Talk:Coriolis force/Archive 6

Three distinct situations to contemplate

(1) Large scale cyclones. The authors of this article believe that the cyclonic behaviour in large scale cyclones in the atmosphere is caused by the Coriolis force, within their own understanding of the concept of Coriolis force.

(2) Tornadoes are mostly cyclonic. But the authors here do not believe that Coriolis force is involved, as they understand the concept of Coriolis force.

(3) Water swirling out of a bathtub is not cyclonic. The authors here do not believe that Coriolis force is involved.

Cyclonic of course refers to a connection with the Earth's rotation. I would agree with the authors on points (2) and (3).

So if Coriolis force, as described in this article, is not the cause of (2) and (3), then what is? The answer will of course be related to conservation of angular momentum. But conservation of angular momentum is not a cause. This takes us to Kepler's second law. Conservation of angular momentum will result from an interplay of Coriolis acceleration and angular acceleration caused by the intermolecular bonds in the fluid. Kepler's second law involves two effects which cancel mathematically but not physically. That is exactly what is happening in all three of the vortex situations listed above. We can witness a real Coriolis force in all three situations listed above. As the fluid moves radially inwards, there is a tangential deflection which changes the radial direction. That is the real Coriolis force in the analysis, exactly as per the Coriolis force in an elliptical Keplerian orbit. But the cyclonic direction in (1) and (2) is a consequence of insufficient Coriolis force for the purposes of constraining radial motions to the radial line, due to the Earth's rotation. The Coriolis force as per this article does not exist. It is not even fictitious. This fact has been recognized as regards tornadoes, but unfortunately, it has not been recognized as regards the larger cylones.

As regards the examples in this article involving free projectiles as observed from rotating frames, there is no Coriolis force involved in any shape or form. There is merely a fictitious circular motion imposed on top of the already existing motion. The only one of the three inertial forces that can ever be fictitious is the Euler force. We can view a fictitious Euler force from an angularly accelerating frame of reference.

The real Coriolis force, as envisaged by Coriolis himself is a hydrodynamical effect which has got nothing to do with the Earth's rotation. It is viewable from inertial frames of reference. The real Coriolis force in all three vortex situations described above is viewable from outer space, whether or not there is the additional cyclonic factor. David Tombe (talk) 06:50, 3 February 2009 (UTC)

David, I have collected some typical numbers for the cases at hand. As you will see, for wind (depressions) and typhoons, the Coriolis acceleration is in the order of 30% of the pressure gradient. For tornados and bath tubs it is about 0.01%. So the first two are determined by it, the latter two are still influenced by it, but to such a small extent, that other (random) factors normally dominate.

Furthermore, since the Coriolis force is always perpendicular to the flow of air, it does not increase the airspeed (although the air is accelerated). Increased air speed comes form the conservation of angular momentum.

qty	unit	wind	typhoon	tornado	bathtub
pressure 1	mbar	1020	1013	1013	23
pressure 2	mbar	980	970	990	20
delta pressure	mbar=hPa	40	43	23	3
delta pressure	Pa=N/m2	4000	4300	2300	300
distance	km	1000	500	0.075
distance	m	1000000	500000	75	0.6
pressure gradient	(m/s2).(kg/m3)=N/m3	0.004	0.0086	30.7	500
movement speed	km/h	50	130	175	1.8
movement speed	m/s	13.889	36.111	48.611	0.500
earth rotation	rad/s	7.292E-05	7.292E-05	7.292E-05	7.292E-05
latitude	N	30	30	30	45
coriolis factor		7.292E-05	7.292E-05	7.292E-05	1.031E-04
coriolis acceleration	m/s2	0.00101	0.00263	0.00354	0.000052
density	kg/m3	1.2	1.2	1.2	1000
coriolis force	N/m3	0.00122	0.00316	0.00425	0.05156
fraction		30.38%	36.74%	0.01%	0.01%

−Woodstone (talk) 20:41, 3 February 2009 (UTC)

Woodstone, we're not in total disagreement here. The problem is over what we are actually calling the Coriolis force. You are using the term Coriolis force for the fictititious effect which causes the cyclonic behaviour in the large scale phenomenon. I agree with you that there is such a fictitious effect and that it can cause a real cyclonic effect. That sounds strange, but the reason is that the moving elements of air will go straight as per their inertia. In isolation, this wouldn't be viewable from outer space. But these moving elements are bonded to a larger co-rotating body which applies a real partial Coriolis force on the moving elements. The combined result is the cyclonic effect. But the fictitious bit is not Coriolis force. It is not even negative Coriolis force.

Moving on to the smaller effects such as tornadoes and kitchen sinks, the above effect doesn't happen. However, in the case of tornadoes, the cyclonic effect will be the result of the fact that the already existing angular momentum has been determined due to the cyclonic effect in the larger body of atmosphere in which it forms. With the kitchen sink, there is no cyclonic effect because the effect described above would be so weak that it would not overcome the existing angular momentum.

Now we move on to a completely different subject. That is real hydrodynamical Coriolis force as conceived by Coriolis himself. It is not cyclonic in general but it exists in all vortices from kitchen sinks to large cyclones. It is related to conservation of angular momentum. You have been overlooking the fact that there are two aspects to conservation of angular momentum, just as there are two aspects to Faraday's law. There is both Coriolis force and angular acceleration. They cancel mathematically, but they are still both clearly present physically. Kepler's law of areal velocity is a special case, and the exact same two effects can be observed in an elliptical orbit.

Watch the water swirling down the sink. There will be an angular acceleration in one direction. There will be an equal and opposite Coriolis force in the other direction. The Coriolis force is the bit that involves the right angle deflection of the radial motion.

From your letter above, it would appear that you thought that I was saying that the Coriolis force causes the angular acceleration. It doesn't. It acts in the opposite direction. It doesn't even prevent the angular acceleration. The two of them act in tandem leading to conservation of angular momentum.

So wherever we have a vortex in hydrodynamics, unless there is an externally applied torque, we will have conservation of angular momentum and there will be a clearly visible real Coriolis force present that is viewable from outer space.

That is why I wanted to make some short amendments to the introduction. Most of the rest of the article needs to be binned and re-written with a clearer understanding of the topic.

When the term Coriolis force first started to get applied to meteorology, it was probably being used correctly for the real hydrodynamical effect that exists in conservation of angular momentum. But somewhere along the lines, some textbook writers have got it all confused in line with the modern science of fictitious forces. David Tombe (talk) 05:13, 4 February 2009 (UTC)

Which CoriolisForce?

I haven't been able to read this paper in full. But which Coriolis force do you think they are talking about? Are they talking about the cyclonic effect as per this article, or are they talking about the real hydrodynamical Coriolis force that I am trying to draw attention to,and which is what Coriolis himself had in mind?

[1] David Tombe (talk) 13:53, 5 February 2009 (UTC)

Common misconceptions : magnitude of effect dependent upon azimuth

"The magnitude of the drift depends on the location, azimuth, and time of flight."

The formula for the Coriolis acceleration in the Coriolis effect page doesnt show the direction of fire to affect the magnitude, as both north and easterly components of velocity affect the coriolis acceleration equally.

However in the External ballistics page of wikipedia there is a section which states that the magnitude of the coriolis effect is dependent upon the azimuth.

If the azimuth does not affect the Coriolis acceleration's magnitude, then maybe this could be a candidate for common misconceptions, as it has obviously slipped past many people in the external ballistics page. Please correct me if i am wrong, and the azimuth does affect the magnitude of coriolis acceleration/force.

Only the horizontal components are equal for every azimuth. In meteorological events these are the only important ones. For ballistics, the vertical component cannot be ignored and does depend on the azimuth. See the words on Eötvös effect. Firing North, initially does not generate a vertical acceleration. Firing East, makes the missile reach farther. −Woodstone (talk) 10:23, 22 February 2009 (UTC)

No difference

"In the inertial frame of reference (upper part of the picture), the black object moves in a straight line. However, the observer (red dot) who is standing in the rotating frame of reference (lower part of the picture) sees the object as following a curved path."

Where´s the difference? Either is the object following a curved path or the object which you call frame of reference is following one, because the object itself can also be seen as a frame of reference. By the way: in the first picture there are two observers which differ from each other (the person who sits in front of the display and the moving red dot) while in the second picture the observer behind the display (that´s you) is the same as the red dot - because they both don´t move.

In the first picture the black dot only makes a move down the y-axis, while the red dot moves in the x-axis to the right and on the y-axis upwards. In the second one the red dot doesn´t move at all while the black dot moves down the y-axis and first moves the x-axis to the right, comes to a halt and then moves the x-axis to the left. Therefore it´s not a fictitious force but the movement of the red dot on the x-axis in the first picture is fragmented into two parts of movement of the black dot on the x-axis in the second picture.

91.19.40.170 (talk) 11:54, 1 March 2009 (UTC)

Coriolis effect on Sinks and Toilets

My question has to do with the section Corrections to common misconceptions about the Coriolis effect. Anyway the part about Shapiro's experiments states something about a 'perfect sink'. What is that? It's not defined in this article, nor the article on Ascher Shaprio

--SunshineOdyssey (talk) 22:41, 26 March 2009 (UTC)

Confusing the Coriolis force with the cyclonic effect

The conservation of angular momentum means that there is no net transverse force, hence,

$2{\dot {r}}{\dot {\theta }}+r{\ddot {\theta }}=0$

The first term on the left hand side is the Coriolis force which is the transverse deflection of a radial motion in planetary orbits and in all vortices, and it is real. Coriolis force even exists in the water that swirls out of a kitchen sink. The Coriolis force is mathematically balanced by an equal and opposite angular force, $r{\ddot {\theta }}$.

The Earth's rotation sets the direction of angular momentum in the large scale cyclones in the atmosphere and in the ocean currents. The cyclonic direction is set by inertia. The cyclonic effect is too weak to be involved in small scale vortices such as the water swirling out of a sink and so the initial angular momentum is arbitrary. Tornadoes are cyclonic because of the existing angular momentum in the larger cyclones within which they form.

This article has got the Coriolis force mixed up with the cyclonic effect which is why they can't explain how a so-called fictitious force can cause a real effect that is observable from outer space. David Tombe (talk) 00:53, 14 April 2009 (UTC)

This article has got the heads mixed up with the tails on a coin, which is why it can't explain how a so-called head can mean that there is always a tail that is observable from the other side. I claim that there is no such thing as a head, there is only a tail, and there must be only one article that covers that. YHBT- (User) Wolfkeeper (Talk) 01:55, 14 April 2009 (UTC)

Wolfkeeper, I'm not sure that I get your point. All I was saying was that the Coriolis force lies inside the conservation of angular momentum, and not inside the cyclonic mechanism. By 'cyclonic mechanism', I am referring to the mechanism which causes the initial direction of angular momentum to be determined by the direction of the Earth's rotation. The Coriolis force will be present in all vortex phenomena and in non-circular planetary orbits. Even you are one of the few to have acknowledged the Coriolis force that defelects the radial motion in an elliptical orbit. That is a real effect.

The cyclonic mechanism is the inertial effect that is associated with the Earth's rotation and it determines the direction of large scale cylones and ocean currents, and even tornadoes. But it doesn't affect the water swirling out of a kitchen sink because it is not strong enough to overcome stray currents on that scale. The cyclonic effect does not involve Coriolis force. The apparent deflections that are associated with the cyclonic effect are only superimpositions. The real deflections that are associated with the Coriolis force can be viewed from outer space.

This article has got two effects confused. Nevertheless, a well written article would carefully explain both of these effects. There is no need for two articles, and I think that you agree with me on that point. David Tombe (talk) 11:03, 14 April 2009 (UTC)

There are not two separate effects. David Tombe is not correctly understanding the meaning of the term "fictitious," which doesn't mean "unobservable" or "nonexistent." He is also confused if he thinks there are two separate effects, one of which has to do with inertia and on of which doesn't; according to an observer in an inertial frame of reference, the a fictitious force is always attributable to inertia. He hasn't provided any sources for his statements, because his statements are incorrect, and reliable sources for them don't exist.--76.167.77.165 (talk) 00:32, 14 June 2009 (UTC)

Anonymous 76.167.77.15, you are confusing the Coriolis force with the apparent transverse deflection which is observed on top of the inertial path when we observe a motion from a rotating frame of reference. The Coriolis force is in fact already in the inertial path and it is tied up with the conservation of angular momentum. The Coriolis force does not require a rotating frame of reference. If howevever we have a constrained radial motion in a physically real rotating frame such as a turntable, then we will feel the Coriolis force resisting the dragging force. There are alot of editors here who are making the mistake of assuming that this topic is cut and dried. This weblink [2] which I have just found on the internet makes it clear that the issue is far from cut and dried. David Tombe (talk) 10:44, 21 June 2009 (UTC)

The so-called important lost sentence

Woodstone, would you kindly explain what exactly was so important about that sentence. I was trying to shorten the introduction by removing unnecessary sentences. We all know that force equals mass times acceleration.David Tombe (talk) 15:43, 25 April 2009 (UTC)

Ah, yes indeed, so normally, the heavier the object is, the less acceleration a force causes. However all the pseudoforces always cause the same acceleration, regardless of the body acted on. So the force itself is proportional to the mass. It is one of the clues giving away a pseudoforce. −Woodstone (talk) 19:49, 25 April 2009 (UTC)

Woodstone, The situation is no different than in the case of gravity. The acceleration of an object due to gravity, relative to the common centre of mass, is independent of that object's own inertial mass. And the very involvement of a centre of mass, as per Newton's third law, means that in actual fact, the acceleration is ultimately dependent on its own mass. This is an interesting topic which can only become fully understood once we introduce the concept of charge to mass ratio. The charge to mass ratio is constant when we are studying gravity, large scale centrifugal force and large scale Coriolis force and so the 'same acceleration' effect which you have mentioned above is somewhat of an illusion. The proportionality of these forces with mass is not a feature that is in anyway connected with the fact that the latter two, centrifugal force and Coriolis force, are connected with rotation. That's why I don't think that it needs to be mentioned in the introduction to this article. David Tombe (talk) 00:40, 26 April 2009 (UTC)

According to the equivalence principle gravity is an acceleration of the reference frame. As such, gravity may be considered to be due to a non inertial frame of reference, and that is why the 'charge to mass' ratio as you put it is constant.- (User) Wolfkeeper (Talk) 03:42, 26 April 2009 (UTC)

Wolfkeeper, When all the facts are in, you will see that the sentence which Woodstone insists on having in the introduction is nothing more than a statement of Newton's second law of motion. Consider the radial equation as applied to a planetary orbit. The two planets will orbit about a common centre of mass. That is where both their masses becomes of importance. And that is equally so for both the inverse square law gravity term and the inverse cube law centrifugal term. See problem 8-23 at the end of chapter 8 of Taylor. Here is the relevant equation,

${\ddot {r}}=-k/r^{2}+l^{2}/r^{3}$

The apparent inertial mass independence is as relevant to the centrifugal term as it is to the gravity term, and it should be noted that it is only apparent. It is only apparent because their inertial mass determines their actual acceleration relative to the common centre of mass. David Tombe (talk) 12:36, 26 April 2009 (UTC)

Bad Coriolis

There's an interesting web link here called 'Bad Coriolis'. It's a few questions and answers, and one of them highlights the ultimate controversy in this topic. See [3].

