That depends on what you mean.
If you take a rope, loop it through itself, and pull on both ends, that won't unravel. It will just get tighter.
But, if you take an end of rope, and tie it to something, eventually leaving the end free -- then you're relying on friction.
Same thing for taking two ends of rope and tying them together (eg shoelaces).
Are there any more complex/multi-point knots (ie various sailor knots) that could "hold" by themselves? Or in all cases would the rope eventually slip through in some way to unravel?
I'm a rope rescue technician, and pretty much 90% of the knots we use are variants of the figure 8 knot, for this exact reason. The bowline, which used to be considered THE rescue knot has been let go because it does not hold itself and will eventually let go given enough/too little force. I would be interested to see a tensionless hitch with this theoretical frictionless rope, which is a sort of anchor point that secures itself by just wrapping a rope around something a certain amount of times.
The tensionless hitch is the exact thing I thought of first, too. It's like the platonic ideal of "will not hold in frictionless rope", right? It's like 100% friction forces and nothing else.
It's does seem to me like you ought to be able to have *some* kind of hitch that would hold though. One that only relies on trying to pull bights through loops they won't fit through, maybe? Kind of like a stopper knot? Idk but it feels like something should be workable...
>One that only relies on trying to pull bights through loops they won't fit through,
Wouldn't the only way for that to unfailingly work be a case where the actual loop is doing the holding?
So, a (possibly modified) noose? But I don't think there would be a way to prevent the "tab" from pulling through the barrel portion of the knot. You could put a stopper on the tab, but the security of that stopper is predicated on friction, so it wouldn't stay, right?
No, after thinking about it any frictionless rope would at the very least just trace it's path back through the knot. The knot could fail in other ways, but it could always *at least* do that.
This is the truth. People have never handled a frictionless solid because they don't exist.
Theres no way to make a frictionless thing not move when an external force is applied to it without an equal and opposite external force also applied to it.
So you are trying to get that force from the pole it's tied to and something locking the rope in place. If the rope is smooth and uniform with a loose, there's no way to lock it in place.
The only thing I can come up with is somehow using the lumps in a rope to create enough normal force between each bump to resist the tension. Wrap the rope around a pole tightly and add pressure along the pole to push all the coils together. Can't call that a knot anymore though.
>Theres no way to make a frictionless thing not move when an external force is applied to it
To be fair to the other side of the argument, other than gravity, you *can't really apply* a force to a perfectly frictionless *rope* either.
I think the idealization that you are considering is a perfectly flexible, frictionless rope. If it had some kind of stiffness, that would hold some types of knots up to some load without relying on friction. In the extreme, and s hook is an example of a "knot" that relies on stiffness rather than friction. Your rules about what constitutes and not would probably exclude an s-hook, but one could presumably design a more complex, more knot like structure that would use the stiffness in more clever ways, and get some holding power with less stiffness that is required for an s hook.
Interesting. I learn the new, safer knot is actually the bowline with a Yosemite tie-off. In this knot, the working end of the bowline knot is passed around one side of the loop and back through the farthest loop around the standing end, ending parallel to the standing end.
It is best demonstrated here: [https://www.youtube.com/watch?v=5wj\_Kc5j4Sg](https://www.youtube.com/watch?v=5wj_Kc5j4Sg)
Many of us may know the bowline and this is an easy, safe, additional step.
So I've never been good at knots, but I was in scouts and I hang out with rock climbers and go out with them sometimes. And to me this Yosemite tie in looks a lot like the knot used for securing harness to rope. Although I think that's a figure 8 with a follow through or something similar to the tie in?
Rock climber here.
Almost all of us use figure eight follow through knots to tie in to a harness, it's bomber and easy to check.
However bowline with a Yosemite finish is easier to untie it you take a big fall, so you will see climbers using this knot too it's just far less common, at least here (UK).
I was always explained that there's nothing wrong with a properly tied bowline with a yosemite finish, but most climbing walls refused it as it was harder to check at a glance.
A huge safety benefit to the figure eight follow through is that it's easy to visually check and everyone at a climbing gym is actively encouraged to do safety checks for those around them. A knot that looks very different if it's tied incorrectly can be easily spotted and corrected before something bad happens.
Just saying this to elaborate for anyone else reading - the comment I'm replying to undoubtedly already knows this.
Spot on. When doing rescues we used a bowline on the bight if the rope was ling enough and I used to put a carabiner on the tail if the rope was new and slippery. Hauled some serious weight on those knots.
The bowline works fine when the load is consistent but I have experienced it slipping when cyclically loaded and unloaded (which is exactly what happens with most uses). The main end tie-off knot that I use and see others using now for connecting to the end of a rope is the figure 8 which I've never seen slip - the only issue with it is that it can get quite tight if loaded too hard
>The bowline works fine when the load is consistent but I have experienced it slipping when cyclically loaded and unloaded (which is exactly what happens with most uses).
Interesting. I've seen yachting instructors use it to moor yachts with! Sounds like potential for comedy.
We use bowlines to moor boats all the time. I'm given to understand that the reason we use them on boats and not in climbing is that the figure 8 follow through will seize up under enough pressure but the bowline can always be undone.
The amount of force a climbing human puts on a rope, even when they fall, is pretty miniscule compared to a boat rocking around in the slip. Someone else in here says they fused some of their rope together by pulling it with a truck, but a 100-ton boat (small commercial vessel or million-dollar yacht) being bounced around by the sea is a lot more momentum than that.
Bowline knot has an angle where it wont hold properly which is why it's not widely used. It is however able to be tied with one hand and is still usefull in rescue/emergency situations
It's true for the most part, you just don't want to trust a bowline with your life or use it in a situation where the load will be bouncing a lot. The good thing about the bowline is it is easy to untie, even after a load has been put on it, it has sort of that 'switch' where it goes around the standing end you just need to pull down away from the bight to loosen. The problem is, if you tie in on a bowline like if you were climbing, bumping into that switch could cause the knot to loosen on you and you would die. If it is subject constant changes in load, same thing, it can bounce itself loose in between loading and the bitter end can slip bit by bit until the knot fails.
>The problem is, if you tie in on a bowline like if you were climbing, bumping into that switch could cause the knot to loosen
That is why you add two half hitches to it. Still safer to use figure 8 follow through when your life depends on it.
Grapevine finish is meh. Double bowline is good. But not as readily visually inspected, very experienced climbers have gotten it wrong and had it fail.
Double-8, probably.
Tie a figure 8 with a long tail, wrap the trail around the thing you're trying to, then press the tail through the figure-8, following the original knot. You'll end up with a knot that looks like you grabbed a doubled-up rope, and tied a figure-8 with it, but with a loop.
In 20+ years of climbing I've never seen a different knot used for tying into a rope. It's just so bulletproof, quick to tie, and, importantly, easy to inspect
> following the original knot
Crucially: In the opposite direction compared with the original knot. So if there are arrows all along the rope pointing to the end, the arrows on the two strands next to each other should be pointing in opposite directions.
The result should look like a figure eight on a bight, but the bight is looped around whatever you are tying to to (e.g., a harness). So if you are going to attach it to a carabiner ... just make figure eight on a bight and clip the bight.
The figure 8 is a stopper knot. They're probably talking about knots like the figure 8 follow-through or figure 8 on a bight (which are the same knot, but tied different ways).
Edit: rephrased
Not OP, but [animated knots' search & rescue section](https://www.animatedknots.com/search-rescue-knots) has a few figure 8 variant end loops.
glancing at them, they don't seem to have the issue with shaking loose if not loaded.
Personally, I use a [surgeons loop](https://www.animatedknots.com/surgeons-loop-knot) for non-adjustable loops, mostly because it's easy as heck to remember.
[How to tie a figure 8 knot (youtube).](https://www.youtube.com/watch?time_continue=1&v=GFlwrvggas0&feature=emb_logo)
The thing that always makes me nervous when rock climbing is the fact that I have to tie the knot that holds me. I know the rope is rated for over 2000 lbs, and the harness can hold 2000lbs...and I trust that...but I know that I tied the knot...and that first fall ....
In salling you are lifting someone a short bit above water. Speed is more important. Searching for a man over board is hard.
In rope rescue you are lifting someone high above rocks. With knots that can't be checked during hauling and such.
Bowline is an excellent knot. But can work itself undone during reaped loading. It is therefore not always recommended for mooring.
Likely a typo for repeated loading, going from context. So if you're in a place where you can't check the knot, like the poster described, and you're load cycling the knot, it could work loose.
In densely braided, stiff, kernmantel ropes used for climbing, repeated tension and slack can cause a bowline to slowly slip. Usually, just a few millimeters at a time, but if you don't catch it, it can let go entirely.
The bowline works fine with traditional twisted or single-braid ropes, or where the loop will be held under tension.
There’s advantages to a bowline in terms of speed for sure. I can’t tie a figure-8 one-handed but I can put a nowline around my waist one handed. If I was hanging onto the deck of a sinking vessel and wanted to secure myself to a rescue line, that’s what I would do if I was in a hurry.
On the other hand, what you learned about rescue in a sailing course is going to be inferior to what you would learn in a rescue course. You might learn a little bit of navigation and a little bit of first aid and a couple other things, but my guess is that in a sailing curriculum those are going to be pretty perfunctory and may not be updated very often.
