Will a larger rigging ring always make more friction?

Location
SECT
We only use one size ring at work. Can tell a large diffrence in amount of friction when using a 1/2 inch rope vs a 9/16th. I know the rope diameter will make an increase in friction but if one was to use a smaller ring with 1/2 inch would that make more friction? From a smaller bend radius? Or is it just purely the larger the ring and the larger the rope the more friction?
 
Gonna go out on a limb here and say that the amount of friction you get is not only determined by the ring size/ rope size but by load (rope diameter decreases with loading), vector forces and bend angles, rope coatings and wear, etc. So probably, academically at least, not a simple calc. to get an exact number. But practically do we need to know the exact amount of friction to four decimal places and then apply a safety factor of 5 or 10 to the system? Probably not. So the old rules of up high, rings for lowering, blocks for raising/ tensioning? To "read across" from another rope user discipline - boat rigging:
This morning, my 2 cents.

Addenda (following AgentSmith post below): Assumption number 3 in the Wiki reference below is that the rope is "rigid" or non-elastic (not, say, Dynasorb with a lot of rope in the lowering system, hence more 'elasticity' for given loading??) for the capstan equation to be valid, that ϕ (the total angle swept by all turns of the rope, measured in radians) is known (as above in my comment), and that the diameter of the bollard/ capstan/ windlass is considerably greater than the diameter of the rope/ belt. In terms of the equation, the bollard size doesn't matter per se. Intuitively it would seem a larger ring (an orthotropic surface, as is a bollard) with larger bend radius should offer more friction, however, note that, if say a biner (which produces a sharper bend angle for given size rope) is used up top (as in a climber belay) instead of a ring or a block, the friction produced goes way up (as does stress on the rope)? So . . . does a smaller ring, again with constant size rope, then produce more friction not less (mindful of the bend radius of the rope under load and 3D "rule"or whatever, so it doesn't cut the rope)? The largest rope, into the smallest ring (that fits) gives the highest friction? Does rope size v.s. ring (bollard) matter only insofar as it may change rope contact angle? The Euler-Eytelwein formula describing this friction required modification, for example in knitting machines, where the rope (thread) and the bollard were the same size (citation below). Or is this a rabbit hole we don't want to go down? Capstan equation was cited other threads including one earlier this year I believe, containing a discussion regarding single ring or double ring configured slings - great discussion here too (and thank you TreeSpyder and AgentSmith).
Euler-Eytelwein formula modification
And a link from the past (see particularly, Gord from Gibson's posts perhaps): Archival discussion of Capstan Equation
Also, in sizing your system for load, it's good to remember that the load the top sees is ~ 2X and size rings/ rope accordingly (a good point stressed by Craig Bachmann in his rigging/ Treestuff video).
 
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Stumpsprouts

Branched out member
Location
Asheville
We only use one size ring at work. Can tell a large diffrence in amount of friction when using a 1/2 inch rope vs a 9/16th. I know the rope diameter will make an increase in friction but if one was to use a smaller ring with 1/2 inch would that make more friction? From a smaller bend radius? Or is it just purely the larger the ring and the larger the rope the more friction?
If you have a 1/2 inch rope and you run that through two different rings with different sized openings, imagine the change in surface area contact. The smaller ring will have a smaller inner diameter and more of the surface of the rope will come in contact with the surface of the metal. Whereas the larger diameter ring will not contact as much of the surface of the rope. Giving you a system with less friction.

my intuition is that the change in bend radius between the ring sizes will have more of a change in overall friction.
 

TheTreeSpyder

Participating member
Location
Florida>>> USA
When pull across a flat ground, have 2 directional forces: horiz travel to your cos/cause and 90 degrees sin across force of vertical to ground for friction mated against that surface also carried as work load. This is how most works as commonly seen, and eye L-earns. Then always does primary decode of view and gives brain that data.
>>So have Load pull as one function(cosine), and friction drag from cross force(sine).
2 separate systems, separately controlled.
Garden hose force as cosine for work thru core, pinch across as sine to control/ restrict full force passage. 2 Separate utilities , powered by separate directional forces, defined down to cosine/sine. The flowing force is the major, cross force minimal degrading interruption when nominal, as simple passage tax/dribble bleed. Until another force added, especially if it larger..
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Linear vs. Radial always matters so,...
Very counter-intuitively to the (now lyin')eyes, partially what Ancients tried to show;
Compounding arc frictions are calculated by degrees of host contact for Radials,
not distance of host contact like as for nonRadial / Linears. *

