Ampersand TIB bowline

[xarax]

  The "by definition" was referring to the "inside" - a point "inside" the knot s nub, is a point which can be reached only ( if the flow of the force has already gone ) through the "outside" - so, only if some load, however small, has already been uploaded, at the segments occupying this "outside", "at the segments at the outer shells of the nub", as I wrote. In short, I do not believe that the point of the maximum load can be located deep inside the nub, at its core - most probably, it will be located at its outer shell, right after the entry of the straight continuation of the Stranding End into the nub, where the tensile forces are still at their peak, at the 100%. However, the line seldom breaks there - why ?
   I think that the breaking point is determined ( if we can use this word, for such a mess...) by a combination of many factors - where the maximum load is, where the minimum curvature is, where the maximum temperature, generated by friction, flows, which part is compressed, which is elongated, and who knows by what else, but it does not coincide with any of them.   
   

[xarax]

once a crack/tear/whatever starts, I believe that is the end of the maximum force attained.

   Nooo ! You confuse the cause and the effect ! The cause is the existence of the nano-crack at this particular point, and nowhere else, the impurity in the composition of the material which makes its "local" MBS lower, etc. The force which will  break the rope at this point, can well be less than the maximum load. The chain breaks at its weakest link - BECAUSE this link is weak ! The maximum force may well be attained elsewhere, where it may be confronted by a stronger link...     

  For the purpose of this thread and many others, some simple pull and drop tests should suffice.

  I am not sure about what "the purpose of a thread" really is !    Perhaps the purpose of a thread is the purpose of the thread : just to be long, continuous, and connect many things together - but never end ! 

[xarax]

   The most important segment of the ampersand-shaped collar structure, is the last segment of the Tail End, which is squeezed in between, and it is nipped by, four segments of the nipping structure, from four sides :
   1 : From the "lower" side, it is nipped by the arced continuation of the Standing End into the nipping loop ( near the nipping loop s crossing point) which is also part of the first curve of the Standing Part.
   2:  From the "upper" side, it is nipped by the arced continuation of eye leg of the Standing Part into the nipping loop ( near the nipping loop s crossing point ) which is also part of the first curve of the eye leg. 
   3:  From the "rear-right" side, it is nipped by the first leg of the collar - which, in its turn, is pushed towards it by the first curve of the eye leg of the Standing Part.
   4:  From the "front-left" side, it is nipped by the second leg of the collar - which, in its turn, is pushed towards it by the first curve of the Standing part.

   Moreover, at all those four points, the last segment of the Tail End meets the segments of the nipping structure at an angle very near the right angle ( which right angle, is the right angle, indeed, two segments which are squeezed onto each other should better meet, in order to be able to bite hard and deep into the flesh of the material, and block the mutual sliding / slippage more efficiently ).
   Until this last segment, where the blockage of the sliding/slipping takes place, the Tail follows this easy ampersand-shaped path, so I guess that, in a tight nub, the whole collar structure will be tensioned - so, when the knot will have closed around itself, there will be no parts that will run the danger to remain rather slack, and do not participate in the working of the knot as much as the rest.
   All this sounds nothing else - and it may well be nothing else - but boring blah-blah, of course ! All the interested reader is kindly requested to do, is to take the cord which happens to be closer to him, form a nipping loop, attach within it an ampersand-shaped double collar, draw the eyeknot taught, and see, by his own eyes of his own mind, what happens !   
   

[xarax]

