Help with Pulley System

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16 years 11 months ago - 16 years 11 months ago #129710 by moss
Replied by moss on topic Help with Pulley System
And lastly (for this round of comments) I've never seen the upper pulley move down in actual practice with this system. Not saying Jim's calculations are incorrect but think that the data set that predicts failure is incomplete.
-moss

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16 years 11 months ago - 16 years 11 months ago #129711 by jimw
Replied by jimw on topic Help with Pulley System
Thanks for continuing to think about this, moss.

Response to the first of moss's immediately preceding three posts---

---quote---
Jim, are you missing that the redirected force (though the pulleys) when the climber ascends (pulls on the down rope) is loading the left side of the rope going over the branch and countering potential downward movement of the upper pulley? Did you account for this force value in your analysis and physical model?
---end quote---

In order to accelerate the mass of the climber, pulling on the rhs does temporarily increase tension in the “three ropes” (as I called them/it in my most recent post). This temporary increase in tension is shared equally among the “three ropes” (per the “fundamental fact” I stated). I did not account for it in the analytical model because it is irrelevant. It is automatically accounted for in the physical model.

Question: What is your thinking when you say that this is “countering potential downward movement of the upper pulley?” What are the forces that would cause this to occur?

Regardless of this transient condition, my point still is that the static condition is one of imbalance at the CS. Even if the dynamic condition changed the direction of the resultant force at the CS (it does not), one should consider that we spend most of the time in a static condition (which I contend is unsafe for this configuration).

---quote---
Something not shown in the drawing is that normally the screwlink "noose" should choke the limb. This may provide additional stability.
---end quote---

It may provide a bit more friction at the CS, but, again, this is irrelevant to the point of the discussion: Let’s return focus to the question, which is, “are the forces balanced at the CS?” There are three possible categories to the answer to this question:
(1) It is balanced;
(2) the net force tends to pull the rope ccw through the CS;
(3) the net force tends to pull the rope cw through the CS.

If condition (1) is true, all is well and I’ve wasted a lot of your (and my) time . . . and we have some certainty (so the time has not been “wasted”).

If condition (2) is true, the “locking carabiner” (as Tom pointed out, should be a screw link) will be cinched more tightly around the limb and, again, I’ve wasted a lot of your (and my) time . . . and we have some certainty (so the time has not been “wasted”).

If condition (3) is true, the system is potentially unsafe. In this case, if we are prudent, we should determine the magnitude of the net resultant force. If it amounts only to a few milligrams, we could safely assume that friction in the CS would keep us safe. If it is much more . . . . Well, “you pays your money and you takes your chances.” If this condition is true, the time has been well spent.

I assert that condition (3) is true, and that the net force is one-third of the weight of the climber.

Peace.

Jim

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16 years 11 months ago - 16 years 11 months ago #129712 by jimw
Replied by jimw on topic Help with Pulley System
Response to the second of moss's immediately preceding three posts---

---quote---
Analysed as a static system (when the climber isn't ascending) it is imbalanced.
---end quote---

Good!

Question: Now tell us the magnitude and direction of the imbalance.

---quote---
The Blake's Hitch however locks off and prevents movement of the rope so there is no pulley movement.
---end quote---

Question: What is the force analysis that supports this assertion?

---quote---
When the climber pulls on the down rope there is still imbalanced force in a static analysis of the pulley/climber/rope configuration but... the redirected force of the downward pull through the pulleys ends up on the left side of the system and successfully counters the static imbalance on the right side of the system. I don' think friction between the rope and the inside of the pipe is a factor.
---end quote---

I don’t follow that---I need more specifics, including specific forces at specific nodes. As for the “friction between the rope and the inside of the pipe” not being a factor, one of my theses is that it indeed is a factor. If it were not for that friction, the system would collapse, as I have all along been saying.

Peace.

