Copyright Charles HAMEL aka Nautile
page 1 on 12
2012 Oct
NESTED-BIGHT CYLINDRICAL KNOTS (NBCK) : THREE CONCEPTS THAT NEED TO BE MASTERED
CORDAGE ROUTE CODING PATTERN ( Arrangements of Over / under ) COLOUR PATTERN ( in term of the arbitrary colour given to each STRAND Any knot-tyer who does not fully understand those points will just remain a dabbler in knotting ; may be, if lucky, someone able to, sometime outstandingly , SLAVISHLY COPY and IMITATE, a COPYCAT ONLY. To hope to be someone able to CREATE WITH A FULLY CONSCIOUS PERSONAL INTENT AND PROJECT and not be simply relying on getting help from RANDOM LUCK ( in the best cases : STOCHASTIC LUCK )-fortunately Lady Luck can be generous-- one needs to master some abstract concepts. As experience has taught me again and again that many a knot-tyer rely mainly on “visual capture ” rather than on “abstract reason” I will give visual definitions that even an intelligent and well educated child can “feel at ease with”. All illustrations were done using ARIANE, Claude HOCHET’s superlative program. A number of those illustrations have SCHAAKE’s THE BRAIDER as source of inspiration. Fig 1
CORDAGE ROUTE Just as in sailing or driving one projects the intended ROUTE, the ITINERARY, the lines along which one wants to journey, the basic diagram of a cordage route shows the trail along which, like a snake, the cordage ( one or several STRANDS ) will make its course. Only the directional indications are given, no altitude indication is present, so no indication of OVER or UNDER passages ; we are here in FLATLAND. a FIVE STRANDS cordage route. This one is for a NBCK which is a SYMMETRIC NBCK ( equal number of BIGHT-RIM on each BIGHT-BORDER (TOP and BOTTOM -- by the way this means that we are in VERTICAL CYLINDER frame of reference as the HORIZONTAL MANDREL frame of reference has BIGHT-BORDERS on the LEFT and RIGHT side -- Mandrel is Fig 1 is
Cylinder after a Pi/2 or 90° trigonometric or anti-clockwise rotation )
No need to be particularly bright to immediately “see” that there are many, very many DIFFERENT WAYS OF PUTTING OVER and UNDER on those 360
Copyright Charles HAMEL aka Nautile
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2012 Oct
crossings, in fact at each crossing you are free to put either an OVER or an UNDER so you have 2 power 360 (that is 234.854.258.277.000.000.000.000.000.000 followed by 80 zero) CODING PATTERNS which are “possible” for this one. Most of those CODING PATTERNS will be quite uninteresting, a few will be pleasant. You must take the greatest care in not thinking as identical cordage routes that are, in fact, quite different. Fig-1036-5-3-13-1
Fig-1036-5-3-13-3
Despite having the same number of CROSSING, BIGHT-NEST, BIGHT and distance’ x “ (spacing in Ariane) those two cordage routes are quite different from each other ( a coding pattern that you can apply to one may not be acceptable by the other one. ) The difference is due to a different value for the OFFSET between TOP BIGHTS and BOTTOM BIGHTS One route is 1-STRAND,
the other is 5-STRAND.
Fig-1036-5-3-13-1 is
*not* a PERFECT HERRINGBONE-PINEAPPLE as you can see a mix of 1-PASS, 2-PASS and 3-PASS in its maimed herringbone pattern while the other has a 3-PASS Herringbone pattern all over *but* is *not* a STANDARD HERRINGBONEPINEAPPLE as instead of 3 strands it has 5 strands So CORDAGE ROUTES need to be carefully analysed. The four following coloured illustrations are in correspondence with the greyscale one above and reveal more elements.
