What defines a Bowline? - structure, characteristics, topology

X11 · 1 July 2012 15:24

If you read carefully, you will see what I had meant…It was not the length itself of your previous post that bothered me. After all, my posts are 10 times as lengthy ! :). It was the style, which was sarcastic a little bit, like you have just uncovered an obvious mistake of a pupil, and you are proud to reveal this fact piece by piece to the poor boy… Well, you could have said what you said in just 2 lines, and I would have answered in 4. And you should have learned by now that I was not mistaken, so the style missed its purpose…I do make mistakes, A LOT of them, but not sooo silly like a mistake in addition of 50 +50… ! You forgot to take into account the friction between the rim of the turn and the two legs of the collar that penetrate it. If the mechanism could work without friction on this particular point, it could have not been in equilibrium, and the turn would have started walking on the tensioned line, and would have reached the tip of the bight in no time ! So, when the mechanism is encountering yet overcoming friction forces and it is moving, you can not expect a neutral sum of the forces that act on it, like this 50% + 50% = 100% you have stated in your comment. I know that most people would be surprised by a “single turn” component of the bowline walking along the standing part, but this is exactly what would have happened had it be no friction between the turn s rim, the wheel, and pair of the collar s legs, the wheel s axle. If you glue the two legs together, and pass them through a ball bearing, and then roll the turn around this ball bearing, as soon as you load the bight the one leg will wind around the rim of the bearing while the other will unwind , the turn, as a whole, will move towards the direction the collar pushes it, and the bowline will be transformed in a " double turn component" at the tip of the former bight !

Yes, the two " half hitches" will hold almost everything, and the four “half hitches” will hold anything ! A series of “single turns” , where each single turn is not a hitch, behaves like a compound hitch - because the last leg would be completely untensioned, i.e.free.
However, I have to point out this : A sufficiently large number of wraps around a pole, will behave like a hitch also ! I guess that 8 wraps will hold anything, and this has to do with friction and the capstan effect. Should we call a single wrap " a hitch" ? It is exactly the same : When examined in isolation, both the “single turn” and the “single wrap” are not hitches, but a sufficiently large number of then makes them behave like a compound hitch, indeed. I prefer to examine each and every individual component in isolation from the others, that could well interfere with it and generate something new, something that was not expected to happen. If it happens, it happens because of accumulation of friction forces, not because of something inherent in the individual component. So, I will not call “a hitch” any such component, even if their superposition behaves as a hitch, indeed.

Constant

DerekSmith · 1 July 2012 19:18

Hi Constant,

I know that you know me well enough not to think that I was descending to sarcasm, so I am relaxed that on that score you are simply playing the torment.

However, on the above quote, I am afraid I do not understand what you have said, so I will paraphrase my suggestion.

If I hang 100 kg on a single turn of cordage which has a coefficient of friction of 1.1 against its static bar, then the weight of just a few inches of cord will be sufficient to hitch the 100kg load on the SP (see capstan equation with cfs set to 1.1, a 360 degree turn give a thousand fold shedding of the load into the bar).

In this situation the load is effectively hitched using only the Single turn Component. Under this special case, do you accept that the Single turn Component is then a hitch?

Derek

X11 · 2 July 2012 01:21

I have to repeat that a genuine " hitch component" has its two legs asymmetrically loaded, because of the interaction of the one leg upon the other. In a hitch, the first leg goes over the second, as a riding turn, and the result of this interaction is the effective hitching of the second leg - and of the whole knot mechanism, in relation to the object around which it is warped. So, in a hitch component:

The one leg is loaded, while the second is not.
This asymmetry is due to the position of the one leg relatively to the other.
A " single turn component", on the other hand, has its two legs symmetrically loaded ( more or less). These two legs do cross at a point ( the crossing point), and they can even twist the one relatively to the other, to a certain degree. However, even if this symmetry is not absolute, we can not say that the one leg is less loaded - to some degree- than the other, because it is effectively hitched by its passing underneath the other ( as we have said in the case of a " hitch component") . So, in a single turn component :
Both legs are loaded, to about the same degree.
This symmetry may not be perfect, but broken to a certain degree. However, that is not due to any asymmetry in the position of the two legs relatively to each other.
I believe that, in the past, even if I could not define with the precision I would have wished what was a nipping loop and what was a hitch, I could tell what was what the moment I saw one. Now, with this “single turn component” and this " hitch component" , I am not so sure any more !