See the question a few sections down entitled 'the teacher was right'. The debate is over whether or not the Coriolis force acts on any velocity, or only just radial velocities. When textbooks are dealing with the topic 'rotating frames of reference' the Coriolis force is free to rotate in any direction according to the inducing velocity, like a weather cock on a pole. This view comes from looking at the final mathematical result while ignoring the restrictions that were implicit in the derivation. But in planetary orbital theory, the Coriolis force is strictly and unequivocally confined to the transverse direction, and specifically induced by radial motion.

So we have one lot of textbooks attributing the Coriolis force to the inertial effect, and we have other textbooks putting it down as a real transverse force that is connected with the law of conservation of angular momentum.

Both cannot be right. Should this controversy be highlighted in the main article? David Tombe (talk) 19:33, 21 May 2009 (UTC)

The Coriolis force as arising from a rotating reference frame cannot rotate in "any direction". It is always perpendicular to the rotation axis. In the derivation there is no assumption preventing a radial component. −Woodstone (talk) 21:39, 21 May 2009 (UTC)

These is indeed no such conflict as David imagines. In the planetary orbital theory that he describes, the reference frame co-rotates with the planet, so the planet's motion is necessarily only radial in that system, limiting the Coriolis force to tangential, just as the usual theory says it would be. Dicklyon (talk) 22:03, 21 May 2009 (UTC)

Dick and Woodstone, And just what makes you so sure that the derivation of the rotating frames transformation equations does not restrict the Coriolis term to the transverse direction? In planetary orbital theory, which uses the exact same calculus, the Coriolis force is strictly a transverse force that is tied up with Kepler's second law (conservation of angular momentum). And if you are genuinely interested in this topic, I can easily point out to you exactly where this same restriction is implicit in the derivation of the rotating frames transformation equations. You are only looking at the final result and turning a blind eye to the restrictions that were implicit in the derivation.

And that is the whole problem surrounding the entire issue of Coriolis force and centrifugal force. One lot of textbooks don't know what another lot are doing. Indeed in some cases, one chapter in the same textbook doesn't know what another chapter is doing. It is the height of nonsense to superimpose Coriolis force on top of centrifugal force in the radial direction. They are basically both two mutually perpendicular aspects of the same effect.

And indeed, in the course of time, you will hopefully realize that there are indeed three mutually orthogonal pressure effects which arise out of the dipolar nature of space. These are (1) the radial centrifugal force, (2) the transverse Coriolis force, and (3) an axial Coriolis force that arises in gyroscopes and rattlebacks. David Tombe (talk) 13:05, 22 May 2009 (UTC)

Coriolis Force in Lagrangian Mechanics

This article needs to have a section on the Coriolis force in Lagrangian mechanics which includes a worked practical demonstration. It will involve the product of mutually perpendicular generalized speed coordinates. It will therefore need to involve the product of a radial and a transverse velocity which apply to the same particle but which are physically distinct effects. In other words, the two mutually perpendicular velocities can't simply be the components of a simple motion. We would need to look at some kind of compound motion that involves a rotation containing a constrained radial motion. David Tombe (talk) 13:35, 11 June 2009 (UTC)

I would be very surprised if you found a source in which the velocity vector with radial and tangential components couldn't be treated as an ordinary velocity vector. Dicklyon (talk) 15:21, 11 June 2009 (UTC)

Dick, and since when have we been able to obtain a Coriolis force by multiplying together the two mutually perpendicular components of a single velocity vector? The Lagrangian formulation claims that Coriolis force is just such a product, and so it requires some elaboration as regards the underlying physics. David Tombe (talk) 12:21, 12 June 2009 (UTC)

Never, obviously; not clear what's confusing you here. Dicklyon (talk) 12:42, 12 June 2009 (UTC)

Dick, the ones who are confused are the ones who have got Coriolis force mixed up with the apparent circular motion that is imposed on top of the inertial path when we make an observation from a rotating frame of reference. The Coriolis force is actually in the inertial path itself, and it has got nothing to do with apparent deflections. The Coriolis force is part of the conservation of angular momentum. It is a real transverse force in a vortex and it is the product of two mutually perpendicular velocities which arise in a compound motion ie. a constrained rotating radial motion. That's what is meant by the product of Vi and Vj in the Lagrangian section on the centrifugal force page. We feel the Coriolis force as an inertial resistance to dragging forces that constrain a radial motion on a rotating platform. David Tombe (talk) 11:24, 14 June 2009 (UTC)

Figure 3 - suggestion for correction

the angle between green line (or better tangent to green line) at point green 1 and red line should be also theta! (the cannonball starts at point green 1 under angle theta to the target) —Preceding unsigned comment added by Boed00 (talk • contribs) 16:55, 28 July 2009 (UTC)

The Coriolis Force as a product of two mutually perpendicular velocities

Recently, the introduction was corrected to the extent that the centrifugal force is more accurately proportional to the square of the angular speed. This is correct. But what about the Coriolis force? For those who believe that the Coriolis can sometimes be in the radial direction, then by the same reasoning, the Coriolis force can also sometimes be proportional to the square of the angular speed. According to Lagrangian mechanics however, the two velocity terms in the Coriolis force will always be mutually perpendicular and there will be no such thing as a radial Coriolis force, in which case the introduction is absolutely correct as it now stands. I totally agree with the Lagrangian formulation in this respect. However the textbooks in general allow for a radial Coriolis force. So how do we cater for this in the introduction in relation to whether or not the Coriolis force might also sometimes be proprtional to the square of the rotation speed? David Tombe (talk) 07:33, 6 August 2009 (UTC)

Since no one reacted to this remark so far, I might as well give a late answer. The intro says correctly the the Coriolis force is proportional to the rotation speed of the frame and to the velocity as observed in the rotational frame. If the latter factor happens to be proportional to the rotation speed as well, the combined effect of both proportionalities is quadratic. This is the case for objects that are stationary in the inertial reference frame. Nothing mysterious here. And no need to change the intro. −Woodstone (talk) 21:45, 6 September 2009 (UTC)

The coriolis force is only fictitious when observing from a different frame of reference it is a real force in many situations. The simplest one to explain is to imagine water travelling along a hose pipe at a fixed speed v. Now imagine taking the hose pipe from the tap end and swinging it around, parallel to the ground with the water still flowing. You have added a rotation w and the water column will experience a real force equal to 2vw. v and w are both vectors( in this example the w vector will be a vertical axis so multiplying them produces another vector at right angles to both using the right hand rule you can find the direction of the force. If you constrain the hose to be rigid you will then generate a considerable radial acceleration of the water in the hose! When weather system migrate from the equator, say northwards, they are forced to travel at reduced radius as they go north and the coriolis acceleration and forces are real there too, they are essential to understand the rotating and vertical components of the airstreams.--Profstandwellback (talk) 17:10, 24 October 2009 (UTC)

Rossby number

The Rossby number compares the inertial and Coriolis forces. This characterization is a bit confusing because Coriolis and centrifugal forces are often referred to as inertial. A more accurate description is to say that the Rossby number is the ratio of the convective and Coriolis terms in the Navier-Stokes equation in a rotating frame.

The convective term and Coriolis terms are

$\mathbf {v} \cdot \nabla \mathbf {v}$ and $2\Omega \times \mathbf {v}$,

respectively, while the centrifugal force is

$\Omega \times \Omega \times \mathbf {r}$

See Navier-Stokes Equations--Rotational.

There is also centrifugal force connected with circular motion in the rotating frame itself, subsumed in the inertial term of the Navier-Stokes equation. But it is confusing to conflate the this inertial force with the centrifugal force caused by the rotation of the reference frame. I've modified the discussion on the Rossby number in this article to reflect the distinction.

--Drphysics (talk) 20:15, 6 September 2009 (UTC)

Is this sentence correct?

"Moving objects on the surface of the Earth experience a Coriolis force, and appear to veer to the right in the northern hemisphere, and to the left in the southern."

To me, it seems that an object moving south in the southern hemisphere would appear to veer to the right, not the left as stated in the sentence.

Mark.camp (talk) 03:08, 12 December 2009 (UTC)

Left and right are defined relative to the movement. Imagine a driver moving forward due south. Veering to his left turns out to be eastward. Looking at the globe North up, that may look to the right to you. −Woodstone (talk) 12:52, 12 December 2009 (UTC)

Yes, left and right are defined relative to the movement. But the direction relative to earth of an object moving initially south, and not subject to a sideways real force becomes more westward, not more eastward, correct? As you say, veering to his left is eastward, so veering westward is veering right, not left as the sentence says in the case of the southern hemisphere.

For the sentence to be correct, wouldn't one need to specify whether the object is moving south or north? Or am I misinterpreting the sentence?

Mark.camp (talk) 20:14, 22 December 2009 (UTC)

The relative direction of deflection does not depend on the original direction, only on the hemisphere. In the southern hemisphere any moving object experiences a Coriolis force to the left of the moving direction. So an object initially moving south will veer east. Note that an object moving north in the northern hemisphere will also veer east. In both cases, moving away from the equator will make the object veer in the direction of rotation. The rotational speed it had closer to the equator makes it run ahead of the ground under it. −Woodstone (talk) 21:16, 22 December 2009 (UTC)

I understand the error in my thinking now.

I had pictured a clockwise-turning carousel, with a line painted on it from some point X to the center. A free object moving straight toward the center is at X at time zero, so it is on the line at time 0. Moments later at time "t1", it is to the right of the line, and to an observer on the carousel appears to be moving to the right. Since it was moving straight to the center and was on the line, and now it is to the right of the line and appears to be moving to the right, I inferred that it had veered right to the observer on the carousel.

My mistake was in not realizing that at time zero the object is already moving somewhat right in the carousel frame of reference; the fact that it is moving straight to the center in an inertial frame is irrelevant to the question of how it looks to one on the carousel . At time t1, yes it has moved to the right of the line, and yes it is still moving right perhaps, but the important thing is that its direction is less to the right than before. So, it has now veered leftward, as it must in order to hit the middle post of the carousel.

Simple explanation

I really miss a simple explanation of how the Coriolis effect ACTS. There are all these kinds of equations and diagrams describing it, but not a single iota about why it is like it is.

[This link] is now on the article page -- it does a good job of explaining the effect without requiring the reader to have a master's in mathematics.

The first thing to realise is that it is basically an inertial effect causes by the rotation of the earth. So if everyone could be nice enough to leave that comment in it would help basic understanding without going into detail.

Saying C.E. is caused by C.F. says nothing. —Preceding unsigned comment added by 95.176.124.31 (talk) 10:44, 16 September 2010 (UTC)

It does not say nothing: it introduces terminology. The statement about rotation of the earth does not fit where it was put, because at that point in the introduction, the focus is on rotating systems in general, not only the earth. Rracecarr (talk) 13:53, 16 September 2010 (UTC)

Incorrect explanation of the Coriolis effect?

I'm still reading up on my Coriolis effect so correct me if I'm wrong, but isn't the following explanation insufficient or even false?

The effect on Earth is due to this fact: the Earth is rotating fastest at the equator, and rotates not at all at the poles (in km/hr). A bird flying north, away from the equator, carries this faster motion with it (or, equivalently, the earth under the bird is rotating more slowly than it was) - and the bird's flight curves eastward slightly (though its heading stays straight north). In general: objects moving away from the equator curve eastward; objects moving towards the equator curve westward. Moving away from the equator, the land underneath rotates more slowly, and vice-versa. An object gains or loses relative speed over ground as it moves away from, or towards, the equator, respectively.

If the coriolis effect is due to variations of the earths speed of rotation, then there should be no effect at all on objects traveling strictly in a west-east/east-west direction. In this case the earths speed of rotation is constant along the objects path and no drift off would be observed. But since the coriolis effect exists in all directions of travel, the above explanation is insufficient.

