testing physical theories of knots

[bcrowell]

I'm a physicist with an interest in rock climbing, and recently I've been getting interested in the physics of the conditions under which friction is strong enough to make a knot hold. There is a huge mathematical literature on knot theory, but much less on actual physical knots and how friction makes them hold together. There is a little bit of published work on this topic -- I've been able to find two papers, which I've referenced below for anyone who wants to look them up. (Neither is available online, unfortunately, except behind a paywall.) Both of these papers are almost 100% theoretical, and it seems to me that it would be worthwhile and fun to test whether their predictions are even correct.

Two predictions in the Maddocks paper are that a square knot fails if the coefficient of friction is less than 0.24, whereas the magic number for a sheepshank is 0.09. They also have some predictions about hitches. I'm posting because I'm interested in finding out if folks here can give me any pointers in trying to test this stuff, e.g., in how to locate cheap ropes with a variety of coefficients of friction.

To test the predictions, the materials I was able to come up with around the house were some nylon rope with a coefficient of friction of about 0.22 and some teflon plumber's tape, which I twirled to form it into a thin cord. Teflon on teflon is supposed to have a coefficient of friction of about 0.04.

Square knots held with the nylon but failed with the teflon. Although this appears to be contrary to the prediction of the theory in the case of the nylon, I'm not sure what the margin of error is on my own determination of the coefficient of friction, and the paper clearly presents the prediction only as a rough estimate.

The sheepshank held with both the nylon and the teflon. This seems to clearly contradict the prediction, since the teflon's coefficient of friction is less than half the claimed minimum.

It would be interesting if anyone could try similar tests with other materials. For example, dyneema (a.k.a. spectra) has more friction than teflon but less than nylon, so it would be interesting to see whether a dyneema rope (without a mantle of some other material) can hold a square knot. I see that there's already a thread on whether a sheepshank should be expected to hold in dyneema: http://igkt.net/sm/index.php?topic=4072.0 Very few materials are slippery enough to make a square knot fail, so it might be interesting to find out whether other materials fail when made into weaker knots (e.g., a granny). There may also be knots or hitches such as a Munter that are not normally expected to hold with ropes made of ordinary materials, but that might hold, for example, when tied in a high-friction material such as a rubber o-ring. Mountaineers often have to work with icy ropes, and I wonder if it's possible to get any useful insight into what knots would hold under such conditions. I'm not really sure that my tests with the teflon tape are fair, since the stuff doesn't really behave like normal cordage. There does seem to be teflon-coated cordage commercially available, such as some thin line sold for ice fishing. Does anyone have any teflon-coated cord that they could try knotting?

In general, the calculations for hitches seem to be a lot more solid than the ones for knots, because in a hitch, the cylindrical post forms the rope into a predictable circular shape, whereas a knot controls its own complicated shape in three dimensions. Testing the calculations for hitches gets a little more complicated, though, because there are at least three variables: the coefficient of friction between the rope and the post, the coefficient for rope on rope, and the ratio of the rope's diameter to that of the post. (For example, it's easy to verify that a clove hitch always fails when the rope is too thin compared to the post, and the theoretical calculations get this fact right.)

Bayman, Am J Phys, 45 (1977) 185
Maddocks, J.H. and Keller, J. B., "Ropes in Equilibrium," SIAM J Appl. Math., 47 (1987), pp. 1185-1200

[X1]

