Author Topic: Naming ropeParts as components in a working support structure/architecture  (Read 10990 times)


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The 'compounding point' is the apex of the arc that most opposes the load pull as on opposite side of the host than load .
(Hitch and Bend only, not Round Binding)
In a rope machine, this is simply the 2/1 of a  pulley, and in a knot the compounding is used as the point of Best Nip.

All rope/flexible supports against gravity need a rigid support at least as high as load.
This in chain/as wiring connects to the Earth; if no such trailed connection/strong enought, gravity calling the positive load to the negative Earth ground wins out and load falls to satiate the calling in this model.
i use electric schematic ground symbol for anchor points of Zer0 relief, bomb pruf theoretical.
But also to show need + load imposed at one end and trace to ground at other, and all points between as loaded.
Just as electrical, for force is force; just carried by wire or rope here as conductors of the specified force.
>>Commonly, water pressure from a tower downward into pipe and it's width etc. are given to understand volts, amps, resistance.
E=MCsquared   fairly matches Total Watts of Power = Resistance x AMPS squared.
>>E and WATTS are both force total sums in equation
>> M and Resistance are both weighted resistances against change
>> C and AMPS are both the speed of the force applied
>>AND both are the squared factors of compounding change
>> each escalate to be the real 'killers' much quicker than the other formulae multiplier of static load resistance
>>so each formulae has a static weight of resistance component then it's multiplier of dynamic speed that is squared
Force is force, down a wire or rope; bound by many of the same laws.
>>can at times use one to model the other for more comprehensive view, especially a more familiar one.
In either the dynamic element is most important.
Physics of speed is such that:
If have 2 matching trucks and make 1 weigh more than the other w/o changing rigidity yet welded in.
>>in a head on of matching speeds the heavier truck marches on thru the lighter thru virtue of it's 'M'  static mass of resistance to motion change.
BUT, if the lighter truck in head on moving 2x as fast, will walk thru the 2x heavier truck like it was water.
>>the dynamic speed part of the formulae trumps the static day every day, even in electrical changes.
>>thus this is a continuous theme really across both, not separate lessons, except for cross-verification to each other for better, fuller view
An Extra ground connection in electrical, can change forces; just as it can in rope.
>> If just the load and support points is a 'closed' system, most simple
>>with other added point(s) of input positive load or negative ground it races to the system is then more 'open' to other than nominal forces of 1 load against 1 support.
i do, in my head, use other electrical schematic symbols to visualize rope workings in minimal, undressed skeleton of forces:

To sweat or swig a loaded line is to pull across it at right angle drawing it from Zer0 degrees deflection in single run,
>>to separate legs support against the right angle
>>if total spread on the angle is less than 120degrees (60 deflection each side of sweat/swig interruption for cosine 50%) are increasing the line tension
In electrical, like ignition coil, they term loading the coil as 'exciting the coil', then the inducting force is brought in 'from the side'(?) to induce higher voltage pulse/impact to system for spark.  Comparable to an extent of inducing higher tension to already 'excited'/tensioned line.
A one way Friction Hitch would be as like a safety on a pulling rig, that had a prussic around the line, and a small pulley or carabiner on the effort input side to 'comb' the hitch further up the line as pulled rope, release rope and prussic holds load (minus prussic slack/slop) >>  Only works 1 way like a diode.  Whether diode in old time crystal radio or newer age LED, that unlike older bulbs must be connected in 1 direction/doesn't work if switch polarity(so must be DC)
For me this is a more comprehensive level of understanding each alone, or together.
And in each, once can understand the micro-blocks of independent pivotal utility functions,
>>can move to more familiar macro-block assemblies of them found in many things
>>then to fully engaged systems of the macro-blocks whether electric, water or rope systems etc.
« Last Edit: December 25, 2020, 01:14:08 PM by KC »
"Nature, to be commanded, must be obeyed" -Sir Francis Bacon
We now return you to the safety of normal thinking peoples.
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A summary I found interesting for mechanical-electrical analogies can be found here Link:

These analogies appear to be useful for understanding and solving specific types of problems, especially those involving elements from two or more energy domains (such as Electrical, Mechanical, Fluid, Thermal, Magnetic and Chemical).  These situations often include transducers (devices that convert energy from one form to another). The example given in the above reference is the mechanical parts of acoustical systems such as the pickup and tonearm of record players (see especially the section called "Applications").

So far, I am having better success at understanding knots and ropes from a purely mechanical perspective than adding an electrical perspective.
« Last Edit: December 25, 2020, 08:05:49 PM by DDK »


