It is expected that the double, triple, or even multi-line version of a certain knot would suffer from slippage less than the single line one. That is due to the fact that, at any knot crossing, there would be more rope strands in touch with each other, so the total number of contact points, and the total area of friction surfaces, would be larger.
Multiple-line bends behave like they are tied on a material with greatly flexible cross section. If the ropes had such a flexible cross section, that would deform under compression in a large degree and extent, the knots tied on them would hold much better.
So, why we do not have such ropes ? We are accustomed to modify our knotting choices according to the material we have, but why not just do the opposite ? Modify the ropes so our knots tied on them would hold better ? Of course, such considerations have already been made by the knot industry manufacturers, and now they provide ropes with specially designed external sheaths, chosen for better grip when placed within knots ( among other requirements). Going only one small step further, one could envision a rope made of six rope strands tangent to a central flexible pipe of equal diameter, and all of them put inside a binding and protecting external sheath / envelope. When bent, a rope with a composite strand cross section made like this will tend to flatten to a great degree and extend, and the rope strands, which happen to be in a crossing or elbow configuration within a knot, will be entangled together more efficiently. ( 5- or 7- line cores would also be a possible configuration, with a central flexible tube of smaller or larger diameter ).
Why knot ? Is it such a crazy idea ? It sounds very logical and straightforward to me, but I am not pretending to serve as a benchmark of knotting rationality… 
Frictional resistance is a function of the coefficient of friction and normal force, not area.
This simple model for friction is presented in high school physics. It is an approximation for easy use. If it were correct, you would not see wide rear tires on drag racing cars. I have a doctorate in physics.
Here is a link to a page on Friction. http://hyperphysics.phy-astr.gsu.edu/hbase/frict.html
It is not as simple as we would like. Many things can and do influence friction. Just movement alone changes things, even if minute and momentary.
SS
http://www.physicsforums.com/archive/index.php/t-330790.html
http://www.newton.dep.anl.gov/newton/askasci/1993/physics/PHY2.HTM
In rope, we are not relying on adhesion.
Before we jump into an exchange of views or references about friction, let us talk about the crux of the matter :
I have seen that in practice, and I believe it is a common experience of many knot tyers. I have tied many knots using double and triple lines : They all behaved better, in relation to their slippage characteristics, than their parent knots. That was my starting point.
Starting from that, I thought of incorporating this multiple-line structure into a single rope. To help the individual strands re-position themselves according to the forces they are subject to inside the knot s nub, I thought that a very elastic central core, made, say, by a flexible hollow tube, a plastic pipe, would allow the peripheral rope strands to adjust themselves easier into their new positions. And that, in those positions, they would be tangled into a better holding multi-line knot.
I’ve experienced multi-strand knots having certain strands slip out because other parts were holding parts of the knot open. But I think some of the effect you are noticing can be better attributed to the increased flexibility of using many smaller lines. But this can cause other undesirable effects that I’ll leave you to imagine.
Oh no, you didn’t get it… The strands are allowed to move in relation to the cross section of the compound strand, not lengthwise ! You have to be sure that the many individual smaller lines are first connected to each other in a certain point. ( So, they are not so “individual” after all ! ) Otherwise, you do not have a collective action, one knot, but a superposition of many interwoven knots, some of which can very well slip and some can hold !
This is also true, but contributes to a small only degree to the enhancement of the holding power of the knot. The reposition of each line relatively to is neighbourhoods, and the adjustment of its position according the local forces, that is the main cause.
Bit quick reading, so my apologies for noise if so,
but to Roo’s point about slippage, I concur in that something
that has been advocated --viz., a two-lines sheet bend
(say, two lined tied in twin to an eye (some might want
“becket hitch”))-- I think that there is GREATER slippage
of one of those two lines, as the other somewhat protects
it from the direct, biting nip of the eye. I’ve seen this in
some such knotting : I’ve discovered that with say a small
spliced eye in a dock line to be tied around several bound
(-together) piles, one can form a bight in the SPart and use
it qua single line/entity and tie it to the small eye in a
sheet bend --but only one of the doubled parts will
see the full load, and, yes, this can do some alarming slipping!
Xarax’s reply to Roo suggests some odd sort of cordage with
many tentacles ?!
–dl*
I understood what you were talking about, I was just addressing your underlying premises. I think those premises need to focus on different explanations.
The stiffness avoidance of using low-thickness materials may have some benefit, but it has not translated into people abandoning their round rope for flat webbing very often, for example.
Of course application/use/task will help decide the knot, I can think of at least one multi-line knot to look at where the action on one line would be the same on the rest of the lines.
A multi-line Mathew Walker knot > http://farm3.static.flickr.com/2216/1545274374_f319e45c59.jpg .
This could be made with doubled ropes that would leave a number of loops on one side of the knot and the other side ends free for the task(s). Say hammock attaching (used as the clew) or multiple eye knots for tie ins, etc. An “octopus rig”.
It wouldn’t necessarily be easy to untie after loading, but maybe that won’t be a criteria item.
SS
Yes, in some sense. The 5, 6 or 7 rope strands, placed around a soft core, ( be it a flexible hollow plastic tube or else), can move transversely and reposition themselves into the cross section of the compound rope : So, if pressed, there can be three of them in contact with a flat surface, for example. However, they should not be allowed to move longitudinally, and one or more of them slip, while the others stay attached to the surface by friction.
I described only one possible solution for a compound rope, that can be flattened much more in extend, and much more easily, than the normal ropes do. Knots tied with such a rope will hold better, I believe. Another possible solution is a braided hollow rope, also with a soft flexible core, which can be flattened in a similar way.
From another thread… That is exactly what a multi-line rope, with the lines arranged around a soft core, could achieve better.
True. There are also other considerations in favour of ropes with a stiff circular cross section. Easiness of handling, storing, go through pulleys, etc.. I guess that there would be some compromise to the degree that such a rope will be designed to be flattened, depending upon material, use and specific application.