An Exploration of Stopper Knots: Using Knot Theory to Examine Knot Strength
Williams, Lauren D.
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Nine stopper knots were tied, tested for strength, ranked, and then analyzed. The two strongest knots were the figure eight knot and Oysterman's stopper knot. The weakest group of knots was comprised of the overhand (or trefoil), double overhand, triple overhand (the septoil), and quadruple overhand (the nonoil) knots, which are all part of a closely related series. So when asking "Is there a way to predict which knots will be stronger than others based on the mathematical invariants associated with the given knot?", I at least had a ranking of knots from strongest to weakest with which to analyze the question. My material and educational limitations, however, prevented me from creating a more precise ranking, and from analyzing in depth certain knot invariants. But even within these limitations, I was able to find invariants that separated the two strongest knots from the rest of the group. In this way, the knot invariants of symmetry type and alternating or non-alternating rose to the forefront as possibilities for strength predictors. In a more practical realm, my experimental results are also useful in deciding what stopper knots to use while sailing, hiking, climbing, etc. Because they are the weakest knots of the tested group, the series of overhand knots is not a wise choice when looking for a knot that won't easily slip. The Stevedore knot would be adequate, however there are better knots out there, namely the figure eight and Oysterman's stopper knots. While both of these knots showed extreme strength during testing, Oysterman's stopper knot is significantly more complicated than the figure eight knot, meaning that it takes more rope and more time to tie. This complexity would be a problem in the middle of a storm, when it is key for a sailor to be able to tie a stopper knot with speed and accuracy. This gives the strong yet simplistic figure eight knot the advantage in everyday situations. There are now experimental results to back up what sailors have known for years; the figure eight knot, 4 1, is the king of all stopper knots.