Naming ropeParts as components in a working support structure/architecture

[KC]

Personally i think tho rope is a continuous ribbon, rope under load has separate 'ropeParts' as mechanical functions,
Just as other support against load architectures, of separate connections in other materials.
>> only rope provides own connections between these parts/functions so seamlessly, that fools the eye
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Arcs are the worker bees in this, able to use all tensions for controlling frictions and support as one.
nonArcs/linears are only extensions to/from arcs, with some of tensions, rest used alone and separately for controlling frictions ( that arcs use all tensions for). 
Arc of 360degrees or more can give grip.
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i name most Turns as compondings of 180degrees arcs, Turn as 180degrees, a Round as 360degees so adds together to be a Round Turn 540degrees etc. w/some consistency and definition away from RT as 360degrees view.
180.    name.                          abbrev.         
1x.        Turn.                            T.
2x.         Round.                        Rnd
3x.         Round Turn.               RT
4x.         Double Round.          dbl.Rnd
5x.         Dbl. Round Turn.       dbl.RT
6x.         Triple Round.             3xRnd
7x.          Coil.                            Coil
the Rounds that end opposite direction than input are not seen that much.
Inside knot internals of turns, crossings, bends etc.
i determine where endpoints for each 180degrees arc and nonArcs (linears) are by if are either in direction or counter- direction of the empowering pull ( mostly SPart) to define.
Also midpoint 90degrees of 180degrees arc creates a force of own in same direction as ends.
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The 90degrees/ 'half-arc' is a different matter, as a cross-axis lateral mechanic.

[agent_smith]

Thank you for your post KC - all very interesting.

I am trying to extract some practical understanding from your post...

Have I got this brief synopsis correct:?
1. An 'arc' or curve within the core of a knot is key to understanding its response to load.
2. Linear (straight) segments are merely conduits to transfer force from one place to another.
3. U turn is 180 degrees, a turn is 360 degrees, a round turn is 540 degrees.... with U turns (180 degree changes) being a fundamental component of all arcs/curves?

How does core compression fit into this conceptual framework? (that is, as load is applied to a knot, its core undergoes compression).
From a practical standpoint, we know that some knots resist compression more than others - which relates to why some knots are vulnerable to jamming while others are resistant to jamming.
Rope segments crush/trap adjacent or underlying segments - which inhibit slippage but allow s-t-r-e-t-c-h.
A rope segment that overlays and crushes its neighboring segment within the core affects transmission of force through the rope segments. Distribution of force within the knot core is not uniform or linear - there can be localized stress concentrations and heat build-up.

Note: I am simply trying to understand your post and place it within a practical meaningful framework - I am not denigrating your post or trying to derail it.
I am respectfully trying to extract a simplified meaning!

Edit: Typos/grammar corrected! Got to turn auto-correct/spelling suggestions off...

[KC]

At different times 360degrees has been said as Round Turn, i've always felt 540degrees was correct.
To naming general arcs that are the real magic or working ropes in their simplest forms;
i think the below picture is my best concise take on it.
>>note most top arcs shown as types of 'turns' until coil, while bottom arcs are  consistently 'rounds'
>>Also how a Turn + a Round = a Round Turn in this naming scheme

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i think tho the rope goes round and round; it presents different force patterns directionally thru from a linear input (SPart)
>>thus best nip is always on opposing side of the host from the linear DIRECTION of input load imposed
>>and then under the most intense, raw primary Turn
>>this best nip position only changes inside that primary Turn when a change of direction
Just as with a fanbelt on pulleys, the position of the most harshest, complete seating is on opposite side of the DIRECTION of pull on the host mount/pulley(s).
.

[KC]

3 basic knot parts in simplest Half Hitch(HH) working in arcs non/90/180:
Standing Part(SPart) forms a nonArc (linear) that imposes the load into knot
>>even tho bent is a linear with endpoints pulling opposite (vertical) directions
Feeds into a 180 Arc
>>ends of 180 Arc point in same direction
>>Being the primary Arc, points same direction as SPart pulls
Feeds into a 90 Arc
>>whose endpoints are at right angles/90 degrees to each other
.