      Hi bcro-well, and well-come to the forum,

   I had thought for quite some time about the proper way I could possibly reply to your post ( which, incidentally, belongs to one of the two other - the 4th or the 5th - sections of the forum ), so I would be able to convey to you what I think about the subject / issue / problem you describe. At the end, I decided that, in a few words, I would probably achieve more than with many :
   In short, " appearances can be deceiving ", and "Everything should be as simple as it can be, but not simpler". 
   In physical knots, even the most simple of them, "testing the calculations" gets A LOT more complicated, because there are DOZENS of variables ... Even if the physical knots are not "knotted material", they are material-made knots - so the material plays a paramount role. And by "material", I do not mean only the friction coefficient, the elasticity, etc., all those things that could possibly be measured in detail. Any rope is a complex weave of fibres, a many-elements construction, and their elongation, the dislocation of their initial positions and the deformation of the rope s diameter, the tension and compression forces within the rope at each point of the knot, the temperature and even the humidity, all those things are tangled into a complete mess... As you know, one of the best kept secrets of physics is how complex and difficult to model is the phenomenon of friction. And we are not talking about the friction of the surface of the rope only here, but of the surface of each and every individual fibre ! And not only friction...Ropes that are soft, or that can be compressed, can be tied in a secure knot, while the same knot, tied on stiff or hard material, will slip at once.
   Having said that, I have to stress that we are dying here because we do not have the experimental data we should - data we need not to "test any calculations" of the ones that do not have, but at least to learn which f... variation of the Sheet bend or of the bowline will slip/break before the other ! So, we would be VERY happy if you could possibly offer your knowledge, and your enthusiasm.
   My advice is to start testing the most simple knots, on a 1/4' or 1.2' inch solid braid cheap nylon rope, and to take pictures of the procedure. You will also need a winch or a high-lift car jack, and some protective measures - because knots are rope-made mechanisms, and mechanisms can be dangerous. After some initial tests, you will find out that the existing theories do not predict a thing - and if they do, like the Clove hitch example you had mentioned, they do it due to shear coincidences... At this scientifically primordial stage we are, we do not need theories, we need observations, and tests - and a lot of them. "Theories", and "calculations"  will come - if they will ever come - only after we start to learn what we are talking about - because, after almost 2000 years of knotting literature, we are still into the Dark Ages of the science of physical knots. 

[struktor]

 
Experiment 1.
Take one spaghetto.
Tie a knot on it and pull it by its ends. Gently!
Observe, where it breaks.
 

http://etacar.put.poznan.pl/piotr.pieranski/SpaghettiKnots.html

[X1]

   Two examples of the limitations ( to say the least...) of the existing theories.
1. The cornerstones of the theory of friction most physicists know and use, are Amontons 3 laws of friction, right ?  Well, I have tested those 3 laws in the most simple case of two tensioned straight rope segments - the one loaded through both ends ( a segment of a standing part ) and the other through one ( a tail ) - crossing each other at a point, or at a small area of contact. It is like entering into another, parallel universe !  No relation whatsoever between any of those laws, and the physical reality they are supposed to model and approximate. The local deformations on each of the two ropes are such that ALL predictions of those laws fail... For example, I have seen that, ceteris paribus, there is a non-linear relation between friction and the angle of the axes of the two segments. Is this only a minor detail, not worth of taking into account ? No, not at all ! The angle between two crossing lines is perhaps the most important thing that determines if the tail will slip , or not ! Moreover, it is something we can change - we cannot change the ropes we have in hand, or the loading of the ends of the knot, but we can change the knot itself ! And we can use a knot where the tail meets the squeezing standing part at an angle close to 90 degrees.
2. The paper by Bayman you mention, describe the case of the Clove hitch, right ? Wrong !  If it did, it could have been able to describe a two- or multi-wraps Clove hitch, shown at (1). The real effect of the round turns being squeezed upon each other by the oblique riding turn, and so unable to slip, is missing, the accumulation of tensile forces within the torsion coil spring is missing, the elongation of the rope length is missing..._ I wonder what, if anything, is there, after all ! 
   Do not take me wrong, I am a great admirer of the theories about everything, including physical knots, and, why knot, ourselves !  However, we have to admit that those theories are still at a very early stage of development. To be able to proceed to calculations, and to make any predictions, we have to try a lot more, and a lot harder. This is a great field of glory lying ahead for the future physicist / knot tyer ! Bon appetit, with the spaghetti (2).

1. http://igkt.net/sm/index.php?topic=4139.msg25019#msg25019
2. http://iopscience.iop.org/1367-2630/3/1/310/fulltext/

[KnotMe]

To test the predictions, the materials I was able to come up with around the house were some nylon rope with a coefficient of friction of about 0.22 and some teflon plumber's tape, which I twirled to form it into a thin cord. Teflon on teflon is supposed to have a coefficient of friction of about 0.04.

In aid of your research, the slippery-est generally available cord I know of is rayon satin cord.  Available at some bead shops and most fabric shops. 

