A rotating frame equation for the "carousel experiment"

[Simon F]

TL;DR

The "carousel experiment" is the worst case to show the Coriolis force despite claims it show the "Coriolis effect".

As was repeatedly shown by Anders Persson,

https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.2477
<link removed>

the "carousel experiment" is a poor case to show the Coriolis force despite claims it show the "Coriolis effect". Indeed, the Coriolis force, if it was alone (which is true for an elastoid), would should a narrow circle that oceanographers know well under the misleading term "inertia circle", quite different from the wide deflection occuring in the "carousel experiment".

This led me to a very short exercise:

An alternative rotating frame equation, without the Coriolis force, is simply as follows:
a_r = a_a - 2 Ω x v_a + a_cp
with a_cp a centripetal term

In the "carousel experiment", a_a=0 and v_a=cst => a_r = cst + a_cp .

The Coriolis equation was implicitly a choice made by G.Coriolis because he has chosen not to try another decomposition whereas geometry allows an infinite choice and in some cases there are better choices than his. Geophysicists understood afterwards that his decomposition is exactly the right one to show the fundamental "elastoid-inertial" planetary mode, but this is another story, very different from the "carousel experiment" (which does not include any elastoid).

 

[Dale]

What is the carousel experiment?

 

[Roberto Pavani]

Foucault is the answer / corollary

 

[Simon F]

The carousel

What is the carousel experiment?

In the context of the Coriolis force, the carousel experiment is the observation of an all straight motion by one sitting on a rotating carousel.
For a disputable reason, this carousel experiment has been tied to the "demonstration of Coriolis force" which explains its huge success. I have worked in the same idea of a Newton-like equation, as G.Coriolis did, but with other terms which are maybe more intuitive to this carousel experiment.

 

[Dale]

In the context of the Coriolis force, the carousel experiment is the observation of an all straight motion by one sitting on a rotating carousel.

So you start with an inertially moving object and you simply write its equation of motion in the rotating frame?

Is it supposed to be just one inertial motion or is the process repeated with multiple inertial motions? Your description is very unclear.

For a disputable reason, this carousel experiment has been tied to the "demonstration of Coriolis force" which explains its huge success.

That something is “disputable” is uninformative. Some people will dispute anything, even whether the earth is round. Here the standard is whether something is disputed in the modern professional scientific literature.

I have not seen any professional scientific literature disputing the Coriolis force based on what you call the carousel experiment. Even the reference you give in the OP doesn’t do that as it is discussing non-inertial motion.

Do you have any actual professional scientific reference that makes this claim?

 

[Simon F]

Hello,
You can read Persson 2015 in details which is the most documented article recently.
Also you can read Edwards and Edwards 2021.

The carousel experiment is famous for the Coriolis force topic, I am not lying. Irony is that it is a poor/fake demo of the force. The Coriolis force is a mode that can enter any modal decomposition of a signal depending on the modellist choice. It is meaningless saying that you can demonstrate...a modellist choice!

 

[Dale]

You can read Persson 2015 in details which is the most documented article recently.

The one you linked to above? It doesn't even support your claim.

Also you can read Edwards and Edwards 2021.

Give the actual reference.

The carousel experiment is famous for the Coriolis force topic, I am not lying. Irony is that it is a poor/fake demo of the force. The Coriolis force is a mode that can enter any modal decomposition of a signal depending on the modellist choice. It is meaningless saying that you can demonstrate...a modellist choice!

If something is a matter of choice then it can be chosen. If it is a matter of choice then the most that can possibly be shown is that other choices are possible, which is already implied in the fact that it is a matter of choice.

Do you think that scientists are unaware of the fact that the Coriolis force is a matter of choice?

 

[Simon F]

Hello,

Persson 2015 :

"whereas the condition that the Coriolis force is solely responsible for the deflection is justified on a rotating planet, but not on a turntable" [turntable=small carousel].

"A proper intuitive understanding of the [Coriolis-only] deflection over a rotating planet, on a rotating parabola or in a rotating water tank, might require more mental effort than a scant reference to the ‘illusory’ [not Coriolis-only] deflection over a turntable"

This is my topic introduction: the carousel experiment is a poor case to demonstrate the Coriolis force since the deflection is not Coriolis-only.

