Chain Fountain (Mould Effect)

The trick, and why it's weird

Coil a long bead chain — the metal ball-and-link kind from a lamp pull or a bathroom plug — into a tall jar. Pull a short loop over the rim and let it go. You'd expect the chain to flop over the edge and slide down. Instead, the chain flies up out of the jar, forms a graceful self-supporting arch a hand's-width above the rim, and only then plunges to the floor in a continuous stream. The arch hangs there for the whole minute it takes the jar to empty.

That's the chain fountain. The puzzle is simple to state: gravity points down. Nothing in the room is pushing the chain up. So where does the upward push that lifts the chain above the container come from? The answer turns out to be the jar itself.

How it works — the pickup point

Think of the chain in three pieces: the slack pile at the bottom of the jar, the long fast-moving section that has already left, and the place where stationary chain gets accelerated up to speed. That place — call it the pickup point — is where all the interesting physics lives.

The falling section is heavy and moving at speed v. It tugs on the next link, which is sitting still in the pile, and has to whip it up to speed v almost instantly. Accelerating mass requires force, and that force is what pulls chain out of the jar. So far this is just a moving chain — the same physics as a falling chain or a self-siphoning rope.

The surprise is what the pickup does to the pile. A bead chain is not a smooth string: it's a row of small rigid rods (the links between balls). When the moving chain yanks a link, that link can't simply translate — it has to rotate about its still-anchored neighbour, like a tiny see-saw. To swing its far end up, the link's near end has to push down on the pile underneath it. By Newton's third law, the pile pushes back up on the chain. That extra upward shove is the "kick" that launches the fountain.

The physics — momentum and the anomalous kick

Start with the momentum equation for the rising side. Let the chain have linear mass density λ (kg/m) and move at speed v. New chain is being set in motion at a rate of mass-per-second:

dm/dt = λ·v

The momentum picked up per second — the force needed to accelerate the chain from rest to v — is:

F_pickup = v · (dm/dt) = λ·v²

If the pile were perfectly passive (a flexible string), that's the whole story: the tension just above the pickup is T = λv², and the chain leaves the jar moving but flat — no fountain. The classic "falling chain" result even predicts that energy is lost at such a pickup, because each link is jerked inelastically up to speed.

Biggins and Warner's insight (2014) is that a rigid-link chain delivers an extra upward force at pickup. Model each link as a rigid rod of length ℓ lifted by a force applied at one end while the other end still rests on the pile. As the rod rotates up, the resting end presses on the pile and the pile reacts with an upward force R. The total momentum picked up per second is still λ·v², but now it is shared between the chain's own tension T and the pile's anomalous reaction R:

T + R = λ·v²,    with   R = α·λ·v²

where α ≥ 0 is a dimensionless "kick" factor set by the link geometry (how the rod pivots). α = 0 recovers the boring flexible-string case (the pile does nothing, T = λv²); α > 0 means the pile actively throws the chain upward, so the tension above the pile is only (1 − α)·λv². Energy conservation caps the kick at α ≈ ½; Biggins and Warner's link model estimates α ≈ 1/6, and their measurements give α of a similar order — enough to lift the fountain well above the rim.

The fountain height follows from a force balance along the arch. The steady-state apex height h of the fountain above the rim scales as:

h / H ≈ α / (1 − α)     (≈ α  for a small kick)

where H is the drop height from rim to floor. For the observed α ≈ 1/6 this gives a fountain roughly a fifth of the drop height. Crucially, the fountain feeds on the falling chain's speed, and that speed grows with the drop, so a taller drop gives a taller fountain — the opposite of most intuition about "running out of push."

Where the energy comes from

The whole show is powered by gravity acting on the long falling section. In steady state the chain moves at a near-constant speed set by the balance between the gravitational drive on the descending side and the inertial cost of accelerating new chain at the pickup, less the energy lost to the inelastic jerk:

½·λ·v² (KE per metre gained)  ⇆  λ·g·H (PE per metre released)

Roughly half the released gravitational energy goes into kinetic energy of the moving chain; the rest is dissipated in the snatch at the pickup and in air drag. The kick that makes the fountain doesn't need new energy — it just redirects part of the pickup interaction into an upward impulse, the way a diving board redirects a jumper's downward push into lift.

