Crossing knot, a foundamental knotting tool to build jam-proof knots

[Dan_Lehman]

If it is jam resistant (which I think it will be)

thousands of such knots, and even way better than this),

"Way better"?  --show me!

where exactly does your excessive optimism,
about the jam resistance of the knot come from?

Unless one regards (any) optimism as excessive ... ,
I didn't see Mark going so strongly affirming that.
But where one CAN gain that optimism --if not a surer
state of belief-- is in examining the loaded knot and
seeing how the S.Part pulls back and keeps spread
quite some space in the Fig.8 base, whose S.Part-end
turn includes the intrusion of part of the finishing OH.
Even with the diminution of material radius upon the
elongation under load, and closing up things so to
accommodate an effectively lesser-diameter'd cordage,
which upon relaxed loading will now swell, stopper-like
in potential effect, I think that some good pressure on
this F8's turn gets off of the hard-bearing point and
... loosens the 8; the OH isn't such an issue, given
its particular stopper-like loading geometry.

the combination of a figure eight and an overhand
is a volatile cocktail component ..., don't you think?

That's a simplistic view; the particulars need to be considered,
per knot.

Could you please define the upper limit of loading zone (%MBS or in KN),
 in order to declare a knot as jam resistant?

Material matters.  Jamming/breaking ... are attributes
of a physical entity, not a *logical* *knot*.

Let me also bring to mind that, you, the professional climbers,
were the first that acknowledged the "bad, prone to jamming form"
of a figure eight, where its prime SP nipping turn, is placed on top of the returning turn,
as in this profile.

The term you want is "exterior" vice "on top of" --that
part of twinned parts that bears into its twin (vs. pulling
away from).  And, yes, it seems to be the case for the
Fig.8 knots that one's loosening hopes are better
realized with the interior-loaded knot.  (And the Slovakian
testers found strengths to be effectively equal --so much
for my theory (unless my dressing & setting shows better).)

But my purpose in designing the Lehman8 was to give
that bearing-into part for the sake of (presumed --not confirmed!)
strength, and to look for BWLesque (relatively) easy loosening in
how the knot then was completed.  (On top of these criteria,
it seems that slack-security is pretty well achieved, too.)

I, for example, would place the overhand nipping turn at the
top of the figure eight turn, near the eye, to avoid additional core constriction,
but i estimate that this modification would probably give me 1 or at most 2 KN,
extension of the jamming threshold.

... and you might, and even tuck out the Tail beside
the S.Part's entry, in opposite direction.  One more knot
for the taking; and IMO one morEasily loosened than
you're believing.


--dl*
====

[agent_smith]

Dan,
To clear up any doubt about your Lehman 8 eye knot...
I've uploaded some images (below).
Hopefully this clarifies what the original Lehman 8 eye knot geometry looks like... ?

Personal note:
I tried searching for images of the original Lehman 8 eye knot - and its hard to find anything still in existence.
I had an old image on my computer - which was mixed in with a lot of other very old images from more than a decade ago.
So I've used some of my personal time to re-photograph and edit new images - so the records are straight.

With regard to the Offset Lehman 8 bend - I think you might have presented this some years ago?
Again, there are 'genus' variations to this - there are a few different ways of integrating a Figure 8 and an Overhand knot - which produce different results.
I'll try to load test these - time permitting - but I don't think they will ever catch on with the wider climbing/canyoning community (they perceive these structures as too complicated).

With regard to 'EEL' (Either End Loadable) eye knots, I agree that 'TIB' (Tiable In the Bight) eye knots that are also 'EEL' wont necessarily have a distinct 'S.Part' and a 'tail end'.
Examples of TIB eye knots that may have no defined 'tail' include (which are also 'EEL'):
[ ] Bowline on bight (#1080)
[ ] Double Figure 8 (#1085)
[ ] Butterfly (#1053)
Indeed, they may have 2 'S.Parts'.
I should have been more clear about this... a non 'TIB' eye knot that is tied end-of-line will have an 'S.Part' and a 'tail end'.
With regard to the 'TIB', 'EEL' eye knots, they can (if so desired) be tied so that there is a defined 'S.Part' and a 'tail end'.
For example, #1080, and #1085 are often tied by climbers end-of-line with a distinct 'S.Part', and a 'tail end'.

This is one of the interesting properties of 'TIB', 'EEL' eye knots - they provide the user with different options in terms of loading profile.
However, sadly, not all 'TIB' eye knots are 'EEL'.
For example, the inline/directional F8 eye knot (#1058) is not 'EEL'.

An eye knot that is both 'TIB' and 'EEL' is very useful to roping technicians and climbers.
If you add jam resistant to that mix of metrics, then it is even more useful.

[agent_smith]

Quote

where exactly does your excessive optimism,
about the jam resistance of the knot come from?