Aspartam (talk) 11:19, 28 March 2010 (UTC)

The explanation given is a simplified statement of the complete effect, but is correct in broad terms. Similarly simplified, a particle travelling straight East, would tend to follow in a straight line lifting up perpendicular to the axis. The projection of that on the ground, to which the particle is bound by gravity and pressure, veers off towards the equator. Conversely, a particle moving West is overtaken by the groundspeed and pursues its straight course down towards the axis, sliding off towards the pole. This is a tricky issue, that should be understood by looking at the full 3-D picture. −Woodstone (talk) 15:38, 28 March 2010 (UTC)

Well put, I got it now. Personally, I would like the quoted section above to be extended with what you just wrote to clarify the effect when an object is traveling east/west bound. However that might just overcomplicate the simplification, so I won't be pushing the issue. Thanks for the clarification! Aspartam (talk) 16:36, 28 March 2010 (UTC)

I guess you could then say that the travel of hurricanes is first a retarded drift of the developing storm along the trade winds latitude to the point where it stops that and then drifts north and east due to the coriolis effect. Does that sound right?WFPM (talk) 18:25, 16 May 2010 (UTC)

Coriolis force

I am afraid I do not understand paragraph 2: which way is the bird flying, parallel to or at right angles to the equator; where is the particle starting from, etc.?Ardj (talk) 12:02, 28 April 2010 (UTC)

The bird is "flying away" from the equator. That is enough information to make it veer eastward. The easiest case is evidently flying North or South and noting that after a while it will certainly not be on the equator. −Woodstone (talk) 15:10, 28 April 2010 (UTC)

Tossed ball

A person holding a ball at the 12 o'clock position is holding a ball that is rotating counterclockwise, and consequently moving to the left. If he then pushes it in the direction of the center of the carousel it is going to veer to the left, and the outside observer is going to see that. I don't think that's what the image is illustrating.WFPM (talk) 13:56, 15 May 2010 (UTC)

I presume you're referring to the account given in this section of the article. The opening sentence of the account is admittedly ambiguous, but where it says the ball "is tossed from 12:00 o'clock towards the center" I don't believe it intends to suggest that the thrower has aimed the ball directly at the center, but that he has aimed it in a direction which will cause its motion to be directed towards the centre after it has left his hands. Since, as you say, the thrower is moving to his right at the time, he will actually have to aim it somewhat to the left of the centre to get it to move in the proper direction. Nevertheless, I agree that the sentence should be reworded to make it clearer.

David Wilson (talk · cont) 20:35, 15 May 2010 (UTC)

Yeah, he would have to make a pretty quick and nifty calculation to correctly determine the direction to throw the ball, and most would throw in the line of sight direction. And isn't it the coriolis effect that is causing the tossed ball to veer to his right?WFPM (talk) 00:29, 16 May 2010 (UTC) I think my confusion was where I read that the ball was tossed "toward the center".

bounced ball

I'm afraid i'm giung to have to disagree with the bounced ball images, because the ball bounces before the time of arrival of B at the site of the bounce, and since it bounces away at the same angle of exit as was the angle in incidence, so B will have to move away from the rail to catch the ball, which is not the implication of the image. To catch the ball at the rail, he would have to move to the next point of impact of the ball with the rail.WFPM (talk) 00:18, 19 May 2010 (UTC) And that's a pretty complicated double-banked throw trajectory even on a nonrotating pool table.WFPM (talk) 00:24, 19 May 2010 (UTC) But think about it, and maybe we've invented a new sophisticated game of Pool or better Snooker, where we use a rotating table.WFPM (talk) 00:27, 19 May 2010 (UTC)

inertial circles

In the inertial circles section all the measurements of distance and direction and resultant motion characteristics are related to the "inside frame" or the rotating frame of reference. And with reference to this phenomena it should be noted that there is no "stationary frame of reference" location where such motions could be taken and measured without an elaborate corrective calculation relative to the position of that location. A distorted view of such motion could be observed from either a polar view of the activity, or that from a synchronized rotation orbit of the observer with that of the rotating object of observation (as would be needed to observe the described "circular motion" in the atmosphere). And neither of these locations would tell us as much about the details of the phenomena as do the rotating frame (inside) measurements. But if you're inside of a rotating carousel and carrying a strain gauge tied to the center of rotation and noting the increase in the restraining (centripetal) force that is occurring in the retaining line as you move away from the center, it is hard to not believe that that there aren't at least two real physical properties related to that observed motion. And they are 1: The increase in the competing static forces, which is proportional to the square of the velocity. And 2: The increase in the angular momentum (Mvr), which can also be called (M times omega times r squared), which can again be called (M times the unit kinetic energy value times the angular rotation rate of change). So as we know from watching ice skaters, and increase in the radius of constant angular motion involves a conversion of potential energy of position to a kinetic energy of motion based on measurements taken within an inertial frame of measurement.WFPM (talk) 19:50, 20 May 2010 (UTC)

Intuitive application to Earth

Disputed section:

A particle traveling east would tend to follow straight on, lifting off in a plane perpendicular to the axis. The projection of that on the ground, to which the particle is bound by gravity and pressure, veers off towards the equator. Conversely, a particle moving west does not keep up with the ground speed and pursues its straight course bending down towards the axis, sliding off towards the pole.

How is this wrong? The particle moves west relative to the ground, so in absolute view it does not move fast enough to keep up with the ground moving east. Try to imagine it. A moment later the ground has rotated a certain angle, so the original horizontal direction now cuts into the ground going west. Anyway, it cannot be wrong, because it follows from the exact formula. Other people found it enlightening (see under 2). −Woodstone (talk) 16:15, 19 August 2010 (UTC)

Maybe it's not wrong. But it is not explained clearly enough to avoid giving the wrong idea. I don't understand exactly what it's trying to say, and I'm pretty good with geometrical reasoning. To me, an intuitive explanation is that since motions on the surface of the earth are constrained to a 2D surface, only the component of the earth's rotation about local vertical contributes to the Coriolis effect. Wherever you are you can think of the ground rotating beneath your feet, just as it does at the pole, but the rotation rate is given by the angular velocity vector of the earth projected onto the local vertical. That makes it clear that east-west motion is fundamentally no different from north-south motion.Rracecarr (talk) 13:27, 20 August 2010 (UTC)

Yes, that is fully correct, but it is just stating in words what is said by the formula in the next section. What people have been asking for is an explanation more from an inertial viewpoint, so without invoking the formulas. For North/South movement that is easy to do by showing the inertial gain/loss over groundspeed. For East/West movement it is more difficult, since it involves both the 3rd dimension (up/down) and the 2 dimensional limitations imposed. That is what the contended phrases try to do. At least one other editor liked the explanation. −Woodstone (talk) 14:59, 20 August 2010 (UTC)

I don't think there is anything wrong with stating in words what the math says. Some people find it easier to read words. If there is a way to avoid words like "angular velocity vector," I'm all for it, but as it stands I don't understand what the meaning of the explanation. The explanation for an eastward moving particle sounds like it just explains curvature toward the equator along the great circle route, which would occur without rotation and has nothing to do with Coriolis. For westward moving particles, I don't understand what is meant by "does not keep up with the ground speed". Rracecarr (talk) 17:17, 20 August 2010 (UTC)

Perhaps the analogy to the skater's spin would help. After all else, the Coriolis effect is that of conservation of angular momentum: as a particle approaches it's center of rotation (the sun, the axis of the earth, the skater's vertical posture) it's mass and kinetic energy (speed) are constant, but it's length of orbit (circumference) decreases. If it's speed is constant, and there is less distance in the orbit, it will travel more (degrees) of its orbit in any given time. (The converse is also true: a constant speed yields a decrease in RPM for increase in radius.)
This seems counter to experience, but we directly view small orbiting objects differently than free trajectory (thrown) objects, in that we perceive the increase in RPM as an increase in speed, even though it is measurably not. I presume this is because, during most of human evolution we have had little direct experience with changes in orbital distance of free (perpendicular deflection only) moving objects. The only exceptions I can think of are the bolas, certain yoyo tricks, and more subtly, toilet/sink drains. These seem to have been common for less than a few thousand years, apparently not enough exposure to sufficiently influence development of our neurological processes to predict/perceive these object movements clearly. Although the Coriolis effect is subtle, it affects all "moving" objects on the earth, except at the poles. An object thrown straight up at the pole, is not affected. (There are no exceptions at the equator.)

• This should not be confused with the (unnamed?) phenomenon that all stationary objects of the earth, except at the axis and equatorial plane are subject to another subtle influence: there is a difference between their constant tendency to follow a 'natural' orbit around the center of the earth in a great circle, and their actual orbit (due to their attachment to their surroundings) around the axis of the earth at their current latitude (following a circle of latitude). Because of this, tall objects cannot stand exactly straight up. They must compensate for the divergence of the two paths by force or balance, leaning into this apparent centrifugal force.
  

It is easiest to visualize the effect under simple conditions, and then extrapolate to the more complex conditions between them. The Coriolis effect is based entirely on the change in the instantaneous distance from the axis of the earth, not altitude from the surface. For this exercise, I will ignore many subtle conditions for the sake of simplicity, so try not to be too picky. To get a more 'objective' understanding, let's first consider standing at the North Pole in the autumn, on a relatively smooth, stationary, sea level ice field there. While facing the sun (compensating for the earth's rotation by turning westward at 4deg/min), throw a baseball straight toward the sun, just as your catcher in the distance passes under the sun. You will see the ball straight toward the sun until it becomes obvious that it is being pulled straight down toward the horizon (the center of the earth), still in the plane of you (the axis of the earth) and the sun. But during its flight, your still standing friend has moved eastward (to your left) with the rest of the world. While staring into the sun, you knew it was a good pitch, but your friend wonders why you threw a stupid curve ball, and if you had moved your fixation to your catcher after the ball left your hand, you too would see your 'perfect' pitch as a stupid curve ball to the right. You can blame it on the fictitious Coriolis force which you both see pushing your ball to the west. You might both be surprised to see the ball bounce, not straight south, but slightly to the east, as it catches up with the earth's spin.
When he throws it back, he fails to compensate for his eastward movement (which he cannot perceive without looking closely at the stars behind you), and you both see the ball curve to the east as his rotational momentum, imparted as it stopped rolling, before he even picked it up, continues to carry it eastward of the line between you (still rotating about you at 4deg/min, after his release, because the orbital speed component (horizontal vector perpendicular to the line between you) of his pitch (same as that of his body) translates to a greater number of degrees per second.
In both cases so far, the thrower sees the ball pushed to the right as it follows the trajectory you sent it on before your own references continued moving. In these two pitches, we ignored the less significant effects of our moving around the sun, so you can take this one step further down in scale, and repeat it on a playground platform merry-go-round or empty carousel, where the effects will be satisfyingly severe. At this point I will pause to mention that as a general rule, projectiles track over a great circle. That is because the instant they leave the projector, their deflection from a straight line into space, is primarily due to gravity. No matter their direction, they are 'in orbit' around the center of the earth, until they hit its surface.

The other extreme situation is on the equator, where the effects will be much more subtle, because there is usually less change in orbital radius (OR), and no difference in OR between the pitcher and catcher, whether you throw along the equator or across it. The only Coriolis effect is in the flight path, and that of coming down compensates for that of going up, producing a sinuous rather than simple parabolic path. So to change the scenario slightly, if you fire a mortar straight up, the ball would curve to the west, just as your spin slows down as your hands extend, and the descent would almost retrace its curve, back to the east (just as your spin hastens as you pull your hands in), and land back near your mortar, still 'orbiting the earth, with you, at 1040mph. It might help to also imagine yourself standing in space, on the axis of the earth as it spins in front of you, and watch the mortar on the equator, in profile as it fires.

• I will leave it to you to repeat the polar scenario at the south pole.
• Later, you might like to explore the similar issues of Solar sails.

In between these simple extremes (pole & equator), we have much more complicated situations, and illustrations would be helpful (but I have none). For this last example, you might fire a cannon ball (along Lon. -80.5) toward the north pole, from Cape Canaveral (lat=28deg & about 3,480 miles from earth's axis, 3963mi from its center, and spinning eastward at 911mph). At reasonable muzzle velocities, you would need to fire at a fairly high angle (greater than 28deg). The ball (ignoring drag losses) would first go somewhat away from the axis of the earth, slowing it's angular speed with respect to the axis, and diverting somewhat to the west (as all things going straight up would also do) until a little before its parabolic apogee, where it starts back toward the earth's axis (not yet toward the earth). At that point, because it is approaching the earth's axis it will begin to increase its angular velocity as indicated by the Coriolis rule. By the time it passes its apogee, and again reaches 3480mi from the earth's axis, it will have 'caught up' with Cape Canaveral (about lon=-80.5), and will continue increasing its angular velocity, hitting the earth east of the Lon. -80.5 we aimed at.

• The above description needs work, but it might be useful as is.

At the micro/macroscopic level the slight imbalance in the Coriolis effect on dropping water or air, allows the formation of whirlpools and typhoons.
Wikidity (talk) 22:48, 30 May 2011 (UTC)

• Earth rotates at about 4deg/min or 7sec/sec. :-) 'English is not as good as I wish telepathy were.'
• Standing on the equator, you're traveling around the earth at about a thousand mph. At the poles, 0mph. (less significantly, you're about 13mi closer to the center. What is your difference in weight?
  Wikidity (talk) 22:48, 30 May 2011 (UTC)

Acceptable editing practice

rracecarr . Please do NOT blanket revert changes like this:

http://en.wikipedia.org/w/index.php?title=Coriolis_effect&action=historysubmit&diff=385164056&oldid=385155741

there are many edits here that were inserted individually to allow discussion of each issue and individual mods as needed. The only thing these have in common is that they don't suit you. That is not a valid reason to delete them , neither do many even relate to the comment you give as reason for the edit.

