Twists and Turns: A Love Note To Knots

It all started on the balcony – I was frustrated that I could not tie a slippery synthetic rope to fix some plants in place the way I wanted. This started my knot journey that lasted for many weeks. Only a few months later I needed to remember a suitable knot, but was barely able to. This gave me the nudge I needed to finally take some time and write up what I once learned before I forget it completely. So this post is both my knots 101 and a selection of my favorite knots. If you are just getting started with knots, I hope this can be a decent starting point for your own explorations.

What’s a Knot and What It’s Not

Knots have been used since ancient times, but studied in-depth by both enthusiasts and academics only recently. Mathematical knots are surprisingly complex topological objects with various representations and open questions, whereas practical knots suffer from a lack of a widely accepted structural classification and didactics mostly focused on rote memorization.

I might be the odd one here, but I found it rather hard to understand and remember knots before I developed some intuition and a more attentive eye for some patterns and building blocks appearing over and over. Dipping my feet into mathematical knots did help me to make more sense of it all.

That said, maybe it was simply the fact that pondering the math made me sit down and playfully explore the topology of a piece of rope in an open-ended fashion. Whatever your learning style is, I warmly recommend to just sit down and try wrapping your head around some mind-knotting questions, such as:

• at which point of your movement does the rope becoming knotted?
• what are natural building blocks and operations to describe any knot?
• can you classify knots that you know by some similarity or common patterns?
• what is the nature of loops and crossings, do they even really exist?

Mathematical Knots

Note: If you do not care about the math at all, just skip this section.

In mathematical knot theory, a knot is an embedding of a circle (1D) into space (3D). A knot diagram is a planar (2D) representation of a knot consisting of line segments and (over/under-)crossings. It is easy to see that there are infinitely many diagrams for the same knot. Two knots are considered equal if there is an ambient isotopy between them. This just means that you can transform one into the other in a smooth way, without cutting the string or passing it through itself. Equivalently, we can say that two knots are equal if you can transform a knot diagram of one knot into a knot diagram of the other using a sequence of Reidemeister moves. Clearly, the latter definition is more suitable for practical implementation. The unique knot diagram without any crossings is also called the unknot. There are various notations to describe knot diagrams, such as the extended Gauss code. Knots can be oriented (i.e. the direction in which you trace the crossings) and reflected (i.e. mirror reflecting the knot). These two operations may or may not change the knot, resulting in 5 possible knot symmetry types.

Computationally, knots appear to be pretty challenging. For example, there are no known efficient algorithms to determine for some given knot:

• a diagram with the smallest number of crossings (crossing number)
• whether it is equal to some other knot (including equality to the unknot)

There is much more that could be said about mathematical knot theory, but all I will say is that I really underestimated the depths of it. To me it is somewhat mind-blowing that such a supposedly simple thing can cause so much headache. My brain certainly was knotted for a while after thinking too much about knots. ^[1] But if this still sounds somewhat interesting, the the knot book is a decent introduction to the basics of mathematical knot theory.

Practical Knots

Mathematical knots are about as close to practical knots as Turing Machines are to actual computers. This is absolutely not to say that knot theory is useless. It is a perspective providing many interesting questions and answers, only that these are rather detached from real-world knots and their applications.

To get from a practical knot to a mathematical knot, just connect both ends to form a closed loop and just pretend that instead of a rope we hold an infinitely thin one-dimensional string with no properties whatsoever, except for the coordinates of points in space.

However, most of the practical value of knots comes from friction, so abstracting away all the material physics removes most interesting properties and distinctions that people care about who actually tie functional knots out of real rope.

There are many cases where topologically the same knot

• is known under different names
• which are knotted in different ways
• and used for different purposes

In some cases this is redundant and arbitrary, but in many cases it is not at all. Depending on what you want to achieve and what your starting point is, one way of tying can make much more sense than another. Also, depending on whether you form knot around something or not and which loops in your knot you pull tight, you might get the same topological knot, but completely different practical behavior. On the other hand, there are knots where you can switch out some steps or partial knots without affecting the result too much. So there is a rich tradition of folklore knowledge about knots rooted in empirical usage over millennia of human history.

In some way, practical knots remind me of protein folding. Local and global structure of a one-dimensional string results in a three-dimensional object with concrete functions, once subjected to the laws of physics (and, consequently, bio-chemistry). Sometimes you can mutate parts of the recipe and it does not make a difference, but sometimes small mistakes can be deadly.^[2]

The Ashley Book Of Knots is considered to be the reference bible of practical knots, but to just quickly some useful common knots there are much more accessible resources, such as

• Animated Knots
• 101Knots
• Knots3d
• Knotspedia

I recommend checking out all of them, because they have different selections of knots and also different presentation styles. I made good use from these websites, and there are many more.

