testing physical theories of knots

Practical Knots
21

Hi bcrowell, I have tried to get hold of a copy of the Maddock paper but failed. I wonder, if you or anyone else that has contact with Maddock, might ask him if he would agree to releasing a copy in pdf format to the IGKT?

You comment that you find it strange that the SS has more grip than the square knot and that you have read that the square knot is considered to be more ‘reliable’. Indeed, the square knot when used as a binder knot is regarded as very reliable. The sheepshank on the other hand is neither a bend, nor a binder knot, and concerns regarding its ‘reliability’ stem from the fact that it can easily fall apart when it is left uhloaded. Of course, part of the SS functionality is that it can be dismantled so easily even after heavy loading.

However, when you tie the SS as a bend, and particularly, if you use this bend configuration as a binder knot (close relative of the Gleipner) then it is stunningly reliable because the load is maintained relatively constant.

‘Reliable’ is a relatively loaded term, and whereas this thread is dealing with the ability of knots to function as the cf is progressively reduced, i.e. failure by slippage, ‘reliable’ has much wider aspects built into it including (as in this case) resistance to flogging and unloading.

I am surprised that you find the SS ability to tolerate a lower cf ‘strange’. The SS has a significantly better load transfer structure than the square knot has, so potentially far less of the load is transmitted through to the W/E. You should be able to demonstrate this by replacing the half hitches with clove hitches or multiple half hitches until it no longer fails with the reduced cf cords.

Derek

22

But one needs to note the nature of “failure” : a sheepshank
is not a stable knot when untensioned, and IMO is vulnerable
to capsizing --these are serious problems but are not slippage.
A “squaREef” knot --my names-letters merging-- can also assume
some different geometries : staying as illustrated in good symmetry,
or having one side’s tail be drawn out of this symmetry.
(And with laid ropes, there is the matter of handedness.)

–dl*

23

I’m feeling stunned, but insecure : how is a sheepshank at all
an end-2-end or binder knot? Well, there is that Ashley-presented
mused idea of cutting one’s line after tying the structure for then
a shake-&-retrieve potential after lowering. But, really, … !?
Meanwhile, the mention of the Gleipnir brings to mind its behavior
I’ve witnessed, which was nowhere near so secure as I wanted.
Maybe it would be a good one for these tests, tied with the knotted
part mid-span of a (doubled) circular sling and ring-loaded. (Beware
the various ways to orient the Gleipnir --I illustrated four ways
in that thread.)

–dl*

24

Hi Dan,

Had to chuckle there, of all the people on this forum, I expected you to have the SS as a bend drawn up with numerous variants already trialed and tested.

The version I was referring to is not quite Ashley’s ‘cut through method’, so I have sketched it with Dave Root’s latest version of Knotmaker. To tighten simply pull the loop legs going out to the SPs.

Derek

25

This is a little bit technical, but i’m having trouble with a math thing. I am trying to find out how to calculate the total normal force in a hitch for lengthwise pull, and i can do it fine in 2 dimensions, but i fail to see how it works on a three dimensional pole. I understand how there is torque and tension on the rope, but i don’t get what the actual integration for the normal force comes out to, because i don’t know what counts as an instantaneous force. My physics teacher is being less than useless in this regard. Can anyone help?

26

This is a common but unfortunate situation, and I don’t know of a good solution other than reforming copyright laws. Since ca. 1996, physicists have generally been putting their papers on arxiv.org, where anyone can access them for free. But older papers (many of them done with grant money paid for with your and my tax dollars) are being held hostage by publishers. Here is Maddocks’ contact info if you want to try: http://lcvmwww.epfl.ch/~jhm/

I’ve written up a short description of Bayman’s theory of hitches, along with a description of some experiments I’ve done: http://www.lightandmatter.com/article/knots.html

This is a reasonable kind of idea, which I have been pursing semi-systematically in my free time. Find a set of knots, and rank-order them by strength. Test them with ropes having different coefficients of friction. There is a table near the end of the write-up I linked to above summarizing my data. The good news is that I have a set of knots (granny, square, figure-8 bend) that is able to distinguish the different frictional characteristics of the materials I’ve been able to obtain. That is, if you want to estimate the coefficient of friction of a given rope, you can try those knots, and get some idea of how it compares with other materials.