"undo many edits. the coriolis effect is fictitious in just the same way as the coriolis force"

As well as the fact that you don't seem to understand the subject if you can write that. The coriolis effect is REAL (at least the oceans and the atmosphere think to) , it is a real and direct result of inertia and the earths rotation. What is fictitious is the coriolos force. This fictitious force is needed in order to use newtonian mechanics in a rotational frame. You still don't seem to have grasped the basics here but persist in reverting any attempt to improve the article.

From now on please make single changes and justify each change with a credible comment rather than just undoing everything I do. —Preceding unsigned comment added by 95.176.116.89 (talk) 12:23, 7 October 2010 (UTC)

"Flow around low-pressure area" correction?

In the section, “Flow around a low-pressure area”, should “At high altitudes, outward-spreading air rotates in the opposite direction.” actually read “At high latitudes, outward-spreading air rotates in the opposite direction.”? And, does the writer mean “At high northern latitudes low-pressure areas turn clockwise.”? 76.212.128.2 (talk) 22:29, 18 December 2010 (UTC)

Bathtubs

Moved from the article. Materialscientist (talk) 05:43, 4 February 2011 (UTC)

The text below does not seem to state why water does indeed always drain one way out of the basin. It implies that only in rare cases would planetary rotation effects cause this, and yet it is observed to be true every time we flush or drain a sink (it always goes the same way). Even if this is due to 'residual' rotation in the 'container', would that not also be due to planetary rotation and the water in the container lagging being it? — Preceding unsigned comment added by 24.91.83.115 (talk • contribs)

I agree. The text covers the subject in detail and does not, in my opinion, contain any actual errors, however it does not give a clear answer on the subject to the casual reader. I suggest that some wording is added to the effect that the Coriolis effect is completely insignificant in all practical cases. Martin Hogbin (talk) 11:22, 6 February 2011 (UTC)

Draining in bathtubs and toilets

In 1908, the Austrian physicist Otto Tumlirz described careful and effective experiments which demonstrated the effect of the rotation of the Earth on the outflow of water through a central aperture.[27] The subject was later popularized in a famous article in the journal Nature, which described an experiment in which all other forces to the system were removed by filling a 6-foot (1.8 m) tank with 300 US gallons (1,100 l) of water and allowing it to settle for 24 hours (to allow any movement due to filling the tank to die away), in a room where the temperature had stabilized. The drain plug was then very slowly removed, and tiny pieces of floating wood were used to observe rotation. During the first 12 to 15 minutes, no rotation was observed. Then, a vortex appeared and consistently began to rotate in a counter-clockwise direction (the experiment was performed in Boston, Massachusetts, in the Northern hemisphere). This was repeated and the results averaged (Averaged? - What were the actual numbers? Goes a long way toward giving the reader a sence of just how subtel the effect is. :-))to make sure the effect was real. The report noted that the vortex rotated, "about 30,000 times faster than the effective rotation of the earth in 42° North (the experiment's location)". This shows that the small initial rotation due to the earth is amplified by gravitational draining and conservation of angular momentum to become a rapid vortex and may be observed under carefully controlled laboratory conditions.[28][29] — Preceding unsigned comment added by 67.110.217.161 (talk) 07:25, 3 January 2012 (UTC)

I would be inclined to double check that over a number of experiments. I have never found any preference as regards which direction water swirls out of a sink. Are you sure that you are not using the same sink each time and using water which has been given its angular momentum from the same tap? We all know that conservation of angular momentum occurs and that the vortex in the sink is a concentration of the existing angular momentum. But that existing angular momentum is generally speaking random. It's only in large scale atmospheric cyclones that the Earth's rotation is involved in determining the direction of the initial angular momentum. If I were you, I would do a few more experiments and report back if you are still getting anti-clockwise rotation everytime. The demonstrators at the equator, where the effect is least likely of all to occur, use squarish basins and they rotate as they stand up while picking the basin off the ground, so as to generate the preferred angular momentum. David Tombe (talk) 20:54, 6 February 2011 (UTC)

I think I may have misread the OP. In all practical cases the direction of rotation of water has nothing to do with Coriolis force. Martin Hogbin (talk) 21:34, 6 February 2011 (UTC)

In a demonstration at the equator in Ecuador I saw, they filled a tub with water and released on north side, south side and on the equator. North it went counter-clockwise, south it went clockwise and on the equator it went straight down without a vortex. The tub was on a stand and not moved by the demonstrator during draining. —Preceding unsigned comment added by 203.38.62.211 (talk) 06:52, 27 February 2011 (UTC)

Wow. I once saw a magician saw a woman in half and then a minute later she was in one piece and unharmed. Will miracles never cease?AE Logan (talk) 02:39, 23 December 2011 (UTC)

Correct. It has got nothing to do with the Coriolis force in relation to the rotation of the Earth. There is however a Coriolis force in the vortex in relation to a rotation axis centred on the vortex itself. This Coriolis force in the vortex is equal and opposite to another inertial force which causes the transverse speed of the elements of the water to increase as the radial distance from the sink decreases, and hence angular momentum is conserved. But the direction of the angular momentum of the vortex will not be determined by the rotation of the Earth. It's only in the large scale cyclonic phenomena where the Earth's rotation determines the actual direction of the angular momentum. Theoretically of course, the same principle applies to the small kitchen sink vortices, but in practice, local currents will always over ride the negligible effects of the Earth's rotation. David Tombe (talk) 23:01, 6 February 2011 (UTC)

The consensus here is that Earth's rotation is not going to have any practical effect on sink and toilet drains. That's a relief, because the difference in Earth's velocity between two points even 6 feet apart is spectacularly small. Yet this section of the article is worded in such a way as to suggest it's possible the Earth's rotation can have an effect on these things. I realize this isn't the most scientifically meaningful segment of the article, but I have a feeling a lot of barroom bets are based on it. I think it would help to state explicitly in this section that the Earth's rotation has no practical effect to which way toilets and sinks drain. (69jpil69 (talk) 22:25, 9 May 2011 (UTC))

I believe the text was simpler before than now in the Coriolis_effect#Draining_in_bathtubs_and_toilets section. The reader gets lost through details and cannot conclude whether or not draining toilets significantly causes water to rotate in Northern hemisphere opposite to that in Southern hemisphere. It would be recommended to make this point clear before going into the story and details.--195.94.11.17 (talk) 20:16, 27 August 2011 (UTC)

I agree that we should make clear that there is no practical effect of Coriolis force on the draining of a sink. The currebt article is thoroughly misleading. Martin Hogbin (talk) 23:16, 27 August 2011 (UTC)

In contrast to the above, water rotation in home bathrooms under normal circumstances is not related to the Coriolis effect or to the rotation of the earth, and no consistent difference in rotation direction between toilets in the northern and southern hemispheres can be observed. The formation of a vortex over the plug hole may be explained by the conservation of angular momentum: The radius of rotation decreases as water approaches the plug hole so the rate of rotation increases, for the same reason that an ice skater's rate of spin increases as she pulls her arms in. Any rotation around the plug hole that is initially present accelerates as water moves inward. Only if the water is so still that the effective rotation rate of the earth (once per day at the poles, once every 2 days at 30 degrees of latitude) What? is faster than that of the water relative to its container, and if externally applied torques (such as might be caused by flow over an uneven bottom surface) are small enough, the Coriolis effect may determine the direction of the vortex. Without such careful preparation, the Coriolis effect may be much smaller than various other influences on drain direction,[30] such as any residual rotation of the water[31] and the geometry of the container.[32] Despite this, the idea that toilets and bathtubs drain differently in the Northern and Southern Hemispheres has been popularized by several television programs, including The Simpsons episode "Bart vs. Australia" and The X-Files episode "Die Hand Die Verletzt".[33] Several science broadcasts and publications, including at least one college-level physics textbook, have also stated this.[34][35] — Preceding unsigned comment added by 67.110.217.161 (talk) 07:38, 3 January 2012 (UTC)

General Relativity

There is an article on the Coriolis field. I think it should definitely be merged into, or at least referred to in this article because the Theory of General Relativity is designed to deal with these matters without any need for inertial frames or fictitious forces and has been proven correct for a while also. I am sure someone with enough mathematical skills can do this properly. The article about the Coriolis field still has no references or formulas, so it needs some work.Viridiflavus (talk) 18:09, 12 May 2011 (UTC)

Sun and distant stars

A recent edit removed the section The Sun and distant stars from the article on the alleged grounds that it was "erroneous". A subsequent edit restored it on the alleged grounds that it wasn't. I nearly did this myself until I checked the calculations more carefully and found a couple of problems with them.

In the first place, because of the Earth's annual revolution about the Sun, the origin of any coordinate system which is fixed with respect to the Earth must be undergoing an acceleration, which therefore gives rise to a pseudoforce in the opposite direction in the equations of motion in that coordinate system. Although the magnitude of this pseudoforce's action on the Sun is some two orders of magnitude smaller than those of the Coriolis and centrifugal pseudoforces, it is not negligible, because—except at the equinoxes—it has a non-zero component along the Earth's axis, which the other two pseudoforces do not. In the fixed-Earth coordinate system, therefore, it is only the pseudoforce resulting from the acceleration of the coordinate system's origin which can account for the Sun's apparent motion in declination, which can amount to as much as 0.4° per day (at the equinoxes).

Strictly speaking, the same considerations apply to the apparent motions of stars other than the Sun, but even the closest of those is so far away that the effects of the pseudoforce resulting from the acceleration of the coordinate system's origin are effectively negligible (unless one wants to account for the annual parallax of those stars that are sufficiently close to have it).

The second problem is the (to me) confusing and unnecessary distinction between stars with zero declination (i.e. directly above the equator) and those with non-zero declination. Provided the equation Ω ⋅ r = 0 is replaced with the more general Ω · r = |r| Ω sin(δ), where δ is the (fixed) declination, exactly the same equations can be applied to any star, regardless of whether its declination is zero or non-zero. Nor do I understand why the case of stars with non-zero declination should be described as "more complicated", or the explanation of this supposed complication that was given in the previous version of this section. In a coordinate system which is fixed with respect to the Earth all distant stars, regardless of their declination, move around circles centred on, and perpendicular to, the Earth's axis.
David Wilson (talk · cont) 03:05, 29 September 2011 (UTC)

It said the motion of the Sun was dominated by the Coriolis and Centripetal forces, which is correct. The additional gravitational force on the Sun is much smaller than the C&C forces, as evidenced by the fact that the annual (orbital) motion of the Sun is about 365 times smaller than the daily (rotational) one. The section was inserted at a time when there was a vehement discussion whether the C&C forces would apply to static objects and was kept as simple as possible. Why did you remove the section that pointed out the observed curved path of rising, culminating and setting, caused by applying Buys Ballot's law to stars? It is the ultimate consequence. −Woodstone (talk) 09:05, 29 September 2011 (UTC)

"It said the motion of the Sun was dominated by the Coriolis and [centrifugal] forces, which is correct."

The problem with that statement—which, by the way, I neither asserted nor implied was incorrect—is that it was completely irrelevent to the rest of the section (as currently written), in that it talks about the Sun's (and only the Sun's) apparent motion, whereas the rest of the section is devoted entirely to a discussion of the apparent motion of distant stars. When I wrote in the summary of my edit to the article that "it's at least inaccurate for the Sun", the "it" in that statement was referring specifically to the explanation of the effects of the Coriolis and centrifugal forces on the apparent motions of distant stars. That explanation would be inaccurate for the Sun for the reasons I have already explained above.

After opening with the above-mentioned statement about the Sun's apparent motion's being dominated by the Coriolis and centrifugal forces, the previous version of the section under discussion switched, in the very next sentence, to considering the case of a distant star. It then went on to give the very nice explanation of the effects of the Coriolis and centrifugal forces on the apparent motion of such a distant star without ever returning to the case of the Sun or mentioning it again. Now if you're only going to give an explanation which applies to distant stars, but can't be applied without significant modification to the Sun, why on earth mention the Sun at all in the first place? At best it's apt to puzzle readers (as it did me) as to why the Sun was mentioned at all, and at worst it could mislead them into thinking that the given explanation was supposed to apply just as well to the Sun as to distant stars.

I have no particular problem with a statement about the effects of Coriolis and centrifugal forces on the the Sun's apparent motion being included, but if it is, it needs to be accurate. Here is a draft of a possible wording (which I am as yet far from satisfied with):

"The apparent motion of the Sun or a distant star as seen from Earth is dominated by the Coriolis and centrifugal forces. First consider a distant star ... [skip explanation for distant stars] ...

The apparent motion of the Sun is a little more complicated. In the course of a year the Sun moves up to 23.4 degrees north and south of the celestial equator, and since the Coriolis and centrifugal forces are directed perpendicular to the Earth's axis, they cannot account for this motion. It is in fact accounted for by a third fictitious force arising from the Earth's acceleration towards the Sun. Although this fictitious force is very much smaller than the Coriolis and centrifugal forces, it has a component of continuously varying magnitude which acts in a direction parallel to the Earth's axis and thereby accounts for the Sun's apparent motion in that direction."

Personally, I don't believe such an inclusion would at all improve the article, but I'm not going to complain if someone wants to add it.

Answer to question:

"Why did you remove the section that pointed out the observed curved path of rising, culminating and setting, caused by applying Buys Ballot's law to stars?"

Mea culpa. Perhaps it would have been better to tag it with a request for clarification. I removed it because:

1. The vector algebra (as now modified) seems to me to provide perfectly adequate and complete explanation of how the apparent motion of any distant star is accounted for by the Coriolis and centrifugal forces. I couldn't (and still can't) see that any special explanation was needed for stars that are not directly above the equator; and
2. I found it almost completely incomprehensible (as I also do the statement that Buys Ballot's law is applicable to the stars).

