### Abstract

We consider the influence of aerodynamic forces on the shape of a whirling filament that is held at both ends, i.e. a jump rope. At high Reynolds numbers, the rope curls out of the plane and towards the axis of rotation-a feature we demonstrate via experiment. We derive a pair of coupled nonlinear differential equations that characterize the steady-state shape of the rope, and the resulting eigenvalue problem is solved numerically. The solution depends on two dimensionless groups: the ratio between the length of the rope and the distance between its ends, and the relative magnitude of the aerodynamic to centrifugal forces. As the latter ratio is progressively increased, the tension in the rope and the outof-plane deflection increases, until eventually the rope reaches a limiting shape. Finally, we show that the airflow-induced shape change leads to a relative reduction in drag and has implications for successful skipping. This journal is

Original language | English (US) |
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Pages (from-to) | 720-730 |

Number of pages | 11 |

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

Volume | 468 |

Issue number | 2139 |

DOIs | |

State | Published - Mar 8 2012 |

### All Science Journal Classification (ASJC) codes

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

### Keywords

- Aeroelasticity
- Eigenvalue problem
- Fluid-structure interaction
- Skipping-rope curve

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## Cite this

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

*468*(2139), 720-730. https://doi.org/10.1098/rspa.2011.0389