The B bend

[xarax]

   It seems such a small step from the Water bowline s cousin, or "Ice bowline", I have tied 7 months ago (1), to this simple B bend. I am wondering why I did nt take this step all those months...I had understood the mechanism, I had the concept, the picture, even the image, but it had not crossed my mind to tie the bend ! I wonder how many other things are waiting for us, right under our noses. And this is a general question, that has to do with knots, constructions, social structures, human relations and ways we can live our lives. Perhaps it is comfortable to believe that anything that could be invented and could be useful has been invented already, that the world and the society is the best possible of all we can imagine, but this is not what is really happening. Our lives is full of steps we did not take and turns we have not followed, for whatever reason, but better late than never !  

1) http://igkt.net/sm/index.php?topic=1929.0

P.S. 2011-02-19
   For a similar structure, see ABoK#1459, ABoK#1460 ( "Reeving Line Bend" ).
 

[Dan_Lehman]

Nah, the simple step from that eye-knot to a corresponding bend
in terms of mechanics is to finish [by] collar[ing] the white loop's S.Part
with the orange tail (matching that done to orange with white).
THAT preserves the load-on-both-ends-of-nipping-loop mechanics
of the eyeknot.

What you present above is not that, and really is a poor-whipping
with strangle version of the ancient hawser bends, though lacking
the sure grip of seizing (cf. ABOK #1459 seizing bend ).
You might as well send the ends in the opposite direction, and
maybe even take the whatnot (#1407) orientation, to ensure
that there is tension on, to help lock, the strangles.

And that oddball end-2-end joint that I presented in the "#1452 & Its
Ilk" thread --fuzzed orange + dark blue kernmantle-- is a compact
similar version, stuffing 4 diameters into the nipping loops.  See at ... :

Here is a knot that arguably belongs in this thread on account
of its being non-jamming and having some similarity to the
Carrick bend, which can be seen as a seed for discovering
the interlocked-overhands knots shown above.

Notice the shift in the order of *choking* & *being-choked* :
in your middle image, insofar as one can tell loading by the one
shown end, your lines choke before being choked; in the #1459
reeving-line bend , the order is reversed --each line
passes through a choke (is being-choked) before choking.
In the bend-from-IceBwl I describe, the lines choke first.
In my own cited bend, one might see all of this captured in
the single central action --no separation.


--dl*
====

[xarax]

   I am sorry to say it, but you missed the point of this bend, completely !
  That is telling of how many things we miss, if we see them through things we know already...And the more we know, the more we are inclined to see new things through the eyeglasses of the past. Many times this is good, but sometimes it is not.
   The two closing/end knots of the two ropes can be as far apart as wish. They do not have to be in any contact with the two nipping loops mechanism. Also, the two nipping loops can be as far apart as we wish. They do not have to be in any contact with their twin nipping loop. There are four elements in line, no one has to be in any contact with its neighbour(s).  In the picture they are, because I had dressed and tightened the bend so to have the minimum length. With the 1 B bend, the two nipping loops will probably slip, in sleek ropes, and will approach and kiss each other somewhere in the middle. With more B s, nipping loops that were set apart at first, may move towards each other, or stay on the point on their own line where they were put in the first place, depending upon the moment they "lock" the other line.
   The knot works entirely through tension between the four in line elements ! Compression exists only inside each element, inside the loops, the two blocking nipping loops, at the middle of the bend, and the two closing double overhand knots, at the two ends.
   So, no relation whatsoever with the bends you describe !
   Tie the bend, try it with 1 or 2 B s, with the two (or the four) nipping loops interlinked into one (or two) Pretzels, and you will understand it. May be that is why I have not seen it immediately : It is too simple ! If it is tied as a hitch, with the main line going through without having any nipping loop on it, it is more comprehensible. I have reached it through the B hitch looong way, not through the Waterbowline-like bowline/Water bowline s cousin/ Ice bowline much shorter one !
  