Since you appear to understand whatever it is that the final paragraph was trying to say, it would be helpful if you could provide a more detailed explanation (it's quite possible that I'm simply missing something obvious). A detailed explanation of why I find the paragraph confusing is likely to be quite lengthy, so I won't try to give one here. However, if you believe the issue is worth pursuing I will provide such an explanation in a separate section below.

David Wilson (talk · cont) 15:36, 1 October 2011 (UTC)

Article name

As things are now, Coriolis force is a redirect to Coriolis effect. However, usage would suggest it should be the other way around: a Google book search "Coriolis effect" -poem, -poems turns up 93,500 results, while the search "Coriolis force" turns up 334,000 results, almost four times as many, and without the spurious links that "Coriolis effect" turns up when used without restrictions. Brews ohare (talk) 16:15, 10 December 2011 (UTC)

"Left and Right"

Where the article currently says "veer to the left" and "veer to the right", I would argue that the terms "Left" and "Right" are too ambiguous, as they assume (without even mentioning) the observer is facing in a particular direction. Left and Right do not even have specific meanings in this context, unless one expects readers to remember something like the Right Hand Rule, which is anything but intuitive.

Rather, I propose that the article state that it "veers to the West" in both cases. This is completely unambiguous, and does not assume that the observer is facing any particular direction. -- Jane Q. Public (talk) 03:07, 7 January 2012 (UTC)

Right and left are relative to the movement of the particle. It's like saying that a car turns right. Nothing ambiguous there. On the contrary, saying West or any other direction is wrong most of the time. For example, a particle moving East will veer South on the Northern hemisphere. Only particles moving towards the equator would veer West (in both hemispheres). −Woodstone (talk) 09:01, 7 January 2012 (UTC)

Left and right are not ambigous in this case. To be sure that left and right are properly defined, we need two perpendicular directions, one that is "forward" and one that is "up". Forward is of course the direction of movement, and up is easy as long as there's gravity or some "ground surface" to use as reference. If we were talking about stationary objects, we would have a problem. If we were talking about objects in outer space, we might have a problem. But we're not, so there's no problem. 131.116.254.198 (talk) 09:56, 14 January 2012 (UTC)

Vandalism

Blatant vandalism inn the section on Bathtubs/Toilets. "Big floppy donkey dick"

173.79.117.146 (talk) 19:45, 20 February 2012 (UTC)

It was reverted by a bot within a minute, you're seeing a cached page. Materialscientist (talk) 00:00, 21 February 2012 (UTC)

Question

What does this mean from the article: Perhaps the most important instance of the Coriolis effect is in the large-scale dynamics of the oceans and the atmosphere. In meteorology and oceanography, it is convenient to postulate a rotating frame of reference wherein the Earth is stationary. In accommodation of that provisional postulation, the otherwise fictitious centrifugal and Coriolis forces are introduced.

Why are the otherwise fictirious forces now real due to a purely abstract analytical formulation (fixed earth and rotating frame). There must be something missing in this explanation such as the motion constraints introduced through the atmospheric friction cause a real force that is like coriolis. the example I can think of is the merry go round. You are constrained to follow a curved path and to do so the seat pushes on you with a real force of opposite sign but equal magnitude as the centrifugal force (i.e. the centripetal acceleratoin required to make you follow th edge of the merry go round) Skimaniac (talk) 04:56, 3 March 2012 (UTC)

The Coriolis force is an inertial (also called fictitious) force that is only present in rotating frames of reference. Newton's laws only apply in inertial frames. If we wish to use them, unchanged, in a non-inertial (for example rotating) frame we can do so by inventing some new forces. The Coriolis force is one example of such a force.

If the article does not make this clear perhaps you might suggest ways in which it could. Martin Hogbin (talk) 10:13, 3 March 2012 (UTC)

If only I could. I am quite familiar with the coriolis apparent acceleration in trajectories which is why I have a hard time accepting the common explanation of coriolis for spinning. As I stated earlier, the centripetal and the centrifugal terms are of equal magnitude and opposite sign. the centripetal force is put on the body by some structure or force that enforces the trajectory constraint. Since the air is flowing into the low pressure at the center of the hurricane and the low is somewhat "stuck" to the earth's surface through "friction" (aka viscosity) effects, the low is dragging the pressure field around with the earth's rotation. Since the clouds of the hurricane stay with the earth as seen from an inertial observer from space, viscosity effects are dragging the air around with the earth. I believe the poor explanations arise from writing the dynamics of the air particle in the earth fixed (non-inertial and spinning) frame where the coriolis apparent acceleration properly appears and people see that and blame it on that term. Skimaniac (talk) 18:02, 3 March 2012 (UTC)

Is this image you used incorrect?

Hi, I'm not entirely sure if this is the right place to post this so please forgive me if it's not. I was just reading up on some facts about coriolis effect and was very interested in this article, but i couldn't get my head around this image. given what i've been reading, is this going the opposite direction that it should be?

http://upload.wikimedia.org/wikipedia/commons/6/69/Coriolis_effect14.png

any responce would be greatly appreciated Dean Deanobrowne (talk) 00:29, 19 March 2012 (UTC)

The picture shows inertial circles, being the path a particle would follow if there were no forces on it. So no air pressure differential, no drag (friction). As the caption states, the direction is opposite to the case where the air pressure gradient is the driving force as in a depression. −Woodstone (talk) 06:14, 19 March 2012 (UTC)

 Fixed (I think) [No fix was needed]

(edit conflict) Thanks for letting us know about this—here is indeed exactly the right place to post about difficulties with understanding the article. Because of the diagram's location and the incompleteness of the first part of the caption, it may not be entirely clear that it's intended to illustrate airflows around high-pressure areas. I presume Deanobrowne was might be having difficulty because he quite reasonably assumed it was supposed to be illustrating airflows around depressions. If Woodstone's explanation and the amendment I have made to the article hasn't cleared up the problem, a follow-up on Deanobrowne's part would be welcome.

David Wilson (talk · cont) 06:38, 19 March 2012 (UTC)

The picture shows the theoretical trajectory of a particle under no force other than inertial (fictitious). A high pressure area would exert a real (not fictitious) force. Reverted the "fix".−Woodstone (talk) 07:01, 19 March 2012 (UTC)

Yes. Apologies for the blunder and the bogus "fix". I had somehow got the nonsensical notion into my head that circular flow couldn't occur without a pressure gradient. A more careful reading of the article's section on inertial flow, or your above explanation, ought to have been enough to dispel it, but I only skimmed them without properly taking them in. Perhaps it might be worth adding a slightly fuller explanation of why the flows have the directions they do to the section on inertial flow, although it's probably also worth waiting until Deanobrowne has explained why he thinks they should be in the opposite directions.

David Wilson (talk · cont) 10:40, 19 March 2012 (UTC)

My apologies. And thank you for clearing this up with me. I'm very new to this and I just needed to keep reading over it. I think i'm confusing it with hurricanes. For instance even though, in the north, the flow is thrown into a clockwise direction, would a hurricane be forced into counter-clockwise? Im sorry if this is already explained

Deanobrowne (talk) 15:00, 23 March 2012 (UTC)

Deanobrowne, have a look at the diagram above the one you asked about:

As air moves toward the center of a low pressure system from all directions, it is deflected to the right. The result is counterclockwise flow, counterintuitively following a trajectory which curves to the left. Rracecarr (talk) 20:11, 26 March 2012 (UTC)

The Euler force

The lead currently says, 'When Newton's laws are transformed to a rotating frame of reference, the Coriolis and centrifugal forces appear'. In general, there is also the Euler force, unless the reference frame is rotating with constant angular velocity. I cannot think of any way to add this neatly. Any ideas? Martin Hogbin (talk) 10:18, 24 March 2012 (UTC)

How about, ' 'When Newton's laws are transformed to a uniformly rotating frame of reference, the Coriolis and centrifugal forces appear.'? Martin Hogbin (talk) 09:19, 25 March 2012 (UTC)

Good. Done. Rracecarr (talk) 19:56, 26 March 2012 (UTC)

History

I have moved some history details from lead to the History section. I note that a reference cited in Theory of tides (http://siam.org/pdf/news/621.pdf) attributes the first recognition of Coriolis effect in tides to Colin Maclaurin not Pierre-Simon Laplace. No date is given in the ref so I have not made any changes. --Kvng (talk) 20:35, 2 July 2012 (UTC)

cyclonic storm

I did not read the whole article so maybe my point was clarified in another section. The diagram of winds into the low pressure shows a north wind and south wind deflected in opposite directions. It seems to me that they would both deflect east (in the Northern Hemisphere), but since the rotating Earth has a faster linear speed in the south, the deflection would be geater for a south wind, forcing an overall counterclockwise rotation. — Preceding unsigned comment added by Barnsward (talk • contribs) 12:22, 8 July 2012 (UTC)

Perhaps you should read more of the article. You would find explained that on the Northern hemisphere airflows always deflect to the right relative to their movement. The size of the deflecting force at a certain location is equal for flows of the same speed in any direction. −Woodstone (talk) 15:50, 8 July 2012 (UTC)

Maybe it's because I ignored the math, which I also did not read this second time. The cannon ball (near the beginning of the article) released from the center of the turntable moves with a component away from the rotation, which would be east in the northern hemisphere. But further in the article a ball bouncing around a rotating disk moves from center with a component toward rotation (with an initial component opposite rotation, even). Maybe the parabolic profile of the disk has something to do with it. — Preceding unsigned comment added by 69.113.118.117 (talk) 01:17, 15 July 2012 (UTC) But wait, the force will vary among winds of equal speeds at different locations? How does it vary? — Preceding unsigned comment added by 68.194.161.51 (talk) 14:38, 16 July 2012 (UTC)

As you can read in the article the force is proportional to the sine of the latitude. Don't confuse the examples about turntables (which do not have hemispheres) with the ones for Earth.−Woodstone (talk) 16:15, 16 July 2012 (UTC)

Second paragraph suggested modifications

So how about this for the second paragraph? I think the terms are introduced in a more orderly fashion. What do you think? "Newton's laws of motion govern the motion of an object in a (non-accelerating) inertial frame of reference. When Newton's laws are transformed to a uniformly rotating frame of reference, there's a need to introduce additional accelerations, and thus, forces, in order to allow the application of Newton's laws to the system. Those are the Coriolis and the centrifugal forces, and are termed either as inertial, fictitious or pseudo forces due to the fact that they are correction factors that do not exist in a non-accelerating or inertial reference frame, and are added ad hoc in order to make the equations work from the Newtonian perspective of an observer within the rotating non-inertial frame, as opposed to the straight line perceived by an external, inertial observer. Both forces are proportional to the mass of the object. The Coriolis force is proportional to the rotation rate and the centrifugal force is proportional to its square. The Coriolis force acts in a direction perpendicular to the rotation axis and to the velocity of the body in the rotating frame and is proportional to the object's speed in the rotating frame. The centrifugal force acts outwards in the radial direction and is proportional to the distance of the body from the axis of the rotating frame." Jordissim (talk) 00:37, 16 June 2012 (UTC)

The statement about "need to introduce ... forces" is rather weak. The transformation generates them outright. They are not correction factors, but direct consequences of the transformation. −Woodstone (talk) 09:41, 16 June 2012 (UTC)

Ok, then. Even though I don't fully agree with you -you're right if you think a mathematical transformation has a physical meaning, which I don't, since I believe the Universe doesn't do maths (that's an off-topic not to be treated here)-, I think the structure I proposed is better than the one in place. So, how would you change the phrases you don't like? Any ideas? I'm not very good at writing, and when I tried incorporating your point I didn't like the result -due to my lack of skill, basically... Jordissim (talk) 23:10, 18 June 2012 (UTC)

How about something like: 'If Newton's laws are to be used, unchanged in form, in a uniformly rotating frame of reference, it is necessary to introduce additional forces. Those are the Coriolis and the centrifugal forces, and are known as as inertial, fictitious or pseudo forces as they do not exist in a non-accelerating or inertial reference frame, and are added in order to make Newton's laws work within the rotating frame. Both forces are proportional to the mass of the object'. Martin Hogbin (talk) 17:13, 16 July 2012 (UTC)

The first line is rather contradictory: unchanged form, but additional forces? The formula including Coriolis and Centrifugal forces is simply the way Newtons law looks after transformation to a rotating frame of reference. The transformation creates the extra terms. It is not "necessary to add" the terms. So the proposed phrasing is more confusuing than clarifying. −Woodstone (talk) 23:52, 16 July 2012 (UTC)

That is not quite right. The transformation creates acceleration terms. We can choose how to treat these terms. We can either leave them as a change to the form of Newton's laws or we can add in some inertial forces, in which case Newton's laws themselves remain exactly the same in the rotating frame as they are in an inertial frame. Martin Hogbin (talk) 08:21, 17 July 2012 (UTC)

I would replace "Newton's laws" in the above text with "Newton's first two laws". As pseudoforces are normally conceived, they don't satisfy the third law.