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i think that the original water pressure/volume of flow for electric comparison
>>is to get fuller more comprehensive view of related aspects and how widely they are consistent to reaffirm by similarity to give depth etc.
>>of something familiar vs. other not as much or again just to give firmer more confirmation and reaffirmation
>>and to get a physical more instinctual feel that can relate to
And also, prove to self you know more than you think if just slow down to eventually go faster
>>if see ways related
As an ol'buddy used to jokingly say "Exactly the same but different"! for i have l-earned from many!
So part of that is whatever cross verifies to something more familiar to each person as bridging and firming of cross-verification
>>so actually for me that runs into a yin/yang equal/opposites philosophy
>>and the gradient field between
i can't count all the times someone asked me how i figured out something in rope and/or tree to make what seemed impossible work
>>i could only say looking for yin/yang model etc. >> for it was where i ended up so many times
>>just started starting there!!   >> as found concepts so saturated in all that i do! 
So tend to offer more normal, electrical equal and opposite extremes and the loaded path that only exists in between...
>>but still look at electrical path etc.
>>this and other presented models have given me many of the answers i've sought in rope usage, to include knotting
i could not have chased these things out so confidently thru the counter-intuitive turns w/o all these models.
Once finding the principles continuing to where wouldn't think would go, mind opened up more
>>and this became light play as thought about times had stacked this against efforts and times fell into the patterns correctly and things suddenly worked:

So maybe another person would learn from rope and carry to wire etc.
>>concept of force is force and similar controls are needed for many things even in a different 'format' prevails
The matching total watts and total force analogies i think ir-refutable
>>usually watts shown as total watts power in system = Volts X Amps
>>but digging further we can see that Volts = Amps x Resistance
>>terms collect to watts total power = Resistance x Amps x Amps
Look at Mass as resistance to change
>>and find Amps is the speed squared as velocity squared
Leaves me at my E=MCsquared  matching Watts=R Isquared   (I is amps in electric) proclamation
>>but whatever gets us home to the truth!
 i think these things in thread are the real view/model of most answers  >> and how i got there/my 'pruf'
Similarly , mechanical force parallels in rigid vs. flexible leverage systems for more tangible fabric to grab on how pervasive across these principles are.
>>as constantly try to show rigid support against load imposed matching of rules between normal rigid classes and the single exclusive flexible class supports.
Older sketch on views of using a single pulley as pivot in 'flexible lever' systems.
>>with the the same 3 lever classes as rigid levers
>> that define by the same directions of motion input/output
>>with the same 3 positions of the static position pivot
>>2nd and 3rd class levers being to increase or decrease power as reciprocal to speed
>>and 1st class levers in each reverse of direction between input/output with central pivot between

The rigid lever can resist on the cross axis, so length of lever from pivot matters
>>but w/o cross axis resistance, the flexible lever classes do not have length factor multiplier for leverage.
« Last Edit: December 26, 2020, 12:30:19 AM by KC »
"Nature, to be commanded, must be obeyed" -Sir Francis Bacon
We now return you to the safety of normal thinking peoples.
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Hello KC,
Hope you had a nice Christmas.

With regard to your posts at reply #15 and #17, I am unclear how this relates to knots and naming segments/parts of a knot (assuming that knots are central to this forum and the reason for its existence). That is, the IGKT is a knot tying forum - isn't it?

With specific regard to posts #15 and #17, I am of the view that this largely falls under the realm of mechanical advantage systems and Newtons laws of physics. Yes, mechanical advantage systems do employ rope (both wire rope and synthetic rope) but, there are no knots within the moving parts of a mechanical advantage system.

Your electrical and/or water flow analogy is interesting - but it is Newtons laws of physics that applies to M.A. systems.

Your pulley diagrams employ double sheave pulleys - which may not be clear to the casual reader (ie pulleys can be single sheave, double sheave and less often, triple sheave).

In your diagrams, the casual reader has to pause and ponder where the mass to be lifted is located - which in your orientations, the mass is above (ie at the top of the image diagrams). Your ground symbol is simply an anchor point - the position where the M.A. system is attached and anchored to.

The top right M.A. system is your image at reply #17 isn't an 8:1 M.A. system. It is still a 5:1 system.
You should consider velocity ratio as a method for calculating the M.A. of a system.

I would suggest that you start a new topic thread and title it, Mechanical Advantage systems.
Within a knot, forces are not transmitted in the same way that force is transmitted in a M.A. system.

Also, you do not appear to mention that M.A. systems can be:
[ ] ideal M.A.
[ ] theoretical M.A.
[ ] actual M.A.
Pulley inefficiency plays a role as does the terrain over which the M.A. system is operating (eg cliff edge).


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Merry Christmas to All !
My view and naming these things are contiguous to my background i find.
In seeking a more tangible thicker fabric of related principles instead of individual scattered points to collect.
>>and each giving the other more relevance in chain.
Also, if i think i 'prove' something in 1 framework, i have to find it in others to cross verify and view from different angle to understand.
>>or i heavily question and do not state it until i get re-affirmation in different ways.
>> as stated these things are my confirming elements, as persistent across the other platforms too, not skipping knotting in their wake.
>>thus examinations from rope should prevail across flexibles as a class
>>and across rigid class materials, exclusive of the properties unique to flexibles>>but all else same!
>>and should play forward or backward in all as further confirmation and firmer more tangible fabric to grab rather than a basket of loose points.
If i find a hole in any of this as assembling, i know i am missing something
In presenting these differing views I bring the bridges that helped me.
Knots are a ropeLogic mechanix to me. 
Mechanical uses of ropes in pulleys, capstans, bollards etc. are a magnified view to me of internal knot secrets, at different friction values and arc sizes
>>to include fanbelt seating, idler pulley being like a Half Hitch bend on Standing Part etc.
whatever i can assemble in these larger exercises to give insight and more firm and comprehensive understanding into the interior  happenings of a knot.
>>when same forces are exerted in same materials, only shrunk down to the microcosm of a knot.