Jim

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16 years 11 months ago - 16 years 11 months ago #129713 by jimw
Replied by jimw on topic Help with Pulley System
Response to the third of moss's immediately preceding three posts---

---quote---
“I've never seen the upper pulley move down in actual practice with this system.”
---end quote---
Again, I have to say that that is not the point. What we’re doing here (or, at least, what *I* am doing) is “following the science” to determine if this system is “in balance,” and, if it is not, what is the magnitude of the imbalance. Anecdotal incidents are not science.

If we find that the system has a net resultant force at the CS, and we know the magnitude of that force, we can make an informed decision as to whether to use the system, or maybe modify it so it is safe.

---quote---
Not saying Jim's calculations are incorrect but think that the data set that predicts failure is incomplete.
---end quote---

I am fully willing to explain any of my calculations, and am fully willing to comment on calculations submitted by others. If I have not addressed some data, where might those data come from? I have specified each and every component of the system.

From the lack of comments, I can only assume that no one has actually made a physical model of this system with pulleys, and then pulled on the point where the climber would be. Doing so will cause “the climber to descend” until the two pulleys jam together.

I ask that someone perform this to independently examine this so we can see what our next steps are to be.

I, of course, think that the next step would be for one of you to do as I asked and specify the forces on the “right hand side” of the system.

Veritas.

Peace.

Jim

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16 years 11 months ago - 16 years 11 months ago #129714 by moss
Replied by moss on topic Help with Pulley System

Originally posted by Jim W
---quote---
“I've never seen the upper pulley move down in actual practice with this system.”
---end quote---
Again, I have to say that that is not the point. What we’re doing here (or, at least, what *I* am doing) is “following the science” to determine if this system is “in balance,” and, if it is not, what is the magnitude of the imbalance. Anecdotal incidents are not science.


I'll try and test/photograph it today.

Because of the way the Blake's locks the system down (empirically observed) when the climber is at rest - the imbalance is irrelevant. It's only what happens when the climber pulls the down rope and advances the hitch to ascend that is of interest to the problem (I think). Look at the drawing again, how can there be any movement of anything when the climber is hanging on the system (not ascending or descending). The Blake's weighted by the climber is creating a fixed length loop, nothing can move if the loop isn't shortened or lengthened (the Blake's moved up or down).

When the climber is at rest the Blake's/climbers weight locks the "loop" to a fixed length. In that state I just see the pulley's as rope redirects of the force in a continuous loop (convoluted but still a continuous loop). I can't describe it in mathematical terms but it seems obvious looking at the drawing.

I'm not anywhere near being a scientist or mathematician. I know empiricism has a bad rap but... if a result is reproduced consistently then data/theory calling for a different result must be questioned. Anecdote implies second-hand he said/she said or rumour. I'm talking about direct observation.

Jim can I get you to agree that the system is stable or static when the climber is not ascending or descending? I challenge you to set it up and see if you can get anything to move without the Blake's being advanced or released. I am confident you will find it to be very stable in that state.

Fun discussion by the way even if I have no math language skills to make it easier :-)
-moss

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16 years 11 months ago - 16 years 11 months ago #129715 by link774
Replied by link774 on topic Help with Pulley System
I'm glad this thread is still going, I find it quite interesting.

Jim, you make some good points and it is pretty convincing, but I still feel like you're wrong. Hopefully I can figure out why I feel that way. It is really tempting to go get some pulleys and test this out, but alas I have none!

I did the same calculations you did, and also arrived at the conclusion that 2/3 of the weight is on the RHS of the CS, and 1/3 is on the LHS. I think this calculation might be incorrect, but I don't know why. I think you have justified it as much as possible, I just think that there might be something out there that we are missing that causes it not to be true. Don't worry about trying to prove that there is no other possible way to calculate this, I think the burden to prove that there is something out there lies with me and others who disagree with you, since I'm making the assertion that there might be something.

Regarding using a pulley as the CS in the model, I do agree that the system is imbalanced to a degree. Just having TP higher than BP causes an imbalance, but relative to the friction at the CS, this is negligible. This could be what caused your model to fail, due to the drastically reduced friction at the CS. So I guess you could say that I technically agree with you that the system will fail at some point, when the friction is sufficiently low. I guess we just need to figure out how close we are to that point.