The bad news is that I haven’t succeeded in finding any reliable way of measuring the coefficient of friction of a rope reliably, so it seems impossible to compare quantitatively with the theoretical predictions.

One method I’ve tried for estimating the c.f. is to make a “tightrope” out of the cord, then sling an inverted “U” of the same cord on the tightrope. Then I elevate one end of the tightrope and see at what angle the U starts to slip down it.

Another method is to wind a bunch of loops of the cord tightly around a book. I then take another piece of the cord and make a wad or small, tight coil out of it. I place the wad on the book and tilt the book until the wad starts to slide.

These methods don’t seem to give results that agree with the published coefficients of friction for materials like teflon, nor do they agree with the observed rank-ordering in terms of ability to hold a knot. For example, my nylon cord clearly holds a knot better than the rayon satin, but the tightrope and book methods give a c.f. for rayon satin that is almost twice that for the nylon cord.

27

Thank you. (Although I’m unsure of the meanings of some of
the mathematical symbols ; and would be unsure of the math,
even so, by myself.)

You list “figure eight bend” : this is ambiguous, as the knot has
various dressings/loadings --the loading question for such trace
knots is typically ignored (which of the parallel ends is loaded?).
Can you show which version of “fig.8” you actually tested?

For common reference,
www.pbase.com/chris_craggs/image/76852983
here’s an image of a fig.8 eyeknot tied off
with a strangle knot ; this is in what I call the “perfect form”
dressing, loaded on the interior path --i.e., of the twin strands,
the one bearing 100% tension turns around the eye legs on
the inner rather than outer side (and thus it bears against
other parts of the knot, not against the twin strand).
I’ve called this particular form the “weak form”, based on some
indication that loading the exterior strand is stronger (and
that strand will bear into its twin as it makes its U-turn).
(In fig.8 eyeknots, the symmetry is often lost in the turn
of the eye-bight --e.g., the cover image on [u]The Outdoor Knots Book
by Clyde Soles).

You also write about the Dyneema cord slipping out of a “bowline” :
you could emphasize that surprise by rightly specifying “double bowline” !
–quite the eye-opener, for me!! Wow, that pretty much jettisoned
some dreamy thoughts I had about crafting a knot for HMPE !!
(I did have some (5) tested; all held to rupture (at 35-41% tensile).
((oh, eyeknots, tied at each end of the 5 specimens))

The bad news is that I haven't succeeded in finding any reliable way of measuring the coefficient of friction of a rope [], so ...

I’d suggest some sort of weighting method and seeing how
it flowed thus. There is some concern that e.g. running rope
through an eye of itself could see varied pressure of the eye
legs with varied loading, but there might be a way to work
out something reasonable --esp. in ranking, even if not
of much actual-value sense. (same can be said of knotted ropes’
strength)

Then there is the tact of trying to see how one’s theory matches
others’ results. How well do you think that you can come up with
reasonable estimates --again, perhaps more sure in relative terms–
for the security of the sheet bend, double sheet bend, bowline,
and fisherman’s knot ? I ask about these particular knots because
there is a test report that gives indications of slippage among them
–which varies per material in some cases. And this is for real rope
(nylon kernmantle, 7mm, 10.5mm, 12.7mm)!

–dl*

28

It’s basically this: http://www.animatedknots.com/fig8join/index.php I.e., the opposite ends of the two different strands are loaded, as in those photos. I tried to dress them neatly, but some of the materials were hard to work with. (The dyneema I have is the loose fibers stripped out of a 2 mm kernmantle rope.)

There really isn’t a physical theory of friction knots at all (or if there is, it’s not in the papers I found). The Maddocks paper shows a couple of attempts to calculate results, but their method isn’t systematic. There’s a systematic physical theory of hitches, but not knots.

