Author Topic: TRANSPOSITION (exploring the concept)  (Read 772 times)

agent_smith

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Re: TRANSPOSITION (exploring the concept)
« Reply #15 on: October 30, 2024, 08:53:58 AM »
The 'Mobius Butterfly' is a wonderful example of the result of
a transposition.

'Mobius' presented this structure to the IGKT forum on May 12, 2015.
At that time, the concept of 'transposition' was not well understood,
and neither was the 'correspondence' between bends and eye knots.
Link: https://forum.igkt.net/index.php?topic=5315.0
Alas, 'Mobius' has disappeared from the IGKT forum...

Mobius did not present a parent Butterfly bend and then derive the
corresponding eye knots from the 4 principal linkages.
The 'Mobius Butterfly' is one of the 4 principal linkages.
Phil D Smith was possibly the first to publish the 'Butterfly bend' in 1953.
This is where I think Harry Asher missed an opportunity to explore and illustrate
the corresponding eye knots derived from a Butterfly bend - had he done so, he
would have discovered the 'Mobius Butterfly'.

The Mobius Butterfly is remarkable because it can sustain multiple loading
profiles:
[ ] transverse loading
[ ] circumferential (hoop stress) loading

It is jam resistant.
And, it is Tiable Without Access To an End ('TWATE').

Dressing:
In order for Mobius Butterfly to achieve its remarkable capabilities, it
must be carefully set and dressed into a very tight and compact form.
Once this is achieved, it remains stable and secure.

NOTE:
In my opinion, the Mobius Butterfly is a better alternative to
the 'Wrap 3 - Pull 2' knot for SAR teams (vertical rescue).
It can be quickly and easily tied around a sturdy tree, using low stretch
(EN1891) rope.
It provides a multi-directional self-aligning anchorage.

EDIT NOTE:
Image added showing corresponding eye knots.
This image is off-topic, but aids in clarity and understanding.
« Last Edit: October 31, 2024, 01:23:07 AM by agent_smith »

Dan_Lehman

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Re: TRANSPOSITION (exploring the concept)
« Reply #16 on: October 30, 2024, 06:34:25 PM »
The 'Mobius Butterfly' is a wonderful exam
Quote
It is jam resistant.
And, it is Tiable Without Access To an End ('TWATE').
Really ?!  --it looks to be quite jammable.
"TWATE" = "NSE"-> "Noue' Sans Extremites"
(I think we can omit the "access to" bit,
 something that came to rid me of "utilizing",
 as that allowed in a way a need for "access".)

Quote
NOTE:
In my opinion, the Mobius Butterfly is a better alternative to
the 'Wrap 3 - Pull 2' knot for SAR teams (vertical rescue).
It can be quickly and easily tied around a sturdy tree, using low stretch
(EN1891) rope.
But W3P2 is about security-on-the-object --that one
unpulled wrap giving the securing binding.

Quote
EDIT NOTE:
Image added showing corresponding eye knots.
This image is off-topic, but aids in clarity and understanding.
Not so.  You have at the top the "same" knot (not quite,
given asymmetry of Lineman's Loop), one each for the
two S.Parts.  Well, you would need that at the bottom
for Mobious, no?  And then you also have but one of
the implied pair for your 3rd case --need the one for
the other S.Part to complete this set.

As for you criterion of "same geometry",
I don't see that at all for the Mobious :: what are clearly
--and to-untie helpfully-- "proper collars" of the parent
are lost in Mobius --drawn to collapsed snugness.
(Likely --varying per material & load-- in the knots
with one S.Part of parent vs. the united Tails, the
collar around the unloaded parent-S.Part will be
collapsed to the core, also.  This is one of the problems
with analyzing/testing mid-line EKs :: establishing what
forces have acted upon them when the loading moves
from one way to another and back ... !  <sigh>


--dl*
====
« Last Edit: October 30, 2024, 06:46:24 PM by Dan_Lehman »

agent_smith

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Re: TRANSPOSITION (exploring the concept)
« Reply #17 on: October 31, 2024, 12:06:19 AM »
Quote from agent smith:
It is jam resistant.
And, it is Tiable Without Access To an End ('TWATE').

Reply from Dan Lehman:
Quote
Really ?!  --it looks to be quite jammable.
Curious: Have you actually load tested the Mobius Butterfly?
Or are you speculating?
Which is it?

