A quantitative analysis of the chain fountain

TL;DR

This paper provides a comprehensive experimental and theoretical analysis of the chain fountain phenomenon, quantifying the motion and forces involved, and developing a simple model that accurately predicts the chain's behavior.

Contribution

It introduces a new quantitative model for the chain fountain, explaining the physics and predicting the chain's height and speed with experimental validation.

Findings

The chain's height is proportional to the force exerted by the container.

The model accurately predicts the chain's motion for different chains and distances.

Experimental measurements match theoretical predictions closely.

Abstract

The chain fountain is an entertaining, counter-intuitive phenomenon. When a chain flows up over the edge of a container and then falls to the ground below, it is observed that the top of the chain rises up above the containers edge. Here the steady-state motion of the fountain is analyzed experimentally and theoretically. Measurements are given for the speeds and heights for three different chains and three different distances from the container to the floor. It is shown theoretically that the distance the chain rises above the container is proportional to the force from the container on the chain. The basic physics behind this force is readily understandable and can be illustrated with simple examples. To quantitatively predict the chain's motion a simple model is developed for how the chain interacts with the container. This model shows that a link lifts-off from the container after rotating by a relatively small angle. The model's predictions agree very will with the measurement for the two ball-chains.