   0.
   So, you do want to tie the Ampersand bowline in-the-bight... Evidently, you have to start from a bight !  Place its tip at the right side, so you will tie it using mostly your right hand. ( Left-handed people should do the exact opposite. )
   1. 
   With your right hand, twist this bight three times, 180 degrees each time, clockwise, like you turn a screw : righty-tighty.
   Why "three" times ? Because there are "three" bights in a bowline : the eye, the collar and the nipping loop.
   Have you swallowed this "because" ? I hope not !     Just remember to twist the initial bight three times, 180 degrees each time. I guess that there should be a number of other mnemonic ways to remember the number "three" - I have just utilised one which, although it means absolutely no-thing about why, in this particular tying method, this particular bight of this particular TIB bowline should be twisted three times, it does mean something about the three bights of the bowline, in general...
   2. 
   At the "upper" line leading to the twisted three times bight, and with your left, now, hand, form a right-handed nipping loop, and hold it by squeezing its crossing point in between your thumb and your index finger. Notice that, when they hold the nipping loop by squeezing its two legs at its crossing point, the thumb and the index finger themselves form an eye, too, symmetric to the eye of the nipping loop . Notice also that, if you have formed a right-handed nipping loop, indeed, and not a left-handed one, both its legs would be perpendicular to the corresponding finger they are in contact - not parallel to it. If you would find out that your fingers are parallel to the legs of the nipping loop they are in contact, you would have formed the nipping loop wrongly : straighten it out, and then form it again, with the correct handedness. ( I like this haptic way of self-assuring that a nipping loop is right-handed, by just touching it - so one may use this way even if he ties the bowline in the dark ).
   3a.
( This 3a is step used only to paint an easy to remember mental  image, and to describe its various parts. It can be bypassed after some time and practice ).
   Push the tip of the twisted bight somewhat to the left, towards its twisted legs, in order to form two smaller sub-bights : the "upper" one, which will become the collar of the bowline, and the "lower" one, which will become the eye of the bowline. So, now we have the three bights of the bowline we were talking about when we were trying to memorize the number "three" ( we have to twist the initial bight "three" times, 180 degrees each time, clockwise - remember ?  ). In fact, we don t even need to separate the initial twisted bight into two smaller ones : we can just grab the "upper" half part of the initial twisted bowline, move it to the left, and reeve it through the nipping loop, following a "first under / then over" path, leaving the remaining half part outside the nipping loop, at the right. After we will complete this stage, we will need two, only, moves, to tie the Ampersand bowline.
   3b.
   Reeve the "upper" bight ( the one which is going to become the collar of the bowline ) through the nipping loop, from "right" and "below", to "left" and "above" of the nipping loop. So, now the "upper" bight has been moved, and it is located in the left side, and the "lower" and "right" bight has remained where it was, in the right side. We can now see the nipping loop, and the collar which goes through it - but, how on earth will this collar manage to encircle the Stranding and the Tail End, which do not penetrate it at this stage?
   4. 
   Piece of cake ! By pure knotting magic : Just reeve the whole knotted part of the line you have already formed through the "upper"/left" bight of the collar, so that the two free lines, the Standing and the Tail Ends, will become encircled by it ! In fact, after some time, you will find out that it is much easier to do the same thing the other way - that is, it is much easier to move only the bight of the collar, first "over", then to the right, and then around the rest of the knot, and engulf / encircle it. So, doing this, you will have to move only the "mouth", the bight of the collar, and not what will be "swallowed" by it, the rest of the knot. When this "mouth" will be all around the bights of the eye and of the nipping loop, just push it to the left, to the side of its final destination.
   5.
   After you push the "upper"/left" bight ( which will become the collar of the bowline ) to the left, now pull the "lower"/"right" bight, ( which will become the eye of the bowline) to the right, all the way - until the bight of the collar, which is communicating with the bight of the eye, shrinks as much as possible. Congratulations ! You have just finished the tying of the Ampersand bowline, in-the-bight. And you may even have memorized the number "three" !

[xarax]

  I do not know if I should had expected this - but I did not !    Without any access to the tip of the eye ( that is, without tucking or un-tucking the bight of the eye ), the Ampersand TIB bowline can be transformed into the Scot s TIB bowline, and vice versa. A nice knotting puzzle for the interested reader ! 

[Dan_Lehman]

  The "by definition" was referring to the "inside" - a point "inside" the knot s nub, is a point which can be reached only ( if the flow of the force has already gone ) through the "outside" - so, only if some load, however small, has already been uploaded, at the segments occupying this "outside", "at the segments at the outer shells of the nub", as I wrote. In short, I do not believe that the point of the maximum load can be located deep inside the nub, at its core - most probably, it will be located at its outer shell, right after the entry of the straight continuation of the Stranding End into the nub, where the tensile forces are still at their peak, at the 100%.
 However, the line seldom breaks there - why ?

How do you know where line typically breaks?
As you have surely read (ABOK/Ashely, e.g.),
that is precisely where the break is said to occur
--or even "slightly outside of the knot"!! (?!)

My take on the "outside" observation is of a double
mitigation, so to speak : (1) that the actual breakage
has been started within the knot, and it only seems
that "the break" occurred outside (I think that this is
partly what you argue, elsewhere); and (2) that the
broken area has been grievously weakened when
inside, and only later broke though it had moved
farther from that point.