DerekSmith · 2 July 2012 09:12

Hi Constant,

You have made the same mistake with the capstan equation that I did when I first came across it, but then I could be excused because I am not an engineer. The capstan frictional effect works by the effect of cord tension force acting inwardly on the capstan and is a function of angle of contact not length of contact. You will see from the capstan equation there is no diameter factor, only angle of contact in radians and the coefficient of friction -

http://notableknotindex.webs.com/formula3.gif
from http://notableknotindex.webs.com/friction.html

So as in the Simple turn Component the contact angle is fixed at roughly 6.28 radians, contrary to your statement that the “friction coefficient is irrelevant”, it is in reality, the only aspect which matters…

Your ‘whole world’ analogy you propose does not apply to the capstan effect because in the whole world case the frictional force is generated by gravitational attraction - i.e. the weight of the cord - not from tension.

You have mentioned the ‘nipped tail’ aspect of some hitches - this is an important positive feedback mechanism and perhaps we should consider this as a micro component or a component variant - what do you think?

Derek

X11 · 2 July 2012 11:52

As the reader would have understood by now, I think that the “nipped tail” is exactly what characterizes the “hitch component”. It is the ONLY mechanism that can transform a “single wrap” component into a “hitch” component. So, it is the only geometric characteristic that is different between the “single turn” component and the “hitch” component - the other characteristic, that is not shown in the pictorial representations of those two quite different things - is, of course, the asymmetry in the loading of the legs. ( With the provisional term “single wrap” component" I mean something like the “single turn” component, but where only the one leg is loaded. I repeat, in a 'single turn" component, both legs are loaded, to the same , more or less, degree. In a :“hitch” component, only the one leg is loaded, the other has been transformed into a more or less free end. (Derek Smith will probably figure out a more appropriate name for this " single wrap" element, I guess.)
I can not see how a " turn" , in general, could function as a “hitch” , without incorporating this 'nipping tail" characteristic. This is exactly how the one leg can “absorb”, in a sense, the load that would otherwise have been transported throughout the other leg. So, it is the only geometrical transformation required, with the help of which a “single turn” component to be turned into into a " hitch" component - the mechanical transformation required is the loading of only the one, not the two ends.
Now, of course there are more complex hitches that do not use this " nipping tail" trick… but another way to prevent the slippage of the second leg through the knot s nub, at a first stage, and off the object, at a final stage. I was only considering the most simple case, of the most simple rope path, able to hitch/be hitched around an object, and so be able to remain stationary even if only one of its two leg is loaded.

(2012-6-3 P.S.) I have edited my previous posts, by removing anything that had to do with an analogy / joke I have made about the very large friction forces on a very long rope, laid upon a flat (or warped around a round) Earth ! The fact that - as the " capstan equation" and Derek Smith show-, even the very light load of the weight of short segment of a chord one the one leg can withstand any very heavy load on the other leg - provided that the rope is warped around a round object a sufficiently large number of “single turns”- does not, in my view, forces us to call a multi-warp system by the generic name of “a hitch”. The mere accumulation of friction forces by the repetition of many turns can serve to attach a line on a pole or rope, indeed, it can serve to attach a line on an object, it can play the role of a hitch - but, at least according to my view of what is a knot (1), it is not a knot - so it is not a hitch, therefore and we should not call it “a hitch”. Why it is not a knot ? Because it can be untied, without any obstacles imposed by the topology, the friction, or the mere bulk of the rope. What is prevented by friction ( by the capstan equation and by Derek Smith :)) is its motion/rotation, as a whole, around the encircled object - or the motion/rotation of the encircled object around it . The multi-warp system is not entangled within itself in a way that would allow us to call it " a knot" .
However, we could well call a single wrap as a " hitch component" ( when it is loaded only from the one leg ), just as we call a 360 degree bight around an object “a single turn component” ( when it is loaded by both legs ) - although nor the " single wrap" nor the " single turn" are genuine knots, in the sense described above. They are elements of knots, and when the knots do have a certain name, these elements can well shear the same name.
Then, why I do not wish to call this " single wrap" element/component, a " hitch" element/component ? Because I think that it is better, and more convenient, to reserve the use of this name for the case where we have a riding turn over a tail - the first one ( the loaded) leg going over the other, and squeezing it in between the riding turn and the surface of the encircled object.. Out of this embrace, this second leg walks out as a free end - well, more or less, this is but a simplified, general, abstract picture. In this picture, there is a geometrical characteristic that distinguishes it from a “single warp”, this asymmetric position of the two legs relatively to each other, which is the cause of the difference in the loadings - the one leg is loaded ( and remains loaded), while the other is not ( because it does not) .
I believe that, if we keep in our mind those simple distinctions, we can analyse a certain knot in a more useful way, in order to reach a point where we acquire a deeper understanding of how this knot works, in particular, and how knots work, in general. A " single warp component", a " hitch component" , a " single turn component" - after all, it is not rocket science!