SPart input + primary turn are most rigid parts of knot, and form a hook to hold the load
>>rest of knot is keeper and ballast to the 'hook' to keep it working in place carrying load.
SPart functions as loader(of forces), arcs as reducer(of forces) followed by tailer/keepers(ballast against reduced forces)
(tailer as in sailor that keeps tension pull/reeling in after capstan as crew cranks capstan)
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As long as the linear input pull of the SPart is 'South', the best Nip will be at 'North' side of host mount, under the primary Turn.
>>the only way to change that position and where endpoints are (that define arcs etc.)is to change the DIRECTION of the linear input SPart
A radial imposed load (as in Binding) would have NO directionality, as the force is evenly diffused all around.
>>a linear imposed loading will be focused (not diffused) directionally, and this influence carries even into the subsequent arcs
This focused linear input imposed is converted to radial control, so degrades thru the rope to nip(s).
>>radial imposed loading into same arcs is not a conversion, so gives equal tensions all around to nip(s).
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The 90 Arc shears across the sole supporting column of support to the load (SPart)
>>rendering it less efficient support against the load, but is tighter on host in trade.
>>you can even crank this area sequentially tighter, this will render SPart even less efficient as grips host tighter
>>thus same load force can be used to power efficiency or tightness but not both at once in simple HH
If take advice in ABoK lesson #1669: "...Round Turn on the Standing Part adds materially to the strength of the knot."
>>The Round Turn as a contraption pulls more along SPart more like splice or Cat's Paw
>>more than shearing across the SPart support perpendicularly.
This is done under the same loading, the tradeoff is less of the loading used to tighten more on host
>>so RT around SPart is 'stronger' but grips host less in trade vs. Turn around SPart shearing across.


edit.
Dan Lehman has said finds this effect of RT around SPart to be more efficient/stronger as reduced if an RT on host mount pre-fixed the RT on SPart.
>>i think that would be because of the reduced force passed from the pre-fixing RT on host,
>>to receiving RT on SPart, and less able to grab as hard to pull along the support column against load
>>rather than across it.  So cuts more across SPart, more like HH.
So a trade off between RT on host that can spread out rope wear in small host mounts to be more enduring
>>or put RT on SPart instead to increase that durability
When working 500# and greater; in the air, w/stiff impacts on rope, right next to you; tend to tweak strength where can to best possible, quickly for scenario.  With habitual overkill on the bright side, so no overkill on the dark side!  So as days become routine, any natural complacency is mostly covered by the good habits and fought thru puzzle of architecture to control target tweaked to scenario unlike any other challenges to self.

[KC]

i think that principle is where this tidbit just mentioned in passing(as many things in ABoK seem to be as eye is called to race thru flurry of knots) comes from :

.
As then these too examinations:

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The stronger hitches pull along SPart more  like a splice,
>>while the less efficient/weaker pull across the SPart more like Samson across the temple pillars as they supported load.
As consistent with any other support architecture mechanix against load imposed; just this time the material of support is rope, of the flexibles class (only rigid support, when against loading)
.

[KC]

The first ropePart in the flow of force thru knot node of Bend or Hitch is the Standing Part (SPart) .
To me the SPart is a specialized part of Bends and Hitches, thus purposefully named separate.
.
SPart of Bends and Hitches is where load is imposed onto the passive/but responding rope system;
so functions as a force input into the knot internals, linking the outside world to the hidden microcosm.
It feeds directly into the Primary Arc on opposite side of host.
.
Primary Arc  is where the knot node/load hangs from (in a simple gravity pull) against host.
SPart and Primary Arc make what i call a 'hook'
>>This hook is the most rigid part of knot node
>>rope after this point is less rigid, and just works to keep the hook in place against the loading.
The hook is also the point of conversion from focused linear input to dispersing around to radial control
>>so functions as a linear force to radial force converter as first stage of rope control management
>>as it also physically connects the load to the host mount.
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In reading knot books etc. over the years;
a SPart stops before the host or any other rope part.
>>totally, VISUALLY separate from those parts
(am always squinting to look past the visual and see force flow)
In trying to understand these things by function, rather than look;
>>and find a consistent point to point, over-ruling definition
i see SPart functionally ending where the primary arc begins as they both form the hook
>>halfway around the round host
>>and segregates by the Arc Naturally seats firmly to host, the SPart, Naturally pulls away
>>even if SPart is drawn to host>>some part of forces are pulling away, while all of forces in Arc seat to host as 1.
The Arc Naturally can use cosine sine together as one, like an arc bridge does.
>>while linears (SPart etc.) can only use the raw focused cosine part of tension for support
>>and more deflected sine part of tensions for friction control
Arcs can use cosine and sine together/all tensions for support and friction; linears only part of tensions to each support and friction.

