A Study of the Chain-Fountain Effect

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A Study of the Chain Fountain Effect

How does the minimum bend radius of a chain affect the maximum height and average velocity of the fountain, in a setup preventing the kickoff effect, and a setup allowing the kickoff effect?

Researcher

Peter Graham

Class of 2023

What is the chain-fountain effect?

The chain fountain effect is a counter-intuitive physical phenomenon involving a bead chain. If a beaker is held above the ground with a bead chain inside of it, and one end of the chain is yanked over the rim of the beaker towards the ground, the chain will appear to siphon out of the beaker on its own. On top of this, while being ‘siphoned’ out of the beaker, the apex of the chain will rise to a certain height above the beaker.

Problem Statement

There is a problem with our understanding of the chain fountain effect. Despite having many papers written on it, there is still much debate on the mechanisms behind the effect. Fully understanding this effect can improve our efficiency of using chains and tethers in applications such as space and satellites.

Significance and Value of Study

The chain fountain effect is not fully understood yet, and there is still no consensus on the cause of the effect. By collecting data on the effect of changing the characteristics of the chain, we can possibly come closer to a complete understanding of this effect. With a full understanding, we can possibly use the information to increase efficiency of chains and tethers in space and on satellites. Tethers could be replaced by a chain fountain, enabling the tethers to deploy themselves, instead of requiring extra equipment to deploy it. Youtube videos on this topic have accumulated millions of views, also demonstrating a real public interest.

Proposed Method of Study

True Experimental

Hypothesis

I believe that in a setup preventing the kickoff effect, the minimum bend radius of a bead chain will have no effect on the qualities of its chain fountain. Additionally, the height and velocity of this fountain will be less than that of a chain fountain in a setup enabling the kickoff effect.

Assumptions

In the setup preventing the kickoff effect, the chain is receiving no extra upwards force
In the setup allowing the kickoff effect, the chain is receiving an extra upwards force
The chain fountain is in a steady-state throughout the data collection.

Definitions and Variables

Kickoff Effect:

when the chain receives an extra upward force when the linkages reach a minimum bend angle, allowing it to “kickoff” the object below it

Bead Chain:

a chain that uses balls or beads in place of normal chain links.

Steady-State

when the height and velocity of the fountain become constant

Results

The setup allowing the kickoff effect suggests that the minimum bend radius has no effect on the velocity of the chain.

The same is true for the setup preventing the kickoff effect, as this data also suggests that the minimum bend radius has no effect on the velocity of the chain.

For the setup preventing the kickoff effect, the linear regression line shows that there is an inverse relationship between the maximum height and the minimum bend radius. When looking at the results of the setup that allowed the kickoff effect, the opposite relationship is observed. The data from this setup suggests that there is a positive correlation between the minimum bend radius and the maximum height of the fountain.

It is also worth noting that the maximum height of the fountain in the setup preventing the kickoff effect was significantly higher for every minimum bend radius tested.

Conclusion

This study was not an attempt to explain the cause of the chain fountain effect, rather, it was an attempt to gain insight into how the aspects of a chain affect the qualities of its chain fountain. The specific question asked was: If the kickoff effect is being prevented, how does the minimum bend radius of a bead chain affect the qualities of its chain fountain, in comparison to the classic chain fountain? Through the analysis of this study, multiple relationships were observed.

The original hypothesis stated that, when the kickoff effect is prevented, the height and velocity of the fountain will decrease, and the minimum bend radius of the bead chain will have no effect on the qualities of its chain fountain. The results of this study refute this hypothesis. As predicted, when the kickoff effect was prevented, the minimum bend radius had no effect on the velocity of the chain. However, the regression models suggest there is an inverse relationship between the minimum bend radius and the maximum height of the fountain. This was not predicted by the hypothesis.

Next Steps

This investigation suggests that the minimum bend radius of a chain will affect its chain fountain differently, depending on whether or not the kickoff effect is prevented. Because this study only investigated one setup that prevented the kickoff effect, future studies should investigate a variety of setups that prevent the kickoff effect, in order to see if these trends hold true or change. This is especially true because the major application of this study is in space tethers.

Space and satellite tethers have multiple uses, including connecting with other spacecraft, propelling other spacecraft, and propelling their own spacecraft. Tethers could be replaced by a chain fountain, enabling the tethers to deploy themselves, instead of requiring extra equipment to deploy it. Investigating different setups is important because the weight and room taken up by equipment on a spacecraft are highly optimized. Depending on the use of the tether, different setups could also optimize its performance. For example, if someone wants to optimize the velocity of the tether, the results of this study suggest that a setup allowing the kickoff effect would be best.

Key Sources

J.S. Biggins, EPL (Europhysics Letters) 106, 44001 (2014). https://arxiv.org/abs/1401.5810
J.S. Biggins and M. Warner, Proc. R. Soc. A. 470, 20130689 (2014). https://royalsocietypublishing.org/doi/full/10.1098/rspa.2013.0689
H. Yokoyama, Popular Physics (2018). https://arxiv.org/abs/1810.13008
S. Mould, The Chain Fountain (YouTube, 2013). https://www.youtube.com/watch?v=_dQJBBklpQQ

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