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Page history last edited by PBworks 14 years, 2 months ago

Saturation Index


Saturation is an attempt to subclassify knots by describing how many times the cord changes its position from High (i.e above its crossing cord) to Low (i.e. below its crossing cord) or alternatively, from Low to High.


The Carrick knot for example, is fully saturated in that no crossing cord stays in the same orientaion of High or Low. Every crossing the cord makes it changes orientation from H to L or from L to H. Other knots by contrast are not fully saturated, the cord making a number of crossings of other cords without changing its status of H or L.


If a knot has been classified into an OI group which contains several possible knots, the Saturation value can be used to further break down the alternatives.


To calculate the Saturation of a knot




1. Lay the knot out and count its Crossing Index, this will prepare the knot for counting its saturation.


2. If the knot has one cord, follow the cord around the knot counting the saturation until it exits the knot.


3. If the cord leaves the knot (for a loop for example) or if the knot has more than one cord, count cord seperately and total the counts for the final knot saturation.


4. As a cord enters a knot its first crossing point is counted as the first saturation count.


5. If the knot has an essential component which is of a stiffer material than the cord (or is even rigid), then treat this component as if it were a flexible cord and add its saturation count to the total knot saturation.




Example No1 using the "Bk,Blt" knot.


The "Bk,Blt" knot is the basic knot behind many other well known knots, i.e. the Bowlines, the Sheetbend and the Becket, all of which have a function derived from which of the four legs are loaded in use. The dressed but unloaded knot looks like this :-


To calculate the Saturation, first rationalise and 'lay out' the knot and calculate its Crossings index;


Each crossing point is coloured in the above image and there are seven of them, so the knot is an OI-7


Rule Three states that if a knot has more than one cord then each cord must be assessed and its saturation added to the total for the knot.


Follow the red cord into the knot starting at point A.


As it enters the knot it passes UNDER the white cord - count 1

Next it passes OVER the red cord. It has changed priority from Under to Over so - count 2..

Next it crosses OVER the white cord, the priority has not changed so the count does not increase.

Next it passes UNDER cord D. It has changed priority so - count 3.

Next it passes UNDER cord C. No change in priority so the count does not increase.

Next it passes OVER cord C. Change in priority so - count 4.

It then passes UNDER itself. Change in priority so - count 5.

Finally it passes OVER cord D. Change in priority so - count 6.

The red cord has a saturation of 6. (Note, its saturation would have been exactly the same had you started at point B, so it doesn't matter which end you start from)


Now follow the White cord into the knot from leg C.

As it passes into the knot it goes first OVER, then UNDER, OVER, UNDER twice and finally OVER. That is a saturation count of 5.


The total knot saturation then is 6+5 = 11 which makes the Overs Index for this knot {OI-7:11}


In the picture above the knot is declared as {OI-7:11-0} The final character zero is an arbitrary designation used in the Wiki Knot Index to classify separately all the knots which share the same crossings and saturation values. In the case of the "Bk,Blt" knot family, there are at least 75 knot loading configurations possible, but as the "Bk,Blt" is the 'naked' knot in its unused, unloaded form, it has been allocated the designation of zero.

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