29

There are NO other practical knots than friction knots. The Gordian knots, which do not require friction to remain tied, are not practical knots - otherwise there would had been NO need to cut them by a sword ! :slight_smile:
To my mind, hitches ARE knots, they are a subset of knots. I am not aware of any definition that will be able to point out the difference - if there is any difference.
There is NO systematic physical theory of hitches - although there might be one so-so physical theory of a few hitches… which is a tottaly different thing ! :slight_smile:
There ARE some attempts to physical theories of knots, although they are still at their infancy :

Contact-friction modeling within elastic beam assemblies: an application to knot tightening
Damien Durville
http://link.springer.com/article/10.1007%2Fs00466-012-0683-0#page-1

Dynamics of elastic rods in perfect friction contact
Francois Gay-Balmaz and Vakhtang Putkaradze
http://arxiv.org/abs/1207.3540
(PDF copy freely available)

http://prl.aps.org/accepted/1c07dY65Hf11393b270522a8a34dcf01ed2796dc6

30

Hmmm, I emphasize “i.e.” for that makes no sense : we’re
talking of an end-2-end knot, so “of course” it’s that; what
is questioned is the fine points of geometry --and I see that
Grog puts forwards (perhaps w/my urging …) what I call the
“perfect, strong form”, load going to exterior twin parts,
UNlike the reference (for an eye knot) I gave above, where
it goes to the interior twin. (To the Animated Knots dressing,
I’d set it by hauling firmly on the tails, setting up the curvature
in SParts that will take and give way to on serious loading,
which will make this dressing of the knot compress and fatten
and assume a sort of 30-35degree angle re the axis of tension.)

As for working w/HMPE mere fibres …, good luck! :wink:

Thanks,
–dl*

31

Not true. A girth hitch doesn’t require friction.

32

I see. I didn’t make any systematic attempt to dress all these knots identically or in any predefined way. The Maddocks paper doesn’t make any attempt to take into account the detailed geometry of non-hitch knots. (They do it for hitches, but not non-hitches.) They make some ad hoc assumptions about forces, which they don’t justify. The assumptions are not unreasonable for various possible realistic dressings, but they’re not calculated based on any particular dressing, and are not exactly correct for any possible dressing.

33

The world would have been a veeery different place, if what you say was true - and what I said was not… :slight_smile:
Imagine we had discovered a hitch, which would not require friction… that is, which could be tied with any rope and hold on any pole, however slippery… I wonder, would this be the knot tyers paradise, or the knot tyer s hell ? :slight_smile:
See the attached pictures for two knots that do not require friction, indeed. They are not very practical knots, are they ? :slight_smile:

( I do NOT believe you mean that a girth hitch does NOT require friction, as a round turn does NOT require friction ! If you place one or more invisible hands, that can hold with their invisible fingers the rope in any point of the knot you wish, NO knot will require any friction - you would have managed to remove the knot-tyers from the paradise of friction, and put the fingers-makers in their place ! )

34

Hi Constant,

On the premise that we accept that friction is different from the forces involved in forming chemical bonds (which is probably isn’t), then I am afraid that I must disagree with your assertion that there are no practical knots other than friction knots. I can think of two situations where this is not the case, one of course is the case of a loop made girth hitch as proposed by Ben.

It is very easy to construct a loop without a knot, relying solely upon chemical bonds. If we make a cylinder of polymer, then take a slice off the end, we effectively have made a monofilament loop which is essentially a single huge molecule made by crosslinking the polymer strands. Such a loop can be fashioned into a Girth Hitch and it must function even if the monofilament had zero friction.

The second situation utilises obstruction rather than friction. If we again take a monofilament cord and form a stabilised nipping loop component such as a Strangle, then we can take the WE around a hitching point (or an opposing loop in a bend) and pass it back through the nipping coils. Now by utilising friction we can form a perfectly usable knot simply by putting a stopper knot in the WE. So the question is, can we form a stopper function without friction, and of course, the andswer is yes. If we heat the polymer to soften the molecular bonds, then deform the monofilament into a ‘blob’, then cool the polymer to reset the bonds, then we have made a frictionless stopper. The nipping loop has leverage in its favour and carries 100% of the SP load, while the ‘blob’ has reduced mecahnical advantage and carries only 50% of the load. Even with zero friction, the ability of the blob to pull through the nipping loop is down to which component has the greater mechanical advantage. Nothing to do with friction.