When the fountain appears — and when it doesn't

Condition	Effect on the fountain	Why
Rigid ball-link bead chain	Strong, tall fountain	Each link levers cleanly against the pile → large α
Soft thread / fine string	No fountain (flat pour)	No rigid segments to push down on the pile → α ≈ 0
Taller drop H	Higher fountain	Faster chain → larger λv² and larger kick
Higher rim / deeper pile	Slightly higher launch	More room for links to lever before clearing the wall
Chain neatly stacked vs tangled pile	Smoother, steadier fountain	Tangles add random jerks and snag the kick
Vacuum vs air	Marginally higher in vacuum	Effect is contact-driven; air only adds drag
Free fall / no gravity	No fountain at all	No falling section to drive the chain

Numbers from the real experiments

Steve Mould's viral demonstrations and the Biggins–Warner paper give concrete figures worth knowing:

Quantity	Typical value	Note
Chain used in the famous drop	50 m bead chain	Released from a tall building / cherry-picker
Fountain height above rim (tabletop)	~5–20 cm	Pot on a table, chain falling to the floor
Fountain height (large drop)	Tens of cm	Grows with drop height H
Steady chain speed (tabletop)	~2–4 m/s	Set by gravity vs pickup inertia
Kick factor α	~1/6 (≤ ½ max)	Geometry-dependent; α = 0 means no fountain, α = ½ is the energy-conservation ceiling
Bead diameter (lamp-pull chain)	~3–5 mm	Link length ℓ sets the lever arm
Energy split	~50% to KE, rest lost	Inelastic snatch + drag at the pickup

A useful sanity check: with λ ≈ 0.02 kg/m and v ≈ 3 m/s, the pickup force is F = λv² ≈ 0.02 × 9 ≈ 0.18 N — about 18 grams-weight of tension at the rim. The kick adds a fraction of that as an upward impulse, which is plenty to lift a chain that weighs only grams per metre.

Where the same physics shows up

• Falling-chain and rope dynamics. The pickup-momentum term λv² is the core of every "chain falling off a table" and "rope uncoiling from a pile" problem — and the place textbooks famously disagree on whether energy is conserved.
• Anchor and cable pay-out. Ships paying out anchor chain, and reels feeding cable or wire, feel exactly this snatch force as stationary links are accelerated to the running speed.
• Yarn, thread, and filament handling. High-speed textile and fibre-optic spooling has to manage the inertial tension of picking line up off a package — too fast and the line whips and snaps.
• Tape and film transport. Magnetic tape and film moving over reels and idlers experience pickup tension that engineers must damp to avoid flutter.
• Granular and link dynamics. The rigid-link kick is a clean tabletop example of how contact between rigid bodies and a pile can produce reaction forces in unexpected directions — relevant to granular flows and chain-mail mechanics.
• Science communication. It's one of the best demonstrations going for Newton's third law and momentum flux — a single jar and a chain produce a result that surprises physicists.

Common misconceptions and edge cases

• "The chain is pulled up by the falling part." The falling part supplies the drive and the speed, but pure tension can only pull along the chain — it can't make the chain leave the rim moving upward. The upward leap needs the pile's reaction (the kick).
• "It's an air or static-electricity effect." No. It works in a vacuum and with non-conducting chains. It's pure mechanics: momentum flux plus a contact reaction.
• "Any rope does this." A floppy string shows essentially no fountain. You need rigid links so that lifting one end levers the other against the pile.
• "Energy isn't conserved, so the demo is fake." Energy is conserved overall — about half the released gravitational PE is dissipated in the inelastic snatch and drag, which is exactly why the chain settles to a steady speed instead of accelerating forever.
• "The fountain gets lower as the jar empties." It actually stays roughly steady, then collapses near the end when the remaining pile is too small to maintain a clean pickup. Tangles cause the visible stutters.
• "A taller drop wears out the push." The reverse — a taller drop makes a faster chain and a taller fountain, until air drag and chain damage cap it.