Thanx Struktor! i understand a graduated/piecemeal arc to make larger arc and then also linear list of opposing arcs like rappel rack for this, just not that 2x45 going over rocks as
att_frict research paper shows near end, to be then half the friction of a 180. A 90 itself would have apex forces of 1.414 w/o friction, a 180 would have 2 such 90 positions, but also a 2x at apex seating into host' proven even in knots by best nip there, but not in 90 etc. Similarly don't see how can show same brake force around a 4x4 of 2x90 contact as equal to 180 frictions, but still squinting and reaching for it..
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This wiki article on the capstan equation may also be helpful:
Link: https://en.wikipedia.org/wiki/Capstan_equation
(note that angles are measured in 'radians').
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This really mathematically matches the
Dr. Attaway paper that wiki uses as it's second reference, except the wiki table is shown in 360degree counts, but table in research paper is in 180degree counts more in line with the radians base both use in same formulae. The only previous reference in wiki is a fan belt example that the paper and i both show as the directionality and pruf of the concept as an important point to viewing all this. Radians is more proper than degrees here, and the capstan theory is built on amount of Radian PI's x frictions of the mated materials as exponent to Euler's Number(~2.72 as Natural log of 1, that is even called the Natural number in math).
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Ancients rounded 365.24(total amount of nights for stars etc. to form circle*) to 360degrees simplification fitting into their base60 math as slight, but inherent error not found in radians concept. The degrees can be found on the clock used also for time and calendar, thus my shortcut between clock and degrees is a rounded works thumbrule for more quick realtime decoder reference outside lab tools/guesstimations on the fly that i have L-earned much from and so offer.
*So we have leap year every 4yrs, EXCEPT if that falls on a century mark UNLESS century mark is divisible by 400. So Y2K gets a leap year but not 1900 nor 2100 to keep calendar inline with 365.24 stardate(Star Trek) over time/not always immediately.
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Although in the context of the title of this topic thread: "Naming rope parts as components in a working support structure/architecture"... there hasn't been a lot of actual naming of 'rope parts' (as far as I can see). For instance, at one point, a lot of attention was given to mechanical advantage systems.
Actually the Turns listed in the first post is example of easily seen components, then 3rd where tried to expand on that etc. as went along from there broke down deeper into the individual elements of arc 0,90,180 that comprise the components singly or in groups. Then expanded back out to HH etc. Thus the HH w/degree markings each one is a component of single element, all 3 possibly viewed elements represented in the HH example. All the attention to 180 arcs to show how see this etc. and many examples of similarities and contrasts. To go by how the architecture sits in Sheepshank during USAGE, not how it was made etc. to weigh and measure by , the 2x90 not being same as 180 to differentiate. All this is to the architectural structural part as show the geometries that have been discussed, hopefully seen as keeping within title.
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And yes, how this carries into pulleys etc. because i think rope mechanix are rope mechanix and as such are found in knots, not evaded by them. An arc around a rope just has friction dialed up higher than pulley, but to same force pattern mechanix as in any other material. Besides in Trucker's, Poldo dynamic/moving knots i see this effect even in static Prusik etc. to grip from either side from both center pulls. Just like would be in a non-moving Trucker's still holing pressure tho. If we made a Prusik around 2 spread drums (and keep rope parts from crossing each other)mounted as pulleys and drew them together, the Prusik would have MA and same contact area/degrees(as on 1 drum) as the inner sides of the 2drums not used in 2 drum build. Drums get squeezed together, rope contacts only on outer sides still. So for Prusik on single drum i simply see both RT halves of the form as the same early 2 drums; just already squished together by each 180 turn element, but the force not stopping to do so/wants to persist. This becomes the grip instead of pull(just as top apex 2:1 is also best nip), what would be anchor and output mounted pulleys and pressures are now grabbing to either side of the host etc. on into other forms. The rope just works, w/o realization that both the 180 rope contact faces are drawn/squished together already or not, the mechanix still seek to play out blindly. Just as if the drums spin but not move towards each other, the force pattern would still persist. Stop drum spinning increases friction, that same force pattern simply degrades more thru.