Basic Terminology

In this section I provide some of the most common terminology for practical knots. See here and here for more terminology, I only selected a few key concepts to make this post more readable for someone without any background in knots.

Standing End: typically the fixed end of rope that you cannot move

Working End: movable end of rope, the one you can use to make knots

Bight: U-shaped piece of rope, i.e. a folded rope (without access to any end)

Turn: what you get whet you cross the legs of a bight

Dressing: Carefully bringing the knot into the right shape to make sure that it behaves as it should.

Basic Knot Properties

Jamming Knot: When pulled tight, the knot becomes hard to untie.

Quick-Release Knot: Can be untied easily, often just by pulling on a single end.

Slipped Knot: If in the last knotting step you pass through a bight instead of the working end, usually to make a knot quick-release.

Knot On A Bight: A knot that can be tied without access to either end, assuming that there is enough slack to form a bight (which is then used like a working end).

Basic Knot Types

Stopper: Knot to prevent that an end of rope slips out or undoes the knot.

Bend: Knot to connect pieces of rope into a longer rope, or to form a big loop.

Hitch: Knot to tie the rope to some other object. Usually consists of some loop.

Loop: Well, a loop. A circle of rope you can either create around something or pull something through later. Usually held together by some kind of knot.

Mid-Line Loop: A loop that can be made on a bight.

Adjustible Loop: A loop allowing controlled resizing without unknotting.

Self-Tightening Loop: A loop that will shrink under load. Be careful!

Fixed Loop: A loop that is neither self-tightening, nor adjustible.

Basic Knots

Overhand Knot Family

The overhand knot is the one everybody knows how to do. The overhand family is just the natural generalization of the idea to a double, or triple overhand knot, and so on. First form a turn, then wind the working end one or more times around the rope, finally pull tight.

Twist Knot Family

The twist knot family can be described in a similar way. Start with a bight, then twist it one or more times, finally pull the working end through the apex loop. One twist gives the overhand knot, two twists gives the Figure 8 knot, more added twists can be seen as systematic generalizations of the Figure 8.

Jack Of All Trades: Figure 8

Some people love it, some people hate it. However, no knot introduction is complete without mentioning the versatility of the Figure 8. The Figure 8 is a climber’s favorite and a superb generalist, even though there are more suitable knots in most situations. All of them are pretty strong and if you remember one, you remember all. However, in my opinion these knots are pretty cumbersome to (un)tie. Whether this is good or bad depends on the situation.

• Figure 8 knot
• Figure 8 bend
• Figure 8 end loop
• Figure 8 mid loop
• Figure 8 double loop

As it is often the case, I have a minority opinion. No idea how this always happens. After doing all my research I concluded that I neither like the Figure 8 knots, nor the Bowline-based knots. Instead, I will show you several (in my opinion) much more interesting knots.

A Fine Selection Of Knots

Originally, I wanted to be lazy and just choose at most a dozen of knots to learn and remember. I really tried, but I failed. Instead, I succeeded in learning even more useful knots for various situations. So in the following, I present to you the smallest list of knots I could make without feeling like I am leaving out something important. Of course, this is fully subjective, and based on a mix of research I did, experiences I had with various knots I tried to use, and things I want to use the knots for.

Stoppers

Stoppers are what you can use to prevent accidental opening of other knots, slippage of rope through some opening, or to prevent the rope from unwinding at the ends^[3]. The overhand and twist knots families are all usable as stopper knots. Add more winds for more strength and knot size.

For something quick and simple, the Ashley Stopper Knot is a good choice. Make a slip knot (i.e. basic slipped overhand), pull the working end through the loop, dress it a little bit into shape, pull it tight - done. A nice round-ish stopper, for when you need a bit more width than the overhand knot alone has.

If you need more thickness or want to make it more pretty - the Celtic Button Knot is even more bulky, but I never quite get it dressed just right. If I did, though, it would probably look neat. Finally, if you have too much time, you can try to make a Monkey Fist. It is the only knot I mention here that I never actually made myself. I never had enough motivation for it, but one day, when I need a huge and beautiful stopper knot, I maybe will.

Bends

Bends are indispensable if you need to connect two ropes or to form a closed loop from a rope that will not come undone.

For a temporary and quick solution, there is the Double Sheet Bend. The single sheet bend is considered dangerous. By adding more turns, you make it more robust. Still, people often warn that sheet bends are not suited for safety-critical applications. However, supposedly it is particularly good to connect two ropes of very different thickness, probably due to the specific asymmetric way the knot makes the ropes grip into each other.

