Growth and shape of a chain fountain

Abstract

If a long chain is held in a pot elevated a distance h1 above the floor, and the end of the chain is then dragged over the rim of the pot and released, the chain flows under gravity down into a pile on the floor. Not only does the chain flow out of the pot, it also leaps above the pot in a “chain fountain”. I predict and observe that the steady-state shape of the fountain is an inverted catenary, and discuss how to apply boundary conditions to this solution. In the case of a level pot, the fountain shape is completely vertical. In this case I predict and observe both how fast the fountain grows to its steady-state height, and how it grows if there is no floor. The fountain is driven by an unexpected push force from the pot that acts on the link of chain about to come into motion. I confirm this by designing two new chains, one consisting of hollow cylinders threaded on a string and one consisting of heavy beads separated by long flexible threads. The former is predicted to produce a pot-push and hence a fountain, while the latter will not. I confirm these predictions experimentally. Finally I directly observe the anomalous push in a horizontal chain-pickup experiment.