Why take a chance with friction? I think the same thing could be said for any of the methods we use to climb rope. Blake's hitch, decscenders, knots, they all use friction. Even though we don't know exactly how much, we know that it is enough to keep us from falling.

The friction at the CS is roughly proportional to the weight of the person using the system. If the system is even imbalanced by 1/3 the weight, this incresed friction due to a load on the system might be what's causing it to not slip. That's sort of the problem I have with your model. Your force analysis might be right, but perhaps the friction *is* always enough to overcome this tendency, we just don't know why. That's why you can't really think of the 40 pound imbalance as pulling on the TP with 40 pounds of force, and no force on the other side.

Consider this situation, you have a rope tied to 40 pound weight, going up through a CS and back down to an 80 pound weight. Do you think that will slip? That is something that can be tested. Of course, it depends on the branch diameter and the CS, but it is something we could test. Keeping the weight constant, how big of a differential do we need before it slip? I think as the total weight increases, this permissable differential will increase. I don't have a CS to test this with, unfortunately.

My point about the kinetic friction is that even if you jerk the ropes in such a way that you briefly overcome the static friction, the kinetic friction might be great enough to bring the system to a stop immediately. Of course, you think that the system at rest has the tendency to collapse if the friction is low enough. I just think that the friction is probably well above what is needed, such as in the case with a blake's hitch knot.

Your example about wrapping a rope around a limb a sufficient number of times is pretty persuasive, but I find it to be an innacurate analogy. If this system slips, you start losing wraps and then the system has even less friction (both static and kinetic). The system we are discussing does not have that property, so I would feel much safer with Geof_K's system than with your wrap system.

Moss, I'm not sure that the blake's hitch locks off in the way you describe. If TP spontaneously descends 1 foot due to slippage at the CS, the climber would descend 1/2 foot. I modeled this with some audio cables, since I was too lazy to go down to my car and get some rope. :)

I need to get some pulleys and one of those vertical fish scales to verify the imbalance that our calculations are predicting.

To summarize:
1) I arrived at the same conclusion regarding the imbalance of the system, but I'm going to keep trying to figure out why that might be wrong
2) Even if the force analysis is right, the friction might always be sufficient to prevent slippage

- Link

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16 years 11 months ago - 16 years 11 months ago #129716 by jimw
Replied by jimw on topic Help with Pulley System
Thanks again, moss, for the continuing discussion. You said, “. . . I have no math language skills to make it easier.” That is one very strong reason why I appreciate your involvement in this. You are willing to work your way through the problem despite that obstacle. I wish others were involved, asking questions, making assertions, modeling the system. Learning follows such involvement.

I note that you didn’t respond to any of the questions that I posed in my preceding three posts (I labeled each with the word “Question” (I am not very imaginative)). I suggest that if you take the time to consider the questions and respond to them, that we will reach a resolution sooner.

I recently was involved in a protracted thread where the other party would not answer questions, but rather continued to assert variations of the same incorrect assumptions. It was rather painful (for both of us, but for different reasons). I don’t want to do that again.

You said, “I know empiricism has a bad rap but... if a result is reproduced consistently then data/theory calling for a different result must be questioned.”

Yes, some do scoff at anecdotal evidence; I am not one of them. In the “hard” sciences, there must be an identifiable reason for a different (or unexpected) result.

That’s what we’re faced with here: Theoretically, this system will fail (I know that I haven’t completed the proof of this yet---I’m waiting for one of the many thousands of lurking readers of this thread to do it). You cite instances when it has not failed. The task, then, is to resolve that and either locate the error in the theory or determine the factor(s) that explains the anecdotal instance.

That is what we are in process of doing. I contend that the theory is solid and that the factor explaining the discrepancy has been identified. It’s all already here in the thread.

---quote---
Look at the drawing again, how can there be any movement of anything when the climber is hanging on the system (not ascending or descending). The Blake’s weighted by the climber is creating a fixed length loop, nothing can move if the loop isn't shortened or lengthened (the Blake’s moved up or down).

