See the first curve of the Standing End ( which is what, presumably,
determines the strength of the knot more than anything else,
because it bears the 100% of the load )
NB "presumably" : we lack good data from actual
testing, et cetera. And we often lack knowledge of
exactly what this bend
is --i.e., when forces are
applied, there are often changes to the geometry
of which we might not suspect/consider/know!
(A "first curve" might be straightened; by how much
force and with what effect ..., but likely then the point
of rupture is found beyond it.)
when the Alpine Butterfly loop ( or the bend, for that matter ) is loaded by the one or by the other end : the one curve is much wider than the other.
Please show this in imagery; I don't see it.
AND, I do note that there is the
common geometry
--where "end abut" and rise up (as tails or into eye legs)--
and the "crossed legs" (of eye) geometry,
where one side is in much the "pretzel" orientation
and the other is like a minimal "timber hitch" shape;
in this latter tying (what Wright & Maggowan specified, fyi),
both geometries appear to give nice curves, albeit
different. And some of prior loading, precise
setting and
so on could make determining (likely minor) differences.
But, really, IMO, the "common"/legs-abutting geometry gives
equally not-so-good-looking, nearly 1diameter u-turns, vs.
both of the turns of the legs-crossing orienation. And, though
I favor the latter (have pointed out in another thread that
Alan Lee shows this, in his video), I must admit that some
of the good test results surely resulted from common tying.
We seek symmetry not per se, but because it leads to easily inspected knots
( an erroneously tied symmetric knot, is spotted instantly ),
and also because it means that the distribution of the tensile forces within the nub is optimum,
and the differences between the more and the less tensioned parts are minimized.
This asymmetry is not only formal, it is functional, and I believe it would manifest itself under heavy loading.
Noope, not so. Firstly, as suggested by your elsewhere-posted
guess-the-"correct"-
fig.8 dressing, discerning knot geometry
can be difficult, even in what we might regard as simple knots.
Secondly, as I note above, the
butterfly looks good in both of its
differing parts, in the legs-crossed version (one could imagine the
difference showing in, e.g., one material on average doing better
in one end, another doing better in the other, largely attributed
to material friction or stiffness or compressibility !?)
And in actual practice, end-2-end knots will at times see
unmatching ends --differences between lines.
(All of which above consideration/speculation gives rise to Agent_Smith's
warning that talk of knot strength is nonsense, especially in the
acknowledged absence of well stated theories
given good testing
and generating good data for further study!
--and is thus merely indulgence for the theoreticians
(or is that "idealists" ?!)
)
--dl*
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