Unless one regards (any) optimism as excessive ... ,
I didn't see Mark going so strongly affirming that.

That's right... I don't recall making any definitive or absolute comments about any knot in particular.
At reply #59, I found the language quite confronting and unnecessary - bordering on a personal attack.
I disengage when there are posts such as reply #59.

[SS369]

I would like very much if we can remain on topic from here on.
And if those interested would care to edit or remove the off topic items, it will be appreciated.
Thank you ahead of time...
SS

[Dan_Lehman]

Dan,
To clear up any doubt about your Lehman 8 eye knot...
I've uploaded some images (below).
Hopefully this clarifies what the original Lehman 8 eye knot geometry looks like... ?

Yes, the bottomost image does it best, as it ALONE
shows the proper face of the knot --where one can
readily SEE the Fig.8 aspect--; I can't fathom why
you otherwise show the knot bassackwards which makes
ID-ing things already being challenging in this crowded
lookalike neighborhood of knots!?

In a left-to-right flow of reading (that being a bias of
Western world?), one would normally begin with the
"original" from which variations are cited.

And still in you showing of presumably --though you don't
expressly so say-- what you regard as the "principal" and
"primary" (are these synonyms!?) corresponding-to-e2e_joint
eye knots are being inconsistent :: we should expect just
ONE end of each piece in the 2-tangle to serve qua EK S.Part,
joined to one then other end of the other piece; so we have
always ONE of the e2e joint's S.Parts qua EK S.Part.

[ ] You can only link segments of opposite colour [GOOD ILLUSTRATION USE, THX!]
[ ] The are 4 'principal' corresponding eye knots (which are derived from the parent bend, and are relative to the existing logical 'S.Parts')
[ ] Each of these 'principal' corresponding eye knots has 2 possible 'S.Parts'  - a primary and secondary S.Part
 (the primary follows from the parent bend's S.Parts).


I tried searching for images of the original Lehman 8 eye knot
 --and its hard to find anything still in existence.

BUT, we have just such an image --of the L8 tangle--
courtesy of Alan Lee ; one need only see the eye legs
as being the two parallel parts, and the coming-out-side
part being the L8's Tail.

With regard to 'EEL' (Either End Loadable) eye knots, I agree that 'TIB' (Tiable In the Bight) [NSE = Noue' Sans Exte'mites]
eye knots that are also 'EEL' won't necessarily have a distinct 'S.Part' and a 'tail end'.
Examples of TIB eye knots that may have no defined 'tail' include (which are also 'EEL'):
[ ] Bowline on bight (#1080)
[ ] Double Figure 8 (#1085)
[ ] Butterfly (#1053)
Indeed, they may have 2 'S.Parts'.

Not the same point.  Yes, "mid-line" EKs are a tough nut
to crack in classification.  --and, we should note, tough
to put strength/etc. data to, as loading order / variety
might play a big role in the disposition of the per-use knot!

But in each loaded-qua-EK there is a Tail, albeit a part
that can also in another loading be S.Part.
My e.g. was with an un-Tail'd eye splice, tied into a
BWL (use the back-flip method of the BoaB, say!),
which might be practically done so to yield a LARGE eye
for some use.


--dl*
====

[agent_smith]

In reply to Dan:

I can't fathom why
you otherwise show the knot bassackwards which makes
ID-ing things already being challenging in this crowded
lookalike neighborhood of knots!?

I generally make an effort to show 'front' and 'rear' aspects as this allows the reader more opportunities to examine the geometry.
There is no "backasswards" / "bassackwards" per se... its simply a case of showing both sides of the coin.
Why restrict oneself to showing only one side of a coin?
Readers who want to tie the knot will have 'blueprints' to check against - to compare their tying effort against that which was depicted.
It also reveals any symmetry inherent in the structure - whether present or not.

And still in you showing of presumably --though you don't
expressly so say-- what you regard as the "principal" and
"primary" (are these synonyms!?) corresponding-to-e2e_joint
eye knots are being inconsistent :: we should expect just
ONE end of each piece in the 2-tangle to serve qua EK S.Part,
joined to one then other end of the other piece; so we have
always ONE of the e2e joint's S.Parts qua EK S.Part.

The body of work surrounding end-to-end joining knots ('bends') and corresponding eye knots is largely unexplored.
There is very little published information about the relationship between a parent bend and its corresponding eye knots.
Harry Asher [may] have been the first to explore this? But he did not expand on what he published, or try to offer a solid theory.
I don't see any definitive discussion or analysis in Ashley Book of Knots.
I also dont see anything in Cyrus Day.

As far as I know, I am the first to try to explore the theory in detail and offer a supporting explanation.
And this is where I posited there are 4 principal eye knots that can be derived from any 'parent' bend.
But there are what I refer to as 'secondary' corresponding eye knots (based on choice of S.Part and tail).
I think I'll open a new topic thread rather than elaborate further here...

