Janus Bowline Sub... Strength

[DerekSmith]

There are two sub issues re strength that I believe merit some consideration.

The first is what I have referred to as the Bowlines 'G' Spot ('G' for grief) and the second is the issue of the diameter of the simple hitches loop.

Starting then with the 'G' Spot created at the nipping loop.

KC makes the point about naming incongruities, so to clarify the situation I will talk about the structures defined by AS, and forces rather than try to utilise the confusing knotting nomenclature.

Our we saying the 'lock' in a SheetBend is a Half Hitch; even though all the force terminates on one side of this 'mechanical module'/no Tension in its Bitter End?  And Simple Hitch is a Half and not a Full Hitch?  Or would it be a Hitch if mounted to something else, but as a Bend, it is then a Half Hitch?

To me a SheetBend has a Hitch to a Bight, and a SheetBend to self to form eye is a Bowline, but also the Hitch has tension on both ends, so is now a Half (in a BowLine)?  Another difference, i call an eye a Becket(and SheetBend to Eye a Becket Hitch, and an Eye with Hitch around (but not thru); then Bight of Hitch leg pulled down thru eye and locked with rod a Toggled Becket).

There are just three further descriptors I would add and they are the two side legs of the eye.  On the RHS in Agent Smiths diagram above, the Eye leg connected to the 'Loop' is the 'SP Eye Leg', and the other side leading up through the 'Loop' to the 'Bight' is the 'Bight Eye Leg', and finally the 'G' Spot, the junction between the SP and the 'SP Eye Leg' marked in red.

Finally, before jumping in with the 'G' Spot discussion, it is important to mention that the stylised image above is great for naming purposes, and is the form most of us will recognise having just tied a Bowline, when a knot goes to work it starts to respond to forces way in excess of the simple elasticity of the untensioned rope.  It adopts shapes you would not normally see and as the load continues to increase the rope elongates and narrows and considerable flow of rope through the knot will occur.  These changes occur to some degree on all parts with the exception of the 'Tail' which remains untensioned and simply points in whatever direction it is forced to face by the 'Bight Eye Leg' and the 'Loop'.

So far so good, I will now go and load the knot to 100kg and photograph it under this very modest loading, so come back soon for the next instalment.

Derek

[Dan_Lehman]

There are two sub issues re strength that I believe merit some consideration.

The first is what I have referred to as the Bowlines 'G' Spot ('G' for grief) and

the second is the issue of the diameter of the simple hitches loop.

Frankly, the naming here bugs me:  the GeeSpot I hope doesn't lend itself to
prurient searches, and inevitably carries connotations not charitable to knotting.
And this thread's "Janus" suggests a narrower focus/domain than I think is wanted
--which would be any Bowline variation, esp. as revelations here might lead us to!?
(And incl. your 4-diameters-nipped-by-knot-loop and like variations--giving us the
Two, Three, Four (, & more) diameter knots for comparison.)

KC makes the point about naming incongruities, ...

Which tied in to recent discussion of the "Single/Half hitch", and are appropriate for
a thread re nomenclature.  How about we just regard as equivalent for these discussions
any of the "hitch", "half-hitch", "loop", "central nipping loop", & "turn" terms; the last might
be most amenable to use, in the case of "double turn" variations.

There are just three further descriptors I would add and they are the two side legs of the eye.
On the RHS in Agent Smiths diagram above, the Eye leg connected to the 'Loop' is the 'SP Eye Leg',
and the other side leading up through the 'Loop' to the 'Bight' is the 'Bight Eye Leg',

Or "end-side eye-leg".  I can show variations in which this leg doesn't go
directly to the bight (it can, e.g., make the "end-binding" wrap, as I did for
my "Bowl-in-a-Bowl" variation).  But it's clear enough, and a needed ID.

it is important to mention that the stylised image above is great for naming purposes,
[but] when a knot goes to work it starts to respond to forces way in excess of the simple elasticity
[and] adopts shapes you would not normally see and as the load continues to increase the rope
 elongates and narrows and considerable flow of rope through the knot will occur.

Amen!  And I can point out immediately that the hitch's crossing-point that you
want to sermonize about will completely DISAPPEAR in any practical sense
in some cases--such as those mooring-line bowlines I see for trawlers.
The Katherine Milne paper on where knots break (Bwl, Angler'sLoop, & Fig.8 )
found that the bowline breaks farther in-around the loop/hitch than your
point, where it must u-turn around the bight-eye-leg.  And one can dress the
common Bowline in anticipation of these forces, setting the end back against
the inevitable SPart-draw, so that AT LOAD it is only then coming into the
position commonly shown for it!

And all these factors are missing from test reports on knots breaking,
so we have little to build an understanding upon, until intelligent testing
and examination (as Derek is setting to do with varied loading) develops
a detailed set of results.

 --dl*
====

[DerekSmith]

Although we will doubtless be covering theoretical strength issues for several bowlines here, I left the title 'Janus Bowline Sub...' to indicate that this thread was an attempt to sub out an aspect of the discussions in that parent thread.