    

[xarax]

   The adjustable B loop. A B 1 loop, shown in the attached pictures.
   There are two variations of it : We can have the B tied on the eye leg of the Standing part (variation 1), or on the eye leg of the bight (variation 2).
  I believe I would not be able to give a satisfactory description of how we can adjust the size of those two loops, so I will not even attempt it here. Readers that will try this loop, in its two variations, with more experience in other, different types of adjustable loops than me, will be able to acomplish it much better.
  I can only give an indication : When the B is tied on the eye leg of the Standing part (variation 1), we rotate the nipping loops so they move downwards on the loop, the one after the other, and then we adjust the size of the loop, moving the sliding "neck" of the Double Overhand downwards, towards the new position of the B s, alongside the eye leg of the Standing part. When the B is tied on the eye leg of the bight, we release the tension of the nipping lops, so they do not block the movement of the Standing part through them any more, we adjust the size of the loop, and they we leave the nipping loops free to block the Standing part again. The reader is advised to tie the two variations and try / compare them under various conditions.

P.S. 2011-02-19
 For a similar stucture, see ABoK#172, ABoK#173 ( "Bell Ringer s Knot" ), "probably a knot of considerabe antiquity".

[Dan_Lehman]

  I am sorry to say it, but you missed the point of this bend, completely!
...
   So, no relation whatsoever with the bends you describe !

Oh no, I see it.  And I see the corresponding end-2-end & eyeknots,
as I described.  What you show is Ashley's #1459, as I stated, but
with strangles vice its seizings.  And, yes, it slips.  Add more hitches,
such as #1460?  --and still more?

The two closing/end knots of the two ropes can be as far apart as wish.
 They do not have to be in any contact with the two nipping loops mechanism.
 Also, the two nipping loops can be as far apart as we wish.
 ...

Not so fast : there is a relation between the distances between
the nipping loops and the amount of compaction those loops
make under load.  For a given strain, the rope will stretch X
amount; for a given strain, the loop will compress so much,
and *yield* material into the span parallel to the stretching
rope that runs through it.  Assuming that this yield comes
more easily than stretch, there will be less friction required
of the anchoring knot to hold its position, and as the yield
is absolute of the loop, the distance stretched is proportionate
to the span --lengthen the span and diminish the benefit of the
loop's yield, and increase the frictional demand (or slippage)
on the anchoring knot.

(I have wondered how some of these seized structures --e.g.,
the commonly presented seized lattice form of the carrick bend--
can be effective, other than essentially --via the seizing-- creating
eyes, with 50% of the tension offloaded onto the seized end?!
--because, given the seizing, that end must stretch just as much
as the part it's seized to, and stretch = tension, and ... !?
At short spans, however, some bit of *wiggle* in the seizing
has greater effect on needed tension, being a greater portion
of the stretch needed.)


Trying this in two 11mm-ish ropes (old & fuzzy with retired-gym
line in fairly good shape) with 3 nipping turns (per half), going
cow->clove in orientation away from center, and strangle knots,
I get an imbalance : the smoother rope tightly nips at its center
turn with its following HHs less tight; the other rope slips and
contributes little to the friction (beyond fuzz).

--dl*
====

[xarax]

To the reader that would ask :
  " Who ordered THAT ? "
   I would reply :
   The same gentleman that ordered the bowline, some thousand years ago...
  "And why did you make so long ?
    I would admit :
   Oh, I was busy making other plans...

   The B bend in a bowline form, where we have put collars in the place of Double Overhand "necks". Right handed and left handed variations.

   

[xarax]

 Add more hitches,

THEY are not hitches. They are nipping loops, more or less like those we have on the bowline, Gleipnir, etc.
  People often do that mistake, and confuse the two distinct, different in function mechanisms, beause they "look" the same. This is happening also because people do not see, or try to imagine, what the "Main line" rope "feels" when it goes through the one or the other mechaism/rope formation:
   In a hitch, a rope (or a pole) "feels" mainly compression, compressive stress. In a nipping loop, a tensioned rope "feels" mainly shear, shear stress. In materials science, those two thngs are quite different.
   Regarding slippage : If the B 1 might slip in some materials, tie the B 2 !

... there is a relation between the distances between
the nipping loops and the amount of compaction those loops
make under load.

  Yes, but negligbe and insignifficant, compared with the whole mechanism. You are splitting hairs here !

  The B bends, B hitches, B adjastable loops and B bowlines, in general, do not slip, they are easy, conceptually, and easily inpected, too. We can put as many "in line" B s as we wish, we may have the pair of nipping loops of each of them interlinked in a Pretzel, or not.
 
 The B thing is here to stay !  

[Dan_Lehman]

 The B bend in a bowline form, where we have put collars in the place of Double Overhand "necks". Right handed and left handed variations. 