In the view of 0,90,180 arcs as basic micro bloc of assembly, the principals are consistent and perhaps easier to see in pulley systems to me.  If asked how does something work in a knot mite have 1 layer answer.  More firmer pruf would be same in and not for other knots.  But most assuredly the depth of belief and understanding is when show prevails across all things, even counterintuitive corners.  Then chase it out to even more things more confidently.  This is that.
Also, as show in these things is more of things can understand more intuitively thru feeling the forces as can't inside  a knot, as the water tower example tries to lend to electricity as a model of understanding.  Indeed quiet listening thru bod and adjust forces to is carryover from gymnastics.  L-earning forces by using own self as a monitoring and adjusting part of a machine inset self into.
The point of the upper right hand pulley picture(4th) potential of 8x claim (that was measured) is that it has 2 inputs.
>>if actively pull right hand and left is solid in position it is a receiver of force passively and not exerter
>>so does pass force from rigidly held hand for more power..
>> if actively move that hand in opposite direction of primary input hand , then I think we see more speed as well
To me this is like a martial arts working of a pulley system vs. common input.
>>The first class lever (flexible or rigid) returns an opposite direction value
>> capitalize on this to be a receiver of equal and opposite of own effort
As the Eastern mind came up also with differential windlass etc. by recursing the principle back on self.
This is a 3x pull insertion point to the system independently in 3rd pic just as in 4th/8x pic , only 8x pic adds the 5x pull point of input
If hanging on the rope with bodyweight , and right hand pulls on 5x, left had pulls on 3x position autonomously
>>if not hanging part an input can come from bodyweight and not recursive thru the system as 'free' usually 'wasted' equal and opposite.
But imagine if weigh 150# and stand on a scale and do the 2hand inputs as shown
>>if still 150# on scale during the motion are getting the 8x, nothing is working against bodyweight as equal oppoi9site
>>if getting less than 150# on scale as doing the 8x, that amount less is input point for into the 5x position on top of the 8x effort
>>if heavier than 150# shows on scale then part of the 5x input is using feet on scale as equal /opposite not the 3x input hand position.
This value is shown as the output of the common compression jig
>>because initial most powerful input goes to top of system, there would be less power using this as a lifting jig, so showed as compression jig service.
This started out as a set, and yes should show theoretical /impossible friction free/ideal system thanx.
But, the numbers stand even as they are so consistent they trace around counter-intuitive turns
The rigid vs. flexible matching lever classes examination i think gives each more relevance in a repeating pattern across all.
This examination all started sitting in rope saddle in DdRT as arbo's do (like riding a dumbwaiter in old movies) and the 2/1 involved in this 'electrically' 'closed' system of single ground
>>quite a chase, but i got my answer i believe and expounded from there to many wonders making big differences, simply!
Forces are awesome, but more fun being their master than slave!
i will start separate thread and call it Mechanical Advantage systems.
But i think rope should be taught to Boy Scouts in a working tool view of simplest tools to command forces to bidding
>>and part of that is pulley work
>>all along am trying to line up proper and prioritize to how this should all be passed on
>>to line up on the real view and not take full journey at start, but have start more correctly aligned to full journey in case goes on..  Smaller boy overpowering adult (even if adult plays it up a little) or against 4 kids thru pulley move or wraps on tree holding would be quiet memorable to him and all.   See in many things from there.

And i am of the opinion, errant or not, that these rope forces are relevant inside knot internals workings hidden away.  That a turn anchored to ground and loaded does try to pull branch down with more force than load, and that reduced if terminated to Half Hitch, but still tries to crush it's host with same collective forces, just not move the host mount down towards anchor.
Overall i try to show how counter-intuitive, yet consistent across other fields these things are as one continuous body of study who's full picture can't be gotten from 1 exclusive corner pond on 1 island.  And believe have unlocked and answered many things with this view that i simply try to share.
As i became more familiar with these confusing points, it became only light play to command them in pulleys etc. and more relevance as took to rigid levers and back again for fuller view, affirmations and sharing all lessons as bodies of knowledge rather that particular to one thing.  Become so familiar if see these things all around in many things daily.
i have never met nor read of another that can on the fly give cosine/sine/tangent on a clock; but the simple view and decoder ring has taught me many lessons thru a common day just looking at things and reading them with the decoder.  i have a different view for sure, but will caution i look at things very deeply and my words are more weird than wrong.
« Last Edit: December 27, 2020, 02:22:11 PM by KC »
"Nature, to be commanded, must be obeyed" -Sir Francis Bacon
We now return you to the safety of normal thinking peoples.
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per KC:
i will start separate thread and call it Mechanical Advantage systems.
Good decision!

Although all of this is way off topic - I'm responding to you in good faith (best if you start a new topic thread and title it "Mechanical Advantage Systems").

Mechanical advantage systems (ie M.A.) don't have much relevance to knots.
I had previously pointed out that within the working parts of a M.A. system , there are no knots.