Copyright Charles HAMEL aka Nautile
Fig-1036-5-3-13-1 BIS
Fig-1036-5-3-13-1
TER
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2012 Oct
Fig-1036-5-3-13-3
Fig-1036-5-3-13-3 TER
Copyright Charles HAMEL aka Nautile
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2012 Oct
So TO
ONE PARTICULAR CODING PATTERN (MIRROR images are excluded in this discussion ) ONLY ONE CORDAGE ROUTE MAY CORRESPOND [ Despite their “almost perfect likeness” Fig 2 and Fig 3 are quite easy to differentiate one from the other and so have two different cordage route] Fig 2
Fig 3
*
a STANDARD HERRINGBONE-PINEAPPLE 5-PASS 23 L 20 B (4 B ) Meaning that it has 5 Turk’s-Head COMPONENTS ; as it is a TYPE IV they are in TWO SETS ( here both SETS are ‘populated’ , there are cases where one set is ‘empty” of any THK components ) and here OF COURSE ALL components are 4B (there are * 4 B or 4 BIGHT-NEST ) and in the two sets the number of LEAD is ODD and between the two sets those number of LEAD differ by 2 ONE SET FOUR THK 5L 4B SECOND SET ONE THK 3L 4B Fig 2 is
Fig 3 is the 5-PASS STANDARD HERRINGBONE GRANT KNOT associated to the SHPK shown in Fig 2 Note that it is not a “pure” 5-PASS, it is rather a COMPOUND of 1-PASS and 5-PASS as there are FOUR 1-PASS o ( FOUR sequences of “single” OVER crossing )
Copyright Charles HAMEL aka Nautile
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2012 Oct
ON ONE PARTICULAR CORDAGE ROUTE ( Fig 1) ONE MAY APPLY MANY DIFFERENT CODING PATTERNS A very smallish sample is shown in Fig 4 and Fig 5 Those Fig 4 and Fig 5 use the Fig 1 cordage route but with a different CODINGPATTERN as it is quite plain to see. Fig 4
Fig 5
ALL of Fig 7 to Fig 10 use the same cordage ( Fig 6 ) yet show different CODING PATTERNS Fig 6
Fig 7
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Fig 8
Fig 10
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2012 Oct
Fig 9
Copyright Charles HAMEL aka Nautile
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2012 Oct
Let us play with another CORDAGE ROUTE and see what we can do with it in term of CODING ( all are from SCHAAKE ) Fig 1036 cordage route
Fig 1039 Arrangt 1
Fig 1041 Arrangt 2
Fig1043 Arrangt 3
Copyright Charles HAMEL aka Nautile
Fig 1045 Arrangt 4
Fig 1049 Arrangt 6
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2012 Oct
Fig 1047 Arrangt 5
Copyright Charles HAMEL aka Nautile
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2012 Oct
ON ONE PARTICULAR CODING PATTERN ( if more than ONE STRAND of course ) ONE MAY IMPOSE MANY COLOUR PATTERNS First we will see a VERY SIMPLE CODING PATTERN on an IRREGULAR NESTED-BIGHT CYLINDRICAL KNOT : a GRANT knot It is a 2-STRAND so Using ANY 2 colours we can get 4 different COLOUR PATTERN Using 3 colours among 2 strands we can get 8 different COLOUR PATTERN Using 5 colours among 2 strands we can get 32 different COLOUR PATTERN Fig 11
Fig 12
Fig 14
Fig 13
Copyright Charles HAMEL aka Nautile
page 10 on 12
2012 Oct
Lets us see another PAIR OF CORDAGE ROUTE AND CODING PATTERN leading to different COLOUR PATTERNS. Fig 15
Fig 16
Fig 17
If someone is daft enough to think this is THEORY ONLY and so to be junked then in my opinion this someone will be better letting well enough alone any knotting activity as he will for ever be a simple copycat ! This is PRACTICAL KNOWLEDGE which when mastered leads to invention and creation.
Copyright Charles HAMEL aka Nautile
page 11 on 12
2012 Oct
I do hope that along the way every one will have seen the light and engraved in their brain that STRAND and PASS are separate entities. If interested read this web page on CROSSING, FACE, PASS, PLY
The NUMBER OF STRAND DOES NOT GOVERN THE NUMBER OF PASS or one could not have a PERFECT HERRINGBONE-PINEAPPLE which is SINGLE STRAND that is a 5-PASS Fig 18
Nor could you have a 6 COMPONENT SEMI-PERFECT HERRINGBONEPINEAPPLE which with its 6-STRAND is a 3-PASS Fig 19
Fig 20
Copyright Charles HAMEL aka Nautile
2012 Oct
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Nor could we have a 2-STRAND SEMI-PERFECT HERRINGBONE-PINEAPPLE which is a 5-PASS Fig 21
Nor could we have a 2-STRAND COMPOUND HERRINGBONE-PINEAPPLE sporting a mix of 3-PASS 4-PASS 5-PASS Fig 22
