Author Topic: Displacements of Rope Rigidity  (Read 570 times)

KC

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Displacements of Rope Rigidity
« on: July 20, 2020, 11:17:36 AM »
Bends and Hitches take a focused linear force input thru SPart;
And de-focus/disperse it radially around arcs to reduce tensions to the further ropeParts.
>>This also makes these further/later ropeParts less rigid
>>because same container size(rope) is now less full of tensions.
.
So that in crossings of WE(Working End) of lesser tensions,
>>can cross under existing, more rigid ropeParts to pinch/nip lesser under greater OR
>>WE can cross over and 'paste' the greater rigidity to firmer frictions against host
The intensity, of how the present tensions (that cause rigidity) are used to pinch/paste
>>is at most premium of each arcApex whom's axis lies in same direction as input force axis
(not necessarily same axis, but same axises directions)
180 arc ends also feed into same directional axis, as input, but not necessarily same axis/just directions
>>while nonArcs, who's ends pull in opposing directions give the least crossing forces (pinch or paste).
For the arcs can use both sine and cosine for friction force of control;
>>BUT nonArcs use cosine for the load and sine for frictions
>>BUT in arcs the cosine is the greater determinant force, that nonArcs don't use for frictions...
(so nonArcs not only forsake 1 of the 2 forces(cosine)as friction usage, to only keep lesser sine for crossings)
This is what makes common HH worst Nip position, is load side under nonArc.
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Top side/opposite side of host than load pull line is Natural gravity line; shows the effect most intensely.
>>Lesser pressure crossing just firms/increases frictions for greater tension reduction.
While greater pressure crossing can totally 'squash' tensions, to not pass further/ 'nip forces in bud'

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Scheduling other ropeParts at crossings instead of hand can give same effects of 'Paste or Pinch'
As the greater tensioned ropePart is more rigidly force dense is crossed over by WE
>>the lesser firms, but cant displace firmer rigidities so can allow greater to tunnel under/thru the lesser.
Where as if WE(lesser than the previous tensioned rigidities that are closer to source/input)
>>the greater tensioned rigidity can stomp/squash closed the passage of tensioned force
>>fully nipping to secure if no force makes it thru the crossing.
Pasting firms frictions for some force displacements/reductions, slowing down force travel intensity thru rope
>>while full nipping of greater rigidity sandwiching lesser to host fully displacing tension forces
To stop force flow, the sandwiched rope part MUST be equal to or lesser RIGIDITY than crossing part.

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Note how, the 'rope circuit' is the same exact pattern in above pic
>>only the tension force is  (as if electric force thru same circuit) is ported backwards thru the 'rope circuit' for different effects.
>>just as routing electric force backwards thru same circuit of transformers, diodes, transistors etc. would give different effect
(or even sometimes, just reversing polarity to same electric circuit)
« Last Edit: July 20, 2020, 11:24:29 AM by KC »
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KC

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Re: Displacements of Rope Rigidity
« Reply #1 on: August 02, 2020, 11:27:55 AM »
Looking at a Clove as opposing HHs has helped guide many to forming the Clove properly.
BUT, in force trace of utility of functions,
>>watching if the lesser/softer WE serves over or under the greater/more rigid ropeParts
We can diagnose 1 paste, and even (pressure wise) 1 pinch/nip/hitch
>>but the pinch/nip/hitch is softened a bit towards the paste side
>>as is NOT sandwiching the WE against the host with full force
The radial position does give the 2nd crossing pinch close to full sine of arc + some cosine

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The only way to get a top Nip from the Clove formation is to ballast the other leg
>>else the crossing rotates from top to the side of the imposed pull.
In this position, neither crossing gives nip/pinch/hitch type function
>>SParts (linear input)as the most tensioned/rigid parts, can't be pinched/nip to HH fn(computerese for function)
>>for it can only be crossed by lesser, later rope tensions to 'paste' SParts firmer to host NOT pinch as to nip/hitch
Even tho is at greatest radial position to exert the ropeTensions to 'express' those forces
>>onto the leads from SParts.
(Nip not really needed, as each 'Bitter End' is but an EXTERNALLY ballast to secure,
>>NOT dependent on internal knot structure to give Nip as securing ballast against input force imposed.