David Wilson (talk · cont) 11:29, 17 July 2012 (UTC)

Good point. Martin Hogbin (talk) 13:18, 17 July 2012 (UTC)

So should we have, 'If Newton's first and second laws are to be used, unchanged in form, in a uniformly rotating frame of reference, it is necessary to introduce additional forces. Those are the Coriolis and the centrifugal forces, and are known as as inertial, fictitious or pseudo forces as they do not exist in a non-accelerating or inertial reference frame, and are added in order to make the first two of Newton's laws work within the rotating frame. Both forces are proportional to the mass of the object'? Martin Hogbin (talk) 17:31, 17 July 2012 (UTC)

To stress the automatic appearance, we might better write along the following lines:

'When Newton's law is transformed to a uniformly rotating frame of reference, two additional acceleration terms arise, which are commonly written in the form of forces proportional to the mass of the object. They are called the Coriolis and the centrifugal forces, and are known as as inertial, fictitious or pseudo forces as they do not occur in a non-accelerating or inertial reference frame.' −Woodstone (talk) 17:47, 17 July 2012 (UTC)

Reference

Bathtub-reference password protected

Reference 28 ('Otto Tumlirz "A new physical evidence of the axis of rotation of the earth" (in German)') needs a password to view - I think it should get removed or (better) replaced by a viewable version. --78.43.172.49 (talk) 11:57, 8 September 2012 (UTC)

I have now replaced the link with a full citation to Tumlirz's original article.

David Wilson (talk · cont) 14:55, 8 September 2012 (UTC)

the observer is stationary in the bottom animation but not in the top. is this the intention of the illustration?

I'm confused about the animations as well. It shows that objects moving in a straight line can be made to appear to move in a curve when the observer is moving in a curve. What's the connection to the Coriolis effect? Watchwolf49z (talk) 18:12, 31 October 2012 (UTC)

What you have described is the Coriolis effect. It sounds from your comments as though you are familiar with the Coriolis effect only in the context of large weather systems on earth. But that effect arises because the earth is spinning about its axis. An observer at rest with respect to the earth's surface - someone like you or me, that is, or the storm itself - is moving in a circle with respect to an inertial (or close to inertial) observer. So the storm is subject to the Coriolis force (or pseudoforce if you like), and therefore tends to spin in a certain direction. I'm sure the article can use improvement, but focusing it on storms or weather systems is not a valid way to do that, because the Coriolis effect is a basic phenomenon that has all sorts of other manifestations. Waleswatcher (talk) 17:23, 1 December 2012 (UTC)

CORIOLIS EFFECT: AN INTELLECTUAL ILLUSION

AN INTELLECTUAL ILLUSION The alleged Coriolis "effect" is nothing more than the statement of the obvious. If you want to hit a moving target you have to aim where it is going to be when the bullet arrives at the target. Beyond that the article is nothing more, I am sorry to say, than an illusion of being correct. Not unlike for 1500 years the "learned centers of the world" insisted that all the stars rotated around the earth. And both suffer from the same mental illusion and logical mistake.

That is....they take a "human, LIMITED VISUAL PERCEPTION" that is, MOST OFTEN, different than the true complete picture of a reality environment and treat it as having some meaningful effect:

In the rotation of the stars illusion,they placed meaning on the "false" human visual perception that the stars were moving from one side of their limited field of vision, to the other side...that therefore it was a factual reality that the stars were moving in the direction of their perceived motion.

Illusions are based on the assumption that my limited point of view....is conveying to me ALL THE RELEVANT INFORMATION TO MAKE A DECISION ON WHAT THE TRUE REALITY IS. Magicians make use of our willingness to make this kind of unwaranted assumption all the time.

In the star case, however, we fail to take into account, because it is not also readily apparent, that in fact...we are also moving because we are standing on the earth which is revolving. When we do, we quickly come up with the correct description of reality.

In the present intellectual Coriolis exercise...you will note that it does the exact same thing. In fact, it actually acknowledges that that the peceived motion is a false one. The ball actually travels in a straight line, not the curved one we visual percieve under the unique circumstances arbitrarily imposed on our point of view. But, then the theory goes on to TOTALLY IGNORE THE REALITY just stated that we are perceving something that does not exist.

The Coriolis perception then is switched, BY HUMAN INTELLECTUAL THOUGHT, to an ACTUAL CORIOLIS FORCE THAT CHANGES THINGS in accordance with the characteristics of the FALSE HUMAN PERCEPTION first descibed. But, whether it is the balls thrown over the rotating table.....or what air molecules do in the atmosphere as part of a high or low pressure pattern or the stars....they are not aware of our false visual perspective, could care less about it and which has absolutely NO EFFECT ON WHAT THEY DO.

Unfortunately, the acceptance of the Coriolis "visual effect" as a legitimate explaination has stopped any further human effort to search for and explain correctly several things, including the REAL REALITY REASON and very important reason why the atmosphere rotates around high and low pressure areas AND why the rotation is the opposite in the northern and southern hemispheres.

But what is amazing and useful is....once one realizes that the Coriolis ILLUSION does not explain anything except the obvious....and you start searching again....the real answer is as simple and obvious as the true reality: that it is the earth's revolution on its axis that causes our "false visual perception" and in fact the stars, while they have their own motion to deal with....do not rotate around the earth.

But since this forum's rules do not allow original research....I'll leave it at that, except to say that I now have had 75 years of experience with reality including having obtained a PhD level certificate from these "learned centers; and it would be a mistake, I think, to make the assumption that, in the learned centers of the world, these kinds of "universal acceptance" of many basic premises as correct when they are as "obviously false as Coriolis " are a rare occurance or that they only happened a thousand years ago. Rowland2 (talk) 20:02, 23 March 2012 (UTC)

Perhaps you should re-read the article. The Coriolis force is described as a fictitious force, inertial force, or pseudo-force, essentially for the reasons you state. It does not exist when measurements are made in an inertial frame. It is however a very useful mathematical convenience when working in a rotating frame, such as that of the Earth. It is no doubt possible to calculate the motion of winds and weather systems in a non-rotating reference frame but this would extraordinarily difficult. It is much easy to pretend the Earth's surface is an inertial frame and add the two fictitious forces necessary to make the physics work. Martin Hogbin (talk) 10:14, 24 March 2012 (UTC)

The article is good, and Martin, you are right regarding the description of the force as a fictitious force... ecept in the introduction (second paragraph, I think?). The problem arises because the use of the term "force" depends on the discipline: in Physics (my field), it never is mentioned as a force at all; however, in Engineering, it is useful to treat is as so (same as the centripedal and centrifugal ones). The introduction should be modified so that the definition of the Coriolis effect as a pseudoforce is introduced before treating it as a force - both acceptions are acceptable, but the way it is currently written is not clear enough. Just an opinion, though...::Jordissim (talk) 03:03, 23 May 2012 (UTC)

What's an example of a fictitious centripetal force? —Tamfang (talk) 04:07, 23 May 2012 (UTC)

For one, forces called as such in orbiting movements: they are but (very appropiate) Newtonian approaches to general realtivity solutions dealing with bodies moving in geodesics within gravity wells. Jordissim (talk) 23:22, 28 May 2012 (UTC)

Feel free to clutter up your own writing with unnecessary <br> tags, but please don't add them to mine. —Tamfang (talk) 23:53, 28 May 2012 (UTC)

I sincerely don't understand what's going on here. I sent you a message stating clearly that I didn't want any animosity between two fellow contributors, and least of all with someone I will most certainly cross paths with in the future - yet I'm paid with a polite yet (in my opinion) inappropiate answer. I really would appreciate you telling me why a misplaced <br> tag in a personal Talk page should annoy you at all (I'm pretty new to Wikipedia, and bound to make format mistakes - as anyone else). Yet do mistakes that tiny bother you? I'm sorry, I don't follow. I thought an Encyclopaedia was about content. Different cultures, I guess. If the problem has arisen due to the first paragraph I wrote in my previous entry, I deeply apologize: I admit it was out of line. I've marked the text for deletion. But please, there's no need to be hostile (neither side). Regards, Jordissim (talk) 01:20, 2 June 2012 (UTC)

I ought to have thanked you for the substance of your answer, and I accept the implied rebuke. On the other hand, if you think that's animosity, you must be new to the Net! Since you ask, what offended me was not that you made what amounts to an error of punctuation, but that you presumed to mis-correct the punctuation in a paragraph attributed to me. I welcome true corrections and object to false ones. —Tamfang (talk) 02:02, 2 June 2012 (UTC)

I see what you mean, and I'm sorry. It wasn't done on purpose, I assure you. I won't make that mistake again. Regarding my misunderstaning on animosity, I am actually new on the net, and my deffensiveness has to do with my profession, I'm afraid: people tend to insult or look down on other people's work in a really difficult way to pinpoint, having to read between the lines; and I'm afraid I've become contaminated by that attitude. My world is full of politics and overinflated egoes, unluckily. So again, my apologies. Best regards, Jordissim (talk) 21:31, 2 June 2012 (UTC)

Jordissim, I do not know here you studied physics or what books you read but any physics book on classical mechanics that deals with rotating reference frames will mention the Coriolis and centrifugal (and maybe the Euler) forces. Martin Hogbin (talk) 08:20, 23 May 2012 (UTC)

Well, Martin, if you really think it's important, I studied Physics in Universitat de Barcelona, and got my PhD in high-energy physics from Universitat Autònoma de Barcelona. I also hold an Engineering degree from Universitat Politècnica de Catalunya, and am currently studying a completely unrelated third degree just because I feel like it. I work as a Project Manager in European-funded R&D projects, I am 1'88m, and have brown hair. I fail to see the point, though - how does my biography enter the equation? And yes, of course those forces will be mentioned, but in a whole different manner! All I can tell you is that bibliography is quite different depending on whether you study Engineering or Pure Physics - and terminology is, as well. Since I assume you're a phycisit as well, let me remind you how different the word "metal" is for an astronomer or for a mechanical engineer. I'm not saying the paragraph's content is wrong (did I ever?), I just said that a "force" has a very clear definition in basic Physics, and that it differs from the one in Engineering because the first courses in Physics are theoretical by nature (setting the ground rules for more in-depth subjects), whereas Engineering always takes a pragmatical approach. How can a good article first refer to something as a force, and then as a pseudoforce? It should be the other way round: establishing 1) that something looks and acts like a force, 2) but isn't, yet for most purposes, it is useful to regard is as so. And since you ask for books: "Berkeley Physics Course Vol. 1" (used in the Physics degree), or Paul A. Tippler's "Physics for scientists and engineers", 3rd edition, used in Engineering but not in Physics - in both, the Coriolis aceleration is mentioned, then its effects on a system are introduced as a pseudoforce or a fictitious force, and then the book goes on to treat it as if it were real for purely practical reasons, having already set that in reality it is not so. (Look it up for yourself). See the pattern? That's my point. It has nothing to do with the content, it's got all to do with the order.

Jordissim (talk) 00:29, 24 May 2012 (UTC)

The Coriolis effect is defined as the deflection, it is not caused by a linear force pointing to the right (in North Hemi). Here's a video http://www.youtube.com/watch?v=NpX9oXsbOfw. How does Physics explain this observable phenomenon?. Watchwolf49z (talk) 14:14, 2 November 2012 (UTC)

Jordissim, you seem to be just talking about terminology. I fully understand that CF is a pseudoforce or a fictitious force or, to use my own preferred term, an inertial force but it is common in both physics and engineering to use the term 'Coriolis force'. In my opinion the term 'Coriolis force' is much more common than 'Coriolis effect' so that is what the article should be called. Of course, the article must explain that it is an inertial force. Do we disagree about anything? Martin Hogbin (talk) 08:03, 29 May 2012 (UTC)

Martin, I certainly never doubted you understood the subject. Yet I'm not talking solely about terminology, I'm talking about accurate terminology. As I stated, any good article must assume that the reader has almost no idea on the subject at hand, and therefore it's the editor's job to drive him in the right directions, avoiding misleading twists. My idea, stated before, is to introduce the concept of the Coriolis Force in a comprehensive manner. The steps should be those I wrote right above, and copy here to reintroduce them in the subject at hand (sorry for cluttering the Talk page):

1) Introducing the Coriolis acceleration as a Newtonian "switch" among inertial and non-inertial systems;

2) Stating its effects on a system as a derived pseudoforce or a fictitious force - named as you feel like it;

3) Treat it then, and only then, as if it were real for purely practical reasons, having already set that it's but a useful simplification.

That's all. It's a question of setting a clear, direct(ed) approach to the subject, following a step-by-step method that clarifies things with the bonus of being in line with history of science.

