How many degrees is a Turn?

[KC]

After reading some archives, i thought i should slow down and ask, this too.
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i personally don't count the extension legs if straight or bent in this, only arc(s).

[Dan_Lehman]

I believe that I tend to differ in these statements
and so have voted "90deg" : => 180 [2022-09-15 edit]

"take a turn around ..."
&
"wrap around" --this being 360/540deg.

Where precision is wanted, giving the numerical
value is best, at this point in our terminology.

--dl*
====

[KC]

Personally am strictly 180degrees on the arc increments for Turn and subsequents.
In reading archives here; i was surprised at variety on this as think talking on same page!
My reference is a bight, made with a single Turn/arc180 with leg extensions added
>>linears more extensions compared to arc real powers of change.
So, i don't pay attention so much to legs out of arcs crossed or not, but see the names i know in radial or linear lists of arcs:
ABoK  basics pg.013
Lessons#40-42 describe a radial list of such arcs to such naming more matching
Lessons#34-37 describe a linear list of such arcs to such naming, only 'elbow' used instead of Turn
Still have seen countering info in book, but go by this.
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degs	around	name
0090	0.25	incomplete as either input or output of arc180 basis
0180	0.5	Turn
0360	1.0	(a)Round(?)
0540	1.5	Round Turn/RT (then logically conspired from prev.2)
0720	2.0	Dbl.Round
0900	2.5	Dbl.RT (thought adopted from Dan Lehman)
1080	3.0	Triple Round
1260	3.5	Coil     (thought adopted from Dan Lehman)

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i put Round in for my personal reference for 360/720/1080 hardly used anyway to worry, so doesn't come up(have on spreadcheat)
>>but also logical to the Turn + Round = Round Turn and also circumference type math references i think.
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But i see this all as structural geometry, and mechanical force pulls, frictions, and self binding against self of nip.
And any upgrade from 1x arc180 of a common Turn usage to 3x arc180 RT brings in many ways from common to working class.

[struktor]

Cone

[Groundline]

Full turn or half turn?

[KC]

The first cone drawing to me shows 1x arc180 + 2 matching legs.
Am not sure if force is intended vertical or horizontal where they meet.
Wonder if this is bind of internal force source or hitch from external force source to 'energize' the otherwise light, passive rope(as like electricity to passive wire)
Force direction, and if multi-axis dispersed equal/opposite axises or singular mono, focussed axis of 1 equal/opposite pair is of utmost importance.
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Knots use friction and compressions to hosts to control the forces that course through rope.
arc180s leverage tension force into frictions and compressions more than any other rope part.
Just as/for the same reasons as, arc180 is most unique geometry of bridge support etc.
Both ends and the apex all work uniquely in the same direction, as the whole geometry then too lends to.
Unlike any other geometric form.
Also, arc180 count is a multiplier in the exponent of the capstan formula of compounding radial frictions.
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So from all these perspectives I think arc180 is logically the most minimal increment of Turn, as the basic element of radial force in knots/any loaded rope work.
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Rope is just a material in various geometries that define what mechanics can be extruded from the material, just as any other material.  Subject to the same rigid and nonrigid support laws.  Rope is generally easier and quicker to form, and with care,reused super easily to other tasks w/o pounding, scraping, melting etc.

[DerekSmith]

Hi KC, the introduction of the conical surface imparts an interesting twist.

Our knots have but one purpose - to create a gripping friction in order to prevent the WE from following the force applied by the SP - we achieve this by creating counterposed nipping forces created by the 'capstan formulae'effect.

In order to quantify these forces we need to consider the angles between the legs of the SP and WE as they tangentially leave the Turn / Loop.  Our instinctive perception of the 360 degree turn is that the legs leave in opposite directions at exactly the same tangential point..  For the conical example this is exactly the case for every point on the surface of the cone except for the very apex.  If the legs depart the surface at any point on the cone except the apex, they will be tangentially opposite and so describe the requirements for a 360 .  We should remember that the capstan formulae does not involve the radius of the turn, nor its perfection..

