minimum diameter for nylon cordelette

[ek]

Yes.

[chh]

Then I don't see how the strength of the cord is of any importance. You're pulling pieces, not breaking cord. Also, if we are assuming that all the placements are of equal strength, your going to be flirting with catastrophic anchor failure anyway. If there is any difference though in the quality of the placements, in this configuration, you put the loop on your strongest piece. I'm sure you know this already.
If breaking strength is the issue though and the equalette is working as it should, you would break the single strands first at whatever MBS is for the cord minus whatever weakness you lose in the clove hitch. Again, you've established this. Presuming a shock load that remains slightly above the MBS for a single strand after the first one is broken you'd then pop the next. At that point you'd arrive at the loop, which would withstand twice the MBS for the single strand.
But again, there are still a lot of things going wrong for you to arrive at this point. So presuming you generate this kind of shock load on an equalette, yes, the MBS of the cord would matter, but I don't think it's worth carrying around a cord that has a 20kn rating.

[ek]

Then I don't see how the strength of the cord is of any importance.

I assume you DO think that it must meet some minimal strength. You would balk if we went climbing and I belayed you off an equalette tied from dental floss, wouldn't you?

If there is any difference though in the quality of the placements, in this configuration, you put the loop on your strongest piece. I'm sure you know this already.

No, that is incorrect in a very important way. You put it on the piece you think is strongest. That is more a function of placement than the MBS on the piece. I'd trust a well-placed 7kN piece over a poorly placed piece of...any rating. And you can be wrong about the strength and reliability of your placements. That's the main reason for placing multiple pieces for an anchor in the first place.

You've provided a number of reasons why the cord might not have to be 20kN strong, in some circumstances. None of them are reasons why it doesn't have to be 20kN strong.

Who says this all happens in the first fall? What if you have partial anchor failure due to one fall, resulting in one piece taking more of the load on another fall? It's in a second fall when the rope will be less shock-absorbing anyway.

A more likely situation would be that the angle between the arms is 90 degrees (or becomes 90 degrees when things stretch and tighten down a bit in a fall onto it). Then the load on each arm is about 70% of the load on the power point. Suppose the load on the power point is 10kN. Then the load on each arm is about 7kN. If the cord has a 10kN MBS and the clove hitch reduces its strength by half then each strand of cord with a clove hitch in it is 5kN strong. 5/7 is about 71%. So if 71% or more of the load in either arm of the equalette is on one of the clove-hitched pieces (which will ALWAYS happen once the length of cord from the power point to the clove hitch is sufficiently different), then the cord will fail. This doesn't seem like such an unlikely scenario.

I agree that none of this warrants carrying around 20kN cord. But it might warrant not using an equalette.

But I don't think that either. I think knudeNoggin is on to something, and my assumptions about strength reduction due to knots are wrong. I think that cord doesn't decrease in strength due to knots--even clove hitches--nearly as much as I have assumed.

I'll check into published cordelette tests and post again.

[chh]

Umm yeah, by "strongest piece" I meant absolutely the quality of the placement and not the rated strength of the piece. I thought that would be assumed by anyone who had ever built an anchor. I guess I was wrong.
Half seems like a big strength reduction to me, but of the testing I'v seen or read, there is a bit of a variation in the results, which to me means nothing but even more assumptions.
How much dental floss do you have?

[ek]

My main point was that the piece that you put by itself on one side of an equalette is the one that you think is the best, and it does not follow that if it fails, the others would be in jeopardy.

In fact, I don't know why I didn't just say that.

It probably wasn't argumentative enough for my taste.

How much dental floss do you have?

Good point. I guess if you double it over enough, it would be strong enough...though it might be kind of hard to clove hitch to. It's waxed, which means it will resist water penetration to some extent!

It has been said that you can do anything with dental floss. If it were 3-sigma rated HMPE dental floss, that might be true!

[chh]

My main point was that the piece that you put by itself on one side of an equalette is the one that you think is the best, and it does not follow that if it fails, the others would be in jeopardy.

Actually, I think it does follow. If you are experiencing forces large enough to make the the piece you thought was best blow, I would be VERY concerned about the other pieces. In fact in all probability YOU'RE GONNA DIE!
But you know what they say about thinking. It can be dangerous.....

[knudeNoggin]

I browsed Blue Water's on-line information about accessory cords,
and again I'll point to the problematic aspect of the OP's title
-- "Minimum Diameter[/i] ... ". It isn't really to the point,
nor even is "... [u]strength", which was really intended.

E.g., BW offer
6mm @8.0kN (purely US-made, per "BEC"), and
6mm @8.4kN
with also
7mm @11.5kN (BEC) and
7mm @10.5kN (non-BEC less, in this dia. !?)
but also, esp. for cordelette use,
7mm @13.3kN
yet more appealing is maybe
6.5mm @9.5kN because of its presumed extra elasticity -- "Dynamic Prusik cord"

Would the event that produced a 9.0kN peak impact force on the 6.5mm
cord have produced an 11.0kN load in the 7mm non-BEC stuff?
Or maybe with the much stronger, same diameter, less stretchy cordelette
7mm a PIForce of 12.5kN -- which in this hypothetical musing would still
not break the cordage, but it's extra force on the system.
!?

- - - - -

In the musing above about breaking the stronger anchor and worrying
about the others, there should be considerable force consumed in the
breaking -- like the ruptures anticipated by the rockclimbing "screamers"'s
set of stitches. (And then again there is the point that the anchor you
think is best might turn out to not be so good.)

