snipâ€¦..

Then I thought I'd try my hand at counting some Crossing Points so that I can help fill out the Overs Index. I tied a Bowline and followed the Standing Part as it entered the knot, and the first Crossing Point is where the "rabbit" goes around the "tree." But I found that when I laid the loose Bowline flat on the table, I ended up with **two** Crossing Points due to the angle at which the Standing Part was entering the knot. In addition, if the Working End is long enough, it can create different numbers of Crossing Points depending on the angle at which it exits the main loop.

So it seems that there will need to be a set of "rules" to help ensure that people are able to calculate the proper number of Crossing Points for a knot. But is this turning out to be so complicated that people are not realistically likely to go through this process?

Dave

In order to start developing the guidelines for the

**'Method for Counting the Overs Index for a Knot'** lets follow Dave's start and put a few examples to the test. In doing so we should soon uncover the rules needed to count the Overs Index.

Lets start with a nice simple knot with no name --

Interestingly, some knots have a name outside of their use, this one however seems to depend totally on its application for a name. The knot has many configurations and many names, but if I don't tell you what each of the four ends are connected to, then you cannot tell me which knot this is - interesting. This 'unassigned' knot has two parts. The white part is a loop or a bight or a Becket, so I will call it Bk for short. The second part (red part) clamps itself against the two white strands a bit like the tang of a belts buckle so I will call it Blt for short. For want of a better name then, this little knot is now a "Bk,Blt". It has two strands and four ends. If we now start to assign function to these ends we start to create working knots from the basic functional knot.

Possible setups for this knot include :-

One cord,

Two cords,

No loops,

One loop,

Two loops.

To assign the possible variations, I will use the following annotation :-

W = working part, i.e. it will be under tension and transferring force to or from the knot.

L = loop, i.e. one of two working parts sharing similar forces in the same direction.

E = free (or tying) end. In operation this end has no forces on it.

To view the tables see

here (I couldn't make tables work in this new forum yet)

The tables show that (at least) seventeen possible configurations exist, unless you consider that any of the free ends could also be loaded, which bumps up the variations to 37, and of course, every one of these knots can be tied in its mirror configuration giving an available mix of at least 74 configurations.

[Of note, easily half of these knots are dangerous. If opposing tension exists on C-D and the tension on A drops, then the C-D loop can pull the A leg through the A-B loop, converting it to an overhand slip knot and allowing the C-D cord to pass through unobstructed.]

Half a dozen of these configurations, which are reasonably safe, have fallen into common use and have attracted names dependant upon that use, except perhaps for the "Manx" (my naming), only one variant of which seems to have been taken up in the form of the Eskimo Bwl.

So â€¦. one knot - the "Bk,Blt" and a number of named uses. The point here is that it is just one knot. The uses may define or influence the working shape of the dressed knot. but they are all still one knot. The OI cannot record or tell us anything about the loading or use of a knot, so I feel the first step in defining the OI Method is to stipulate that the knot is assessed in isolation from any use. That is, you assess the "Bk,Blt" -not the Bowline or the Sheetbend or the "Manx".

STEP 1 :- Make a note of the function of each cord entering/leaving the knot for later refinement of the knot identification, then 'cut off' the extraneous connections leaving the knot in a forceless configuration.

STEP 2 :- Open up and rationalise the knot into a two dimensional plane (special note for cylindrical knots). Relax out meaningless twists and folds until the knot is in its simplest form giving the lowest Crossings count. Attempt to achieve a situation where there is no more than two thicknesses of cord at any one point.

STEP 3 :- Count the Crossings being careful not to include extraneous Crossings where ends leave the knot. For example, if an end leaves the knot from the center and has no further function within the knot, then do not count this end as it crosses over other parts of the knot (physically or mentally shorten the cord to its last point of function within the knot). Consider - any end could be wound back and forth over the knot. Clearly, this cord laying on top of the knot has no function within the knot and the crossings it creates are meaningless, so be careful not to count any of these 'external' or 'extraneous' crossings.

STEP 4 :- Count the Saturation by following the cord into and through the knot and counting every time the cord changes 'priority' from above to below or from below to above. If the knot has multiple cords, count each of these separately and total the counts for the final knot. Start the count as the cord enters the knot, counting as one the very first time it goes over or under another cord.

STEP 5 :- Record the Overs Index for the knot in the format {OI-X:Y-Z} Where X is the Crossings count and Y is the Saturation count. Use the {OI-X:Y} to identify the family of knots in the Index and then use the detailed function of each cord recorded in STEP 1 to identify the exact knot from the Index (The WKI). This will give the final designation for Z and access to specific information on the particular variant being identified.

In this particular example;

There are seven crossings i.e. X=7. The red cord has a saturation of 6 and the white cord a saturation of 5, so Y= 6+5 = 11. This makes the Overs Index {OI-7:11-Z} and because this is the forceless knot "Bk,Blt", I have arbitrarily assigned it position 0 in the table i.e. {OI-7:11-0}

Will those five steps do? or is there a need to clarify or refine them?

Derek