Re 'G' (for grief) Spot,  I really have no worries what we call the place in the knot where the forces focus and cause failure.  Anyone with another suggestion for what to call it?

---------------------------------------------------------------------

Dan has referenced the Milne and McClaren paper which you can read here http://personal.strath.ac.uk/andrew.mclaren/Milne%20and%20McLaren.pdf, stating that Milne indicated the 'G' spot to be further into the knot than I have indicated above.  The report is slightly contradictory in that it states the weak point is at the first loaded sharp turn in the knot, which is where I have indicated, but later, in the diagrams, the spot is marked further around as Dan states.  Sadly, there is no supporting detail or photography to clarify which interpretation is correct, however if experience is anything to go by, Dan's comment would be where the smart money would go.

Before we get into the nitty gritty of the 'Spot', let me first set the scene with a couple of examples.

The first is to show how a simple turn around a single diameter influences the geometries within a cord/rope.

So, to start with, take a length of cord and wrap it snugly around a piece of itself two or three times.  Make it snug, but don't pull or stretch it at all, just comfortably, yet closely wrapped around in a 1 diameter coil.  With most cords, it won't want to stay there, so you will have to use a little restraining pressure just to keep it snugly in place so you can mark it and take some measurements.

Mark across the turns where they come around against one another, this will allow you to measure the length of cord needed to make one turn around the core cord.  Next, if you have a calliper or guage, measure the outside diameter of these wraps, then carefully measure the width of the band of three turns (or two) so you can calculate the width of the cord in its wound state.  Finally, lay a number of strands of the cord side by side and measure the width, so that you can calculate the width of one strand in the straight.

The results you get will depend heavily on the type of cord you are using, but the effect will be generally the same, i.e. the inside of the turn will be a lot shorter than the outside of the turn - That bit is totally logical, but the consequences might surprise you.

I made up such a test using a  length of high modulus (dynamic) 5mm cord and created the following diagram from the results --



The upright cylinder denotes the 5mm cord I wrapped the turns around.  The dotted circle to the right denotes the section of the cord before it was wrapped around the core.   The red, white and blue oval indicates the wrapped cord.

The inner circumference of the wrapped cord was 3.1 diameters long, the outer length was 8.2 diameters long and the unwrapped length of one turn was 5.5 diameters long.

This means that the outside of the cord had increased in length by 48%, while the surface in contact with the 'core' had shortened by 46% and the length of cord (5.5 diameters) which just sat snugly around the core accounted for a circle which sat only 0.38 diameters above the surface of the core.

In wrapping itself around the core, the cord had squashed itself flat to the tune of only 0.81 of it starting diameter, and in doing so, it increased its width to 1.15 diameters.

Although some structural realignment was happening (spare sheath on the inside was creeping to 'give' the braid in tension on the outside), essentially what we were doing was stretching the outside (blue), while we were compressing the inside (red).  The outside did not want to be stretched, so it tried to move in towards the mid line (white) and in doing so imparted a compression force on the rest of the cord which was already under compression and trying to swell away from the core.

The key thing to take from this exercise, is that we have not put this cord under any load yet, just wrapped it around a one diameter turn and yet already the outside is stretched by 46% i.e. it is pre loaded even before doing any useful work, while the inside is compressed and is doing no useful holding work at all - before this inner surface can do any useful load taking, the cord will have to stretched by 46% to remove the compression, by which time the outside will be potentially 94% extended (loading will further influence the cord geometry so extension will not in reality reach this level).

In essence, this experiment should show you that a tight one diameter turn starts off by putting the outer fibres into tension and wastes a large proportion of the cord by stopping it from carrying anything like a fair share of the load when the knot is put to work.

If we load the cord and stretch it by about 30%, then about half of the 'dead', compressed zone starts to play a small part in carrying load, but the outside is now nearly 80% extended and the outer stretching fibres are having to take all of the load as well as supplying some compression to overcome the forces from the remaining part of the cord which is still in compression.

Load bearing One diameter turns in a knot are one of the focus points for cord failure.

The second example will cover load transfer.

Derek

[DerekSmith]

In the previous post, we looked at the impact of making a one diameter turn on the structure of a cord and looked at a section through the cord as it wound around the core.

Another way of looking at the effect would be to plot the distortion as the cord progresses around the cord.  If we were able to mark the cord in 1mm increments, then we could measure the changes as the cord entered and made the turn.  The following chart indicates the changes we might see from the inside surface and the outside surface of the cord as it makes contact with the one diameter cord, makes a half turn and leaves contact again.

Before the cords make contact, both surfaces are unstressed, then as contact is made and the cord is forced to tightly turn, the outside has to expand and the inside is forced to contract.  If we were to tension the ends of the wrapping cord, we should expect to see this whole chart rise upwards as more of the cord responded to the tension by expanding.  If we accept that it is a generality which certainly has exceptions, we can also think of the amount of contraction as an amount of compression and the amount of expansion as the amount of tension in those parts of the cord.



Potentially then, we have a tool with which to study the build up and exchange of forces within a rope or cord by studying the amount of surface distortion as the cord progresses through the knot.

