Author Topic: What defines a Bowline? - structure, characteristics, topology  (Read 134699 times)

DerekSmith

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #255 on: July 01, 2012, 12:27:37 AM »

    I have stated time and again this simple distinction :
    a. A hitch has one leg loaded and one not, because the second leg has gone under the riding turn, and has escaped as a free end. The hitch is asymmetric.
    b. A nipping loop has both legs loaded, to a more or less same degree. The nipping loop is symmetric.
    a, b., not even c ! SO simple...

Constant

So then, let us take a little look at this So simple distinction.

In THE Bowline #1010, the SP enters the knot bearing 100% of the load.  If we ignore any load shedding as the SP passes under the collar, then we may assume that the SP enters the Nipping loop with virtually 100@% load.
In the normally loaded Bowline each loop leg carries 50% of the load, and of course, any ring loading can completely unload the SP loop leg.

So by your definition, the Nipping loop which is ( b. A nipping loop has both legs loaded, to a more or less same degree. The nipping loop is symmetric.), so in practice the nipping loop within the Bowline fails your stipulated definition, and is therefore not a nipping loop (even though it clearly is...)

Furthermore, you have stated that (The hitch is asymmetric.), so as the nipping loop in the Bowline is asymmetric (unless the Bowline is ring loaded 100% onto the SP loop leg), then the Bowline nipping loop is asymmetric and is by your definition a hitch...

As you see Constant, making definitions can be a bitch, but at least you are trying to justify your opinion.

Anyway, to end this argueing over a name, let me rename the component to the Single turn Component - and please dont forget - it is not a bend or a hitch or any recognised knot - it is a component...

Happier now?

Derek

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #256 on: July 01, 2012, 02:39:09 AM »
    I guess that YOU are happier- but that does not makes you less wrong... :)
   You have carefully expanded your "stipulated"  counter - argument into many words and paragraphs, trying to make it look reasonable. Well, many words do not make a false claim true - unfortunately.
    In an "ideal" bowline, where there would be no friction, what you describe is what would have happened, indeed. The nipping loop, being in equilibrium ( as the tension forces on the one leg would be the same with those on the other) , would have been free to move , to "walk", to wherever the eye-leg-of-the-bight would have dragged it - i.e., downwards, towards the tip of the bight. And this is what is happening even in this not-so-ideal world ( where knot tyers do not understand each other...), when the ropes are very slippery ( Spectra/Dyneema) and the load is very heavy. It has even been documented in videos, but you have forgotten to mention it...
    When there is friction, and the loads are not so heavy, the nipping loop can not walk down the standing part, because it can not rotate around the legs of the collar that penetrate it. If the pair of legs of the collar , on the one hand, and the rim of the nipping loop, on the other, were not "glued" together due to friction, if they behaved like the two parts of a ball bearing - the one free to rotate in relation to the other - then the nipping loop would have been incapable to prevent the bowline to shrink like a noose, indeed.
   So, the one leg of the nipping loop does not squeeze the other underneath anything, as the one leg of a hitch does to the other. The fact that the 100% of the load on the one leg becomes 50% on the other HAS NOTHING TO DO WITH THE INTERACTION OF THE TWO LEGS, as it happens in the case of the hitch. It is due to the friction between the rim of the nipping loop and the two legs of the collar ( the continuation of the eye-leg-of-the-bight, and the continuation of the tail ). If there would have been no friction there (or if we had been able to insert a roller bearing between the nipping loop and those two legs that go through it ), the nipping loop would have walked down the standing part, right till the tip of the bight .
   I understand that you have jumped out of joy when you have discovered this apparent counter-argument of yours...Well, next time you should better try harder ! :) And with fewer words, because if something is true, it penetrates deeper into your opponents happiness if it is brief. I would have said that :
" The 100% of the load on the standing part becomes the 50% of the load on the eye-leg-of-the-standing-part. So the nipping loop is, according to your definition, not a nipping loop, but a hitch." Period
   To which argument, I would have replied as such:
" The reduction of the load on the nipping loop s legs, from the 100% to the 50% has nothing to do with the one leg riding over the other and absorbing a part ( or the whole) of its load, as it happens in the case of the hitch. It is due to the friction between the rim of the nipping loop and the pair of the collar s legs that penetrates the nipping loop. Were there no friction there, the nipping loop would have walked down towards the tip of the loop, dragged/pushed by the collar, because the tensions on each of its two legs would have been perfectly equal."

