Helical loops

[xarax]

   Although it may well turn out that we will not find any simple, easy and quick way to remember how to tie, and to tie in-the-bight the Helical + Strangle TIB loop(1), I believe that we will find one for the Helical + fig.8 loop, or one of the three Helical + fig.9 loops ( fig.9 comes in three distinct forms (2)(3)), which are also TIB. Actually I have something in my mind, but I have to practice it for a while, to see if it is really easy and quick - we need much more time to evaluate tying methods, than tied forms ...

1. http://igkt.net/sm/index.php?topic=3020.msg22086#msg22086
2. http://igkt.net/sm/index.php?topic=4719.0
3. http://igkt.net/sm/index.php?topic=3020.msg22085#msg22085

[xarax]

   An interesting question about those Helical loops, is if they can be loaded by either end ( be EEL, Either End Loadable ). This question had never crossed my mind, until very recently, when the importance of the EEL condition was pointed out by Moebius. Right from the very post (1), till now, I had always supposed that the helical coil is "tied" ( if we can say that an open helical coil is a "knot", which can be "tied" and "untied", but that is another matter ) on the direct continuation of the Standing End. 
   Now, the difference between this coil tied on the direct continuation of the Standing End ( or being formed at the direct continuation of the Standing End ), and on the direct continuation of the returning eye leg, is that the former is loaded from its one end with 100% of the total load, and from the other with 50% of the total load, while the later is loaded only by its one end, and only with 50% of the total load. However, if the coil is long enough, and has a sufficient number of turns, its area of contact with the knot which it "encircles" can be such that it will not be pulled out, and "open" the eye. The advantage it has is that , if it is "tied"/formed of the returning eye leg, it is loaded, most of the times, only with 50% of the load, so it is easier to it to avoid slippage.
   How long should such a coil must be, or how many turns it must have, to be able to withstand a pull from its one end, while the other end is unloaded, I have no clue. Of course, it will depend on the material, but also on the dressing of the knot, because all Helical loops can be tightened very much, and become rather short, or left almost loose, and remain elongated. So, the rope length of the segment that forms the helical coil is not a constant property of it, but varies, according to the knot s dressing. And, last but not least, it will depend on the load itself...
   One should examine them case by case, load them by the "other" end, and see what happens. He can always add more turns "encircling" the same core, until he finds that they grip the core as much as they should - because most cores can be left long enough, to offer enough surface area for a more "dense" helical coil around them, with more helical turns ( which turns, when they are close the one to the other, become almost indistinguishable from normal, common, "closed" "circular" nipping loops ).

1. http://igkt.net/sm/index.php?topic=3020.msg21688#msg21688

[enhaut]

I had a relook  at the Simple_TIB_loop in order to reevaluate the structure concerning the EEL concept.
Maybe it fits the bill only tourough testing would gives us an answer.
The coil is this particular construction is reliable (stable) because it is "locked" (secured) at both  "ends" ; it cannot slipped.

[xarax]

   How can one be sooo stupid, I wonder...!  !@#$%^&*()_+
   I had tied the Constrictor-based Helical loop three and a half years ago (1), and I had even tried to figure out an easy tying method ( which was a tying method, indeed, but not an easy one !  (2)) - and all that time it had never crossed my mind the very first thing I should had thought about all those Helical loops, the very first moment I saw them : that if you loosen the helical turns enough, you can drag them out of the nub by pushing them "downwards", just like you drag the sock out of your foot - or, which is the same thing, you can drag the nub out of them by pulling the nub "upwards", like you drag your foot out of the sock. Then, when you would have removed them, and they will not "encircle" anything any more ( they will not have any "core" ), you can straighten them out - and so you can turn the helical coil, no matter how many turns it has, into a straight segment ! This transformation does not involve the ends of the knot, it is a transformation in-the-bight.
   Reversing the temporal sequence of those moves, you can start from a simple Helical loop with zero turns, and end with a complex Helical Loop with a helical coil with as many turns as you wish. And here is the crux of the matter : The Helical loop with zero turns, being a much simpler knot, can be tied much more easily and quickly. Therefore we can tie the much simpler zero-turn Helical loops at first, and afterwards we can add to them as many helical turns as we wish /need, in order to tie secure loops for the available materials and the expected loadings.
   This way we can transform the Constrictor noose ( which is a noose as easily tied as the Buntline hitch ) into a Helical loop around a Constrictor core, where the Constrictor tied on the returning eye leg, and around the Standing Part before the eye, can have as many helical turns as we wish.
   Miraculously, and all of a sudden, the Helical loops become much more interesting, because they can be tied easily, and with any number of helical turns, starting from their "degenerated" versions, where their "zero-turns-helical coil" is not but a straight segment running at the side of the core, not a helix "encircling" it.
   In fact, we have to do nothing else than to apply the "haltering/haltered collar" method, and reeve the whole knot through this degenerated "bight" which is formed by the degenerated "helical coil". We have to "see" this straight segment which runs parallel to the core, and which is going to be transformed into the helical coli, as a "straightened bight", and make the opening between this "bight" and the core "swallow" the whole knot.
   Of course, I know that nobody will follow my keystroking exercise  - but believe me, when I will take some pictures, the simplicity of the whole method will be revealed at an instant.
   The important thing is that we have a general, simple method to turn the degenerated, much simpler zero-turn Helical loops into their corresponding more convoluted Helical loops with any number of turns, which we did not know how to tie easily and quickly till now : as the TIB one based on the Strangle and the other TIB based on the asymmetric Pretzel.