When the climber is at rest the Blake’s/climbers weight locks the “loop” to a fixed length. In that state I just see the pulley's as rope redirects of the force in a continuous loop (convoluted but still a continuous loop).
---end quote---

I’ve discussed this before. Reduce the system to its bare essentials (one rope and three pulleys). Create a physical model and see what happens. I fully admit that attempting to determine what happens “on paper” is quite difficult; at least it was for me. I had to build the model before I was able to understand what was happening.

---quote---
Jim can I get you to agree that the system is stable or static when the climber is not ascending or descending?
---end quote---

Nice try, moss, but I respectfully decline. The math and the physical model both show otherwise.

Instead, as a counter-offer, can I get you to agree to this:
Conditions:
(a) allow the rope to pass freely through CS;
(b) fix (lock) the rope at TP;
(c) fix the climber in space;
(d) allow the climbing hitch to remain in place.

This results in one easily observed fixed loop.

Q1: Do you agree that TP can freely move down until it touches BP?

Q2: If so, does that free up any rope?

Q3: If so, once that rope is allowed to move through BP, how far would that allow the climber to descend?

Q4: Can one now proceed with the same process and allow the climber to descend even further?

---quote---
I challenge you to set it up and see if you can get anything to move without the Blake’s being advanced or released. I am confident you will find it to be very stable in that state.
---end quote---

I’ve stated before that I did model it and that it did collapse. So I again “challenge” you to set it up and see what happens.

I have not responded here to your questions or comments about what happens when the climber is pulling on the “end of the rope.” I am not ignoring you; it’s just that these concerns are just a red herring at this time. I will be willing to discuss them when the basics are resolved, but I think you’ll find them irrelevant by then.

As an aside, the “life cycle” of this is interesting (to me, anyway): Here is a system that someone, somewhere developed and used. It reportedly has been used successfully by others.

Then I read Geof’s description (along with his excellent artwork) and, out of intuition (whatever that is), questioned it. The intuition was very important here: Remember how I said that I woke up one morning with that “inner voice” telling me that I should mathematically analyze it?

I did that and for a while really struggled with what I found. That struggle was caused by one (unwarranted) assumption. So far, all the respondents here seem to be making that same erroneous assumption.

The resulting inconsistency did confuse me for a while, but only because I clung to the incorrect assumption. Once I gave it up, the entire system made sense and truly became something so simple that no high-school physics student would have a significant problem with it.

This is not the first time I have gone down a wrong path because of an incorrect assumption. (I hope I have opportunities to do the same many more times.)

The next step in the life cycle was that I saw (a) that the system should collapse, and then (b) asked why it didn’t (or hadn’t). The answer is obvious, although not altogether satisfying.

That’s where we are now.

Do note that this all has come about almost entirely out of intuition, or a “hunch.” “Hard” science and mathematics are invaluable, yet often there is more to problem-solving than just those things.

I will repeat something from an earlier post: This system is an accident waiting to happen. Please don’t use it.

Peace.

Jim

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16 years 11 months ago - 16 years 11 months ago #129717 by jimw
Replied by jimw on topic Help with Pulley System
Link, I really like your thinking here! You discussed some things I had not thought of, and have opened up some new paths for exploration.

I have only a few minutes just now, but do want to make some comments.

Friction: Yes, everything we do in the rope world depends on friction. Your idea of using two unequal weights pulling against each other through a CS is really good! As you point out, the question is, do we reach some amount of total weight where the weight differential will always exceed the “static friction force” of the rope against the CS.

The answer depends on the rope, on the CS, on the temperature, on the relative humidity, on the . . . . It is because I believe all that to be so dicey that I assert that this system is unsafe. As an extreme, if we had a very slippery Su sleeve (or maybe it's Tom's latest ones that are so very slippery), plus very smooth rope, the system would be more dangerous than if we used hemp rope with sand particles in it passing through a rough leather sleeve.

