Over 2.5 million viewers, including many physicists, have been astonished by Steve Mould’s videos of a chain flowing along its own length from a pot to the floor below. Apparently defying gravity, the chain rises above the pot as a fountain before falling down. Proceedings A has published a paper which explains why this fountain occurs by considering the forces bringing successive links into motion. In this podcast, authors Mark Warner and John Biggins explain what is going on.
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For a collection of related problems to work through go to
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great demonstration of science!
It's the same exact force that causes a whip to accelerate beyond the speed of sound. I don't anything needs to be explained does it?
Sorry. my dears. That was not the thing at this phenomen. There is no repulsion, because the Leverage is to less against the mass-acceleration. The spaghetti example should have made the guys think? Spagetti are homogen and there is no leverage.
There is only a higher initial-accelereation of the stationary chainpart, as the chain falls down. This results in a mass-acceleration, that must build an bow, because the chain falls slower, as the initial-acceleration of stationary chain is.
And that faster acceleration comes from circuited lying chain, what reduces the resistant against the acceleration from falling-speed chain. You Guys better go work as an electrician or go fisching, because kabels and ropes build the same phenomenal bow, if both lying circuited onto and the fish pulls the line at constant fast speed out of it.
If the inituial-acceleration of stationary chain comes to the circle-point, when there must longer chainpart accelerated, then it comes to an accerelerating of more mass, that result then in an faster and stronger cross-accelerating, as the falling chain can effect and pulls the chain faster out of the glas, when the fluctuating resistent against the accelerating at the lowest point. That results in an bow, because this little part of the chain is connected with the chain, but more/faster accelerated, als the rest of the chain, that falls maximum at gravitational constant.
And this royal Society better shuold erasure this "Explanation", because it is embarrassing.
Steve & Co are mostly wrong.
The question(s) are not whether there is a reaction force, they are
(1) whether the reaction force is needed to create a fountain,
(2) whether the reaction force affects the height of the fountain.
The answers are No & No.
In relation to the horizontal fountain, the answers are Yes & Yes.
But, the original questions relate to a chain from a bucket/beaker/container/can — not from a horizontal surface.
So, that was their first mistake.
Now to their second mistake.
The mere existence of a reaction force does not make the answers Yes & Yes.
The reaction force (at launch, in the bucket) borrows power from the falling chain.
So, it can't add to the height of fountain (at launch, from a bucket).
Links landing on the floor do add to the tension in the falling chain.
Hence they add to the height of a fountain.
But the lever action (kick) at launch in the bucket does not add to the height of the fountain.
There are (can be) two kinds of kick.
Kick 1. One is the simple lever kick (due to a say 90 deg bend in the chain).
The other is a similar kick that is due to the chain having a bend beyond 90 deg.
Kick 2. We sometimes see a bend of 180 deg, or more.
That large bend creates a slower & possibly greater kick.
But, both kinds of kick (at launch) borrow power from the chain, hence they don’t add to the height of the fountain.
Except in the case of launching horizontally from a horizontal surface, where there would be no vertical fountain were it not for these two kinds of kick.
Except that there is a third kind of kick that will give u an enormous vertical fountain offa horizontal surface.
Kick 3. And this kick can be created by laying the chain such that as it is being yanked horizontally it has to jump over itself.
It’s a jump-kick, & has zero to do with lever action.
Whereas the other two kinds depend on lever action.
Kick 1 & Kick 2 do not add to the height of a fountain, koz they borrow from the system.
Kick 3 also borrows from the system, hence at launch from a bucket it can't add to the height of a fountain.
But, from a horizontal surface, Kick 3 does add to the height of the fountain, koz, without it, the height would be zero.
Kick 4. However, Kick 1 & Kick 2 can give a small non-zero height from a horizontal surface, but this usually arises due to the chain clattering over the (usually) sharp edge at the end of the surface. This can be called Kick 4. It thrives koz its effect is cumulative (as are Kicks 1 & 2 & 3).
Steve & Co are wrong.
I don't buy the "kick from the table" portion. You get the same fountain holding the container, which would significantly reduce/absorb any energy transmitted to the container or table, which would reduce the fountain effect IF such a kick existed.
This is wrong. I think I have the answer. The pivot force may play a small role but it isn't the primary role. The problem stems from your diagram – which is wrong. The arc is not symmetrical. The downward side arcs outward because it still carries the horizontal momentum from the top of the arc.
You must then ignore that part of the chain below the top of the pile in the pot. It is not contributing to the fountain – it is merely maintaining the driving force of the system. The weight of chain equal about the arch does not have equal vertical forces acting on it. The downward side contains an outward force. Because the tension is equal throughout this must mean that the downward force is less on the downward side than the upward side causing a net upwards force.