So much for the tool, now for the problem.

The 'Strongest' way of joining cords, where the objective is to transfer force form one cord to another, is to do it gradually over a large contact area with minimal distortion of the loaded cord from a straight line.  The example posted some time ago of the strongest loop knot I have ever tested demonstrated this effect.



Tension between the loop and the SP caused to SP to attempt to straighten and in doing so it pressed laterally against its neighbours.  This gentle squeezing embrace increased friction between the adjacent cords and allowed the force in the SP to be progressively transferred to the loop parts, which n turn increased in tension and beagan to progressively resist the lateral force of the weakening SPart force.  So, in this construction, we did not distort the cord significantly (bending it around one diameter cords) and we transferred the load force over a significant length of the cord.

Now we will take a look at using our new tool on a 'knot' application at the very opposite end of the strength spectrum.  If you want to break a cord in a specific spot, then short of forcing it against a very small diameter curve (say 0.0001 diameters - AKA a knife blade), then you might resort to the method shown to every farm lad (at least when I was a boy)

[DerekSmith]

As a child on the farm, there were two types of 'string' available.  A nice white cotton string which came on a cardboard tube from the Post Office which Mum would use to tie up the Sunday joint - touch it at your peril - and there was bailer twine.  It was stripped from the bales as they were used and hung everywhere in great hanks placed conveniently for later re-use.  And re-used it was, for everything from hanging up a Goose or a brace of Pheasant, to the string handle of your 'Go Cart', Dad's bean strings or the infrastructure of the gangs 'Tree House'.

Farmhands would never bother to cut the twine, they would just wrap it around one hand, yank it with the other and - snap, the length they wanted  broke off.  My Dad showed me the 'Trick', but although I could manage to break Mum's parcel string, I could not manage the Bailer twine until I was a teenager.

The 'Trick' was simply to create the weakest knot possible in the palm of the hand, then apply a shock load which was greater than the strength of this 'knot'.

[Disclaimer]
If you want to try this, and you have twenty first century hands (or if you are a Cowboy) then put on a pair of stout leather gloves for protection (rope burns and string cuts can be very painful).  If you hurt yourself, I don't want to hear from your Solicitor, because you are a masochist and you tried it knowing in advance you were going to hurt yourself, so you should be paying me...
[/Disclaimer]

So here then is how to break cord in the hand...

Take the length you want to break off and lay the point you want to break it in the palm of your left hand (right handed).
Draw the cord around and down the back of your left hand, then back up over the palm again.
Flick the end of the piece to be broken around this cord and over the top of your left hand, down the back of your fingers, then wrap it tightly around the fingers several times.
Now lay the reel end, back down across your palm making two intersecting bights in the palm of your left hand - this is the 'knot' which we will break.

Take the reel end, leaving about 2 foot of slack between the hands and wrap the reel end around your right hand (tightly).  Close your hands and grip the loops even tighter.

Bring your hands together (forming a slack loop) - and get ready for the pain.

Yank your hands apart with full force - if you wimp out, all that will happen is that you will hurt yourself and look a plank to anyone watching.  At this point you will appreciate the advice of having the loops tight, any slack will have fed forward and caused a rope burn.

If you did it all right and hit the knot with sufficient force you will break the cord at the 'G' spot which is at the junction of the two loops (and perhaps your hand while you are at it).

Anyway, enough of making yourself look like a hero or a plank, now for the reason that brought us to this knot.

Using the tool we developed above of looking at the extension of a high modulus cord to show us where the forces change, we can look into the heart of this knot under load.

I used a cord with a fleck every 4.7mm.  I tied the knot and put it under 'extreme' load, then measured the distance between flecks along the cord.  Where the cord made a tight one diameter turn at the 'G' spot, I measured the outside distance, but I had to calculate the inside distance.  I then plotted the extensions involved.  (Note - I also have to admit that I cheated slightly by tying the construction and tensioning it around a chunk of MDF as a 'third hand' to help take steady measurements).

Here is the assembly - The cords to the left are the ones running over the top of the hand, and the upper one on the right is the 'snatched' cord.




and here are the results --



The light and dark blue lines are the cord on the left, the red and green lines are the cord on the right.

The red / green lines are the cord which is 'snatched'  and the first set of readings with an extension factor of about 1.8 are in the 'snatched' cord from the right hand (the upper right hand cord in the photo).  The red line shows the extension of the outer radius as this cord passes around the the tight single diameter turn at an amazing stretch factor of 2.7 (remember, this is high modulus cord), while the cord after the knot is hardly loaded at all - ALL of the load has been dumped into the cord in a matter of a half turn and nearly all of this is focussed into the outer surface of the cord.

By contrast, shall we call it the 'anvil' cord, while it has just as tight a radius, the load is shared virtually equally in both legs, and the load in the outer covering is notably lower.

The cord fails somewhere along that red line, dumping the force onto fewer and fewer fibres as the cord fails intil eventually the whole thing gives way.

Next we will use the technique to look at how the forces flow into a Bwl.

Derek