BTW, when I talked of wrapping a rope around a branch several times for friction, I was thinking of leaving a long tail so that if it slipped, there would still be the same number of turns. But even considering that, once it slips, it will continue to slip (mu-sub-s is greater than mu-sub-k).

---quote---
I did the same calculations you did, and also arrived at the conclusion that 2/3 of the weight is on the RHS of the CS, and 1/3 is on the LHS. I think this calculation might be incorrect, but I don't know why.
---end quote---

In solving such a “statics” problem, because we have no concerns about torques, or about any direction other than the vertical one, the only thing we have to address is this:
---at any point, the sum of the forces in the vertical direction is zero.

We also have the “fundamental fact” about tension in a rope.

That’s all we need, and you apparently have used those things properly. The rest simply is the mind getting in the way. We shouldn’t ignore it (that intuition), but when the facts all point in only one direction . . . .

I agree with you that the intuitive thing about the friction in the CS seems strange. That’s why, in my most recent post, I said, “The answer is obvious, although not altogether satisfying.”

Gotta run---more later.

Peace.

Jim

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16 years 11 months ago - 16 years 11 months ago #129718 by moss
Replied by moss on topic System test
I can't answer all Jim's questions directly because I don't know the answers. I'll continue on the empirical end. Perhaps with my observational data and Jim's and other's math analysis we can gain more understanding.

I rigged the system on a 40' high crotch with the following ingredients:
Liquid-tight conduit cambium saver
150' 1/2" 16-strand rope
12' split tail, 1/2" 16-strand rope
2 rated pulleys (large at top, smaller at bottom.
Screwlink (top)
Locking carabiner (bottom, will use screwlink in the future to prevent possible rotation and cross loading)

Top


Bottom


Comments
I climbed on the system with a second DdRT system as backup. Made two climbs (in the dark). On the first climb the upper pulley started coming down at roughly 1/3 the rate of ascent. Because it was dark I wasn't sure that I had cinched the system as close to the branch as possible. I stopped climbing, descended and cinched the upper system against the branch. Climbed again. The upper pulley stayed put. When I got near the TIP I could see that the top pulley had moved down about 2 feet during a 40 ft. climb. This leads me to think that the change in rope direction caused by cinching the screwlink closer to the branch is overcoming the system imbalance.

Safety
To test what would happen if the top and bottom pulleys came into contact by either the upper pulley moving down, or by the climber reaching the top I climbed until the two pulleys were forced together. I exerted considerable force to lock them as tight as I could. Then I pulled down on the Blake's to see if I would be able to descend. There was no problem. I was able to easily initiate descent. I repeated and found the same result.

Conclusion
The MA system is unbalanced. Friction (or leverage? not sure) caused by the rope (angle) redirecting through the screwlink is overcoming the imbalance. Before putting a climber on the system care must be taken to load the 1/3 side of the system to cinch the screwlink as far as it will go. Once weight (the climber) is on the rope the upper pulley may creep down slightly over the length of the climb. If the climber causes the lower pulley to contact the upper pulley there is no danger. The pulleys merely stop, the climber stops.

Safety note!
The climber on the system should not descend without asking permission from the responsible person on the ground. The person on the ground must hold the down rope as the climber pulls down on the Blakes. Because of the very low friction of the upper pulley the climber could easily cause an uncontrolled descent if they forgot to belay with their right hand. This is the most dangerous aspect for beginner climbers, not unique to this system but inherent in any false crotch setup using a pulley.

Wrap up
Assuming a competent climb facilitator I consider this a safe MA system. Worst case scenario is that that installer does not move the upper screwlink as close as it can go to the branch before putting the climber on rope. If this step is not taken, the upper pulley may move down, reducing the potential height of the climb. When or if the climber causes the lower pulley to contact the upper pulley there is no problem. The ascent is stopped but the climber is not stuck. They can initiate descent by holding the down rope with one hand (self-belay) and pulling down on the Blakes with the other as in standard DdRT descent.