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Making a Clove on load side (or rotating normal Clove to this position)
>>places the crossings off of the host, giving greatest deformity to SPart as Cow, Muenter, Prussik etc. do
>>also gives least nipping, in fact can use on carabiner(sometimes 2 carabiners w/opposing gates for softer rope arc/bend)
to lower a light load.

.
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KC

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Re: Displacements of Rope Rigidity
« Reply #2 on: August 06, 2020, 12:08:28 PM »
In the geometries of space taken or force invoked, it is about DISPLACEMENT.
To control, with force, takes displacing into that space, with enough force to match or beat the existing force
>>for positively commanding displacement to rule/Nip situation ('in the bud')
.
The ruling rigidity is gained by matching linked target forces or being greater/not lesser.
>>The base/unloaded rigidity of the materials matters for this advantage
>>The amount of tension force
>>and how densely that force is packed into each part as yet another rigidity adjustment
Different force loads in diameters for the crossing over to be great enough to Nip the sandwiched ropePart

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Sometimes see questioned if Square Knot should be still taught
>>i always think YES, for is a minimal structure study, with fewest parts
>>on edge of make or break(fail) and things that change that
(errant bend usage, unequal diameters, formations or disturbances that 'pull out of square' form etc.)

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i first note many things in the minimalist study of Square family(Square/Thief/Granny/Grief)
>>and would usually forsake American upbringing and call as original name Reef in respects to how many knots born at sea
BUT, the name Square is so excellent to force chase, and constant reminder that all rope mechnix best if 'square' to purpose
>>the minimalist Square Knot, just more sensitive to that, as Thief/Granny/Grief fail by pulling out of square, as does tugging end.
The SheetBend invokes a locking hitch that can free stand off of host mount (unlike Square that is dependent on host to nip against)
>>so has another layer of simplest/base lessons, and how a more rigid locks on softer rigidity etc.



(originally http://mytreelessons.com/images/matching-or-denser-force-nipping-other-sheetbends.png,
edited per Dan Lehman post later in thread after much consideration and respects)
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Friction Hitches show the matching or greater principle too
>>advise a single leg of pull (A) can match rigidity to single line and control (Taut-Line, ProLaska/Blake's etc.)
But dividing load to 2 legs pull on host /receiver and are trying to grab greater rigidity with lesser(B) can fail
>>using a smaller cord to pack lesser divided force into a denser/more rigid container can resolve(C)

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The smaller 'cord' can also be a more rigid /unyielding braid, too stiff to seat properly like this on own diameter
>>but flexible enough to seat well on larger diameter host
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i think the term (Friction) Hitch is accurate, as the function is to slide the hitch up/down to repeatedly grip
passive 'rail' whether rope or not , the rigidity examination tho is for rope on rope
.
Friction hitch grabs on smooth pole can slip some as rope can't 'dent' impose into the host

« Last Edit: August 24, 2020, 11:44:28 AM by KC »
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KC

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Re: Displacements of Rope Rigidity
« Reply #3 on: August 17, 2020, 12:22:44 PM »
Still in the mix, is the surrounding "ropeParts"
>>Separate rope sections, that give defining utility functions to the whole
>>And in another 'medium' of architecture (wood, metal, plastic etc.) could logically be a separate part
But, as part of rope magic, flow continuously from 1 utility to the next in connected chain of ropeParts w/o other formal connection points.
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RopeParts can perform their own functions AND also alter the impact of change on another ropePart.
>>such as in Clove, the crossing closest to the load muting part of the sudden nip on the next crossing
>>by primary crossing's firmer loaded form 'tenting' or 'bridging' up the crossing turn's
>>nip on the real 'hitch' part of equation, of greater over lesser crossing in Clove.
So the nip is softened, not left to it's own/neutral of unchanged (greater) nip potential
>>but then so can press down/not lift up; around same nip to make even greater >>if holds shape
For, another function of other ropeParts can be as to be 'ropeGuides' to the focused ropePart alignment
>>as the ropeGuide could be perhaps carved into host, but is not, so a ropePart can oblige this guide function to another.
.