*kN*

[chh]

It would be interesting to peak forces in a drop test on the dynamic prussic cord versus static cords for a cordolette. It would be difficult to tie them in exactly the same way I would imagine. And angles are never the same in the real world.
But still, I think it would shed a little light.

Knudenoggin, you are right, the peak force would be significantly reduced after the first piece in your anchor blew and the forces on the subsequent pieces would be less than the peak force on the first. The above scenario is really more about the quality of gear placement than the strength of the anchor cord, so maybe it's not fit for this discussion. I'll just say this, if your "strong" piece blows, counting on the the reduction in peak force especially when the remaining pieces are cloved on a single strand seems like folly to me. You are counting on some things to go right after they have already started to go pretty wrong. Maybe this is an argument against the equalette? Allthough, I don't necessarily disagree with it. Every tool has it's place. Judging placements accurately is part of the anchor construction, and in my opinion just as important as, say, tying in. I guess you could argue that this is precisely the point of redundancy in an anchor. But again, another thread entirely.

I sure am glad to have other nerds to argue with on a rainy day

[gdstorrick]

Post deleted.

[knudeNoggin]

John Long [Climbing anchors, p. 70] "defines" a codelette as "a 16-foot section of 6MM perlon," ...

Oh, that is soooo, ah, 1st edition. (And "perlon" is a clue. :o)

He's less definitional in the revised, 2nd ed., where given his vaster experience
he decided to actually test the darn thing (I think that this is the marketer's
order: hype & sell, test if you have time); his enthusiasm runneth under.

p. 148:

Until recent testing showed its shortcomings, ... .
A standard cordelette consists of an 18-foot piece of 5.5mm high-tensile cord
or 7mm nylon ...

though Clyde Soles in Outdoor Knots puts the length at about 21'
-- this could be a difference of rough and less-rough conversions of "6 metres"
(and is greater than could be fudged by omitting the ends-joining knot).
(On-line sales blurbs support the longer figures.)

[gdstorrick]

Post deleted.

[PseudoFission]

Are you considering these questions with the intent that the cordelette rigged anchor is not being used for climbing? As a rescue anchor? Because they are very different applications that steer the conversation in different directions. As a climbing anchor, the worst case fall would be a lead fall shortly above the anchor and possibly falling directly onto the anchor. This would be incredibly bad form not to have a piece clipped in above the anchor, but possible. As a multi-pitch lead-climbing anchor the anchor should never see significant load in the first place - as the weight of the belayer combined with the energy absorbing properties of the system (belay device, pieces in the rock, and rope) should arrest his fall independently without loading the anchor. Wide weight variances could pull the belayer into the air on a hard fall, but even then the distances and forces are small and you would be loading the anchor upward - in the direction opposite for which it was primarily built. Even in a worst case fall on a sheer vertical wall in such a scenario, the leader would fall past the belayer and be caught directly on his belay device, which would load-limit the catch. Belaying a second up directly off the power point wouldn't be a FF2 and would be less severe. A rescue anchor is another conversation entirely, but would require extreme circumstances in which a cordellete was warranted in the first place (and highly unlikely).

What makes this problem so hard to analyze is the fact that you're looking at very unlikely failure mechanisms in a incredibly dynamic system (equalette) designed primarily to protect against said failure mechanisms. Furthermore it is governed by variables and conditions that are entirely unique to the people and gear being connected to it. The type of belay device, rope, and terrain make a huge difference (and typically for the better).

But let's go with some worst case scenarios. Most belay devices only limit to 2-5 kn, and anything more will cause them to slip until that force has been reached. Thus in the case of the falling lead climber directly onto the anchor, the rope would slip a large amount until the force dropped to 2-5 kn, in which the device would arrest the fall. With a tube device it would likely be less than 3kn, with a grigri or cinch - as high as 6kn. My memory is that John Long says in his second edition that the highest real world force that a climber can exert on a piece is somewhere in the range of 5.5 to 8.5 kN but that would be on a piece (of rock protection on the face, and not used in the anchor) that sees the initial loading in a lead fall (per general trad technique), thus a carabiner being progressively loaded closer to 180 degrees. With the biner friction the rope on the belay side would be seeing only half or two-thirds that figure, but again not at the anchor. Thus it would be very difficult to achieve a 10kn load on the equalized anchor with any kind of belay device being used. It could be possible with a tied-off rope. But again the scenarios in which it could develop would be extremely rare. At this point you get into the slippery philosophies of safety factors and statistics. On which numbers, which statistical average are you going to design your safety system? It depends entirely on the applications and areas in which is will be used, and with what discretion by the user.

A traditional statically-equalized cordellete (per your picture) has an impressive breaking strength, as typically three legs are used making for a 6-strand knot. With that amount of material the breaking strength is phenomenal (larger size means bigger radius of bend and higher strength). For me, the decision to use an equalette is if there is an extreme need to equalize. Typically this is due to less than ideal placements or a possible pendulum loading. chh is absolutely right when he says the blown piece will absorb energy - assuming the piece isn't complete trash, the peak force will likely be just before the piece blows out. The extension is a mere 5" or so, as half the equalette collapses and the biner falls onto the overhand limiter, which will likely roll and absorb some energy should the force be extreme. I agree with chh in that if you've reached the point where your equalized anchor is cascade-failing, then you had already set yourself up to die long before the cord diameter of your anchor mattered.