Of course, the grippy-est cord would be a hairy natural cord like unpolished hemp or jute or the like.

[Luca]

Hi bcrowell, 

I do not really understand much about these things, but I found this, I hope it(maybe you already know) is useful for you!

http://books.google.it/books?id=T0z882H1928C&printsec=frontcover&dq=knots+and+physics&hl=it&sa=X&ei=_iCxUNbKKonGtQbYzYGwAw&ved=0CDMQ6AEwAA

                                                                                                         Bye!
                                                                                                       

[dfred]

Luca, a while back I borrowed that book from the library with high hopes, as it is part of the same book series as HIstory and Science of Knots.

However a more accurate name for that Kauffman book would be (Theoretical) Knots and (Theoretical) Physics.  That said, it does contain one telling passage, on pages 6-7, where the author is discussing the importance of grounding one's theoretical knotting in real knots in actual rope.  He cursorily discusses the behavior of a few basic, practical knots and then states:

(And I quote for those who may not be able to access the link above, and for posterity.)

It is important to come to some practical understanding of how these knots work.  The facts that the square knot holds, and that the granny does not hold are best observed with actual rope models.  It is a tremendous challenge to give a good mathematical analysis of these phenomena.  Tension, friction and topology conspire to give the configuration a form -- and within that form the events of slippage and interlock can occur.

I raise these direct physical questions about knotting, not because we shall answer them, but rather as an indication of the difficulty in which we stand.  A book on knots and physics cannot ignore then physicality of knots of rope in space.  Yet all of our successes will be more abstract, more linguistic, patterned and poised between the internal logic of patterns and the external realizations. . . .

While Kauffman does return briefly to the ground covered in the Bayman(1977) paper, most of what follows is 700 pages of the most ludicrously complex mathematical notation and discussion a layman might ever encounter.  Given his apparent expertise in mathematics and physics, I find it very interesting he believes that modeling real knots is a tremendous challenge.  One might dismiss it as a cop-out, since his focus is on the theoretical, but I tend to think it is probably genuine and accurate assessment on his part.

Like bcrowell, X1, and many others, I have continued to be surprised at the lack of progress in the modeling and prediction of physical knots.

Regarding X1's specific comments...  I tend to think we are still (and perpetually) at the spherical cow stage.  The models are far too simple to actually tell us anything that folks who play with string as much as we do don't already know.   However the problem with a bunch people playing with string is that is is not science; it is really more akin to something like alchemy.  For whatever reasons, the scientific method has mostly bypassed physical/practical knots.  I would very much like to change that state of affairs.

I've actually thought quite a bit about this, and as I see it there are still many basic unanswered questions, but also a number of possible avenues of attack.  I doubt they can really all be covered in a single thread, but I'm happy to see this subject getting some attention.

[bcrowell]

Thanks, all, for the interesting and helpful comments. As dfred points out, the Kauffman book doesn't really have much about frictional knots tied with physical pieces of rope. Kauffman just gives a short and incomplete summary of Bayman. The only online expositions of the material in Bayman that I've been able to find are a couple of student papers, both of which seem to be mostly cut-and-paste plagiarisms of Bayman:

http://www.cs.cmu.edu/afs/cs/academic/class/16741-s07/www/projects06/stolarz.pdf
http://www.math.ucla.edu/~radko/191.1.05w/matt.pdf

Note that there is an important mistake in Stolarz's equation at the bottom of page 5, which should read 1 <= 2 mu e^(pi mu). (He's presenting an analysis from the Maddocks paper, but he garbles Maddocks' equation.)

Jearl Walker did a very nice Amateur Scientist column on this topic in Scientific American:

Jearl Walker (Amateur Scientist column), "In which simple equations show whether a knot will hold or slip," Sci Am 249:2, p. 120, August 1983.

Sci Am, mysteriously, does not seem to want to sell people copies of old articles. You can find copyright-violating copies of the article by googling for "are some hitches securer than others".

X1 is certainly correct that knots are in principle very complicated. However, good science does not have to be exact. Part of the art of being a good scientist is figuring out how to make models simple enough to provide some insight, while keeping in mind the limitations of the models.

