Hi K4u,
Thanks for the reply. I think we are moving forward, in that your reply suggests that you see the fundamental flaw as the need for the hitch to " stretch out into relatively long ellipsoid coils in order for it to grip".. Would I be correct in assuming that it is the amount of stretch that you see as the flaw? If my assumption is correct, then perhaps I have a basis to work from.
The definition of a knot that I choose to work with is that a knot is a Force Machine - physically simplistic, technically highly complex (it follows from this definition that cordage constructions that are not involved in force processing are either tangles or Decoratives , but that is the subject of another discussion). It goes without saying, that knots do not work by magic, they work with tensile and lateral forces, compressive forces and of course, putting it all to work - FRICTION. All cordage has a modulus of elasticity - some low, some surprisingly high, and as a tensile force is applied, the cords will stretch and slightly narrow under the applied load.
When a load is applied to a bend, the geometry of the knot applies the laterally generated forces to create internal grip of cord against cord.
When a load is applied to a hitch, the geometry of the knot applies the laterally generated forces to create grip against its 'host' object.
Paraphrasing that - load causes extension and creates force vectors, geometry creates tangential pressure and from this, friction with(against) the 'host' object.
Taking then the group of knots you have cited, essentially they all comprise a bunch of turns around the 'host'. None of them are drawn particularly tight (there is no 'Truckers Hitch' type elements in their make up), consequently they can all be relatively easily slid along the host.
So now we put them to work - in order for these round turns to grip, they need to develop tangential pressure in order to engage the coefficient of friction, and they all do it in the same manner - when a load is applied at right angles to the coils, they are subject to infinite leverage, so they move along the host in the direction of the load. If we are lucky one side moves while the opposite side stays put - this causes the cord turns to elongate into an ovoid shape and this stretching puts the cords under tension and the tension gives rise to the tangential pressure which builds the friction. The round turns continue to extend (become longer ovals) until the friction generated becomes great enough to hold the dragging force.
The problem with the coils opening, is that as the angle increases beyond 90 degrees, then the vector starts to express not only a compressive component at the back of the coils, but also it generates an increasing vector in line with the drag force. In low friction situations, this force is eventually great enough to force the back of the loops to slide forwards, and the moment this happens, the knot has failed.
This weakness is what the KC was designed to avoid. In the KC, there is no connection between the drag input and the back of the hitch. The only way a drag vector can reach the back of the hitch is if the friction is so low, that every turn is pulled open - then the KC will fail - this is why the stipulation is made that there should be sufficient turns that the last two do not open - these are the 'anchor' or 'root' of the hitch - if they have not been pulled open, then no slip force has reached the back of the hitch and the oval turns have generated all the necessary tension to create the required tangential force and hence frictional grip.
So now we have it - the fact that the first turn (or two or three... turns) have progressively opened is not a flaw at all - it is the reason why the KC has to hold while other hitches which are flawed by having the dragging force transmitted to every coil simultaneously will fail (in low friction situations).
Derek
