Author Topic: Physicists untangle the geometry of rope  (Read 7621 times)

xarax

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« Last Edit: February 11, 2011, 05:01:05 PM by xarax »
This is not a knot.

alpineer

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Re: Physicists untangle the geometry of rope
« Reply #1 on: April 21, 2010, 01:51:18 AM »
Thank you for that very interesting news item xarax.

alpineer

KnotMe

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Re: Physicists untangle the geometry of rope
« Reply #2 on: April 21, 2010, 03:35:10 AM »
The ropemaking list (ropemaking@yahoogroups.com) are very skeptical about the accuracy/usefulness of the article...

DerekSmith

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Re: Physicists untangle the geometry of rope
« Reply #3 on: April 21, 2010, 12:27:31 PM »
Sticking my neck out as usual, my opinion of this 'paper' is 'utter bunkum'

The Z or S rotations formed in a laid rope are the result of an automatic balancing of twist in the threads with twist in the rope.

Take a piece of laid rope and attempt to untwist its turns.  As you do so, notice how the threads become more twisted and fight the attempt to twist them more.  Now attempt the opposite - twist the rope more tightly - the threads untwist and loose their ability to hold the tighter twisted rope coils in place.  There is only one balance point where the twist in the threads equals the turns in the rope and this is where the threads take the shortest path down the rope.

As for the optimum angle, again, this is surely utter nonsense.  The paper stated that the zero twist point for a 1m length of threads is ca 32.5 turns giving a twist angle of 42.8 degrees.

Try this - take three bunches of threads (bunches of straight fibres if you wish to go purist, or otherwise just three pieces of string), tie one end of the three bunches together and fix it to a peg.  Now put ten turns (twists) into each bunch of threads - keep them tensioned to stop them kinking.  When each bunch has been twisted ten times, clip the free ends together, hang a small weight on them and gently let go.  The twist in the threads will want to untwist, and in doing so, will twist the three bunches into a laid cord.  If your starting threads were ca 1m long, then the laid cord is going to be a very very soft twist - roughly ten turns over the length of the newly made piece of laid cord - no where near the 42.8 degrees claimed for zero twist but this very loose lay cord will indeed be in a natural stable state (zero twist) - if you try to 'untwist it' it will twist back up and if you try to 'over twist it' it will undo itself.  Try the experiment again, but this time put 50 turns into each bunch of threads (if you can) - then see what sort of a rope you form - much sharper angle, much harder rope, but still stable balance between thread twists and rope twists.

The number of stable turns in the final cord is directly proportional to the number of twists you put into the starting threads.  It is a matter of balancing twist forces and nothing to do with geometry as claimed.


Still, having stuck my neck out, it is quite possible that I have completely misunderstood the paper http://arxiv.org/PS_cache/arxiv/pdf/1004/1004.0814v1.pdf, and if I have I am sure that someone will quickly step up and explain the error of my thinking.  But until then, I remain convinced that there is a high probability that the authors have never made a piece of laid cord or rope in their lives, and this is reinforced by their claimed understanding of the need for tension, the function of the 'top' and their observation that material tends to have little impact on the 'lay' of a rope (at least they got that bit right).

Alternatively, they might simply have discovered the maximum helical twist for a three strand wrap with a zero core diameter...

Derek

Dan_Lehman

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Re: Physicists untangle the geometry of rope
« Reply #4 on: April 23, 2010, 09:29:43 PM »
Just a hasty remark to say that I, too, find the cursorily presented conclusions
about some optimal twist to be in contradiction to the offered/extant variety
of twist in cordage -- from "soft" to "hard" lays, the former being generally for
high strength and the latter for more energy absorption and perhaps abrasion
resistance.  One can check this by looking at manufacturer's products (though
sometimes data sheets themselves seem contradictory such that one must
question the way they are made).