My observations suggest that compression at a bend
plays a big role, with the inner / compressed fibres
being what break (first).  In one case of slippery, HMPE,
the break seemed to come well inside, which I credit
to the material being able to deliver high tension
--w/o mitigation /"off-loading" via friction-- much
father along the SPart's path (this seemed to be
past the SPart's U-turn, of all things!).

And I think that (single strand!) spaghetti is not a good
model for normal cordage!  Monofilament might suffer
some of the same problems for representing rope.

--dl*
====

[xarax]

  Perhaps I had not expressed what I was thinking clearly enough. I wrote that :

... the point of the maximum load ... most probably ... will be located ... right after the entry of the straight continuation of the Stranding End into the nub... However, the line seldom breaks there

  , meaning that, as I had read and seen in many pictures of broken knotted lines ( for example, in the pictures of ruptured loops by Alan Lee, presented in this Forum ), the line typically breaks before "the entry of the continuation of the Standing End into the nub", not "right after" it, at the point of maximal curvature, as we would had expected.

the broken area has been grievously weakened when inside, and only later broke though it had moved farther from that point.

  I think that a severe weakening of the line can only happen during the last stages of the tightening, when any slack that could had been consumed by the pulling of the Standing End(s), would had been consumed already, and the knot s nub would have been shrank to near its most compact form. So, during those last stages, there can be no such "further movement" of a point, to the degree it can transport a point which was in the "inside", to the "outside".

My observations suggest that compression at a bend plays a big role, with the inner / compressed fibres being what break (first). 

  You had expressed this theory before, but now you use a more careful language : you do not claim any more that it is compression that is the cause of the breakage, as before, but that "the compressed fibres are the fibres that break (first)" - a different thing. It can, indeed, be the case, that the real cause of the breakage ( which, IMHO, is the tension, combined, perhaps, with torsion, NOT the compression ! ) generates a cascade of effects ( elevated temperature due to friction, vibrations due to the enlargement and propagation of already existing micro-cracks, etc. ), and that those effects, for some unknown ( to me ) reason, are especially efficient when they are applied on the compressed fibres. In short, that the compressed fibres are the weak links, in a temporal, spatial, and material chain of complex phenomena - and, as weak links, they break first. Perhaps the compression plays a smaller or bigger role in which fibres break first, but this does not mean that it is the cause of their breakage, as you were claiming till now.

  In one case of slippery, HMPE, the break seemed to come well inside, which I credit to the material being able to deliver high tension --w/o mitigation /"off-loading" via friction-- much father along the SPart's path (this seemed to be past the SPart's U-turn, of all things!).

  This may be used as an evidence supporting your argument, indeed - but, to my view, it is only an ad hoc effort to somehow fill the GREAT voids of it... This effect can well be explained by a number of other arguments : If friction is low, the amount of temperature that would be sufficient to melt the fibres can only be accumulated further along the Standing Part s path, where it will also be enhanced by some contribution of the temperature generated by friction between other segments of the knot. Also, it may be the case that, in this particular material, sharp bends can tolerated much less than in the case of other synthetic fibres - so the breakage point is closer to the point of maximum curvature, which is located deeper in the nub, not at the "outside". We do not even know if the mechanism of the breakage itself does not depend on the friction coefficient of the rope : perhaps a theory that would be able to explain, and predict with numbers, the breakage of manila ropes, would not ne able to explain the breakage of "ordinary" synthetic ropes - and a theory that would explain the breakage of the very different, very slippery HMPE materials, would also be very different ! Friction is a very complex phenomenon, which is not very well modelled / explained, and this also happens with the effects of temperature on synthetic macromolecules - so we can imagine what happens when we try to deal with both of those problems in one go !
   I will repeat here what has made a great impression on me : the exact path of the line in an overhand stopper, even in the case of ideal knots, with perfectly cyclical cross sections and no friction at all, is NOT known yet ! If the mathematics of the most simple knot is not known, we can imagine what happens with the physics !   

