Why some knots are much stronger than others

Settled in 2020 by Vishal P. Patil, Joseph D. Sandt, Mathias Kolle, Jörn Dunkel (MIT).

Sailors, climbers and surgeons have long known by trial and error that some knots (like the reef knot) are notoriously weak or slip-prone while others (like the fisherman's knot) hold fast, but no predictive theory connected knot topology to mechanical stability. In 2020 Patil, Sandt, Kolle and Dunkel combined mathematical knot theory with mechanical experiments using fibers that optically reveal internal stress, and identified simple topological counting rules — based on the number, handedness and arrangement of crossings — that predict a knot's relative stability. Their theory correctly ranked common knots by strength and explained why certain 'friction-adding' crossing patterns hold while others cancel out and slip, giving climbers, surgeons and sailors a first-principles design rule rather than pure folklore.

Millennia of knot-tying folklore turns out to be governed by a simple topological counting rule linking crossing handedness to mechanical strength.

Explanations that circulated

• Knot strength is just about how many times the rope crosses itself (crossing number) — the 2020 study showed that the handedness and 'twist charge' of the crossings, not just their count, determine whether a knot dissipates or amplifies friction, which is why some seemingly complex knots hold weakly and simpler ones hold strongly.

References

• Topological mechanics of knots and tangles, V. P. Patil, J. D. Sandt, M. Kolle, J. Dunkel, Science, 2020