In short, see 3x arc180's continuous radially applied, and the forces produced externally to host of each individually;
from the internal tension imposed throughput.
Then, the force geometry dimensions from 1,2,then 3rd continuous arc180 elements radially applied to make RT component, workhorse in some of the best knots.
The RT form in ABoK, to me is a component seen as part of many knot, capstan, bollard etc. rope works.
The individual arc180s and their powers as elements, then how they are applied in numbers to create component RT that carries SAME ratios of functions to each usage.
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Internal forces of Tension imposed(on otherwise dormant rope, tension empowering as electric does passive wire), relay different forces to the external faces per geometry of rope material tension ported thru.
These external force expressions from the internal force are what can seat to host to capitalize on as frictions, nips and grips. The friction taken on, in turn works to reduce the internal tension input, to lesser output tension. This also, in turn, reduces the rigidity of that output vs input section of the force processing arc(as a machine).
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Working from 100# tension imposed internally into arc180 in full potential/friction free model to acquire 200# at apex as the 2 usable full potential benchmarks(100# and 200#), to then 'simply' apply cos/sine to for the reveals/translation of forces.
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This picture above highlights simpler 1point(at degree mark) of pressure for nip, but these same forces over the full arc180 range/not just one point; powers frictions, and in opposing points:grips. This form is shown many times in ABoK, this is where i think it leads to:
From linear input thru SPart, different points per radial clock position in arc180 outwardly express different forces to drive arc180 element as a machine of conversions and then even further as evolves to RT as a component from the series of same elements (arc180s) to greater dimension machine.
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Mr. Ashley shows very specific on radial position choice in a real fave:
ABoK Lesson# 0465/pg.076: "Sailor's Hitch"/un-named (i think statically to this model, and dynamically in swing should not go past 45degrees as then more side than downward force, so angles to there with nip)
And further, the pattern very visible in fave chaps_20-22 starting with
ABoK Chapter# 20/pg.283: BELAYING AND MAKING FAST Very Distinctly applied at start of next chapter, that opens with 3Half-Hitches illustrating nip force by position, that evolves to Timber, pictured high nip, where i think of the previous tucks/twirls as spacers to this premium nip point range, as does also #1666 fig8 form of HHish, where the cast over before tuck instead of under to tuck gives spacer to better nip position, at cost of frictions against tension to be even more so better. Not a fan of 'dropping a stitch' of 1 less twirl/tuck if fig8 form of Timber, but he makes his point well with the claim.
ABoK Lessons# 1662-1668/pg.290: Start of chapter_21 :HITCHES TO SPAR AND RAIL (RIGHT-ANGLE PULL) very first Half Hitches and Timbers .
These are just my words and logics to what i think ABoK faithfully shows more comprehensively in between the lines.
