Skip to Content

Knotty by nature

A new mathematical model reveals which types of knots are strongest—and why.
February 26, 2020
knot
Courtesy Image

Any seasoned sailor knows that one type of knot will secure a sheet to a headsail, while another is better for hitching a boat to a piling. But what exactly makes one knot more stable than another was not well understood—until associate professor of mathematics Jörn Dunkel created a mathematical model to study them.

Dunkel teamed up with Mathias Kolle, an associate professor of mechanical engineering, whose group had engineered stretchable fibers that change color in response to strain or pressure. His team used Kolle’s fibers to tie a variety of knots, including trefoils and figure-eights, photographing each fiber and noting where and when it changed color, along with the forces applied as it was pulled tight.

Using this data, they calibrated a model simulating the distribution of stress in knots. Then they simulated more complicated knots and drew up simple diagrams to represent them.

In comparing diagrams for the common granny, reef, thief, and grief knots, along with more complicated ones such as the carrick, zeppelin, and Alpine butterfly, the researchers identified some general rules. Basically, a knot is stronger if it has more strand crossings, as well as more “twist fluctuations”—changes in the direction each segment of a strand rotates as a knot is tightened. These changes create friction that promotes stability.

They also found that a knot can be made stronger if it has more “circulations”—regions where two parallel strands loop against each other in opposite directions.

“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,” says Kolle. “We can play knots against each other for uses in suturing, sailing, climbing, and construction.”

Keep Reading

Most Popular

computation concept
computation concept

How AI is reinventing what computers are

Three key ways artificial intelligence is changing what it means to compute.

still from Embodied Intelligence video
still from Embodied Intelligence video

These weird virtual creatures evolve their bodies to solve problems

They show how intelligence and body plans are closely linked—and could unlock AI for robots.

seeing is believing concept
seeing is believing concept

Our brains exist in a state of “controlled hallucination”

Three new books lay bare the weirdness of how our brains process the world around us.

We reviewed three at-home covid tests. The results were mixed.

Over-the-counter coronavirus tests are finally available in the US. Some are more accurate and easier to use than others.

Stay connected

Illustration by Rose WongIllustration by Rose Wong

Get the latest updates from
MIT Technology Review

Discover special offers, top stories, upcoming events, and more.

Thank you for submitting your email!

Explore more newsletters

It looks like something went wrong.

We’re having trouble saving your preferences. Try refreshing this page and updating them one more time. If you continue to get this message, reach out to us at customer-service@technologyreview.com with a list of newsletters you’d like to receive.