Benefits
Why use this system? 3:1 MA simple to configure, can be easily installed and deinstalled from the ground.
-moss

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16 years 11 months ago - 16 years 11 months ago #129720 by link774
Replied by link774 on topic Help with Pulley System
Jim, I was thinking about the experiment, and the system described had a figure eight on either side of the CS. As you mentioned, this has an impact as well. I would suggest that if anybody has a chance to test what kind of weight differential is required to cause this setup to slip, they should be sure to use these figure eights. This will also eliminate the effect of various ropes, and just make it a matter of bark vs CS friction.

moss, thanks for testing the setup (in the dark!) you must be quite anxious to put the debate to rest.

Jim, the fact that moss's setup slipped somewhat but then stopped in evidence enough that the system once slipping won't necessarily continue to slip. I would venture that the slips occured when there was more than 2/3 of moss's weight on the RHS of the system, probably caused by pulling on the downrope to ascend. This caused the static friction to be overcome briefly, but once the initial jerk of moss's pull was complete, the kinetic friction caused it to go back to rest.

I think that if you had a figure eight before the CS, the system wouldn't have slipped at all. Hopefully somebody can see what kind of weight differential is required to cause a CS with figure eights on either side to move. Remember to keep the weight constant, so the friction stays the same. Once we figure that out, then I guess we just need to figure out the likelyhood of that differential ever occuring...

- Link

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16 years 11 months ago - 16 years 11 months ago #129721 by moss
Replied by moss on topic Help with Pulley System

Originally posted by Link774
...they should be sure to use these figure eights. This will also eliminate the effect of various ropes, and just make it a matter of bark vs CS friction.

Only one F8 needs to be added on the left side of the system (just before) the CS to transfer the friction to cambium saver/bark. However this makes the system less easy to install from the ground (one of the main benefits of the system). Still can be done but it can be tough to pull a conduit sleeve over a crotch pulling on a throwline. It's not clear that the F8 is needed if all that happens in a less careful setup is that the upper pulley moves down.

Originally posted by Link774moss, thanks for testing the setup (in the dark!) you must be quite anxious to put the debate to rest.

I climb frequently in the dark, not a big deal, I wanted to get a climb in and I always enjoy engaging a problem with direct experience and observation. It was frustrating climbing 3:1, so easy but so slow!

Originally posted by Link774Jim, the fact that moss's setup slipped somewhat but then stopped in evidence enough that the system once slipping won't necessarily continue to slip. I would venture that the slips occured when there was more than 2/3 of moss's weight on the RHS of the system, probably caused by pulling on the downrope to ascend. This caused the static friction to be overcome briefly, but once the initial jerk of moss's pull was complete, the kinetic friction caused it to go back to rest.

That makes sense (some pulley movement down per pull) but I still think that the position of the upper screwlink (choke effect) is a major controlling variable for pulley creep rate.

Originally posted by Link774I think that if you had a figure eight before the CS, the system wouldn't have slipped at all.

Correct

Originally posted by Link774Hopefully somebody can see what kind of weight differential is required to cause a CS with figure eights on either side to move. Remember to keep the weight constant, so the friction stays the same. Once we figure that out, then I guess we just need to figure out the likelyhood of that differential ever occuring...


CS/bark friction will be variable with different tree species and bark texture (assuming conduit CS). The choker effect seems to be dampening the slip rate quite a bit without the F8 on the left side so I think it's not going to budge once an F8 is added to the left side and the rope is weighted by the climber. Even if the CS moved off the branch there would be no danger for the climber. I think it's academic at this point as far as safety goes. There is no danger for the climber in this system beyond the usage dangers of any DdRT system.
-moss

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16 years 11 months ago - 16 years 11 months ago #129724 by geofk12
Replied by geofk12 on topic Thank you!
I never thought I would get so many responces to my post. Thank you so much for giving this system your time. I've learned so much from you all!

In my own experience using this system (almost 2 years know) the worst I've encountered is the creep a few times. I've found it a great help for a client that is heavy and needs a little help.