http://igkt.net/sm/index.php?topic=3610.msg20611#msg20611

DerekSmith · 2 July 2012 17:01

Hi Constant,

I am not an engineer, so I am guessing that the mistake is mine. But I went to the source which you quoted as being superior http://en.wikipedia.org/wiki/Capstan_equation but still found no mention of radius of the object, only exactly the same as Roo’s web page -

The formula is:

[i] T_\text{load} = T_\text{hold}\ e^{ \mu \phi} ,

where T_\text{load} is the applied tension on the line, T_\text{hold} is the resulting force exerted at the other side of the capstan, \mu is the coefficient of friction between the rope and capstan materials, and \phi is the total angle swept by all turns of the rope, measured in radians (i.e., with one full turn the angle \phi =2\pi,).[/i]

I know that Wikipedia sometimes has several pages on the same subject, can you give me the link to the more informative source you refer to.

I think your ‘whole world’ model is descending beyond analogy/joke. Not only would your hypothetical world have to be 'empty, but it would also have to be stationary, because without gravity and spinning at 24,000mph, the cord would fly off into space kissing goodbye to any hypothetical capstan effect.

Re you apparent need for a nipped tail in order to call a fixing a hitch, the so called Tensionless Hitch does not need a nipped tail, the load being shed through the capstan effect into the static object providing that the coefficient of static friction is high enough.

Constant, I have read your posts now for some considerable time and consequently I know full well that your command and comprehension of English is excellent (probably better than my own), so I cannot accept any excuses that we have a language barrier here. Either the capstan formula does, or does, not include a radius function, in which case your assertion is either right, or wrong (with or without f’s). As you are the engineer here, I believe the onus is upon you to educate the chemist by pointing me at the appropriate reference to demonstrate your claim, and explain to me where I am misreading the science.

Derek

X11 · 2 July 2012 19:56

I will not go as far as to call this mechanism a " hitch", I prefer to call it a single or a multiple warp. A sufficiently large number of single warps, around a cylindrical drum of a sufficiently large diameter, tied on a rope with a sufficiently large coefficient of friction ( one can consider any combination of those parameters ) can, indeed, function as a hitch, that is true. However, that should not force us to use the “hitch” name anywhere we have such an accumulation of friction forces, that at, the very end, would inevitably lead to a knot and an object entangled together in one whole.
Of course, literaly, and if you are ready to use far-fetched analogies, a “tensionless hitch” is a hitch. However, I can imagine many other rope mechanisms which would be able to function as hitches, if they include an extreme number of turns, extreme rope dimensions and extreme friction coefficients. It would be better, and more convenient, if we reserve the use of the generic name “hitch” to situations that resemble the hitches we see in everyday life.
So, to my view, a “hich component” is something that includes, as a sub-component, or as an essential part, this “nipping tail component” you are talking about. The turn of the rope here plays the role of a riding turn, The one leg is the continuation of this riding turn and the other is sqeezed underneath this riding turn, in between the riding turn and the surface of the object (or the rope, if the “hitch component” is tied around one ore more rope diametres ). The one leg which forms the riding turn is nipping the other, which is the tail, so we have an asymmetry in the relative positions of the two legs, so the second leg is squeezed at some point, but at the end walks out of this embrace as a free leg ! One leg loaded, one free, the loaded leg making a riding turn, the other leg escaping under this riding turn, as a not-loaded leg . That is the general picture of a 'hitch component" I have in my mind…
Does this picture resembles a nipping loop, a “single turn component” ? I believe not, and I have tried to explain my view with/at the lengthy previous posts. The “single hitch component” has two legs loaded, to the same, more or less, degree. We can not speak of a tail. Any "hitcing effect " is only a colateral one, it is NOT due to the assymmetry of the two legs, either the asymmetry of their position, or the assymmetry of their loading - like what happens in the case of the “single hitch component”.