Dropping the bead chain over the rim has formed a small bend of curve on the top already and with sufficient initial speed of the inelastic cord circling around the curve, centrifugal forces acting on the chain are created inevitably on that portion of the chain and the resultant force is an uplifting force only. That force is intrinsic to withstand the weights of chain hanging from both sides over the top bend, when the length of chain at the dropping side is more than two times of that at the lifting side a steady flow of chain fountain can thus be maintained.
Please note, basic equilibrium equations of forces on all FBDs of either side chains as well as the moment equation about the curve center of the bend section are essential to reach the right conclusion.
Your reasoning of the back-kick force by the lever models is faulty because it will close the connecting gaps of the levers and inadvertently stop the pulling actions from the lifting levers above.
I think I solved this puzzle. the answer is seesaw principle. every ball in the chain is a seesaw acting in the air. when one side of the seesaw is being pulled down the other side of the ball would produce a upper force to pull the other side chin upwards.
They start with a model — then apply math.
If the model is wrong, then the math aint of much use.
I think that every model to date ignores the rotational momentums of a link/bead.
RM(1)90. Launch RM. A link/bead has zero RM at first — then a max of Rm halfway throo launch — then, later, zero RM again, during ascent.
During this idealized launch phase the chain passes throo say 90deg.
RM(2)180. Fountain RM. As the link/bead goes over the top of the fountain, we have the same — zero RM during ascent — then a max of RM in the fountain — then during descent zero RM.
During this phase the chain passes throo say 180deg.
RM(3)180-90. At launch, what we see is that the chain sometimes forms an180deg half loop, then it has a dose of RM(1)90 to get back to vertical.
Here there are 2 phases, the 180deg phase having a RM in one direction (eg CW), then the 90deg phase having a RM in the opposite direction (CCW).
RM(4)??. In tests the chain can have lots of complicated phases of RM.
Sometimes we see tangled loops doing crazy stuff.
Anyhow, no model (that i have seen) allows for whether the power of RM's are totally lost — or whether partly lost — or whether totally returned in some way.
I think partly lost & partly returned — the losses being due to friction etc.
But, RM is a minor issue (or praps not so minor).
All of this is just a side issue — just saying.
Anyhow, in the end — all models are wrong.
The diagram with the flat bars is close to the truth of what's actually going on, IMO. The issue many of you are having is that the chain isn't a series of bars with short connections between them, but a series of balls with short connections between them.
However, the spherical beads in a ball chain are held together with metal wires – very inflexible wires, at that. There's no flexibility to allow the bead itself to rotate individually as it is being pulled up, because of that rigid wire holding it to its neighbors on the chain. That rigidity forces the wire in between the beads to lever and push against the neighboring bead, imparting that force to the next bead, which makes the bead being picked up by the rest of the chain jump upwards.
The only difference between the flat bar diagram and the bead chain is that the lever point for a bead chain is in the center of the inflexible wire between the beads, not the center of a flat bead, like in their diagram. I hope I've explained it clearly and succinctly, as I'm running on no sleep, and it's 5 AM.
(Edited typo)
Why the 2 chains are failed because it need more power in the 180 degree turning only！The rod hit the glass edge very hard before it turn, you need to provide a larger turning radius when starting the turning. Please think of a roller coaster, why the most rear seat accelerating upward while the roller coaster reach the top of the hill and start going down.
Should have more views and likes.
Every piece of the lever effect and inertia and friction adds energy to the chain that resonates and must escape it's held by some degree in the pot and chain at the same time and your seeing the energy meet in the arch and accumulates. Like anytime two waves collide they combine momentarily while passing through each other… Well what your seeing is a resonance of that effect in the wave. you both already know this as explained in your other vids about energy waves!
Clear idea please , as I want to frame a numerical on it.
The Cambridge explanation is rubbish.
There is never a bonus-kick at the container/jar/beaker.
There is indeed a bonus-kick when a falling chain-link hits (collides with) the floor of the laboratory, & this adds to the downward pull of a chain, & increases the size of the fountain etc (by say 1%).
But that extra (bonus) force is initiated by the falling/colliding link itself.
Meanwhile, back in the jar, a rising/yanked link will indeed get a kick from the floor of the jar (or from the links supporting that link), but, that kick is not initiated by the rising link, it is initiated by the preceding link.
The preceding link has a limited amount of impulse to give.
The kick from the jar results in a similar (but opposite) kick being given to the preceding link.
But the kick from the jar is not a bonus-kick.
The initiating impulse from the preceding link is not added-to by the kick from the jar.
The impulse of the kick experienced by the rising/yanked link has been borrowed from the preceding link.