Derek

35

Thank you, Derek,

As you know much better than me, it is not. However, the same “forces” ( electromagnetic fields, electron/photon interactions,) acting on greatly different scales and between greatly different number of things, are described by different physical models/theories - and they have different names.

If you refer to the girth hitch, and not to the single round turn, you, too, have probably not understood what I was trying to say… It is inherent into the definition of a knot, either a mathematical or a physical one, that it can not change its topology - and an untiable knot, due to its topology, will remain untied, for KnotGod sake ! If you melt and join the two ends of a simple loop, or of an overhand knot, or of a fig.8 knot, etc., you can not untie this thing - unless you move to higher dimensions ! :slight_smile: When you " join" the two ends of a girth hitch, or of a round turn, by using the friction between your fingers and the rope, you can not release/untie this knot, that is for sure - but this is due to its topology, and its topology only, it is not due to the presence or absence of friction. If you wish to say that you can not untie a hitch due to its topology, even if there is no friction, you do not have to mention the girth hitch ! The single round turn hitch is more than enough… :slight_smile: The single round turn with joined ends, and the girth hitch with joined ends, and sooo many other hitches with joined ends, will not be released or untied, but this has nothing to do with them being practical knots - their corresponding “ideal” knots will do the same thing, merely because the topology of knots do not change, by definition ! I said that there are no practical knots that do not need friction, I had not said that there are no knots that can retain their topology without relying to friction ! :slight_smile: EVERY knot will do this, either a mathematical or a physical one, so this can not be an issue, which one should “disproove” with the “counter example” of the girth hitch :)( and, curiously, not any other hitch topologically equivalent to the closed loop, or to the overhand knot, to the fig.8 knot, etc.) Otherwise, it is like you suppose that there is something else, mysterious, unspoken, beyond the self evident topology or the presence of friction, which makes a knotted rope remain knotted… Well, in fact there is, the bulk of the rope itself, or the bulk of tangled segments of the rope, as it happens with the Gordian knots. However, as far as I know, there is no practical knot based on this pure Gordian knot mechanism, without also relying, to some degree, to friction. I have shown the two simplest Gordian knots that can not be untied, not due to their topology or friction, but because a wide incompressible thing can not pass through a narrow inextensible thing - as we all know ! :slight_smile: If this is what you mean by “obstruction” , we agree ! ( it happens ! :)).

PLEASE, read again my old post about Gordian knots, and what a knot is. (1)( I copy some parts here )

A '“knot” is a 3 D configuration - formed by one, or more, “ropes” (*) - that cannot be transformed into a figure resembling one, or more, separate straight lines and/or perfect circles ( i.e., cannot be “untied”) due to one, at least, of the following three conditions :

  1. Topology
  2. Friction
  3. Constant length and cross section.
    Most people believe that, if a knot cannot be untied, this is due to topology or friction only (condition 1 or condition 2). The existence of “Gordian knots” (**), proves that this can also be due to condition 3 only. So, although we cannot help untie Gordian knots, they, nevertheless, can help us understand and define what the knots that can be untied are.

(**) A “Gordian knot” is an Ideal or a Physical knot that cannot be “untied”, even if this is not due to Topology (1), or Friction (2).
Conjecture: the only thing that can prevent a Gordian knot to be “untied”, other than Topology or Friction, is the fact that the Ideal and the Physical knots have constant length and cross section, i.e. condition (3). That is, the fact that the cross section of the ropes that make ideal and physical knots cannot be altered ( be shrinked or deformed ), together with the fact that they are defined/supposed to be flexible/stretchable only in their transverse dimension, means there might be cases where some part of one knot, that happens to be knotted, due to its volume, its bulk, cannot pass through another part of the same knot that happens to be a small ring. If this is the only way that those two parts can be separated, this knot cannot be untied, i.e. it is a Gordian knot. (At present, I am not aware of any mathematical proof or disproof of this conjecture.)

Three Gordian-like knots that do not use friction, and could possibly be considered as practical knots ( but they are not…), are the knots shown in the attached pictures.