X11 · 3 July 2012 08:02

The fact that - as the " capstan equation" and Derek Smith show-, even the very light load of the weight of short segment of a chord one the one leg can withstand any very heavy load on the other leg - provided that the rope is warped around a round object a sufficiently large number of “single turns”- does not, in my view, forces us to call a multi-warp system by the generic name of “a hitch”. The mere accumulation of friction forces by the repetition of many turns can serve to attach a line on a pole or rope, indeed, it can serve to attach a line on an object, it can play the role of a hitch - but, at least according to my view of what is a knot (1), it is not a knot - so it is not a hitch, therefore and we should not call it “a hitch”. Why it is not a knot ? Because it can be untied, without any obstacles imposed by the topology, the friction, or the mere bulk of the rope. What is prevented by friction ( by the capstan equation and by Derek Smith :)) is its motion/rotation, as a whole, around the encircled object - or the motion/rotation of the encircled object around it . The multi-warp system is not entangled within itself in a way that would allow us to call it " a knot" .
However, we could well call a single wrap as a " hitch component" ( when it is loaded only from the one leg ), just as we call a 360 degree bight around an object “a single turn component” ( when it is loaded by both legs ) - although nor the " single wrap" nor the " single turn" are genuine knots, in the sense described above. They are elements of knots, and when the knots do have a certain name, these elements can well shear the same name.
Then, why I do not wish to call this " single wrap" element/component, a " hitch" element/component ? Because I think that it is better, and more convenient, to reserve the use of this name for the case where we have a riding turn over a tail - the first one ( the loaded) leg going over the other, and squeezing it in between the riding turn and the surface of the encircled object.. Out of this embrace, this second leg walks out as a free end - well, more or less, this is but a simplified, general, abstract picture. In this picture, there is a geometrical characteristic that distinguishes it from a “single warp”, this asymmetric position of the two legs relatively to each other, which is the cause of the difference in the loadings - the one leg is loaded ( and remains loaded), while the other is not ( because it does not) .
I believe that, if we keep in our mind those simple distinctions, we can analyse a certain knot in a more useful way, in order to reach a point where we acquire a deeper understanding of how this knot works, in particular, and how knots work, in general. A " single warp component", a " hitch component" , a " single turn component" - after all, it is not rocket science!

http://igkt.net/sm/index.php?topic=3610.msg20611#msg20611
[/quote]

DerekSmith · 3 July 2012 09:41

Thanks Constant,

I think you have something there.

Derek

X11 · 17 July 2012 18:24

Here is what I have described as a “double, crossed-nipping - loops bowline”.
A "bowline ? ? ? Without a “proper” collar ? ? ? The collar of the standard bowline, where the two legs that penetrate the nipping loop are almost parallel to each other ? What happened to the aphorism “no “proper” bowline collar = no bowline” ?
There were two things that persuaded me to use this description - which I had denied earlier for the ABoK#1033 “Carrick” bowline-like loop.

This loop is very similar to the standard double bowline - the only difference is that the second nipping loop is placed in between the first nipping loop and the standing end - and not next to the first nipping loop, at its other side. The only reason the leg of the “not-proper” collar does not enter into the nipping structure from the same side from which it had left it, is a security precaution. In the past, I used to tie this loop with a “proper” collar, as a “proper” double bowline. However, I had noticed that there were cases where the second nipping loop (that should have remained in between the first one and the standing end ), sometimes went over it , and, as a result, the loop degraded into the standard double bowline. The great benefit of this “crossed nipping loop” configuration is the self-stabilization of this nipping structure, that relieves the collar of any relevant duty. This is possible only if the second nipping loop retains its position in the middle between the standing end and the first nipping loop. The particular “not-proper” new path of the working end in this “new” knot separates the two nipping loops permanently, so their relative position remains fixed under any loading conditions.
So, the great similarity of this loop with the standard double bowline, was the first reason that made me move against my earlier statements.
Now, there was also something fishy in my earlier position, that I knew right from the start, but I had hoped it would have remained under the carpet - so it would not complicate matters much more than they already are… I was eager to accept a generalization of the notion of the “nipping loop”, so that it would be able to cover the standard double nipping loop, as well as some other similar double "nipping structures" ( like the Pretzel double nipping loop, for example ). However, when it came to the “collar” , I had accepted a much more restricted strategy : I had wished to name as a bowline only a loop that used a “proper” collar, i.e. a collar similar to the collar of the standard bowline. I have though/feared that, if we would have accepted different, more general types of collars, we would have been forced to describe as " bowlines" too many loops… that do not “look” like the standard bowline to most people.
The problem with this noticeable difference of how broad a definition we use for the “nipping loop structure” and for the “collar structure” , is simple : The main/principle element of the bowline is the nipping loop. So, if we accept the use of more general nipping loops, can we deny the use of more general collars ? Accepting a broad, loose definition for the main part, and a narrow, tight definition for the secondary part, does not seem such a great strategy to me…
That was the second reason which made me to name this “double, crossed-nipping-loops” bowline-like loop as a 'bowline". Of course, if there would be a contrary consensus on this matter, I would continue to call this loop as a “bowline-like” end-of-line loop, as I did till now, not as a 'bowline" - just as the ABoK#1033.