In reality, borrowed from the full/whole chain.
Hence, at the jar, links or beads, it makes no difference.
In reality, there is no rising/yanked link. Duznt happen.
What i mean is, we mostly have a rising/yanked arc, made of many links.
In slow-mo u can see that there is mostly a long arc of moving links (talking bout metal beads here).
And the movings usually involve being dragged gradually horizontally for a time, & gradually upish.
There is no sudden kick — it is a gradual kkkiiiiiiiiiiiiiiiiiicccccccccckkkkkkkkkkkkkkk.
https://www.youtube.com/watch?v=qTLR7FwXUU4
World Record Chain Fountain? The Mould Effect Explained
1,133,201 views Jul 23, 2021 Steve Mould 1.14M subscribers 7633 comments
Look in slow-mo at the bead chain fountain at 15:06 of 21:36.
There are indeed say 4 adjacent beads acting as pseudo-links being yanked/jerked up.
(a) But, these pseudo-links are not rigid, they have a lot of give.
(b) And, these & the trailing say 5 or even 10 beads are moving horizontally & have daylite under them.
(c) The pseudo-links never have a solid floor to kick (down) against.
(d) And, even if the last bead in the pseudo-link does enjoy an upwards (very very weak) kick, this kick is off a slippery & lose bead or two, & the kick moves thems beads sideways (or forwards)(or backwards)(they are after all lose in every way).
So, beads do not provide anything like a solid surface to kick offa.
Sheeeesh! Stone the crows! Milo give me strength! Are we blind!
The fountain (ie the arch)(the half circle) is simply due to the inertia of a chain.
If a stationary chain lays over the top of a wall, it forms a sharp V-bend.
If the chain is pulled down on one end, then it will rattle up & over the wall, with some speed.
If the speed is sufficient, the sharp V-bend will become a U-bend, due to centrifugal/centripetal forces opening up the V.
If speed increases, the U-bend opens further.
If speed increases a lot, the rising chain leaps up clear of the wall, & stays clear, the zenith/crest depending on gravity, & the U-bend opens some more.
And we have our fountain.
The height of the crest/fountain depends on speed (& is probly higher if chain heavier).
The radius of the U-bend/fountain depends on speed (& is probly larger if chain heavier).
Steve Mould at 10:50 of 21:36 says that the radius of curvature cancels out in the equations, & doesn't play any roll in these dynamics.
Steve is wrong.
If he were correct, then that would mean that the radius can vary greatly, for any given setup.
It might mean that if u initiated the fountain with a given radius then it would affect the final (maximum)(steady state) radius.
But i reckon that the radius (for a given setup) tends to one number.
And i reckon that the radius (for a given setup) varies with speed (ie varies with drop).
Just koz the radius cancels out in some dynamical equations duznt mean that radius duznt play any roll in the dynamics.
Steve at 17:13 of 21:36 shows how a horizontal tight pattern of rows of chain (beads) gradually moves away to the west (due to the kick-effect) when the end of the chain is pulled east.
Yes, there is some kick effect, due to the pseudo-links.
But, the greater part of the effect is due to a chain's inclination to retain a pattern.
Here, we see that at each end of each row the chain forms a loop, looping around & back throo say 220 deg, such that the rows are hard up to each other.
As the end of the chain is drawn east, the end loops move across & back & across & back etc.
Now, Steve knows that a chain has a memory, ie it tends to retain a pattern.
In this case, that pattern is a 220 deg loop.
And, as the loop or loops traverse across & back etc, the loops slowly push the rows west.
That westwards slow pattern-push is a different animal to the quick jerk of a pseudo-link kick.
The slow pattern-push duznt suffer from the hi losses suffered by a pseudo-link kick.
Pseudo-links are not rigid, they have give. Give aint a problem for a slow westward pattern-push.
I said that yes there is some kick-effect.
But, i have already said that these kicks are not bonus-kicks.
They borrow from the overall power of the chain system.
They don’t add to the fountain.
It is virtually impossible to load/store a chain in a jar without having loops.
And loops result in jumps.
If u have a close look (in slow-mo) u can see that chains have a lot of horizontal movement before exiting vertically, & the chain sometimes suffers little jumps in the jar, as each leg of each loop jumps (horizontally) over its mate.
Jumps magnify the fountain, kicks dont. OOPS. No, i am wrong. These little jumps are not bonus-jumps, just like the kicks are not bonus-kicks. Any vertical impulse gained by a jump must have been borrowed from preceding links.
Also, the horizontal movements seen in the container/jar/beaker are a waste of impulse.
But, in any case, we don’t need bonus-jumps nor bonus-kicks to achieve a growing fountain, & to achieve a very high fountain.