If you want a bend for your life to depend on, the Double Fisherman’s Bend seems to be the most recommended choice. It is a bit cumbersome to tie, but in the end you get a very secure and often jamming knot. Ultimately, this is just two double overhand knots tied with each of the ends around the other. Like with the sheet bend, you can make Fisherman bends more secure by using more turns, which means using triple (quadruple, etc.) overhand knots instead of the standard choice.

But none of these is my favorite bend. Instead, I am in the smaller fan club of the much less known Zepplin Bend. It is much faster to tie than the Double Fisherman’s, but is of comparable strength (according to some experiments). But this is not all - unlike other bends, this one is still easy to untie even after it was pulled tight and the rope has been under load. A clear winner, and a knot all others should aspire to be!

Mid-Line Loops

Mid-line loops, i.e., loops knotted on a bight, have a clear winner to me: the Alpine Butterflies! The regular Alpine Butterfly is a favorite of many, and I absolutely agree with this. What is less known, is that there is even a double and even triple butterfly knot that can all tied in a similar way.

In general, I really recommend checking out that knot page I referenced for Alpine butterflies - it is the only serious website I know that even has a dedicated triple loop category, and it has the best and most consistent method for tying all the three of them! Absolutely underrated resource.

Self-Tightening Loops

The simplest self-tightening loop is the slipped overhand knot. It has the pretty unique property among such knots that when you pull it tight, the loop shrinks down into nothing leaving no trace, i.e. no other knot in the rope. So if you need a temporary loop to attach something, but want it to come undone easily, this will just do.

If, on the contrary, you want the loop to be pretty robust, there is a simple noose-like loop family beginning with the

• Noose Knot, the
• Poacher’s Knot, and the
• Scaffolding Knot.

They are forming the same kind of natural progression as the overhand family. It is literally just the overhand knot you make loop with - single, double or triple overhand! Just take a bight and make the turns towards the bight end, finally pull through all the turns away from it! Why make it more confusing than necessary by giving variations on a single theme so different names?

This loop is adjustible before, self-tightening while and jamming after it was loaded. Which means that it is dangerous and you should not put your body parts into such loops.

Resizeable Loops

There are many loops you can adjust while you do them, but not many that are resizeable when you are done in pulled everything tight. Two related knots are simple and effective members of the second, more interesting family. Both use a Rolling Hitch as the key to make the loop easily adjustable when not under load.

The Midshipman’s Hitch is great at keeping the loop size constant when under load (assuming suitable, not very slippery rope). Form a loop, make two turns of the working end in the loop, then make one hitch in the other direction outside the loop. Pull everything tight. The formed knot is resizeable the rope while it is loose, but the loop will also keep its size under reasonable tension, unlike noose-like knots.

The Reverse Midshipman’s Hitch is a different version of the same idea - you do the initial turns outside, i.e., around the bight forming the loop, and then complete with a hitch inside the loop. This one behaves slightly differently - it can be pulled tight easily (but it is not self-tightening like a noose knot, unless your rope is very slippery), but also can be released without effort when not under tension. Can serve as a substitute for a zip-tie in many situations.

Fixed End Loops

The Kalmyk Loop is the only one from the Bowline knot family that I consider worth knowing. It is both quick to tie and quick-release while having decent (but not bet-my-life-on-it) strength. Its main disadvantage is that it is very sensitive to dressing. I manage to mess it up regularly, so that I looked for some alternative.

I ultimately settled on the Zeppelin Loop as my hidden champion. It takes a bit more rope, is slower to tie and untie, and is not quick release. So why do I still think this is an amazing knot? Because it is the loop version of the best bend, the Zeppelin bend, and inherits most of its nice properties. The Zeppelin loop is fool-proof and insensitive to dressing, and while not quick-release, it is non-jamming and very easy to undo afterwards.

The one-pull quick-release of the Kalmyk is ultimately a gimmick. How urgently do you typically need to undo a knot? How many do you tie or untie per day? For my use-cases it is clear: in most situations I should just do a Zepplin loop and not worry about messing it up. Unlike the Kalmyk, I’d say the Zepplin loop also remains trustworthy under serious load. If you trust the Zepplin bend, you should trust the Zepplin loop.

These two loops are pretty versatile, but for the specific use case of creating a loop around some object I think the Backhand Hitch needs to be mentioned. It is very easy to tie, it self-tightens around the object (but not in a locking way like the reverse midshipmans) and even remains easy to undo under load. Just create a loop around the object, cross over the standing end, then loop in the other direction around the object, finally secure with two half hitches around the standing end.

Special-Purpose Knots

Carrying

If you need to hang or carry something cylindric, the Barrel Knot could be pretty useful to know. Here is another interesting one for similar purposes, but I don’t know how it is called.

Binding

There are many loops and knots that could be used to bind things together. But to bind some stick-like things tightly together, a useful dedicated knot is the Constrictor. If you want it even more secure and tight, there is also the Double Constrictor. These are not easy to untie after pulled tight, which can be either good or bad, depending on what you want.

