Butterfly knot - various loading profiles

[agent_smith]

#1053 Butterfly knot has been a workhorse in the rope access, climbing and vertical rescue communities.

I am currently writing a new technical paper on this knot.

There is some discussion in another thread that is drifting into the realm of academia and knot topology  - and this new topic thread may be more in tune with that particular discussion.

A precise definition of various loading profiles on knots has not been peer reviewed and published in a technical paper (as far as I am aware).
For instance, the notional concept of 'ring loading' may be diluted to encompass specific loading profiles on the eye of a Butterfly knot.
I am of the view that the term 'ring loading' may be too general - and not define (with precision) the direction of loading on various rope segments linked to the knot core.

Circumferential loading (ie cylinder/hoop stress) is expanding the eye in all directions - rather than a single defined axis.

The eye of a Butterfly can be loaded in several different ways - all inducing various effects on the knot core.

The term 'Offset loading" is also being applied and interpreted in differing ways.

I will be investigating all of these definitions and resulting effects in my new paper...
I have already corresponded with some colleagues - who have collaborated and contributed in the past.

Topology is a complex subject dealing with a mathematical knot (which has no ends).
While indeed very interesting, practical knots do have ends... with various loading profiles and jamming thresholds - which are not accounted for in topology.

[KC]

Very nice!
i think the eye is best loaded less than the SParts;
and if eye not unlooaded /used to isolate damage or just as stopper
>>that any pull on eye is best perpendicular to the competing SParts.
Thus the opposing pulls of the SParts forms the major axis
>>and eye the lesser, and if any pull 90 degrees is most balanced
>>and geometry flows smoothly to that.

[agent_smith]

per KC:

i think the eye is best loaded less than the SParts;
and if eye not unloaded /used to isolate damage or just as stopper
>>that any pull on eye is best perpendicular to the competing SParts.
Thus the opposing pulls of the SParts forms the major axis
>>and eye the lesser, and if any pull 90 degrees is most balanced
>>and geometry flows smoothly to that.

Thanks... I am going to run some eye loading tests of #1053 Butterfly in human rated EN 1891 rope.
I will experiment with various dressings of the eye (eg twisting the eye).
I'll also through load (SPart-to-SPart) with the eye isolated - and see if it remains jam resistant right up to MBS yield point.

Am also going to include various modifications and alternative TIB bi-axially loaded knot.
Will also investigate the 'Mobius' dressing of the derived Butterfly eye knot that is Either End Loadable (EEL).... including all of the derived eye knots from the Butterfly bend.
There will be numerous high quality images of #1053 Butterfly and its derived Butterfly bend along with some history (eg AA Burger; Wright & Magowan; and Phil D Smith).

If you are interested to be a contributor and be cited in the paper, PM me.

[agent_smith]

Xarax has pointed me to the following:
Link: https://igkt.net/sm/index.php?topic=3827.msg22680#msg22680
Derived from #1408?
Is this an original creation?
I have not investigated jam resistance in various loading profiles... is there test data in existence?

And a discussion on symmetry:
Link: https://igkt.net/sm/index.php?topic=4425.msg27940#msg27940

All possible candidates for inclusion in new paper on the Butterfly (bi-axially loadable TIB eye knot).

[Dan_Lehman]

Xarax has pointed me to the following:
Link: https://igkt.net/sm/index.php?topic=3827.msg22680#msg22680
Derived from #1408?
Is this an original creation?

Yes, so far as I'm aware.  (I.e., while I know that
*I* tied it while fiddling --though I think with actual
goal in mind, this time!  --, I can't say for sure
that someonElse hasn't done similarly.)

Beyond that then came the symmetric, "twin-eye"
versions.  I did like above with the zeppelin
--i.e., had first asymmetric than symmetric finds--,
and shakehands, and #1452 (and the same-rotation
butterfly, with one fig.8 half, the extra twist
getting the rotational agreement with the remaining
overhand half).

And then gazillions of other *directional* eye knots,
though I realize that that qualification comes with
some challenge : who's to say that loading it in the
*other* direction is verboten?!  In CMC Rope Rescue
testing, they found the offset fig.8 eye knot stronger
than the inline one, through loaded !

--dl*
====

[Kost_Greg]

How about a bowline knot, based on ABK's TIB nipping structure?

Perhaps, it may not be directly related to the midline concept, but it seems to me like a secure and compact way to load the eye of this pretzel/butterfly based nipping structure, when stabilized with a conventional U braced bight for a bowline construction.

Xarax has submitted a knot like this, long before, at his pretzel/Eskimo thread, so i have attached a pointer to his work.