We have four distinct strategies : The first is to have a broader concept of the collar … and the second is to have a broader concept of the nipping loop… The third is to have both, and the fourth is to have none of them… I will not hesitate to adopt the one or the other, or both, or none, provided this will help us to study better the knots we already know, and the knots we are going to learn, if we adopt any one of the those four strategies.

Double crossed nipping loops bowline (2).JPG

Dan_Lehman · 18 July 2012 22:16

Oh, yes. ;D

... I was eager to accept a generalization of the notion of the "nipping loop", so that it would be able to cover the standard double nipping loop, as well as some other similar double [i]"nipping structures[/i]" ( like the [i]Pretzel[/i] double nipping loop, for example ). However, when it came to the "collar" , I had accepted a much more restricted strategy : I had wished to name as a "bowline" only a loop that used a "proper" collar, i.e. a collar similar to the collar of the standard [i]bowline[/i]. I have though/feared that, if we would have accepted different, more general types of collars, we would have been forced to describe as " bowlines" too many loops... that do not "look" like the standard bowline to most people.

I’m less concerned about look than fundamental function
–hence, look towards (only) the central nipping loop as
the essence of “a bowline”. But my fish tale wags, too,
in not recognizing the problem of tacitly accepting various
things as “a nipping loop”, when I should be vigilant against
them, at least as acceptance w/o comment. E.g., even
the common double/round-turn bowline must be noted
as having something other than a simple “nipping loop”
–it has a coil. --and so, too, the water bowline and many
other constructs one can think of. For these, though,
we might establish a means to recognizing them in their
place of kinship to the canonical “bowline”!?

What I did realize, at least, was that some of the
bowlinesque eyeknots I’ve discovered should be held
as “false” (or some better, more accepting qualifier)
bowlines --they’ve much the look & feel, etc.,
but deviate in the full nature of their nipping loop
–in that it doesn’t directly flow into the eye (and
thus bear that 50% of tension one would expect).

Your outline of “strategies” for our nomenclature is good,
and we should proceed at least in classifying things into
various groups, w/o concern about whether that group
is later considered fully part of bowline or rather some
like-a-bowline naming : the group will stand together
regardless, distinct from other groups, later to see if
they share one or have more nominal umbrellas.

–dl*

X11 · 18 July 2012 23:59

To flow directly into the eye, is much less than 50% of the “full nature” of the standard, common bowline s nipping loop ! The nipping loop of the bowline works as effectively as it does, because it is the direct continuation of the standing end ( the loaded end), which bears 100% of the the tension - and not because it is the direct continuation of the eye leg of the bight, which bears 50% of the tension. Having one of its limbs tensioned by 100% of the load, the nipping loop can grip the leg(s) of the collar with full force.
At the double, crossed-coils “nipping structure” of the loop shown in the previous post, the ( first, main) nipping loop/coil grips the second leg of the collar as effectively as the nipping loop of the standard common bowline, because one of its limbs ( the direct continuation of the standing end ) is also tensioned by the 100% of the load. The other limb flows into the second nipping loop/coil, that is squeezed in between the first nipping loop/coil and the tensioned standing end - therefore it bears less than 50% of the tension. However, I do not believe that this fact diminishes the gripping power of the first, main nipping loop substantially - or that it makes this nipping structure deviate from the true “nature” of the nipping loop of the standard, common bowline.

X11 · 19 July 2012 22:24

Let us examine the “Sheet bend “bowline”” - the end-of-line loop derived from the Sheet bend ( shown at the attached pictures).
If, in order to call an end-of-line loop “a bowline”, we do not demand the existence of the “proper” collar of the standard, common bowline, then I am afraid that we will be forced to call this loop “a bowline”, too. Now, to my view, although this loop might superficially “look” like the bowline, it works in a very different way. Its not-proper “collar” is, in fact, nothing but a half hitch, and the second leg of this collar/hitch is not nipped inside the nipping loop s ring ( as it happens in all bowlines). Moreover, the nipping loop itself is not a closed ring, but an open one ( although it is not as open as the helical coils of the “helical loops”, shown at (1),(2).
So, here is an end-of-line loop that, although we may say that it “looks” very much like a bowline, indeed, it functions very differently, as two interlinked half hitches - or three interlinked half hitches, if we take into account all the three limbs of this knot. Now, the standard common bowline does not function like this - it is a close relative of the Gleipnir knot rather than the Sheet bend. Neither the “proper” collar, nor the “proper” nipping loop of the common bowline are “half hitches” ! This is an example of the difficulties we will encounter if, in order to generalize the notion of the “bowline”, we do not pay much attention to the characteristics of the collar structure, and we are ready to accept more general “collars” than the “proper” bowline s collar.

