Having tied and played with all of the variations illustrated, I am leaning towards the last image - the 720 degree variant.

Why? Because:
[1] It has 3 rope diameters which are encircled and gripped by the loops
[2] It It has double loops acting to encircle and grip the bight
[3] The collar describes a larger radius
[4] The tail parallels the Spart leaving the eye clear
[5] It is simply an extension of ABoK 1013 and improves upon it (in my view)
[6] The structure exhibits a degree of symmetry and compactness and also appears to be secure and stable
I would of course welcome opinions/feedback...
I'm absolutely amazed/appalled: that you can HAVE the EBDB, and yet go on to produce and
preferthe grotesque derivative "#1013 720deg" variant!? --incredible!
Firstly, your presentation should
orient all knots the same (re SPart turn/handedness)which will make comparisons easier and surer. Currently, you have reversed handedness.
And there is still the problem with some "rear/front" view labeling--540 is *wrong*. Yes, it entails
the most work--as it's the most annotated/labeled--, but starting the series off correctly with a
nice "FRONT view" for the Common Blw #1010 will set the tone & orientation basis.
(You could also anticipate some criticism (pretty much just baseless hearsay/rumor) of the
Cowboy Bwl (#1034.5) by having a ready image of it and 1010
ring-loaded, and indicating
what part (the end) will often slip out in the 1010 form abnormally loaded--that should shut
a few mouths (maybe).
Secondly, your #1013 variant is more varied than you state in that it is a "Cowboy" (1034.5)
collar direction; that could lead someone to a bit of confusion. This change was made presumably
to have the end finish adjacent to the SPart.
Re criterion #2, that begs a
So what? challenge. I found it quite interesting to see in the cited
(above) Dave Richards testing that in the low-elongation-rope cases (12.5 & 7mm), the DOUBLE
Sheet Bend slipped (but not in the 10.5mm dynamic rope)--and for the 12.5mm rope, the single
SB did NOT!? This goes to question the efficacy of the double turn, which I'd have thought would
improve security. (It also begs the question of What-form-of-sheet-bend?, sadly--I don't think that
I found out (yet).) In any case, for THIS eyeknot, given the follow-on securing of the end, and the
materials, I don't think that one should put much weight on this. (Note, before Spydey chimes in
with relationships between ... , that the eyeknot (normally loaded) tensions the nipping loop from
both sides, whereas in a sheet bend, the end-side is untensioned, just nipped--significant re security.)
Re #3: how is this at all beneficial, vs. detrimental, even?!
--detrimental in that with a larger collar there is more material to all knot deformation at high loads.
And I think that it's partly illusory in regards to the stuffing of the end back through it (and having,
at the point of setting, some sense of added tightness): for, on serious loading, the end will likely
swing around behind (in proper "front" perspective) the SPart, and the looseness of the enlarged
collar will lead to an inferior orientation of the nub--SPart then going too directly into the nipping
turn vs. pulling over the dble.turns into it (for note that the other end of this dbl.turn coil is going
to be farther away and trying to capsize it--SPart pulling back in opp. direction, to flip ... ).
Re #4, well, big whoop. One
can do that with the EBDB. One can do that in a better way with
the Water Bwl (or should we better say, "The Clove Bwl"--as it seems there's been an unjustified
shift of the postion of the added HH/turn from removed to adjacent by authors not well advised!),
taking the end back towards the SPart through the original nipping loop. A clear eye seems a
pretty trivial distinction to me, for many uses. The EBDB leaves the eye clear, too, even w/o
pointing the end SPartwards; there are various ways of dressing ... .
Re #5, no, as noted above, it is not simply an extension (any more than it is of 1034.5).
But I sense that you hope to buy credibility sort of
ad hominen vis-a-vis such a comparison.
Big whoop, again. Now, EBDB **is** such a quite simple extension (though, it too can be tied
in a Cowboy orientation)--one repeated tucking of the end (and one can choose inside or outside
of the collar, for that.
But the EBDB binds the central nipping dbl. loop at the one point
where the binding has sure, lasting effect (in the materials of concern here); "720" does not.Finally, re #7, as Roo noted, we are some distance from compactness now. Not that it's unheard
of to add a Strangle tie-off for the Fig.8 even (oh, yes, a flame debate that flares up every so often
between climbers), which adds to consumption. I have some inkling that using a variety of knots
to tie off --and consequently sharply bending the rope at different places-- might less quickly
degrade the strength of the rope ends--"the sharp end".
If you want efficiency, the Lehman8--D.Britton linked image now lost--would do well.
"Do Not Pass Go" is the old board-game saying I'll lay on the latest innovation. You have much
better & detailed hints above to explore, really.
As for Roo's
"what you think '3 rope diameters which are encircled and gripped by the loops' ... actually achieves" ,
it has pretty obvious implications for what must happen for the knot to come untied--that the end
must go back out of the loops the extra time, and in cases to repeat this (to come completely out)
it must then go in the opposite direction, which gives some assurance that it won't happen
(and there should be a longer, flapping end to notice, for a climber and her tie-in, anyway).
The
presumption re strength is, yes, just that; but it seems plausible, though I note some
aspects that might be unfavorable (re friction); also, OnRope1.com had a MythBuster that
challenges this notion--YMMV.
--dl*
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