So, the defining factor is not the 'perceived' angle of rotation, but rather it is the final angle between the departing legs ans they leave the contained object / surface.

So, if the loaded legs depart in opposite directions, then it is a 360.  However, if the legs depart at the very apex of the 'point' then they will not have completed the full 360 rotation and therefore we cannot expect them to have achieves the same degree of nipping force that the full 360 would have produced.  Indeed, because the legs depart in an unbalanced manner, they will impart a force vector away from the core of teh turn, this part of the force will be lost from the nipping effect and this should be possible to demonstrate by experimentation.

Derek

[KC]

Thank-you many times for many things, glad to see you here a-gain in the weary travels.
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Personally i find the conical fitting still my imagery of only 3 raw geometric elements in force loaded/working ropes.
All 3 geometries ruled by reigns of DIRECTION and AXIS. 
arc0(linear) endpoints in simplest opposing directions,
arc180 endpoints pull in same direction and
arc90 as endpoints in cross axis directions, changing the power axis by attacking it at it's Achille's Heel of Samson angle disrupting across; where arc0 and arc180 maintain the same power axis, only in opposing directions, making the arc90 that unique to itself.
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To me the top arc180 of conical pulls from input and output and even the machine point of the apex between all in 1 unified direction, as unlike any other geometry ever, and as such the 'secret' of arc bridge etc.
BUT, each of the input/output legs from the upper arc180's endpoints to their lower conical point, decidedly do NOT pull nor apply so in concert and cannot mechanically deliver the same as true arc180  'simply' per the geometry of pull directions.  Just as in a binding usage, would NOT expect equal binding force at all points with equal growth all around.  Would also suspect the binding force to be strongest and most consistent thru the arc180 member only.
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The lower part of the conical, does try to evolve more towards arc than many as a structure, but makes more of a 'keystone' on top of linears (thus not a keystone) that  slightly listing inward to minimize the destabilizing sin(e) against the structure YES, but still not an arc with force of arcs thru a real keystone as apex not complementary piece on top of the inputs and outputs.  But structurally was evolution towards arc known as 'corbel'; left behind in history mostly, as we found the arc as FAR superior. corbels/these are NOT arc180s by this measure:


Their geometries do not invoke arc180 magic, and so i only see the arc180 support and frictions back in the top part of the conical, not the lower 'corbel' of the bottom half of the conical shown, as does not have the royalist geometry of arc.
Working in stone, we had to find the arc magic to go forward, for stone tension resistance is 10% of the compression resistance!
>>could not survive much sine byproduct from cosine compression.  This necessity was such a 'mother' it birthed the arc.  It took many generations of 35year old life expectancies to build in stone, so had to make last many, many more; as many still have.  Arc as the only efficient way to the marvels.
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So, i continue to seek 'directional geometry' as key to all this.
Will look to not shy away from explaining the arc0,90,180 for new year, that i have started many times.
Hopefully to outlast quantum of exercise apps downloaded worldwide on that same day!
This arc0,90,180 breakdown has truly answered my questions many times over, while at same time from other direction can't 'break' it with examples given or remembered in experience, to persist as most evolved ongoing model; and to the 'simplest' of most organic rules of shape and direction, just as any other material.. 
Only just have to unload to shape to next geometry, not pound, chip, heat nor scrape.


i think human intellect and creativity was challenged and developed by this most usable form(flexibles), from before we learned how to pound, chip, heat , scrape rigid class materials.   In perhaps covering feet and head and feeding to survive, perhaps before taming of fire or even organized speech.  Perhaps we owe the challenges of rope/flexibles for being the root of much of our seat engineering intellect, expansion, combining of ideas physically outside of self etc.; for there just wasn't anything else.  Shame it still only calls out to a few carriers of the heritages!

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