(Eye tells brain is same story, need to interrupt/retrain)
To that theory, a larger host drum stresses rope less, spreads out heat dissipation (and even more so if heatsink material), can be stronger host. Until host too small to function for seating etc. But gives same frictions per degree as smaller drum.
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Rope 180 arc, really different than other rope parts, just as 180 arc in any other support material architecture has very unique properties.
>>cosine also seats into the host along with sine for compound seating effect not seen in nonRadial.
>>load bearing cosine is the greater force, usually not seen in other rope seating's fully tho.
>>controlling frictions and nips greatly compounded, and some nominal grip
>>getting compound grip of 1D(imensional) w/2x180 opposing arcs,
>>2D grip framework possible with more 180s
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Pour plastic, metal, foam, water/freeze, cement etc. to force radial form, has specific key properties as a radial.
Rope is same, pour it around host form to get key radial shape, just maintain the host form during usage, as flexibles class/rope needs a rigid/nonFlexible, to work rigidly against a force.
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Calculating friction compounding they use same Euler's number (~2.72) as for calc compounds of : interest, population growth, disease spread, rust etc. very accurately.
So, 2.72(euler's) Raised to the power of Standard Engineer Friction Table for Mated Materials (for linear surfaces) then
Multiplied by PI (convert engineer linear friction value of mated materials to radial value)
and then multiplied by amount of 180s for 'distance' of multiple increments.
(or rather amount of times arcs reverse flow direction as a conversion, but maintain same power axis as a stability).
.
Ancient's stone arc(h)s so magnificent in size and weight bearing;
for the stone crumble in tension vs compression strength and the 180arc allowed all forces:
all of the cosine directness and sine drift to bear as compression w/o the tension weakness fail.
>>Rope, can't carry under compression, so same arc(h) now allows to reverse force
>>to use all forces, cosine and sine as tension in rope (rather than compression of stone) .
Totally using the the total force sum as control, in the 180 arc(h) bridge etc..
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At least that is my personal take after working this from this base for decades as math to explain the raw forces we deal with, witnessed and ushered:
Mechanics of Friction in Rope Rescue -Dr. Attaway
He takes this to rope brake pipe, fig8, rappel rack etc. with this radial friction concept.
then perhaps to My tables spreadcheat

Ring contact can be different contact footprint/sides than Linear pipe run,
>>but heavily radially influenced as above sciences i'd think.



* From a Linear force input converting to Radial control conversion loss
>>not seen in Round Binding controlling radial force swell as input into same radial control arcs .


i always wanted to start a myFriend Cosine thread back several boreds now/chicken out..
>>as most key concept base of rope and hinge; as any other physical displacement against space or force; but few to such raw force vs. simplest of tool to express these things clearer.
 

Dan Cobb

Branched out member
Location
Hoover
I can't say I've ever understood much from your unique writing style, but did note the article on Mechanics of Rope Friction in Rope Rescue was by Steve Attaway. I first met the Attaways 35 years ago through caving. Steve passed away in 2019 and was honored by Sandia naming their new supercomputer the Attaway Supercomputer in recognition of his contributions to their high performance computing program.
 

agent_smith

New member
Location
Townsville
Hello 'The TreeSpyder'.

I can see that you are very passionate and want to share that passion with others - which is a very noble cause - and I thank you for such efforts :)

Some feedback - which I hope you will receive in good faith!

When I read your post: I tried to make sense of the following words:
Garden hose force as cosine for work thru core, pinch across as sine to control/ restrict full force passage.
This sentence makes no sense (sorry).
Your use of the analogy of a garden hose and pinching across a trigonometric function to restrict flow lacks a reference frame within a defined coordinate system (2 dimensional versus spherical coordinate system).

And:
The flowing force is the major, cross force minimal degrading interruption when nominal, as simple passage tax/dribble bleed.
The use of the words "dribbling" and "tax", along with; "degrading interruption" (when nominal) makes no sense.
The reader needs a reference frame and a context to make sense of this in terms of the original posters question.

