Trefoil knot

Mechanics of knots


The simplest type of knots that we tie everyday is known as the overhand knots. The topology of overhand knots is defined by the unknotting number, n ( number of times the knot must be passed through itself to untie it, see figure above). Shoelaces are commonly tied using the reef knot, which comprises two overhand knots each with n=1. We combine experiments and theory to study the mechanics of  overhand knots, and essentially answer the question how much force has to be applied to tighten the knot. Excellent agreement is found between theory and experiments for overhand knots over a wide range of crossing numbers.


  1. Jawed, M. K., Dieleman, P., Audoly, B., Reis, P., “Untangling the mechanics and topology in the frictional response of long overhand elastic knotsPhysical Review Letters 115:11, 118302 (2015)
    Press coverage: Science, selected for Physical Review Focus, Nature PhysicsMIT News,  Featured as  Today’s Spotlight on MIT Homepage on 09/09/2015, Science Daily,  Gizmodo, ViceSueddeutsche Zeitung (in German), Le Monde (in French)



Peter Dieleman (Leiden), Basile Audoly (CNRS), Pedro Reis (MIT)