SPart Naturally hangs off side if simply rope over branch, hang weight, and anchor other end to ground
>>Discrepancy can come in when release from external anchor and bend SPart against bottom half of round host as to Half Hitch etc.
>>for me the SPart still starts at that halfway point, but is just simply now bent;
>>but no shorter rope length, endpoint is still in the same position of where the host roundness started receding/halfway mark.
>>that endpoint still pulls opposite direction than load>>so this is still a linear ropePart for me, just a bent linear.

But, it is not a 180 arc of end points in same direction, nor a 90 arc of end points in lateral/right angle direction to each other.
>>LINEAR force feed input remains a directional of degrading force even thru the arcs to the Nip
>>RADIAL force feed from round binding is not directional, so doesn't degrade around the rope arcs before the Nip.
In Hitches and Bends the linear directionality of the input thru the portage of the SPart
>>counter intuitively persists thru the radial arcs, to give 1 single best Nip position in a simple build of Single Bearing against opposing side of host from load.
>>but then too,  linear fed arc can give a 2/1 effect at peak apex as Nip function from linear pull, that can't get in round binding, for all points equal in binding..
Arcs control and rule the linear connections. 
>>Round Binding has no linears in usage
>>AND their radial 'glow'/dispersed force fed arcs handle forces differently w/o conversion from focused linear type force fed arcs of Bends and Hitches.
>>Better Nip not a radial position under simple single crossing in Round Binding as is in SPart pulled Hitches and Bends
>> As all ropeParts equal tension before Nip in Round Binding>>compound crossing only point of possible better Nip

[agent_smith]

Thanks for your good work Mr KC (aka Treespyder);

Is your theory as a whole intended to apply only to hitches?
Or does it equally apply to bends (end-to-end joining knots) and standalone knots such as 'eye knots (eg #1047 F8)?

I would like to see your theory explain why Zeppelin bend is jam proof while Riggers bend (Hunters bend) jams.
Or; in the case of #1047 F8, there is one form that resists jamming while another form has a higher vulnerability to jamming (the difference being principally influenced by relative position of SPart).
Note: I do not know the load threshold at which the jam resistant F8 form will begin to jam... I dont know of any testing to probe this?? I mean, both versions of F8 are eventually going to jam... just that one is more resistant than the other. A simplified explantation is a problem looking for a solution!

[KC]

