To stop or not to stop: The stopper knot as a friction device

A stopper knot tied to the end of a climbing rope prevents it from retracing through a narrow passage in the climber’s belay device. Numerous other applications of stopper knots are found in stringing of tennis rackets, sailing and fishing. If a single-stranded stopper knot meets the requirement of preventing a rope from escaping the system, it is able to unfold its full potential by converting a high-traction force into an insignificant stress state. This sharp tension drop results from the complex interplay of the topology, the tightness of the configuration, and the nontrivial frictional interactions in regions of self-contact of the elastically deformed rod. Existing models in knot theory or Kirchhoff’s theory for elastic rods are insufficient to describe this functional behavior due to the importance of finite elastic deformations of the cross-section and frictional interactions. We tackle this problem by performing a combination of mechanical testing and X-ray tomography on a variety of stopper knots. Our experimental data, combined with finite element simulations, allows us to systematically explore the different ingredients at play that conspire to dictate the mechanical performance of stopper knots.