And:
Ancient's stone arc(h)s so magnificent in size and weight bearing;
for the stone crumble in tension vs compression strength
I do respect the ancient stone builders, but I find this concept awkward to apply to the original posters question - in the context of a rope bending around a metal ring.

...

In my most humble opinion, another way to try to answer the original posters question is something like the following:

A key concept is the 'capstan effect' - which mathematically describes the boost in holding power you receive from bending a rope around a pipe (ie some type of radius).

This boost in frictional holding power created by a rope bending around a radius is largely determined by the following three (3) factors:
1. The angle that the rope turns through (ie the amount of bending around a ring);
2. The coefficient of friction (ie, the frictional force that resists the motion of two surfaces in contact with each other - which in this case is the rope bearing against the metal ring).
3. The load on the rope (load causes the rope to flatten and press harder against the bearing surface).

Therefore, a larger ring radius will mean more contact angle as the rope bends around that ring. The original poster asked about "a larger ring"... I'll assume that he meant a larger radius (ie a much thicker/wider ring).

There is wiki web page on the capstan equation here: https://en.wikipedia.org/wiki/Capstan_equation
 
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Location
SECT
Well I appreciate the well thought out and researched answers. A coworker and I had this conversation and we came to the same argument of amount of surface area vs bend radius. So i decided to ask here and can't say I got a solid explanation. Sounds like a time for some good old fashioned anecdotal evidence. Any first hand experience out there?
 

TheTreeSpyder

Participating member
Location
Florida>>> USA
My experience over years hauntingly reflects the same patterns as numbers shown in Mechanics of Friction in Rope Rescue -Dr. Attaway also as i sift memory; and all i have written as i work with what i think i know, but am always looking to acid test it to break it/prove self wrong when opportunities present. And that even includes the smallest things in everyday life and play. i tried many 'shoes' that simply did not fit nor take far enough to figure out especially rope brake tools for this, and the paper was a true Natural fit for me. These things, models i offer, even explain to me why Half Hitch isn't to be trusted, why Pile, Sailor's etc. are special, friction hitches, rigging, 2/1 in pulleys etc, is all inescapably in model as much as i have thrashed it fully from side to side and it just pulls straight along that line.
All i write, has surpassed such gauntlets for me; of defining points i can't break nor sift down further(generally).
Or i would simply not speak so otherwise; over these decades here and preceding ISA 'bbs'.
.
your unique writing style
or lack there of!
Am immediately jealous of meeting the Doc; that has truly lit my way, enough to inspire to keep going as connected many points for me !
Agent Smith thank-you again for your critique efforts of my conceptualizations.
The wiki page you offer is fine, and does have the att_frict research paper as a source_2. But, i prefer the Doc Attaway research paper primary, especially in explanation and specific rope tools hands on real world aspect; along with the charting examples in 180 units as following the Natural radian PI directional form more tho, rather than than 360 increments of wiki chart. Belt Friction is only listed source above the research paper, and a very important comparative to my L-earning as well; including to the 180 increment base i think.
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i just try to offer the cross verifying comparatives, and how deep they go that illuminates this to me so well; as fairly would not have seen forward without same i offer; myself. Following examples/lessons of understanding voltage as water pressure, speed and volume etc.; so offer same. Knowing a few specific points is one thing, but grasping the whole connective fabric of logic, quite another to me. Including as a better grooming guide to knot/system finishing.
Working and understanding these things so rawly with so little against such large force volumes is simply one of tree work's greatest gifts to me, for all put into it, as truly a 'toughest job you will ever love' top contender.
.
Especially in awe when been told to us, by those dealing so simply with rawest of forces w/simplest tools too as us, but w/o our distractions. Millenniums ago; the keys given already that even command the stars movements as all else! Understanding as all about the same electrical schematic of flow inside of different externally visual dressings people might try to sell you; i try to squint past to tune into the same root principles inside to weigh and measure by the less visual. Finding, aligning, and compounding the few pivotal points is how most of this works; following rules is how it is commanded.
.
To me, so much written of wonder of arc(h) in so many ways; especially in dealing with stone tension weakness to command HUGE things; would seem shame not to mention/link to that knowledge bank in presenting parallel/yet connected wonders it verifies in rope arc; as i try to lend the view at just what kind of animal we are studying. Anything less would shortchange just how unique arc is and why can trust that so; the depth int permeates thru all things.
.
The root concept here is model of rope where cross force sine is the controller of force friction is applied against host; and is a lessor to the major hold force down length of rope against Load. So, force passage thru from 1 rope slice to next, there may be a small, nominal, trace, dribble of tax for passage to next rope part by light sine press to host in nonRadial.
Model: "Wages of Sin(e)" as a side tax shearing across your work as Samson to pillar:
Sine-friction-across-rope-length-gives-nominal-friction-control-against-host-until-compounded-in-arc-or-corner-direction-conversion-8bit.png