Model of Arc control of linear fed force.
Rope as a running linear line as peak manufactured usage.
Degrades rope column of support against imposed load at any node of deformity (Hitch or Bend) to the pure line run.
>>Hitch as a termination  of force flow via rope line of force, handing off force to host, 1 sided rope force at node of deformation/knot
>>Bend as a continuance of force flow via rope line of force, handing off force to other, 2 sided rope force at node of deformation/knot
Both linear force fed thru SParts to Primary Arcs , Hitch has 1 SPart, 1 most rigid hook,
>>Bend has 2 evenly matched force hooks>>a smaller and/or tighter rope side can present as more rigid than other force udner matching load
>>In Bend each rope simply functions as the other's host mount
>>Bend, as a dbl.sided Hitch that continues rope force line w/only the other rope as host in the hand off of force
Either termination or continuance (to logically cover all) of linear force
>>either terminate as Half Hitch(HH) or flow thru as mid joint HH pre-fixing Timber to produce Killick  in total
>>can same as/show a HH termination or 2 termination HH's back to back w/shared Nip point to same Hitch to Bend simple to compound relationship of termination or pass thru model.
Show Hitch first as the 1 sided, simpler, non-compound model(part of search is a logical flow in teaching, simple to compound lessons etc.)
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Round Binding is radial input force into controlling arcs during USAGE (tho might be preset linearly and feed thru a SPart in that stage)
>>So don't need linear to be a knot but do need arcs>>arcs rule, linear is just a connector,
>>usually define all as types of Arcs: 90 degrees, 180 degrees and nonArc (linear)
>>arc fed by focused directional linear SPart is different than by radial, dispersed glow of no directionality
>>arcs use ALL of tensions for support AND frictions, linears use only part of tensions for each
Linears are subject to, but do not rule; cosine & sine the way an Arc does.
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Rigid is what resists with most firmness, we say flexible class (or at least i do) that rope represents
but in USAGE rope is rigid(along long axis in tension direction) just enough against load, as if load forges the ropes iron in usage but only to the point needed, but don't have to heat to reforge(nor pound, chip, carve nor later bind or drill to connect), just unload; but a structural material none the less.
>>just as a dead weight is an active force
>>and rope etc. passive like electric wire  without force applied>> and then only carries that force no more, a passive responder
>>rope defines a support class of like wise passive rigidity against load, of just enough rigidity to do job, otherwise not rigid, nor pulling.
Hook is most rigid part of Hitch, thus of Bend, and has the point of most compounding/best simple(non-compound) Nip at peak apex of the Arc.
Zeppelin has side by side hooks of matching most rigidity to each side slightly offset, not pure inline, SPart/spine of hooks opposing
>>so makes complete guarded circle of most rigidity
>>rest of rope just binds the 2 hooks together to insure all focused, even those side by side on the Bitter Ends(BE) squarely, just amount as needed
>>False Zeppelin has both SParts same side to leave an open side of the hooks framework>>not pure inline force can tumble out, carrying rope
Thus,trace side force in side by side bound hooks + open side is too much relief and side force finds way out model.
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Rigger's similarly has no open side relief, but is different in that the hooks of most rigid parts are interlinked for more focused compounding pure inline, interconnected linear no miss, dead on 2 mad, matching  bulls w/o side relief either
>>recursively(?)onto the similarly placed (as Zepp)BE's like 2 mad bulls horns locked w/o relief equally matched, nobody given up nothin'
Seems like too much overkill, overly focused on both axes deadlocked matching
>>for can flip 1 hook arrangement and give open side like False Zepp as change and seems light and happy as a Butterfly Bend
>>as just seem let just a tad of steam out from full linear focus >>break out of the recursive cycle prospect model?
>>but have strong, serviceable (can untie and rework) connection, secure, and fair efficiency of force handling/strength for type of utility

Working from benchmark of Rigger's that i find to be simply double dead locked (inline and cross axis)
>>dead on inline compression and from secured sides too>> especially expressed in hard loading to deadlock
BFly corrects benchmark Rigger's with simply tipping scale slightly by not guarding cross axis as well, leaving open side but has interlinked pure alignment anyway
Zeppelin serviceable after hard loading, uses opposite strategy than of some relief on inline axis only, guards hard both escapes on cross axis and good thing because not purely aligned/interlinked
>>dbl.fault in False Zeppelin slight fails on both inline and cross axis compounds to tip scale over>>fail

edit per Dan Lehman (rightful)comment

[Dan_Lehman]

Spydy, note that your "False Zep." isn't that
but a not-quite butterfly; the FZ is like SmitHunter's
(aka Rigger's) but w/o the interlocking/crossing of
the SParts (blue & violet parts) --hence the Z-like appearance.

(-;

[KC]