 

[haruspex]

https://en.wikipedia.org/wiki/Coriolis_force lays it all out very clearly. Correctly describing the motion in a rotating reference frame needs three virtual forces, known as the Euler force (involving the angular acceleration and object location), the centrifugal force (involving the angular velocity and object location) and the Coriolis force (involving the angular velocity and object velocity). The equation "without Coriolis" you offer in post #1 omits Euler but has Coriolis:

a_r = a_a - 2 Ω x v_a + a_cp

The carousel experiment you describe involves the object velocity, so does depend on Coriolis.

 

[Dale]

the carousel experiment is a poor case to demonstrate the Coriolis force since the deflection is not Coriolis-only.

It will never be Coriolis only. There is always the centrifugal force too. What’s the problem?

 

[haruspex]

It will never be Coriolis only. There is always the centrifugal force too. What’s the problem?

Except when the object is, instantaneously, at the rotation axis?

 

[Dale]

Yes, except then.

 

[Simon F]

It will never be Coriolis only. There is always the centrifugal force too. What’s the problem?

My topic was about presenting an alternative equation without Coriolis and centrifugal terms.

I dot not want to spend too much time talking about the problem of associating the Coriolis force and the carousel experiment. Geophysicists know since Klebba and Stommel 1951 how to see the Coriolis-only deflection in a lab setup that can can be shown to any student, which implicitly means that the carousel experiment is a problem. Persson is maybe the only one having turned the implicit critique into a well expressed one but the problem has been known for decades.

 

[Dale]

My topic was about presenting an alternative equation without Coriolis and centrifugal terms.

You can always transform to a different frame if you don’t like the centrifugal and Coriolis terms. But if you are using a rotating frame then they are not optional.

Even Persson's expression still contains both the Coriolis and centrifugal terms. The only difference between his approach and the more common one is that he uses an apparent gravitational force instead of the Newtonian gravitational force. His apparent gravitational force is the sum of the Newtonian gravitational force and the centrifugal force. That is certainly OK notation, but it doesn't get rid of the centrifugal force, it just hides it inside the gravitational force (which is fine to do).

Klebba and Stommel 1951

Again, give the actual reference. For all we can tell these references you are stating are AI hallucinations that don’t even exist.

 

[Simon F]

Klebba and Stommel 1951 https://pubs.aip.org/aapt/ajp/artic...ion-of-Coriolis-Force?redirectedFrom=fulltext
Edwards and Edwards 2021 https://pubs.aip.org/aapt/ajp/artic...ion-laws-for-motion-on-our?redirectedFrom=PDF

Anders Persson, the leader of the contestation since Henry Stommel, wrote his last accomplishment "Experiences of teaching the Coriolis effect" in Hydrometeorology and Education, Roshydromet (Russia), 2020 , so technically there is a published Persson (2020) article.

However, my topic was not about contesting too much but about proposing another equation, mathematically equivalent.

 

[Dale]

I read the Persson and the Edward’s articles. I liked the Edward’s one. But all they are doing is making an effective gravity which includes the Newtonian gravity plus the centrifugal force.

They don’t get rid of the centrifugal force, just hide it. There is nothing wrong with that. Indeed, that is essentially how GR treats the local Newtonian gravitational force anyway.

But the fact that you can do so in no way invalidates the usual expression nor the carousel example.

 

[Simon F]

I think I was wrong making a proposal on a web forum. Anyway, I hope it could illuminate some minds here about how wrong the mainstream education communicates about the Coriolis force.

In 1876, Adolf Sprung showed that it was necessary to curve down the turntable to get the Coriolis-only motion, which is the true demo of the Coriolis force. It is even older than 1951 Klebba and Stommel.
Without this deformation you can not activate any physical mode and you just can see a complex total fictitious force which may be formulated in different ways.

 

[Dale]

how wrong the mainstream education communicates about the Coriolis force.

I think this is the issue I take. Just because you have a way that you prefer does not make the mainstream approach wrong. You are overstating things substantially with this. You are free to prefer a different approach and to suggest why you think it is a better approach. But saying that other people with a different but correct approach are "wrong" just alienates people.

the true demo of the Coriolis force

Similarly here. You are overstating things substantially. You can truly demonstrate the Coriolis force with the standard "carousel experiment". It may be more clear to demonstrate it with a curved turntable, and you may have a preference for doing that. But your preference does not make it "the true demo".

Stating personal preferences as though they were facts and truth is not persuasive. You can, and should, instead simply explain the advantages of your preferred approaches as you see them. Saying your preferences are "true" and other approaches are "wrong" diminishes your credibility and invites antagonism.