When one s theory is confronted with experimental results that do not quite fit smoothly into it ( to call the total dissonance as mildly as possible ), he has to choose whom he should follow : the dinosaurs (and their descendants, the birds), and bury his head in the sand - or the mammals, and try to create a new theory. I have used to imagine a more or less simplistic, "mechanistic" model of the strength of the knots, where invisible pre-existing mini-cracks looming into the bulk of the material, enlarge, propagate and emerge near the regions of maximal tension, and, finally, cause the catastrophic rupture.
However, in this model,
friction and the generated by friction
temperature, are curiously absent - they do not play any role at all. If the rupture of the rope is due to the deterioration of the mechanical strength of the fibres by the local high temperatures generated by friction - which temperatures, in their turn, are causing the breaking of the molecular bonds -, the "mechanistic" theory of knots strength should be reconsidered ( to call the trajectory towards the wastebasket as mildly as possible, again...
).
In this theory, the fibres that are elongated more, i.e., the "outsiders" of the rope s path inside the knot s nub, are the only ones that are maximally loaded during the last stage of the loading. That would suggest that we should try to make the curvilinear paths they follow smoother, that is, try to make the standing part follow wider curves. So, more fibres would be offered the chance to be maximally elongated, and to be able to absorb the total loading, and so the knot s strength could be elevated.
I have tried to figure out some bends with a geometric shape that would allow wider than average first curves of the standing part - in an effort to offer to the fibres that would be maximally loaded at the moment of rupture, the chance to absorb and dissipate the tensile forces along a more extended area. (1)(2)(3)(4)
Is this the optimum strategy we should follow to elevate the strength of a knot ? I am not sure about it - in fact, I am even more sceptical about it than I was before the publication of J.P. results.
It had even crossed my mind this crazy idea : to somehow insert some quantity of a lubricating substance ( oil, for example ) in between the fibres of the rope ( at least just before and along the standing part s first curve ), so the magnitude of the friction forces would be lowered there, and the temperature that would be generated and could lead to a local catastrophic melt down, would be dissipated more easily towards a longer segment.
That was the meaning of the title of this thread - but I had to reveal only at the end of the post, in a hope that somebody would be forced, by sheer curiosity, to read it!
1.
http://igkt.net/sm/index.php?topic=3148.msg188332.
http://igkt.net/sm/index.php?topic=2154.msg15144#msg151443.
http://igkt.net/sm/index.php?topic=2154.msg16808#msg168084. The A4 bend, at :
http://igkt.net/sm/index.php?topic=3611.msg20614#msg20614