Climbing

A Prusik knot is a simple way to attach a separate fixed loop (which was usually made with some secure bend), called a Prusik loop, to another rope. This is a very common knot in climbing. Under load the loop grips into the rope and locks in place, but without load it can be easily moved. It is impressive that you can use it for climbing equipped with basically nothing but rope, no other mechanics like pulleys needed, just a few carabiners. Even for other applications, I think this is nice to remember whenever you need a movable loop on some other rope. The Sliding Double Fisherman’s is a more fancy loop you can use instead of a simple Prusik loop.

Tensioning

Sometimes you need create tension with rope. Be it to prepare a slackline, or to secure a load in a vehicle. For this purpose there are special constructions which are more like meta-knot recipes that explain how to create the right gadget out of a combination of loops and knots.

The Trucker’s Hitch is probably the most common choice for tensioning. Fix the standing end, create a mid-line loop at a suitable distance, wind the working end around some object, pull it through the loop you created earlier, pull the rope tight up to the needed tension, finally fix the hitch by two half hitches or some other knot of your choice. You should have 1.5-2x the length of rope compared to the distance of the two points between those the tension is applied.

If you have the rope and the time, the Versatackle is a more fancy variation. It not only has a higher theoretical mechanical advantage (i.e., tension you get vs. the strength you pull with), but it is also self-locking, which means that unlike the Trucker’s Hitch, it will hold together even without any finishing knot, just by pulling it tight. Take 2.5-3x the length of the needed distance, and start like before - fix the standing end at point A, create one mid-line loop slightly more than halfway between point A and B, wind the working end around point B.

Now create a second mid-line loop, and wind the working end through both loops in an alternating fashion at least three times. Finally pull tight and secure the working end with a some hitch. While pulling, the tension on the rope will also pull both loops toward each other. So make sure that the loops are of adequate size - large enough to pull the rope through multiple times, but small enough that the loops are far enough apart even when pulled toward each other.

Learning The Ropes

The whole topic of ropes - what kinds of rope exist, what materials are used, how they are made - is an important related topic that I do not want to discuss in-depth here, but leaving it out completely feels like a serious omission. To make it short - ropes can be made from twisting thinner strings (classic) or built with a braided core (more modern and resilient), and it can be out of natural or synthetic materials. Rope can be certified to hold load up to some weight (in kg) / tensile strength (in kN), and you should only use such rope in safety critical situation. Cheap synthetic household rope sucks, I talk from experience. But high-quality, braided synthetic rope has multiple advantages over natural rope, including easy handling, resistance to natural decay and controlled strength and thickness.

What I should have done sooner is buying a 50m roll of 3mm thick paracord. It is such an upgrade from what I was used to! Like all synthetic ropes, you can easily cut it and seal the ends with some heat from a lighter. Almost like natural rope, they are textured and not slippery, unlike cheap synthetic rope I used before. With some ropes, handling knots is a chore. With serious rope like paracord, it is a joy! If there is another thing to take from this post - get some paracord! Pick a thickness that fits your common use cases. In my opinion, paracord should be considered one of these essential items, like duct tape. You should have it around, just in case. Many problems can be solved with just paracord, scissors and a cheap lighter, assuming that you know a few useful knots.

Conclusion

Who would have thought that there is some much depth to be explored and fun to be had with just a piece of rope? And also - how did it take me over 30 years to discover this topic? In any case, the world of knots is both interesting and useful and I hope that this post could serve as a little appetizer.

Once you start digging into knots, you understand that knots are also a kind of language with recurring words and sentences. You start recognizing, but also improvising - to both read and speak the language of knots.

As some knotters say - those who do not know how to knot, knot a lot. After learning the knots I presented above, I use many of them regularly for various household purposes. Now instead of creating a mess out of string and hoping for the best, I can think for a moment what I want to achieve and pick the right tool for the task. Like every useful skill, it needs some learning and also regular practice. But I can also confirm that the saying is true, and that learning a few versatile knots is a good time investment that will pay off for the rest of your life.

1. I played around and experimented with some of these concepts for weeks, only to ultimately accept defeat. Still, if you ask me what the essence of a knot is, I would say: repeated twisting and self-crossing of a loop. Take it or leave it. If I ever manage to formalize this intuition and make it useful, I will write another dedicated post. ↩

2. That is why climbers tend to prefer knots that are not only strong enough, but also easy to remember, tie and check. ↩

3. For this specific purpose there are also specially dedicated knots, called whippings, which are knots made of thinner strings around the strands of the thicker rope to hold it together. In many cases you can instead just create a tight slim stopper at the end of your rope. ↩