i go with the capstan equation in the
att_frict paper (mia still so using webarchive wayback machine).
It has a very logically built formula, to this target. In fact shares some similarities to Euler's(pronounced Oilers) Identity, called the most beautiful formula in math etc. (eccentric crowd). Euler was one of the greatest mathematicians ever, popularized PI symbol from math club to worldwide use and much other math notations. Schooled under the Bernoulli 'math dynasty', and carried on from them.
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Euler's number is logarithm of 1, logarithms added together multiply numbers on sliderule well enough to put man on moon and bring back whole.
Euler's number (e) is used in calculation compounding interest, population growth, disease, rust growth etc.
So is basis here for compounding friction radially, similar elsewhere linearly but by distance.
Then take the accepted table of cF for2 linear mated materials and multiply by PI to get a 'Radial cF' conversion (my translation of his work).
Take then 'e' and raise it to the power of how many 180 arcs x Radial cF.
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winCalc or other in scientific mode:
On page_6 he gives his rule of thumb .25 for (nylon)rope on aluminum
>> this is a standard linear friction cF , convert to radial cF i say by multiply by PI = 0.785398.. as 'Radial cF'
>> (Mr. Attway paper shows formula of all 3 elements, for table i created compound element of Radial cF' logic)
on most scientific key boards have 'e' for Euler's number and x^y (x to the power of y)keys and '(', ')' keys
tap 'e', 'x^y','(' paste saved Radial cF '*' then number of180 arcs , then tap ')' then '='
should give matching numbers to his page_7 showing 3,5,7 arcs for leveraged multipliers of 10,50,250 of control leg over load leg
(more accurate if calc and save PI x .25 and use whole string)
i get some variance on 7arcs with what he states, but then carries well to the rappel rack and fig8 next 2 pages.
e to the power of the reusable Radial cF (saved copy to paste) x number of 180 arcs
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i hope that is clear logical explanation of what is used and why
>> and once have the 'Radial cF' just multiply by arc count (180=arc), and use as a power of compounding element 'e'
>>as minimal math knowledge to reachable target
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His analysis is very root to my own, including watching the amount of 180 arcs, fan belt examples, usage of PI etc.
>>but i only find in linear input to controlling arcs
>>and directional effect from same as like pulley, as a reciprocal opposing end of arc force range in all rope arcs, including inside knots
But only if linear force input, not Round Binding radial force input to same arcs,
>>then no linear to radial conversion, so no capstan effect nor no retained linear direction for pulley effect
>>So all points in Round Binding against radial 'glow' swell are equal until nips, not receding tension of capstan nor compounding force of pulley
My capstan etc. spreadcheat (link).
Crushing forces inward from linear input to me would be a pulley effect of competing compounding arcs.
>>2 opposing pulleys with rope around both, has 2 x 180 arc contacts, just as single capstan does(as Truckers w/pulleys also)
>>crushing inward as if 2 pulleys pulling together towards center
This is all connected, and math is the language of tracking and comparison to give definition.