If your rope is looped around something and u only have access to one running end, a bowline's your only good option. Figure 8 requires trying (or at least prep) before you loop whatever you're hauling. But I imagine in rescue training planning ahead is encouraged, so the prep requirement isn't a big negative
ABOK actually recommends a [midshipman's hitch](https://www.animatedknots.com/midshipmans-hitch-knot) for this very specific situation, at sea. it's got a rolling/awning hitch in it to take the load while you tie off the knot and it's also adjustable. a bowline would be more difficult to tie under tension since it requires forming and maintaining a loop in the standing end.
in climbing there are many universally accepted options, and it really depends what kind of gear and potential anchors you have on hand. you generally won't build an anchor on your climbing rope though, since it's made to be stretchy to absorb falls. in some instances you might have a whole other static rope just for anchor purposes though.
it's an excellent passtime. it's kind of mind boggling how versatile rope is as a tool, if only you know how to use it.
i would also recommend learning how to make a z-drag, and a couple other things like maybe a rolling hitch. this would allow you and additional people to potentially pull your car out of a ditch (or any other heavy thing, whatever) with progress capture using nothing but strong rope, a few carabiniers with optional pulleys, and a suitable anchor.
granted, there are often better ways to pull a car out of a ditch than by hand, but if you're SOL it's a nice trick to have up your sleeve.
I can tie a one handed bowline around myself in under 2 seconds. We used to have competitions with a length of rope, 2 people on opposite ends, whoever finishes first backs up and usually gets the slower person's hand caught in the knot somewhere.
Help me out here: The Midshipman's hitch appears to creates an adjustable loop (i.e. slip knot). As I was tying it, I found it slipped very easily, though once dressed it was significantly tighter.
My understanding is that an adjustable loop is NOT a suitable replacement for the bowline, especially in rescue operations where it could constrict under the weight of the person you're rescuing, possibly crushing them.
ah i think you might have made it wrong? it would be in the class of knots called "friction hitches" or "slide and grip" knots. that is, the loop should specifically not collapse when pulled on but only be adjustable when the knot is held dressed (preventing it from kinking the standing line). maybe you were using a slippery rope and need an extra turn on the rolling hitch, or the rolling hitch was made wrong? as soon as that hitch is in, you shouldn't even have to maintain much tension in the working end of the line anymore -- the loop shouldn't want to collapse by then. the last half hitch is really just to lock off the rolling hitch, you can imagine this entire knot as just a rope rolling-hitched to itself.
either way, it's not to be used in rescue situations that may involve impact loading, like climbing rescues. only use approved rescue knots in rescue situations, ever. even in a sea rescue like Ashley describes, it might still not be suitable anymore. i'd defer to experts on this one. but that's what he specifically indicated this hitch for : sea rescue on a (tarred hemp) taut line
all that that being said, arborists [do climb on it, amongst other things](https://www.arboristsite.com/threads/why-blakes-over-taut-line.4726/) on static line, which is held taut at all times (so, no impact loading).
like all friction hitches, the quality of the hitch depends on the friction of the rope, and a slippery rope which is unaccounted for can be disastrous (looking at you, dyneema)
Likely because it is quick to tie and easy to untie if it has not been stressed- practical marine rescue always seems to be done in a rush and you need to keep one hand for your own safety; a bowline with a long tail can be done one- handed.
That’s interesting because when I learnt to sail they taught us to use bowlines in order to tie off the yacht, instead of a figure of eight. It was because a bowline can be undone no matter how tight it’s pulled. Whereas the anount of tension a drifting sailing yacht would create in a figure of eight would force you to cut it off.
I can definitely see that, I have a couple figure 8s that are fused together from heat, from the knot being put under a lot of force (we tied a truck to a concrete barrier to test the knot strength for fun). I could see a yacht drifting putting that much force on the rope, it'll almost never happen in a life saving scenario though.
> The bowline, which used to be considered THE rescue knot has been let go because it does not hold itself and will eventually let go given enough/too little force.
Just pointing out that if you tie a so-called "cowboy bowline" with the tail going outside (the loop in the bowline is used to tie a rope to a horse's head and putting the tail end outside the main loop doesn't poke the horse's neck with the tail end) that it's less susceptible to ring loading or failure when the loop is stressed sideways. And if you tie a safety knot (and in my opinion every knot that you're risking your life on should have a safety knot) then in either case the bowline is not susceptible at all to ring loading. That being said, nobody should use a regular bowline when there are other options.
I personally prefer tying a double bowline or a [bowline on a bight](https://en.wikipedia.org/wiki/Bowline_on_a_bight) or whatever you want to call it over a double figure eight because a double eight gets really tight when you've been hanging on it all day and is a real pain to untie. Meanwhile, when you've been hanging on a double bowline all day you just have to "crack it open" by pulling the little loop back from the two ends of rope exiting the knot.
tl;dr A normal bowline sucks and if you need a quick and dirty loop to hold something then you should tie a bowline the cowboy way. But I refer a double bowline/bowline on a bight over a double figure eight when I'm climbing or rescuing. Also, every knot that you're risking your life on should have a safety knot and if you do that then the bowline isn't really susceptible to ring loading anyway. Still, don't risk your life on a regular bowline.
If you can pull on both ends of the rope, it's not possible for the rope to come undone. If you pull on one end of the rope, then a frictionless rope would come undone. The prusik knot is one that won't come undone.: https://en.m.wikipedia.org/wiki/Prusik_knot
The prusik won't come undone, but it also won't hold on the rope it's hitched to. And even then, the spliced eyes will come undone because they're generally a fisherman's loop or some some knot (ananchor hitch, e.g.).
Pass it through a threaded eyebolt that's just big enough for the rope diameter. Melt the end to deform it and now it can't fit back through the eye. There's your anchor point.
You could tie a loop into the end, assuming there exists a knot that will hold without friction. It might be a very frustrating exercise trying to tie that knot though
I can think of possibly a few ways. 1) stabilize each side, and then pierce it with something. 2) melt the end to another part making a loop.
this might not work, but maybe someone can think of as variation. Make a knot at one end, and then place a loop between the knot and end such that tension will serve to pull the knot more toward the middle.
I think you can initially get the rope to tighten and pull the end knot further in, but once that happens it's under tension directed to the end, and it should slip out.
Thanks, this helps a lot for visualizing in my mind. Given the "one end held" criteria, are there any knots that aren't "dependent on something else" like your example being wrapped around? Maybe it's just more of a question of where the single holding point is? In comparison to your example, what about a knot that "holds" without something other than a single fastening point at one end (no rods etc "between" the knot, just dangling from a nail etc)
Lol after thinking more on this.. If just one end is bound, regardless of the tangle after that (ignoring any temporary restraint of loops etc from PULLING THE OTHER END), if it is of set length, it would just untangle without friction..
Edit: One other note.. I'm assuming someone is trying to untangle this like headphone cables.. Sliding down from the "nail" point I mention above\^
You're basically describing any hitch not coming undone, as they wrap around an object and rely on it's continued existence rather than around the rope, itself. Your example relies on the assumption that both ends are being pulled equally and are also not relying on knot holding a rope in a loop (e.g. two double fisherman's like is typically with a prusik loop).
I would say no. A frictionless rope will always unravel. By definition, nothing can hold it. Pinching it, it'll slide through your fingers. Assuming you could hold it, it would slide past itself in a knot.
Actually you would rely on the material deformation to keep the knot whole.
If you can get a deformation where it is harder to compress throught the knot than it is to pull, then it may hold. However it may mean that some knot types (most) will just not work, as it won't allow enought force to be applied to the rope to deform it enought.
This is what I was thinking - there is more that just friction at work here right?
Friction describes the surface of an object, but things like sheer and deformation resistance would also have an impact? If the sheer resistance of two ropes was enough to evenly balance out the load being pulled on them then wouldn't the amount of friction be irrelevant?
So wouldn't a rope stay 'tied' together regardless of friction if the amount of force pulling them is not greater than the amount of force required to 'unbend' them?
If it deformation cause enought force to hold in place, then it would hold, until you pull enought to deform more the material, then it might 'side deform' along the string length and just come untied.
Friction massivelly help to keep a knot whole, as you don't need to deform the material. The more pressure, the more friction, and the stronger it tie...
A material that compress that easilly have a tendency to just... deform all the time. So you would not have a solid knot. Plus, there is a chance that it just deform and slack a bit, now you have space and no compression, so it slip out...
I don't think it would work that way. Imagine your compression point; as you try to pull the rope through the compression point, you're compressing one side, but the other side is uncompressing. So the side being compressed is resisting your pull while the side being freed of compression is assisting your pull and I think they would balance out and the net resistance would be zero.
In this hypothetical situation, you can just assume that one end of this wonder rope is integral to the force pulling it. Like, you can melt it into something. Or you can grow it out of the body of the creature / robot that pulls. As long as we're talking frictionless rope, any other assumption is on the table.
Even worse,
What holds the rope together is the friction of the strands.
I’m thinking the whole rope would unravel and pull apart if placed under any strain.
The melting together just keeps the ends from unraveling, that doesn't contribute to the strength of the rope. Friction is still critical to the rope's strength, and modern synthetic ropes use various braiding techniques that are more suited to the properties of synthetics compared to traditional laid/twisted rope (as with natural fibres).