But in each loaded-qua-EK there is a Tail, albeit a part
that can also in another loading be S.Part.
My e.g. was with an un-Tail'd eye splice, tied into a
BWL (use the back-flip method of the BoaB, say!),
which might be practically done so to yield a LARGE eye
for some use.

Again - best to open a new topic thread...

I will briefly comment that a 'splice' is an outlier - and not part of the subject area pertinent to hand tied knots in kernmantel type synthetic rope.
Although modern synthetic ropes can be spliced using special tools, its outside of the scope and intent of this knotting forum.

BUT, we have just such an image --of the L8 tangle--
courtesy of Alan Lee ; one need only see the eye legs
as being the two parallel parts, and the coming-out-side
part being the L8's Tail.

But - we never had an actual image of the original Lehman 8!
We had your typed words trying to explain the 'correspondence' between what Alan had tied and what you had tied earlier.
This is why it was obvious (at least to me) that we needed to look at the parent bend - and then show all the eye knots that can be derived from it.
I can appreciate your use of words to try to explain the geometry of a knot - but not all forum members can decipher your description.
A picture speaks a thousand words (where have I heard that phrase before!)...

[alanleeknots]

     Hi Mark,
                 Please don't mix up my knots with Dan's knot. it don't relate at all.
                 My, I call it Lee's Lock and Lee's Tail Lock. Dan has no business with my knots.
                 You have a great morning. Thanks alanlee.

[agent_smith]

Hi Alan,
I'm not sure what you meant by; "Dan has no business with my knots"?

This is a free and open forum for knot geeks - and to promote discussion and theoretical analysis (right?).
My role in this discussion was to show common ground between your presented eye knot and Dan's original 'Lehman 8'.
Both of your eye knots are from the same 'genus' - in that they share a common knot core structure.

This is why I uploaded a picture of the 'Lehman 8 bend' - and traced out how one can derive corresponding eye knots from that 'parent bend'.
We can learn a lot from bends - and their corresponding eye knots.

I could not find any existing high quality photos of Dan's original 'Lehman 8' - even a google search turned up nothing (some old links are long dead).
I appreciate that it can be difficult to decipher Dan's written descriptions of his knots - and a picture speaks a thousand words

[alanleeknots]

What I mean is, Dan's knot has no business to pull my knot under and under his Lehman knot category.
Dan had Dan's tail lock
Lee has Lee's tail lock &
Lee has Lee's lock
There is different chemistry with these locks.
The Figure 8 knot and overhand knot are for everyone to play with.
Thanks.

           

[Kost_Greg]

Thank you Dan for your feedback at reply#60 without even asking you!

That's a simplistic view; the particulars need to be considered,
per knot.

Fair enough, but when i see your components at your Lehman 8, in their primordial form, without some sort of anti-blocking mechanism, i 'm starting to break out in a cold sweat, when i load it with my prone to jamming ropes. Maybe yours are more manageable at heavy strain  than mine.

Material matters.  Jamming/breaking ... are attributes
of a physical entity, not a *logical* *knot*

I know this Dan, i was just wondering about the range of a sufficient loading, in order to draw some firm conclusions about the knot's jamming profile.

I recall asking Xarax about the same concept, he had told me that 50% of MBS, is a very decent loading level.

"Way better"?  --show me!

If i get this right... you want me to show you a figure eight based knot, with an overhand returning structure which i believe it's way better than your Lehman 8?

I usually do not proceed in knot comparisons, unless the are mine, but for the sake of argument, and the concept disccused here, i shall make an attempt to show you one.

I don't know if it's better, but i have the sense that it would possibly raise your optimism levels, about its ease of untying.

I'll use a U-fold overhand returning component, taken from an old knot of yours, to stabilise  a fliiped eight in a bowlinesque fashion.

Have a look, and if you wish to delve into more detail, here we are again.

[alanleeknots]

Hi All,
         I have this loop,  " Lee's Figure 8 knot Loop-1 "
         I may have accidently deleted it. Here is the restore knot. alanlee.

         Nov 21, 2023  Add two more loops here. Both can handle heavyweights, and are easy to untie.
                               is great for soft rope.

         

[Kost_Greg]

The concavity hitch/bowline

In previous replies, i had stated (especially to Dan Lehman), that i was willing to delve more deeply into the girth hitch structure, in the light of the crossing knot concept, discussed in this thread.

More specifically, i had defined the girth hitch, as nipping turn/loop, nested within a crossing knot of reverse polarity, formed with an inward SP curving.

First image illustrates a formation, whereon the nipping turn of a random girth hitch nip, has been subjected to an additional inward curving, getting the crossing knot state as well.

