Falling chains
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 (DEM) 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 which 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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BibTeX
@article{geminard2026falling,
title = {{Falling chains}},
author = {Jean-Christophe Géminard and Nicolas Taberlet},
journal = {Physical Review E},
year = {2026},
month = oct,
doi = {10.1103/d3kf-nsml},
url = {https://hal.science/hal-05756808v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Falling chains
AU - Jean-Christophe Géminard
AU - Nicolas Taberlet
PY - 2026
DA - 2026/10/16
JO - Physical Review E
DO - 10.1103/d3kf-nsml
UR - https://hal.science/hal-05756808v1
AB - 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 (DEM) 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 which 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.
SN - 2470-0045
SN - 2470-0053
ER -