The configuration, or “topology,” of a knot determines its stiffness. For example, a granny knot is much easier to undo, as its configuration of twists creates weaker forces within the knot, compared with a reef knot. For centuries, sailors have observed such distinctions, choosing certain knots over others to secure vessels — largely by intuition and tradition.

Now researchers at MIT and Pierre et Marie Curie University in Paris have analyzed the mechanical forces underpinning simple knots, and come up with a theory that describes how a knot’s topology determines its mechanical forces.

The researchers carried out experiments to test how much force is required to tighten knots with an increasing number of twists. They then compared their observations with their theoretical predictions, and found that the theory accurately predicted the force needed to close a knot, given its topology and the diameter and stiffness of the underlying strand.

“This is the first time, to the best of our knowledge, that precision model experiments and theory have been tied together to untangle the influence of topology on the mechanics of knots,” the researchers write in a paper appearing in the journal Physical Review