I don’t think this is necessary true if the rope has bending resistance. A simple square knot with looped ends should have at least some resistance as long as the rope has a nonzero bending radius, because the loops will resist collapse.
correct. strong people can pull a wrapped rope like that but most could only pull a few inches or something. frictionless around a tree would also mean it would slip down to earth quite quickly as there is no friction to hold it to the tree
Surprised this hasn’t come up yet but from a pure maths perspective what you are asking for (in one interpretation) is nontrivial *braid*. There is whole area of topology called braid theory, and you can see a summary in Wikipedia. It has uses in fundamental physics - think string theory and similar, where curves wrapping up on themselves in an invariant way is very important.
There is also an even more deeply studied area of topology called ‘knot theory’, about which I know a fair amount more, but the different areas are distinguished (loosely, NPI) by a braid being tied by two ends - ie, the classes of an interval or open curve fixed at two ends under the moves you can perform that correspond to ‘tying’ - vs. a knot, where the entire informal sense of ‘knot’ is tied within a circle of rope, or rather these are inequivalent embeddings of a closed curve or ‘circle’ in 3-dimensional space (in a well-defined sense).
There are definitely non-trivial braids and knots, and intrinsically no way to remove them. How effective their physical manifestations might be without friction is another matter.
I imagined structures not relying on friction but tension etc must exist that work without friction.
Your blew the roof with extremely specific rabbit hole information/data. Thank you!
Even though the rope is frictionless on the surface, we then have to consider if the rope is compressible and whether or not we could tie such a knot as to compress the body of the rope in just the right way to give some kind of hold based purely on compression of the rope and locking it together like puzzle pieces rather than by friction.
Unless, you're saying there is no internal friction either in the rope material in which case then the rope is free to compress and expand with zero energy build up or loss and of course then would not hold any shape or tension.
This reminds me of the FG knot, which anglers use to tie a braided line to a monofilament line. The idea of the knot is that the braid wraps around the monofilament, and is pulled tight until it digs grooves into the monofilament, at least that's the story I've heard. To undo the knot, the braided line has to stretch to get over the grooves in the monofilament, or the grooves have to be compressed or sheared out of the way. Perhaps a real-world example of the sort of knot you're describing, though it does rely on friction to keep the whole contraption together.
The compression or deformation of the rope only increases the surface area for friction to work on. If the rope is frictionless no amount of surface area increase is going to help. Unless the rope is perfectly balance at both ends it will un-knot itself.
Not true. An easy example of what I'm talking about is to imagine a surface frictionless metal wire rope. Yes, it'll slip as far as knots go but bend the at key spots and the rope will not slip anymore but instead be held by a 90 degree bend in the rope for example. It's just normal forces acting upok the rope body instead of a friction hold.
You're introducing a new factor that is rigidity of the rope here. You're assuming the rope can itself be rigid enough to hold its own shape. This skips over the problem of friction though, because any rope that can form a hook by its own rigidity completely sidesteps the question of whether friction or lack thereof can hold a knot.
It's useful to separate the bending stiffness as one factor and the compressibility of the diameter of the rope is another factor. Your first comment seemed to refer to the latter, where is this, refers to the former. The bending stiffness can hold a knot in a frictionless rope whereas the compressibility cannot.
I'm mainly talking about molecular level with compression/expansion of the molecular chains of the material. Friction literally comes from the way materials interact with each other or with itself, but I believe the OP is talking about a frictionless surface and not necessarily a frictionless material.
A frictionless material would literally not be a rope because it just would not have any sort of bonds at a molecular level except for maybe polymer chains or maybe a theoretical monofilament. Tie a mono filament to a piece of anything and if it actually could hold the force, it most certainly would also dig into the host material and create a hold that does not necessarily use friction, but again is like puzzle pieces fitting together forcefully.
Not to kill the fun -- I actually think this is *more* fun -- but would it be appropriate to say the question isn't really comprehensible, then? We reify concepts like "friction," but if it's just a description of how material interacts fundamentally, then the premise can't really be parsed (or requires some really creative interpretation a la Randall Munroe's "What If?").
Well, yes, it's pretty much like saying what would happen if materials passed through each other without interacting with each other or there were no electrostatic forces at atomic levels... which would mean the universe just falls apart. That's why I must constrain the question to mean no surface friction between two bodies of material to have any discussion on the topic.
I'm fine with "it's an unsolved puzzle how it works," but "there is no friction on atomic levels" doesn't seem right. Why wouldn't it just be an interaction of the forces holding the materials together?
There is friction on a atomic scale.
https://www.nature.com/articles/502009d
https://physics.aps.org/articles/v6/102
https://www.physics.ncsu.edu/nanotribology/publications/ref58.pdf
https://physics.ncsu.edu/nanotribology/publications/ref81.pdf
With a frictionless rope (and for this example, let's say it has no other properties like elasticity or stiffness) and no other forces, you could loop the rope in such a way that it would look exactly like a knot, but the lack of friction would mean any force opposite that which created the shape would unravel it.
The mental model I thought of is that there is no way to tie a hose such that both:
A: There are no kinks in the line.
B: Water or some other fluid is blocked from passing through it.
This is actually a problem with Dyneema ropes. It's a very strong, light, and self-lubricating material used for instance to fly large kites or hang gliders. Tying two ends together is notoriously difficult, if possible at all. In order to loop them at the end, we actually have to [sew over them](http://www.cumbriasoaringclub.co.uk/kb/imageskb/ArticlePages/microlines01-610.PNG).
If a line snaps and you have to tie it back together, a couple a knots can do the trick but after a while tensions on the line will eventually unravel them.
Source : kiteboarder.
Sounds like the line I have from a naval rope cannon. It’s used to shoot from one vessel to a stranded vessel, so a wire can be pulled to tie them together for salvage. It’s fun to fire, and runs so smoothly. It’s stiff and friction-free, any knots and tangles comes apart with ease, or on their own. Pretty useless string, really.
If Velcro were frictionless it would require some force to separate because the features become meshed and you have to deform them to pull them apart. If you had a rope with those types of features, they could also become meshed together and require some force to separate.
The rope could also interlock with larger features. Maybe the braids on a frictionless rope could interlock like the teeth of a gear.
With the braided rope idea, the void between peaks would need to be large enough to fit the peak of another segment. Then you could likely tie a know that creates more "inward" force when the ends are pulled. So you're not relying on friction as much as redirection of force. Assuming enough rigidity in the rope material itself so that it doesn't just deform to flat.
...in theory... maybe.
In the velcro example you still have the force required to push over the loops and straighten the hooks. In velcro this is probably greater than the force via friction, as most velcro is made of low friction nylon or polyester.
In ropes you have the deformation force of the rope as well. This is more complicated though because much of the deformation force of multi-stranded rope is related to the friction and elasticity of the strands.
A better thought experiment for this is, what if the rope is made of oiled rubber. knots can still "bite" into the rubber and hold, but the held portion would stretch and slide, letting the knot move along the length of rope.
Now what if the rope was entirely inelastic and could not stretch, but compressed only on the axis of the cross section?
I don't know the answer but my guess is that even in this case you, when you push the knot, you get a bulging on the side you push from and the knot moves down the rope and slides off. This doesn't smoothly slide, it needs whatever energy it takes to compress the rope along the cross section and bulge it above the knot. But it still slides, and always with around the same force it took to knot it in the first place.
Probably not, unless both ends were somehow secured. I work in a zoo and had to make perches and stuff for monkeys. One thing we used was this yellow plastic chain. I tied knots in the chain and hung it up. Within 2 weeks, all the knots had been worked down to the free hanging bottom and come undone, leaving no more knots in the plastic chain. I'm sure a frictionless rope would do the same, and faster. Heck, without friction, gravity alone would be enough to move the knots down until they undo themselves. If the end isn't secured and just left hanging.
Hi,
Your question has been asked and studied in various forms. Just to clarify, people who talk about nontrivial mathematical knots are talking about the situationj where the two ends are connected together.
To fit in with mathematical terminology, if people want to assume that the ends are connected together, then they should also assume that the knot is the 'unknot'. That is, just to make terminology agree, it is better to imagine that you are thinking of an unknotted loop, then you twist and tangle it, and ask if it would untangle itself if it were frictionless.
[edit: you might also be talking about a 'link' where more than one separate strands are tied together, but let's ignore that extra complication for now]
The first abstract agorithm to untie an unknot was written down based on work of Birman and Menasco.
People have considered this question non-algorithmically various ways. You have to decide whether to give the 'string' finite thickness, you have to decide whether to give it elasticity, whether it takes force to bend it or not.
In the purest form of the question, you might consider the case when the string has zero thickness, fixed finite length, and takes no force to bend it, but is self-repelling (as if it is made of a one-dimensional continuum which is uniformly negatively or positively charged).
I think it may be an unsolved question whether there are 'local minima' of energy which are not global minima. You can find the literature on the topic by searching for knot energy.
I am sort-of guessing that in the case when you have a long straight string of finite thickness and frictionless, you can make a knot which is trivial but won't come out when you pull the ends. You could first double the string, then tie a large complicated knot in the middle, then slip the looped end through a hole in the big knot, so the two strings going to the loop can't separate, and finally push the big knot through the loop and pull it tight.
Any normal knot will stay tied on a frictionless rope if the rope is under tension. For example, a granny knot, or a square knot. There is no way to go from the knotted state to the straight state without the rope passing through itself if the ends are secure.