The paper by Bayman you mention, describe the case of the Clove hitch, right ? Wrong !  If it did, it could have been able to describe a two- or multi-wraps Clove hitch, shown at (1). The real effect of the round turns being squeezed upon each other by the oblique riding turn, and so unable to slip, is missing, the accumulation of tensile forces within the torsion coil spring is missing, the elongation of the rope length is missing..._ I wonder what, if anything, is there, after all ! 

Actually I think the multi-wrap clove hitch is an example of the kind of thing that Bayman's theory handles quite nicely. Walker uses Bayman's theory to calculate the behavior of these.

For example, I have seen that, ceteris paribus, there is a non-linear relation between friction and the angle of the axes of the two segments. Is this only a minor detail, not worth of taking into account ? No, not at all ! The angle between two crossing lines is perhaps the most important thing that determines if the tail will slip , or not ! Moreover, it is something we can change - we cannot change the ropes we have in hand, or the loading of the ends of the knot, but we can change the knot itself ! And we can use a knot where the tail meets the squeezing standing part at an angle close to 90 degrees.

Interesting! Have you posted your results anywhere? I'm not sure that what you're describing is necessarily inconsistent with the standard Amonton-Coulomb treatment of friction. I would like to see a more detailed explanation of what you measured. Are these two free-standing ropes, or ropes wrapped around a post as in a hitch? If it's the latter, then the normal force between the top and bottom ropes varies because in addition to the angle between the planes of the two ropes, there is a second angle that varies, which is the angle between the two segments of the top rope.

But I agree that there does seem to be frictional behavior in ropes that is not accurately described by the Amonton-Coulomb model. It's just one model of friction. One type of non-Coulomb behavior I've seen is that you can get one rope to creep through another at approximately constant speed. Someone posted a link on this site to a video showing a dyneema rope doing this. I've also seen this behavior in a simple test setup. In this setup, I wrapped n loops of rope helically around a horizontal post and hung unequal weights M and m from the ends. The Amonton-Coulomb model predicts that the condition for slipping is M/m>e^(n mu pi), where mu is the coefficient of static friction. What I've observed instead is that for a fairly wide range of values of the ratio M/m, the weights creep at an approximately constant velocity. This is probably evidence for internal viscoelastic friction. The simplest model of this type of behavior is the Kelvin-Voight model http://en.wikipedia.org/wiki/Kelvin%E2%80%93Voigt_material .

A much more complicated model is presented in this paper for actual rock-climbing ropes:

Bedogni and Manes, "A constitutive equation for the behaviour of a mountaineering rope under stretching during a climber's fall," http://www.theuiaa.org/upload_area/files/1/sdarticle.pdf

Although the model is complicated, they seem to do an excellent job of simulating the actual motion when a lead climber takes a fall. As a rock climber, I find this "creeping" behavior very scary. The last thing in the world I want to do is tie a knot at the top of a rappel, lean back over a cliff, start descending, and have the rope creep out of the knot while I'm hanging in the air!

[bcrowell]

In aid of your research, the slippery-est generally available cord I know of is rayon satin cord.  Available at some bead shops and most fabric shops. 

Thanks for the tip! I've found suppliers for a few different low-friction substances, including rayon satin.

[X1]

Actually I think the multi-wrap clove hitch is an example of the kind of thing that Bayman's theory handles quite nicely. Walker uses Bayman's theory to calculate the behaviour of these.

   We are probably talking about different knots...The multi-wrap Clove hitches shown at (1) are not explained in any of those papers... nor any of the effects I had described there, and in my previous post( friction forces between the round turns, enhanced by the oblique riding turn, stored tensile forces in the "coils spring", possibility of the riding turn to jump over the side round turns as it becomes more oblique (its angle relatively to the axis gets smaller), etc.)
   If they did, my question would have been answered : What is the optimum number of turns, for a most tight multi-wrap Clove hitch ?
   I have not gained ANY insight about the multi-wrap Clove hitch out of those theories, I am afraid... The proof of the pudding is in the eating !  If this theory cannot explain even such a simple hitch, one can imagine what are its chances to explain something more complex - like any of all the other less simple hitches.

