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.

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