A team of mathematicians and engineers at Massachusetts Institute of Technology have researched knots and discovered what sailors already knew: Some knots are stronger and more resistant to untying.
The team developed a mathematical model that predicts knot strength. To test the model, they developed fibers that change color when stretched, and were able to see the areas of greatest stress. After tying numerous knots and noting the color changes, the team compared their experimental results to the model and found the two in agreement.
As explained by Jennifer Chu in an MIT press release: “In comparing the diagrams of knots of various strengths, the team was able to identify general ‘counting rules,’ or characteristics that determine a knot’s stability. A knot is stronger if it has more strand crossings, as well as more ‘twist fluctuations’ — changes in the direction of rotation from one segment to another.
“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 tightened, it creates a twist fluctuation and opposing friction, which adds stability. If, however, the segment is rotated in the same direction at two neighboring crossings, there is no twist fluctuation, and the strand is more likely to rotate and slip.
“They also found that a knot can be made stronger if it has more ‘circulations,’ defined as a region in a knot where two parallel strands loop against each other in opposite directions.
“The team was able to explain why a reef knot, for instance, is stronger than a granny knot. While the two are almost identical, the reef knot has more twist fluctuations, making it more stable.”