.
The real rope control force as we know it is the much greater COMPOUND seating; of lessor sine now INCREASED in arc AND major cosine now works ALSO to seat to host frictions too!! In fact now using all tensions in rope for friction, when usually nil to nominal from tension force for controlling frictions on linear/nonRadial parts(even on radial host) offered in cross force sine then for Load control. It does this at arc as a long RANGE of conversion/interruption of force flow to new direction. On linear faced host(4x4) ; a corner conversion of direction on Linear face does give this as more of a POINT of direction AND axis change/directional force conversion. Then continue to next corner with minimal sine/contact force across between. Rope 180 arcs/radian Pi arcs convert direction, but maintain same power axis in contrast to a linear part direction change by degree to new direction and axis. Different game.
.
Radial friction is totally different(as in all things radial is different) ;
than Linear friction that is more simply calc'd by distance of contact as eye relates.
Radial friction is calc'd by degree, not distance of radial contact; cosine/sine is decoder key, to what eye thinks sees. Clock i've shown for cos/sin/tan numbers; is my decoder ring of angles and values mnemonic. Always with me, for all things. Driving forward is cosine, throwing to side some on curve is sine; you can feel what the numbers say to key in more, especially with decoder ring handy in head. That and other mnemonics thrown out(cosine='columnsine, cos is support, flow direction to your cause, sine the sin across, Samson angle on pillar) i could not have fully wrapped head around without as common life guides to see all around what did not before(so seek to offer same bridging fairly). Then see easier in rope and hinge as focus back to that.
.
Host is the key form passed to the rope architecture just as a form for plastic etc. allowing arc properties. A radial host, allows radial structure of rope in some or all parts. Linear faced host does not allow even the option, only corner concentrated points of conversion; not arc gradual for increased to real frictional control over Load running down core of line, from the frictions achieved across the same line to host.
 
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treesap

Participating member
Location
east TN
My experience over years hauntingly reflects the numbers as shown in Mechanics of Friction in Rope Rescue -Dr. Attaway also as i sift memory; and all i have written as i work with what i think i know, but am always looking to acid test it to break it/prove self wrong when opportunities present. And that even includes the smallest things in everyday life and play. i tried many 'shoes' that simply did not fit nor take far enough to figure out especially rope brake tools for this, and the paper was a true Natural fit for me. These things, models i offer, even explain to me why Half Hitch isn't to be trusted, why Pile, Sailor's etc. are special, friction hitches, rigging, 2/1 in pulleys etc, is all inescapably in model as much as i have thrashed it fully from side to side and it just pulls straight along that line.
All i write, has surpassed such gauntlets for me; of defining points i can't break nor sift down further(generally).
Or i would simply not speak so otherwise; over these decades here and preceding ISA 'bbs'.
.

