Homemade version of Metolius Equalizer sling

Marty C wrote:For a better understanding of "single vs. multiple" strands in an anchor a good paper was presented at the International Technical Rescue Symposium - "Tying it all together - Considerations for equalizing multi-pitch anchor systems." You can read the article at: riggingforrescue.com Click "Research" then "Recent Projects"

Thanks.

Hard link for those who are lazy:
riggingforrescueassets.s3.a…

I think the underlying problem with the debate about how the loads would distribute in some ideal system is that the answer cannot be a consequence of just the free-body diagram. You have to consider elongation in order to solve for the anchor loads; without the additional equations provided by the deformation descriptions, the two equilibrium equations (one for horizontal equilibrium, one for vertical equilibrium) have more unknowns (four, one for each strand) then there are equations and so are indeterminate in the sense that there are infinitely many solutions (linear agebra 101). Both of the solutions advanced by David and Brian are valid solutions to the equilibrium equations, you can settle on one or the other as well as infinitely many other choices, not from the equations, but only by imposing some predetermined view of how things ought to be. But that's theology, not physics.

In the case of fully rigid arms, i.e. the cordelette replaced by a truss, one can also enlist the fact that the net torque at any point has to be zero and so get more equations that way. But with cord (or cable or chains), no torque is available and deformations (possibly quite small for the metal examples) are still required to pin down a solution.

There is a big literature on this in the engineering world; the buzz words are statically indeterminate systems.

rocknice2 wrote: In a 100% static anchor [Unobtanium] all 3 legs would get the same load.

If the material were purely static (think steel cable), if the legs were even 0.001% off balanced, one leg would get 100% of the load, the others 0. Easier to picture this with a two leg anchor - at anything other than the magic loading direction, one leg gets ALL the load. So static material is NOT the answer.

Sorry guy's, but you aren't correct. I was going to post more words, and possibly a proof, but I figured most people reading this aren't engineers, or physicists, or mathematicians so it might not do much good.

But they say a picture speaks a thousand words. So here's 5 pictures.

I made two roughly equal anchor's, and hung 50lbs of weights from them. I had a scale on the center piece to measure force on that point. The first anchor had 2 strands going to the scale, as per the OP. The second has only a single strand.

Result: The anchor point on both set-ups were supporting similar loads (46lbs and 44lbs respectively). The difference can be attributed to the anchors not being 100% exact. But it's close enough to demonstrate the point.

Pictures below:
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Static load?

You don't seem to have understood my point. The simple geometric arrangement, without considering deformation, cannot determine the anchor loads and there are infinitely many possibilities, all of them depending on the specifics of how the rigging deforms. You and David are engaged in an empty argument if the only data is the free-body diagram---speaking about who is or isn't correct is meaningless.

Meanwhile, in your test you've forgotten another aspect, which is that the length of the arms matters, and the original argument you had with David tacitly assumed equal arm length. You've literally "rigged the system" to emphasize the role of the center arm by making the side arms much longer than the center arm, and then added even more give to the side arms with the knots holding them to the frame. The result is that you have about 90% of the load hanging on the center anchor, and with almost all the weight on the center anchor you are trying to detect the effect of 1 or 2 strands. With the side arms contributing so little, the results are not surprising and don’t clearly confirm or disconfirm anything.

Before you redo the experiment, let me say yet again that arguments based on the free-body diagram alone can't be confirmed or disconfirmed with an experiment, since the experiment brings in the deformations which, mathematically, are essential for pinning down a solution from the infinite set of free-body diagram solutions.

The testing done in riggingforrescueassets.s3.a… is of course more careful and more controlled. They found, among other things, that

The untied 2-strand leg recorded forces that were generally around five times as great as either of the two “1” sides...This simply serves to illustrate just how much more this particular 3-point anchor system equalization method favors the 2-strand leg.

...which is to say that the middle anchor got about 70% of the load.

This load imbalance is greater than the theoretical prediction of 50% of the load on the middle strand, based simply on the arm elongations. But in their tests they had knots on the two outer strands just as the Equalizer/Snake Cord does, and the deformation of these knots would explain the further diminished loads to the side strands.

