Author Topic: Same knots, tied on a thin and on a thick line. Do they have similar properties?  (Read 3009 times)

X1

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   Same knots, tied on a thin and on a thick line. Do they have similar properties ?
 
   We suppose that the material is the same, the density is the same, the stucture / the pattern of the individual fibres is the same - and that the forces by which the ends are loaded are proportional to the area of the cross section of the rope ( or to the weight per unit of length of the rope, which is the same thing in this case ).   
   I have conjectured that, statistically, the thick lines will be stronger, because any structural failure on one small part of a thick line would not matter so much - while, at a thin line, the same default could cause a catastrophic event / a rupture. So, I have suggested that we should better test our knots tied on ropes in the scale we use, and not in a smaller one - because, if we do use a smaller scale in order to use lighter forces or cheaper ropes, our results will probably be inconsistent, and they will not reveal the properties of the knot when it will be tied on a thicker rope. This conjecture implies that, if a knot is sufficiently strong when is tied on thin lines, it would be at least so strong when it will be tied on thicker lines. If it passes the test in the small scale, it would pass the scale in the larger scale, too - and in any large scale. Knots get stronger on larger scales, not weaker.
   However, this conjecture is only about the strength of the knots - not their security. What happens with security ? Can we suppose that a knot which will not slip in a smaller scale, will not slip in any larger scale ? How friction scales up with size ? ( By "friction" I mean the force that prevents two segments of rope that are pressed upon each other, to slide on each other, to slip. That depends on the friction coefficient of the surface of the ropes, of course, but also on the degree of the local deformation of the two ropes - because how deeply the body of the one segment bites into the other s, the depth of the "dents", depends on many other things...)
   So, what can we say about the various
   
exhortations ...that knots cannot be assumed to behave the same when tied in different sized lines

   ( :) You would nt believe that I was going to let it pass by sooo easily J.P. would you ?)
   
   Are they valid regarding strength, regarding security, or regarding to the other, more complex properties of a knot ? Should we trust "scaled down" test of knots, performed when the knots we wish to evaluate are tied on ropes of the same material composition and structure, but of different size ? 
« Last Edit: December 23, 2012, 10:26:25 PM by X1 »

Dan_Lehman

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On some quick consideration, I think that one will find
it very hard to vary the sizes of material in practice without
bringing into the variance other factors (and thus avoiding
the pure comparison sought, per size --and likely per <F>
for any factor F)!  It's possible to think of a set of e.g.
monofilament nylon fish lines, or kernmantle dynamic
or low-elongation ropes, but these seem scalable only
within a narrow range, before one worries about getting
differences in stiffness, flexibility, and so on.

I concur in thinking that wile one might see size as what
can be e.g. shown in a drawing and then have values assigned
across a range (of diameters) and reason that things should
be the same, surface effects are more likely of some nearly
absolute *depth* and so have diminishing effect overall
on larger diameters.  (But then we might wonder if we
can compare 2" to 5" diameter w/o concern for surface
effects mattering?)


--dl*
====

X1

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very hard to vary the sizes of material in practice without bringing into the variance other factors

   A dublication of diameter ( quadrapulation of the area of the cross section, and the loading Force ) would not be so difficult, I guess. Of course, I can not predict if, in such a "small" difference of size, one would be able to observe any significant differences of strength or security...

surface effects are more likely of some nearly absolute *depth* and so have diminishing effect overall on larger diameters. 

  That is what the gut feeling of mine, too, tells me - but I would like to see some evidence. Perhaps the future experiments of J.P. will offer us some indications on this issue - which might be significant, regarding extrapolations of small-scale result in the every-day-life scales.

James Petersen

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  That is what the gut feeling of mine, too, tells me - but I would like to see some evidence. Perhaps the future experiments of J.P. will offer us some indications on this issue -

I had been thinking along those lines. But I will need to upgrade some of my equipment before I will be able to proceed.

James Petersen

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I recently visited two local factories where cord/rope are braided/laid and came to realize that, outside of using more threads/filaments, there are other variations between sizes of seemingly identical ropes. The only kind of line that I have yet to come across that seems to increase size by simply increasing the number of threads is the kind of z-laid nylon rope/twine I have been using to test the round-turns/lazy-dog loop/bend. Pictures of the line are in the post with the test results in that thread. http://igkt.net/sm/index.php?topic=4150.msg25773#msg25773)

One kind of cordage that is pretty consistent between sizes is Chinese knotting cord, which I acquired direct from the factory in sizes 2 through 6 ( no one seemed to be clear on what, exactly, the numbers mean other than that the smaller the number, the larger the cord). The cord is made (not exactly braided -- there is warp and weft rather than the continuous opposing coils in braided line)  from very fine nylon filaments and the manner of production is fairly consistent between sizes, although the largest sizes are softer than the smaller ones.

When I finish with the 30-filament Z-laid nylon line I am currently testing, I plan to move up to the next size and compare the results. After that perhaps I'll start testing braided/knotting line/cord/rope.

X1

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increase size by simply increasing the number of threads

   My understanding about the issue was much more naive... I thought that, if the pattern of the weaving of the threads and the density of the material would remain the same, at a larger size rope there would be more threads, so the experiments would be more consistent - because the probability that a local catastrophic event on one single thread would be critical would be smaller. I have not thought of two ropes that differ ONLY in the numbers of threads !  :)
   However, with laid ropes, I can not see how this can be possible. Imagine one thread (yarn) closer to the axis and one other closer to the outer surface of the twisted bundle of the yarns that make the one of the three strands. They can not follow geometrically similar paths, so they will be loaded differently.  Why ? Because each thread either retains the same pitch ( same number of complete turns around the axis, per unit length ), or retains the same angle ( same angle with the axis, at each point ). It can not do both ! So, the individual yarns would be loaded differently, depending upon their position inside the strand, and the more the yarns, the more pronounced this difference would be. Of course, i do not have the slightest idea about the details of rope construction, so I do not know the details of how the yarns are twisted inside the strands... but I do not see how the results of laid ropes can be scaled, when the outer yarns are loaded differently than the inner ones.
   With ropes where the yarns do not follow helical paths ( bundled in strands that also follow helical paths ), but remain parallel to each other ( are there ANY such ropes ? ) the scaling would be possible, indeed, because all yarns would have a similar geometrical shape, so they would be loaded in the same way.   
   Having said that ( which was, most probably, an insignificant spliting hairs comment ), I have to say (again) that I admire the systematic way you proceed into this... Go on !