Stopper knot topologies and equivalent eyeknots

[kost_greg]

Does anyone share the view that some topologically equivalent states stemming from conventional stopper knot configurations, might exhibit certain resistance to jamming?

For instance, below, the illustrated figure 9 profile, can easily point topologically to the well known F9 stopper, if subjected to some linear core modifications.

Despite my best efforts , i was not able to induce any jamming.

So i was wondering if the derived follow through F9 eyeknot, might have equivalent releasability.

There are some observations i’d like to point out, that endorse the above assertion of anti-jamming property.

1. Both overhands are blocked from an irreversible lock by the four strands(SPs, eyelegs).
2. The SP is compressing the overhand, eye leg continuation and the eye legs are compressing the overhand SP continuation.
3. The four strands are loaded in opposite orientation, and they appear to work on creating a slack/opening, in the loop that all four are passing through.

[Dan_Lehman]

Ahhh, now you’re scoring! This has long been one of my
favorite EKs, though with the REL-Tail part making only
the OH part of the tracing journey, 'a la #1425. (The stopper
is Ashley’s #525.)

The EK is NSE, and one can put the Tail (2 B…) in either
of 3 places before taking the working U-fold
around to form the EK. Although I’ve not well tested it,
likely one of those positions & consequent twinning of the
knot will work better than the others for MID-line loading
–i.e., "through (e2e) loading & tail-loading.

I had this knot (one of the versions) tested in urethane-coated(?)
Samson blue 12-strand HMPE (not sure if it was Dyneema SK-60
or -75). THERE --in that slick, static stuff–, the knot did somewhat
jam --the material flows tension! That said, I think that in many
common ropes, it’ll work fine. It takes some bit of working
to loosen after loading, but … it does loosen. And otherwise,
though not set super tight, it resists slack-loosening.
And it’s good for bungee/shock cord in that --so far as I’ve
seen, in 5-6mm such cord-- it pulls and elongates the S.Part
but not tightening so much the rest of the knot, and thus
the S.Part easily returns to un-stretched state (vs. the knot
holding some tensioned part thereafter, which e.g. Angler’s
Loop might do).

There is yet another formation of the Fig.9 :: just look at the
mid-flype, PRETZEL state of the Fig.8, and give the two
ends another twist --an alteration one can repeat and so
do Fig.10,Fig.11, … Fig.N,
just as the familiar Fig.9 in near-Stevedore-stopper form
can be given another (half-)twist and so on, for also getting
“Fig.10/Stevedore, Fig.11, Fig.12 .. Fig.N”.
(Another method of conversion :: see the conventional form
–that straight S.Part making a loop and then wrapping itself
down the shaft until reaching up to tuck out through the loop–
as a dancer holding up one leg high through joined arms
(the loop, these), then pulling down the leg still w/arms
around, and evening out the wrapping around S.Part to
be equal “twsiting” of these two parts.)
THIS form itself doesn’t seem to be much help, practically,
but for the F9 & F10 (maybe not so much/well beyond these)
the starting center twists can be, um, rolled/pealed back
down around and --w/care to keep things from going amuck,
which they might want to do-- the knot(s) can be set tight
and take both a high load (500# in 10mm Slim Gym dynamic
kernmantle) in end-2-end loading OR qua stopper (I’ve
recently used one jammed to my pulley hook in stressing
some other knots).

I’m currently trying to see how THIS presented-above
form gets similar Fig.10-11-..N extensions; what I’ve done
so far isn’t convincing me I’m doing a proper continuation
of a series vs. just coming up with some other geometry
that the general/math knot can get. [argh]

I think that this “what I’ve call 'Semi-Symmetric Fig.9”
–where I’d seen “semi” denoting that only-to-OH part
not full ‘9’–, a dubious naming, I admit. Maybe easier
to see e2e Joint #1425 making one tail do bit of further
reeving so to run out parallel to the opposing S.Part
with which it fuses to make an EK.
Well, calling “Fig.9” we can see from above varieties
of geometry as itself being less than perspicuous.
[sigh]

–dl*
==== *

[Dan_Lehman]

Btw, I regard your photo’d EK states as ::
eye-side, S.Part-side, with “Bottom” one you should show,
or the twinned parts holding it all together, and being
what one works upon–pushing apart from each other–
for loosening-untying.
Note that were the S.Part & eye parts reversed
in over/under, it would be a double-Strangle.
(I find these two knots bumping into each other
occasionally in my fiddling.)