In a three-point anchor with the three anchor points arranged horizontally, overemphasizing the load to the middle point is probably a good thing. If it blows, you default to a two-point anchor with no extension. It is much worse to have one of the outer arms blow, because then the entire load goes to the middle arm with no contribution from the other outer arm. This sets up the cascade failure scenario in which the three-point rigging fully loads each anchor point in sequence.

No offense rold, but I think you've missed the point of the discussion David and I were having.

We aren't discussing the load relative to other arms in the system. We are discussing the load on two different, but equally set up anchors. Specifically looking at the center point (as related to how the OP set up his anchor).

In one anchor there are 3 strands, each going to independent anchor points.

In the other anchor we are examining what happens when the center point is connected with a doubled strand. Specifically we were discussing a static system, because that's where the disagreement arose. (so elongation isn't a factor).

Arm length doesn't matter. Even anchor configuration doesn't matter (although the case of perfectly parallel strands did open up the opportunity for a logical fallacy).

None of the examples you, or Marty C posted look at this situation.

"The untied 2-strand leg recorded forces that were generally around five times as great as either of the two “1” sides...This simply serves to illustrate just how much more this particular 3-point anchor system equalization method favors the 2-strand leg."

For instance: this isn't relevant to the discussion. I don't disagree with this. But they didn't examine the case where the "2-strand leg" going to point A2 was only a single strand (mostly because it's impractical to create). That's what's being discussed.

This issue of the impact from elongation is separate from the issue. It dependent on the elasticity of the materials, and the loads applied.

I didn't misunderstand anything, but a moment comes when all I can do is repeat what I've already said, and that's the moment to quit.

Chris Gabrielli wrote:I was looking at the metolius equalizer sling metoliusclimbing.com/equali… and was wondering if there is any reason why you couldn't just make one of these yourself out of 3/4 inch tubular webbing with a water knot tied on each end to make the loops. Is there anything blatantly wrong with a setup like this or am i missing something and everyone's gonna tell me i'm gonna die?

What's the point of the bag in the Metolius product?

Rgold has understandably had enough. But I'll jump in for a bit.

Brian L. wrote:Specifically we were discussing a static system, because that's where the disagreement arose. (so elongation isn't a factor).

Elongation is a factor in statics. Everything stretches, the stiffness of each arm matters in load distribution.

Brian L. wrote:Arm length doesn't matter.

Yes it does. Stiffness is proportional to length.

This is all fairly basic statics. Now appealing to authority is poor form of argument but be aware that Rgold is a college professor in mathematics has decades of climbing experience. He knows what he is talking about.

Brian L. wrote:But they didn't examine the case where the "2-strand leg" going to point A2 was only a single strand

I'm not entirely sure I understand this statement but I believe the first setup on page 8 demonstrates a 1 strand and 2 strand setup. The equalisation results are worse than stiffness analysis predicts. (Likely due to 2nd order effects, aka geometry changes.)

Incidentally, I just completed a short research paper on load distribution on a propriety foundation system. Suffice to say existing design approaches by some engineers were somewhat lacking based on simple theoretical analysis. Site analysis on one installation was a little shocking, with signs of failure self evident.

Ok. I'm tired of arguing this. You guys missed the point of the discussion David and I were having. It's pretty pointless to continue.

Brian L. wrote:Ok. I'm tired of arguing this. You guys missed the point of the discussion David and I were having. It's pretty pointless to continue.

I don't believe we did.

For example YOUR WORDS:

Brian L. wrote:The force on each anchor if the loading is truly parallel (impossible) is the load divided by the number of anchors. THEN you can analyze the load on the stands. So the load on the doubled strand would be 2kn each.

The static analysis here is quite plainly incorrect. For reasons already stated.

patto wrote: I don't believe we did. For example YOUR WORDS: The static analysis here is quite plainly incorrect. For reasons already stated.

Sigh. That was a very simplified explanation of why this analysis was wrong:

David Gibbs wrote: strands, each carries 4 kN to wherever they go. With 4 strands, each strand carries 3 kN to wherever they go. If two go to the same anchor point, that anchor point will be loaded at 6 kN, and the other two at 3 kN. So, adding a 2nd strand to an anchor will increase the load (on that anchor point).

Please use context to understand the conversation.

patto wrote:I'm not entirely sure I understand this statement

Anyway. Here's the point you're missing. I'm not evaluating a climbing anchor. The discussion I had with David wasn't specific to a climbing anchor. We were talking about loading in a rigid system.

