An introduction to the mechanics of the lasso.
Trick roping evolved from humble origins as a cattle-catching tool into a sport that delights audiences all over the world with its complex patterns or 'tricks'. Its fundamental tool is the lasso, formed by passing one end of a rope through a small loop (the honda) at the other end. Here, we study the mechanics of the simplest rope trick, theFlat Loop, in which the rope is driven by the steady circular motion of the roper's hand in a horizontal plane. We first consider the case of a fixed (non-sliding) honda. Noting that the rope's shape is steady in the reference frame rotating with the hand, we analyse a string model in which line tension is balanced by the centrifugal force and the rope's weight. We use numerical continuation to classify the steadily rotating solutions in a bifurcation diagram and analyse their stability. In addition toFlat Loops, we find planar 'coat-hanger' solutions, and whirling modes in which the loop collapses onto itself. Next, we treat the more general case of a honda that can slide due to a finite coefficient of friction of the rope on itself. Using matched asymptotic expansions, we resolve the shape of the rope in the boundary layer near the honda where the rope's bending stiffness cannot be neglected. We use this solution to derive a macroscopic criterion for the sliding of the honda in terms of the microscopic Coulomb static friction criterion. Our predictions agree well with rapid-camera observations of a professional trick roper and with laboratory experiments using a 'robo-cowboy'.
Laboratory of Fluid Dynamics and Instabilities, EPFL, Lausanne 1015, Switzerland ; Laboratoire FAST , Université Paris-Sud and CNRS , Bâtiment 502, Campus Universitaire, Orsay 91405, France ; Sorbonne Universités , UPMC Univ Paris 06, CNRS, UMR 7190 Institut Jean Le Rond d'Alembert, Paris 75005, France.
Pierre-Thomas
PT
Brun
Laboratoire FAST , Université Paris-Sud and CNRS , Bâtiment 502, Campus Universitaire, Orsay 91405, France.
Neil
N
Ribe
Sorbonne Universités , UPMC Univ Paris 06, CNRS, UMR 7190 Institut Jean Le Rond d'Alembert, Paris 75005, France.
Basile
B
Audoly
Flat Loop; bifurcation; friction; lasso; trick roping; whirling