I don't like running the tails beside the nipping loops (hitches)
and through collars ; rather, run the tails back through (and so
broaden/?strengthen) the nipping stuctures.

--dl*
====

[xarax]

   A few moments ago I have acquired The Bible.
   What can I say ? Not much, because my jaws have dropped...I now understand why nobody has written a book like this since this miraculous gift was offered to us. And I now bet that nobody will ever write another book that will replace the Bible in the Knot Pantheon.
   Now, on the B thing. OBVIOUSLY the ABoK # 1459 and ABoK#1460 are almost identical with the B 1 and B 2 bends, respectably ! I say "almost", not because of the slight difference in the way this bends closes ( Ashley uses seizings, I use Double Overhand or Strangle knots), but because of something else.
   With seizings, one has to be sure that the lengths of the two links, from the point of the seizing on the Standing part, to the end of the tail, are exactly the same, so that the two links are loaded simultaneously and evenly - or else, one has to make the seizing on a bend after it is already loaded, and only then. With the Double Overhand or Strangler "neckband", that can slide freely alongside the "Main line", this is not happening, and the bend is almost self-adjusting, so that the two links block the "Main line" that passes through them at the same instant, and with the same nipping power. With this, the bend can reach the maximum of its strength because, up to the breaking point, it uses the sum of maximum of each individual s link strength potential.
   Also, the B bend as I have tied it, is much easier tied and untied. ABoK#1459 and ABoK#!460 are more like permanent rope fasteners, not every day rope bends.
    
  P.S. I am now travelling very near the event horizon of this black hole...If you do not hear anything else from me, you should conclude that I was swallowed by it, like so many other knot tyers.    

[Dan_Lehman]

 Add more hitches,

THEY are not hitches. They are nipping loops, more or less like those we have on the bowline, Gleipnir, etc.
  People often do that mistake, and confuse the two distinct, different in function mechanisms, beause they "look" the same. This is happening also because people do not see, or try to imagine, what the "Main line" rope "feels" when it goes through the one or the other mechaism/rope formation:
   In a hitch, a rope (or a pole) "feels" mainly compression, compressive stress. In a nipping loop, a tensioned rope "feels" mainly shear, shear stress. In materials science, those two thngs are quite different.

Talk about splitting hairs --how about playing semantics?
The nipped line feels compression of the turn around it,
as it will in e.g. the midshipman's hitch (a noose-hitch).
It feels this *grip* try to hold and stop its (main line's)
movement through it (as opposed to being unmoving).

  Regarding slippage : If the B 1 might slip in some materials, tie the B 2 !

But I'm already well elongated for this task of end-2-end joining,
and my nearer-to-anchoring-knot nips are not getting tensioning
as it is --why would I want to add any more of such unhelping
structures?  Rather, these turns need greater loading on them
for greater tightening & compression & thus nipping, but that's
not coming.

... there is a relation between the distances between
the nipping loops and the amount of compaction those loops
make under load.

 Yes, but negligible and insignificant, compared with the whole mechanism. You are splitting hairs here !

Hardly.  The difference must be significant, or how else
could any of these seized structures be better than just their
seizing along (e.g., no carrick bend of any sort in the structure).

Use the old seized-eye w/turNip as a case : how can this be stronger
than just the seized eye w/o ?
This is what I don't understand.  Unless there is some difference in
tension as I suggest (which lessens the load upon the seizing).
(Well, hmmm, I suppose that in the no-turNip case around a pulley
wheel (diminishing in effect as friction rises in whatever the eye surrounds)
there would be 100% load of tail into seizing, essentially being an
end-2-end joint (the S.Part-size eye leg you see not really resisting);
with great friction at the eye end, then both legs resist and the
loading of them into the seizing is more 50/50%, with 100%
going away into the S.Part, of course.  Putting in the turNip then
helps to convert the structure to the latter state.  But it seems
that the seizing isn't really expected to take even 50% tension?)

With seizings, one has to be sure that the lengths ... are exactly the same,
so that the two links are loaded simultaneously and evenly ... .
With the Double Overhand or Strangler "neckband", that can slide freely alongside the "Main line",
this is not happening, and the bend is almost self-adjusting,

so that the two links block the "Main line" that passes through them at the same instant, and with the same nipping power. With this, the bend can reach the maximum of its strength because, up to the breaking point, it uses the sum of maximum of each individual s link strength potential.

