Humans have known for generations that some knots are stronger than others. This is evident during navigation, where different types of knotting are used for different needs. Until now, it was not known what type of knot was more stable than other knots. Mathematicians and engineers at the Massachusetts Institute of Technology have developed a mathematical model that can predict the stability of knots. The model uses several key attributes, including the number of intersections and the direction in which the rope segment is distorted when the knot is tightened. One researcher said the differences between knots determine whether they are strong or not.
The new model means that researchers can look at almost identical knots and determine which one is better. The team used stretchable fibers developed in 2019 that change color depending on strain or pressure. When they pulled the fibers, the team was able to demonstrate that their color had changed, especially in areas where stress or stress was greatest. The team used this special fiber knot, including a three-leaf knot and an octagonal knot. They took pictures of each fiber and studied what force the fibers were changing under.
The team found that if a knot had more strands of cross and more distortion softened fluctuations, it would be stronger. The team says that if you rotate the fiber segment to the left at a intersection and rotate the fiber segment to the right when it is tightened, it creates distorted fluctuations and opposite frictions, creating a force path. The rules in the algorithm allow the team to explain why one knot is stronger than the other.