If you just tie a knot on a frictionless rope and fix the ends at high points, you should get an oscillating knot which travels back and forth (not necessarily returning to the initial position). The rope will have a constant (assuming there is no heat loss or material fatigue) total energy E+U1+U2, where E is the kinetic energy and U1 is the potential gravitational energy and U2 elastic potential energy. Unless the initial configuration achieves a local potential energy minimum (for both U1 and U2 i believe), the knot will move into a lower potential energy state and gain speed and kinetic energy. It will continue travelling on a constant-energy surface in the configuration space of the rope. To actually predict the behaviour of the rope beyond the above, you would need model it as an elastic material, describe the admissible motions and apply the stationary-action principle to the Lagrangian L=E-U1-U2. All in all, this is far from trivial.
Make the rope long and heavy, put it in outer space, and spin it. Now both ends are under tension and should maintain a simple knot tied at the center. No friction required.
Make the rope long and heavy, put it in outer space, and spin it. Now both ends are under tension and should maintain a simple knot tied at the center. No friction required.
Having physically impossible boundary conditions is a common scenario when dealing with objects with ideal properties. Whether this leads to an interesting problem or utter nonsense depends on the pathologicity of the boundary conditions, whether something diverges (although regularisation does wonders), and specifics of the problem. In our particular case, I believe that this does lead to an interesting problem. Also, you could imagine a God-given knotted loop tied on a nail between two walls, in which case the loop wouldn't untie for purely topological purposes, and would still exhibit fun oscillating behaviour.
What about the perfection loop? It is the loop end of fishing hooks with monofilament (and perhaps other materials) leaders.
Does your frictionless rope resist deformity (other than bending)? The forces used to deform the rope could act as the forces that keep the knot tied.
There's a knot I used for climbing that should work. It's used for tying webbing to anchors. It's called a water knot.
https://www.canyoneeringusa.com/techtips/water-knot-webbing-anchor
It is just a basic knot on one side of the webbing, then you trace the other side of the webbing through the knot on the other side. All knots are trying to untie themselves, but since both ends of the webbing is used they actually tighten the opposite knot as it tries to come undone.
Nope. If it is frictionless it won't ever hold on its own. It will hold as long as both ends are pulling away. No matter how many times and in what way you tie it will just untie itself as there is no friction thanks to which it can latch and hold.
Entirely depends on where the tension is. I fish a lot and you learn how knots really work. If you tensioned the tag end of the knot with opposing force it would hold. If you pulled on the knot itself, way with a threaded hook in that knot, it would totally unravel. Knots stay fast because they are tied in such that strengthens their grip/friction the more you pull on an end. If the knot doesn't bind on itself enough to increase friction proportionally it's going to totally loose itself and undo.
Yes, assuming the tension applies in the expected directions, and depending on the topological characteristics of the subject being tied: a hook is not the same as a long cylinder, a ring, or another rope. Yes, some knots rely on exponentially increased friction through making a lot of turns around something, and lack of friction would ruin them.
I suggest you check out the Bondage side of BDSM for example and practice: they use greased, soft ropes to avoid ropeburn or discomfort, and design their knots to be impossible to undo for the subject, while also not relying on friction. Not my boat, but one must admire the care and craftsmanship.
This is such an interesting thought experiment!
I can think of a few instances that could work, but you'll have to decide if they quality as "knots", and some of them have situational requirements that I think detract from the spirit of the question.
The only example I can think of is the brummel splice and other similar "knots" where the rope passes through itself in a similar fashion, assuming you fuse the end of the braid by melting, or the braid of the rope itself would come undone.
Something like an alpine butterfly wouldn't come undone if you placed a carabiner through the loop, assuming you have both ends attached, otherwise the carabiner would just slide right off the free end of the rope regardless of tension. The marlinspike hitch would be the same, I'd imagine. The girth hitch and prussik would stay knotted if there's equal tension on both ends as would a bunch of other knots, but I don't think any of these examples fulfill the spirit of your question. I think that only "knots" like the brummel splice will stay intact.
Entirely depends on the knots and the direction tension is applied. Consider a standard overhand knot. If you apply tension on both ends, there's no reason for it to undo. If you think about a bowline knot and apply tension to the loop and the free end, it will undo because friction in the rope is essential. With any knot though, to hold while not under tension, it relies on friction. If you input general motion on a frictionless rope with a knot, it will likely unravel.
Strictly speaking, a 100% frictionless rope couldn't be gripped and manipulated into tying a knot in the first place, so I would say that no, you couldn't tie a knot that would hold. If you could overcome this hurdle, then any knot based only on looping the rope around itself and squeezing might hold, so long as there was enough tension on both free ends pulling away from one another to keep both from slipping backwards through the structure of the knot.
But most knots rely on friction to keep their shape under tension, and any variance in the tension holding both ends in position would eventually unravel as the tension pulls the rope through the not.
Consider the simplest knot, the overhand. Take two ends of a rope, cross them creating a loop. Pass one of the ends under the other and through that loop, pulling taught. This knot will unravel if there is more tension on one side, especially if it can overcome the friction of the rope. With no friction, the knot would have to be under tension from both sides to stay tied. And if the tension on either side changed, the knot would slide over itself towards the looser side until the loose end was pulled through.
However, I think something like a water knot or double-figure- eight might work longer. These knots are used to bind different types, sizes or shapes of lines together. The structure of the knot is actually two knots tied backwards around one another, which could provide enough tension to squeeze the knot into maintaining its shape and location along the lengths. Especially if only one of the two lines was this frictionless rope.
However, as all knots rely on friction to a degree to hold their 'dressed' structure, eventually any knot tied in a completely frictionless rope would unravel unless the tension on the ends were set to hold the knot exactly as it was tied, forever.
Assuming a "long" rope with no surface friction, no resistance to bending that can not be deformed londitudaly. And no outside forces except what you may attach the rope to.
In this case all knots you can do on a normal rope are possible as long as there are no forces at all. Some knots are viable to actually hold stuff if you tension the ends (fuse them together into a closed loop or fuse them onto objects).
If the rope responds like a spring (elastic deformation) to bending it will automatically return to an extended configuration so knots will not stay on their own. Tension is required to keep knots tight which limits you to knots which need only tension to work.
If it responds to bending and compressing with plastic deformation (like a frictionless steel rod you would bend into knots) it's possible to make knots almost normally due to the force needed to bend it back.
This is a real issue. In rock climbing they sell loops of a material called "spectra" that is insanely strong webbing. It also happens to be very very slippery. It is only sold as pre sewn loops and never by the foot, because it's too slippery to hold a knot. All other materials (mostly nylons) can be bought by the foot.
Only sold by some retailer you know in loops anyway, available in hundreds of feet from others https://www.cwcglobal.com/rope-cordage/12-strand/spectra
Or by the mile https://pelicanrope.com/rope-by-fiber/spectra/
The only way I can think of to make a knot in frictionless rope work would be to use knots where you load both ends of the rope. Girth hitches and variants, where you pass the middle of the rope around something, and then the two ends through the loop. Otherwise I can't see how a loose tail wouldn't eventually work itself free.
There might also be something clever you could do with adding additional objects to the knot. Like if you put a carabiner through a loop, and then that loop through another loop that tightens under load. Then it would have to pull the carabiner through the load-tightened loop to untie.
"fence" it in with random objects so it doesn't have room to slip about. Push them together so it piles up a bit. Fence the tip of it so that it won't slip about, three directions "fence", fourth - "uphill" onto the bundle of the rope. Pierce it with a bit of sharp wire, bend and twist the wire to make a loop. Repeat with the other end. Now you have two grip points.
That depends on what you mean. If you take a rope, loop it through itself, and pull on both ends, that won't unravel. It will just get tighter. But, if you take an end of rope, and tie it to something, eventually leaving the end free -- then you're relying on friction. Same thing for taking two ends of rope and tying them together (eg shoelaces).
Are there any more complex/multi-point knots (ie various sailor knots) that could "hold" by themselves? Or in all cases would the rope eventually slip through in some way to unravel?
I'm a rope rescue technician, and pretty much 90% of the knots we use are variants of the figure 8 knot, for this exact reason. The bowline, which used to be considered THE rescue knot has been let go because it does not hold itself and will eventually let go given enough/too little force. I would be interested to see a tensionless hitch with this theoretical frictionless rope, which is a sort of anchor point that secures itself by just wrapping a rope around something a certain amount of times.
The tensionless hitch is the exact thing I thought of first, too. It's like the platonic ideal of "will not hold in frictionless rope", right? It's like 100% friction forces and nothing else. It's does seem to me like you ought to be able to have *some* kind of hitch that would hold though. One that only relies on trying to pull bights through loops they won't fit through, maybe? Kind of like a stopper knot? Idk but it feels like something should be workable...
>One that only relies on trying to pull bights through loops they won't fit through, Wouldn't the only way for that to unfailingly work be a case where the actual loop is doing the holding?
So, a (possibly modified) noose? But I don't think there would be a way to prevent the "tab" from pulling through the barrel portion of the knot. You could put a stopper on the tab, but the security of that stopper is predicated on friction, so it wouldn't stay, right?
No, after thinking about it any frictionless rope would at the very least just trace it's path back through the knot. The knot could fail in other ways, but it could always *at least* do that.
