i think that just as there are stronger Nip positions by radial position of towards load, side or opposite side of host than load
(Ashley's 3 Half Hitches of basic, fig8 and top nip)give the same pattern of changing intensity as intensities of change per 'frapping'/crossing/riding turn by position of application
>>that the riding turn crossing just emphasizes pressures against host at that position, per the radial position from source input directional axis
>>unless changes to the cross axis with a 90degree rope arc
>>otherwise expect arcs central compounding point to express in vertical axis if vertically imposed (like gravity powered load)
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From more pivotal/deeper cosine view:>>i view cosine as the raw axis of load force , the rawest, strongest, most intense axis confined to that single dimension with load
>>where the focused, linear force is most pure
>>sine is the spray to the sides of deflected force, not raw in this model
The intensity of how the remaining/persisting rope tensions at a given point around host are 'expressed'/used against host
>>is most intense on the cosine axis , not the deflected to sine axis
Even tho by my definition, the arc uses all tensions for frictions, just as stone arc uses all load in compression
>>so that uses tension x cosine + tension x sine (thus all) and sine increases as cosine decreases
>>the cosine is rawer, not deflected and so the most intense usage/expression remains on that cosine axis
This gives the 'compounding point' of 2/1 potential in pulley, greatest seating to host and in any crossings
>>greater over lesser more nip expressed by more raw cosine position than reversed sine and cosine values (so would think to same sum)
>>even if closer to SPart as original force source/input imposed
>>with more added frictions but better radial POSITION>>greater effect of crossing lesser force Working End(WE) over greater force already existing turn( closer/less frictions to SPart as source) to further reduce beyond nominal frictions the force persisting thru that point
>>or even WE as lesser force crossing under existing greater force turn as to try to Nip.
i call this radial dominance or radial apex dominance
>>and find simply that the 2/1 factor and position of a pulley is the compound point of the arc
>>and in knot this compound point is greatest increase in nip or crossing position forces.
>>and then by same maths >> the best crossing position for greatest effect/least persisting original force remaining after
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So that the crossing/riding/frapping turn in a Clove, is less intense at the side very close to source input with very little frictions between;>>than the top crossing/frapping/riding turn at the top of a Sailor's Hitch
>>even with more previous frictions between that position and the same source load in Sailor's vs. Clove
>>so less tensions running thru that part of rope in Sailor's crossing top point
>>but more intense nip and crossing changes persists >>even from less tensions after greater collective frictions!
>>as the directionality of the original source load imposed as input counterintuitively persists thru the turns
>>but only if from focused linear input converted to arc control
>>NOT if radial source of force from Binding usage, even in same knot, such as SAME Constrictor (or Bag, Groundline etc.) used as Hitch or Bind
>>because the source force type is different>>the linear is focused and thus directional vs. dispersed w/o direction radial
The focused directional axis persists thru the turns
>>when the source force is linear pull of Hitch or Bend onto SPart>> then converted to controlling arcs
>>but, not in Binding where the source force input to same arcs is radial dispersion w/o focused direction by contrast
Axis and direction are VERY important values in support, especially of linear/non-raidal force
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Sailor's Hitch is a very special model, extreme in this fashion and others.>>it not only has a turn crossing another, but they both also sit on top of the Bitter End!
>>it squares forces to this position with branches of an X to either side as Constrictor and Bag do
>>it is a compound build of a Clove like crossing turn (but rotated to top) and a Backhand Turn like a Cow
>>but the Cow like turn around SPart deforms it very little if loaded from proper end where the Clove type crossing is encountered first
>>when this crossing is at top region, most opposing a gravity load very little force trails out after
>> so not much left later to deform SPart with the Cow type Backhand Turn.
If we rotate the crossing in Sailor's Hitch to side where i show SPart ends, to make more like Clove
>>there is now more pressure left over to press against SPart to lower strength efficiency etc.
Rotate crossing back to top and the knot switches gears, to very little tension left after the crossing
>>premium example of greater crossing pressure, at a position with more frictions/less remaining force
More fascination w/Sailor's Hitch:In lesson#1209 Ashley seems to chuckle:
" The LIGATURE KNOT is commonly called by laymen the SURGEON'S KNOT. But surgeons do not speak of the "SURGEON'S KNOT" any more than a sailor would speak of a "SAILOR'S KNOT."
Then, doesn't name knot in lesson#465(top crossing) and #1693(side crossing) that we call Sailor's..
Lesson #465 notes: "To make fast a swing: The accompanying hitch is recommended, as it stays in place and does not chafe against the crossbar or limb."
i think this doesn't give sawing action on limb, as the force flow is so completely cut off at top region crossing, that just pivots from there more than completes across to sawing motion or rocking/swing
>>The crossing shows at top region slanted to opposing side of SPart, this would make it at top at swing away to SPart side, the most critical leveraged angle of moving force test of the lacing in this usage..
Round is very important in knotting and other rope mechanics
>>Sailor Hitch 'poofs'/serves the crossing up higher with Bitter End as trestle as Ashley also shows in slips w/lesson #1708:
"The loop of the SLIPPED HALF HITCH bulks larger than the single end of 'N 1707; for that reason it is perhaps a better hitch."
>>giving exaggerated roundness at that point
>>so even as is getting super top nip, from 2 ropeParts, braced on sides so can't escape that focus
>>barely any force makes it that far in top region nip
>>as the top nip, especially with exaggerated roundness about clamps shut on the 'garden hose' to turn off the force flow thru.
These parts of ropeMechanics is why i call these lessons and look for the mechanix to cross compare in other things, and to carry to yet other's lacking their attributes
In this way i find a very consistent theme across much of this
>>that in review is not an isolated island of principles particular to rope or this knot
>>but rather a larger engulfing sea of same principle all around an item in larger mechanics shared by everything.
This gives cross verifications and different aspect view of the same gem, to fold back to original topic with deeper understanding
>>and confidence , and urgency to learn, for now see get so much more out of it than before,
>>for same lessons now cover many more things, and have fuller view!