What’s The Strongest Knot, And How Do We Know?

You’d think someone might have moved it in the centuries since it was originally placed there – but nobody could. The knot keeping it in place was so strong, so complex, that unraveling it was impossible. In fact, like the sword in the stone of Arthurian legend, the only person who could manage the feat would be not just a community-minded citizen, but a king, handpicked by the gods themselves.

Of course, Alexander had no time for crafts. He broke the knot open, quite literally – with a sword – and went on to rule all of Asia. But what might a real Gordian knot – reputedly the strongest knot to ever exist – have looked like? That’s an interesting question.

And, thanks to modern technology and theory, we can take a decent stab at an answer.

The strongest knot 

We don’t often think of knots as a type of technology, but they are – and one of the oldest and most reliable types, at that. They predate the wheel and the axe; we were potentially tying knots before the discovery of fire. Some scientists even think knots may be older than humanity itself.

We’ve had a lot of time to experiment, is the point. And we’ve gotten good at them over the years: there are hundreds if not thousands of different types out there now, each with its own advantages and drawbacks.

Choosing which is the “best”, then, is an impossible task – but the more specific question of “strongest” might be answerable. While comprehensive scientific investigations of every type of knot would be unfeasible, the more popular types have been studied pretty well, with results that agree closely enough to rank them fairly reliably.

But here’s a quick question: how exactly should we expect these results to look? It’s not exactly intuitive; rather than a positive measure of strength, knots instead have an “efficiency” rating of how much breaking strength the rope it’s knotted into retains.

That’s because, perhaps counterintuitively, “simply placing a knot in the rope before loading it will reduce its strength,” pointed out leading cavers Georges Marbach and Bernard Toute in their 2002 book Alpine Caving Techniques: A Complete Guide to Safe and Efficient Caving, “and, apart from the case of localized damage, the rope will always break at the knot.”

It makes sense with the application of a little physics knowledge: in an un-knotted rope, all the fibers are sharing equal tension and weight. But knotting the rope – whether around itself, a pole, or something else – introduces bends in some areas and compressions in others, shifting the tension around unevenly. It’s where the tension is highest that the rope becomes weakest, and where it’s likely to break if yanked too hard.

The question, therefore, is: which knots reduce rope strength the least? Ask a mathematician, and they’ll probably give you the stinker answer: no knot at all – known in knot theory as the “un-knot”. It’s technically correct – a piece of rope with no knot in it will theoretically have 100 percent efficiency – but it’s not exactly helpful. So which actual knots come out on top?

Knot what you expect 

Despite knots being used every single day, a technology as ancient as it comes, and so intuitive that even non-human apes can figure them out, it turns out that we don’t really understand them all that well. At least, not at first glance. 

“You can show people real pictures of knots and ask them for any judgment about how the knot will behave,” said Chaz Firestone (real name, incredibly), an associate professor of psychological and brain sciences at Johns Hopkins University, in a statement last year, “and they have no clue.”

“Humanity has been using knots for thousands of years,” he said. “They’re not that complicated – they’re just some string tangled up.” And yet, he explained, “people are terrible” at intuiting how strong or stable these ropey constructions should be.

And for proof, look no further than the study Firestone and his colleagues had recently put out. In it, they showed participants four superficially similar knots – the “reef”, the “thief”, the “granny”, and the “grief” – which “are quite visually similar,” the paper explains, “and yet they vary widely in their stability.” 

Objectively, the correct order of strength should be reef first, then granny, then thief, and finally, grief – a ranking confirmed “not only according to the cultural knowledge and practices of the communities that use (or avoid) these knots (such as sailors and scouts), but also according to recent scientific studies of them,” the paper points out. But when asked to judge from photos which knot would hold out longest, study participants were basically hopeless.

“We tried to give people the best chance we could in the experiment, including showing them videos of the knots rotating,” said Sholei Croom, a PhD student in Firestone’s lab and coauthor of the paper.

But “it didn’t help at all,” she explained. “If anything, people’s responses were even more all over the place.”

Evidently, some physical experimentation is needed if we’re to find the strongest knot possible. And luckily, some scientists have done precisely that.

A knotty problem

Key to Firestone and Croom’s experiment was the fact that the four knots involved had to look similar. And they did – to someone with no sailing or scouting experience, they were virtually indistinguishable. 

But that raises an interesting point, doesn’t it? Why, if they’re so closely related, do they behave so differently? 

In 2020, a team of mathematicians and engineers from MIT set out to investigate, developing a mathematical answer to the question “What makes one knot stronger than another?” Their research made use of an invaluable new invention: a type of rope whose fibers would change color in response to strain or pressure.

It was an opportunity “to actually study the stability of knots,” Jorn Dunkel, a math professor at MIT who worked on the project, told NPR at the time. “Because before, obviously, nobody was really able to look into knots and see where the strain goes and how the forces are distributed.”

By analyzing the color changes in various knots, the team was able to figure out which ones could take the strain – and perhaps more importantly, why. They found, for example, that “twist is quite important in how knots behave,” Vishal Patil, then an MIT grad student, told NPR. In fact, it’s the property that separates the reef knot from the granny, the team discovered.

Overall, however, the takeaway was this: the strongest knot? We kind of already knew the answer.

Knot for nothing

Yep: it turns out that, after all that research into the math and physics of what makes a good knot, the answers were staring us right in the face the whole time. “It seems like humans just lucked out and discovered some good knots,” Patil told NPR, “but it’s kind of unclear how.”

So, for example, there’s the “blood knot”, or barrel knot – a bend knot used to join two pieces of rope together. Described in the Ashley Book of Knots as “the best bend there is for small, stiff or slippery line,” the blood knot reduces rope strength by only 10-20 percent, making it one of the most stable ties available.

Or another pretty strong knot, familiar to the climbers, cavers, and sailors among our readers: the figure-eight, which also boasts about a 20 percent strength reduction. It’s a stopper knot – used to secure a rope from slipping through a hole – and it is “much easier to untie than the overhand […] does not have the same tendency to jam and so injure the fiber, and is larger, stronger, and equally secure,” per Ashley. Marbach and Toute agree, saying that “every caver should know how to tie [the figure-eight knot] perfectly with [their] eyes closed.”

Dunkel and Patel favored the zeppelin based on their research – stronger than the Alpine butterfly used in climbing, but possibly harder to untie. And coauthor Mathias Kolle, the Rockwell International Career Development Associate Professor at MIT, envisioned using the results to perhaps create some new, even stronger future-knot, the likes of which our seafaring, scouting, or just generally scatterbrained ancestors could only dream of.

“If you take a family of similar knots from which empirical knowledge singles one out as ‘the best,’ now we can say why it might deserve this distinction,” Kolle said in a statement at the time. “We can play knots against each other for uses in suturing, sailing, climbing, and construction. It’s wonderful.”

“Empirical knowledge refined over centuries has crystallized out what the best knots are,” Kolle said. “And now the model shows why.”