Sheet bend bowline (1).JPG

Sheet bend bowline (2).JPG

Dan_Lehman · 21 July 2012 03:05

I disagree : the nature of the “nipping loop” is that it is
exactly that : a loop --with consequent implications!
Otherwise, one has any sort of thing coming into play,
and, i.p., one can have a “hitch” (component) as you ascribe
to the sheet bend --100% feeding into 0%/free tail!

Let us examine the "Sheet bend "bowline" -- the end-of-line loop derived from the [i]Sheet bend[/i] ( shown at the attached pictures).

Well, most people regard the bowline as derived from
(or kin to) this end-2-end knot; but the asymmetry of the
latter enables two directions for eye derivation.

Moreover, the nipping loop itself [u]is not a closed ring, but an open one[/u] ( although it is not as open as the helical coils of the "helical loops", shown at (1),(2).

And that fact might be what casts it out of the group.
(There are some “anti-bowlines” that tend towards
helical vs. “closed ring” geometry --and, indeed, we
have even examples of this in the [i]common bowline/i–,
but they do so by forces upon the nipping loop, and not
by the physical presence of another part impeding closure.)

So, superficial “looks” should be discarded as a criterion.

Now, the standard [i]common[/i] [i]bowline[/i] does not function like this --it is a close relative of the [i]Gleipnir knot[/i] rather than the [i]Sheet bend.[/i] Neither the "proper" collar, nor the "proper" nipping loop of the common [i]bowline[/i] [is a] "half hitch" !

And nota bene that the revered Gleipnir has no “proper collar”!
You might find my accommodations about collars consistent
in this essence? --that whatever structure sustains the nipping loop
serves to keep the eyeknot in candidacy for bowliness ?!

–dl*

X11 · 21 July 2012 11:34

Of course, a nipping loop should, at the first place, be a loop. However, all loops are not nipping loops… The “generic”, “perfect” nipping loop should be loaded from both legs. Moreover, those legs should barely touch each other - otherwise the total sum of the tensile forces that are supposed to flow into the nipping loop s ring by both legs is diminished. If the tensile forces are “wasted” at the crossing point between the two legs, the total gripping potential of the nipping loop is also wasted.
Those conditions do not happen in real life. No nipping loop is a “perfect” nipping loop ! We try to have nipping loops that utilize as much of the tensile forces present at the outer ends of both their legs, as possible. If the one (second) leg of the nipping loop flows directly into the eye of the bight, that is good, because we are assured it will be loaded by 50% of the total load - most of the time. However, if the other (first) leg does not flow directly into the standing end, that advantage can be wasted, because this leg would not be loaded with 100% of the total load. Given that wasting a certain percentage of the 100% of the total load is more severe than wasting the same percentage of the 50% of the same load :), I am more concerned with what happens before the first leg, than what happens after the second leg. If the flow of the standing end into the first leg of the main nipping loop is not direct, the nipping potential of this loop on the penetrating legs of the collar(s) would be severely wasted, and the negative result would be much more important than the result of a similar situation on the other (second) leg.

Well, most people are wrong… And I believe that they are wrong because they have been brain-washed by Ashley, for too much time ! Had Ashley put the two loops side by side, and pin-pointed their obvious differences, this thread would have been MUCH shorter. Those two end-of-line loops are two altogether different animals, and that is what I am trying to say, over and over again, right from Reply#2, 275 posts ago ! The bowline is a Gleipnir or a ABoK#160 or a Sheepshank with a “proper” collar, while the “Sheet bend loop” is more of an entanglement of three half hitches…I always hope that Derek Smith would modify his theory, otherwise we would miss an opportunity to analyse the bowline in more detail than we were doing two thirds of a century ago.