1. http://igkt.net/sm/index.php?topic=3020.msg21688#msg21688

[xarax]

   And what is the bowline ( and all the bowline-like loops ) ? Just a Helical loop with a helical coil of one turn, only twisted around its crossing point. So, we can tie and untie the bowline-like eyeknots by loosening / enlarging their nipping loops, and make them swallow, or throw up, the rest of the knot. In other words, we can apply the "haltering/haltered collar" method in the case of the nipping loop, if we "see" it as just another "collar", loosen/enlarge it, and push the knot "upwards" out of it, or pull it "downwards" out of the knot. The "haltering/haltered collar" method is more general than I had thought, because it can be applied to any bight that stems out of the nub, be it a collar, a helical coil or a nipping loop.
   Who knows how many bowline-like knots can be tied or untied more easily this way !   

[xarax]

   I am grateful that I had been offered the rare chance to tie this beauty... Thanks, dear KnotGod. 
  ( The parallel ends do not mean that this loop is EEL. This has to be examined by further trials.)

[xarax]

  I believed that I would never find a simple and easy method to tie it in-the-bight - and I had found how in 3 1/2 seconds ( after 3 1/2 years !    )
  Better late than never... 

[enhaut]

Impressive!
Cant wait to see to photos of the tying method.

And what is the bowline ( and all the bowline-like loops ) ? Just a Helical loop with a helical coil of one turn, only twisted around its crossing point

Totally verifiable and easy to understand.

[xarax]

   I had already described the method, at Reply#19. One has just to read it slowly, to decipher it  - because, evidently, my English are much worse than my knots, that is for sure ! 
   In the "haltering collar" method, the knot tyer should "see" the TIB loop as if the collar does not encircle the ends yet, neither it is inserted into the "nipping tube". ( See the pictures of (1), where this is shown, and explained. ) The tying method of the TIB Girth hitch bowline, and of many other TIB bowlines, the moment we "see" it this way, becomes immediately obvious.
   Now, something like this happens here, too. We have only to "see" the Helical Loop with 0 number of turns - that is, where the helical coil has been degraded into a straight segment, entering-into and exiting-from the very same openings of the nub as the ends of the helical coil did. That is a MUCH simpler loop, which can be tied very easily.
   Then, after we have tied the "simplified" Helical loop with 0 number of turns, we can drag those "turns" out of the nub, we can multiply them by twisting the straight segment, and then place the twisted, now, ex-straight segment ( which became a helical coil ) back in its initial position.
   The simple idea, and the trick derived from it, is that a Helical loop with X number of turns and a Helical Loop with Z number of turns are topologically equivalent, and we may easily turn the one into the other, by simply dragging the coil out of the nub, twisting or untwisting it, and inserting the nub again inside it, as a "core". So, we first tie the loop with 0 turns, then we add more turns, and so we end with a loop with as many number of turns we wish.
   That is also very useful, for yet another reason : We may decide, after we have already tied the loop, that the number of turns is not adequate, because the rope slips more than we had anticipated, the load is heavier, etc. Then, we can easily increase the number of the already existing turns, and add one more, at an instant.