  1. http://igkt.net/sm/index.php?topic=3610.0
36

Hi Constant,

So we agree that the second of my two examples is an example of a practical (if somewhat impractical) knot which does NOT rely on friction.

However, I do not understand your comments about the Girth hitch.

If I take an endless loop of monofilament, form a bight and pass it through a ring or around a post, then pass it through the rest of the loop, I make a Girth hitch, which is real, functional, tyable and untyable, and functions purely because of its topology and not because of any friction.

Surely this demonstrates Bens claim that the Girth hitch does not rely on friction and is a practical knot?

Derek

PS, the diagram suggests that that particular knot can be easily untied ?

37

No ! :slight_smile: It is an impractical ( = not practical) knot that rely on the Gordian knot trick described at the thread I have mentioned… plus some melting ! It is not a practical knot, just as the knots I have shown at the previous post, that do not rely on friction, are not practical knots. I have been chased in this Forum for publishing knots that, to my view, were practical, but “the experts” said that they were not, am I going to be chased now for the exact opposite ? :slight_smile: Are we going to consider as practical, knots that rely on melting, gluing, metal parts, etc.? No, Derek, a stopper does rely on friction, unless it is the monster stopper based on the Pile hitch, shown in my post ( or the similar one shown by Pieranski et all). If this is a practical stopper, then we agree ! :slight_smile: ( If you are searching for such ad hoc, deus ex machina solutions, I have many other to offer…How about immersing the knot in water, then freezing the water ? :slight_smile: It uses temperature just like your solution, but, just like your solution, it needs no friction at all ! :slight_smile: In some already near-freezing environments, it will consume much less energy than your solution… So, in Siberia, for example, it will be a practical knot, indeed - enviromental friendly…)

Oh my knotGod ! You didn?t read any of my posts very carefully, did you? :slight_smile: Who said that there are no knots that rely on topology? Read my lips ( actually, the first number…):

A '“knot” is a 3 D configuration - formed by one, or more, “ropes” (*) - that cannot be transformed into a figure resembling one, or more, separate straight lines and/or perfect circles ( i.e., cannot be “untied”) due to one, at least, of the following three conditions :

  1. Topology

Is the girth hitch your favourite example of a knot relying on topology ? Very strange gustibus, indeed…because mine is the overhand knot, or the single round turn “hitch” . :slight_smile:
If somebody tells you that all " all practical knots are relying on friction" , and you do not answer that " Not true ! There are knots that rely on topology", but offer as a counter-example the girth hitch (!!!), then one of the following is happening :

  1. You do not understand that, in the absence of rope-to-rope and rope-to-pole friction, but in the presence of the rope-to-fingers friction ( fingers holding the two ends of the rope ), the girth hitch works in exactly the same way as a single round turn - so, if you are afraid of simply speaking about topology, or if you believe that the other guy does not know what topology is, you just offer the single round turn as your supposed counter example, for knotGod s sake, not the girth hitch! - not any one else of the dozens of hitches that, if their two ends are 'joined" together by melting, freezing, gluing, sticky fingers, etc, they do not need friction to remain attached to the pole ! By the same token, if somebody tells you that " all practical knots are relying on friction" , you do not mention, as a counter example, a hitch, not even the most simple of them, the single round turn… You just mention the most simple knot, the overhand knot ! :slight_smile: But if you do not understand that, you have to search for something that is a little complex, believing that complexity offers something else, something more than what topology alone offers… and you discover the “girth hitch” ! :slight_smile: The single round turn, or the overhand knot, had not crossed your mind… :slight_smile:
  2. You do not understand that it has no meaning to offer a counter example for a member of a subset ( the practical knots are a subset of knots ), when you could well use a characteristic of a member of the parent set itself. So, when somebody tells you that “all practical knots are relying on friction”, you do not offer as your counter example a particular practical knot ( the girth hitch !), when you could well had mentioned a general knot ( the overhand knot), be it mathematical and/or physical ! So, "if you are afraid of simply speaking about topology, or if you believe that the other guy does not know what topology is ", you simply tell him : " What do you mean ? The overhand knot does not rely on fiction ! ", i.e., you speak about topology, in the most clear and simple way, using the most simple and clear knot that illustrates this essential characteristic - you do not try to figure out which knot seems complicated enough, so this simple topological characteristic will be hidden below two round turns and a bight ! ( the girth hitch…)

