There are
hundreds, perhaps even thousands of possible end-to-end knots ( bends ) : the most easy thing in practical knotting, is to tie a new bend !
Each of them "corresponds" to two eyeknots, and, if we take into account their "reversed" knots, to four.
Most of the bends are symmetric : however, there is no structural advantage to use a symmetric bend as a base of an eyeknot, because, contrary to the end-to-end knots, eyeknots are asymmetrically loaded : the one of their four limbs is loaded with 100% of the total load, the other two with 50% and the last one is unloaded. The only advantage is that it is more easy to inspect a symmetric eyeknot ( "symmetric", regarding the paths of the two parts of the Standing Part, the part
before(ante) the eye, and the part
after(post) the eye ) : generally, it is more easy to distinguish a flaw in a symmetric pattern, than in an asymmetric amorphous shape.
Therefore, the already huge number of all possible eyeknots gets even bigger, because the one link of the base end-to-end knot may belong to one bend, and the other to another ! Chaos !
Is there a way out of this mess ? I believe there is, and that it is dictated by an additional property we should demand from our eyeknots, to be easily "un-knotted". And this "
easily" depends on
two things :
1. The very well known, but not very well understood issue of the PET eyeknots. A PET eyeknot is an eyeknot which can be un-knotted in just one stage - so, the very moment its Standing Part after (post) the eye is untangled / un-knotted, and its eye "opens up" and it is released from the anchor or from the object it encircles ( so, its parent line is not attached to the anchor or to the object any more, and it is free to be dragged away ) there remains no 'relic" knot still tied on the Standing Part before the eye, which should be untied in a second stage ( IF there is enough time to be untied at all, because, after the release of the eye and the detachment of the eyeknot from the anchor/object, the main line may start to slip away, and it may be too difficult to untie a knot while the line on which it is tied is not stationary !
)
2. When the one or both links of the end-to-end knot which is turned into an eyeknot is a "
closed" knot, the eyeknot itself may become too tightly clinched around itself after heavy loading, and its untying may become difficult. By the tem "
closed knot" ( which I admit that it is not as precise as I would had wished...) I denote a knot which is not topologically equivalent to the unknot ( the
overhand knot and the
fig.8 knot are the simpler such "
closed" knots ), and which "work" as a tensile forces accumulator, as a ratchet device, storing any induced tension and "locking" it within its core. This is NOT a theoretical problem ! I have seen it in practice, in many eyeknots I have tied and tried - and what now surprizes me are some rare cases where I can untie easily some eyeknots that use "closed knots" on the Standing Part after the eye ( which is tensioned by the 50%, only, of the total load ), or even, much less often, on the Standing Part before the eye ( which is tensioned by the 100% of the total load ). ( My objection to the so-called "Zeppelin loop" is that, while in the genuine Zeppelin-like knot, the
Zeppelin bend, the overhand knot is not clinching around itself, and so the
Zeppelin bend can be untied most easily, in the "Zeppelin loop" the one overhand knot is loaded by both ends, and so it becomes too tight. In fact, it becomes so tight, that sometimes it does not allow the other overhand knot to close at all, and we get a knot where a large part of it is not utilized, i.e. it remains redundant ! )
That is why I do not like eyeknots with
overhand knots of
fig.8 knots tied on the Standing Part before or after the eye - unless one TESTS them, and persuades me that they will remain easily untiable, even after heavy loading.
One may argue that in climbing/rescue situations, the loading never gets heavy enough - but, personally, I am interested on knots as knots, independently of the particular application which they may serve. In rigging, construction, transportation, mooring, etc., the loads get very heavy very often - and sometimes they become heavier than expected / predicted - while the need for an easy and quick untying is always there...
P.S. I am not saying that the PET-2 condition is
sufficient, to generate an easily un-tiable eyeknot - I am only saying that it seems it is
necessary, in most cases. It may well be the case that PET-2 eyeknots, like the beautiful, symmetric
Tweedledee and
Diamond ( ABoK#787) loops, will become also not easily untiable after heavy loading - because, although in those loops the
topology of the knots tied on the Standing Part before and after the eye are topologically equivalent to the unknot, their
geometry, with all those segments weaved around a central area, seems not "open" enough, and prone to a tight "closing" around itself.
