MIT Creates A New Mathematical Model To Predict The Stability Of A Knot

Humans have known for generations that some knots are stronger than others. This is apparent in sailing, where different types of knots are used for different needs. What exactly makes one type of knot more stable than others hasn't been well known, until now. MIT mathematicians and engineers have developed a mathematical model that predicts how stable a knot is.The model uses several key properties, including the number of crossings involved and the direction in which the rope segments twist as the knot is pulled tight. Those differences between a knot determine if they are strong or not, according to one of the researchers.

The new model means that you can look at two knots that are almost identical and determine which is better. The team used stretchable fibers developed in 2019 that change color in response to strain or pressure. The team was able to show when they pulled a fiber that its color changed, particularly in areas of the greatest stress or pressure.

The team used the special fibers to tie a variety of knots, including trefoil and figure-eight knots. They photographed each fiber, noting where the fiber changed color only with force applied to pull it tight. The team already knew what pressure correlated to the color of the special fibers. The team tied several types of knots in their research and found some interesting data.

A knot is stronger if it has more strand crossings as well as more twist fluctuations. The team says that if a fiber segment is rotated to the left at one crossing and rotated to the right at a neighboring crossing as a knot is pulled tight, that creates twist fluctuations and opposing friction and creates strength. The rules in the algorithm allow the team to explain why one type of knot is stronger than another.