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Falling chains

Jean-Christophe Géminard and Nicolas Taberlet*

  • *Contact author: nicolas.taberlet@ens-lyon.fr
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Phys. Rev. E 114, L043501 – Published 16 October, 2026

DOI: https://doi.org/10.1103/d3kf-nsml

Abstract

This study investigates the shape of a flexible, inextensible ball chain initially straight and horizontal, which is arrested at its center by a cylindrical obstacle while in free fall. Motivated by practical applications in high-voltage line installation, we combine experiments, discrete element method simulations, and a theoretical model. Our key experimental and numerical findings reveal that the extremities and adjacent horizontal portions of the chain continue in free fall, while the remainder wraps around the rod. The theoretical model successfully captures this behavior by representing the chain as two straight segments: a free-falling horizontal end and an inclined section connected to the obstacle. The model's core principle is that the junction point between these segments, or “kink,” is a transverse wave that propagates along the chain at a wave speed determined by the tension induced by the acceleration toward the center of the horizontal portion, which nevertheless remains in free fall. The model accurately predicts the positions of the tip and the kink, demonstrating that the chain's shape is independent of its mass per unit length and scales with the total length. Furthermore, the dynamics are governed by a single dimensionless parameter, the Froude number, which compares the initial impact velocity to the effect of gravity, with the analysis capturing the limiting cases of zero initial velocity and negligible gravity.

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Outline

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Phys. Rev. E 114, L043501– Published 16 October, 2026
  • Received 29 April 2026
  • Accepted 17 September 2026
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