I started with the Butterfly Loop, http://davidmdelaney.com/alpine-butterfly-loop/Alpine-butterfly-loop-m1.html, but when I tested it with thin stretchy braided nylon cord, it was very jammy. ...
You should note that the Butterfly knot is
asymmetric,
and what eyeknot results from it will depend on which of the
non-eye ends is loaded; additionally, the knot can be dressed in
a variety of ways. E.g., your page on the end-2-end knot (bend)
--which I refer to because of color-coded rope strands--
shows two dressings (between Method-1 & -2): in the upper one,
the green rope makes what one might regard as a "minimal Timber
Hitch" with its Overhand; its tail should cross more rightwards & over
the white tail --and will be held in this position by the draw of its SPart
when loaded, and other parts will get pressed into this rope's
collar(this turn & tuck teardrop structure) and keep it open, easier to pry
loose. (And your end-loop geometry is like Method-1's.)
In the lower photos, it is the white rope that takes this position,
and while here its tail isn't passing under the green, it also doesn't
extend (in this case) enough leftwards and thus over the green.
(This was the geometry urged by Wright & Magowan; but after
loading the eye with --resp. of Methods-1/-2-- the white/green
ropes (so this described like-a-Timber-hitch part has a slack end),
I think the knot will loose the geometry.)
Your "Butterfly Bend Loop" has the better(?) geometry just described.
As you realize in your exploration, there are different ways to derive
an eyeknot from an end-2-end knot. The Butterfly knot started
with the mid-line eyeknot and by one line of reasoning birthed the
end-2-end companion by simply cutting off the eye. It's a natural
relation to take, as expected usage of the knot would load it just
in that way. Of course,if one does this with the Fig.8 & Overhand
eyeknots, one gets the related
offset end-2-end knots, not the
usually associated ones(!).
A third way to derive an eyeknot from an end-2-end knot is what
I presented in the thread on the Zeppelin Loop. This is tantamount
to making a bend of a single line with the ends of a bight, and then
fusing one of the bight ends with the single line's end. You might
try this for the Carrick bend, e.g. -- and beyond the proof-of-concept
result, there will come some yearning to get better dressing and so
on: refinements to play with. This
"twinning" of one of the E-2-E
halves of course puts bulk into the knot, and arguably not in the
places that might best receive it (e.g., in the
collar around the
eye legs rather than (better->) the SPart). But, it's another way;
and as with the Zeppelin Loop it's TIB (Tiable Inthe Bight).
--dl*
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