One point I'm still unclear about is the benefit of using a delta or rapid link vs a carabiner. Can anyone explain that in a different way for me?

Again, thanks!
If any of you visit the Tampa Bay area, let me know and I'll take you on a climb!

Geof

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16 years 11 months ago - 16 years 11 months ago #129725 by moss
Replied by moss on topic Help with Pulley System

Originally posted by Geof_K
One point I'm still unclear about is the benefit of using a delta or rapid link vs a carabiner. Can anyone explain that in a different way for me?


The triangular shape for of the delta is perfect for the three parts attached or contained by the delta (F8 on a bight, pulley and rope) and helps to maintain correct position for each element. With a carabiner there is the very slight possibility that moving rope could open the gate or that the biner could become cross-loaded. As you probably know the delta can be loaded any which way. The scewlink should be positioned away from the moving rope side.
-moss

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16 years 11 months ago - 16 years 11 months ago #129728 by geofk12
Replied by geofk12 on topic Phone Call from Sherrill Tree
I shared my drawing with Sherrill Tree to get their feedback too. I just got I nice call from them saying that their "OSHA guy" sees no issues with the drawing.

Moss - I understand the benefits of a delta. That makes sense! Now I have to go get more gear ;) Yippie!

Again, I'm loving this interaction.
The next time I set up this system, I'll take come pics.

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16 years 11 months ago - 16 years 11 months ago #129745 by markf12
Replied by markf12 on topic The hidden banana peel
I haven't picked up on this thread until recently; I've been out of town for a few days, and now the end-of-semester rush is eating much of my time.

I'm worried by this set-up.

I'm worried for the same reasons JimW is.

Now let me get this straight. There IS a consensus at this point that when this system is loaded there is a force that, in the absence of friction, could pull the friction sleeve over the branch (in a clockwise direction as it is usually pictured)? If there isn't a consensus on this, I think there should be - I'm very sure JimW has that right. So what's holding the system stable is friction (more properly shear force - more on this in a bit) between the sleeve and the branch (if the figure-8 knots are present as in the original illustration).

I need to develop the argument for why I'm concerned about this system carefully, but the short version is that the forces opposing that slide into instability are tricky to predict, and they don't just involve classical friction.

Friction and shear forces: Two surfaces sliding against each other exert frictional force. The direction of the frictional force is parallel to the contact between the surfaces and is opposed to the direction of movement. Another word to describe the geometric arrangement of forces involving movement of surfaces past each other is shear force. The idea of shear forces is a little more general because you can talk about shear forces within an object, not just along the surfaces between two objects.

Classical friction is mathematically very well-behaved. Frictional force between two flat surfaces depends on just 3 things: the coefficient of friction between the two materials, the force pressing the surfaces together, and whether or not the surfaces are moving against each other. The classical friction model works REALLY WELL for strong, homogeneous materials like steel, aluminum, polyethylene, nylon, etc.

But,
if the materials involved are mechanically weak, things can slide by the failure of one or both materials under shear forces. A banana peel isn't slippery because it has a low friction coefficient with the ground (I would guess that that friction coefficient would actually be pretty high). A banana peel is slippery because when you step on it, the banana peel itself fails under the shear forces and gets smeared all over the ground and/or your shoe as you are doing your pratfall.

So,
the friction sleeve can slide if:
a) the static coefficient of friction is too low (wet bark, stiff material - I had the devil of a time getting a cold friction sleeve to stay on a branch in the middle of the winter), or
b) the bark itself or stuff on the bark is weak under shear stress or becomes weak after being crushed (Anybody stepped on wet lichen lately? Wet algae that sometimes grows on bark surfaces?).
The point is, these factors are COMPLICATED, and some of them depend on stuff that you can't even see from the ground.

Why not use a system that doesn't depend on this? Granted, the force imbalance in this pulley system may often be small enough compared to the shear strength (friction and material yield strength), but it just seems so hard to predict when there will be a hidden banana peel. A 50 foot pratfall is no joke.

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