[ ] M.A. systems employ pulleys and sheaves - the sheaves freely rotate.
... the are no pulleys and/or freely spinning sheaves within a knot

[ ] Force is transmitted uniformly within an 'ideal' M.A. system
... force is not transmitted uniformly within a knot

[ ] I'll assume that you are aware of and understand the rigging and arrangement of rope and 'pulley' within a "3:1 assisted hoist" (a belay person uses it to assist a climber over a difficult section of a climbing route). The climber grasps a rope segment and pulls down...thereby 'assisting' in the haulage - ie, provides a 'boost' by injecting additional force into the M.A. system.
Regardless of the fact that the climber injects additional force into the system - it remains a 3:1 M.A. system.
I refer to it as a 'boosted' 3:1 M.A. system.
I've attached 2 images of M.A. systems.
Both yield 3:1 M.A. (one is 'boosted' by the climber grasping and pulling down to inject force - but the velocity ratio remains the same).
The velocity ratio in both systems is the same (3:1).


I would comment that mechanical Advantage systems may not be relevant to many IGKT members.
However, a 'truckers hitch' might be of interest...
Or this link:

And a 'Poldo' tackle may also be more relevant to the IGKT readers:

See also this interesting link:


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To me a pulley arc is just a lower friction arc.
Trucker's and Poldo are 2 of the examples that lead me to see knots as machines
There is no such thing as friction free pulley.
>>what little friction there is , does compound thru the arcs cos + sine  by degrees to decrease output from potential.
>> the linear parts of the pulley systems only add friction per side forces(sine only) of rubbing while on the linear path
>> the linear frictions compound by distance not degree
i'm sorry i really don't believe that there are separate rules for the same forces in the same materials
>>just same rules at different friction values etc.
>>with the differences we can define further thru each other
When i say velocity, i mean speed
The powers of the pulley systems can be increased from their usual nominal given potentials by working other input point with added force
>>even if that force is the reflected equal and opposite effort of the other input
>>instead of that promised equal and opposite showing outside the system]
>>i have found to fold it back into for a single recurse of force
>>i have measured this many times
>>in the end it is just collecting all terms and asserting bodyweight + effort + equal and opposite of effort against target at given inputs with none of those forces showing outside the system.
The power increase from effort (setting bodyweight input aside) is always 2xNormal - 2 in a compression jig as shown
So a 3/1 can give 4x effort - frictions (+ 3x bodyweight)
>>a 5/1 8x etc.
You get the 2x expected from using the 2 hands but then
You lose 2xEffort as the top pulley in compression jig does take forces from the 'left' hand on that last turn.
This is just kinda Conservation of Forces as it is so pervasive even races around this counterintuitive turn
i offer this as lit my way in times of doubt; wondering why the compression jig was inset, not serially added to end and much playing and testing lead me  to these things.
From "The Marlinspike Sailor" by Hervey Garret Smith:1956
(won't embed)
i believe this was my drawing used by Brion Toss for 2 months of a monthly puzzle he used to run to similar counterintuitive principles:

(may have to open in new tab depending on browser settings)
(from during my msPaint period !)
« Last Edit: December 27, 2020, 09:26:15 PM by KC »
"Nature, to be commanded, must be obeyed" -Sir Francis Bacon
We now return you to the safety of normal thinking peoples.
~ Please excuse the interruption; thanx -the mgmt.~


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Hello KC,
And thank you for your nice work.

I am replying in good faith - and would like to point out some issues with your posts...

In the context of this forum (the IGKT) and the fact that fundamentally, this forum is dedicated to knots and knotting concepts - mechanical advantage (M.A.) systems is an entirely different subject area.
I am trying to think where the topic of M.A. systems would best fit within this forum?
Maybe under "Chit Chat"?

Just some quick replies:
Trucker's and Poldo are 2 of the examples that lead me to see knots as machines
Yes - the truckers and poldo would be a better fit for this forum - particularly the 'truckers hitch' since it is a composite structure that consists of hitches (and is designed to be non jamming).

I reaffirm to you that an arrangement of pulleys and rope to create a M.A. system does not in fact contain knots - obviously knots within the system would cause fouling and jamming (a knot wont run through a pulley - it will jam/foul).

i'm sorry i really don't believe that there are separate rules for the same forces in the same materials
I am unclear why you think you need to apologise? I'm confused...

what little friction there is , does compound thru the arcs cos + sine
I note that you often refer to trigonometric functions in your explanations of hitches.
I am unclear what your reference frame is when you do this? Is there an 'up' or 'down' or 'left/right'?
How do you assign a cosine or sine to a segment of rope? There are many twists and turns within a knot or a hitch or a bend. In assigning a trigonometric function, what universal rules exist for such an assignment? And further, if a segment of rope within a knot core is assigned a trigonometric function, how does that explain conservation of energy within the knot structure?
We know that energy enters a knots via the 'SPart' (eg in the case of an eye knot). By the time that energy has reaches the tail, it is greatly diminished - to the extent that it is effectively zero at the tail end. We know that the core of a knot undergoes compression in response to load and there are localised stress concentrations all of which give rise to heat build up. Failure likely propagates from one of more of these localised stress concentrations (in my view).

I honestly think that you should invest in a high quality thermal imaging camera (eg Flir):
There would be much to glean from such observations of a knot as it undergoes core compression.
You would be able to see in real time what is actually going on within a knot.