So the effect of the rope present crossing's greater vs. lesser density performance
>>may represent/perform rawly as expected or be exaggerated or softened by surround ropeParts.
.

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While also the radial position, from the direction of linear input, to the precipe of radial dominance
>>of host 'direction' (clocked from center of host), most opposing from imposed/input load direction of pull
>>12noon from a 6o'clock pull on round host
.

.
So, ropeParts can also be as spacers, serving other ropeParts into greater(or lesser radial positions
>>especially on smaller host:rope ratio
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agent_smith

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Re: Displacements of Rope Rigidity
« Reply #4 on: August 20, 2020, 02:04:44 AM »
Hello KC,

Thanks for your detailed analysis and drawings.
You are introducing some concepts - at times without a clear and basic explanation.
For example, you often like to use mathematics to explain some concepts - particular sine and cosine.
When doing this, you don't provide the reader with background depth on why sine and cosine are 'significant' or relevant.

Your use of the Clove hitch as a basis to explain how a hitch functions is interesting.
I would challenge you to closely examine the 'Silent Partner' device made by Rock Exotica (USA).
It employs a Clove hitch which is tied on a rotating drum.
Link: https://www.rockexotica.com/media/wysiwyg/rockexotica/tn/silent-partner-tech-notice.pdf

Note that on a rotating reference frame, the Clove hitch slips. Indeed, without the ability of the Clove hitch to 'slip' - climbing progress would be difficult.

KC

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Re: Displacements of Rope Rigidity
« Reply #5 on: August 21, 2020, 01:48:40 AM »
WORKING rope usage, is all about support architectures against an imposed load, and controlling frictions, then some crossings etc...
Support architectures are defined by cosine/sine.  Just different here as flexibles are tension only supports.
Cosine and sine in rope arcs give the controlling frictions.
>>Cosine is more direct intense linear, Sine a deflected value in these frictions
>>so cosine can be more intense part of frictions even if less than sine
Added both together, sums to 1 only at extremes of 0 and 90,
>>otherwise the sum is always GREATER, greatest at sum of cosine + sine = 1.414 at 45 degree median
In rope linears, cosine is segregated to support extension (SPart etc.), and any friction is thru sine only(theory).
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In True Gifts from Ancient Babylon thread i try to show this as also show my personal clock mnemonic of translating a single 'event' into cosine/sine number pair 'layer' that then 'expresses' out to rest of event/system with clock mnemonic for reading/decoding things and transferences .
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Silent Partner manual very nice, what i've pointed to in Clove, persists even in the free rotating host.
That gives way for more walk of the continuous direction turns of Clove to total of 3 arcs as like RT, but then with crossing.
At free spin reduces frictions to negligible allowing walk, then as centrifugal clutch engages increases frictions to translate out thru the 3 arcs and the crossing/'frapping' turn to brake.  Very Nice!  And continuing reminder of how key friction is, as this smooth drum manipulates that one key factor to key utility usages (brake/non brake) here.
Note how Backhand constructs of '1 leg thru' /Muenter would not play out, because is non-continuous direction of the reverse torquing in the off host crossing.
Also like in manual:
>>You cannot learn to solo climb by reading this manual.
>>We cannot, however, teach you to solo climb over the phone...
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Clove here too is continuous turns as noted, but the tent pole of greater force/rigidity under lesser crossing, that doesn't allow full normal nipping to the lesser crossed rigidity is also key to the metered walk allowed.
.

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Dan_Lehman

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Re: Displacements of Rope Rigidity
« Reply #6 on: August 22, 2020, 12:36:55 AM »
Btw, those sheet bends are of the opposite-sides
version which has greater ill repute (though it seems
to be a worthwhile debate at least per cordage type!).

And, <argh>, I'd sure re-orient them to make them
more LOOK like the finished knot will look!

