Color-changing fibers help reveal mysteries of how knots work

Deciding whether a knot is fit to be tied just got a bit more scientific.

Some knots are stronger than others, but scientists have struggled to explain why. Now, with the help of color-changing fibers, researchers have developed simple mathematical rules that can determine the relative strength of various knots based only on the knots’ topology — the geometry of how the knot is tied.

“Despite the fact that [knots] have been around for thousands of years, not much is known about why they work the way they do,” says applied mathematician Vishal Patil of MIT.

To better understand the simplest knots, Patil and colleagues studied color-changing fibers, with hues that reveal areas of greater and lesser strain in a knotted strand. The strain seen in knots in those fibers agreed with the strain calculated in the researchers’ computer simulations — which also estimate the relative strength of different knots — the researchers report in the Jan. 3 Science. The team used that simulation technique to predict the relative strength of more complicated knots known as bends, which connect two separate pieces of rope.

Patil and colleagues then found that three characteristics could explain a knot’s strength. First, the more times the strands cross, the stronger the knot. And the twisting of strands as they cross one another also plays a role: If the strands are twisted in opposite directions, the twist balances out, locking the knot into place. Finally, if adjacent strands slide in opposing directions as a knot is tightened, that also strengthens the knot.

The rules predict only the relative strength of each knot, meaning whether one knot is stronger than another, not its overall strength. For that, the researchers would need to consider details such as the characteristics of the rope or fiber used to tie the knot.

Still, the results explain, for example, why a square knot is stronger than another similar knot called a granny knot, which is notorious for causing loose shoelaces (SN: 4/11/17). Unlike a square knot, the granny knot has an unbalanced twist — and that could really trip you up.