ALSO, there are various ways to arrange the twinned
parts. Looking at your eye-side (middle of 3) image,
the upper eye leg comes into knot through twinned
parts, turns clockwise away from view to emerge
on the LEFT of its twin; it could be dressed to be on
the right. --and so on with such things. (I think there
will be a dressing more vs. less favorable re how the
S.Part reaches to/around it.

–dl*
==== *

[Dennis_Pence]

I had not realized that ABoK #525 was the same knot as ABoK #521, which is the formulation that is usually used to form a loop knot by climbers and cavers. These are just tightened differently, and yours seems to be closer to 525.

By the way, here is another positive application for a figure nine loop (admittedly tied more like 521). Many tie an Overhand Loop in webbing. A Figure Eight Loop does not work nicely at all in webbing, but a Figure Nine Loop does.

[Dan_Lehman]

@Dennis_Pence

I had not realized that ABoK #525 was the same knot as ABoK #521

This simple, natural expression, glosses over the profound
challenge(s) in defining what a knot is, compared with
(potential) other knots !
I’m not saying that you wanted to tickle that challenge,
but here’s a nice place to point it out. In this case with the
various “fig.9” instantiations, the commonly known form
is asymmetric, some others symmetric. The common form
makes for a secure, strong EK; but the presented one here
(and I include the ones w/REL->Tail segment being only an
OH not 9 structure) might be the better one for regular
tie-in; and I’d love to see data of these and other EKs
taking repeated FF1 (& some other forces) :: might we
see some knots that relax vs. snug-set-w/o-jamming
ones that do not? --that the peak impact forces on
the resetting ones stay lower (from offering repeated
knot-compression force-reduction) than the jammed-form
knots where the rope takes (increasingly per drop) more
force!? (Maybe one has a case where the number of drops
is roughly the same, and one “stronger” knot breaks at a
higher force (but same #drops) than the other (which has
been putting less force on the system)!?

(-;

[Dennis_Pence]

Dan, you are very correct when you say that we do not always agree as to what constitutes a “knot.” I should have said that the two (521 and 525) are equivalent in the sense that you can move from one to the other without untying (with the free end). In abstract mathematical knot theory, two structures are mathematically equivalent if you can do a sequence of Reidemeister moves (which are TIB steps without access to an end) to get from one to the other. Of course, that makes all TIB knots (like the Jug Sling and the Butterfly) mathematically equivalent to the “unknot”. In practical knot theory, how we rearrange and tighten a knot makes a great deal of difference. In my previous experience with what was called a Figure Nine Knot or Loop, it was always more closely related to 521 in structure. The name itself implies a close relationship to a Figure Eight (520). Looking at a different rearrangement is certainly a valid thing to consider, and it probably should not continue to be called by the same name.

[kost_greg]

Thank you Dan and Dennis for your valuable contributions.

Truth is, this F9 geometry, located in Abok as 525 knot, escaped my attention, it just came up for me from the conventional , known F9, 521 configuration with core manipulation.

The following F9, topologically equivalent profile, emerged in exactly the same way as well, and perhaps this is not based in Abok. I have demonstrated it before, but i believe it shoud be also intergrated here, as most images from the old forum have crashed and can not be retrieved.

A follow through eyeknot formation, derived from this stopper, would be a rather challenging endeavour, and would also leave a very bulky core, with less practical features than i would have expected.

Nonetheless, a two rope diameter, returning bight, reeved under the SParts, at the very point where they embrace one other, would prevent the structure to lock, making an excellent adjustable eyeknot.

[Andreas1]

I was looking for this several times. There it is. Easier to adjust after loading than any slipped eye, I ) know.

[Dan_Lehman]

It’s from THIS orientation of the “9” that I get from
the common, asymmetric one to the one you’ve
presented above that I’ve so much favored in past
years (& current, 2 B Sure) ! IMO, it’s the best
“slack-secure” version, yet mostly non-jamming.

–dl*
==== *

[kost_greg]

Andreas, i agree it was a gοod opportunity to repost it.It might not work as well as the previous F9 (fixed form) eyeknot in terms of jam resistance, but besides the adjustable loop shown in my previous reply, it can also work properly as a returning structure stabilizator of a nipping loop, or in other words, a bowline with this F9 collar structure.

We have seen bwls with rather complex (Stevedore) returning structures (see EBSB), working very well, so why not this one too?

Dan, to which structure are you refering as mostly non-jamming, the first or the second?

After some quick tests, the second F9 geometry, in fixed eyeknot formation, haven’t convinced me at all, i believe it operates on conventional F9, jam resistance levels, or even worse.

[Dan_Lehman]

“The derived follow through F9 eyeknot” (= OP)
IS
which structure.

(-;