Thanx, very much, at the time the toughest knots i had drawn,
'bout broke my brain
 re-working now..
The words, intent, principle stand tho i think
DONE
re-adjusted layers to weave properly
Please let me know if that were to ever happen again!
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The Hook concept is my lead approach to dissecting any Hitch/Bend.
>>it is the most rigid part of the knot, iron like compared to the rest of the flexible ribbon of rope
>>it contains the directionality of the raw input force
>>it also contains the most compounded Arc force, as it has the Primary/most loaded Arc
Viewed as a simple rope mechanic of power:
>>SPart is input as to Bitts/bollard
>>Primary Arc opposing gives only nominal friction reduction of peak forces
>>subsequent Arcs compound Primary and any other previous Arc frictions to more substantial
>>tailer is final ballast/control just as in feeding out thru bitts/bollard or slight pull with capstan turning to engage the frictions to Arcs and reel in the purchase of more line thus moving load and/or raising line tension.
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Linear fed Arcs of Bends and Hitches have the same trio of input force, reducing force thru Arcs, final ballast that ensures rigidity and frictions thru system as also secures, kinda like the tailer man in bitts/bollard/capstan controls of rope. 
The hook model is an overlay to that, as to location of most fiercest forces, direction and hand off to host connection.
i find many of my answers by starting with it, as here.
Chasing rigidity in usage to something that is called flexible seems counter-intuitive, but is key; for rigidity against load is the basic output of the passive system.
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Another lesson here is the round hosts give frictions by DEGREES of contact not distance of contact, as bollards etc. do
>>larger round host mount just gives softer arc to rope as spreads out concentration of frictions to more distance of same degrees
>>so less heat build up and if host is heat conductor (metal, electric conduction) not insulator(wood, nylon etc.) better heat sink to drain heat off
(Diamond is ONLY thing ever that is thermal conductor but not electrical conductor, sibling graphene does tho as newest strongest known material )

[agent_smith]

Hello KC,

Your depicted image of #1425 Riggers bend at reply #7 appears to be incorrect.
Can you please re-check the geometry of a 'Riggers bend' and compare to your posted image?

EDIT NOTE: You appear to want to depict a Riggers bend with S/S chirality.
Obviously, #1425A Riggers bend can also exist (and is equally valid) with Z/Z chirality.

Your #1053 derived Butterfly bend should more closely align to the Riggers bend... that is, at least one of the overhand knots should be identical to the adjacent Riggers bend. This would allow readers to see the relationship between these 2 bends. It is possible to derive the Riggers bend from a Butterfly bend (which is how I believe Phil Smith arrived at his Riggers bend).

[KC]

Wow, thanx,
Will check when get home, think posted wrong edit, sorry.  Tough project, over 50  layers mite have to start over as do things much different now.  My most problematic drawing. But, rope concepts still stand i  believe.  Rigidity against is key to support, and Hook is most rigid, connects directly from load to host and has single point of most compounded forces.  Without final stop , would be like w/o capstan tailer.
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edit: i guess what are saying is Rigger's could be flipped, and maybe all the pink/purple ropes could be orientated and laced same to clarify and emphasize the differences(?) between each as traced thru changes of blue?
If is can play with that this week, this is where wish was tying not drawing knots
>>tho many more things etc. can show in drawings
>>and a lot of observations from the depths of the drawing perspective!
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Still, thru these things persists that a linear fed/input/imposed load into the inevitable rope arcs (that control all knots, exist even in round binding where there are only arcs, no linears during usage) maintains an axis of directionality  (up/down on vertical axis or left/right on horizontal etc.) counterintuitively linearily thru the radial controlled arcs.  Otherwise there would not be a best Nip position on opposing side of host, graduated tension reductions, hook concept etc., w/o directionality of the linear rather than radial initially input force imposed on the rope structure.
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This is where i see this witnessed more clearly in use of a Half Hitch(HH) pass thru (more like Bend function between ropeParts) pre-fixer rather than a terminating HH (more like Hitch function).
In the first pic w/90 degree hook, this linearity persists thru the rope that is in a line along host NOT the serial rope path around host.
>>tension force cuts across to the shorter inline path as electric would be so opportunistic does.

The 180arc build shows force following the serial rope path as expected; but that is because it is inline to the force; as proven in 90arc build.
Both have the more rigid hook of Standing Part(SPart) and Primary Arc of  90 or 180 degrees from this linear to arc conversion point/function.  Support is about power of rigidity against, and Hook is most rigid and the main connection as also converts linear input to arc controls.  Also the apex of the arc in Hook has the most single compounded  forcepoint in the knot.  Besides all that, the Hook carries the linear axis direction of input force, who's directionality persists into arcs.  The primary Arc is the most nominal amount of real arc frictions, a frictionalized redirect also in the Hook.  All further arcs of control compound the initial nominal friction and becomes less loaded, thus less rigid.  Arcs use ALL of tensions for frictions and compound by degree, linear parts use no raw force tensions for friction, just deflected side force tensions that compound by distance instead.  Arcs Rule!  Linears only connectors with some friction tax.  Primary Arc and Linear (SPart) are the Hook that connects load to host as converts linear input to radial control.
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This (purports) to show a Half Hitch as termination, the linear maintained presence, Hook of SPart + Primary Arc and how all kept rigid by the final 'tailer'/controlling  stop position at the end of the loaded rope mechanism.