--dl*
====

kolsen

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Re: Physicists untangle the geometry of rope
« Reply #5 on: April 24, 2010, 10:39:09 AM »
The curve shown is for a
three-stranded rope formed from strands each being 1m long and having a strand diameter of 5 mm. The
shape of this curve is universal for triple-stranded ropes, while the specific number of rotations depend on
the diameter and the length of the rope. At the zero-twist point, the length of the formed rope is always
68% of the length of the individual strands.


Of course ropes can be laid with higher pitch angles if one wants specific properties. The paper explains the
unyielding nature of classical ropes.

Kasper Olsen

DerekSmith

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Re: Physicists untangle the geometry of rope
« Reply #6 on: April 25, 2010, 09:28:17 AM »
The curve shown doesn't even make sense...

At zero turns, it shows the length as 1m... as expected.

At ten turns, the length has shortened slightly... as expected - but at ten turns, the chart also shows the length to be 0.18m, and at zero turns, it is shown as being both 1m long and 0m at the same time  --  quantum rope with a touch of Schroedinger thrown in for good measure ?

Granted, I have no idea what my twiddling cord gets up to in the dark recesses of my pocket (I wonder sometimes) - but at least when I 'open the box' so to speak, it at least knows what length it is supposed to be...

Derek

kolsen

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Re: Physicists untangle the geometry of rope
« Reply #7 on: April 25, 2010, 10:57:35 AM »
Remember:

the strands are in contact with each other

The pitch angle is 90 deg. at the top (1m long) and decreases until it reaches 42.8 deg. at the zero-twist point. At the bottom the length is 0m with a pitch angle of zero deg. and increases by adding rotations until it reaches .68 meters at the zero-twist point (42.8 deg). It derives from the equation (1.1).
 
Kasper Olsen

DerekSmith

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Re: Physicists untangle the geometry of rope
« Reply #8 on: April 25, 2010, 12:49:20 PM »
Hi Kasper,

I just realised - you are one of the authors of the publication.  Welcome to the forum and apologies for so openly dissing your work.  It is so rare for a researcher to publish and then have the balls to come here to discuss their work.  AgentSmith did it a while back and we haven't heard from him since.

Whether I agree with your work or not, it is an honour to have you here, and despite your rough reception I hope you stay around a while to help me understand more clearly what you were getting at in the paper.  We all have our own perspectives, and I feel fairly confident that I have read your paper from a completely different direction than it was intended to be taken.

If you are still in a mood for talking to me, could I kick in please with a question.

If we simplify the model by ignoring the all important 'twist' in the strands, ignore any elasticity and compressibility (other than that needed to bend the strands) and work only with three solid, round, mono-filament strands that simply stay in the shape of any 'n' turn helix we form them into (i.e. forget rope and think only of a helix), then for a three 'strand' system with 'n' = zero, the small hole between the three strands has a radius of roughly 15.5% of the strand radius.  As 'n' increases, the radius of this hole gets progressively larger, fattening and shortening the 'rope' - but there is no limit point.

Going back to real rope now - why, as we make rope tighter and tighter (more turns / unit length) do we seem to hit a brick wall as we approach your magical 68% mark unless we add cores into the centre of the rope?

Derek

kolsen

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Re: Physicists untangle the geometry of rope
« Reply #9 on: April 25, 2010, 02:10:14 PM »
Hi Derek

Not to worry - I can take it..  ;)

For the packing of helical structures, I can refer to our earlier paper:

http://www.springerlink.com/content/911472572836003x/

And yes, the interpretation is that you so to speak hit a wall at the 68% mark. The number of rotations needed for this depends on the diameter of the strands.

Kasper (Olsen)


kolsen

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Re: Physicists untangle the geometry of rope
« Reply #10 on: June 11, 2010, 10:37:21 AM »
thank you for all your comments

Our paper has been updated, now with a clearer discussion of the fact that it is now always twisted maximally (to zero-twist):
http://arxiv.org/abs/1004.0814

Kasper (Olsen)

kolsen

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Re: Physicists untangle the geometry of rope
« Reply #11 on: June 14, 2010, 09:07:15 PM »
correction: now->not !, that is the rope is not always twisted to zero twist..

K.