I should have stressed that I was speaking about the dressed and tensioned by hand knots only…Under heavy loading, the geometries vary - unfortunately, I have not been able to examine heavy loaded and/or capsized bowlines till now…

Right ! Please, keep it in mind, and tell it also to Derek Smith, and all people that keep telling that the bowline is something of a Sheet bend transformed into a loop…

A very general - and I may add quite bold, too - view of the bowlineess…It will lead to a definition of what I have called "collar structure " as a structure that might not involve any “collar” at all, nothing that “looks” like a “collar” - be it the “proper” common bowline s collar, or not.
Up until now, I have called such loops as “bowline-like” end-of-line loops, meaning that the moment the "collar structure " is pulled out of the standing part, the knot degenerates into the unknot. ( Notice that the "collar structure " might not even be necessary for the integrity of the “nipping structure” under moderate loading - as I have seen in the case of the “double, crossed nipping loops bowline” presented at (1). ) However, this was a consideration of the topology of the bowline, not its behaviour under (heavy) loading. To go as far as to characterize by "collar structure " anything that serves to stabilize the nipping loop,even if it does not look like a collar at all, or to disregard the “collar” element and concentrate on the “structure” , is a very bold movement, that only a few knot tyers would be ready to follow. The bowline is the king of the knots, no question about it, a marvellous thing that should come first in any knot compilation. Millions of people know it by its name, are able to recognize it and to tie it. This fact puts a certain limit on the generalization we may offer to the notion of the bowline. I have seen that the community of the knot tyers is conservative - to my view, too conservative…-, so will it accept such a very general characterization of its most used and admired loop ?

http://igkt.net/sm/index.php?topic=3233.msg23683#msg23683

X11 · 26 July 2012 22:48

There are two forms of the common bowline : the “left-handed” and the right-handed"" one. Similarly there are two forms of the “Eskimo” bowline, the left-handed and the right-handed.
Right ? Wrong ! The two legs of the collar of the standard, common bowline remain almost parallel to each other - just like the penetrating-the-nipping-loop rope segments at the Gleipnir, the ABoK#160 and the Sheepshank. On the contrary, the two legs of the collar of the “Eskimo” bowline are crossing each other, at an angle of about 90 degrees. (The more round the bight of the loop, and the larger the angle between the two legs of the bight of the loop, the smaller is this angle. At 120 degrees, it is almost zero - just as at the common bowline). So the second leg the collar ( the tail), can pass over or under the first leg ( the continuation of the eye-leg-of-the-bight). That means we do not have two, but four different forms of the “Eskimo” bowline.
It can be seen that, when the second leg of the collar, the tail, passes under the first, it gets itself into a position where it is squeezed in between the first leg of the collar and the rim of the nipping loop - so, at the end, we have a “hitch-like” knot, and a most effective prevention of any slippage of the tail.
Therefore, from the 4 different forms of the “Eskimo” bowline, the two -where we encounter this “hitch-like” configuration between the two legs of the collar- should, presumably, be more secure than the other two. I guess that the difference should be quite apparent with very slippery material ( like Spectra and Dyneema) - but I have not made any relevant experiments.
Now, I have noticed that the Sheet bend “bowline”, -the bowline-like loop mentioned at Reply#275 (1), with its “not-proper” collar and “not-proper” nipping loop - is the “reversed” form of one of the two “hitch-like” “Eskimo” bowlines (2). Does this mean anything ? Probably not - but I have imagined that the “Eskimo” bowline might have been discovered accidentally, when somebody would have grasped the (long) tail - instead of the standing end - of a "Sheet bend “bowline”, and has realized that this “reversed” loop could also hold very well. I guess that the standard bowline is probably a later refinement of the Sheet bend “bowline” - because the “proper” collar and the “proper” nipping loop would have not been such obvious solutions to the knotting problems of our ancestors, as they seem to us now. .. In fact, the “proper” collar and the “proper” nipping loop are quite advanced, sophisticated, maximally evolved and simplified rope mechanisms, where any redundant element has been omitted. The Sheet bend “bowline” looks much more primitive, naive, because its not-proper collar and its not-proper nipping loop have not reached their final, maximally simplified, perfect form.

http://igkt.net/sm/index.php?topic=3233.msg23702#msg23702
However, this “Eskimo” bowline is not the one that seems to be the most secure of the four forms .

