Yes. Abso-friggin-lutely, and Radial is always different than Linear is what Ancients tried to tell us so long ago!!
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Compound frictions(radial only) can work very hard against ye, or may be commanded under your employ.
Linear frictions increase more simple scalar; 2x as far = 2x as much friction just like 2x as much weight, 2x CoF, easy peasy, intuitive math, pre-geometry in school. All participants have equal standing in multiplier chain.
Always look for big differences in radial vs linear; in all ways. Linears vs Radials are commanded by and use, the pivotals of cosine and sine differently. *
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Linear only can command simple separate usage of cos/sine.
(cosine for load support or direction; sine as deflected byproduct for frictions etc.).
While radial can more easily in some ways use cos/sine together as one like in bridge support as does in rope, the compound frictions from seating to host in rope as the same science of numbers. Linear frictions will be (sine <1) xTension frictions then in more scalar progression. Radial Frictions more 1to2 xTension frictions then in more compounding progression. Linear ropeParts, very minimal sine multiplier the more purer the linear is.
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Clip below of spreadsheet
(full view), showing effects of compounding frictions as turns (arc180s) added, and in different materials for cross comparison. Also, formula for this broken down to it's logistics. It is called in fact the Capstan Theory, for yet another thing rope has taught us. Note the 'non-scalar' , more counter-intuitive WOW jumps in friction 'leverage' per arc180 as given CoF increases for several times. Then can also compare added 'pepper'/spice of higher/lower CoF. Both those factors are equally placed exponents of Euler's Number (as approximation of the logarithm of 1).
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All factors then are represented in friction model as a formula: a repetitive 1 for compounding base with exponent of linear CoF x PI x number of arc180s. That is the pattern, just raised then to the initial/input of xTension factor to then play the pattern out; ALWAYS same pattern. Compounding pattern, not all participants have equal standing/not simple scalar progression. Euler's number also used similarly for calcs of compound interest, population growth, disease spread etc. similarly, as is all very real math in our world, not some sideshow!
The logic of exponent classically is shown as linear CoF xPI_Radians(180 degree units xPI);
i look at it as linear CoF X PI as to now make a radial CoF, that could be a new table to reference of 'Radial CoFs',
then just take that radial CoF (that incudes PI already) x arc180s(as mechanical 'strokes') in some simplification, especially if always using same mated materials CoF.. Then that is exponent of Euler's log of 1 for the pattern, xTension for the multiplier gives compounded frictions.
Same math, no matter how name it to understand; maybe even remember the logic then.
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Same link as before to de-scribe:
source: International Technical Rescue Symposium (1999) The Mechanics of Friction in Rope Rescue by Stephen W. Attaway, Ph.D.
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Mated materials may have coatings, contaminants, glazings, wears etc. some discussion on if same CoF as stated sometimes.
The math and theory are sound tho, once get the right CoF i believe
>> "aluminum port-a-wrap. is that a bad idea?" thread
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The more common linear friction tables are an accepted standard in engineering circles etc.
engineeringtoolbox.com/friction-coefficients
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i picture a radial list(capstan) or linear list(rack) of arc180s as like competing arc180s of opposing directions (capstan is innie, rack outie equivalent force manipulation versions) as to like play ping pong with the force until it is 'gone' thru the recursive compounding frictions back and forth whittling away. Whereas linear can just only try to outrun the forces with lesser sine only frictions(usually less than the cosine) scalar, non compounding maths. Radial is a compounding powerhouse by comparison for frictions. Starts with more than sine xTension and then compounds! Would always urge to true/fine tune senses to the math when is correct. These larger machines(capstan, rack and pulley) more openly show what happens hidden away inside the microcosm of a knot with rope science. But then the reduced output tension reduces also rigidity, for fiercer nip crossing by a more raw, primary force of earlier rope part. This is favored to be 'expressed' thru radials rather than nip in more linear rope part for the same cos+sine seating logic used in frictions, nips and grips of rope controls.
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Roo's Notable Knot index has a great example and google calculation of using friction like a lever of 7#effort holding a ton; and links another usage with frictions for inserting board thru center turns and using board and rope as a pipe wrench.
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O, um, truly this is the shortened version
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* Cosine and Sine can be used to define ANY displacement against distance or force; in computing terms any layer that can define these dueling antagonistic twins(cos/sine displace each other as 1 grows other shrinks to still define the whole) would be as an abstraction layer to view the whole works at that point.
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i have own personal theory of 3 rope elements: linears, arcs 90, 180 to pretty much define all working/loaded rope systems and knots i believe, to tear down and understand. Or at least get great head start!
Finding it all is in the geometry of the support material of rope; just like anything else!
i think knot drawings get better and smoother ; as i practice what i preach(geometry) then on into drawings(even in internal and external shadowing by cosine patterns of change for more organic feel and depth) !
Still lots of Aha moments when getting new palmprint on the now increasing freely open forehead space.
www.treestuff.com