This resulting concave figure, may be interpreted, as a crossing knot within a crossing knot structure, with a very long, vulnerable to distortion, collar.

Now, from all four, possible bowline formations, there is one and only one structure which surpasses the other three in terms of stability.

More specifically, in every potential concave scheme, there is only one knot or anti-knot bowline configuration, that sets the long collar in constriction mode, by placing it in between the bowline collar and the SP, as shown in second, third, (and fourth), image.

Note 1: The water-like mode has been rejected due to core instability issues.

Note 2: If the stability path is chosen, only one knot (bowline or anti-bowline) sets the long collar's topology in the constriction conditions mentioned above.

For example, in fourth image topology, it's the anti-knot, the one that fulfills these requirements. There's simply an additional tail tucking under SP, as a counter-measure, against the distancing developed between the two main lines.

Complex nip or not, the two main lines (SP, out going) of this design, are loaded in a stable, anti-water mode, within the boundaries of an accessible, manageable, restricted, securely locked down, long collar, with minimum chance of crossing knot distortion or entering in the jamming zone.

[Kost_Greg]

An advanced Cossack-like knot. S-hitched girth hitch

This, more advanced approach, is based on the stabilisation of the nipping turn of a girth hitch nipping structure, as a second, out-going crossing knot, with just returning line maneuvering.

As shown in first image, the out-going crossing knot formation, prevents the first U returning line from an irreversible, locking, exploiting the out going loading force.

However, most of the tension would probably be accumulated, near the SP crossing knot, which would probably render the decompression more challenging at extreme loadings.

Assuming that the nipping line that bridges the two crossing knots , is the weak link of the system, it is clear that it is securely locked down, by this returning line interweaving (overs and unders) through the crossing knots.

[Kost_Greg]

                                  Dragon knots

A short preface about the double dragon knot of first image, probably one of the most favoured knots, overwhelmingly (and justifiably, in my view, dare i say), promoted by knot enthusiasts.

What exactly is the double dragon, and which knot it can be related to?

It is clearly, a different loading profile of the TIB version of ABOK#1013 (tail tucked back through the collar), double or round turn bowline, or in other words, 1013 loaded from the returning eye leg side, as a crossing knot based profile.

In comparison of those two, from a jam resistance point of view, i would claim that double dragon's, crossing knot nipping structure appears to form a more pliable core than the two nipping wraps of the double bowline.

But, is double dragon's second wrap through the nub a must component?

I'm afraid it is, provided that the knot is going to be heavily loaded, because it enhances the crossing knot stability, leading to a distortion proof knot, compared to a single wrap configuration.

Moving to an alternative design of my own invention, I have transfered double dragon's complexity (two wraps) from the returning structure, to the nipping structure, adding a helical SP formation.

It's one of those cases i refer to as systems with qualitative complexity at the nipping stage with an excellent response at heavy stress.

    In short, a few words about a very easy tying method......

1. Form a bight on the SP continuation and place the returning line over the bight and under the SP (second image).

2. Fold the bight over the returning/out-going line,  and pull the two lines up through the bight in marlin spike fashion (third image).

3. Lock the tail under those lines and the helical SP formation.

The tail toggle component of fourth image (Xarax would define it as a rope made hinge), is a major influence in the system's stability and pliability because:

1. It stabilises the helical SP formation.

2. It prevents most of the tension to diffuse through the second nipping stage (crossing knot).

3. It counteracts crossing knot's tedency to distortion.

4. The out- going loading force restrains the toggle from  an irreversible locking deep through the helical SP formation.

5. Moreover, under loading conditions, the helical SP formation, creates a small slack in the returning structure loop, which makes the knot accessible from both nipping stages.

On this basis, along with some stress tests, i'm confident to claim that the knot goes unblocked right up to the MBS yield point.

To be clear, i'm not claiming that the double dragon jams, but i'm not absolutely sure for loadings near the rupture zone.

[Kost_Greg]

Dragon knots continued.....

If someone wishes to develop a dragon knot, regardless of his handedness, he'd better start with a transposed crossing knot, according to the new term.

This means that the SP is designated as a direct continuation of the crossing knot collar, while the out-going line, is a direct continuation of the crossing knot loop.

On this basis, the previous knot at reply#73, is a transposed munter X dragon bowline (X as for the crossed, transposed munter lines).

First image illustrates the other dragon bowline that i know, or double flash bowline, which i think it was first indroduced by Enhaut (link not available at the moment), which is similarly another loading profile of the TIB version, of the round turn cowboy bowline.

By the same token, transfering the complexity at the nippping stage with a transposed munter configuration this time (not X), we obtain the dragonised topology of the knot when interweaved with a single returning loop.

Of course the transposed munter bowlines, are not TIB as the original dragon forms, but the five remarks i highlighted at the previous reply #73, are still in force.