X11 · 13 August 2012 10:11

We all understand the difference between the bowline-like end-of-line loops based upon a single “proper” nipping loop knot, and those based upon a single crossing-knot. The problem is that, if we do not consider the end-of-line loops based upon a crossing-knot be included in the family of the bowlines, we run the danger to exclude the “Eskimo” bowlines as well- and this is something that the knot tying community is not ready to acept ( And, it is a debatable issue, because, when the angle of the two legs of the loop is greater than 120 degrees, the “Eskimo” bowline behaves exactly as the common bowline. See Reply#118, (1))
One possible escape is to narrow the definition of the crossing-knot based end-of-line loops, so that it will not include the “Eskimo” bowlines any more. Then, we can exclude those more narrowly defined crossing-knot loops from the family of bowlines, without throwing away the baby with the water - the “Eskimo” bowlines with the not-so-bowline-like crossing-knot loops. I know that this is a compromise, and as such, it will not satisfy 100% anybody ( except me - perhaps :)).
So, we can define as a “proper” crossing-knot loop a loop based upon a particular knot, where the standing part touches the nipping loop s rim for a second time, at a second point. Then, we can exclude this family of end-of-line loops from the family of bowlines, reduce the number of loops that are considered as bowlines, but at the same time leave the “Eskimo” bowline in its traditionally occupied place.
At the double nipping loop end-of-line loops, where we have a second nipping loop, we will consider as “proper” crossing knot loops only the loops where the standing part touches again the rim of the nipping loop from which it has just left, i.e. before it has formed the second nipping loop. So the Constrictor based loop(s), for example, will continue to be considered as bowline(s), along with most of the “8” shaped, double-nipping-loop based knots.

http://igkt.net/sm/index.php?topic=3233.msg19858#msg19858

Dan_Lehman · 13 August 2012 19:33

I’m unmoved. There are fuzzy boundaries no matter
–consider the potential for the common bowline to capsize
into what might be called a “helix-based” knot (that with
a broad, helical curvature in the SPart as it passed through
the nub), and that other knots we’d (or at least I) like
to regard as “bowlines” have similar potential transformations
under load and with various dressings.

.:. I think that we must simply accept that fuzziness exists,
that the (sub)sets are close & interlinked by degree. We
might find that overhand-based knots come next to ask
association and by similar arguments of proximity. Maybe
under some discomfort in the setting out of all of this
we find some way to tighten definitions … , but at time
time, I see nothing compelling in that. (Just setting out
all of the knots --grouping & classifying put aside or as
mere conveniences to the task of enumeration-- will be
an accomplishment (and exhausting, if not overwhelming).

–dl*

Sweeney · 13 August 2012 20:35

I have watched and sometimes marvelled at the development of this thread which so often seems the pursuit of a definition y for its own sake. “Bowline” is simply a word applied now and in the past to a knot and extended to more knots by qualification (eg double bowline) - and it is now extended to a family of knots for no obvious purpose. I would agree with Dan as above - there is some merit in setting out all knots which have some link however tenuous to a bowline - but the link to a bowline serves only to make such a task feasible by drawing a (fuzzy) boundary. Logical extension of this is to try and identify all knots and simply give avery one a designation. the fact that a knot has relatives or not has no relevance whatsoever because it is a human perception not based on anything but a desire for order. I know that Dan has a penchant for a description in words of eg how to tie or describe a knot - I do admire that - but give a computer a set of pictures and it will find a match in a very short time as long as a reference picture is available. In short defining the bowline is as big a waste of time and effort I have seen in recent years - but it’s not my time or effort so carry on by all means.

Barry

X11 · 13 August 2012 22:56

I was sure you would have not (be moved, or see something compelling), but for other reasons : If we prefer to classify knots by their functions/mechanisms, and not by their looks/appearances, we can not distinguish the crossing knots from the "proper"crossing knots I propose - where the leg of the nipping loop does touch the nipping loop s rim another time, at another point ( not the “crossing point” of the nipping loop). The crossing-knot is a knot where the second leg does not run directly at / is not a direct continuation of, the eye-leg-of-the standing part of the loop, as the first leg comes directly from the standing end / is a direct continuation of the standing end. Instead, it makes a more or less sharp turn, because, when it leaves the nipping loop s rim, it has a direction “upwards” i.e., it could not have reached the tip of the bight had it not made this turn.
However, I think that I have “succeeded” to reduce, a little bid, the number of what we can consider as end-of-line loops that belong to the class of bowlines - and I have done it in an unambiguous way : It is easy ( NOT fuzzy) to see if the standing end or the eye-leg-of-the-standing part touches the rim of the nipping loop a second time, or not !
I am very happy that I have removed a considerable number of ex-bowlines from my (large) bowlines picture file, and have sent them to the (smaller) crossing-knot end-of-line loops file !