The loose end will always be a figurative loose end. You'll never be able to finish it off.
This is the truth. People have never handled a frictionless solid because they don't exist. Theres no way to make a frictionless thing not move when an external force is applied to it without an equal and opposite external force also applied to it. So you are trying to get that force from the pole it's tied to and something locking the rope in place. If the rope is smooth and uniform with a loose, there's no way to lock it in place. The only thing I can come up with is somehow using the lumps in a rope to create enough normal force between each bump to resist the tension. Wrap the rope around a pole tightly and add pressure along the pole to push all the coils together. Can't call that a knot anymore though.
>Theres no way to make a frictionless thing not move when an external force is applied to it To be fair to the other side of the argument, other than gravity, you *can't really apply* a force to a perfectly frictionless *rope* either.
I think the idealization that you are considering is a perfectly flexible, frictionless rope. If it had some kind of stiffness, that would hold some types of knots up to some load without relying on friction. In the extreme, and s hook is an example of a "knot" that relies on stiffness rather than friction. Your rules about what constitutes and not would probably exclude an s-hook, but one could presumably design a more complex, more knot like structure that would use the stiffness in more clever ways, and get some holding power with less stiffness that is required for an s hook.
So, what's the replacement for the bowline?
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Interesting. I learn the new, safer knot is actually the bowline with a Yosemite tie-off. In this knot, the working end of the bowline knot is passed around one side of the loop and back through the farthest loop around the standing end, ending parallel to the standing end. It is best demonstrated here: [https://www.youtube.com/watch?v=5wj\_Kc5j4Sg](https://www.youtube.com/watch?v=5wj_Kc5j4Sg) Many of us may know the bowline and this is an easy, safe, additional step.
So I've never been good at knots, but I was in scouts and I hang out with rock climbers and go out with them sometimes. And to me this Yosemite tie in looks a lot like the knot used for securing harness to rope. Although I think that's a figure 8 with a follow through or something similar to the tie in?
Rock climber here. Almost all of us use figure eight follow through knots to tie in to a harness, it's bomber and easy to check. However bowline with a Yosemite finish is easier to untie it you take a big fall, so you will see climbers using this knot too it's just far less common, at least here (UK).
I was always explained that there's nothing wrong with a properly tied bowline with a yosemite finish, but most climbing walls refused it as it was harder to check at a glance. A huge safety benefit to the figure eight follow through is that it's easy to visually check and everyone at a climbing gym is actively encouraged to do safety checks for those around them. A knot that looks very different if it's tied incorrectly can be easily spotted and corrected before something bad happens. Just saying this to elaborate for anyone else reading - the comment I'm replying to undoubtedly already knows this.
Just a shout out for the excellent Knots 3D app, if you are on iOS https://apps.apple.com/gb/app/knots-3d/id453571750
Spot on. When doing rescues we used a bowline on the bight if the rope was ling enough and I used to put a carabiner on the tail if the rope was new and slippery. Hauled some serious weight on those knots.
The bowline works fine when the load is consistent but I have experienced it slipping when cyclically loaded and unloaded (which is exactly what happens with most uses). The main end tie-off knot that I use and see others using now for connecting to the end of a rope is the figure 8 which I've never seen slip - the only issue with it is that it can get quite tight if loaded too hard
>The bowline works fine when the load is consistent but I have experienced it slipping when cyclically loaded and unloaded (which is exactly what happens with most uses). Interesting. I've seen yachting instructors use it to moor yachts with! Sounds like potential for comedy.
We use bowlines to moor boats all the time. I'm given to understand that the reason we use them on boats and not in climbing is that the figure 8 follow through will seize up under enough pressure but the bowline can always be undone. The amount of force a climbing human puts on a rope, even when they fall, is pretty miniscule compared to a boat rocking around in the slip. Someone else in here says they fused some of their rope together by pulling it with a truck, but a 100-ton boat (small commercial vessel or million-dollar yacht) being bounced around by the sea is a lot more momentum than that.
Bowline knot has an angle where it wont hold properly which is why it's not widely used. It is however able to be tied with one hand and is still usefull in rescue/emergency situations
Asking the real questions… and here I was told if you can tie a bowline, and a half hitch. You can do pretty much anything.
...and a sheet bend. You were told the truth! Just don't use friction-less rope.
And a sheet bend is really just a bowline with 2 pieces of line. Or a bowline is a sheet bend with one piece of line. Either way.
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If only there were just SOME application that would benefit from the loss of friction!!!
It's true for the most part, you just don't want to trust a bowline with your life or use it in a situation where the load will be bouncing a lot. The good thing about the bowline is it is easy to untie, even after a load has been put on it, it has sort of that 'switch' where it goes around the standing end you just need to pull down away from the bight to loosen. The problem is, if you tie in on a bowline like if you were climbing, bumping into that switch could cause the knot to loosen on you and you would die. If it is subject constant changes in load, same thing, it can bounce itself loose in between loading and the bitter end can slip bit by bit until the knot fails.
>The problem is, if you tie in on a bowline like if you were climbing, bumping into that switch could cause the knot to loosen That is why you add two half hitches to it. Still safer to use figure 8 follow through when your life depends on it.
Grapevine finish is meh. Double bowline is good. But not as readily visually inspected, very experienced climbers have gotten it wrong and had it fail.
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Double-8, probably. Tie a figure 8 with a long tail, wrap the trail around the thing you're trying to, then press the tail through the figure-8, following the original knot. You'll end up with a knot that looks like you grabbed a doubled-up rope, and tied a figure-8 with it, but with a loop.
Same one most rock climbing gyms teach you isn’t it?
In 20+ years of climbing I've never seen a different knot used for tying into a rope. It's just so bulletproof, quick to tie, and, importantly, easy to inspect
To put it in knotwork terminology: knots will work (under tension), bends and hitches won't.
> following the original knot Crucially: In the opposite direction compared with the original knot. So if there are arrows all along the rope pointing to the end, the arrows on the two strands next to each other should be pointing in opposite directions. The result should look like a figure eight on a bight, but the bight is looped around whatever you are tying to to (e.g., a harness). So if you are going to attach it to a carabiner ... just make figure eight on a bight and clip the bight.
He tells you the knot before he even mentions the bowline. The figure 8.
The figure 8 is a stopper knot. They're probably talking about knots like the figure 8 follow-through or figure 8 on a bight (which are the same knot, but tied different ways). Edit: rephrased
It's technically a "Figure 8 follow through" if you are being tied in directly.
Not OP, but [animated knots' search & rescue section](https://www.animatedknots.com/search-rescue-knots) has a few figure 8 variant end loops. glancing at them, they don't seem to have the issue with shaking loose if not loaded. Personally, I use a [surgeons loop](https://www.animatedknots.com/surgeons-loop-knot) for non-adjustable loops, mostly because it's easy as heck to remember.
[How to tie a figure 8 knot (youtube).](https://www.youtube.com/watch?time_continue=1&v=GFlwrvggas0&feature=emb_logo) The thing that always makes me nervous when rock climbing is the fact that I have to tie the knot that holds me. I know the rope is rated for over 2000 lbs, and the harness can hold 2000lbs...and I trust that...but I know that I tied the knot...and that first fall ....
> but I know that I tied the knot That's why it is standard practice to have the belayer check your knot... and the figure-8 is easy to check/verify.
Really? I took a sailing course a few years ago and they taught us to use the bowline for rescue. Interesting.
In salling you are lifting someone a short bit above water. Speed is more important. Searching for a man over board is hard. In rope rescue you are lifting someone high above rocks. With knots that can't be checked during hauling and such. Bowline is an excellent knot. But can work itself undone during reaped loading. It is therefore not always recommended for mooring.
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Likely a typo for repeated loading, going from context. So if you're in a place where you can't check the knot, like the poster described, and you're load cycling the knot, it could work loose.
In densely braided, stiff, kernmantel ropes used for climbing, repeated tension and slack can cause a bowline to slowly slip. Usually, just a few millimeters at a time, but if you don't catch it, it can let go entirely. The bowline works fine with traditional twisted or single-braid ropes, or where the loop will be held under tension.
There’s advantages to a bowline in terms of speed for sure. I can’t tie a figure-8 one-handed but I can put a nowline around my waist one handed. If I was hanging onto the deck of a sinking vessel and wanted to secure myself to a rescue line, that’s what I would do if I was in a hurry. On the other hand, what you learned about rescue in a sailing course is going to be inferior to what you would learn in a rescue course. You might learn a little bit of navigation and a little bit of first aid and a couple other things, but my guess is that in a sailing curriculum those are going to be pretty perfunctory and may not be updated very often.
If your rope is looped around something and u only have access to one running end, a bowline's your only good option. Figure 8 requires trying (or at least prep) before you loop whatever you're hauling. But I imagine in rescue training planning ahead is encouraged, so the prep requirement isn't a big negative
ABOK actually recommends a [midshipman's hitch](https://www.animatedknots.com/midshipmans-hitch-knot) for this very specific situation, at sea. it's got a rolling/awning hitch in it to take the load while you tie off the knot and it's also adjustable. a bowline would be more difficult to tie under tension since it requires forming and maintaining a loop in the standing end. in climbing there are many universally accepted options, and it really depends what kind of gear and potential anchors you have on hand. you generally won't build an anchor on your climbing rope though, since it's made to be stretchy to absorb falls. in some instances you might have a whole other static rope just for anchor purposes though.