Are these two free-standing ropes, or ropes wrapped around a post as in a hitch?

  Free standing ropes ( the one stationary, the other loaded from the one end only ), squeezed in between two plates, so that there some deformation of the surfaces of the two rope segments. In other words, the most simple arrangement to measure something we see in every knot every day : As the angle becomes closer to 90 degrees, the deformation gets deeper, and the friction forces ( or however else one can describe the cause of this effect ) prevent the slippage of the pulled segment much more efficiently. On the contrary, when the angle becomes closer to 0 degrees, the pulled segment tends to slip relatively to the stationary segment, "riding"  on their greater contact area . 
  I do not have the laboratory that would allow me to perform detailed experiments - but I always hope that, someday, somebody will start testing the most simple rope arrangements we meet in every knot.
  Let me describe another simple problem. We have a thing we call "nipping loop", a 360 degree part of a "closed" helix ( an "open" helix is something that we normally see only in cases where the nipping loop has capsized ). Now, a tensioned nipping loop constricts any loaded segments of rope that penetrate it, and so it prevents their slippage. There might be one, two, three or even more rope segments going through a nipping loop. If we suppose that only one of them is loaded ( a "tail" of a knot ), what is the optimum number of segments so that this tail will slip less easily ? That is not only a theoretical, or academic question...We need to know if it makes any difference to have more than two rope segments going through the nipping loop of a bowline, or not. And the bowline is the simplest and most widely used end-of-line loop.

As a rock climber, I find this "creeping" behaviour very scary. The last thing in the world I want to do is tie a knot at the top of a rappel, lean back over a cliff, start descending, and have the rope creep out of the knot while I'm hanging in the air!

   
   So, start performing some simple experiments, with simple rope arrangements, and leave the "theories"  and "calculations"  for later !  We do not have enough measurable observations or experimental data, so I guess we should follow the normal route of science before we jump into any premature conclusions. I would be glad if our problem would have been a wrongly solved equation, but we are FAR AWAY from this point, I am afraid.
     
1. http://igkt.net/sm/index.php?topic=4139.msg25019#msg25019

P.S.

A much more complicated model is presented in this paper for actual rock-climbing ropes:
Bedogni and Manes, "A constitutive equation for the behaviour of a mountaineering rope under stretching during a climber's fall," http://www.theuiaa.org/upload_area/files/1/sdarticle.pdf

  The eight coefficients ci ... were defined by means of a best fitting process minimizing the sum of the differences between the measured and calculated forces.

  I believe this sentence speaks for itself : The proposed model is not complcated because it takes into account many parameters, but because it uses complicated formulas for few parameters. It is a very phenomenological model, where we can change ( cook ... ) the values of the chosen few parameters in order to aproximate, in a somewhat ad hoc manner, the experimental results...Too many epicycles, for my taste ... If there were some different experimental data, this model would easily " predict " them as well, by properly cooking/best fitting those 8 coefficients. Anyway, it is a very good thing we have, at last,  some models, even if they are not what we had hoped them to be. Rome was not built in one day.
 

[roo]

recently I've been getting interested in the physics of the conditions under which friction is strong enough to make a knot hold.

There's an elephant in the room that should not be overlooked:  rope construction.

Some types are stiff, some are supple, some stretch, some don't (much), some some maintain their roundness, some flatten easily or even start somewhat flat, some twist when tensioned, some thin considerably under strain, some don't, etc.  Every rope is a different machine.

When you multiply rope construction by rope material type, you get a truly dizzying array of variables. 

[Dan_Lehman]

Welcome to the IGKT forum, BCrowell!

In general, I concur in the caution that knotted ropes present
many factors to consider in predicting behavior, and I think that
many of these are not well understood nor easily measured.

For now, I'll make a few comments, only.

Note that in the Bedogni&Manes pdf article the clamping of the
rope is done contrary to recommended procedure : two clamps
are used, and they are put in opposed orientation --i.e., the
one clamping the tail's end had the U-part binding the tail
and the broad clamp base pressing the SPart, whereas the
one closer to the eye/attachment-point is reversed.  (The
recommended orientation is the former --shown at the tail.)


