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.

(-;

[Dennis_Pence]

Although I could quickly see that you could move back and forth from a Figure Nine to a Tweenie [ABoK #525], I took me awhile to diagram it exactly.

Figure Nine___________________________________[#525]

[#525]________________________Figure Nine, transposition

The whole process is a complete flip of a Figure Nine to the transposition of a Figure Nine. When you do a similar complete flip of a Figure Eight, you get another Figure Eight in the opposite direction. Thus, the Tweenie can be an intermediate step in this complete flip of a Figure Nine.

If you do a Google Search of “tweenie knot”, one of the early results is a YouTube video of one tripled for macrame.

TWEENIE KNOT Macrame Wall Hanging | Minimalist Macrame | New Macrame Design

After I saw this, I found that Ashley actually has the Tweenie Knot Doubled in [ABoK #550].

This is pertinent to this discussion because of what Ashley writes in the description of [ABoK #550].

There are two rim parts and only one top part; the end is nipped under the top part; and the knot is pleasing. But it easily distorts unless it is doubled. If, however, it is doubled, it is distinctive and handsome and not too difficult to tie.

Without the doubling, this [ABoK #550] is just [ABoK #525]. When you tie a Tweenie with a single strand as a stopper knot, it is all too easy to move at least part way in the progression above, either toward the Figure Nine or toward the transposition. You may not go all the way, but it is too easy to go part way (in either direction) and loose the symmetry of a proper Tweenie. We do not want to try to use a knot for life-critical applications which “easily distorts.” But at the start of this discussion, you are tying the knot in a bight to get a fixed loop (or eye knot). This seems to be another kind of “doubling” like Ashley’s [ABoK #550] in that is does not so easily distort.

One final thought about this Tweenie Loop Knot. Often in climbing and other life-critical applications, it is common to have the knot inspected and approved by another person. This is not an easy knot to inspect and confirm, particularly as it can distort so easily. While none of these distortions seems to affect the safety of the knot, with so many variations, it would be too easy to actually get something else which is less safe.

[Dan_Lehman]

When you do a similar complete flip of a Figure Eight, you get another Figure Eight in the opposite direction. Thus, the Tweenie can be an intermediate step in this complete flip of a Figure Nine.

Well, with the F8 one can get a “mid-flype” state which
is what corresponds to the F9 in #525 state. But there’s
more (for the F9, & F10/stevedore) :: consider your first
F9 image as a dancer leaning wayyyy (unrelistically) far
back --head rightwards-- with arms connected in circling
to hold the one leg up head high ;
now have this led lowered
(bringing the connected circling hands with it)
back leftwards , the connected arms thus seen between legs
in the crotch.
In most likely formations of the F9 one will have one “leg”
slightly wrapping the other, straight leg and … make the
dressing adjustment to have the two “legs” evenly “twist” together.

And in this position/form one can also see that mid-flype F8
as taking --sort of, with its lesser material-- merging what
are distinct orientations for F9 & beyond : the two
opposed ends flowing into each other,
rising in a twisting dance (to whatever number it
is --F8/9/10/-- and then turning away from each other
to connect (in my “connected circling arms” way..

Now, the challenging adjustment is to jointly /
/ simultaneously fold back the “turning away…” lobes
down around the rest of the knot, and with some
iterative setting via one --a bit-- then the other --a bit–
an attractive knob knot is got. (I’ve not tried other than
F9 & F10, so not sure how accommodating the higher
numbers will be!). (Challenging when torsion rears up
to defeat one’s efforts! )

I’ve played with these series of OH - F8 - F9 - F10 - … -Fn
knots over the years. I’m not sure I’ve got a grip on how
to continue the 525 orientation,
but the Fig.9 - Stevedore - & beyond are simple additions
of another (half-) turn around a part I keep straight (but
which Dennis shows wiggled),
and the yes-you-want-pictures(!) other form verbally
sketched above, it’s also simple to get it (i.e., “it” without
that folding down lobes dressing) by putting in one
more twist (as the OH pretzel twists ends into F8).

–dl*
====*

[Dan_Lehman]

@Dennis_Pence

There are two rim parts and only one top part; the end is nipped under the top part; and the knot is pleasing. But it easily distorts unless it is doubled. If, however, it is doubled, it is distinctive and handsome and not too difficult to tie.

Please note that Ashley’s assertion re nipping is wrong for #525
–and doesn’t that mean also for #550 unless it’s more changed?
(not willing to get a brain strain trying to follow his 550 image!)-- ::
#525 nips the Tail with a rim part.

Without the doubling, this [ABoK #550] is just [ABoK #525]. When you tie a Tweenie with a single strand as a stopper knot, it is all too easy to move at least part way in the progression above, either toward the Figure Nine or toward the transposition. You may not go all the way, but it is too easy to go part way (in either direction) and loose the symmetry of a proper Tweenie.

Perhaps if you tie #525 the, um, long way --your transformation
into it-- vice going directly there, but my favor is to tie the simple
pretzel OH keeping track of the tail-tuck into the loop to form
it as where I want to finish with the next tail tuck. And from
this point, snugging up should be safely done.
AND in stopper loading, the knot isN’T symmetric; it would be
for say being among many such knots in a rope intended for
hand-over-hand-&-foot climbing --where it might be favored
vs. OH as being non-jamming.