1. http://igkt.net/sm/index.php?topic=4695.msg33927#msg33927

P.S. The simplest similar case I could imagine, is the one shown in my " Three and a half seconds puzzle " :
       http://igkt.net/sm/index.php?topic=5310.

[xarax]

   Pictures of the Helical loop shown in the previous posts, with one helical turn less.
   As one can see, the knot looks much simpler now, and its structure much more transparent. If we try to imagine it with 0 turns ( when the curvilinear direct continuation of the Standing Part will become a straight segment, without any other change : it will enter-into and exit-from exactly the same openings of the rest of the nub, as it did before the further "untwisting" of its helical coil ), it will become VERY simple, and its structure and method of tying will become obvious immediately.
   That is the whole idea I try to explain in the previous posts. The Helical loops should first be "seen" as having 0 number of helical turns, and then they should be enhanced with as many added turns we want/need. Their TIBness, if it exists when their helical coils have 0  turns, will remain, when those coils will aquire no matter how many turns more.

[xarax]

   Going back to 2012 and the thread about mid-span bends (1), we can simply apply, to the very first genuine Helical loop presented there, the topological trick described at (2) : " Retuck the Tail end through the collar - you may end up with a TIB bowline ". This first "Constrictor"-based Helical loop was not TIB, but if we re-tuck its Tail thorough its collar, it becomes TIB. This means that we have to add a half-turn = 180 degrees more to the helical coil of the Standing Part, which will now enter into the opening of the "lower" or the "higher" collar by its other side.
   Since the ends of the structure of the inner core ( which I had called "Constrictor" back then ) leave its nub towards directions almost parallel to the axis of the loop, I now prefer to call it by a less knotechnical name : 8 !  It looks like an "8", so let us simply call it an 8...
   As I had noticed elsewhere, any "Helical loop" which happens to be TIB, will remain TIB if we add or subtract more turns to its helical coil, or if we replace the left-handed helical segment with a left-handed helical segment, or vice versa ( just as it happens with the TIB bowlines and their number and/or handedness of their nipping loops/turns ). Therefore, there are two versions of this loop - I had not been able yet to decide which is better and which I like more, but, most probably, their differences regarding slippage, strength and easiness to be tie and untied would be very small. ( See the attached picture ).
   I think that this Helical 8 TIB loop is much simpler than the Strangle-based one, without being inferior / less secure, and, since it is based on an "open", 8-shaped knot, it is PET -2 - which may be considered as a bonus regarding its versatility. As we add mote turns, its advantage regarding the adjustability of the size of the eye disappears, but still it can transported "up" and "down" its Standing Part more easily than a secure bowline. The really important and very interesting question, is if it will be stronger than such a bowline, because the path of its Standing Part, as it enters into the nub, is smoother, without any sharp turns - but this can be answered only by systematic tests/experiments.
     
1. http://igkt.net/sm/index.php?topic=3020.msg21688#msg21688
2.  http://igkt.net/sm/index.php?topic=4695.15

[xarax]

   The same Helical loop(s), with fewer turns.
   The knot shown in the last two pictures is very simple, yet it is surprisingly stable and secure. Such a simple knot should had been tied on purpose or by accident many times, but I do not remember to have seen it published anywhere. Myself, I had tied it for the first time only recently :
http://igkt.net/sm/index.php?topic=4965.msg33814#msg33814
 

[xarax]

   Another view of the nub of the simple Helical loop shown in the third and fourth pictures at the previous post.
   I do not know which pair of ends should better be used as ends and which as eyelegs - because there is some ( slight ) difference between the two options (the nub is not symmetric ), but I have not decided yet if it is important or not. See the third attached picture for the one of the two possible options.

[xarax]

   The one Helical 8 loop, with a one-and-a-half-turn helical coil.
   I am not saying that such a few-turns helical coil will be sufficient in all applications - it may be, it may be not. I just can not tell, because I have not loaded it very heavily. I show those pictures just to show a typical representative of this class of knots, which, due to the symmetry of the 8-shaped core, it is very easily inspected and it is also quite nice. I prefer it from the its corresponding same-number-of-turns / opposite-handedness Helical 8 loop, for example.