[xarax]

   In this post I will try to illustrate with another example what may appear as a "knotting magic", but, in fact, it is nothing more than the result of the simple reeving of the whole knot through a bight of it.
   At the first attached picture, we see the bight of the eye of a loop, with a slipped overhand knot tied on one ( the "upper" one) of its free ends. The bight which is slipped through the overhand knot in not encircling the pair of the free ends - or, in other words, the pair of free ends does not go through / does not penetrate this slipped bight.
   At the second attached picture, we see the SAME knot, where the slipped bight does encircle the pair of the free ends : it has became a collar around those lines. Now, in contrast to what was happening in the previous stage, shown in the first picture, the pair of free ends does go through this collar, does penetrate it. How did this knotting miracle happen ?
   No miracle whatsoever, unfortunately : if we are not confused by the tangled wording and the image of the tangled lines, we can easily figure out that, in order to pass from the knot shown in the first picture to the knot shown in the second picture, we have to just reeve the whole knot through the slipped bight, which will now become a collar. Doing this, all the lines of the knot will go through the collar, so, if we will move some of them to the right, what will be left at the left  , the pair of free ends, will now be encircled by the collar.
   In the case of the Ampersand bowline, I have described this simple trick with those words :

how on earth will this collar manage to encircle the Stranding and the Tail Ends, which do not penetrate it at this stage?
 
   Piece of cake ! By pure knotting magic : Just reeve the whole knotted part of the line you have already formed through the ... bight of the collar, so that the two free lines ... will become encircled by it ! In fact, after some time, you will find out that it is much easier to do the same thing the other way - that is, it is much easier to move only the bight of the collar, first "over", then to the right, and then around the rest of the knot, and engulf / encircle it. So, doing this, you will have to move only the "mouth", the bight of the collar, and not what will be "swallowed" by it, the rest of the knot. When this "mouth" will be all around the [knot], just push it to the left, to the side of its final destination.

   When we want to transform the geometry of a knot without altering its topology, this simple trick is the easiest and first thing we try. However, I do not know a word / term which can describe it. The interested reader is kindly requested to imagine something.
   The procedure reminds me the sequence of moves which turns a glove inside out - perhaps the term "turn the collar inside out" , for the reverse procedure ( the move from the stage where the collar does encircle the free ends, shown in the second picture, to the stage where it does not, shown in the first picture ), would be able to offer a useful mental image of it. 
    At the third and fourth attached pictures, one can see the same thing in the case of tying the Ampersand bowline in-the-bight. The third picture corresponds to the shape of the knot after stage 3b, and the fourth picture corresponds at the shape of the knot after stage 4, that is, just before the  Ampersand bowline is drawn taught in its final form.
   That is the reason I had chosen to present this particular tying method, and not another one ( starting from a slipped overhand knot ), which is faster. After we form the twisted three times initial bight ( three times, as one should had memorised by now...  ) and the right-handed nipping loop, and after we reeve the upper part of this twisted bight through this nipping loop, from "under" to "over", we reach to the final stage. All we have to do from now on, is to perform this elementary knotting magic, and make this reeved upper part of the twisted bight be encircled by - and so become a collar around - the free ends.
    Imagine we have agreed to use a term for this trick ( if it is possible to agree on anything ! ). I denote this term as : <term?> . Then, to tie the Ampersand bowline in-the-bight, one has to :
 
   1. Twist a bight three times / three 180 degrees turns, clockwise ( righty-tighty ).
   2. Form a right-handed nipping loop on the "upper" one of its two free ends.
   2. Reeve half of this twisted bight through the nipping loop, from "under" to over".
   3. <term?> this reeved half of the twisted bight, to/on/around/ (or whatever proposition describes it better) the rest of the knot.

   

[SS369]

Nice presentation, thank you.

1. Twist a bight three times / three 180 degrees turns, clockwise ( righty-tighty ).
   2. Form a right-handed nipping loop on the "upper" one of its two free ends.
   2. Reeve half of this twisted bight through the nipping loop, from "under" to over".
   3. <term?> this reeved half of the twisted bight, to/on/around/ (or whatever proposition describes it better) the rest of the knot.

Using the two pictures from reply #18 and adding picture #4 (Stage 4) Does the trick.
The key is to take the bight of the half twisted, opening it and bring it over the bottom of it all and place it at the collar location, then dress it.

SS

[xarax]

   I had not presented the picture#4 at Reply#18, on purpose : I thought that I had first to show the turned-inside-out-collar trick in a simpler case, and ask for a proper term for it. This reeving of the whole knot through one bight stemming out of it, although it is conceptually elementary, it looks quite complicated in pictures ! Picture#4 seems too complex, if it is not seen as a mere implementation of the trick after the under/over half-reeving of the twisted bight through the future collar.
   

opening it and bring it over the bottom of it all and place it at the collar location

  I do not believe that this is the term you propose... What about the "turn a collar inside-out", or "turn a collar outside-in" ? Any other idea ?

