How rope holds

ATH

ATH

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Ran across this article. Seems pretty intuitive, but apparently mathematical formulas continue to elude those who look at such things.

I'd imagine once that is mapped out, we'll see yet another generational kind of jump in rope technology.

physicsworld.com

Friction does the heavy lifting in ropes and yarns – Physics World

New research reveals how small twists multiply into massive frictional forces
physicsworld.com
 
I gathered that this research involves ropes and yarns comprised of relatively short fibers, inherent with organic materials such as cotton, wool, manila, etc. I have the impression that modern synthetic ropes are spun with continuous fibers running unbroken the entire length of the rope. Seems like this research has more bearing on why your clothes don't fall apart than anything to do with the ropes I use.
 
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"they found that yarn strength scaled with the exponential of the square of the twist angle"

So much for cos and sine of the helix angle...
 
If you've ever had to fit equations to data, it's about straightening the line or least squares polynomials when you're desperate, so I figure they got an exponential to fit after squaring the angle. On new stuff it's a trial and error thing.

Redirects do work on the bollard principle. When I ran the math in the SRT Basal tip force thread it turned out quite interestingly. Similar idea to diminishing returns as you increase the number of pulleys you're trying to get extra advantage from. The tension ratio keeps jumping up and smacking you between the eyes.
 
Devil's Advocate view:tanguero:: some thoughts(abbreviated)
If the non-continuous threads have frictions;
a continuous thread in same position, angle etc. at least has potential for frictions from that examination given i'd believe then.
>>especially in more elastic forms i would think of 'failing' to slide like non-continuous threads/but not failing at end of run. So, internal frictions from rope 'scrubbing' self internally.
>>might get some friction to sides and then some tail stabilization down length too in total sum.
Hard Lay 3strand a good, simple example i think.
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i must maintain my root model of ANY displacement against existing physical space, can be shown/explained/modeled with cos/sine.
>>so true, that even works on reciprocal/physical force paid for a change against space/distance
>>so that also in tandem ANY displacement against existing physical force, then too can be explained/modeled with antagonists cos/sine.
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Model I see extends to an input of linear force (ALL Bends, Hitches, Rigs, NOT Round Binding) pulls down length of line, capitialzing on cosine that presents no friction. Controls of friction, nips and grips all coming from byproduct sine produced from cosine inefficiency this way. These controls can only use cosine at apex (cos+cos like that offers best nip and 2x force of pulley) or in arcs (cos+sine) instead of most simplistic cosine against load only and only sine for controls. The compound /dual usages of cos and/or sine to one utility only occurring in compounding structures of apexes and arcs I think. Not most simplistic sole linear rope parts. Round Binding by contrast exclusively works against force with sine as the force TBones the rope length, rather than force pulling 1D linearily along rope length as ALL Bends, Hitches, other supports and rigs.
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Linear arcs/twists etc. down the length of line can pull straighter on loading to be more efficiently inline/stronger; but dynamic part of load can be dampened by the internal frictions to do so. The frictions also allow load balancing/sharing down the length of rope most evenly; 'smoothing' even microscopic length differences etc. autonomously on the fly.
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Organic materials mentioned would be more internally 'frictive' (knudeKnoggin strikes again), than modern synthetics as yet another factor.
 
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