New Mathematical Model To Predict The Strength Of Knots

In any activity out there that requires the securing of ropes, such as construction, rock climbing, or sailing, some knots are stronger than others. Any sailor knows that, for example, one type of knot will secure a sheet to a headsail, and there’s another one that’s better for hitching a boat to a piling.
But there’s a reason why some knots are more stable than others, and we now know why.

The new mathematical model for knots

Mathematicians and engineers from MIT developed a mathematical model that predicts how stable a knot is, based on its key properties and some crossings that are involved and the direction in which the rope segments twist, as the knot is pulled tight.

These differences between knots show if a certain knot is strong or not. This comes from Jörn Dunkel, associate professor of mathematics at MIT. By getting this model, you should be able to take a look at two knots, which are almost identical, and then you should be able to say which one is the better one.

Mathias Kolle, Professor at MIT, stated that “Empirical knowledge refined over centuries has crystallized out what the best knots are.” Right now, we can see why, with the help of the model.

The color of the pressure

Back in 2018, Kolle’s group made stretchable fibers that are able to change color when they respond to pressure or strain. Researchers showed that when they pull on a fiber, its color changes to one color of the rainbow to another in areas where it feels the most pressure.

Kolle is an associate professor of mechanical engineering, and he was invited to MIT to talk about the fibers. This is where the idea started: the pressure-sensing fibers could actually be used to study the stability in knots.