Overview of this application

This application will simulate a chain of rigidbodies subject to neighbouring forces, gravity and normal forces due to the environment. The app was created to test the origin of the chain fountain a.k.a Mould effect.

Basic controls

Use the left mouse button to apply a force to the last bead in the chain and pull it over the edge of the cup. You can create a chain with different neighbouring effects at the top left. You can change settings to the physics and simulation in the top right. Use the right mouse button and scroll wheel to position the camera. Use the right arrow key to advance time 1 frame. Use the auto pull button to automatically pull the last bead of the chain down at a constant speed.

Chain

Each bead has a mass of 1 and is seperated by 1 unit of distance. By default each bead experiences 9.81N of force due to gravity.

• Distance chain: forces act only along the connecting line between consecutive beads. The force acts very strongly to maintain a constant distance between consecutive beads.
• Spring chain: The forces similarly act only along the connecting direction, but in this case they are a more flexible harmonic force, that allows for more stretching and squeezing.
• Hinge chain: forces can act in torque, forcing 3 consecutive beads to not exceed the given hinge angle. The forces act strongly to maintain this constrained relative angle as well as a constant distance, similar to the distance chain.

Forces

Use forces toggle to display active forces:

• Light blue is the force due to the next bead in the chain (closer to the flying out the cup)
• Dark blue is the force due to the previous bead in the chain (closer to the cup)
• Orange are external forces i.e. due to the cup or manually applied by the user.
• Green is the net force being applied to this bead, including gravity. Ergo this shows the acceleration of the bead.

Other notes

Though the simulation does not have explicit friction it can be induced due to numerical error, similar to numerical diffusion. This effect is minimized for the spring chain.

Chain fountain effect: results

Trying to recreate the chain fountain in different circumstances leads to 2 important observations:
The chain fountain effect does not occur in chains without a torque interaction.
The chain fountain effect does not occur without something it can push off of (the cup).

An important note here is that by the chain fountain effect I mean the effect where the fountain-like path of the chain grows taller as it falls. Without the preceding conditions, one may still force a fountain-like path to occur by whipping the chain up and down. I postulate however, that without these conditions the fountain path can at best be maintained and will usually slowly recede. This distinction is important when considering the evidence, but it also leads to an important insight: The basic physics of the falling chain is enough to suspend the fountain path in free air, therefore a weak second-order force should be sufficient to allow it to grow and create the true chain fountain effect.

In addition to these clues a detailed force analysis shows that some beads can be pushed into the cup at very high forces, prompting a powerful reaction force pusing the chain up. - This effect is most clear in the simulation when the chain fountain effect is occuring and there are only a handful of beads left in the cup. -

My conclusion is that the key factor in explaining the chain fountain is a levering effect: a chain that has some resistance to bending will occasionally push down into the bottom of the cup as it attempts to straighten itself. This relatively minor force is enough to raise the fountain, while a more basic analysis without chain rigidity (i.e. based on conservation of momentum and circular motion) is enough to explain why the fountain would stay suspended.

I welcome any commentary and suggestions on how to improve the app, if you have any please send me an e-mail at info@negotiatorstudios.com.