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Copyright Charles HAMEL aka Nautile 2012 Nov

Version 1.1 correction made page 6

OFFSET, SCHAAKE’s DELTA and FIRST-RETURN cordage route REGULAR NESTED BIGHT CYLINDRICAL KNOTS ( RNBCK) It is counselled to have read and understood the 09/23/2012 10/15/2012 10/19/2012 10/20/2012 topics in this web page

IF BEFORE TRYING TO COMPOSE YOUR KNOT YOU ARE UNABLE TO DECIDE ON THE VALUE OF

A, ∆ ,

B* , x (or spacing) then you still are just an ignorant dabbling with

the knot and hoping that luck, happenstance and a good karma will give you something workable about which anyway you will not have had the first inkling of understanding.

A REGULAR NESTED BIGHT CYLINDRICAL KNOT has circular edges along which are situated the BIGHT-NEST which contains BIGHT disposed “Russian dolls fashion’’, each BIGHT-NEST is made of an identical number of BIGHTS stacked like drinking glasses one inside another. See this image. The (total) Number of BIGHT in a NEST is denoted by

*

A

B * It follows that the total number of BIGHTS is B = A time B The Number of BIGHT-NEST is denoted by

The Number of LEAD of a RNBCK equals to distance ‘x’ (or spacing) + 2 (A-1) == distance ‘x’ + 2A - 2 Distance ‘x’ (spacing ) = c

l

|2( i +

ri ) + ∆ | A = δ

A + | 2 ( li + ri ) + ∆ | A where

where ‘c’ is some integer.

δ is one of the integers 1, 2, 3, 4…(A-2), (A-1), A

A very important concept about RNBCK is the : FIRST-RETURN CORDAGE ROUTE Please for those ill at ease with what RNBCK are they can, for details, go to http://charles.hamel.free.fr/knots-and-cordages/turksheads_15.html http://charles.hamel.free.fr/knots-and-cordages/turksheads_16.html A FIRST-RETURN cordage route is a series of consecutive PERIODS (two immediately successive Half-Periods) *** which, If in horizontal mandrel frame of reference, begins on BIGHT-RIM N° K of the LEFT KNOT BORDER (KNOT EDGE) and ends at the first return on the same BIGHT-RIM N° K *** which, If in vertical cylinder frame of reference, begins on BIGHT-RIM N° K of the BOTTOM KNOT BORDER ( KNOT EDGE ) and ends at the first return on the same BIGHT-RIM N°

K

page 2 on18

Copyright Charles HAMEL aka Nautile 2012 Nov

Version 1.1 correction made page 6 The CLASS of RNBCK can be divided into SIX SUB-CLASSES. In general in each of these sub-classes we have mirror-images pairs indicated by Type 1 (Arabic numeral) and Type 2 ( PLEASE NOT TO BE CONFOUNDED with Type I (Roman numeral) Type III…Type IV…Type V of SHPCK

Type 1 Type 2

∆ = ∆1 ∆ = ∆2

where

=A

1