### Abstract

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, the Flat 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 to Flat 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'.

Original language | English (US) |
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Article number | 20140512 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 470 |

Issue number | 2171 |

DOIs | |

State | Published - Nov 8 2014 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)

### Keywords

- Bifurcation
- Flat Loop
- Friction
- Lasso
- Trick roping
- Whirling

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## Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*470*(2171), [20140512]. https://doi.org/10.1098/rspa.2014.0512