Author Topic: Why are some knots better than others? MIT researchers investigate  (Read 233 times)

Offline Mr. Bill

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Primitive skills, meet computer modeling. 8)

MIT press release, 1/2/20: How strong is your knot?

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In sailing, rock climbing, construction, and any activity requiring the securing of ropes, certain knots are known to be stronger than others. Any seasoned sailor knows, for instance, 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 has not been well-understood, until now.

MIT mathematicians and engineers have developed a mathematical model that predicts how stable a knot is, based on several key properties, including the number of crossings involved and the direction in which the rope segments twist as the knot is pulled tight.

“These subtle differences between knots critically determine whether a knot is strong or not,” says Jörn Dunkel, associate professor of mathematics at MIT. “With this model, you should be able to look at two knots that are almost identical, and be able to say which is the better one.”

“Empirical knowledge refined over centuries has crystallized out what the best knots are,” adds Mathias Kolle, the Rockwell International Career Development Associate Professor at MIT. “And now the model shows why.”...

Science, 1/3/20: Topological mechanics of knots and tangles

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Knots play a fundamental role in the dynamics of biological and physical systems, from DNA to turbulent plasmas, as well as in climbing, weaving, sailing, and surgery. Despite having been studied for centuries, the subtle interplay between topology and mechanics in elastic knots remains poorly understood. Here, we combined optomechanical experiments with theory and simulations to analyze knotted fibers that change their color under mechanical deformations. Exploiting an analogy with long-range ferromagnetic spin systems, we identified simple topological counting rules to predict the relative mechanical stability of knots and tangles, in agreement with simulations and experiments for commonly used climbing and sailing bends. Our results highlight the importance of twist and writhe in unknotting processes, providing guidance for the control of systems with complex entanglements.

Paywall for viewing full article.  But your local library may have it for free:
Science 03 Jan 2020: Vol. 367, Issue 6473, pp. 71-75

Offline David in MN

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Re: Why are some knots better than others? MIT researchers investigate
« Reply #1 on: January 03, 2020, 05:04:17 PM »
Rope and knots are a very vital human skill. It's funny as I have in my 30s become "nautical" and have had to learn a new knot skill set. My childhood was awash in timber hitches for moving felled trees and as a teen I was an avid climber so a figure 8 follow-through was like second nature. It's really cool to be on board and know your rope work from logging to climbing to boating.

To say this is a necessary skill is an understatement. We, as humans, "tie off" at both the top and bottom of the world. From the deep sea to the highest peaks...

Offline Redman

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Re: Why are some knots better than others? MIT researchers investigate
« Reply #2 on: January 03, 2020, 06:00:51 PM »
Here is a book I think is excellent on the skill of knot tying and other rope work. I have 2 copies, 1 bought in the middle 70's that I no longer open, the other hmm, bought maybe 5 years ago.

https://www.amazon.com/Encyclopedia-Knots-Fancy-Rope-Work/dp/0870330217