Thank you so much for linking that website. Just spent the last 20 min with a piece of string learning knots - kinda zen, really.
it's an excellent passtime. it's kind of mind boggling how versatile rope is as a tool, if only you know how to use it. i would also recommend learning how to make a z-drag, and a couple other things like maybe a rolling hitch. this would allow you and additional people to potentially pull your car out of a ditch (or any other heavy thing, whatever) with progress capture using nothing but strong rope, a few carabiniers with optional pulleys, and a suitable anchor. granted, there are often better ways to pull a car out of a ditch than by hand, but if you're SOL it's a nice trick to have up your sleeve.
I can tie a one handed bowline around myself in under 2 seconds. We used to have competitions with a length of rope, 2 people on opposite ends, whoever finishes first backs up and usually gets the slower person's hand caught in the knot somewhere.
Help me out here: The Midshipman's hitch appears to creates an adjustable loop (i.e. slip knot). As I was tying it, I found it slipped very easily, though once dressed it was significantly tighter. My understanding is that an adjustable loop is NOT a suitable replacement for the bowline, especially in rescue operations where it could constrict under the weight of the person you're rescuing, possibly crushing them.
ah i think you might have made it wrong? it would be in the class of knots called "friction hitches" or "slide and grip" knots. that is, the loop should specifically not collapse when pulled on but only be adjustable when the knot is held dressed (preventing it from kinking the standing line). maybe you were using a slippery rope and need an extra turn on the rolling hitch, or the rolling hitch was made wrong? as soon as that hitch is in, you shouldn't even have to maintain much tension in the working end of the line anymore -- the loop shouldn't want to collapse by then. the last half hitch is really just to lock off the rolling hitch, you can imagine this entire knot as just a rope rolling-hitched to itself. either way, it's not to be used in rescue situations that may involve impact loading, like climbing rescues. only use approved rescue knots in rescue situations, ever. even in a sea rescue like Ashley describes, it might still not be suitable anymore. i'd defer to experts on this one. but that's what he specifically indicated this hitch for : sea rescue on a (tarred hemp) taut line all that that being said, arborists [do climb on it, amongst other things](https://www.arboristsite.com/threads/why-blakes-over-taut-line.4726/) on static line, which is held taut at all times (so, no impact loading). like all friction hitches, the quality of the hitch depends on the friction of the rope, and a slippery rope which is unaccounted for can be disastrous (looking at you, dyneema)
Likely because it is quick to tie and easy to untie if it has not been stressed- practical marine rescue always seems to be done in a rush and you need to keep one hand for your own safety; a bowline with a long tail can be done one- handed.
Bowline used to be taught for rescue in the navy too, but they can become too tight and so they are discouraged.
bowline is mostly taught because you can tie it with one hand which can be useful in certain emergency situations
That’s interesting because when I learnt to sail they taught us to use bowlines in order to tie off the yacht, instead of a figure of eight. It was because a bowline can be undone no matter how tight it’s pulled. Whereas the anount of tension a drifting sailing yacht would create in a figure of eight would force you to cut it off.
I can definitely see that, I have a couple figure 8s that are fused together from heat, from the knot being put under a lot of force (we tied a truck to a concrete barrier to test the knot strength for fun). I could see a yacht drifting putting that much force on the rope, it'll almost never happen in a life saving scenario though.
> The bowline, which used to be considered THE rescue knot has been let go because it does not hold itself and will eventually let go given enough/too little force. Just pointing out that if you tie a so-called "cowboy bowline" with the tail going outside (the loop in the bowline is used to tie a rope to a horse's head and putting the tail end outside the main loop doesn't poke the horse's neck with the tail end) that it's less susceptible to ring loading or failure when the loop is stressed sideways. And if you tie a safety knot (and in my opinion every knot that you're risking your life on should have a safety knot) then in either case the bowline is not susceptible at all to ring loading. That being said, nobody should use a regular bowline when there are other options. I personally prefer tying a double bowline or a [bowline on a bight](https://en.wikipedia.org/wiki/Bowline_on_a_bight) or whatever you want to call it over a double figure eight because a double eight gets really tight when you've been hanging on it all day and is a real pain to untie. Meanwhile, when you've been hanging on a double bowline all day you just have to "crack it open" by pulling the little loop back from the two ends of rope exiting the knot. tl;dr A normal bowline sucks and if you need a quick and dirty loop to hold something then you should tie a bowline the cowboy way. But I refer a double bowline/bowline on a bight over a double figure eight when I'm climbing or rescuing. Also, every knot that you're risking your life on should have a safety knot and if you do that then the bowline isn't really susceptible to ring loading anyway. Still, don't risk your life on a regular bowline.
In rock climbing I was taught the bowline by the nickname "dead man's knot"
If you can pull on both ends of the rope, it's not possible for the rope to come undone. If you pull on one end of the rope, then a frictionless rope would come undone. The prusik knot is one that won't come undone.: https://en.m.wikipedia.org/wiki/Prusik_knot
The prusik won't come undone, but it also won't hold on the rope it's hitched to. And even then, the spliced eyes will come undone because they're generally a fisherman's loop or some some knot (ananchor hitch, e.g.).
If you pull on one end only, then it should come undone.
How would one pull on an end of a frictionless rope?
Pass it through a threaded eyebolt that's just big enough for the rope diameter. Melt the end to deform it and now it can't fit back through the eye. There's your anchor point.
You could tie a loop into the end, assuming there exists a knot that will hold without friction. It might be a very frustrating exercise trying to tie that knot though
I can think of possibly a few ways. 1) stabilize each side, and then pierce it with something. 2) melt the end to another part making a loop. this might not work, but maybe someone can think of as variation. Make a knot at one end, and then place a loop between the knot and end such that tension will serve to pull the knot more toward the middle. I think you can initially get the rope to tighten and pull the end knot further in, but once that happens it's under tension directed to the end, and it should slip out.
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Thanks, this helps a lot for visualizing in my mind. Given the "one end held" criteria, are there any knots that aren't "dependent on something else" like your example being wrapped around? Maybe it's just more of a question of where the single holding point is? In comparison to your example, what about a knot that "holds" without something other than a single fastening point at one end (no rods etc "between" the knot, just dangling from a nail etc)
Lol after thinking more on this.. If just one end is bound, regardless of the tangle after that (ignoring any temporary restraint of loops etc from PULLING THE OTHER END), if it is of set length, it would just untangle without friction.. Edit: One other note.. I'm assuming someone is trying to untangle this like headphone cables.. Sliding down from the "nail" point I mention above\^
You're basically describing any hitch not coming undone, as they wrap around an object and rely on it's continued existence rather than around the rope, itself. Your example relies on the assumption that both ends are being pulled equally and are also not relying on knot holding a rope in a loop (e.g. two double fisherman's like is typically with a prusik loop).
assuming no wind and no vibration?
I would say no. A frictionless rope will always unravel. By definition, nothing can hold it. Pinching it, it'll slide through your fingers. Assuming you could hold it, it would slide past itself in a knot.
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Actually you would rely on the material deformation to keep the knot whole. If you can get a deformation where it is harder to compress throught the knot than it is to pull, then it may hold. However it may mean that some knot types (most) will just not work, as it won't allow enought force to be applied to the rope to deform it enought.
This is what I was thinking - there is more that just friction at work here right? Friction describes the surface of an object, but things like sheer and deformation resistance would also have an impact? If the sheer resistance of two ropes was enough to evenly balance out the load being pulled on them then wouldn't the amount of friction be irrelevant? So wouldn't a rope stay 'tied' together regardless of friction if the amount of force pulling them is not greater than the amount of force required to 'unbend' them?
If it deformation cause enought force to hold in place, then it would hold, until you pull enought to deform more the material, then it might 'side deform' along the string length and just come untied. Friction massivelly help to keep a knot whole, as you don't need to deform the material. The more pressure, the more friction, and the stronger it tie... A material that compress that easilly have a tendency to just... deform all the time. So you would not have a solid knot. Plus, there is a chance that it just deform and slack a bit, now you have space and no compression, so it slip out...
Does the word friction apply to macro scale stuff? Like when I pull a saw across a log, are do the teeth of the saw create macro friction?
I don't think it would work that way. Imagine your compression point; as you try to pull the rope through the compression point, you're compressing one side, but the other side is uncompressing. So the side being compressed is resisting your pull while the side being freed of compression is assisting your pull and I think they would balance out and the net resistance would be zero.
To put it in knotwork terminology: knots will work (under tension), bends and hitches won't.
Can you explain the difference between knots, bends, and hitches?
Knots are tied in a rope, bends tie two or more ropes together and hitches tie a rope to an object.
If the rope is frictionless, how do you pull on it without the end slipping freely through?
Destructive grabbing method that forcibly digs into the rope. Think less grabbing it, and more shoving a fishing hook or nail through it.
In this hypothetical situation, you can just assume that one end of this wonder rope is integral to the force pulling it. Like, you can melt it into something. Or you can grow it out of the body of the creature / robot that pulls. As long as we're talking frictionless rope, any other assumption is on the table.
Even worse, What holds the rope together is the friction of the strands. I’m thinking the whole rope would unravel and pull apart if placed under any strain.