And each knot will have different characteristics under load conditions - eg some jam while others remain 100% jam resistant.
Localised stress concentrations are more pronounced in some knots...

Maybe you could try to invent a more efficient 'truckers hitch'?
Or try to gain more M.A. yield/power from an alternative  composite arrangement?
That would be a challenge for you! (without the use of manufactured pulleys).


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To me, i have learned much of capstans/bollards and pulleys that have carried into knot internal secrets and then back to the mechanical devices and back to knots in cyclic growth.  The att_frict paper is a very shining example; i always thought so, especially after years of reading it, and then finally really 'got it'.  They all are studies from different angles of the same tensioned rope arcs.  The linears in knotting are just connectors to arc, input and termination.   Linears controlling frictions are by sine only, and compound by distance.  Arcs use all of tensions, the cosine and the sine for controlling frictions and compound by degrees.  Then the arcs also have the compound point of pressure onto, not around host. BUT only if from linear force input, that then maintains the focused directional axis thru the system but not if diffused directional radial force of round binding against expansion that has no focused direction, therefore no compounding point w/o other strand.  For all tensions equal not degrading to Nipping point.  i could not have found these things in knotting without these other supporting views, so offer them all as the more complete tangible fabric to grab, instead of collection of individual points.
Knots are machines to me, just in stop/locked position.  Poldo and Truckers can take from static to dynamic machine leveraged control, but then lock as static machine again.  The linear focused force thru a SPart is diffused to greater area that is more controllable in arcs.  Trading in leverages focused force to diffused, as also avails to more frictions in an arc to leverage control with the system.  If use lever as a machine to lift dynamically /motion, and then hold the position, it is as knot in a static position, but still a machine taking a linear gravity force and diffusing out to wider arc to control easier with final nip of effort to control remaining force as a ballast against chaining backwards thru the system against load.
Stone doesn't take tension well, but that is what they wanted to make bridges out of to last longest.  Had to find the arc(h) in architecture to do that.  Arc(h) in architecture to me means not to try to support with Zer0 cosine of cross axis.  Necessity being such a mother produced the stone arch allowed to use the borne forces pretty much all in compression that stone can take very well. Rope tension on arc is reverse, all tension used to target as can't use compression for support.  Same science.  Bollard/capstan and pulley are same arc science in knots, just showing different faceted aspects of the same jewel.  Thus can get a view here and there in one and trace in another.  But also, can 'parity check' in same way.  If think have principle in one, must persist fairly in rest that apply : capstan,bollard, pulley, knot.  If can't cross-verify forwards and backwards against own self and between these members then not seeing correctly.  Things i present have run and persisted thru all these gauntlets back and forth over the decades of study.  2 spread pulleys in system only use 180 arc of each given pulley at any time, just as a host mount for knot does, only closer together at higher friction and at end of travel. other wise the same as you take out the straight linear connecting parts.
To me cosine is the focused linear support against load, both directions on that loaded axis of Equal & Opposite pair of load vs. support.
>>sine is anything not on that simple, single dimension.  On tv you don't stand in front or behind a rocket launcher.  That is the loaded axis of target force direction and it's E&O as a loaded axis.  Guns and ropes can have recoil on that E&O axis etc.  Sine is anything not on that single dimension axis, more compound/complex.
Cosine as a number x 100 gives the efficiency of the support column as a percentage form. 
>> if supporting column of rope against imposed load is purely aligned cosine= 1.00, 100% efficient
>>500# tension will hold 500# load, cuz 500/1=500, 100% efficient use of borne tensions
>>if however line deformed or angled to 30 degrees cosine .866 is 86.6% efficient
>>577.35# tension needed to hold against 500# 500/.866 for 86.6% efficiency
>>577.35 tension x 86.6% efficiency = 500#
>>577.35 tension x 50% (sine of 30 = .5) gives 288.68 side force also carried
77.35 more on support axis needed as also handle 288.68 across
>>to carry same 500# that with pure inline support column at most efficiency only was same 500# and only 1 force axis
>>our friend rope only works in tension
>> helpful here as any side force expressed will try to groom system more inline proper.
>> whereas a rigid support may use compression
>> and compression side force pushes the Equal & Opposite more out of line towards less efficiency
>> they are running towards each other and have no place else to go!
Cosine is not a set direction nor axis, it is the benchmark axis to me.  Many books show it as horizontal which very much confused my self study of vertical/gravity fed usage of climbing, rigging and felling.  Cosine of support is how efficiently the support aligns to the load.  So can benchmark force or support and measure to the other.  Many times in talking to school trained folk on cosine, they could only see cosine as horizontal then calc from there and may times struggling to do in the vertical force context.  My imagery now is much more fluid than that.
i follow the force into the dormant (rope)structure of responding force against the imposed loading.
The linear line of force imposed is my benchmark cosine axis and direction.
Anything to sides, the other 2 dimensions are sine.
Mnemonic of cosine is to my cos(cause), and Sine the distraction sin from, to the sides
>>to control the load takes the cosine, the sine is just born as extra costly baggage not to target against the porting device.
Less cosine efficiency needs more tension to give same support sum to ballast against same load.

