Chain Fountain Mechanics
In 2014 Steve Mould presented the remarkable results of his ‘chain fountain’ experiment to a Ted ex Newcastle symposium as shown here:-
https://www.youtube.com/watch?v=wmFi1xhz9OQ
His original video attracted millions of views online, and the ‘chain fountain’ shown in this video produced an elevation of a chain of metal beads to around 300 mm above the jar, after which they fell for around 2 metres to the floor.
Since then others have carried out experiments from greater heights, Biggins and Warner from a balcony at around 5 metres height, which produced an elevation of around 600-700 mm.
And more recently one experiment was carried out at “30 metres above the ground and – the arch of the chain fountain can reach the height about 2.1 m above the jar.”(Wikipedia)
A video of this Chinese experiment, which is not presented in English, is shown here:- https://www.youtube.com/watch?v=UM4lnzhvzdE&t=1800
The numerous debates and the papers generated and presented since Mould’s presentation, as he has since suggested, have not provided a coherent, and testable, explanation for this effect, and today there is still no sensible explanation for this, despite the subsequent publication of numerous scholarly papers and articles.
The actual, the intrinsic, structure of the specific ball chains used in these experiments is not readily available to view online, however after some searching I found a paper presented by Pfeiffer and Mayet in 2017 entitled ‘Chain Fountain Dynamics’, copied here , which included some cross sectional views of this structure, and diagram (A) below is an accurate copy of theirs.
A
On the left is the basic structure, and that on the right is their depiction of the structure and alignments of the components of the loop at the top of the ‘chain fountain’, and if this structure is extended it produces a complete loop as in the diagram B below, where there is no physical contact between the plane faces of the links and the internal plane faces of the spheres as indicated in the central diagram.
B
But this does not conform to the loops formed by the chain in Biggins and Warner as copied below in diagram C.
C
This suggests that Mould’s demonstration in his video of the flexibility of the chain used by him is the limit of flexibility of this type of chain construction, which conforms to the image in Biggins and Warner’s paper of a loop of five to six spheres, and which indicates a resistance to any closer arrangement.
But it is clear, as is evident in the enlargement in the centre of the diagram B above, that the links between the balls in Pfeiffer and Mayet’s diagram are not in contact with the faces of the recesses in the balls, and accordingly cannot generate any leverage on them, and these spheres therefore could not transfer such a force.
But with a loop composed of five to six spheres, as in the enlargement in diagram D below, the link faces are in direct contact with the internal faces of the recesses and obviously all these links between the spheres will generate leverage.
D
It is important to note that each link arriving at the loop, at X above, immediately acts to introduce leverage to the whole hemispherical structure, while on the opposite side each one leaving at Y relinquishes any such influence.
The diagram E below represents the structure of the type of chain used by Mould, where it is obvious that the plane faces of the sockets create an absolute limit to any vertical rotation of the pins, and leverage is accordingly acting in this circumstances here between and upon any two links and spheres.
And, as there is a relatively large, total area of physical contact between the convex faces of the pins and the concave faces of the enclosures there are consequently, and relatively strong, frictional forces generated here.
E
In the filmed experiments, what occurs when the chain is drawn down the side of the container and falls, both the length and thus its total mass progressively increase until it reaches the floor, and this results in a progressive increase in its fall velocity up to the point where the end of the chain touches the floor.
In other words, on the emergent side this upwards motion of a far lesser mass initially increases and, as there is a significant mass imbalance, the rigidity of the loop structure combined with the momentum of the upwards moving section, has the effect of progressively raising the loop upwards, but only to the point where the end of the downward length of chain touches the floor.
As the total mass falling from the jar does not increase from this point, the chain then continues to fall at the same velocity, and the raised loop remains at the same height, until all the chain has emerged from the container, and when the last sphere lifts from the bottom of the jar the remaining length is flipped over the edge of the jar. All of this is confirmed by the video.
On the opposite side, it is obvious that as the velocity on the downwards side increases progressively so does the upwards velocity of the chain, and as the (momentary) composition of the loop acts like a rigid structure, as indicated by the bold dashed hemisphere in diagram F below, and this increasing upwards velocity, combined with an initial and relative reduction in mass on this emerging side, acts to create an imbalance between the two and thus acts to raise the loop of chain.
F
It is also important to note that there may be a variety of chains, of differing manufactures, used in these experiments which may have different internal structures as shown in the diagram G below. And it is obvious that their structural flexibilities would also differ and the heights of the chain fountain loops in experiments will also be affected.
G
However the same effects have been achieved by Slobodan Nedic and his nephew Darko Nedic using ball chains of different internal structures as in this diagram below where the spheres are hollow, and their videoed experiments with these are shown in this link:- https://www.dropbox.com/sh/dh8oq4zh99dp83u/AAA33gGgaH16WrzK5mRuTTRua?dl=0
In the image below on the right, where the rim of the container is of a narrow dimension, a frictional resistance is generated between the rim and the spheres and the chain does not move.
However if the container has a hemispherical rim of a larger dimension the chain begins to move and to fall over it, but it still does not rise above the rim.
But on a further increase in rim width as in the diagram on the left, at some point it begins to rise over the rim as the linkages are extended to the limits of their lateral flexibility and a progressive increase in fall velocity on the downward side, due to the increase in mass, is transferred to the emerging length of chain, progressively increasing its velocity and consequently raising the height of the loop above the rim up to the point where the end of the external length of chain reaches the floor, and from this point the loop remains at about the same height above the jar until all the chain is extracted from the jar.
The diagram below depicts the frictional forces acting at the points of contact between the spheres and the links, which forces acting on the links generate an absolute resistance to their further rotation, and thus to the leverage that is observed in these experiments.
These images below are of an experiment carried out with a piece of plastic tube fixed to the rim of a container, which produced similar progressive elevations above the rim with this type of chain.
Elevations with this type of chain can also be generated by using a glass laboratory beaker (used by Mould in his videos) as depicted in the diagram below where the leverage on the part of the chain leaving the edge of the beaker remains active until the linkages of the chain are vertical.
Finally it should be noted that if the structure of the chain differs from that of Pfeifer and Mayet shown earlier and the link enclosure is spherical, as depicted in the diagram below, then the same leverage effects will occur.
