit. I remember something about this number coming from a military parachute study as the lower limit of serious injury/death.

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I never know quite what to make of these discussions. Academically interesting to a point I suppose, but pretty much worthless on rock unless you really are some kind of a rocket scientist I'm guessing. Or at least I've never found this kind of information particularly useful, but that could just be me as I'm usually trying pretty hard not to think that hard when I'm climbing. Overall, my take on it is most of this stuff either comes intuitively on lead, is learned through bitter and unfortunate experience, and that you're probably operating out of your league if it keeps being an issue over an extended period.

 

 

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