So the cosine in Hitches as terminations and Bends as couplings type node deformities in an otherwise straight rope run is that line itself.  The SPart is the input to the controlling arcs.  It ends in my model where the Primary Arc begins as 180 around host or 90 around other rope  part as a Half Hitch pre-fix does in Kellig.  The input endpoint of this arc must point in direction of force feeding it.
The controlling frictions degrade the tension as you say in a LINEAR decreasing fashion of it running out of gas to the final Nip(s).  Noting, in Binding is radial force induced, thus no conversion loss,  and not degrading tensions to the final Nip(s).
The radial is diffused evenly around w/o direction in Binding, the focused linear induced maintains the directional axis (horiz or vert) until 90 conversion to cross axis or force termination in Hitch or Bend usage, even of the same knot, just by the type and direction of force imposed.
Knots can express compression on a  host to use, but only tensioned parts of rope give force internally except for firmer frictions.  Cannot give lift, pull etc.  If on smaller arc get compression on the interior side as tension pulling on outside, there must be a section between this sliding gradient that is neither stretched nor compressed as rope area segregates to these 3 zones.  Only the tension zone is carrying load pull, that is now leveraged to that smaller section, of greater tension to compensate.
To me, a pulley system tries to maintain conservation of energy towards end output, while a bollard trades it away for friction before, but in total both conserve the same amount, just that bollards are mostly in friction/heat in a physical to heat force exchange.
Trucker's Hitch efficiency loss is from rope on rope and other hosts.  It will always have 3 legs of pull for standard POTENTIALS  of:
>> 3x as a compression jig or 2x as a lift if input is downwards where can use body weight/up to as input
>>unless grab and pull up on something to essentially make self heavier
>>can reverse trucker hitch vertically, to picking up 3x, or compressing 2x
>>this way can use strength, like more powerful leg force as input, but more fatiguing than hanging/sitting or rope as input
'My' method is for the 2nd pull inside the Truckers Hitch as also hang on it
>>this takes us from 2xEffort on one end and 3xEffort on the other
>>to 4xEffort on both, then if can hang on end as input add 3xBodyweight to upper and 2xBodyweight to lower as additives
>>if cannot hang on end as input, hang on the interior input to then give 2x upper and 1x lower bodyweight additives to the 4xEffort.
In normal operation, the Truckers could choose between leg or gravity input.  In this modified version, it can use both and to higher multiplier for the effort.
The 3xEffort potential of the Truckers  is converted to (3x2)-2 for 4xEffort as a potential for both ends
>>  5xEffort potential of a 5xcompress is converted to (5x2)-2 for 8xEffort as a potential for both ends
>>plus bodyweight affects for each.
i would say this conservation of forces, to include those assumed to be outside of the system now folded in
>>is in itself a more efficient Trucker's!
ALSO, with the dual input system of effort and weight, can hold tension in Truckers with effort part and impact with bodyweight thru system(or reverse that strategy) to tweak linearly before leveraging/swig across as potential input.
>>get as tight a lever as possible linearly first, to make less rubbery a lever as come across rope.
So, even tho i can't offer an improvement to this 'sledgehammer' of force; please let me offer to use both hands in it's style of application for the more you seek.
i totally agree on imaging camera but not in budget, and have not seen all could with what have already yet also; but see more than i did before journey started for sure.
Thank you for your fine works and also questions here too!
« Last Edit: December 29, 2020, 03:04:40 PM by KC »
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With regard to compression, I believe agent-smith was referring to the force that an outer wrapping of the knot exerts on an inner wrapping normal (perpendicular) to their contact surface and the axis of the outer wrapping.  This is the force which is responsible for the frictional force which keeps the knot from slipping. 

This is different than the forces, tension/zero axis/compression, seen in the bending of solid objects like a beam.   This bending produce forces within the object which are parallel to the direction of the axis.  In what I believe is common experience with multi-strand ropes, the strands of the rope will move and the circular cross-section of the rope will distort and flatten to more of an oval in an attempt to try to distribute the load.


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Thanx, was looking at it from more of a too tight bight view.
i think of this other as a contact deformity.
i picture rope, even if not moving being pulled clockwise by load
as essentially host is cranking counter clockwise.
Rope between these 2 nonMotions of directional force
>>breaking rope to sections still
>>outer 'race' pulls clockwise hardest
>>inner 'race' pulls counter    hardest
 horizontal line markers across ropeParts that hang off host
>>go diagonal to 'forward slash' Z chirality(there i said it) on host
>>where head of forward slash leans further forward than foot
>>as head pulls clockwise and foot counters
>>find all of rope pulling clockwise except dragging foot being pulled back
i think we see this thin layer of wrong direction also smooshed/compressed as a mating surface sleeve on contact
>>seems this mating surface war must deform rope even minutely from pristine linear form
>>even on a soft arc that gives plenty of support to rope.
Even in flat webbing that presents about nil dimension to be leveraged against it self
>>that we see in round rope as it raises up high on the host's arc, farthest part leveraged distance thru rope away from host
This is an assumed fault to me will have on all hosts
>>then tight bight to compound fault by disallowing even more rope fibers to support that are present on pure inline linear
>>i think this can happen on internal layers too, especially when core is present and load bearing, not just stuffing the sausage to keep round
Round very important concept
>>all cross axises from linear run are equal
>>webbing has flat axis of minimal dimension lays on curve nicely, to make Half Hitch arc
>> but then scrunches to massively deform for lock of Half Hitch as major cross axis of width deforms
Minimal cross axis offers no real dimension to leverage on axis of deformity to arc
>>but offers massive leveraged deforming cross axis across it's width to 'weaken' it's support to less efficient
So round rope more predictable and usable powerband of facing various deformities
>>but think webbing still gets some 'contact' deformity
Round host important too, for the rope arc can use all of tension for support (and friction control)
>> like stone bridge arc uses arc for all compression for load bearing
>>just rope is in tension, bridge compression
>>failing earliest in tension >>just makes stone better barometer to how arc(h) works and how well !
i hope my model of Zepplines, Hunters and B'Fly jamms suffices as
>>overly focused , dualled high load force matching as 2 massive bulls in the ring neither willing to give up ground, and no side releif
>>needs some kind of forgiveness, open side, misalignment etc. to not be too perfect, to not hold too well in such compressed quarters view