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Here we see HHs inside Sheepshank and Bowline, linearity of highest tension trace thru rope arc parts of HH and (any) collar are each tighter if HH or collar is 90 degrees or flattened against the linear force flow from the imposed load.  1 (HH or collar) will flatten to inline to force flow, thus more rigid, and the other (HH or collar) will be 90 degrees to the force line/outside of it and not as tight w/just reflected/indirect force from not being in the linear direction axis of the imposed force ruling thru scenario as initiating input that enforces the responses.

The stiffness of the SPart in Bowline keeps a close collar tighter as inline with force flow.
>>ring of HH always is 90degrees from collar position, so is force out of line of force flow and so is less tensioned
>>and can do same for Sheepshank for more stability
If the ring of HH (if is still a HH in this position and not just a 'Round' of 2x 180 arcs) folds down into the force line instead
>>it is then higher tensioned >> and collar still must be 90 degrees from so it is now looser
>>less stable/failing Bowline (reposition correctly to amend) or regular Sheepshank (that is more stable but not most stable)
>>Bowline type finish to Sheepshank amends but complicates adjustment
Sheepshank just never the best knot, especially in the more slippier ropes of today(would go other route).
.

[KC]

So, to this model Sheepshank fails as looses the Half Hitch(HH) that 'rolls out'.
We faithfully describe and make a HH; but in actual usage/loading
Our faithful HH does not fail, but is lost when forged tight/loaded.
Just morphs into a 2x180(360 circle) full Round on the bight/collar host that is this loose floppy thing w/o SPart fortification,
that can fold and allow rope off this mount.
>>for the 2x180 arcs aren't aligned to hook but rather miss each other
Sheepshank fails at that loading level because we command it to/should not expect anything else!
Does not have the structure to be rigid enough against this turn around it to crush thru it as it folds away.
Can force Bowline to fail similarly w/too long a collar to give enough rigidity to not let this happen
>>SPart reeved thru collar then is 2nd catch to keep bight from folding/crushing out here then.
>>until Bitter End finds way free..

.
This problem is repeated in the only or top Half Hitch in Bellringer; which sometimes is described as just 1 end of a Sheepshank.
The rollout easier to see if instead of making HH in SPart and slipping over bight
>>bend bight in U back to self, then around SPart, then straighten out bight to invert HH into usual place
>>but on loading goes back to mid stage of created 360 around bight by more powerful SPart.
>>over ruling this default by leveraging bight up keeps HH

.
The Hook imagery resembles near miss of side by side arcs of Zeppelins on the Half Hitch rollouts ;
even though setup as HH of 2x90 arcs hooking together.
In Bellringer's the succeeding Half Hitches due keep the linked hooks that can't misalign  of Rigger's and Alpine above in post#7
>>as each strategy tries to grip the soft 'floppy' bight to stabilize, the rollout to side by side lose HH is less stable
>>especially w/o the stiffness and frictions of the old ropes to help compensate
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edit been looking for this reference on Sheepshank locks.
ABoK reflects on Sheepshank more ornamental than functional for the sailor
>> many have questioned it's continual including in collections
>> some have faulted BSA for teaching still as a hold out
Digging thru the way back machine tracked into lost Henry Bushby presentation for Mariner's Museum and his works quoting John Smith's of Jamestown book "A Sea Grammar" in 1627 then another author expounding on this "1644, Henry Manwayring published his Sea-Mans Dictionary, which provided more detailed descriptions of the knots first mentioned by Smith".  This page quotes that they depended on 3 knots at sea mostly: Sheepshank, Wall and Bowline.  But then in picturing 3 versions of Sheepshank 2 are locked against above fault:

Sheepshank dispenses/isolates more rope neatly than Alpine Butterfly (which is otherwise superior) and more trustworthy in the locked forms shown.

