... the one rising to the other's falling-- rather than as you show,
the one changing position over the other
As I said, this is irrelevant ! Which line goes over which, and in which point/side of the knot,
does not matter. The one has to be wider than the other, for pure geometrical reasons.
At the point of U-turn, the reversal of direction,
which is our focus, is where the assessment of
curvature should matter, and in your highlighted
image above one can see that the there-indicated
wider-turning one should simply slide (its crossing
over point) leftwards and sharpen its U-turn (which
is at the right).
OTOH, I'll grant that this U-turn shows more similarity
in sharpness to the other end's when loaded "through"
(end-2-end), than qua eye-knot --where there is some
bearing-against (if not crossing over) of the then SPart
vs. the unloaded other end. (
#1408 does pretty well
in rounding its U-turn as it symmetrically twist-tightens
its ends, I think; whereas these things are problematic
for the
zeppelin.)
Take any flexible rod which retains, more or less, its circular cross-section everywhere,
and try to make a 3D model of the knot in which the two first curves will have the same diameter.
You will see that it is impossible.
Nonsense : in THIS plan, you have --for the
butterfly--
the opposing SParts coming in left vs. right with one atop
the other as they pass across the "abutting" eye legs,
and then one U-turns --the 1dia of eye leg-- from below
upwards, the other complementarily and also 1dia around
an eye leg downwards; and THEN somewhere away from
the U-turns of focus, there is an asymmetric crossing of
over/under --to my side of the debate, make it at the
opposing S.Part's U-turn, reaching then into the collar.
The part that you fill the bottom of your larger/red circle
with I say moves the crossing-over point leftwards to make
that circle a horizontally disposed ellipse, and at its point of
focus ("U-turn") on the right you have an equal 1-diameter
turn as for the opposing side. That is the how-I-see-it that
led me to this question. One will need to set this left-side
eye leg pretty tight to deform the left SPart's shaping
around this area to make the shifting I describe here
such as would then otherwise maybe give curvature,
"bearing against" to that left SPart. --and I don't see
this happening, as a general rule. (And now we're into
vagaries of dressing, fine-tuning an orientation!)
But space is short, and the crossing over ... can it really
influence much the U-turn's sharpness? --and moreover
the vagaries of what happens when eye-loaded?
.:. So, I do see your view, but still find it dubious.
I'm more happy to pursue the crossed-legs version,
with distinctly different overhand components each
of which looks to curve rather favorably (though, again,
when loaded with the eye, how things actually shape up
is less clear, and probably differs with rope type).
--dl*
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