« Last Edit: January 08, 2021, 03:51:47 PM by KC »
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Here is my view of the disallowing of some rope fibers for various reasons in arcs and knots:

Reduction of the amount of rope fiber 'soldiers' to do same work of supporting against same work load,
Leverages more work to each soldier, in some varying ways.
i really like this web page, the century old pics i guess are legally for taking(?) but there is more than one to a single theme from this small port community, and they don't meet very often to answer my email..
The very first capstan pic especially to me shows important knotting concepts and positions:
>>could be rope pulling boat in with capstan, but is chain >>both part of flexibles class that is only rigid under load inline in tension direction
>>has linear SPart feeding into controlling arcs
>>linears only serve as extensions between input, output and controlling arcs
>>tailing ballast >>tailer man keeps system tight by taut ballast position
(other capstans shown terminate on capstan w/o tailer, can't be 'endless' and as turns stack they 'gearing' changes for less leverage)
Knots as other rope mechanics work majorly thru controlling arcs as this capstan.
>>and need final seize or ballast to keep rest of system in working mode/tight.
Knots are part of rope mechanics, and are ruled by controlling arcs.
>>Frictions is a most important part of rope mechanics of arcs
>>Frictions adjust the amount of compounding force at arc apex to host
>>as also control the amount of compound reduction of tension thru rope
Controlling both compounded increase against host and compound reduction of tensions >>BOTH!
>> Just as a pulley models what would happen in a knot arc if turned the volume knob for friction all the way down
>> Capstans/Bollards show opposite view of turning the friction volume knob all the way up inside of a knot!
The ability of these views expands things to be as other sciences where can vary single factor to monitor outcome.
>>simple rope tools of history are not separate puzzles, but rather separate pieces of same puzzle
>>to disallow them from view cripples comprehension with blinders to total effects and testing premises too
>>to be able to view them in their singled state out of know would be paramount in any other science
And so w/o pulley/bollard only delivers incomplete picture with only pieces of puzzle allowed.
Guess should mention no problem using my drawing as done by agent_smith. 
« Last Edit: January 10, 2021, 09:27:20 PM by KC »
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In bigger, over ruling sea of rope mechanics, think that are all arc controlled;
Knot Internals most controlling forces are also by arcs on small 'knot' island inside ruling sea of rope mechanics. 
>>but are not as intense as arc effects in force thru controlling arcs from linear force
>> capstans(metered pull)/bollards(metered relief) of tensions
(that are dependent on reductions to a ballasting tailer to maintain tension thru system)
>>and their reciprocal/antagonistic/other contrary side of arc forces revealed : pulleys (directional compounding)
These tools (capstan and pulley) do benchmark endpoints of reciprocal effects in arcs, encompassing knot arc usage
>>so that knot usage inherits hybrid mix of both reciprocal effects to varying degrees in all arcs
as how they handle compound force increase AGAINST host as also compound force reduction AROUND host
>>and examples of what happens if turn the 'volume knob' on frictions higher or lower than even can in knots
>>per 'setting' of volume frictions 'knob', to favor one over the other (capstan reduction vs. pulley compounding balance in arcs)
Capstan: study of force reduction   effects in arcs AROUND host (Capstan, Bollard etc. of excessive turns frictions)
Pulley   : study of force compound effects in arcs AGAINST host (reduced frictions end of arc force range)
>>amount of frictions volume determines how much of each effect revealed in each arc
>>as reciprocals of each other>>greater friction gives more capstan reduction dropping pulley compounding utility etc. in arc(s)
>>while reciprocally with less friction, less capstan effect >>lends to more compounding pulley effect revealed/expressed.
Round Binding is not EXTERNAL FOCUSED DIRECTION LINEAR input force to controlling arcs as in Bends and Hitches
>>for even if same knot used now to Round Bind >>INTERNAL DIFFUSED NO-DIRECTION RADIAL input already inside controlling arcs
>>All controlling arc tensions same until nip, no friction reduction thru so no capstan effect
>>nor any compounding effects against host like pulley from no focused directional linear/even radial 'glow' of force all points equal until nip