Reply from Dan Lehman:
Quote
(I think we can omit the "access to" bit,
 something that came to rid me of "utilizing",
 as that allowed in a way a need for "access".)
'TWATE' is my invention.
I prefer it in lieu of 'TIB'.
"Without access" doesn't mean without permission (if that's your supposed interpretation?).
Tiable without access to an end nicely captures the concept.
My issue with "tiable in the bight" is that it implies a bight is required or that a bight must first be formed.

With regard to the "Wrap 3-Pull 2" knot used by SAR teams:
Reply from Dan Lehman:
Quote
But W3P2 is about security-on-the-object --that one
unpulled wrap giving the securing binding.
The wrap 3-pull 2 knot provides 3 key benefits:
1. Multi-directional anchor; and
2. Resistance to jamming; and
3. Built from lightweight/compact readily available material (ie webbing).

I propose the Mobius Butterfly as a very capable alternative.
And one that is constructed from robust EN1891 low stretch rope.
That is, instead of webbing, a length of 11mm low stretch rope is used.
It can be rapidly deployed and tied around a sturdy tree.
It is easy and quick to tie (and I would argue faster than the wrap 3-pull 2).
The Mobius Butterfly is resistant to jamming (try it yourself).

...

With regard to adding the second image to aid in clarity and understanding for the casual lay reader:
The second image showed how 4 corresponding eye knots could be derived from a Butterfly bend.
It is providing context.
Reply from Dan Lehman:
Quote
Not so.  You have at the top the "same" knot (not quite,
given asymmetry of Lineman's Loop), one each for the
two S.Parts.  Well, you would need that at the bottom
for Mobious, no?  And then you also have but one of
the implied pair for your 3rd case --need the one for
the other S.Part to complete this set.
You are not making any sense (sorry).
The image showing the parent Butterfly bend and its 4 principal
linkages is correct.
All 'bends' have 4 possible linkages that can be made between the S.Parts
and the tail ends.
To provide some context, I showed how the Mobius Butterfly can also be derived
from the 'Butterfly bend'.
In the top (upper) image, I showed a transposition.
That is, it can also be derived by way of a transposition from the regular
#1053 Butterfly.
The sequence in which I show each of the 4 corresponding eye knots is arbitrary.
There is no required sequence/order in which I must show the eye knots.
I did not also show the further 4 eye knots that can be derived by way of transposition.
The regular #1053 Butterfly is 'EEL' (either end loadable).
The Mobius Butterfly is also 'EEL'.
And so showing the transposed knots in these cases seems to be redundant.

Quote from Dan Lehman:
Quote
As for you criterion of "same geometry",
I don't see that at all for the Mobius :: what are clearly
--and to-untie helpfully-- "proper collars" of the parent
are lost in Mobius --drawn to collapsed snugness.
The collars of a Mobius Butterfly are not 'lost'.
They are present - but simply folded inwards.
The topology is the same - its simply a compact, and very tight dressing.
I would go a little further here... the folding inwards of the 2 collars is
a natural tendency - and once achieved, stays that way.
It retains its compact dressing as a natural (unforced) state.
Of course, in very stiff rope/cordage, it may not perform as well.
My experience is that the Mobius Butterfly is effective in more supple,
soft/flexible cordage.
Some Bluewater low stretch rope has a tendency to stiffen over time.
I have some old Bluewater II rope that is virtually like steel wire rope!
Tying a Mobius Butterfly in very stiff rope would likely be difficult (I haven't tried).

Further commentary from Dan Lehman:
Quote
This is one of the problems
with analyzing/testing mid-line EKs :: establishing what
forces have acted upon them when the loading moves
from one way to another and back ... !  <sigh>
This is an opportunity to declare what your actual in-the-field
experience is with using a Mobius Butterfly.
Have you actually used and applied it?
I have - many times.
I think SAR teams will start to adopt it once they learn more
about it.
It is also quite effective for improvising a dual leg lanyard into a harness.
Rope access operators will find it very useful - not only do they have the dual
connectors, they also have a secondary 'belay loop'.
The 'belay loop' (or eye of the Mobius) - is capable of sustaining
transverse and circumferential loading profiles.

EDIT NOTE:
LOAD TEST OF MOBIUS BUTTERFLY


I just tested the Mobius butterfly to 6.0kN force.
TEST 1: EN892 Beal Opera 8.5mm dynamic rope
TEST 2: EN1891 Edelrid 11mm low stretch rope
Result: No jamming - easily untied.
No jamming in either rope.

FURTHER TEST to 8.0kN
TEST 3: EN892 Beal Opera 8.5mm dynamic rope 8.0kN (approx 800kg)
Result: No jamming, super easy to untie.