    Derek, we are both trained as engineers, but it seems we have been going to different schools together !  :)
   What brings peace in my mind is this ; Whatever we say, any paradoxes we are discovering the one to the other s theory, are only subjective. The real world is there, independently of our semantic blah-blah, and works fine ! The bowline works, thank KnotGod, and neither me nor you can change this by arguments, however "rational' we think they are. Oh, yes, when I see the real world, when I see a bowline or a Zeppelin bend working, I am happier !  :)

Constant
« Last Edit: July 01, 2012, 03:19:46 AM by X1 »

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #257 on: July 01, 2012, 04:57:44 AM »
" Single turn component" for the part of the bowline I call "nipping loop" , sounds fine to my ears...It describes something that makes a turn, but also something that can turn, that can rotate. A "nipping loop" on a tensioned line can rotate, and "walk" towards the one or the other direction. In the case of the bowline, it tends to walk downwards, towards the tip of the loop, because that is the direction to which the collar and the eye-leg-of-the-bight drag it, the first pushing it from above and the second pulling it from below. 
   Why this does not happen in the real world ? Why does the nipping loop remain fixed, placed at one point of the standing part, even if the collar and the eye leg of the bight are pushing and pulling it downwards ?  Because of friction. But not because of the friction between its two legs, as it happens in the case of a hitch. Because of the friction between the rim of the nipping loop and whatever penetrates through the nipping loop, i.e, the two legs of the collar.
    Of course, the nipping loop squeezes the two legs of the collar together, the one upon the other, and this forces them to behave as a more or less unified object. However, this is something that can be achieved with the help of other means - with a bowline s simple "lock", for example. Let us suppose that this has been achieved already, and that the two legs of the collar are "glued" together, metaphorically or literally !  :) If that is so, now these two legs can drag the collar, and the collar, by its turn, can push the nipping loop. What will happen ?
    In an " ideal" world and in an"ideal" knot, where there is no friction, the push of the rim of the collar will force the nipping loop to rotate around the axis formed by the legs of the collar, just like the outer rim of a ball bearing rotates in relation to the inner one. Rotating like this, the nipping loop will walk down the standing part, and nothing will stop it from reaching the tip of the bight - and the bight itself to shrink, like a noose, and finally disappear !
    However, this is not what happens in the real world, thank KnotGod ! Because of the friction between the rim of the nipping loop ( the rim of the wheel) and the legs of the collar that go through it ( the axle of the wheel), the nipping loop can not rotate, so it can not walk, even if it is pushed by the collar from above, and it is pulled by the two legs of the collar from its centre. Of course, friction is all over the place. There is also friction between the two legs of the nipping loop, and between the rim of the nipping loop and the two legs of the collar. However, those effects are less pronounced, and secondary, I believe This is indicated, if niot proven - by the fact that a " half-bowline " where the nipping loop will not open up into a helix, will work surprising well, even without the help of a collar ( with a very loose collar, or even with a collar bight cut into two !) The two nipping loops, in the cases of the Water bowline, the Girth-hitched bowline, the ABoK#160,161 and the Sheepshank, do not need a collar to remain closed - and so they work very well, because their nipping loops, although they are pulled toward one direction, will NOT walk on the line. The lines around which they are " turned" prevent them from rotating, and so they can not move.
   We all have played with such toys when we were kids, but it seems we have forgotten it ! :).  If we make a " turn"  with a string around a pencil, and keep the two ends of the string tensioned, we can "walk" the pencil from the one end to the other - provided the pencil is very slippery, or we enable this "axle" to rotate freely into our palm as we drag it towards the one or the other end. If the string is tensioned, if it does not slip on the surface of the pencil, and the if the pencil itself is not allowed to rotate the turn will not move, even if the pencil is pushed or pulled. I have called such a toy a "half-bowline", and its main component as "nipping loop", but I will be also happy with the name of a "single turn component". The Double bowline has a "double turn component", and the particular double, crossed nipping loops bowline I have presented yesterday will be a loop based upon a " double crossed turns" component, or something like that, I guess. 
« Last Edit: July 01, 2012, 12:01:25 PM by X1 »