Ahem, please read my report of loading this supposed marvel of
constuction and think about that --there was ONE turNip that did
any sort of gripping, only slightly slipping, and all others (and all
of one line's) served only to consume rope & provide decorations
for the armchair (sitting unsuspended, i.e.) theorist to muse about.

When the strangle doesn't hold --and it's a poor friction hitch--,
there is little tension put to the nearest turNip, which in turn doesn't
nip, and so on to the next nearest.  As tension rises, only the two
--or as I found in my test, one (so, just one rope's)-- turNips
centermost will tighten and nip, supported by somewhat non-zero
nipping of its supporting turNips.


Testing now in a small (3mm?) natural-fibre 6-strand cord and in
5/16" laid PP, both with 4 turNips per side, I get better results.
But I still think that as "push comes to shove" and esp. in the
latter material, slippage up to the centermost turNips will occur,
and the strength --if holding to rupture-- will not be great, based
on the gripping single turNip.

 The B thing is here to stay !  

Barring any further "0"s & deletions,
you might have nailed the truth fully, literally, w/"here"
--in this forum, and not in the wild.

--dl*
====

[xarax]

THEY are not hitches. They are nipping loops

Talk about splitting hairs --how about playing semantics?

   So, there is no difference, aside from a minor "semantic" one, between the nipping loop of the bowline, for example, and a half hitch around a rope or a pole, in a clove hitch, for example. The fact that in the one case the "Main line" is parallel to the nipping loop s ends and is loaded, and in the other the "Main line" is perpendicular to the hitch s ends and unloaded. is insignificant !? I am splitting hairs if I dare point the HUGE difference....Well, this is a HUGE hair, and I can accomplish this task easily...

these turns need greater loading on them for greater tightening & compression & thus nipping, but that's not coming.

 

   It is not coming to you, perhaps, because you do not wish to !  To me, it came !
   Seriously : First, do not repeat this "compression" wording , please, however you do mean it, because it can be easily misunderstood. The nipping loops do not have to be adjacent to each other and to the ends, for this mechanism to work.
Secondly : We do not know how much the overall gripping power of the hitch is improved with the addition of more B s. The relation is not linear, that is for sure, and I can not say if it is worth the trouble or not. I suppose it depends upon the materials and loadings vs rope thickness. The same is true to the many coils of a noose : More is better, but not much, and we just do not know how much. You do not know, I do not know, we have to make tests to see...The fact is that the anti-slippage characteristics ARE improved, with 2 B s, but I can not say how much. I have tied two bends, a B 1 and a B 2, and in my "tests", with my loadings, and my material, the B 2 seems to hold faster and better than the B1.

This is what I don't understand.

NOW I am surprised !  You do not understand something ? And you tell it ? Miraculum !

  My seizing "substitute" takes almost 0 % tension ! The Double Overhand or Strangle does not have to be soo tight ! It only has to make sure that the nipping loop will START to nip. AFTER the two nipping loops get their grip on the "Main line", the only thing we need the "neckband" is to make sure the ends of the nipping loops remain parallel to the "Main line". That is the main characteristic of this mechanism. Direction of line, not tension along it, is what we need the "neckbands" for. Of course, to achieve this parallelism, we have to keep the end tensioned, just a little bid. The Double Overhand or Strange do this very well. We just do not need the seizing ! 

and all others (and all of one line's) served only to consume rope & provide decorations for the armchair (sitting unsuspended, i.e.) theorist to muse about.

You may muse as many times as you wish ! I have "tested" the B bends, more than you did, of course. ALL the nipping loops ( read ; nipping loops, not hitches !  ) were rock solid, nipping the "Main line" to the point was worrying about its health, not mine ! Make some tests, and then come back and report them. Because your present claim, that of the 4 B s , only X<4 were tensioned, is suspended in thin air !  Too dangerous for your reputation.

you might have nailed the truth fully, literally, w/"here"

 I hope you do understand your  "obligations"to sustain this "we", which are much greater than mine s, and do not replace the "we" with the "I", as it is often the case, I am afraid...

[xarax]

I don't like running the tails beside the nipping loops (hitches) ...
rather, run the tails back through (and so broaden/?strengthen) the nipping structures.