[SS369]

What about the "turn a collar inside-out", or "turn a collar outside-in" ? Any other idea ?

It could work, but it is not quite a collar yet.  Turn a to-be collar.... nah.

It is an open bight that has to be positioned in the collar location after it has been pass over the rest of the tangle and I don't know of a term for it yet. It is like what we do when we tie a bowline on a bight that results in a double eye.

http://en.wikipedia.org/wiki/Flype

Bightflyping ? Blyping?
 

S

[xarax]

   The term "flype" has already been taken by others, I am afraid...
   
   http://en.wikipedia.org/wiki/Flype

   Also, it would be great if we had a term that could describe both transformations : a future, to-be collar turning into a collar, and a collar turning into an ex-collar - even with an adjective, as "reversed", or a negative sign (-), in front of it.
   

[SS369]

How about - haltering move?

SS

[xarax]

   Like "haltering the white cow", or like "haltering the black cow" ?   

https://www.google.co.uk/search?q=haltering+etymology&hl=en&gl=uk&authuser=0&source=lnms&tbm=isch&sa=X&ei=03xlU4zoF4moO-O1gPAF&ved=0CAcQ_AUoAg&biw=1280&bih=642#authuser=0&gl=uk&hl=en&q=haltering+a+cow&tbm=isch&imgdii=_

[DerekSmith]

My thought is that the inner section of synthetic rope is crushed to a point of high enough temperature to melt, allowing the molecular bonds to release, then the subsequent tensile parts tear.
With natural fibers, it will be the fibers with the greatest tensile strain, the outer ones.

We should not confuse pressure with temperature.

When you do work upon a rope it's temperature may well go up, but heat is mobile.  An increase in temperature will cause a heat gradient and that heat will conduct away.  If we apply a load gradually, any heat generated will conduct out of the rope.  By loading a rope sufficiently slowly, its temperature can be maintained at any chosen value, so heat, i.e. elevated temperature, cannot be the cause of that rope to fail, yet fail it eventually will - but it won't be through temperature melting.

A twist to this argument, is that as you stretch a rope, much of the work done is being stored in the fibres as potential energy.  This energy will be released as heat when the fibres are allowed to contract back to their un-stretched length.  So, as a fibre breaks and snaps back in length, it suddenly sheds it energy as heat, but that heat is released along the length of the contracting fibre.  In this way, heat is released into different parts of the knot than the part where the first fracture occurred.  Fibres stretched around an outer radius may be taken beyond their breaking strain and so fail, and then dump their released heat into a different part of the knot as they shrink back under the released tension.

The second and most often ignored aspect of failure is pressure or compression.  If you take a guillotine or a knife to a cord, it is the point pressure hugely magnified by the tiny area of contact that ruptures the fibres.  All organic fibres are polymers and at some pressure they will flow and deform.  It is not heat but pressure that has this deforming effect.  However, most polymers are very temperature sensitive.  So, if we have a fibre under sever compression, but not enough to cause it to deform, and then suddenly an adjacent fibre releases a load of heat (because it just snapped), then the compressed fibre absorbs some of that heat.  If the consequential temperature rise takes that fibre above its flow point, then it too can rupture, releasing it's stored energy as it shrinks back to unload length.  Again, the released energy will be 'piped' into other parts of the knot.

The failed fibre, not only releases its stored energy into the cord as heat, it also has two other effects.  First, the load it was carrying is now instantly transferred to the remaining fibres.  It might only be a tiny incremental increase, but it is an increase, driving all the other fibres nearer to their failure paints.  The second and potentially far more sinister effect is that because that fibre has lateral frictional contact with the half dozen fibres around it, it transfers its tension selectively into those fibres, along with its released energy as heat.  We now have a tiny bundle of fibres, already under tension, suddenly subjected to an increase in tension and an increase in temperature for some distance away from the break point of the first fibre.  Any weak points in those heated, sections under additional tension are likely to fail and so start a chain reaction of failure, heat release and transfer and further localised load increase.

Hence, we should expect to see, and in fact do see, a scattering of fracture points occurring throughout the knot, as a storm of failure fires throughout it, transferring heat, load and pressure into different parts of the cord and the knot.   We should also expect to see the 'gross' failure of a knot at some point other than the weakest point that actually initiated the avalanch of failure.

Derek