You remark about some "creeping" behavior in reference to this
article, but I didn't find "creep"/"slip" in the text, nor see in any
of the "behaviour" occurrences any discussion of this?!

In any case, your fear of leaning back on rappel only to have an
abseil-ropes joint slip undone (= spill) needs to confront the fact
that abseiling has been done for decades without such accidents
occurring --except in highly infrequent cases.  And the commonly
used knot (what I call the "offset water knot", aka "EDK")
is both old and simple, and somewhat formally tested.  Much the
same can be said of other knots used in rockclimbing.  In general,
knots don't fail; but we have the odd exceptions, which then bring
a struggle to ascertain the facts --seldom satisfactorily done-- and
to understand the causes.

In light of your rockclimbing interest, it's a bit surprising to see a
focus on hitches, as these aren't so commonly used.  The knots
--and I prefer "knots" to be seen only as the catch-all, general
term and not some subset within itself (though, yes, often knots
books trot out this tired attempt to categorize)-- that rockclimbers
regularly tie/un-tie are the tie-in eyeknot, the belay-anchor knots,
and abseil-ropes-joining knots.  Knots tied in slings are often left
as permanent.

Knot "strength" is what is most commonly tested --as there are
simple, known procedures and equipment for that--, although
arguably it is the least important aspect of knots for climbers;
security --both under load and when untensioned (but jostled
about)-- is more important, but less easily tested.

Finally, much testing fails to show appreciation for the variety
of materials at hand, attempting to ascribe implied (usually
strength) characteristics to the *knot* rather than to the
**knotted material**; I assert that this is a mistake, and
that material matters (much, sometimes).


--dl*
====

[DerekSmith]

Hi bcrowell,

Welcome to the Forum and thank you for poking your head up above the surface of the lurker pond.

Your opening lines caught my attention because I am a Chemist with an interest in rock climbing and flying stunt kites.  As a rock climber I use highly elastic (dynamic) ropes with a high cf and in kite flying I use Spectra/Dyneema lines with as low an elasticity as possible and as low a cf as possible (so you can still steer the kite even through a massively twisted group of lines).  The kite lines are rated from 50lb to 500lb and are seemingly impossible to keep knotted unless first sleeved and locked with Superglue, and even then, only a handful of knots resist the inexorable slide of a heavily loaded line.

Like you, I have seen a video of a heavy duty Dyneema rope simply pulling through a knot - too strong to break and too slippery to hold.  I have to disagree with Dan in his statement that some tried and trusted knots have been with us for so long it is unthinkable that they would fail, and lean towards Roo's warning that we must consider the nature of the cordage.  Before too long, someone is going to abseil using one of the new hyper strong ropes (with super low cf) and will rely on one of these tried and trusted knots which will promptly slide through itself as if someone had greased its surface.

Until the advent of modern materials, cordage users had only to worry about the knot weakening the cord or tying the knot correctly - a cord so strong and so slick that it simply pulls out of the knot without breaking was unthinkable.  But this is no longer the case.  Today in the ultra slippery kite lines, most of our arsenal of knots are useless, given enough load, they simply pull though without breaking.  At the rate that technology is developing, it is conceivable that we will soon have access to cordage which is essentially unknottable in that it will always pull though before breaking.

I think that it is important to clarify that the Maddocks paper is dealing essentially with this relatively new aspect of modern cordages reacting to 'old fashioned' bindings which were developed to function in 'hairy string'.

Before the advent of these new slick / strong cordages there was really only the aspect of 'Positive Cogging' which knot tyers needed to take heed of.  In knots like the Whatknot, friction actually causes the load to lead to the components of the knot to rotate one another and so allow the cord to feed through the knot.  But in slick cordage, even knots with excellent 'Negative Cogging' fail to generate sufficient friction to prevent the cord from simply pulling through.

Derek

[Dan_Lehman]

Like you, I have seen a video of a heavy duty Dyneema rope simply pulling through a knot - too strong to break and too slippery to hold.

One should note that although HMPE is quite strong, as measured
in standard pull testing, it isn't "too strong to break" in many cases,
and does so arguably at about the same load as other like-knotted
materials --but which absolute load is a much smaller portion of its
tensile strength as compared with those of other materials.

