The Chain Fountain

Sam Cates

Have you ever placed a coiled chain in a cup, held it about half a metre above the ground, and then pulled one end towards you? If not (and the answer is probably not), then I recommend it. What happens next is, to a person who isn’t well versed in Newtonian physics, somewhat magical. The chain doesn’t stop moving, or dribble along the edge of the cup as one might expect: it self-syphons and seems to levitate, before falling back towards the ground.

There are three questions that need answering. First: why does it move? At the beginning of the experiment, the chain is pulled so that a certain length is outside the cup, which accelerates due to gravity. But then as the section of chain travelling downwards is longer than that travelling up, its weight gives a resultant downwards force, pulling on more chain and continuing the movement.

Right, now for the trickier two. Despite it seeming simple, it isn’t immediately clear why the chain turns around. True, it couldn’t continue accelerating upwards forever, else we have bigger problems on our hands than performing chain experiments; but what causes it to turn? Tempting as it is to consider each section as a projectile, this doesn’t work. If the chain went up and came down like a tennis ball, there would be a point when it was stationary; other chain flowing into that point would begin to pile up, but this isn’t the case: it seems smooth throughout, and in fact the speed is more or less constant. Although it is moving, we must remember that there is tension in the chain, and that its trajectory is curved; when these two things are true, there must be an inward component of force. Perhaps this sounds confusing, but it’s exactly the principle used in a longbow; the very same force that makes the arrow fly works to turn the chain.

Still, undoubtedly the most interesting question remains unanswered; why does it fly in the first place? For the moment, part ways with the idea of the whole chain, and consider each segment individually. The diagram shows a very simplified model of what such a segment might look like, with the rightmost line attaching to the block that has just flown away, relishing a life of freedom. The important observation is that the force only acts on one end, and so induces a rotation. Ordinarily, this would cause the back of the segment to dip below its original starting point, but in this case the cup (or more likely other parts of the chain) sit stubbornly in the way. That is, they provide a reaction force on the back of each segment, which propels it upwards, and above the edge of the cup. So the chain fountain is born.

As understandable as this is, it wasn’t particularly known about until 2013. Certainly, no papers had been published explaining the phenomenon. It was brought into public knowledge by the enigmatic world of YouTube, and is now used at school level to introduce various aspects of mechanics. Beyond what I have discussed, there is still so much to explore. What happens with a heavier chain? What about different distances above the ground? Do some chains produce better fountains than others? Are chains objectively wonderful (this one is less scientific)? Whatever the case, next time you walk past someone holding a self-syphoning chain with a befuddled look on their face, make sure to fill them in.

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