Commentary:
As a general rule, SAR teams do not reach
a force of 6.0kN (approx 600kg) on their anchors.
Typical loads might be in the range 2-4 kN.

In relation to my third test to 8.0kN - I know for a fact that no SAR team
will ever reach an operational load of 8.0kN.
I am therefore confident to declare that the Mobius Butterfly will
meet and satisfy all SAR needs for multi-directional anchors.
« Last Edit: October 31, 2024, 01:16:55 PM by agent_smith »

Dan_Lehman

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Re: TRANSPOSITION (exploring the concept)
« Reply #18 on: October 31, 2024, 01:56:48 PM »
Reply from Dan Lehman:
Quote
Really ?!  --it looks to be quite jammable.
Curious: Have you actually load tested the Mobius Butterfly?
Or are you speculating?
As stated, "it LOOKS..." --clearly that's sans testing.

Quote
Reply from Dan Lehman:
Quote
(I think we can omit the "access to" bit,
 something that came to rid me of "utilizing",
 as that allowed in a way a need for "access".)
'TWATE' is my invention.
I prefer it in lieu of 'TIB'.
"Without access" doesn't mean without permission (if that's your supposed interpretation?).
My point is that the shorter/simpler "without ends"
& "sans extremites" get the point, not needing to
state "access" (there might be no "ends" !).

Quote
The second image showed how 4 corresponding eye knots could be derived from a Butterfly bend.
It is providing context.
Reply from Dan Lehman:
Quote
Not so.  You have at the top the "same" knot (not quite,
given asymmetry of Lineman's Loop), one each for the
two S.Parts.  Well, you would need that at the bottom
for Mobious, no?  And then you also have but one of
the implied pair for your 3rd case --need the one for
the other S.Part to complete this set.
You are not making any sense (sorry).
Let me work through this better, then (for both
of us!).
Quote
The image showing the parent Butterfly bend and its 4 principal
linkages
is correct.
All 'bends' have 4 possible linkages that can be made between the S.Parts
and the tail ends.
Whoa, which is it --"principal" or "possible" :
the former implies a subset of the latter.
Your 4 images show the 4 possible links :
(top=1) white side+ blue bottom;   --aka W-Tail     +B-S.Part
(2nd)  white top + blue side;          --aka W-S.Part + B-Tail
(3rd)  white side + blue side;         --aka W-Tail     + B-Tail
(4th)  white top + blue bottom;      --aka W-S.Part + B-S.Part

Now, if I understand your "principal",
you want there to be one or the other of the
parent joint's S.Parts qua S.Part in the EK.
This would then include your top 3 images,
noting that arrowed unlinked ends of top two
are S.Parts, and then that the 3rd image shows
implicitly the other two, per loading either the
white or blue vertical ("top" & "bottom") ends.

So, Mobious comes as non-principal.  It is
what I'd refer to as "fore<=>aft'ing the
Butterfly --cutting original eye to S.Part/Tail
and fusing original S/T into the eye.  Which
you see as a "transformation".  One might
also note that the Lineman's Loop can be
capsized ... into itself, Tangle ends swapping
duties/loading!

Now, in my *Tangle* ("interlacing" is the sense
to be had here, not "confused" or "random") system,
the images could be defined/labeled as ::

A 2-Tangle of White rope"1-2" with *ends* "1" & "2"
entangled with Blue rope "A-B" ... .

1) 1 -v- 2+A  (a traditional/common EK & joint pairing)
2) A -v- B+1  ( ditto, but preserving opposite S.Part)
3) <loading not indicated, but either of
   1 -v- 2+B
& A -v- B+2.
And your principals preserve 1 or A source-joint S.Parts.
The remaining possible EKs left to this Tangle are :
2 -v- 1+A, ...+B  and  B -v- A+1, ...+2

Quote
Quote from Dan Lehman:
Quote
As for you criterion of "same geometry",
I don't see that at all for the Mobius :: what are clearly
--and to-untie helpfully-- "proper collars" of the parent
are lost in Mobius --drawn to collapsed snugness.
The collars of a Mobius Butterfly are not 'lost'.
They are present - but simply folded inwards.
 --it's simply a compact, and very tight dressing
Yes, very tight; and in my quick check in some small
super-flexible/soft cord I see jamming writ large
--which, of course, stands in stark contrast to your
well-specified check in intended material.  But I
remain skeptical.

FURTHER TEST to 8.0kN
TEST 3: EN892 Beal Opera 8.5mm dynamic rope 8.0kN (approx 800kg)
Result: No jamming, super easy to untie.