Link : https://igkt.net/sm/index.php?topic=4464.msg33112#msg33112

Under closer inspection to its core nip, one can acknowledge the butterfly pattern.

Is it proper to attach a moniker like butterfly bowline? (my term)

PS : Insert the WE down through the center of the two loops, and you will form Alpineer's tresse!

[agent_smith]

Further expansion of loading profiles conceptual framework...

Referencing this post from Dan Lehman: https://igkt.net/sm/index.php?topic=6799.msg46330#msg46330

In reply, please refer to attached images.

I think there is a lot going on here - and we need to tighten loading profile definitions to make it clearer (ie unambiguous).

For example, the term 'eye' loading can have different meanings.
I have introduced concepts such as biaxial through loading and triaxial loading - with accompanying photos to assist in explanation.

I do accept that my use of the term 'biaxial through loading (BTL)' could be simplified to just 'axial through loading'. However, the term 'axial' might be misconstrued as meaning 'uni-axial'.
The term 'biaxial' referring to load entering the knot core from 2 directions (ie both SParts).
The term 'triaxial' referring to load entering the knot core from 3 directions (with the parallel eye legs being conceptualized as one part/segment, not 2 separate parts/segments).
And therefore, I am placing relevance on the direction from which load enters the knot core (rather than a 'cookie cutter' approach - to paraphrase Dan Lehman).

In the case of #1053 Butterfly, eye loading can occur:
[ ] mid-line position - where there can only be 1 reactive SPart
[ ] end-of-line position - where there can be 1 or 2 reactive SParts

Note that eye loading can also be transverse or circumferential.
I prefer the term 'transverse loading' instead of 'ring' loading (with respect to an 'eye').
Circumferential eye loading is akin to hoop stress.

EDIT NOTE:
Tried to improve image quality - within the 100KB file limit imposed by the forum software.

[bushrag]

This guy demonstrates cross loading of the eye at 19:40. It's curious how the AB knot essentially becomes a "bend" that transforms the cross-load into a "sling" load and the break occurs at 104% of the rope strength.

[agent_smith]

In reference bushrag post at reply #7:

This should come as no particular surprise - and I would expect a nominal result as was tested for this loading profile.
Richard Mumford  loaded the eye of the Butterfly in a transverse loading profile (in axial alignment with the SParts).
You'll notice that in this loading profile - there is instability (the knot core capsizes at 20:08 elapsed time).
After undergoing 'dynamic' change in core geometry at 20:08, the core then settles and compresses until MBS yield point is reached at 20:15.

It is a well understood concept that a round sling essentially doubles the MBS of a single leg linear segment (with a factory sewn join).
However, a theoretical doubling effect is not achieved on account of the hand tied joining knot (ie the MBS is not doubled because the joining knot creates a weak point).

[Dan_Lehman]

It's curious how the AB knot essentially becomes a "bend" that transforms the cross-load into a "sling" load

But this is the state from the start --ring-loading is effectively
a round sling w/eye knot become ends joint.  Note that this
butterfly wasn't set much at all --quite loose, and not having
otherwise taken a load as either an ends joint (of butterfly
SParts, not eye legs) or eye knot.

and the break occurs at 104% of the rope strength.

Which is alarmingly LOW, IMO :: one has double the material,
albeit with one side knotted, and ...

(ie the MBS is not doubled because the joining knot creates a weak point)

... it was NOT the knot that broke,
but the line at one of the anchor pins
(the one seeing most rope movement
upon the knot's compaction).


--dl*
====

[agent_smith]

per Dan Lehman:

... it was NOT the knot that broke,
but the line at one of the anchor pins
(the one seeing most rope movement
upon the knot's compaction).

Dan - I'm quite surprised that you did NOT notice any of the following facts:
1. This is a test sample of one (1) - it is not valid to draw conclusions from a statistical sample size of 1!
2. If you look very closely at Richard Mumford's test rig - his 'quickie' shackle is leaning/angled and the rope is moving and sawing over the side edge of shackle (a sharp edge).
3. The moving rope saws over the angled side edge of the 'quickie' shackle - which triggers premature rupture before the knot can reach its MBS yield point.

I assert again that in a pure MBS pull-it-till-it breaks test; a round sling that is factory stitched will always be stronger than a round sling formed with a hand tied knot (I suspect that you already know this as fact!).

[Dan_Lehman]

per Dan Lehman:

... it was NOT the knot that broke,
but the line at one of the anchor pins
(the one seeing most rope movement
upon the knot's compaction).