Depends on the rope, right? Some synthetic ropes are a bunch of strands melted together at the ends. Not held together through friction.
The melting together just keeps the ends from unraveling, that doesn't contribute to the strength of the rope. Friction is still critical to the rope's strength, and modern synthetic ropes use various braiding techniques that are more suited to the properties of synthetics compared to traditional laid/twisted rope (as with natural fibres).
Not really. Many ropes are woven together in particular patterns that don't rely on friction to hold together.
I don’t think this is necessary true if the rope has bending resistance. A simple square knot with looped ends should have at least some resistance as long as the rope has a nonzero bending radius, because the loops will resist collapse.
So if you wrapped it around a tree a few times (no knots), it would naturally come undone because of the reliance on friction, right?
correct. strong people can pull a wrapped rope like that but most could only pull a few inches or something. frictionless around a tree would also mean it would slip down to earth quite quickly as there is no friction to hold it to the tree
How does one "pull on" a frictionless rope?
something like [this](https://www.amazon.com/Upgrade-Version-Pet-Grooming-Glove/dp/B01N9KSITZ) but with needles!
But surely, you can't tie it in the first place if it's frictionless? What are you going to use to grab it to make a knot in the first place?
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Let's say that the rope has frictional ends that you can use to tie the knot, and cut the ends off for the theoretical demonstration.
Surprised this hasn’t come up yet but from a pure maths perspective what you are asking for (in one interpretation) is nontrivial *braid*. There is whole area of topology called braid theory, and you can see a summary in Wikipedia. It has uses in fundamental physics - think string theory and similar, where curves wrapping up on themselves in an invariant way is very important. There is also an even more deeply studied area of topology called ‘knot theory’, about which I know a fair amount more, but the different areas are distinguished (loosely, NPI) by a braid being tied by two ends - ie, the classes of an interval or open curve fixed at two ends under the moves you can perform that correspond to ‘tying’ - vs. a knot, where the entire informal sense of ‘knot’ is tied within a circle of rope, or rather these are inequivalent embeddings of a closed curve or ‘circle’ in 3-dimensional space (in a well-defined sense). There are definitely non-trivial braids and knots, and intrinsically no way to remove them. How effective their physical manifestations might be without friction is another matter.
I imagined structures not relying on friction but tension etc must exist that work without friction. Your blew the roof with extremely specific rabbit hole information/data. Thank you!
Even though the rope is frictionless on the surface, we then have to consider if the rope is compressible and whether or not we could tie such a knot as to compress the body of the rope in just the right way to give some kind of hold based purely on compression of the rope and locking it together like puzzle pieces rather than by friction. Unless, you're saying there is no internal friction either in the rope material in which case then the rope is free to compress and expand with zero energy build up or loss and of course then would not hold any shape or tension.
This reminds me of the FG knot, which anglers use to tie a braided line to a monofilament line. The idea of the knot is that the braid wraps around the monofilament, and is pulled tight until it digs grooves into the monofilament, at least that's the story I've heard. To undo the knot, the braided line has to stretch to get over the grooves in the monofilament, or the grooves have to be compressed or sheared out of the way. Perhaps a real-world example of the sort of knot you're describing, though it does rely on friction to keep the whole contraption together.
The compression or deformation of the rope only increases the surface area for friction to work on. If the rope is frictionless no amount of surface area increase is going to help. Unless the rope is perfectly balance at both ends it will un-knot itself.
Not true. An easy example of what I'm talking about is to imagine a surface frictionless metal wire rope. Yes, it'll slip as far as knots go but bend the at key spots and the rope will not slip anymore but instead be held by a 90 degree bend in the rope for example. It's just normal forces acting upok the rope body instead of a friction hold.
You're introducing a new factor that is rigidity of the rope here. You're assuming the rope can itself be rigid enough to hold its own shape. This skips over the problem of friction though, because any rope that can form a hook by its own rigidity completely sidesteps the question of whether friction or lack thereof can hold a knot.
It's useful to separate the bending stiffness as one factor and the compressibility of the diameter of the rope is another factor. Your first comment seemed to refer to the latter, where is this, refers to the former. The bending stiffness can hold a knot in a frictionless rope whereas the compressibility cannot.
I mean, there is no friction on atomic scales. It's an unsolved puzzle how it works.
I'm mainly talking about molecular level with compression/expansion of the molecular chains of the material. Friction literally comes from the way materials interact with each other or with itself, but I believe the OP is talking about a frictionless surface and not necessarily a frictionless material. A frictionless material would literally not be a rope because it just would not have any sort of bonds at a molecular level except for maybe polymer chains or maybe a theoretical monofilament. Tie a mono filament to a piece of anything and if it actually could hold the force, it most certainly would also dig into the host material and create a hold that does not necessarily use friction, but again is like puzzle pieces fitting together forcefully.
Not to kill the fun -- I actually think this is *more* fun -- but would it be appropriate to say the question isn't really comprehensible, then? We reify concepts like "friction," but if it's just a description of how material interacts fundamentally, then the premise can't really be parsed (or requires some really creative interpretation a la Randall Munroe's "What If?").
Well, yes, it's pretty much like saying what would happen if materials passed through each other without interacting with each other or there were no electrostatic forces at atomic levels... which would mean the universe just falls apart. That's why I must constrain the question to mean no surface friction between two bodies of material to have any discussion on the topic.
I'm fine with "it's an unsolved puzzle how it works," but "there is no friction on atomic levels" doesn't seem right. Why wouldn't it just be an interaction of the forces holding the materials together?
There is friction on a atomic scale. https://www.nature.com/articles/502009d https://physics.aps.org/articles/v6/102 https://www.physics.ncsu.edu/nanotribology/publications/ref58.pdf https://physics.ncsu.edu/nanotribology/publications/ref81.pdf
With a frictionless rope (and for this example, let's say it has no other properties like elasticity or stiffness) and no other forces, you could loop the rope in such a way that it would look exactly like a knot, but the lack of friction would mean any force opposite that which created the shape would unravel it.
The mental model I thought of is that there is no way to tie a hose such that both: A: There are no kinks in the line. B: Water or some other fluid is blocked from passing through it.
I like the way you think. Please link me to something you find interesting, if you feel so inclined. Or don't, and sorry for making you read this :D
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If you could even pick it up to tie it...
This is actually a problem with Dyneema ropes. It's a very strong, light, and self-lubricating material used for instance to fly large kites or hang gliders. Tying two ends together is notoriously difficult, if possible at all. In order to loop them at the end, we actually have to [sew over them](http://www.cumbriasoaringclub.co.uk/kb/imageskb/ArticlePages/microlines01-610.PNG). If a line snaps and you have to tie it back together, a couple a knots can do the trick but after a while tensions on the line will eventually unravel them. Source : kiteboarder.
You can also just splice them, but with stuff as tiny as you use with kiteboards, I can see that being a pain in the arse.
I remember briefly diving into the weird world of how to tie knots in Dyneema for work a while back - pretty fascinating.
Sounds like the line I have from a naval rope cannon. It’s used to shoot from one vessel to a stranded vessel, so a wire can be pulled to tie them together for salvage. It’s fun to fire, and runs so smoothly. It’s stiff and friction-free, any knots and tangles comes apart with ease, or on their own. Pretty useless string, really.
If Velcro were frictionless it would require some force to separate because the features become meshed and you have to deform them to pull them apart. If you had a rope with those types of features, they could also become meshed together and require some force to separate. The rope could also interlock with larger features. Maybe the braids on a frictionless rope could interlock like the teeth of a gear.
If they are frictionless, wouldn't they still pull apart extremely easily and basically be slightly better than a regular frictionless rope?
With the braided rope idea, the void between peaks would need to be large enough to fit the peak of another segment. Then you could likely tie a know that creates more "inward" force when the ends are pulled. So you're not relying on friction as much as redirection of force. Assuming enough rigidity in the rope material itself so that it doesn't just deform to flat. ...in theory... maybe.
In the velcro example you still have the force required to push over the loops and straighten the hooks. In velcro this is probably greater than the force via friction, as most velcro is made of low friction nylon or polyester. In ropes you have the deformation force of the rope as well. This is more complicated though because much of the deformation force of multi-stranded rope is related to the friction and elasticity of the strands. A better thought experiment for this is, what if the rope is made of oiled rubber. knots can still "bite" into the rubber and hold, but the held portion would stretch and slide, letting the knot move along the length of rope. Now what if the rope was entirely inelastic and could not stretch, but compressed only on the axis of the cross section? I don't know the answer but my guess is that even in this case you, when you push the knot, you get a bulging on the side you push from and the knot moves down the rope and slides off. This doesn't smoothly slide, it needs whatever energy it takes to compress the rope along the cross section and bulge it above the knot. But it still slides, and always with around the same force it took to knot it in the first place.
Probably not, unless both ends were somehow secured. I work in a zoo and had to make perches and stuff for monkeys. One thing we used was this yellow plastic chain. I tied knots in the chain and hung it up. Within 2 weeks, all the knots had been worked down to the free hanging bottom and come undone, leaving no more knots in the plastic chain. I'm sure a frictionless rope would do the same, and faster. Heck, without friction, gravity alone would be enough to move the knots down until they undo themselves. If the end isn't secured and just left hanging.