or lack there of!
Am immediately jealous of meeting the Doc; that has truly lit my way, enough to inspire to keep going as connected many points for me !
Agent Smith thank-you again for your critique efforts of my conceptualizations.
The wiki page you offer is fine, and does have the att_frict research paper as a source_2. But, i prefer the Doc Attaway research paper primary, especially in explanation and specific rope tools hands on real world aspect; along with the charting examples in 180 units as following the Natural radian PI directional form more tho, rather than than 360 increments of wiki chart. Belt Friction is only listed source above the research paper, and a very important comparative to my L-earning as well; including to the 180 increment base i think.
.
i just try to offer the cross verifying comparatives, and how deep they go that illuminates this to me so well; as fairly would not have seen forward without same i offer; myself. Following examples/lessons of understanding voltage as water pressure, speed and volume etc.; so offer same. Knowing a few specific points is one thing, but grasping the whole connective fabric of logic, quite another to me. Including as a better grooming guide to knot/system finishing.
Working and understanding these things so rawly with so little against such large force volumes is simply one of tree work's greatest gifts to me, for all put into it, as truly a 'toughest job you will ever love' top contender.
.
Especially in awe when been told to us, by those dealing so simply with rawest of forces w/simplest tools too as us, but w/o our distractions. Millenniums ago; the keys given already that even command the stars movements as all else! Understanding as all about the same electrical schematic of flow inside of different externally visual dressings people might try to sell you; i try to squint past to tune into the same root principles inside to weigh and measure by the less visual. Finding, aligning, and compounding the few pivotal points is how most of this works; following rules is how it is commanded.
.
To me, so much written of wonder of arc(h) in so many ways; especially in dealing with stone tension weakness to command HUGE things; would seem shame not to mention/link to that knowledge bank in presenting parallel/yet connected wonders it verifies in rope arc; as i try to lend the view at just what kind of animal we are studying. Anything less would shortchange just how unique arc is and why can trust that so; the depth int permeates thru all things.
.
The root concept here is model of rope where cross force sine is the controller of force friction is applied against host; and is a lessor to the major hold force down length of rope against Load. So, force passage thru from 1 rope slice to next, there may be a small, nominal, trace, dribble of tax for passage to next rope part by light sine press to host in nonRadial.
Model: "Wages of Sin(e)" as a side tax shearing across your work as Samson to pillar:
Sine-friction-across-rope-length-gives-nominal-friction-control-against-host-until-compounded-in-arc-or-corner-direction-conversion-8bit.png

.
The real rope control force as we know it is the much greater COMPOUND seating; of lessor sine now INCREASED in arc AND major cosine now works ALSO to seat to host frictions too!! In fact now using all tensions in rope for friction, when usually nil to nominal from tension force for controlling frictions on linear/nonRadial parts(even on radial host) offered in cross force sine then for Load control. It does this at arc as a long RANGE of conversion/interruption of force flow to new direction. On linear faced host(4x4) ; a corner conversion of direction on Linear face does give this as more of a POINT of direction AND axis change/directional force conversion. Then continue to next corner with minimal sine/contact force across between. Rope 180 arcs/radian Pi arcs convert direction, but maintain same power axis in contrast to a linear part direction change by degree to new direction and axis. Different game.
.
Radial friction is totally different(as in all things radial is different) ;
than Linear friction that is more simply calc'd by distance of contact as eye relates.
Radial friction is calc'd by degree, not distance of radial contact; cosine/sine is decoder key, to what eye thinks sees. Clock i've shown for cos/sin/tan numbers; is my decoder ring of angles and values mnemonic. Always with me, for all things. Driving forward is cosine, throwing to side some on curve is sine; you can feel what the numbers say to key in more, especially with decoder ring handy in head. That and other mnemonics thrown out(cosine='columnsine, cos is support, flow direction to your cause, sine the sin across, Samson angle on pillar) i could not have fully wrapped head around without as common life guides to see all around what did not before(so seek to offer same bridging fairly). Then see easier in rope and hinge as focus back to that.
.
Host is the key form passed to the rope architecture just as a form for plastic etc. allowing arc properties. A radial host, allows radial structure of rope in some or all parts. Linear faced host does not allow even the option, only corner concentrated points of conversion; not arc gradual for increased to real frictional control over Load running down core of line, from the frictions achieved across the same line to host.
what do you use for making these diagrams if I may ask?
I use MS paint, GIMP, and Krita mainly, but these diagrams are MUCH nicer than anything I make on the listed programs
 
Kudos Spyder. I would love to see a Mech Eng dissection of this (incl video) with various rope types esp such as Teufelberger's rope where they core and cover are "fastened" together to minimize milking (forget what the name was). A TreeFund project Mark?
UK HSE project?
A progression - a tight bend like a biner to two rings like a false crotch to a small ring to a large ring to double rings . . . .
And then there's complex folding and sheath friction as in a Munter.
A fascinating area.
And thank you for also sharing your spreadsheet TreeSpyder.
Cheers from the Great White North - N of the 49th!