[KC]

So in flexible class, such as rope, has the primary directional axis of 2 directions and it's cross axis of any 90degree direction across the main loaded axis.  The primary loaded axis is the most raw force, but as cross-axis can overtake  primary axis, then cross-axis must be a recognized force as always and all ways.
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Also rigidity of parts must be recognized, as above Half Hitches aren't kept linked 90s after host mount so soft allows torque sideways to be misaligned 180s opposing, can fold the nonrigid/ soft bight  mounted on especially our slicker ropes, unlike if same arcs on a log that would hold the opposing arcs and not fold to allow fail.  But still maintain same root rope part selection of 0,90,180 arc deflections from source direction.  Over and again should see these 3 primaries in the preceding knots etc.

If were were working in any of the nonFlexible/rigid classes such as wood(carve able class), metal(malleable class), rock(non malleable class) these would be separate pieces of functionality would group and link together.  Might even use rope to link parts, thus rope can link own parts.  And these parts can be formed by hand w/o carving, heating, pounding or chipping as the rigid classes, for the same support against loadings.  For to forge rope to rigid against, need only to load the architecture.
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The receding tensions on arcs thru rope after linear to radial conversion maintain a directionality that even tho tension receding thru rope, can create mid 180 arc a point of compound force against host greater than either leg to arc.  This gives 2/1 of pulley, and best Nip point of knot.  The only way to do that is with the directionality imposed that is not found in Binding, thus has no compound arc point there.
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SPart determines initial direction, thus directional axis of towards and opposing load directions, but not necessarily inline axis as it also carries greatest raw load.  It connects  from load to control, just as a truck pull.
If this linear reach is deformed from 1dimensional inline with linear force carried, tensions in each case internally leveraged against rope device ported thru to greater than load.  So breaks at same tension as straight but under less load.  The input direction value is as important as the input load value. 

For me, the log w/o Half Hitch shows the Natural , un-altered state of the SPart support
>>Half Hitch is contrived, deformed from the same support function
>>But to this model the SPart linear input ends at same place where hands off to Primary Arc
>>SPart taught as always outside knot is perhaps oversimplification for tying reference to this FORCE trace model of actual usage
Note also how the purple load connectors don't reach as far down:
Just as same length ropes  can't use their full length to reach farthest
>>to displace most against vertical space from originating point
Nor can same architecture use all of it's tensions
>>to displace against vertical force @ full efficiency/ruled by same maths
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Axial Directions (vert or horiz etc.) input is maintained from SPart or other input until 90degrees ropePart.
>>Visually SPart is said outside of knot and 2x90's make a 180 and directionally that is also true
>>but force trace wise, 2x90 is much different than 180!
90degrees has NO force back towards input source direction @ 90degrees termination.
>>but as we make this a pass-thru, not termination, then at the 90 degree point we can get compound force towards source direction with pass thru , when had Zer0 pull towards source input/load on that arc as a 90!

[KC]

With the focused linear input of imposed force/load whose directionality is so important witnessed thru the arcs;
we can start to sift out the endpoints of the individual ropeParts to define them
>>where if rigid parts these could be separate linked parts /functions in a rigid support material
>>that would be linked together in series possibly by rope
So that a set of ropeParts itself is self linking/already in chain.
i think the most micro working block would be the 0,90,180 deflection of receiving endpoint from the source endpoint.

Once again, in recognition of force etc., 2x 90degree ropeParts terminating is not the same as 180 degrees flowing thru the 90 degree point to termination or not.  This is here the compound force of a 2/1 pulley and Best Nip are found at the 90 point, where there was Zer0 directional force before, now can be greater than either leg feeding that arc to the 90 point if 180 arc.
The 90 degree alone is a change to cross-axis, the 180 a compounding as the directional force of the input of tension from both endpoints is now consistent , when is not in other forms 0, 90.   

BUT, without the directionality of the linear input into the controlling arcs, this is not seen in the self contained diffused radial force input from inside the controlling arcs of Binding.  Only external, focused linear input(SPart) into controlling arcs of Hitch as termination or Bend as coupling type node deformities in otherwise continuing undisturbed line of (rope) force.

Because in Binding, the input force to the rope is internal diffused radial not linear, there is no compounding point, for no focused  directional input of linear, thus all rope arcs before nip are equal force, not receding from  input point, not compounding.
But, in same loop that could bind, can show the linear force, compounding just by linear input, and it's direction.