Decoding Patterns of Forces

*useless info*

Well-Known Member
i play with numbers on computer,
to verify, decode, extend etc. understandings to functional models
>>so need for math under fire>>have model references, few benchmark numbers , flow of pattern and sense of what is right/wrong building
But, also, to pick apart things to see if that is what i've been reading into them to true that sense;
>>like trying to align my sense of things to their assured actualities
>>to then be able to read and push ahead more confidently.
The new, re-verified sense of aligning most correctly it's own driving force
>>more intentfull , purposeful, non-stalling, confident driving force flow>>clean, not necessarily racing efficiency
>>others follow more easily >>especially when working so well
i always try to find fitting in big picture, partially for cross comparison to understanding AND cross-verifying checksum
>>another way to do this is buy playing it backwards; many solutions like cheating on a maze, found in strategy alone, let alone getting to target of parity check of each some debit/credit against the other
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Thus, so powerful to me, when find true pivotal key to many questions at once.
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Spreadcheat purports to show Porty etc. brakeForce per half turn, frictions inside of knots etc., and controlling forces of friction hitch over host lifeline etc., also why dyneema etc. are hard to knot,
>>and makes point if same rope and round host mount( materials)
>>ONLY change in turns adjust such a friction force
>>NOT change in rope nor host mount size/friction path(for round on round)
>>larger pipe or branch host mount is for strength AND softer rope arc >>not friction increase
Guess friction is .25 as start point>>remember 3/5/7arcs(half circles) gives ~10/50/250x hold leverage over load as brakeForce and how pattern accelerates (to drop quick on low end, or other materials) and should be golden!
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>>for nylon on aluminum brake (.25 CoF) for 3half circle arcs 540degrees(RT) on Porty etc.
>>hold 100# @10.55x leverage(per chart) to control load of 1055# etc.

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Many, many explanations and distinct pattern here.
i've never seen a chart like this, especially of such cross comparatives of verifications and of lessons to big picture too.
Sheet is all setup to self calculate if anyone has other friction coefficients or degrees of contact questions; would be nothing to add to FREE google.sheets
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Friction coefficients are a set few tho of accepted, engineer stated chart that is much all the same everywhere.
>>but the number can be a guess or interpolation to test!
Once again, root work: jrre.org/att_frict.pdf showing for friction brakes in rescue
 
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*useless info*

Well-Known Member
That is what i felt like for years chasing this, knowing numbers seen here and there reflected what experienced with Porty, wraps on tree, knots etc. but pattern so elusive had to peel deeper to see rhythm thru math.
Hoping i've taken most of the heavy lifting out, for this defines so much of very pivotal points.
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This is how adding an extra turn or 2 on Porty, above what already have
>>can save or ruin day, and only counting in half circles as radical exponential growth is incurred;
As real, load controlling, possibly lifesaving, better explaining and that is actuality are really watching and can help align senses to (i think) once can name and recognize to read/know better and much more re-affirmed etc.
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Guess should save my explanation of my minimization of math to exemplify only factor that changes to change friction are the half turns, rest become constants in formula if same round materials.
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To be clear, common Turn w/Half-Hitch has only 1 half circle, not 2 of this exponential math and intense Nip.
 
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*useless info*

Well-Known Member
How work got done:





2nd pic harder to see it, but tailer sitting on ground pulling rope right.
Back in the'day, would have known to look for tailer in pic
>>things like this are about all that remain of this art of power.
Perhaps not many beyond our own kind would be up to this,
>>let alone understand it in today's world!
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3rd pic shows bollards; also non-spooling for 'endless line' like capstan
but a fixed, also non-spinning drum for brakeForce.
Simply capstan controlled pull in 'purchase' of line, Bollard the Equal/Opposite controlled pay out of line.
 
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Birdyman88

Well-Known Member
I think the exponential nature of the behavior has to do with the fact that the load itself is acting in two manners in the system: 1) first the loads acts is to break the static friction of the rope/porty to achieve the initial motion; 2) to provide the force to that actually determines WHAT the static friction force actually is. Generally, in a flat linear system, the weight of an object and the coefficient of static friction determine what the static friction force is that has to be overcome to move the object; and, a second (independent) force is what acts to move the object. That is not the case here. In this example, the load does both. Anytime you have a system like that, you sometimes get into a feedback type situation which results in the complicated math.
 