!!

--dl*
====

agent_smith

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Re: TRANSPOSITION (exploring the concept)
« Reply #19 on: October 31, 2024, 04:14:45 PM »
To my audience of one (Dan Lehman):
Its getting tedious with copy and paste quotes.

In relation to jam resistance of the Mobius Butterfly:
It is resistant to jamming.
Having reached 8.0kN in a load test with no jamming,
I'm very confident that the Mobius Butterfly will not jam.
However, I have not gone all the way to MBS yield point.
I would point out that SAR teams will never reach operational
loads of 8.0kN.

In relation to my use of the term 'TWATE' (Tiable Without Access To an End):
In my view, 'TWATE' is accurate and nicely captures the salient features of the tying method.
I dislike your preference for deleting the words "access to".
'Access' is an important concept.
"Without access to" is very specific and self-explanatory.

...

The rest of your reply has more to do with 'The relationship between bends and eye knots'.
EDIT NOTE
I have replied in the more appropriate topic thread "Correspondence between bends and eye knots".
...

A further remark from Dan Lehman in relation to Mobius Butterfly jamming:
Quote
Yes, very tight; and in my quick check in some small
super-flexible/soft cord I see jamming writ large
--which, of course, stands in stark contrast to your
well-specified check in intended material.  But I
remain skeptical.
Again, I have taken the Mobius Butterfly up to 8.0kN force.
Result: No jamming, and super easy to untie.
This was with EN892 dynamic rope (Beal Opera 8.5mm).
If you think about it, both the Butterfly bend and the regular
#1053 Butterfly eye knot are well suited to through loading.
In fact, when through-loaded, they are resistant to jamming.
I think you already know this!
And so, why would the 'Mobius Butterfly' be any different?
« Last Edit: November 01, 2024, 12:39:24 AM by agent_smith »

Dan_Lehman

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Re: TRANSPOSITION (exploring the concept)
« Reply #20 on: November 01, 2024, 02:10:29 AM »
EDIT NOTE
A further remark from Dan Lehman in relation to Mobius Butterfly jamming:
Quote
Yes, very tight; and in my quick check in some small
super-flexible/soft cord I see jamming writ large
--which, of course, stands in stark contrast to your
well-specified check in intended material.  But I
remain skeptical.
Again, I have taken the Mobius Butterfly up to 8.0kN force.
Result: No jamming, and super easy to untie.
This was with EN892 dynamic rope (Beal Opera 8.5mm).
If you think about it, both the Butterfly bend and the regular
#1053 Butterfly eye knot are well suited to through loading.

In fact, when through-loaded, they are resistant to jamming.
I think you already know this!
And so, why would the 'Mobius Butterfly' be any different?
Wait, in what loading were your test results given for?
--through?!  I thought it was of both or one of the  S.Parts
vs. the eye around a host?!

(The lineman's loop has been faulted for jamming when
loaded qua EK, the unloaded end's collar being able to
then collapse and bind it.)


--dl*
====

agent_smith

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Re: TRANSPOSITION (exploring the concept)
« Reply #21 on: November 01, 2024, 06:22:50 AM »
From Dan Lehman in relation to load testing of Mobius Butterfly:
Quote
Wait, in what loading were your test results given for?
--through?!  I thought it was of both or one of the  S.Parts
vs. the eye around a host?!
Refer to attached image below.
[ ] Transverse loading up to 8.0kN = No jamming
[ ] Axial loading up to 4.0kN = No jamming

NOTES:
The 'axial' loading profile replicates the use of a Mobius Butterfly
being used as a dual leg lanyard.
User groups being rope access workers and recreational climbers.
In this configuration, the Mobius Butterfly will never see loads
beyond 4.0kN.

In transverse loading, this replicates how SAR teams would use the knot.
eg Tied around a sturdy tree.
SAR teams will never reach operational loads beyond 8.0kN.
In fact, typical loads are between 2-4 kN.
8kN would be extremely remote.

Quote
(The lineman's loop has been faulted for jamming when
loaded qua EK, the unloaded end's collar being able to
then collapse and bind it.)
Correct, when eye loaded, a regular #1053 Butterfly will jam.
The jamming threshold when eye loaded is around 3-4kN (EN892 dynamic rope).
Indoor climbing gym operators often use a Butterfly in their
dual clip-in systems - where the Butterfly sustains all of the load.
After a period of sustained use by climbers, staff often have trouble untying
the Butterfly knots to cycle their belay ropes.

 

anything