  Neither do I !   I made it to have a slim profile, and for decorative purposes !      
  But how do we know that, if the tails pass through the nipping loops, the nipping loops themselves will improve as such ? That the nipping power of the loops on the "Main line" will increase ? We do not ! Because, placing the tails there, we actually diminish the chances of the toroidal structure to encircle and nip the "Main line" completely, from all sdes. The "Main line", from one side, would touch, and be squeezed upon, the tail, along a parallel-to-the-"Main line" s-axis line ( a generatrix of the tail s cylindrical shape). Now, two lines that are parallel, and and adjacent, and pressed upon each other, do "feel" friction in their effort to slide along each other, of course. However, two lines that are perpendicular, and adjacent, and pressed upon each other, do feel a much greater blockage of their effort to move :Their contact area is reduced, so the local deformation of the ropes due to their mutual squeezing upon each other are greater, so their relative motion will be restricted even more. If we place a tail side by side a "Main line" inside a nipping loop, we loose half, at least, of the advantages of this blockage.  
   I have done some testing with two, three, even four lines going through a loaded nipping loop ( ends of the nipping loop being parallel to the ends of the "Main lines"). It seems as that the nipping power of the loop on one of those lines, is, ceteris paribus, reduced, it is not increased, as one might expect. My explanation is that lines block the relative motion of adjacent lines more efficiently, when they are perpendicular, and not parallel, to each other. The curved cylinder that surrounds the "Main line", and is perpendicular with it at each point, is more effective if it is allowed to do this blockage job on the movement of the "Main line" by its whole inside surface : If it is squeezed upon the "main line", unhindered by the interposition of a second or third line in between.
 

[Dan_Lehman]

The reader is advised to tie the two variations and try / compare them under various conditions.

This reader has tried the one corresponding to the end-2-end structure,
and it performs even worse than that, in climbing ropes (doing better
in the very worn-fuzzy one than the old smooth-sheathed one).  These
ropes are fairly flexible to around a 1-diameter bend, and at that they
resist bending further.  I thus tried the "cloverhand" structure vice the
turNips, in the fuzzy rope : it worked better, but standing in the pulley
saw it soon slip and then slide w/increasing ease.

--dl*
====

[xarax]

Thank you Dan Lehman,

This reader has tried the one corresponding to the end-2-end structure,
and it performs even worse than that, in climbing ropes

    So, you tell me that I should add more B s to the loop ? Going to B 1.5, or even B 2 ? Or you suspect that the gain would not worth the trouble?
    I do not understand which one of the two (1) is the "end-2-end" structure. ( Both are "end-2-end", aren t they ?) The "owl s eye" -like or the "clove-hitch", "coil" -like one ? Can you possibly suggest more descriptive names for them ? Also, during yur tests, were the nipping loops in touch with each other, really close, or far apart ? Because those are probably more important factors than we might have expected.

1) http://igkt.net/sm/index.php?topic=2849.msg17221#msg17221

[Dan_Lehman]

Thank you Dan Lehman,

This reader has tried the one corresponding to the end-2-end structure,
and it performs even worse than that, in climbing ropes

    So, you tell me that I should add more B s to the loop ? Going to B 1.5, or even B 2 ? Or you suspect that the gain would not worth the trouble?

I think that, in some firm ropes, the force that simply
moves the unclinching turNip is well less than that that
would make the structure (begin to) bind, so adding more
doesn't really help.  In my one testing, it was the centermost
turNip that got to binding hard, but back-ups weren't so
involved (and in the opposite rope in that case --which was
OldFuzzy joining TrimGym ("gym" ropes are with thicker
mantles & less dynamic, so to endure the belaying)-- the
turNips were all non-binding.

I do not understand which one of the two (1) is the "end-2-end" structure.
 ( Both are "end-2-end", aren t they ?)  ...

I was reporting on the (predictably "fixed") eye-knot,
which matched the end-2-end in having the
turNips in the end-side around the S.Part-side.
In some common built-by-overhanding hitching
seen in commercial fishing and I surmise other
places, often a trio of turNips is in the form of
a clovehitch (aka "two half-hitches ") in the very
end with the eye-most turNip in the S.Part --so,
effectively, and eye-knot.  --which seems to be
a happenstance of tying/setting as to this particular
capsizing of the overhands into a straight side +
turNip.