Why Some Rope Knots Hold Better Than Others (scitechdaily.com) 45
A reader shares a report from SciTechDaily: MIT mathematicians and engineers have developed a mathematical model that predicts how stable a knot is, based on several key properties, including the number of crossings involved and the direction in which the rope segments twist as the knot is pulled tight. "These subtle differences between knots critically determine whether a knot is strong or not," says Jorn Dunkel, associate professor of mathematics at MIT. "With this model, you should be able to look at two knots that are almost identical, and be able to say which is the better one." "Empirical knowledge refined over centuries has crystallized out what the best knots are," adds Mathias Kolle, the Rockwell International Career Development Associate Professor at MIT. "And now the model shows why."
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In comparing the diagrams of knots of various strengths, the researchers were able to identify general "counting rules," or characteristics that determine a knot's stability. Basically, a knot is stronger if it has more strand crossings, as well as more "twist fluctuations" -- changes in the direction of rotation from one strand segment to another. For instance, if a fiber segment is rotated to the left at one crossing and rotated to the right at a neighboring crossing as a knot is pulled tight, this creates a twist fluctuation and thus opposing friction, which adds stability to a knot. If, however, the segment is rotated in the same direction at two neighboring crossing, there is no twist fluctuation, and the strand is more likely to rotate and slip, producing a weaker knot. They also found that a knot can be made stronger if it has more "circulations," which they define as a region in a knot where two parallel strands loop against each other in opposite directions, like a circular flow.
By taking into account these simple counting rules, the team was able to explain why a reef knot, for instance, is stronger than a granny knot. While the two are almost identical, the reef knot has a higher number of twist fluctuations, making it a more stable configuration. Likewise, the zeppelin knot, because of its slightly higher circulations and twist fluctuations, is stronger, though possibly harder to untie, than the Alpine butterfly -- a knot that is commonly used in climbing. The findings have been published in the journal Science.
[...]
In comparing the diagrams of knots of various strengths, the researchers were able to identify general "counting rules," or characteristics that determine a knot's stability. Basically, a knot is stronger if it has more strand crossings, as well as more "twist fluctuations" -- changes in the direction of rotation from one strand segment to another. For instance, if a fiber segment is rotated to the left at one crossing and rotated to the right at a neighboring crossing as a knot is pulled tight, this creates a twist fluctuation and thus opposing friction, which adds stability to a knot. If, however, the segment is rotated in the same direction at two neighboring crossing, there is no twist fluctuation, and the strand is more likely to rotate and slip, producing a weaker knot. They also found that a knot can be made stronger if it has more "circulations," which they define as a region in a knot where two parallel strands loop against each other in opposite directions, like a circular flow.
By taking into account these simple counting rules, the team was able to explain why a reef knot, for instance, is stronger than a granny knot. While the two are almost identical, the reef knot has a higher number of twist fluctuations, making it a more stable configuration. Likewise, the zeppelin knot, because of its slightly higher circulations and twist fluctuations, is stronger, though possibly harder to untie, than the Alpine butterfly -- a knot that is commonly used in climbing. The findings have been published in the journal Science.
It's nice to see this formalized (Score:5, Interesting)
I have an intuitive feel for which knots will hold, even if I were to make up a knot, from rock climbing, but it's nice to see some science applied.
Also, the alpine butterfly is a seriously underrated knot. Need a bight on a line? Have a weak point in the rope? Use an alpine butterfly. You can cut the loop after if you really wanted, and it still holds, because you've basically tied a bend.
Re:It's nice to see this formalized (Score:5, Funny)
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That's the time-tested Gordian knot. You just need a sword to undo it.
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I've had a few knots in my wood that I'd like to understand better, if you know what I mean.
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There is a real twist with knots, if they tighten up to much on the line they hold in place, the knot pulling tighter can sever the line, and whilst the knot does remain the point of it has been lost.
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the alpine butterfly is a seriously underrated knot
Not by me, this is probably my 3rd most used knot, the top 2 being bowline, round turn and two half hitches. After that comes icicle hitch, probably, a knot nobody knows and everybody should.
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The icicle hitch is very similar to what in my native language is known as the "spearfishing knot".
One thing I really like when talking about knots in English is that there is standardization dating back hundreds of years. In Bulgaria, the names of the knots change even inside the country, as I learned in the army, when four different soldiers called a knot by four different names. As an aside, the knot is called the "Double Fisherman" in English, and is about the simplest secure way of joining two ropes.
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European death knot is considerably simpler for joining to ropes and performs well despite the name. Both of these jam. Alpine butterfly can also join two ropes and doesn't jam. But not easy to tie correctly.
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The issue with the EDK and rapelling is that it's lopsided. The double fisherman's is symmetrical and flows through a rap ring better.
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"Not by me, this is probably my 3rd most used knot, the top 2 being bowline, round turn and two half hitches. After that comes icicle hitch, probably, a knot nobody knows and everybody should."
You had me in knots after 1 line.