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #258 on: July 01, 2012, 12:45:07 PM »
   It would be interesting to study the " single turn component " of the bowline knot in isolation, independently from the presence of the collar.

   Let us first examine the simplest case, where :
   a. the " single turn" is a 360 degrees turn around one round object - be it a pencil, or a one or more segments of rope, held there by the nipping action of the turn, by being glued together, or whatever.
   b. the two legs/limbs of the turn are aligned - they leave their contact point to opposite directions. So, the former standing end and the former eye-leg-of-the-standing-part lie on a straight line.
   c. the turn itself and both its legs/limps lie on the same plane.

   This picture is only approximative, of course.  In fact, even in this case, the turn is but a helix, only this helix has the smallest possible pitch, of one rope diameter. So the turned rope is never a ring, it is segment of a helical coil, although the helical path of this coil has a small pitch, in comparison to its width. To speak of a plane on which this 360 degrees turn lies, it is only a convenient abstraction, for the sake of a simplified description.
   As the reader who was brave and patient enough would have read by now, in the two previous posts, if we push this turn to the one or the other direction, it will rotate together with anything it encircles, and so it will "walk" alongside the tensioned line. ( However, if it is NOT free to rotate around the objects it encircles, or if these objects are NOT free to swivel around themselves, it will NOT walk ! That is why the turn of bowline does not walk towards the tip of the bight ).
    Here comes the interesting part. What will happen if, instead of keeping the plane of the turn parallel to the tensioned line, we twist it a little bit ? ( Twist it so that  the two legs/limps of the " single turn component" are also twisted around each other, and get are more embraced around their contact point, not less. We wouldn't twist it so that it would open up to an open helix ...)
    It is evident that, as we twist the plane of the turn in relation to the tensioned line, around the contact point of its two legs/limbs, the friction between the legs would start to get greater and greater. So, the rotation of the turn and its walk  alongside the tensioned line would now be restrained more and more by friction forces betewwn the two legs/limbs. On the area around the crossing point, the two legs would now be forced to embrace each other more, along a longer segment, and this will induce greater friction inside the whole rotating and " walking"  mechanism.
    When the "single turn component" of the bowline knot is twisted ( due to the direction of the lines that pass through it, or for whatever other reason that has to do with its position/orientation inside the knot s nub), then it remains more steadily fixed on a certain point of the standing part, and it does not run the danger to walk downwards, towards the tip of the bight. So, a clever effective strategy is to force the plane of the turn to twist more, to settle to a position where it would be as much inclined in relation to the standing end axis as possible. At some point, we may argue that we should not speak of a common s bowline s turn component any more, but of a crossing knot s turn component. That transformation would be more evident if the turn is also re-positioned upwards or downwards, so that a large part - or the whole- of it lies well above or below the crossing point. In that case, we have a genuine crossing knot bowline.
   