I have to disagree with Dan in his statement that some tried and trusted knots have been with us for so long it is unthinkable that they would fail, and lean towards Roo's warning that we must consider the nature of the cordage.
Before too long, someone is going to abseil using one of the new hyper strong ropes (with super low cf) and will rely on one of these tried and trusted knots which will promptly slide through itself as if someone had greased its surface.

Whoa, you're over-reaching on what I said.  In the world of
abseiling, the conditions are pretty well established and real-world
tested.  Now, the point about using HMPE ropes is worth noting,
especially for canyon(eer)ing, where that material is working into
the main (non-"accessory") lines.  Still, for these, someone should
find out an *easy* (as opposed to the unwanted "hard") way how
the ropes perform, as it's a simple matter to load such and end-2-end
knot with real-world loads.
(BTW, FYI, after reading Brion Toss's long-back SAIL article about
bowlines slipping, I tried with a 5:1 (poor, actually) pulley to see
such slippage in pure Spectra & Vectran (maybe also Technora), w/o
success; my figuring was that I'd generated the force (around 20%
tensile, IIRC) at which he reported slippage, but ... .  (ca. 900#))

Today in the ultra slippery kite lines, most of our arsenal of knots are useless, given enough load, they simply pull though without breaking.

Maybe we should start a separate thread to explore what the
state of the art was prior --name knots!-- and what it has become
after the advent of these HMPE lines.  I remain skeptical that some
solutions can't be found, though in rope, well, breaking strength
too much suffers --but none of my 6 tested eyeknots slipped.

At the rate that technology is developing, it is conceivable that we will soon have access to cordage which is essentially unknottable in that it will always pull though before breaking.

Again, slippage is a factor but the real problem with the current
group is more of weakness relative to tensile strength, no slippage
--that even holding, the knot doesn't meet the need.


Btw, the J. Walker paper I guess copies images from Bayman,
for which I note that their "constrictor" is (a) not that, but the
structure of #1674 (a better behaving kin to the ground-line hitch),
but (b) is loaded on that hitch's tail, so inferior in working!?
.:.  strange that?!


--dl*
====

[bcrowell]

In principle, we can have our cake and eat it too. We can use ropes consisting of a core with the desired elasticity and tensile strength, surrounded by a mantle or coating with the desired resistance to abrasion and coefficient of friction (high or low). This is what seems to have happened in some cases. E.g., you can buy tent cord made of a dyneema core with a nylon mantle, or ice fishing line made of braided nylon coated with teflon. But in reality, I'm sure there are cases where this doesn't work. I guess kite string is one of them, maybe because a mantle or coating would be too heavy?

There have been a lot of comments about how it's difficult to come to any conclusions because of all the confounding variables. But to some extent we can practice control of variables by doing experiments with ropes that have the same core but different mantles or coatings. Here's what I have on order to do experiments with:

2 mm dyneema (comes with a nylon mantle which I'm going to try to strip off)
2 mm rayon satin cord
0.9 mm teflon-coated nylon (can't find a supplier for the 2-mm stuff, although the manufacturer does make it)

I would like to have something on the high-friction end, but haven't found it yet. Maybe rubber o-rings or fan belts?

You remark about some "creeping" behavior in reference to this
article, but I didn't find "creep"/"slip" in the text, nor see in any
of the "behaviour" occurrences any discussion of this?!

The article describes a fancy mathematical model of internal friction in an elastomer. This type of friction is is velocity-dependent, so it's capable of causing a rope to creep at constant speed. Amonton-Coulomb friction can't produce that behavior; the force is velocity-independent, so it results in motion with constant acceleration.

In light of your rockclimbing interest, it's a bit surprising to see a
focus on hitches, as these aren't so commonly used.

The physical theory of hitches is simple, requires few assumptions, and depends on few variables, so it seems like a good target for for experimental testing. Rock climbers and mountaineers do use hitches sometimes. Prusiks are used a lot. Clove hitches are used to tie in to a personal anchor and for other applications. The physical theory of hitches basically applies to force-amplifiers such as belay devices, the Munter hitch, and the leg wrap used to lock off a rappel.