This shows more of how the linears between spread drums just pass force, but the working, force using and converting type components are the arcs. So same examination with or without the straight legs between the 180arc elements; the arcs still pull towards each other, just cant translate to displacing space until single drum crushes or duals draw together etc. The linear stretches between 180s don't matter if exist or not, are just force passers, not so much converters. In an electric schematic they would be wires, just force passers with perhaps some nominal resistance to passage of force, but not a working, converting component like rope arc or electric diode.
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As far as naming, the 180arcs are elements to me, so can be a single element as a component can track thru a structure, or see each side of Prusik as an RT component once affirmed completely understand RT to see and track as a component confidently thru other forms. So trying to get the base pivotals rock solid, to roll forward.
There also appears (at times) to be significant attention given to trig functions...
I am of the view that the underlying meaning and purpose of trig functions is being applied incorrectly to the "naming of rope parts" and indeed to knot structures in general - ie 'KC' appears to assign the cosine function to straight segments of rope? In my view, this is incorrect. Trig functions are not forces or vectors per se, and they are derived from the unit circle (in planar 2D coordinate system).
i think in a dynamic/not just static setting of cosine as thee benchmark line in a scenario, that it is very powerful to use the force line if linear, or the receiving column of support if linear. In either case it is the same angle of deflection as measured to or fro from either. i try to show this from the ruling force perspective into passive elements with water, pennies, columns, hand push (as paper does),rope etc. and would hope the 3 links shown mite validate that view some also:
http://courses.lumenlearning.com/physics/chapter/7-1-work-the-scientific-definitionhttp://sciencetrends.com/the-formula-for-work-physics-equation-with-exampleshttp://drijal.com.np/2021/05/why-cos-theta-is-used-in-formula-of-work-done.html.
Knots are 3D objects - and therefore, spherical trigonometry would be more appropriate (in terms of trying to assign vector quantities to various segments within a knot structure). Link: https://en.wikipedia.org/wiki/Spherical_trigonometry
i agree that knots are visually 3D objects displacing against space, but that blurs for me somehow forcewise trying for 3D primary displacement against force.
i think that rope would have to be rigid against on it's cross axis to break from cosine/sine 2 elements to extrude 3D primary
force. i see rope turns and pulls at right angle on host to grip as 1D, then ABoK's lengthwise direction along host as another D for total of 2D, but not extending off host towards reader with primary force that is 90degrees to both of those 2D's functions , or i'd look at it as a separate system in the flexible material that can't resist on the cross axis especially on round host.
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In terms of rope tension as it turns around a pulley sheave, it is usually assumed (for calculation purposes) that the pulley and rope are massless and the sheave is ideal (no friction). In a real-world situation, we know that a pulley is not massless and there is friction.
In an ideal pulley, tension in the rope is the same either side of the sheave - it is uniformly distributed. But the net force acting on the pulley = 2T.
Interesting explanatory link here: https://physics.stackexchange.com/questions/550501/why-is-force-on-a-pulley-two-times-the-tension-in-the-rope
But again, pure M.A. systems and associated math are not really within the scope and spirit of the IGKT and knot tying (unless of course we are discussing truckers hitches and Poldo tackles, etc which do employ knots and hitches).
i think we properly show weightless and frictionless sheaves to reveal the benchmark outer potential, to define a finite range within. Then can broaden ratio of sheave to axle and reduce friction closer to that potential but never surpass the stated benchmark.
2T is at top apex of pulley only, where ABoK shows best nip. This goes right to once again imagery of only using 180 contact of 2 pulleys only already drawn together but still trying to work the same mechanix blindly by the rope.
Thus i do see where MA as a potential of rope mechanix logic is very applicable, cuz only we would know that it wasn't, but the working rope employing the mechanic does not differentiate to turn on/off this function.
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i never could draw etc. But taught self on computer to show logic i see in all this, and not seen as so collected to this particular target before.
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It is true thread wandered some, answering questions of cosine view/usage etc., but still trying to draw to same points/contentions.
Components are 1 or more of the elements of arc 0,90,180 if disallow the unNatural ,disjointed, harsh corners(to cover as separate topic of less total influences). And i did not see this overnight so try to lend as much to that path as can, before jump in to the further assemblies. Just so many base pivotals questioned still, asks me to slow down for them instead of ignoring and going on?