I just set this loose and in one test found that pull-through
capsizing looks to find yet firm resistance following!?
While Ashley’s Stopper (#526) pulls through to become
Clyde Soles’s “Bowline stopper” --or whatever he called it.

–dl*
====*

[Dennis_Pence]

To answer Dan’s last post, I am not sure I can explain totally what Ashley meant, but I will try. When the Tweenie [#525] is doubled [#550] or when you tie a Tweenie Loop (as in the original post here), the knot tends to stay more symmetrical. You can get this in [#525] if you carefully pull on both the free end and the standing part in opposite directions and keep the knot symmetrical in the middle.

When you do this, the free end comes out of the top (which is what I think Ashley meant to say). {Note here I have drawn the mirror image of Ashley’s [#525] to better match the single version of [#550]. The loop version is even more likely to be in this shape because you put tension on the loop.

But when you are tying with a single strand, it is easy to do the following. Here I tighten the original Overhand Knot first.

This is the way Ashley seems to have tightened [#525], and here the free end comes out mostly to the side. With no doubling of any kind and no tension on the free end, the knot easily distorts to this less symmetrical form.

[kost_greg]

Dennis_Pence, it’s a pleasure to welcome you to the field of knot transformations. I believe you possess a unique ability to visualize all the indermediate states.

However, i’m more inclined to agree with Dan on this, in the sense, that despite all the derived states of a figure 9, that emerge from the process of transposition, this does not mean that a certain form, would transition from one to the other when heavy loaded.

Well, all knots would deviate from their initial forms, if pushed to a higher loading zone, but i think in most of them, especially those closed forms we are exploring here, not to the extent of completely altering their original states.

I was mostly motivated by the fact that a certain state of a closed form knot structure, appears to be less prone to jamming than the conventional nine state.

I’m the biggest fan of bwls, (perhaps after Xarax, he is the ultimate boss of bwls ) but try to imagine a knot with a closed form nipping structure, that would go unblocked right up to the rupture point, what bwl would defeat that?

By definition, a nipping loop, is not considered to be more stable than a knotted nipping structure form such as an overhand, 8, 9 etc…

[Dennis_Pence]

While we are looking at the various knots derived from stopper knots, it is nice to also add nooses. Below I have the Overhand Noose [#1114], the Poacher’s Knot (or Double Overhand Noose) [#409], the Figure Eight Noose [#1116], the Figure Nine Noose [#1118], and the Ichabod Knot (or Figure Eleven Noose) [#1123]. I have also added what I think might work as a [#525]-derived noose. I do not like my new creation as well as [#1118], and I cannot transition between the two because of the different position of the standing part to form the noose. {The closest thing in Ashley to my new creation is [#1125], and I like it better as well.}

I like to fly pre-made cloth kites, and I usually find that the manufacturer has tied the string to a sewn loop of the kite using a Poacher’s Knot. I sometimes have to untie one of these and re-tie if two leads are not quite equal in length. They are not too hard to untie: first you loosen the noose out and then you untie the Double Overhand (or Strangle Knot). I think that the Figure Nine Noose [#1118] is a nice alternative which is slightly easier to untie compared to [#409]. Below is my way to tie [#1118] since Ashley’s novel method cannot be put through a loop.

Poacher’s Knot [#409]___________Figure Nine Noose [#1118]

[Dan_Lehman]

Double Overhand (or Strangle Knot)

Try converting the Dbl.Oh into an Anchor Bend
–might be kinder to the S.Part and less jamming.
(Meanwhile, why does nOne show making a full RTurn
on the object --to better grip object, spread the turns’
bearing on it, and reduce force into the knot (and thus
around the S.Part)?!
)
And further ideas flow from this!

–dl*
====*

[Dennis_Pence]

Dan,

I think that the Anchor Bend [I assume you mean #841] is a relatively permanent knot. Tied in string for a kite, this would be difficult to untie after heavy loading. Notice for a large anchor the sailor in Ashley insists on a service to keep the rope still. As I said, the Poacher’s Knot can be more easily untied by opening up the noose a little. Then the Double Overhand has no tension on either end, making it easier to untie. You can do the same for [#1118], but when you do, the Figure Nine is easier to untie because the final tuck is only under one wrap (while the Double Overhand is under two). Certainly, there are applications where the Anchor Bend is a better choice.

As for suggesting a round turn in the noose around the object, I think that this would work better and be more appropriate when object is sturdy and slick (like the ring I have drawn). The loop for a kite is soft cloth webbing which might tend to twist as you draw up a noose with a round turn.

[Dan_Lehman]

@Dennis_Pence

knots derived from stopper knots, it is nice to also add nooses

Indeed, I have realized a simple method for making
a stopper : have a noose hitch hitch its tail --such as
Ashley’s Stopper does.

The loop for a kite is soft cloth webbing which might tend to twist as you draw up a noose with a round turn.

Sounds then that a better connection is via Eye Knot to eye.

(-;