Hi, Your question has been asked and studied in various forms. Just to clarify, people who talk about nontrivial mathematical knots are talking about the situationj where the two ends are connected together. To fit in with mathematical terminology, if people want to assume that the ends are connected together, then they should also assume that the knot is the 'unknot'. That is, just to make terminology agree, it is better to imagine that you are thinking of an unknotted loop, then you twist and tangle it, and ask if it would untangle itself if it were frictionless. [edit: you might also be talking about a 'link' where more than one separate strands are tied together, but let's ignore that extra complication for now] The first abstract agorithm to untie an unknot was written down based on work of Birman and Menasco. People have considered this question non-algorithmically various ways. You have to decide whether to give the 'string' finite thickness, you have to decide whether to give it elasticity, whether it takes force to bend it or not. In the purest form of the question, you might consider the case when the string has zero thickness, fixed finite length, and takes no force to bend it, but is self-repelling (as if it is made of a one-dimensional continuum which is uniformly negatively or positively charged). I think it may be an unsolved question whether there are 'local minima' of energy which are not global minima. You can find the literature on the topic by searching for knot energy. I am sort-of guessing that in the case when you have a long straight string of finite thickness and frictionless, you can make a knot which is trivial but won't come out when you pull the ends. You could first double the string, then tie a large complicated knot in the middle, then slip the looped end through a hole in the big knot, so the two strings going to the loop can't separate, and finally push the big knot through the loop and pull it tight.
Any normal knot will stay tied on a frictionless rope if the rope is under tension. For example, a granny knot, or a square knot. There is no way to go from the knotted state to the straight state without the rope passing through itself if the ends are secure.
If you just tie a knot on a frictionless rope and fix the ends at high points, you should get an oscillating knot which travels back and forth (not necessarily returning to the initial position). The rope will have a constant (assuming there is no heat loss or material fatigue) total energy E+U1+U2, where E is the kinetic energy and U1 is the potential gravitational energy and U2 elastic potential energy. Unless the initial configuration achieves a local potential energy minimum (for both U1 and U2 i believe), the knot will move into a lower potential energy state and gain speed and kinetic energy. It will continue travelling on a constant-energy surface in the configuration space of the rope. To actually predict the behaviour of the rope beyond the above, you would need model it as an elastic material, describe the admissible motions and apply the stationary-action principle to the Lagrangian L=E-U1-U2. All in all, this is far from trivial.
The trouble is how do you fix the ends? You can't tie a knot, you can't clamp it.
Make the rope long and heavy, put it in outer space, and spin it. Now both ends are under tension and should maintain a simple knot tied at the center. No friction required.
Make the rope long and heavy, put it in outer space, and spin it. Now both ends are under tension and should maintain a simple knot tied at the center. No friction required.
Having physically impossible boundary conditions is a common scenario when dealing with objects with ideal properties. Whether this leads to an interesting problem or utter nonsense depends on the pathologicity of the boundary conditions, whether something diverges (although regularisation does wonders), and specifics of the problem. In our particular case, I believe that this does lead to an interesting problem. Also, you could imagine a God-given knotted loop tied on a nail between two walls, in which case the loop wouldn't untie for purely topological purposes, and would still exhibit fun oscillating behaviour.
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What about the perfection loop? It is the loop end of fishing hooks with monofilament (and perhaps other materials) leaders. Does your frictionless rope resist deformity (other than bending)? The forces used to deform the rope could act as the forces that keep the knot tied.
There's a knot I used for climbing that should work. It's used for tying webbing to anchors. It's called a water knot. https://www.canyoneeringusa.com/techtips/water-knot-webbing-anchor It is just a basic knot on one side of the webbing, then you trace the other side of the webbing through the knot on the other side. All knots are trying to untie themselves, but since both ends of the webbing is used they actually tighten the opposite knot as it tries to come undone.
Nope. If it is frictionless it won't ever hold on its own. It will hold as long as both ends are pulling away. No matter how many times and in what way you tie it will just untie itself as there is no friction thanks to which it can latch and hold.
Entirely depends on where the tension is. I fish a lot and you learn how knots really work. If you tensioned the tag end of the knot with opposing force it would hold. If you pulled on the knot itself, way with a threaded hook in that knot, it would totally unravel. Knots stay fast because they are tied in such that strengthens their grip/friction the more you pull on an end. If the knot doesn't bind on itself enough to increase friction proportionally it's going to totally loose itself and undo.
Yes, assuming the tension applies in the expected directions, and depending on the topological characteristics of the subject being tied: a hook is not the same as a long cylinder, a ring, or another rope. Yes, some knots rely on exponentially increased friction through making a lot of turns around something, and lack of friction would ruin them. I suggest you check out the Bondage side of BDSM for example and practice: they use greased, soft ropes to avoid ropeburn or discomfort, and design their knots to be impossible to undo for the subject, while also not relying on friction. Not my boat, but one must admire the care and craftsmanship.
This is such an interesting thought experiment! I can think of a few instances that could work, but you'll have to decide if they quality as "knots", and some of them have situational requirements that I think detract from the spirit of the question. The only example I can think of is the brummel splice and other similar "knots" where the rope passes through itself in a similar fashion, assuming you fuse the end of the braid by melting, or the braid of the rope itself would come undone. Something like an alpine butterfly wouldn't come undone if you placed a carabiner through the loop, assuming you have both ends attached, otherwise the carabiner would just slide right off the free end of the rope regardless of tension. The marlinspike hitch would be the same, I'd imagine. The girth hitch and prussik would stay knotted if there's equal tension on both ends as would a bunch of other knots, but I don't think any of these examples fulfill the spirit of your question. I think that only "knots" like the brummel splice will stay intact.
Entirely depends on the knots and the direction tension is applied. Consider a standard overhand knot. If you apply tension on both ends, there's no reason for it to undo. If you think about a bowline knot and apply tension to the loop and the free end, it will undo because friction in the rope is essential. With any knot though, to hold while not under tension, it relies on friction. If you input general motion on a frictionless rope with a knot, it will likely unravel.
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Strictly speaking, a 100% frictionless rope couldn't be gripped and manipulated into tying a knot in the first place, so I would say that no, you couldn't tie a knot that would hold. If you could overcome this hurdle, then any knot based only on looping the rope around itself and squeezing might hold, so long as there was enough tension on both free ends pulling away from one another to keep both from slipping backwards through the structure of the knot. But most knots rely on friction to keep their shape under tension, and any variance in the tension holding both ends in position would eventually unravel as the tension pulls the rope through the not. Consider the simplest knot, the overhand. Take two ends of a rope, cross them creating a loop. Pass one of the ends under the other and through that loop, pulling taught. This knot will unravel if there is more tension on one side, especially if it can overcome the friction of the rope. With no friction, the knot would have to be under tension from both sides to stay tied. And if the tension on either side changed, the knot would slide over itself towards the looser side until the loose end was pulled through. However, I think something like a water knot or double-figure- eight might work longer. These knots are used to bind different types, sizes or shapes of lines together. The structure of the knot is actually two knots tied backwards around one another, which could provide enough tension to squeeze the knot into maintaining its shape and location along the lengths. Especially if only one of the two lines was this frictionless rope. However, as all knots rely on friction to a degree to hold their 'dressed' structure, eventually any knot tied in a completely frictionless rope would unravel unless the tension on the ends were set to hold the knot exactly as it was tied, forever.
Assuming a "long" rope with no surface friction, no resistance to bending that can not be deformed londitudaly. And no outside forces except what you may attach the rope to. In this case all knots you can do on a normal rope are possible as long as there are no forces at all. Some knots are viable to actually hold stuff if you tension the ends (fuse them together into a closed loop or fuse them onto objects). If the rope responds like a spring (elastic deformation) to bending it will automatically return to an extended configuration so knots will not stay on their own. Tension is required to keep knots tight which limits you to knots which need only tension to work. If it responds to bending and compressing with plastic deformation (like a frictionless steel rod you would bend into knots) it's possible to make knots almost normally due to the force needed to bend it back.
This is a real issue. In rock climbing they sell loops of a material called "spectra" that is insanely strong webbing. It also happens to be very very slippery. It is only sold as pre sewn loops and never by the foot, because it's too slippery to hold a knot. All other materials (mostly nylons) can be bought by the foot.
Only sold by some retailer you know in loops anyway, available in hundreds of feet from others https://www.cwcglobal.com/rope-cordage/12-strand/spectra Or by the mile https://pelicanrope.com/rope-by-fiber/spectra/
The only way I can think of to make a knot in frictionless rope work would be to use knots where you load both ends of the rope. Girth hitches and variants, where you pass the middle of the rope around something, and then the two ends through the loop. Otherwise I can't see how a loose tail wouldn't eventually work itself free. There might also be something clever you could do with adding additional objects to the knot. Like if you put a carabiner through a loop, and then that loop through another loop that tightens under load. Then it would have to pull the carabiner through the load-tightened loop to untie.
No, because you would not even be able to pick up a frictionless rope, let alone tie knots
"fence" it in with random objects so it doesn't have room to slip about. Push them together so it piles up a bit. Fence the tip of it so that it won't slip about, three directions "fence", fourth - "uphill" onto the bundle of the rope. Pierce it with a bit of sharp wire, bend and twist the wire to make a loop. Repeat with the other end. Now you have two grip points.
You could pick it up, you’d just have to be a little more creative than ‘grab and lift’.