DerekSmith

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #259 on: July 01, 2012, 01:49:11 PM »

    Derek, we are both trained as engineers, but it seems we have been going to different schools together !  :)
   What brings peace in my mind is this ; Whatever we say, any paradoxes we are discovering the one to the other s theory, are only subjective. The real world is there, independently of our semantic blah-blah, and works fine ! The bowline works, thank KnotGod, and neither me nor you can change this by arguments, however "rational' we think they are. Oh, yes, when I see the real world, when I see a bowline or a Zeppelin bend working, I am happier !  :)

Constant

Hi Constant,

No, I am not an engineer, that accolade is yours not mine, I am a chemist.

I am sorry that you found my post excessively lengthy, I try to communicate clearly and so use however many words I feel are necessary to eliminate ambiguity.  After all, there is no point in posting words if all they do is confuse.

I am glad that simply changing the name of the component has resolved your problems with it.  However, it is worth mentioning that if I take four of these components, I will have created the Frictionless hitch...  Indeed, If I use cordage and former with a suitably high coefficient of friction, I could produce a Frictionless hitch out of just one Single turn Component and in that special case the component would indeed be the hitch.

The concept of 'Hitch' is a weak one, historically featuring cordage bound to a non cordage static object, but many instances show that a 'hitch' can be made to cordage objects as well.  Indeed, in compound cordage constructions, one part of the construction can be 'hitched' to another, so is it not reasonable that the term could be extended to describing the hitching of one component of a knot to another?

Derek

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #260 on: July 01, 2012, 04:24:39 PM »
I am sorry that you found my post excessively lengthy,

   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 !


it is worth mentioning that if I take four of these components, I will have created the Frictionless hitch...  Indeed, If I use cordage and former with a suitably high coefficient of friction, I could produce a Frictionless hitch out of just one Single turn Component and in that special case the component would indeed be the hitch.

   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
« Last Edit: July 01, 2012, 04:32:19 PM by X1 »

DerekSmith

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #261 on: July 01, 2012, 08:18:23 PM »

 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

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

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #262 on: July 02, 2012, 02:21:20 AM »
...the weight of just a few inches of cord will be sufficient to hitch the 100kg load on the SP .
   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?

   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:
1. The one leg is loaded, while the second is not.
2. 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 :
1. Both legs are loaded, to about the same degree.
2. 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 !  :)
   
« Last Edit: July 03, 2012, 07:07:56 AM by X1 »

DerekSmith

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #263 on: July 02, 2012, 10:12:37 AM »


  The friction coefficient is irrelevant, you could have supposed a pole/bar of a sufficiently large diameter, whatever the friction coefficient is.
   

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 -

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

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #264 on: July 02, 2012, 12:52:08 PM »
   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!  :) 

1)   http://igkt.net/sm/index.php?topic=3610.msg20611#msg20611
« Last Edit: July 03, 2012, 08:57:57 AM by X1 »

DerekSmith

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #265 on: July 02, 2012, 06:01:05 PM »
I have not said that the friction coefficient is irrelevant ! ! ! I know very well what the capstan equation is ( and it is only an approximative function, of a very simplified description of what really happens !). I said that the friction coefficient is irrelevant in relation to your argument ! You could have used the same argument, without specifying the friction coefficient as you did, by only supposing a sufficiently large drum.
   If you like to learn something more about the capstan equation, please, do not read it from the poor source you have cited !  :)(The Wikipedia article is correct, and much more informative. ) If you still believe that the radius of the drum does not matter, you are excused...You are a chemist !  :)
 

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:

    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 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

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #266 on: July 02, 2012, 08:56:11 PM »
... 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.

   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".
« Last Edit: July 03, 2012, 08:59:54 AM by X1 »

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #267 on: July 03, 2012, 09:02:16 AM »
   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!  :) 

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

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #268 on: July 03, 2012, 10:41:01 AM »
Thanks Constant,

I think you have something there.

Derek

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Re: What defines a Bowline? - structure, characteristics, topology
« Reply #269 on: July 17, 2012, 07:24:01 PM »
   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.
   1. 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.
  2. 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.
« Last Edit: July 17, 2012, 07:37:39 PM by X1 »