Dan - I'm quite surprised that you did NOT notice any of the following facts:
1. This is a test sample of one (1) - it is not valid to draw conclusions from a statistical sample size of 1!

Of course one can : if it happens, that's to be noted.
Doesn't mean that one believes it will always happen.

2. If you look very closely at Richard Mumford's test rig - his 'quickie' shackle
is leaning/angled and the rope is moving and sawing over the side edge of shackle (a sharp edge).
3. The moving rope saws over the angled side edge of the 'quickie' shackle
- which triggers premature rupture before the knot can reach its MBS yield point.

I see what you mean (and now have looked FULL-SCREEN size!),
but I don't see his metal as nearly so sharp.
I do see that there was more outfeed of material on the breaking
side (why so?  that side of knot gives material, but why isn't
the pin-rotation-equalizing achieved at both ends?!).
AND I see that the breaking side had some torsion --follow
the rope's "racing stripes" to see that.

I assert again that in a pure MBS pull-it-till-it breaks test; a round sling that is factory stitched
will always be stronger than a round sling formed with a hand tied knot (I suspect that you already know this as fact!).

That might be so, but it's not the same assertion as
"the joining knot creates a weak point"
--which it indeed DOES, but then in knot compression
there can be weaknesses tickled elsewhere that are
the site of the break.

If a sewn joint achieves, say, 80% tensile,
and yields nothing by compression (because
it has none), then the sling's strength is 2x80=160%.
If a knotted joint achieves 75% (grapevine?),
and yields significant material so to tax the
unknotted side to 100%, the balance might
come to 100 + 70 = 170%.
YMMV.  (just guessing numbers AND breaking time,
to illustrate the idea)


--dl*
====

[agent_smith]

In reply to Dan Lehman:

It is hoped that this back n forth keyboard conversation is not evolving into a knowledge contest (which unfortunately happens all to often in technical discussions).

Some brief observations... (in point form for clarity):

1. In the case of this Richard Mumford test video - I definitely do not place any significance on his test sample size of one (1). Scientists and/or scientific research groups never publish results or conclusions based on a test sample size of one (1). That would be absurd - and they would be laughed out of a job. Imagine if COVID vaccines were tested on only one (1) human and then released into the public domain for mass public vaccinations (imagine the outcry from concerned citizens).

2. Richard Mumford appears to conduct his test of the eye of the Butterfly as an afterthought - it is a 'spur-of-the-moment' procedure.
The loading profile is a transverse direction in axial alignment with the SParts.
This is a very unusual loading profile that would likely never occur in real-world use of a Butterfly knot.

3. Almost immediately after load is applied to the eye, instability manifests.

4. The core of the Butterfly knot undergoes dynamic transformation (it capsizes).

5. Look closely - and you will see that the instability is biased on one side of the knot core.

6. It is the overlapping side that is experiencing instability (in this case, the 'S' chirality side).... when viewing the video, it is on the 'right' side of video screen.

7. In my opinion, if Richard repeated the test - with the 'S' and 'Z' sides transposed (swapped) - the instability would have occurred on the 'left' side of the video screen (the side with the overlapping segment).
However, this is a test sample size of one (1) - and so we have nothing to compare against - and we cannot draw any reliable conclusions from a statistical sample size of one (1).

8. A #1053 Butterfly can be tied as either S/Z or Z/S chirality - within a defined reference frame.
In the specific case of the Richard Mumford test video, when looking at the video screen - it is Z/S orientation (Z on the 'left side' and S on the 'right side').
Richard Mumford has tied his Butterfly with a geometric orientation where the overlapping segment is on the 'S' side (ie to the 'right' when viewing the video screen).

9. I have tried to repeat this test (ie transverse loading profile on the eye) in my own 'homebrew' backyard tests. What I have noticed is that when the eye of a Butterfly is subjected to a transverse loading profile (in axial alignment with the SParts) - instability always manifests from the side of the knot core with the overlapping segment.

10. A #1053 Butterfly knot is asymmetric. The 'front' aspect will have an overlapping segment. The 'rear' aspect will have parallel segments.
The 'overlapping' segment can exist as either 'S' or 'Z' chirality.

...

but I don't see his metal as nearly so sharp.

Maybe you need to rethink your definition of what constitutes a 'sharp edge' (maybe you are conceptualizing a 'sharp edge' as something akin to a Gillette razor?).
Clearly and obviously (in the video) failure propagated from the 'quickie' shackle (rather than the knot).
All knots create a stress concentration within textile materials and that's where failure normally propagates from.
In Richard Mumford's test sample of one (1), the 'quickie' shackle was significantly angled/leaning to one side during the test.
The rope was running over and sawing across the side of the 'quickie' shackle.