 ;)

KC

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Re: Displacements of Rope Rigidity
« Reply #7 on: August 23, 2020, 01:22:30 PM »
In all honesty
>>i do here, so much as you so nicely put(?!) sometimes, 'parrot' prevailing 2nd hand info
>>but then show what i honestly did starting out and was faithful to me/ but then try not to break stuffs
>>in arbo 1/2" climbing/rig lines of the time, and well seated before service for less deforming
>>that does leave a cleaner, more seamless side
in early years wading thru confusing array of sometimes conflicting info noted since was a teen.
Exception being in making Bowline fixed eye, and then Becket to with Sheet, i did prefer clamping hitch to locking side of Bowline
>>but then less notable worry, in 3arc forms of either (DBY /Dbl.Sheet), when evolved to doing both of DBY w/ Dbl.Sheet/Becket, usually slipped, for repeated dragging w/Bowline to preset short lines to stacked brush/wood piles
(sometimes 4 or 5 piles waiting , each preSet with dogged out short piece, waiting to make Becket to Bowline puller of better, non dragged rope)
.
i do see deformation on pulls in that form shown here, more visible in other lines sometimes
>>but less notable seems in bulkier slipped forms side by side or crossed (?)
It seems to have logic of sandwiching BOTH Bitter Ends (BEs)between both SParts
>>that 'left hand' form only sandwiches active/locking/hitch side BE between most rigid SParts
>>but with more square focus, and less deformity in trade for forsaking most intense clamping lock also on more passive bight BE.
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i do remember well our discussions on this and other things as valued so well;
and how i came to be here; including lunch with a mr Randy Penn("Everything Knots Book") as we live in same city(figured someone sent him my way).




Actually go with Dbl./RT forms of most anything, including Sheet Bend and Bowline
But really, in last 80% of working yrs with this, go with 3x180arcs when can; as i champion elsewheres
>>this translates, for me, to really Double/RT form of Sheet Bend, usually with a slip
>>preferring more of 'poofed' /crossed slip more emulating/exaggerating roundness, than 'box car'/side by side slip form(s).
Somewhere deep in early readings, ran into this 40+yrs ago, and saw an author say left had tested better in Sheet Bend
>>but he also distinguished to prefer Right Hand with one cleaner/more seamless side as 'Weaver Bend'(where others showed Sheet=Weaver) for clothing with cleaner line type logic that stuck out to me, but went with the majority..
(can never find the reference in later years)




3x180arc RT as pro upgrade to simpler, single arc Turn
To me 3arc RT forms are generally more of the pro application to a simple/single turn
>>unless purposeful pass of force to next position, quickie, less bulk or shortness of line
The RT in the Sheet Bend forms, makes them more as equals to me
>>for any single Turn by comparison only arcs 1 side, then to non arc-ing but slanted lines feeding from either side of arc
>>are just extensions to arc ends and of far less consequence in 'host hug' ,
>>as do not engulf the now more open/un arc-ed side, as the eye says
>>arc(180 w/ends pull in same PHYSICAL direction , and then arc apex btw 90's of 180 same AXIAL direction) uses both most directly intense cosine + deflected  sine to 'hug host'.
>>but line segments (that pull in opposite directions) use only the deflected, less intense sine quantity
This is so much true, that trailing from most loaded/rigid SPart, to bottom half or round host mount
>>gives much less crossing impact on host (nip of greater over, or paste of greater under crossing)
>>than the top quadrant side trailing, after some friction loss of line tension, to SPart side of the arc
Doesn't look that way to eye, can look like about same 'hug' to host but is NOT
>>in SPart, the most intense, direct, simpler single dimension cosine serves against imposed load
>>leaving only the deflected, less intense sine pulling to host
(where in arc 'hug to host' employs both direct cos + indirect sin are used by contrast to non-arc/linear segments of rope)
So, even as focus here on tensions and therefore rigidities in knots
>>can't outrun the 'radial position' in Bends and Hitches, as benchmarked from SPart(s) DIRECTION initiating  force into knot


EDIT
Eventually went with recomendation of knot guru Dan Lehman
to >> http://mytreelessons.com/images/matching-or-denser-force-nipping-other-sheetbends-EDIT.png
originally>> http://mytreelessons.com/images/matching-or-denser-force-nipping-other-sheetbends.png
« Last Edit: August 24, 2020, 11:46:03 AM by KC »
Rope-n-Saw Life
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We now return you to the safety of normal thinking peoples.
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