Here's the system described in that article you reference:
Anchor 1
Here's the variation I described, that you didn't seem to be able to understand:
Anchor 2
Now, the discussion was in regards to the load on A2 given that both anchors are dimensionally the same, and rigid.

In this case. The load on A2 is identical in both cases. Do you disagree given the constraints above?

Now, to rgold's point, when elongation is taken into account it's reasonable to expect the Anchor 2 to elongate further, thus the geometry changes, and more load is shared by the outlying strand to A1 and A3. However that is materially dependent, and inconsequential to the physics of what was being discussed.

Brian L. wrote:In this case. The load on A2 is identical in both cases. Do you disagree given the constraints above?

Yes I disagree. No the load on A2 is NOT identical in both cases.

The explanation has been give numerous times now.

Brian L. wrote:Now, to rgold's point, when elongation is taken into account it's reasonable to expect the Anchor 2 to elongate further, thus the geometry changes, and more load is shared by the outlying strand to A1 and A3. However that is materially dependent, and inconsequential to the physics of what was being discussed.

Even with negligible elongation (aka 2nd order effects) the "physics" being discussed still leads to non identical loads.

I'm not sure what brand of physics you are using but it isn't recognisable to me. High school physics with normal high school assumptions you would come to the conclusion that loads are indeterminate. And you cannot reasonably make a conclusion about the distribution of forces.

https://en.wikipedia.org/wiki/Statically_indeterminate

patto wrote: Yes I disagree. No the load on A2 is NOT identical in both cases. The explanation has been give numerous times now.

What explanation? Elongation? I already said it's 0 in this situation being discussed.

patto wrote:I'm not sure what brand of physics you are using but it isn't recognisable to me.

I'm going to go ahead an mirror that sentiment right back at you.

Show me the proof, then.

Brian L. wrote: What explanation? Elongation? I already said it's 0 in this situation being discussed.

Stiffness. Imagine if the A2 had a metal chain and A1 and A3 had rubber bands. Do you still think each anchor has equal loads?

(That is an extreme case, instead A2 is twice as stiff as the connection to A1 and A3.)

Brian L. wrote:I'm going to go ahead an mirror that sentiment right back at you. Show me the proof, then.

Proof of what? You are using a brand of physics that is not recognisable to me.

With high school physics the 3 point system is statically indeterminate.
That is to say you CANNOT come to a conclusion regarding what the loads are.

Brian L. wrote:but I figured most people reading this aren't engineers, or physicists, or mathematicians so it might not do much good.

Sorry but I just read this and had to laugh. Have you realised yet that you are not arguing with laymen on this topic?

patto wrote: Stiffness. Imagine if the A2 had a metal chain and A1 and A3 had rubber bands. Do you still think each anchor has equal loads? (That is an extreme case, instead A2 is twice as stiff as the connection to A1 and A3.)

You're still not getting the point of what's being discussed. And I NEVER made a claim each anchor has equal load. (as in A1 = A2 = A3). I have only ever been concerned with the load on A2 between the two different diagrams.

Stiffness is a factor in elongation. I'v already told you (3 time now I think), that we're ignoring elongation for this exercise.

patto wrote: Sorry but I just read this and had to laugh. Have you realised yet that you are not arguing with laymen on this topic?

I'm not convinced of that. At least in your case. But the audience of this forum is more than just you, or rgold.

Brian L. wrote: You're still not getting the point of what's being discussed. Stiffness is a factor in elongation. I'v already told you (3 time now I think), that we're ignoring elongation for this exercise.

Okay lets forget stiffness. Stick to geometry and free body diagrams. In which case you have an indeterminate system and the LOADS are unknown. This has been explained many times.

You are posing a problem with conditions that lead to an indeterminate answer. There are too many degrees of freedom. Mathematically it is equivalent to the question x + y = 10. Find x and y.

Brian L. wrote:I'm not convinced of that. At least in your case. But the audience of this forum is more than just you, or rgold.

I'm not here to convince you of my credentials.

But like Rgold. I'm not out. Because I am now completely repeating myself. I do admire your persistence.

Well, fuck me. I apologize, you're right. For some reason it wasn't clicking what you were saying.