[KC]

i always thought on this vid the slings should be eliminated,
so arcs outside the knot, would be around much larger, not smaller hosts than inside knot;
to best only test inside knot.
Also, if being a purist and not just appreciating the effort here;
on shackles etc. that maintain 90degrees host to SPart lead in>>shifting, angling as stated.
(some RTs from sling side could have helped stabilize i think)
.
i always set backwards thru after making a knot,
imaging arcs as multipliers of my hold against to then equalize/ballast Load on other side of leverage machine(Turns) than me.
>>i have leverage against the Load if only try to hold or payout rope, but leverage against me only if try to take 'purchase'(ABoK) thru Turns from Load side..
So only when am active puller, not just hard preset full or partial(paying out) ballasting as more of a passive responder, holding ground more than trying to take ground.
But if not sure enough Turns, and about to take dynamic Load, would set from tailer man position braced, to tight Turns around capstan device feeding to taut input/SPart out; grooming from me to backwards out;  i want to get the jump on the Load, rather than allow it to get jump on me.  i'm scanning for how to add extra friction or stop in an emergency as doing so.
For Set of TDS in knotting; i likewise tighten from final Nip (before any added stoppers) backwards out to SPart once again;
to give the knot the 'jump' on the potential Load, by same model.
Much of my stuff is on such models of engagement, of feel in such and such a position when it is me in that bullpen.
.
So, i too would set the B'Fly from eye, grooming then out to each leg of SPart.
B'Fly has it's own stopper mechanism built in, of each loaded leg side primary knot, backed up by the stopper of the opposing leg's  knot;
>>even if the other leg is not loaded; still has this 2part/not mono mechanism of checks and balances to each pull.
>>even 1 leg pull to eye has other unloaded half as BFly fall into place as stopper, where usually is end2end ballasting pulls/can be Bend; but her is a stop/termination/Hitch, or reeved as a Running Eye to same as termination/Hitch.
.
Direction ported thru even same structure can be important, but superbly so when changes endpoint or to cross-axis.
But i always think BFly, should be loaded across eye and not thru eye so much,
so dis-favor SPart to Eye primary loading profile of 1 end of B'Fly as BE, as no premium loading usage of the available architecture knot presents.
.
Same for cross-axis, splaying, spreading pull on either eye;
this does not flow the force line to best action offered in lacing of locking clamp;
but rather, picks the lock open more.
A direction  change of pull (which truck pulls against the other as anchor) is an 'inversion of direction'
>>maintains same power axis, so same cosine/sine factors.
A cross-axis change of pull is more of 'inversion of cos/sin' mechanix
>>thus takes opposite locking strategy
>>as the loading profile changes 90degrees, then so does the lock strategy in anti-Bowline.
This is a lesson of Square Knot, is incorrect as Bend, as can't use the primary force to lock the bend
>>Direction of pull changed 90degrees gives the lock tho against a host.
.
As far as multi/dual leg structures, a Lehman Lesson of 165% has always seemed more true than a reputed 200%.
Multi-leg work different than mono-leg supports tho, the mono has only 1 way to go as most rigid path against.
>>multi-leg gets to choose sometimes most rigid stiffness on 1 leg as other leg maybe slipping, stretching etc. as less rigid.
Perhaps fails at a 100% peak + 65% =165% total; but in working range a joining knot after some load shifting/dynamics can be much easier untie as the shocking went against the most rigidity of the solid leg; more just shared static strain on seam.  'Seam' can sometimes be buffered from main load bearing, presenting more 2 solid legs to brunt of loading.

[agent_smith]

With regard to furthering this topic thread (or just letting it die a slow death):
There aren't many eye knots that can sustain a biaxial through loading (SPart-through-to SPart) and maintain stability and security.
A alternative contender to the Butterfly is the 'directional F8' (#1058).
Although this knot can only maintain stability if the eye is loaded is one particular direction.

#1009 simple overhand eye knot (derived from #1412 Ring bend) can be biaxially through loaded, but it is only stable at relatively low loads. It become unstable and capsizes at a certain load threshold (mimicking offset overhand bend - #1410). It also jams.

I think #1053 Butterfly is unique amongst through loadable mid-line eye knots - with few vulnerabilities.
The derived Butterfly bend and its 4 corresponding eye knots (within a chiral domain) are all interesting.
The Richard Mumford test (near the end of his video) demonstrates an unusual loading profile of the eye - which triggers instability - but is expected and unsurprising.

If the eye is expected to remain stable in transverse and circumferential loading profiles, the 'Mobius' Butterfly variant should be used.