A simple dynamical model of a freely-falling train of rigid segments

TL;DR

This paper introduces a simple dynamical model explaining why a train of rigid segments falls faster than freefall and reproduces the coiling behavior observed in experiments, highlighting the role of dissipative locking and spiral structures.

Contribution

The paper presents a novel dynamical model that captures the counterintuitive faster-than-freefall descent and spontaneous coiling in a falling train of rigid segments.

Findings

Train falls faster than freefall due to dissipative locking.

Model reproduces spontaneous coiling and spiral structures.

Downward tensile force is key to understanding the phenomenon.

Abstract

In order to elucidate the process underpinning the apparently counterintuitive phenomena observed in the freefall experiments conducted by E. Hamm and J. G\'eminard [Amer. J. Phys. 78, 828 (2010)], we construct a simple dynamical model of a vertically falling train of one-dimensional rigid segments impinging onto an inelastic horizontal plate in three-dimensional space. Numerically integrating the nonlinear governing equations, we obtain a robust result that the train of rigid segments falls virtually faster than freefall under gravity. The presented model reproduces the coiling spontaneously formed in the pile, which is considered to be a key mechanism of the phenomenon and is shown to be a consequence of the three-dimensional spiral structure that arises due to dissipative locking in mid-air. As one of mechanical keys underpinning the apparently counterintuitive phenomena, we will here focus the downward tensile force exerted by the pile.