However, if you wish to answer in the way we often answer to each other in this Forum, i.e. telling some nonsense with a pompous style, you try to persuade yourself and the (non-existing, imaginary) audience that the other guy does not know that a link (two entangled closed loops) does not need friction to remain entangled for ever…so you offer the most “clever” counter example you can think of… the girth hitch ! :slight_smile: Oh, my knotGod !
I only wish to say that anybody that has something to offer to the - very difficult - endeavour of defining what a knot is, he should better say something more that knots do not need friction to retain their topology :)… and post his thoughts in the above mentioned thread. I will be glad to discuss this issue, without style !

No, the diagram suggests exactly the opposite ! :slight_smile: That the particular knot can NOT be untied, by pulling its ends, because of the Gordian knot trick : the bulk/volume of a knotted segment of the incompressible ideal ( no friction, no extension, round cross section) rope of the one link can not pass through the self-shrinking loop of the other link, so the knot can not be untied, even in the absolute absence of any friction.

I repeat : There are NO other practical knots than friction knots.
( And I am NOT speaking about knots that can not be untied due to their linked topology, be them mathamatical knots or practical knots, for KnotGod s sake …)

38

Hmm, I have taken ‘Practical’ in this dialogue to mean real, as distinct from Theoretical, hyperthetical, imaginary, mathematical etc. i.e ‘not real’, or ‘impossible to make with real cord’. I have accepted the distinction between Practical (real) and Practical (easily and regularly usable) by using the phrase “practical (if somewhat impractical)”.

However, on your comment “Are we going to consider as practical, knots that rely on melting, gluing, metal parts, etc.?” - Yes, indeed I believe that we do consider these things as practical. Techniques of changing the working diameter of cordage are as old as the skill of ropemaking. Even today with braids, the technique of backthreading the braid through its core is a relatively common practice and who would suggest that we deny the Marlinspike its toggle?

But regardless of the practicality or acceptability of melting or back splicing to make a suitable stopper, the fact remains that a fully loaded constricting nip can function in a frictionless material because one of the aspects of the process of driving the stopper through the nip is it’s mechanical advantage.

If we take a fully loaded nip and attempt to drive a very narrow taper through the nip, we will be able to do so with less force than the load on the nip because the narrow taper has a very favourable mechanical advantage - it is a wedge lever. If we increase the angle of the taper we loose MA and we will see that the force needed to drive the taper through the nip increases. The moment the force required to drive the taper exceeds the nip loading, then we have a knot that will not be able to pull through, regardless of friction. By making the MA hugely in favour of the nip by making the stopper change teh diameter rapidly from one to two diameters in a very short distance, we have a practical knot which would function even in the absence of friction.

Derek

39

Derek, we had agreed that the Symmetric Sheet bend is not a practical knot, even if it can be easily and regularity usable, because its dressing is unstable when it is not under constant tension… The “Practical” knots are a much smaller set than the “Real” knots, but also smaller than those “Practical (if somewhat impractical)” animals of yours ! :slight_smile:

I see your point, but let me say this : When I follow this reasoning in my mind, I see one or two tubes of Super Glue, and then I immediately tie an overhand knot, to heal the trauma ! :slight_smile:

It is interesting that you make the same mistake as Kd8eeh at (1) ( Kd8eeh in a competent knot tyer that has exactly the same age as we do, plus a few quarter of a century tucks… :)). He tries to generate an infinite normal force on the pole, in fact, an infinite moving force, and he uses the block and tackle simple machine with (infinitely) many pulleys. Of course, with infinitely many pulleys one can generate an infinitely great moving, lifting or pushing force. You try to generate an infinite blocking force, and you use the wedge simple machine with (infinitely) small angle. Nice try… :slight_smile: It would be interesting to use any other of the 4 remaining simple machines, to see how we can generate, in the field of knots, something infinite out of something finite… ( The golden boys achieved the same thing with money, using even simpler “machines”… :))