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*useless info*

Well-Known Member
i've not been to school for this, and trying to get right base pattern thanx!
>>of course anything is going to take more to init movement than keep it going any here can say.
i actually kinda expected to see a bit of what you say from my collective understandings researching many yrs.
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EngineeringToolBox.com is a reference standard, and the chart of CoF's appears same on it as elsewheres. But they downplay the init-effect some, and say in average it is in the calc. To me, no matter, trying to sift pattern and handful of benchmarks as relevant filed guide in head etc. can accept and go with more to bump-start than maintain model seen in all. Only the Dyneema and extended .2 to .4 nylon sling CoFs are only CoF's not on this standard list, and found them at manuf.DMM site.
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i think rope knots/rigs are ruled by straight lines and half circle arcs. Actually, scrutinize looking for slanted lines, and assume straight happens here and there, so is slant of 0degrees. So think, cosine/sine and capstan maths rule, next would be elasticity and abrasions(not looking at taking that far).
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For our ropes and usages, a single arc Turn is just a hook, not grip, not serious friction reduction of load force, more of a passing of reduced load, w/o grip. A Round Turn (RT) 3arcs turn to me is real working man alternative and power rating with the grip. And whose friction reductions would now show as grip on host for 2 utility functions from same property.
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This view of sheet, takes the 10.5 force reduction of RT of nylon on aluminum pipe att_frict.pdf shows as .25CoF as a benchmark real working hard working/usable mechanic, and compares in various material CoF's as a pattern to sift and understand more by.
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Re-affirming so concretely, how much more 'frictive'(knudeKnoggin again) hemp was/is (shows compared to wood) and how slippery Dyneema/UHMWPE (stronger than Kevlar) is almost slippery/hard to knot as Teflon! Spreadsheets can be jsut a flurry of a bunch of numbers, until can float some patterns out!
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round-turn-exponential-brake-force--compared-in-different-materials.png
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Legend has it in our lore, can be injured or killed from too many wraps/half arcs, by employing too much BrakeForce with these methods. RiP pioneer/scientist/contributor/benefactor Peter S. Donzelli . So, any amount of half circel arcs can be not enough or too much, but in our ropes going from 3arcs to 5arcs and on is a big change, to be heavily 'weighed' i'd think.
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i always tried to look at turns and describe knots and mechanix as definitive. This has re-affirmed that so much as to start over and show knotting start, really focusing on counting the half arcs(and smoothing slants) to l-earn and define.
 
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Birdyman88

Well-Known Member
A simple way to look at it like this. Imagine increasing the load. This will increase the force of the rope against the pipe, which will in turn increase the static friction force. It will also flatten the rope more creating more surface area contact, which in turn will increase the actual coefficient of static friction itself. BUT, at the same time, the very load which is doing all of this is also trying to break the rope free. This interaction can be described by a mathematical function, at which point we call in Russell Crow. So we have the force acting on the system, which is one variable; second we have the force acting to create the static friction, which is another variable; thirdly, we have a flattening phenomenon which is yet another variable. BUT, in this case, each of the three variables is dependent on THE SAME THING - the load. One variable acts to move the rope, and the other two act to keep the rope stationary. This tug-of-war in the math can result in some tricky equations. But one thing is for sure, anytime you have the same input (the load) acting in multiple variables in the equation, you usually get some math that is not linear. At the very least, I would expect it to be a x-square relationship, but it appears mother nature intervened and brought in Euler's number.

Hey, I was just curious if that spreadsheet is actual measured numbers, or if it was calculated? If the latter, then you can get into the sheet and find the actual equations.
 

*useless info*

Well-Known Member
Wow, thanx!
These 'extras' would be more to exponent of loading/'aggravated to flattening etc.
>>am still thinking that capstan equation shows base pattern, to just align to proper benchmarks in actual scenario. And to these models, a'lil extra help is just a safer model that bluffs low, not high.
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Spreadsheet is calculated from base capstan formula found all around on engineer sites and highlighted in att_frict.pdf. Then checked calls against same. i can send you google.sheets link when get home, there is 'flat' CoF's, then sheet for 'radial' CoF's shown above and RT sheet shown here; all locked. But also play area/unlocked sheet can alter half circle/radian arcs or CoF's and hit ENTER and sheet re-calcs. If someone else wants to peek or play(not like that Rico) with sheet, can PM me, just don't want to publicly post open sheet on my acct. Free google docs with google drive, including excel type spreadsheets (and form maker that fills spreadsheet from football pool etc. ) are FREE awesome tools!
 

Bart_

Member
Thanks for the big reminder take away that bollard friction generation/multiplication is not linear with wraps; it's exponential. Explains the huge jumps on the BMS belay spool. I'd completely blanked on the actual bollard equation lately and started thinking it was linear. Kudos.

Years ago on a project a small line drove a mechanism and the change from bushing pulleys to bearing pulleys made/broke the system because the friction cascaded; the first bit affected the next and tension skyrocketed after about 5 stages. Same idea, force makes normal force makes more force makes more normal force makes more force etc cascading. It was really eye opening at the time.
 
per *useless info*
Spreadcheat purports to show Porty etc. brakeForce per half turn, frictions inside of knots
Except that this approach fails when applied to non-jamming knots such as the Zeppelin bend. This 'bend' remains jam resistant right up to its MBS yield point.
I would also comment that in all of the primary Bowlines based on single or double helical nipping loop, the clamping power of the nipping loop overrides any potential capstan effect of the collar performing a U turn around the Standing Part (SPart).
Evidence of this can be found in the collar of a simple (#1010) Bowline while under load - it can be moved - which indicates that force is not evenly propagated across al rope segments in a knot.

So in my view, looking at 'turns' inside a knot structure is not providing a holistic interpretation of how force is propagated in and around the knot core.
 
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