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 ?