Let's hear it for the alpine! (Score:2)
>Also, the alpine butterfly is a seriously underrated knot
Indeed it is. I didn't really fall in love with it though until I learned the hand-wrap method of tying it: https://www.animatedknots.com/... [animatedknots.com]
It makes it much faster and easier to tie, as well as making it incredibly easy to remember, and impossible to accidentally mis-tie it as the almost identical but much weaker murderous "false-butterfly". Said cousin probably being one of the reasons it's not more popular - it's risky trusting a knot that can
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At some point in my life, I determined that the simple shoelace knot (really a square not with the ends run back through itself) hold better when tied using a particular technique that does not result in twisting of the laces. It's really hard to explain the difference in text, but the whole 'make two loops, rabbit around the tree and down the hole' thing creates t
Seiu Ito (Score:2)
would be proud of this work.
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Kinbaku is not much about the strength of the knots, which are actually quite simple, taken individually.
If anything, anatomy is the most important part: the rope is much stronger than the person you are tying up, so the main worry is not that the rope will hold, it is to make sure you don't injure your partner.
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I bet you feel special name dropping like you're intelligent, instead of sharing that bit that makes it special to you like you're a person who finds joy in things.
Ideal knot (Score:2)
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There's no single ideal knot.
I probably tie a dozen different knots regularly. There's tradeoffs for strength, stability, ease of undoing, ease of tying one-handed or injured, hitches, bends, knots for loops, knots that are slipped, more complex anchor and rappel systems like the Texas rope trick, knots for webbing (like the water knot), knots for heaving lines (monkey fist, etc), and so much more.
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Not to mention knots that work with one type of line but not others. Or rather, types of line that work with some knots and not others.
Good example is when braided fishing lines first came out - super thin, super strong. Stuff that was same diameter as 4lb test monofilament would test at 15-20lbs break weight. Due to its make up it was a pain to cut, etc. but it was so strong that it could actually cut through itself when tied in a traditional multi-twist style fishermans knot ( https://www.youtube.com/w [youtube.com]
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If the Gordian knot is your ideal, then I'm sure that the one of best way to find it ;)
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This is a really hard simulation problem, given the flexible material with complex behavior and complex 3D shapes. A high level research project at the moment.
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"In theory, there is no difference between theory and practice; but in practice, there is."
We already have ideal knots (Score:2)
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I actually left Boy Scouts as a child (miltary brat), because they were homophobic and intolerant asshats.
Nice study (Score:5, Insightful)
I have always been interested in knots, and I love to see what is intuitive being formalized.
But what makes a not popular is more than holding strength. Ease of tying, ease of untying, can it be done under tension, resistance to breakage, will it damage the thing you are tying, how big it is, how much rope does it needs, how it works with different rope diameters, etc...
Still, i'd like to see the model at work on some problems like:
- Is there a difference in strength between a "right handed" and "left handed" bowline.
- Does it model the tendency of knots to change shape? The tendency of the reef knot to capsize is the best example.
- The effect of rope type. The best known sailing knots come from a time where rope was made out of natural fibers, nowadays synthetic is much more common. Synthetic rope tends to be stronger but more slippery, which should certainly determine the kind of knots to use.
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The reef knot being almost dangerously prone to capsizing, particularly with synthetic rope is why I very rarely use it. If I'm going to tie a reef style knot, I'll double the turns for a surgeon's knot instead, or just use a hitch of it isn't meant to be permanent.
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The reef knot being almost dangerously prone to capsizing...
What do you mean, "almost"?
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Trying to avoid hyperbole.
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Far from hyperbole. [youtube.com]
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Far from hyperbole. [youtube.com]
What a silly video. The knot was manipulated into a capsized configuration before it was loaded. Might as well partially untie it, then claim the knot is unsafe.
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Silly you. The video demonstrates clearly how the knot capsizes. It does the same under load, try it. I have. You have obviously not, and are an idiot. Please do not advise anyone to trust their life to a reef knot, but feel free to do so yourself.
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You have obviously not, and are an idiot...
Discussion over, cheers.
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Oh yeah, passive aggressive denial of being an idiot. Anything to avoid admitting being wrong, which you were, blatantly, and in a way that could possibly encourage somebody to severely injure or kill themselves. Please suspend yourself from a reef knot, the world needs fewer of the lies of you.
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I don't tolerate rudeness. Why you would call names, yet expect to continue the conversation, is beyond me. If you thought I were a true idiot, you would not be wasting your time engaging in argument. It's just rudeness. I sometimes put up with that from those that are close to me, but not internet strangers.
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There are not words rude enough for somebody who advises others to put their lives at risk. So fuck you and you passive aggressive false civility. Just dangle yourself over a gorge with a reef knot.
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I've read the article and the abstract and I think they didn't consider capsizing and I think they only considered static loads when talking about "strength". Static load strength is not the most important metric for a knot imho.
They had a fiber which changes color when "stressed" and created a model mimicking it. It sounds like that only accounts for static stress which would explain their rule of thumb. Braided knots are known to have the highest strength under static load but not dynamic loads. Internal
What the A.I. actually said (Score:2)
"I'm going to need hands for this one!"
Biggest brain in the galaxy...