Yet I'm not a native English speaker, and styles tend to vary depending on the country. I'm used to European Commission deliverables (a nightmarish world) and to scientific magazines in Europe, so again, it might be a matter of cultural differences. Regards, Jordissim (talk) 01:20, 2 June 2012 (UTC)

I'm deferring from a general discussion of the subject to suggest improvements to the text. The article is titled "Coriolis effect" and should focus on that. There may be a need for a separate article titled "Coriolis force". However, even for someone who has done a little study on the matter, the introductory text is extremely confusing. I would propose replacing all references to "Coriolis force" to "Coriolis effect" and either creating a paragraph to explain pseudo-forces or a whole separate article. Perhaps un-scientific, but it is fair to say this effect is a specific combination of electromagnetic and gravitation forces, any alternative explaination would require the introduction of a third (and yet to be discovered) force of nature. Starting with F = m a, it doesn't matter how small the force is, when mass is even smaller (and we are talking about individual molecules here) we are left with a large acceleration. It's not an illusion that tornadoes are almost exclusively cyclonic. Watchwolf49z (talk) 15:29, 28 October 2012 (UTC)

The Coriolis effect has nothing to do with electromagnetism, nor with gravity. It is solely a result of inertia. And the Coriolis force on something is proportional to its mass, so no matter how light or heavy, the perceived acceleration does not vary.−Woodstone (talk) 17:59, 28 October 2012 (UTC)

My issue is with the introductory paragraph, it is confusing to the casual reader. Read the first sentence, this is not how a majority of English speaking people define "Coriolis Force". Whatever it is that spins storms the same way in a hemisphere is what most people think is the effect. The body of the article is a great place to explain how it's wrong, for those who care. You use "Coriolis Force" without quotes, do you disagree with changing this to Coriolis effect through the article? Keeping in mind our goal (effective prose), both types of inertia are involved, and it causes an effect, namely spinning storms the same direction. This is the information people are looking for here. Bottom line, the definition here is inconsistant with that published by NOAA and WMO, and stands here unreferenced. If you'll review the "peer-review" archives, you'll see why I might believe the text is biased, and inappropriate for the introduction. I'm coming in from the cold here, as it were, and what I read has nothing to do with what was taught when I was in school. Gravity causes pressure, and without pressure you have no weather ... which means you're talking about something else entirely. Watchwolf49z (talk) 12:14, 30 October 2012 (UTC)

The Coriolis effect is the deflection of air moving across latitude, to the right on the Northern Hemisphere and to the left on the Southern Hemisphere (1). It is named after the French mathematician Gaspard Gustave de Coriolis (1792-1843), who studied the transfer of energy in rotating systems like waterwheels. (Ross, 1995). “Coriolis force” is a misnomer, it is an effect of a sphere’s rotation about it’s axis, and is not a force of nature (original research, my bad).[ (1) = http://oceanservice.noaa.gov/education/kits/currents/05currents1.html]

This is a vastly superior definition solely because it is fully referenced, and is in more compliance with the rules of Standard Written English. Watchwolf49z (talk) 14:35, 30 October 2012 (UTC)

That is an inferior definition, because it is specific to the case of weather systems on earth. The Coriolis effect is far more general than that. As for gravity and forces, in modern physics the Coriolis effects is just as much a force (or not) as gravity. Both act on all objects with a force that's precisely proportional to mass, and are treated on equal footing by Einstein's general relativity. It is only from the Newtonian point of view that there is a distinction between gravitational force and "pseudoforces". I don't have a strong feeling about how to handle that for this article, but it should be done carefully and correctly. Waleswatcher (talk) 17:27, 1 December 2012 (UTC)

Comment by Watchwolf49z copied from Waleswatcher's talk page

Thank you for your input, I'm assuming allowance for a brief "general discussion" here on your talk page. I'd like to direct your attention to the animation in the upper right side of the Coriolis effect article. If the upper animation is being viewed from the center of gravity, then the black dot should be showing a slight deflection, and not an absolutely straight line at any non-equitorial position. If you agree with me that this animation is in error, all's good. If you disagree, then I'll chase down the rigid math proof and post it to my sandbox. I'm afraid that we may be stuck with Weather science referencing, not many other disciplines use the effect.

The cause is due to the torque component of the acceleration from gravity at any non-equitorial position, so that when another force is applied, even if it is completely linear, the resultant force on the object will still have this rather small amount of torque. The deflection is the Work done by the torque. As another example, a bullet only experiences the Coriolis effect while in the gun barrel, once the bullet exits the applied force is removed, the bullet flies straight as viewed from the center of gravity. There's an article titled Coriolis field that seems to address your comments about Relativity. There seems to be enough scientific papers concerning the effect in Quantinum Mechanics to create a new article.

If I may be so bold, there has to be a physical reason for the predominance of cyclonic motion. Somehow, optical illusions just doesn't work for me. Watchwolf49z (talk) 14:29, 2 December 2012 (UTC)

Watchwolf49z, the upper panel of that figure is illustrating geodesic motion in an inertial frame. There is no gravity, it's simply illustrating Newton's first law. So no, I do not agree with you that there should be a deflection. I suspect you are misunderstanding what the animation is supposed to show. As for weather, the primary discipline here is physics, not meteorology. The Coriolis effect is a basic phenomenon in physics, that has applications in many fields - one of which is meteorology. Quantum mechanics has nothing to do with it, and I'm not sure what you are referring to regarding the bullet example. Waleswatcher (talk) 14:53, 2 December 2012 (UTC)

I'll be weeks chasing down the proof, and be forewarned, it will include gravity. Clearly you disagree with my statement and any further discussion will have to center on such a proof. If my math is wrong, then I am wrong. Watchwolf49z (talk) 15:44, 2 December 2012 (UTC)

If your "proof" includes gravity (in the Newtonian sense at least) then it's irrelevant to that animation. Again, I think you are mistaken about what the animation is illustrating. It's intended to show nothing or or less than geodesic motion (i.e. motion in the absence of any Newtonian forces, including gravity). The point is that geodesics in inertial frames are straight lines (no defection, that's the top panel), but those same geodesics are curved in a rotating frame (that's the bottom panel). Waleswatcher (talk) 16:25, 2 December 2012 (UTC)

The animation as a whole is demonstrating the Coriolis Force. The black dot scribes a spiral segment in the lower animation, as though a force was acting on it, when in fact the force is acting on the observer. It also demonstrates that the Coriolis Force has no effect on the system. No matter the frame of reference, measured forces on the black dot will always be zero. Let me rephrase my original question: If we give a red dot the initial velocity downward (being red dots are subject to the centripedal forces of the disk), would it show a deflection in the top animation? Watchwolf49z (talk) 04:37, 4 December 2012 (UTC)

"No matter the frame of reference, measured forces on the black dot will always be zero." If you measure the force by measuring the trajectory of the particle x(t) and then computing the second derivative of x with respect to time, multiplying that by the mass of the particle gives you F (in other words, F=ma). In a rotating frame, the acceleration is non-zero, and so is F. If instead you measure the acceleration by an accelerometer attached to the object, you will indeed get zero. But the same is true for an accelerometer attached to an object in free fall in a gravitational field. So if Coriolis or centrifugal forces aren't "real" forces for that reason, neither is gravity. As for your question, I don't understand it - the red dot is just a dot marking a point on that disk/reference frame, so what do you mean by give it a an initial velocity? Waleswatcher (talk) 06:52, 12 December 2012 (UTC)

Watchwolf49z, this is the talk page for discussion on how to improve this article not for discussion of the Coriolis force itself. As Waleswatcher says, the animation in the article is perfectly correct and shows exactly what he describes. Gravity is not included in the animation and is not relevant to a discussion of Coriolis force. I suggest that you read a good text book on classical mechanics. Martin Hogbin (talk) 08:38, 12 December 2012 (UTC)

I think I’ve found what I’m looking for, and it says I’m mostly wrong. Looks like Navier–Stokes equations are involved, so any proof will be non-rigid. There’s also no torque component involved, so statements to that effect are humbly withdrawn. John Marshall, R. Alan Plumb; Atmosphere, Ocean and Climate Dynamics; Academic Press; n.d. (© = inquiring); provides a clear and step-wise derivation of the equation of motion for fluids. George Haltimer, Frank Martin; Atmosphere, Dynamical and Physical Meteorology; McGraw-Hill; 1957 (© = Public domain); begins with this equation as (in a stationary frame of reference) d_aV_a/dt = b + g_a + F where V_a = velocity, t = time, b = pressure force, g_a = gravity and F = friction. From here, Haltimer/Frank explains the how and why the two pseudoforces are created from gravity (= relative gravitation + Coriolis force + centrifugal force) giving the equation of motion in a rotating frame of reference. These are set to zero for the work calculations which cuts down on the triple integrals to be resolved. It’s important to note that the two constructs are not needed to achieve a correct solution, they just eliminate some of the “nightmarish algebraic calculations”. Watchwolf49z (talk) 16:12, 15 December 2012 (UTC)

@Watchwolf49z - For clarification, are you now agreeing with the statements that the Coriolis force/effect is not limited to weather systems and systems involving gravity, but is in fact a result of taking into account the rotation of the non-inertial frame? If not, what specific information in those two references do you feel needs to be included that isn't already in the article? --FyzixFighter (talk) 17:51, 17 December 2012 (UTC)

I'm glad you asked that question. I knew right away this was what I was looking for since it fits so nicely with what is already in the article. What's written now is a fine lead-up to the concepts I posted above. I'd like to see an new section towards the bottom discussing these effects in gravity, maybe try and connect it to a vortex. Watchwolf49z (talk) 01:24, 18 December 2012 (UTC)

Proposed Changes

Aside from the above discussion, there are still a number of small housekeeping tasks in this article. Keeping to the "carefully and correctly" advice, my plan is to start with changes that should be agreeable to everyone. It's important to start out with a positive working relationship, so when disagreements arise (and they will), we'll have a solid foundation to provide what Wikipedia needs of this article. It cannot be ignored that scholarly literature regularly speaks to how confusing this subject is, even at the highest levels of academia.

These proposals are posted for comment, and if none are given or they are positive, the article itself will be changed after a week. The discussion will remain OPEN, as sometimes seeing the change in the article will expose it's weaknesses, and it's need for further editing.

• The term "anticlockwise" appears here and there. I propose this be changed to "counter-clockwise" throughout. This change would provide consistent terminology in the article.

Done Watchwolf49z (talk) 16:06, 29 December 2012 (UTC)

• In the History section, change the sentences `By the early 20th century the effect was known as the "acceleration of Coriolis".[6] By 1919 it was referred to as "Coriolis' force"[7] and by 1920 as "Coriolis force".[8]` to `The effect was known in the early 20th century as the "acceleration of Coriolis"[6], and by 1920 as "Coriolis force".[8]`. We'd be giving up the apostrophe for a cleaner sentence. Watchwolf49z (talk) 16:35, 22 December 2012 (UTC)

Done Watchwolf49z (talk) 16:06, 29 December 2012 (UTC)

• We have a mixture of formats for units of measure. I propose all be giving as "mks units (Imperial units)" throughout.

Done ... except in the bathtub section and tossed ball section. Changes there go past the intent of this proposal. Watchwolf49z (talk) 16:47, 5 January 2013 (UTC)

One suggestion - rather than manually inserting the conversions to imperial units, perhaps template:convert would be a better alternative. I noticed that it's already being used in some of the same parts of the article where you put in some imperial units. Just a suggestion, though. --FyzixFighter (talk) 05:28, 7 January 2013 (UTC)

Agreed, it's just easier to type the numbers in ... I do see the advantage to using the template, just need to learn the attributes &c. Watchwolf49z (talk) 17:55, 12 January 2013 (UTC)

ReDone using convert template throughout, except the "o'clock" units. Watchwolf49z (talk) 16:07, 26 January 2013 (UTC)

• The first sentence in the “Causes” section uses the phrase “exists only”. This is only true for the Coriolis force, and the Coriolis effect as used in Physics. However, the Coriolis effect exists in all reference frames as used in weather science. I propose changing “exists only” with “is best viewed” giving The Coriolis effect is best viewed when one uses a rotating reference frame. Watchwolf49z (talk) 15:00, 29 December 2012 (UTC)

Let's not start to obscure the facts again. In a non-rotating frame, there is no acceleration perpendicular to the flow of particles. Not in physics, not in meteorology. −Woodstone (talk) 15:54, 29 December 2012 (UTC)

Withdrawn Watchwolf49z (talk) 16:06, 30 December 2012 (UTC)

The intent of this change is to make the statement more consistent to the definition being used in this article. If you have a reference, then we can change the definition and leave this alone. Please use the preceding section for challenges to the citations and notability of usages involving gravity. Watchwolf49z (talk) 23:46, 29 December 2012 (UTC)

I'm agreeing with Woodstone here. I also don't see how changing that statement is more consistent with the definition being used in the rest of the article. Where are the other statements that you see being not consistent with that first line in "Causes"? Also, do you have a reference that the definition for the Coriolis force/effect in weather sciences is different than it is in the rest of physics? Those references you cited above do not (imo) support such a view. In the absolute frame (eq 11-6 in Haltimer & Martin), there is no Coriolis force/effect - just gravity, pressure, and friction. The Marshall & Plumb reference also repeats several times that the Coriolis force is a result of describing motion in the rotating frame (bottom of page 172 and top of page 173). For example in its GFD lab V it states: "Notice that the puck is 'deflected to the right' by the Coriolis force when viewed in the rotating frame..." and later "Viewed from the laboratory the puck moves backwards and forwards along a straight line...When viewed in the rotating frame, however, the particle is continuously deflected to the right... This is the 'deflecting force' of Coriolis." And again on pg 186: "The deflection 'to the right' by the Coriolis force is indeed a consequence of the rotation of the frame of reference: the trajectory in the inertial frame is a straight line!" That is not to say that cyclones don't spin - but an observer in space that is not rotating with the earth will not see unexplained deflection perpendicular to the direction of motion and can explain the fluid dynamics in weather systems with just gravity, pressure, and friction. It is only when we attempt to describe weather in the relative, rotating frame of the earth that we need to include the Coriolis and centrifugal forces in order to "take into account the effect of observing acceleration in a rotating frame of reference." (pg 160, Haltiner & Martin). --FyzixFighter (talk) 04:45, 30 December 2012 (UTC)

(ec)

I also disagree strongly with this proposed change, and I can't see how either of the two references Watchwolf49z has cited can be read as supporting either it or his assertion that "the Coriolis effect exists in all reference frames as used in weather science". Haltiner and Martin never use the term "Coriolis effect" at all, and Marshall and Plumb use it only three times, but never define precisely what they mean by it.

Although it's not entirely clear to me from this article's or Marshall and Plumb's exposition precisely what the term is intended to refer to, I have always presumed it referred to that part of a body's displacement relative to some chosen reference frame which is attributable to its Coriolis acceleration in that frame. But both Watchwolf49z's sources—just like all others—tell us that the Coriolis acceleration is uniformly zero in a non-rotating frame, and consequently there can be no displacement attributable to it in such a frame.