Must have ending ballast of some sort after force reduction(s) of controlling arcs from load input/imposed onto passive(but responding) rope.
>>Just as dynamically have with tailer on capstan metered tensioning line or bollard metered tension relief tailer position
>>only to a static /non moving knot (mostly), ruled by same arcs(thus ruled by degrees not distance) in same rope under same tension
Without ending ballast formed somewhere, rope would not load tension, as like electric circuit w/loose ground.
Even between position of arc input, rather than either end:
>>constant spinning/electric etc. capstan needs load pull and tailer/ ballast to load tensions to really do anything
2 points in opposite direction thru rope(load vs. ballast)  forces back and forth buffered/leveraged between by frictions.
>> controlling arc(s); as most potent frictional reducers using cosine and sine, compounding by degrees
>>vs linears  using only sine for controlling frictions and compounding by distance
(cosine is used against load, straight hang = full cosine, no sine = no frictions etc.)
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Ancient Greeks took this from cooking, that from merchandising, another from builders, still more from accountants etc.
>>and said this is all 1 topic called math as combined all individual understandings to 1 larger shared
>>then defined so much more from those views cross verifying and expanding each other into this more over-ruling, more tangible fabric of math
Math is the language of understanding and accounting for the differences in things
>>thus knowing more of 1 thing by comparing to another benchmark etc.
>>well enough to be able to explain and even predict outcomes.
If we extend physically against space or against physical force it is the same math of physical displacements for either
>>one can be understood, viewed, cross verified etc. by the other
Because these 'simple' maths are so pervasive thru all that they are consistent even in light, electric, sound, water etc. waveforms!
Working/load bearing ropes including knots as they displace against a load imposed are subject to these same things as all else.  Kinda abstraction layer of control to whole stack.
Sine and Cosine as their most minimal , consistent representation/expression as in all else:

As much of this is geometry affected, if not out rightly based.

These things apply to lines of force in rigid support objects, that are always rigid at room temp
>>or even in the special flexible class supports (like rope) that are only rigid/forge rigid under load
>>but only along length and in the tension direction along that length as only axis and direction can get rigid against load

They showed us 3 dimensions of space or loading, and to control against a linear dimension of loading
>>need at least some dimension to opposite direction
>>or the load will be outside the column of support of the device (on cross axises)

Thus, this is why i think we see at least 3 arcs in lengthwise loading in ABoK
>>The multi dimensional load (per rope support given) needs a multi-dimensional support system
>>to even properly get up to bat.
Looking at arcs as the ruling controllers of rope mechanics that knots are a part of
>>the greatest force is the directional compounding pulley force in the center of each arc
>>from these greatest forces against host (not around) , connecting the compounding center points
>>only gives true multi-dimensional support at 3 arcs

Even Killik has a 90 in and 90 out angles of Half Hitch to arc in final Timber
>>while also going around host at Half Hitch
>>the Half Hitch 90in90out itself gives some more inline linear architecture against lengthwise pull, as reducing forces and forming 2nd grab on load
« Last Edit: January 27, 2021, 12:55:30 PM by KC »
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The first image naming Uncrossed Turns >> Turn, Round, Round Turn(RT), Dbl.Round,Dbl.RT, Triple Round, Coil(link)
>> i offer Round for 360, so that add 180 Turn = 540 Round Turn
>>what i call out as Round, Dbl.Round, Triple Round are just place holders as less usable forms in working knots anyway.
Odd number of 180arcs usually seen of Turn(1), RT(3), Dbl.RT(5), Coil(7).
A single Turn of 1x180 arc in professional use to me is more of a purposeful pass of force, but then upgrade to 3x180 arcs RT get compounding capstan effect and expands to a 2D support framework geometry of 'footing' if relevant amount of force left at that point.  More arcs expand on RT to give more frictions and extend to greater 2D support framework possible.  Crossings on or off host pit the ropeParts accentuate the force reductions per their radial position from the input force directional axis (vertical, horizontal etc.)
The most effective points to place the 3 arcs is logically at most loaded point of just after most rawly loaded Standing Part (SPart)as Turns on host, frictions accentuated by Crossing/'frapping' turn on host OR around the SPart itself (as off host crossing)w/o significant previous force reduction on host.


So micro components for linear loads still persist as degrees deflections of 0(linear), 90(convert to cross-axis) and 180 (convert to opposite direction on same axis).
While more  modular component assemblies show as Turn, RT, Crossed Turn, Backhand Turn.  Final Nip forces, as other rope crossings, are dependent on radial position from the linear force input thru SPart.
The 180 arcs rule and control the linear force fed knots, linears in knots are just connectors to inputs, outputs and arcs. 
Just as an explosion in a container whether is barrel or manifold, is a 3 dimensional radial unfocused explosion force of all axises, then folded to focus and concentrate all that explosion to 1 axis, with 1 side of relief on that axis to provide direction of now concentrated,focused linear force; a linear fed knot does opposite.  Linear force imposed by the SPart as input feed, disperses the focused directional force to radial to control.  The co$t of conversion from focused linear input to dispersed radial controlling is friction which degrades both the persisting tension and directionality components parted out from the raw linear input.
"Nature, to be commanded, must be obeyed" -Sir Francis Bacon
We now return you to the safety of normal thinking peoples.
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