...in fact, such slipping can be observed in the real world --esp. in HMPE cordage, such as on the video I've linked to elsewhere; but also, to some lesser degrees, in other circumstances.
Exactly !
In the real world, when there is less friction between the two legs of the bight element and the rim of the nipping turn than it is required /adequate to prevent this "walking" of the nipping turn under heavy loading of the eye, this "walking" will take place, indeed !
" It is the friction between the two elements of the bowline, the nipping turn and the bight component, what prevents the nipping turn from "walking'" . Under heavy loading, when there is less friction, there is more "walking". When there would be no friction ( as in my "thought experiment" described previously, with the bearing inserted between the legs of the bight component and the rim of the nipping turn ) this "walking" would transport the nipping turn to the tip of the eye in no time.
increased number of parts ...imply a diminished proportion of load - in theory, disregarding friction
Not "
disregarding friction" !
Friction theory tells us that friction force is
independent of the number of parts, i.e., the total contact area :
Amontons' Second Law : " The force of friction is independent of the apparent area of contact." However,
my theory
is that, with objects whose surface can be deformed under compression, creating "dents", things are even worse ! The less the area, the deeper the dents, the greater the enhancement of the "normal" friction force, described by Ammonton s laws. In particular,
when two straight strands of rope are squeezed upon each, the friction force between them depends upon the angle they meet : Under the same squeezing force, the greater the angle, the less the area, the deeper the dents, the greater the obstacles to any slippage, the greater the "enhanced" ,by the deformation of the surface area, normal friction forces. In fact, it is not only a theory : I have seen this happening in real ropes, although I had not
measured it. The greatest angle, the
right angle, is the angle when the two ropes "bite" each other the deepest, so, regarding our intention to prevent slippage, it is the
right angle, indeed.
So, when we wish to block slippage, multiplying the contact area by multiplying the number of parts in contact to each other is not beneficial to the enhancement of friction forces, and, most probably, it is detrimental to it ! The "
increased number of parts" can slide on each other rather freely, because there are no deep dents, so the normal friction forces are not enhanced at all. No wonder that when the angle two adjacent ropes is almost zero, i.e. the ropes are almost parallel to each other, they can slide on their extended mutual contact area much more than in any other case.
So, what should we do ? : Two things :
1. Keep the number of parts as small as possible. In particular, I believe that a nipping turn encircling two rope diameters is blocking the slippage of any of them more efficiently than if it was encircling three rope diameters. However, we need the three rope diameters for other reasons, that are related to
strength, not to security. A nipping turn that is encircling three rope diameters is almost circular, that is, it is more round, with fewer "weak" points of smaller curvature which can diminish the strength of the rope. ( Also, any one of the three strands that would be squeezed upon each other inside a nipping turn, would have a greater chance to meet an other at a greater angle - so to block more efficiently any one of them which will attempt to slip out ).
2. Make the parts meet each other at as a great angle as possible. The best we can do is to have them settled in a stable position inside the knot s nub, where they will meet at the right angle, the
right angle.