All we need is lots of speed. The chain will crest at any height, depending on speed. There is no limit.
The idea that something special (like a bonus-kick) is needed (if the chain is to rise above the edge of the jar) is silly.
One thing that everyone has missed, in every youtube re the chain fountain (that i have seen), is that vertical jump effects & vertical kick effects (etc) are cumulative, and lasting (tautology alert).
Or at least partially cumulative & lasting. Air friction, & link friction see to that.
Anyhow, cumulative/lasting effects are the reason for some of the slightly weird gyrations/waves.
For example, it (lasting accumulation) is why we eventually get a persevering, vertical component of arc (a mini fountain) when the test seems to be strictly in the horizontal.
In fact, the lasting/cumulative effect is the main reason for the fountain.
There needs to be an initial vertical rise out of the jar.
A horizontal initial exit wont do the trick.
… not a big deal, this is a very simple inertial differential moment being created at the -g zone further magnified by the downward mg, the V(0) has nothing to do with it as can be seen from the chain slomo.
So the pot did it?
3:35 The ball's upward velocity does go to zero. However the same is true for the chain, at the peak the chain has no upward velocity, but it has horizontal velocity. Can the Cambridge team please explain how their solution ties in with the conservation of momentum.
It's the effect of the balls spinning. Tiny gyroscopes, probably alternating CW CCW CW…
Why do you substitute rods for balls. Why not use day old donuts? You are suggesting the balls have the same rigid properties of rods which they clearly do not. Initially the chain rides over the edge of the pot and falls straight down. If the chain hits the floor now there will be no fountain effect. The height of the pot above the floor must be increased As the weight of the chain outside the pot increases the speed of the falling chain increases. In order to leave the pot the chain naturally forms a curve. Reactive Centrifugal Force of the curved section overcomes Gravity and pulls it up away from the edge of the pot. The curve rises as the speed of the chain increases. Nothing is pushing the chain out of the pot. Gravity is pulling the chain downward.
This beittish dude is a dimwit. Damn is he impossible to listen too.
I was originally convinced by Mehdi, but Mould's latest video on the subject two weeks ago not only proves Warner and Biggins correct, but disproves Mehdi.
https://youtu.be/bcsb1xAv7XA
At 3:36 the comparison to a ball's ballistic trajectory is flawed. He claims it can not be like the ball because the ball stops then falls in gravity. This is only true if the ball is moving 100% vertically. Toss the ball with some horizontal component so that it also follow a curve at the top and it does not stop. Only the vertical component of velocity stops and reverses, just as does the chain. This is from the Royal Society? Was their paper peer reviewed?
After observing a few of the videos, I propose that the Mould effect can be attributed to centrifugal force, as the chain changes direction at the top of the arc.) After the process has begun, but before the free end reaches the ground, the chain is accelerated downward by gravity. As it gains speed, centrifugal forces generate an opposing tension. The amount of tension generated in a string traversing a circular path can be shown to be T=λv², where λ is the mass per unit length, and v is velocity. So tension builds quickly. (Note: The arc radius is not a factor.)
This tension can be sufficient to lift the turning point. After the free end hits the ground, equilibrium is established, and chain velocity becomes constant, where the upward centrifugal forces are balanced by the weight of the hanging chain. At equilibrium
λv² = Mg = λgh
where h is the height of the arc. This reduces to
v² = gh
So final height depends on velocity, but not on chain density.
On the entry side, the centrifugal force is pulling chain from off the pile accelerating it. The rate of momentum change (resisting force) is also λv², so (absent friction) there is a constant tension within the chain leading up to the reversal point.
A way to test this proposal is to measure the equilibrium chain velocities at various heights. In an older video by Steve Mould, he siphoned out 50 m of chain in about 12 seconds, at an estimated height of 1-2 m (say 1.5). That’s about 4 m/s, vs a predicted velocity of 3.8 m/s. Accounting for startup delay and height estimation, it’s close.
This is nonsense!
Please look at the actual chain. Observe the angular constraints between the links. Now, get your maths out and have another go.
The 'chain fountain' effect PREDICTS the type of chain used in the experiment. Consequently it should work with most ropes as well. Good luck 🙂
EDIT: I have since watched the whole film and can see you have grasped the basics 🙂 A more accurate sketch/model would have been useful for me to see as the pasta/string is not truly representative of the mechanics of the chain used.
There is no 'kick' to push down on the bowl. If there was a 'kick', then the fountain would decrease in size due to a loss of energy and momentum from the force exerted on the bowl by the chain (which doesn't happen). The momentum and stiff links from Atomic Shrimp is a more accurate explanation of what is observed.