Addenda 2 (after some single malt): "Will a larger rigging ring always make more friction?"
Clarity: the quality or state of being clear
"Nope"

:)
 
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JeffGu

Been here a while
It seems to me that the correct ring size is the one that offers the best bend radius to the rope, and that the amount of friction offered to the rope is only a minor consideration.

I say this because worrying about the friction of the ring would indicate that no control friction is being used at the ground. Since the biggest variable is the weight of the load, which is a "guesstimate" on the best of days, and the friction of the ring (or rings) is fixed for a given rope size and load, you can only ever hope to control the friction for a very narrow range of loads without physically changing the ring friction in the tree (by adding or subtracting rings).

I have used rings to shift some of the friction to the TIP, but I always used a friction brake below for controlling the load. I've seen people manage without this, but it never struck me as a great option, especially if there are targets or contractual conditions that require minimum or no damage to the landing site.

Either way, I'd be a lot more concerned about rope longevity than I would about trying to achieve some ideal amount of friction with a ring. Having said that, I have used an in-tree device (like the Rig 'N Wrench) in conjunction with a ring when I wanted to shift the load range of that device up a bit by adding additional friction to the system. Of course, this works well only when the range of loads is in the light to medium range.

Just some thoughts. The OP didn't actually mention whether or not the ring was being used in conjunction with a variable friction device.
 

TheTreeSpyder

Participating member
Location
Florida>>> USA
Fair enough; but as a support consideration of devil's advocate:
any frictions reduce doubling/pulley effect loading potential of support (to more nominal of load only)with immediate/conversion co$t friction at redirect so less force is broadcast further down control leg pulling on ring that would give redirect/2x potential on the forceline of my cause/cos(anti gravity) X speed of vertical hit squared(E=MCsquared). So friction at redirect is part of hit buffer and follow thru. Also, as another friction point can sweat span
(To lesser consequence more spread frictions heat between total friction points.)
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Ghostice yw, greetings from the Eastern Green Tip:Florida (confession: we occasionally skip legally required 3 days of winter minimum, sorry if you must make up balance !)
Rope construction in my head(beyond braid or not etc) is to where/how the force is carried (inner, outer ropeParts), physical neutrals, state of contact area (load carrying or not) and how disjointed the load carrying parts are, but then need to be in flex. Especially the force carrying parts, for always watch force, but then in twist/paradigm relief of force is a force of power of yield in it's own to watch too.
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Radial vs. Linear faced objects are so key to everything physical, they are only basic drawing tools besides line on many drawing tool pallets etc. everywhere.
i use old version vector Flash Macromedia>> eventually Adobe, their Illustrator vector drawing may be similar also. Wanting to show stuff in head over came never being able to draw.
Games and other Virtual Realities look fakey; don't pass eye test, so not as 'immersive' unless shadowing by cos/sin scales for gradient slide/reduction to no shadow, the term used is 'organic' for the look and FEEL of the proper shadowing to fool eye. Even the moon phases are cos/sin as other astral movements that cos/sin were originally drawn from (no cable yet for tv, so Ancients watched other type stars instead).
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If hang weight on rope from hook; hangs at cosine 1, no sine/ thus no friction etc. control. Shear across with would be host into loaded rope line of forces some; is an interruption in this calm force flow. To steal another word from another field for this, i find radial to be most 'organic', Natural, easy flowing interruption in this force flow, that even Mother Nature uses... Linear, nonRadials hosts have 'harsher', more dramatically impacting interruptions of this force flow that radials finesse so deftly well, Naturally, organically...
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180arc is a most unique, nonLinear deformity in any material, that rope is simply just another material of. In 180 arc BOTH cosine and sine can be used as 1 is part of architecture geometry ; in rope used on direction conversion but back to same power axis thru the whole 'organic' change. Arc is as 2 parallel column pillars, but 'organically' blended at top to trick this out i think(is Corbell if more like 2 pillars soft list together and piece on top, w/o keystone force pass in arc apex). Non-Radial, Linear host change to another face in rope is change in direction of force flow, a drama of conversion no matter how minute the change, is a power axis change. Round host, seems to change direction so gradually, subtly, organically; that it is more stable against the power axis change, so makes arc keeping same power axis until 'flips' to same power axis, opposite direction on that power axis (vert or horiz etc.); or until sheared across at 90 degrees of cosine0 of initial power axis, then that new axis becomes reigning power axis from there. Otherwise, very stable, non changing axises thru smaller changes in direction that are constant in circle, when would be more 'disruptive' for same minute direction change in linear faced host. Kinda 'covenant of the arc' to me i always thought/if i may.... Curiously Babylonians that gave clock, degrees, calendar etc.(many, many things attributed to Ancient Greeks and Romans) stole 'Ark of the Covenant' from history.
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Pivotal basics span out to cover more than individual points as actually better than pareto in distance covered per investmeant!
In the end , pivotal basics truly less to know; but to command more in the layers that pivotals broadcast to/thru of more tangible(tangent) fabric of related and connected, now logical patterns to grasp vs. single elusive point(s) that seems to keep slipping thru fingers here and there...
To me, Leveraged L-earning, of max from min.