You do not need to use the limiting process of more and more pulleys, or wedges with smaller and smaller angles. If the opening of a closed bight gas an area A, that just permits four lines to go through it, it will NOT permit the two interlinked loops, shown in the first picture of reply#32, to go through it. A wide incompressible thing cannot pass through a narrow inextensible thing, and that fact is not relying in any infinitely stretched compound machine. It is a pure geometrical fact. (2)

An extra-terrestrial tells a biologist that, on Earth, life does not exist. The biologist tries to figure out the most devastating counter example, so the extra-terrestrial would keep his mouth shut. If he is a “real” scientist, that is, a person that has more doubts than beliefs, more questions than answers, more question marks than exclamation marks, and he always try to learn from the other guy, be him/her an extra-terrestrial or not, he will reply : A virus ! If the biologist is a “practical” scientist that he searches for ways to do his job, and retain his pay-the-rent salary, he will reply : A living cell : a bacterium, a protozoon, a chomiston, a plant, a fungus, an amoeba. If the biologist is an IGKT “expert” member, he will reply : A horse ! If the biologist is an IGKT junior member that happens to be a scientist, he will reply : A zebra ! ( A girth hitch ! :). Without even understanding that he should better had said " A dead zebra" - because the girth hitch will not remain attached to a pole in the absence of friction - it will slip along its surface, and then only the same deus ex maxhina ( the cavalry…)( the infinite length of the pole ) would be able to save the day…The single or double ring hitch (ABoK#1859, #1862), attached to a hook, would have been the equivalent of a living zebra, I suppose.)

Now, if you need, as a counter-example, a living thing that is “real”, you should probably avoid unicorns, too. :slight_smile: - so you should avoid melting the rope and transforming its cross section into a greatly-non-circular shape, and its end into a spherical blob, in order to make it impossible to slip through a fully loaded nipping loop.

Derek, if we accept the current meaning of “Practical” knots in this Forum ( which excludes even the real, easy to tie and untie, impossible to slip when tied on most materials bend, the Symmetric Sheet bend ) there are no practical knots that do not use friction - and by saying that, we do NOT say, of course ( because it has no meaning to point out something that is inherent in the definition of any knot, for knotGod s sake, be it a mathematical or physical ) that topology will not keep two linked knots linked :slight_smile: - or that a single turn ( just as any hitch, and the girth hitch, and the whoknowswhat hitch…), which we hold by both ends, will not remain attached to a ring or a hook !

  1. http://igkt.net/sm/index.php?topic=4035.msg25434#msg25434
  2. I would be glad if you figure out a proper term for this “effect” : The term “obstruction” which you had used in not bad…Any other idea ?
40

Hi Constant,

Nice try, attempting to divert my argument off into the realms of infinity, but sorry, no infinity involved here.

“A wide incompressible thing cannot pass through a narrow inextensible thing” - indeed, but I cannot rely on this simplistic statement to make my point that a simple, practical knot can be made which does not rely on friction, because the nipping loop is not an "inextensible thing". When the applied load is low, it is easy to open the nipping loop, in fact, no matter what the load, it is always possible to apply a larger opposite force and then for the nipping loop to open.

But when the only available force stems from the applied load which forces the nipping loop closed, then we have to rely on mechanical advantage to generate a force greater than the applied load in order to open the nipping loop. So, if we splice a very simple five diameter ‘lump’ into the WP, then the very poor mechanical advantage this lump enjoys, is utterly inadequate to be able to overcome the clamping force of the applied load. Nothing to do with friction, nor infinity, only mechanical advantage.

As for taking a continuous loop (i.e. no knots), passing it through a ring and forming a Girth Hitch. This is a knot, it is a simple knot, it is a real and a very practical knot and it relies solely upon topology to hold and not friction. This one example destroys your very broad brush statement that "there are no practical knots that do not use friction "

Perhaps you could add some caveates to your claim which allows it to apply to a subgroup of knots which do not contain clear exceptions to the claim which is unquestionably correct for some knots.

Derek