edit: drawing reverse coloring, gradients, layers, to look like weave (pic)
 
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Bart_

Participating member
Location
GTA
Here's a twist on rigging rings. In some other thread I posted a half request/invitation for someone to make a nice diagram of SRT redirect friction. I eventually did an analysis in the Base Tie SRT TIP forces thread, titled SRT redirect forces Corollary or something like that.

Turns out that adding another (2nd) rigging ring is the same as redirecting your SRT line. Instead of a 180 degree rope turn at a single ring, you divvy out part of the 180 degree bend to a second ring. The lesser bend at the original high ring drops its friction (tension loss) by precisely as much as you add by passing the rope through the second rigging ring.

So adding rigging ring redirects just redistributes the same friction, it doesn't add more friction.

ASSUMING you don't add in sideways path changes which would make the system like an overgrown petzl zigzag. This only works out for a clean, planar arc rope configuration. Arc meaning like fishing pole, simplest "arc" being a single extra ring besides rigging tip.

Who'da thunk !

I still need to measure the trueness of the bollard equation vs rope thickness effects on tight bend radius. For now I'm presuming it to be true, holding rope thickness and bend radius constant.


Oh, base tie tension equates to rigging control line tension, if that wasn't picked up on.
 

TheTreeSpyder

Participating member
Location
Florida>>> USA
The collective arc frictions that are compounded;
are counted in 180increments,
but this pivotal work shows can be cumulative sum,
not necessarily whole 180arc counts required in that count.
The Mechanics of Friction in Rope Rescue -Dr.Attaway
In my words:
Even as linear list/series of arcs on a rappelling rack etc.
>>as opposed to radial list/series of arcs on round host
.
In my mind this spread 90s to make 180 can give less harsh/more efficient bend especially on small host, and spread out frictions as well;
which is more important doing this around branches heat insulator, than metal heat sink as host.
The roundness of mated surface host is key tho still.
.
theory:
The raised frictions are in the deformity from simplest 1D straight line.
This can be around a corner as a momentary major frictions in linear face host like 4x4;
or dispersed more Naturally, organically as a softer changing gradient on a deformation in arc.
Linear rope parts, even as applied on radial host give only nominal if any frictions from any trace sine x tension only.
Frictions on deformity, like arc or corner, are full bull, all tension forces used for frictions,
>>(cosine x tension) + (sine x tension) power controls of frictions, nips and grips
>>ONLY on deformity.
Then the frictions and nips are compounded,
>>but nominal grip(sine powered only) like across 90s of a 180 arc
>>until compounding grip w/opposing deformity/to other side; like 2x180 arcs opposing.
3 opposing arcs giving increasing from a simpler 1D compound grip to a more 2D support structure
>>more equipped now to take 2D pulls along the host, as it also grips across host
Like a Killick pulled across host has applicable structure to be 2D support if needed but still a 1D pull
>>pull same along host and is a 2D force, with 2D structure available to work against
>>that a Timber Hitch alone would be a 1D support structure, faced with a 2D Load pull along host
(while must also grip 90degrees from along host to also across host).
 
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