I agree that the wording of the first sentence in the Causes section could probably be improved, but I strongly disagree that this can be achieved by replacing "exists only" with "is best viewed". I would prefer it to be replaced with something like "only occurs" or "is only non-zero" . The latter substitution presumes that the term "Coriolis effect" is intended to have some at least vaguely quantitative, rather than a purely qualitative, connotation, but then Marshall and Plumb do imply just this on page 143 where they refer to it as being "weak" near the equator.

I suppose one could take the view that the Coriolis effect does actually exist in a non-rotating reference frame but just always happens to have a constant magnitude of precisely zero, but I know of no reliable source which actually does so, and I don't believe that the article's doing so would improve it.

David Wilson (talk · cont) 07:34, 30 December 2012 (UTC)

I have no problem with vectors of zero magnitude and yet still have direction, like dF/dt. Turns out Coriolis effect mass flow meters use an oscillating frame of reference (http://www.omega.com/literature/transactions/volume4/t9904-10-mass.html), which gives a zero force twice per oscillation. I think it would improve this article if the general statements were stated generally, and let the specific applications state their own frame of reference. For example, physics uses a rotating frame, meteorology uses a Newtonian frame, mass flow meters use an oscillating frame and so on. Watchwolf49z (talk) 16:12, 1 January 2013 (UTC)

How are you defining "Newtonian frame" and how is it different from a rotating frame? Is there a source that says if and how meteorology uses such a frame? --FyzixFighter (talk) 02:15, 2 January 2013 (UTC)

The definition of a Newtonian frame is left to the reader to choose. Any would be fine as long as rain is observed. I can’t source that statement, no one’s ever researched otherwise. Watchwolf49z (talk) 17:38, 3 January 2013 (UTC)

If I were to read "Newtonian frame", although I don't recall encountering it very often, I would assume it meant a frame where Newton's laws of motion apply, or in other words a classical inertial frame. Using a non-inertial frame, eg a rotating frame, Newton's laws of motion do not hold unless we bootstrap them with "fictitious" forces. From the two sources you mentioned above, I would say that meteorology does not work in a "Newtonian frame" how I have chosen to define it, but in a rotating frame. All this is to say, I think the sources we've seen indicate that the Coriolis effect of physics and meteorology are the same with physics using a general rotating frame and meteorology using the specific rotating frame of the planet. If we did meteorology in an inertial frame where we saw the earth spinning, the Coriolis effect/acceleration/force would not be observed or needed. So perhaps let me be a little bit more direct - in your statement above ("...physics uses a rotating frame, meteorology uses a Newtonian frame, mass flow meters use an oscillating frame and so on") what does the "Newtonian" of "Newtonian frame" mean to you? --FyzixFighter (talk) 19:06, 3 January 2013 (UTC)

How about that, we’re in complete and total agreement as to the definition of Newtonian frame ... go figure. The equation I posted in the previous section in stated in an inertial frame of reference, specifically one that is stationary to the stars as an approximation for the purposes of this discussion. The next step in the derivation gives us d_aV_a/dt = b + ( g_r + f_Coriolis + f_Centrifugal ) + F . This also stated in an inertial frame of reference, as there is nothing inherit to vector addition that changes this frame. That’s a notable example of Coriolis force/acceleration/effect existing in a non-rotating frame of reference. I ask again, why is imperative that Coriolis force/acceleration/effect not exist in such a frame? Watchwolf49z (talk) 18:38, 5 January 2013 (UTC)

Which line in the derivation (page number or equation number) is that - I'm having a little bit of a problem finding it? What I do see is after giving the equation of motion in the inertial frame (eq 11-6) where no Coriolis force is needed, it then proceeds to give the equation for dV/dt (the velocity in the rotating frame) (eq 11-7) and it is here that the real forces have to be supplemented with the Coriolis and centrifugal force in order for F/m=dV/dt to be true when V is given with respect to a rotating frame. But in the non-rotating, inertial frame only the real forces (pressure b, gravitation g_a, and friction F) appear in the equation of motion. The Coriolis force only appears when we express our force balance in terms of relative, rather than absolute velocities. The Coriolis force is a consequence of the rotation of the frame of reference; when the frame of reference is not rotating, there is no Coriolis force. That's what the sources tell us (see also the opening paragraph of section 1.5 in ref 18). --FyzixFighter (talk) 03:33, 6 January 2013 (UTC)

I’m not clear on the answer to my question. Perhaps you could elaborate some on your talk page. Watchwolf49z (talk) 17:55, 12 January 2013 (UTC)

Perhaps I should clarify, “Aside from” means “at the exclusion of” information concerning the equations of motion for fluids in these proposals. “Agreeable to everyone” means that disagreement, even if politely, courteously and briefly stated, would veto the proposal. Watchwolf49z (talk) 16:06, 30 December 2012 (UTC)

• This is a continuation of the above, AND inherits the stated disagreements (and veto). I propose changing the sentence to The Coriolis effect is only non-zero in a rotating reference frame. The issue is usage in English, where "when they are viewed" is not the exact same thing as "only exists". Now, if it's absolutely imperative the syntax be changed from from the definition, then so be it. Just remember that any unreferenced material ... in the article ... is subject to future challenge and removal per Wikipedia policy. Watchwolf49z (talk) 16:06, 30 December 2012 (UTC)

I think that I favor saying "The Coriolis effect only occurs in..." as another editor above suggested since it's not clear from any text I've seen how you actually quantify the Coriolis effect (as opposed to quantifying the Coriolis acceleration and force). IMO, that's more in-line with the sources we have. Do we have any sources that contradict this? --FyzixFighter (talk) 02:15, 2 January 2013 (UTC)

The equation for the deflection can be deduced from the equations of the observed and observer. It’s a lot of analytical geometry, but it can be done. The derivative of this equation establishes existence in a non-rotating frame. The proof of this is in any first year calculus book. I think we both know this proposal is going to be withdrawn. I’m sure the reference to the statement in the article explains why the derivative is discontinuous here as well. Watchwolf49z (talk) 17:38, 3 January 2013 (UTC)

Withdrawn - Hallelujah Watchwolf49z (talk) 16:47, 5 January 2013 (UTC)

• In the Rossby number section, a baseball example would be more accessible to the intended reader. I propose replacing the garden material with (and my arithmetic should be checked): A baseball pitcher may throw the ball at U = 45 m/s (100 mph) for a distance of L = 18 m (60 ft). The Rossby number in this case would be 32,000. Needless to say, one does not worry about which hemisphere one is in when playing baseball.Watchwolf49z (talk) 18:38, 5 January 2013 (UTC)

Done Watchwolf49z (talk) 16:22, 12 January 2013 (UTC)

• I’ve found a reference for the mass flow meter material presented in this article. It looks valid to me and contains a fair amount of referencing itself. I propose footnoting the entire sub-section with http://www.omega.com/literature/transactions/volume4/t9904-10-mass.html.Watchwolf49z (talk) 18:38, 5 January 2013 (UTC)

Done Watchwolf49z (talk) 16:22, 12 January 2013 (UTC)

• Draining in bathtubs and toilets - It looks like the paragraphs got mixed up. The information in the second paragraph is far more notable than in the first. I find it reads just as well both ways, although reversing the paragraphs doesn’t create a contrast. The information flows into each other quite well. I propose reversing the order of these two paragraphs and deleting the phrase "In contrast to the above". Watchwolf49z (talk) 17:55, 12 January 2013 (UTC)

Done Watchwolf49z (talk) 19:32, 19 January 2013 (UTC)

• Distant Stars - This is currently unreferenced. I have the feeling it can be found in all the archives, and someone will need to track it down. On the other hand, I’m not seeing how this is notable. Astronomers just point their polar axis toward Polaris, stars then track a straight line across the eyepiece. I propose deleting this section entirely, based on lack of notability. Watchwolf49z (talk) 17:55, 12 January 2013 (UTC)

This section was inserted after an edit war with an editor with a rather confused mixup with orbital equations. It represents the most pure case, where nothing really moves; there is only rotation. Let's keep it. −Woodstone (talk) 19:04, 12 January 2013 (UTC)

Do you remember how long ago? That's where the reference is I'll bet. Throw up the footnote and it'll be good, far and away more notable than fruit flies. Watchwolf49z (talk) 19:57, 12 January 2013 (UTC)

The current version was entered on 2011-09-30. There is no reference on talk, but it is a straightforward application of the general formula, so none is needed. But isn't it insightful to realise that the curved path of Sun during the day is mostly due to the combined Coriolis and Centrifugal forces?−Woodstone (talk) 04:53, 13 January 2013 (UTC)

Yeah, this would be an edit war alright. After reading WP:OR, I'm left with the impression that this section would cause us to be denied "Good article" grade. Perhaps if the insight was more explicitly stated the reader could understand which secondary source this illustrates. I just don't know, as long as one of us thinks it's notable, then it belongs in the article. Watchwolf49z (talk) 15:14, 14 January 2013 (UTC)

Withdrawn. Watchwolf49z (talk) 19:32, 19 January 2013 (UTC)

An Aside

I'd like to find out what everybody thinks of the idea of moving Tossed ball on a rotating carousel sun-section from Special Cases into it's own section, and then putting this new section just after History section. The reason is to get a simple and more detailed example to the readers' eyes before we go into the formula and causes. I've chosen this particular example because it is fairly common in the literature, and footnoting a reference would be almost a "pick-em" decision. Does anyone have a favorite, or can I just throw one up that substantiates the statements in the article? Watchwolf49z (talk) 16:19, 24 January 2013 (UTC)

• An IP editor tagged the Bullet sub-section for a citation. This is already given in the Causes section as Littlewood (1953). I propose just adding the footnote and clear the tag. Watchwolf49z (talk) 16:07, 26 January 2013 (UTC)

Done Watchwolf49z (talk) 17:39, 2 February 2013 (UTC)

• In the Bathtub section, we have the parenthetical phrase once per day at the poles, once every 2 days at 30 degrees of latitude. I was just in Miami, I rotated once per day. I propose just deleting the whole phrase as not relevant to the statement. Watchwolf49z (talk) 16:07, 26 January 2013 (UTC)

This refers to the factor sin φ, which appears in the horizontal component of the rotation at latitude φ. There is no Coriolis force on the equator. But agree to omit in this context. −Woodstone (talk) 22:26, 26 January 2013 (UTC)

Done Watchwolf49z (talk) 17:39, 2 February 2013 (UTC)

I've undid a couple edits, the IP edit is obvious, the other was because it was duplicated in the references. I'm okay with this duplication and agree that the Persson (1998) is a good selection for "Further Reading". Watchwolf49z (talk) 17:39, 2 February 2013 (UTC)

Thank you, Woodstone ... there's a bit of dialog from last week on his talk page. I'm still thinking of bringing in Waleswatcher in on this, GK can't just call anyone he pleases a vandal. Watchwolf49z (talk) 13:37, 3 February 2013 (UTC)

Please check you minds whether an empty link is worthy of explaining the coriolis force. Vandal might not be the best characteristic of an empty mind. Gabriel Kielland (talk) 20:49, 3 February 2013 (UTC)

Two points:

• Copies of articles once pointed to by dead links can often be found by using the Wayback Machine, as in fact was the case for this particular "empty link".
• While you're entitled to remove dead links from an external links section, there is no requirement—as far as I know—that this must be done immediately. A preferable alternative, in my opinion, is to tag the link with a Dead link template. This should increase the chances that someone who might be a little more enterprising than you are will be able to track down a live link to a copy of the original resource.

David Wilson (talk · cont) 12:49, 4 February 2013 (UTC)

• The Littleton (1953) reference has an addition statement. I propose moving it into the article itself in the Bullet section. Watchwolf49z (talk) 17:39, 2 February 2013 (UTC)

• There wasn't any discussion about moving Tossed ball on a rotating carousel sun-section up in the article. I propose that now, let's see what it looks like. Watchwolf49z (talk) 17:39, 2 February 2013 (UTC)

I undid the IP edit, 1835 is the correct date of publication (see `further reading` section). However, the added `de` might be technically correct, as in Gaspard-Gustave de Coriolis, I don't know enough Italian to know the difference. Watchwolf49z (talk) 20:57, 4 February 2013 (UTC)

I'm sorry that my comment isn't constructive in that it doesn't offer an alternative, but it seems to me that this article is confusing in that it mixes the effects of an object moving over a rotating body when it is NOT BOUND to that rotating body (e.g. throwing an object to someone on a turntable) with the effects of an object moving over a rotating body when it IS BOUND to that body (e.g. weather systems on earth, figure skater spin, office chair spin). THe former of these is simply a frame of reference effect, which is pretty simple; the latter is conservation of angular momentum (and the coriolis effect). What's more the deflection in trajectory is opposite for the two effects. ??

PhilDWhite (talk) 21:34, 6 February 2013 (UTC)

Yes, the article is incomplete. You are certainly welcome to help, there's still quite a bit that can be said in this matter. The physics presented is sound, but the meteorology is somewhat lacking. All I ask is be quick to revert your own edits if someone voices an objection. = Watchwolf49z (talk) 16:22, 8 February 2013 (UTC)

@PhilDWhite - do you have a source that makes this distinction? At least in the case of weather systems, the two sources mentioned previously (Marshall et al. and Haltimer et al.), which talk about this in the meteorology context, seem to derive the Coriolis force/effect based on the transformation from the non-rotating to the rotating frame, which to me would seem to be true for both bound and unbound objects. From my reading, I don't see this distinction made in the literature, but perhaps there's a source out there that does?

I do not believe that there is such a distinction. Martin Hogbin (talk) 13:41, 20 February 2013 (UTC)

If the objects aren't bound to the sphere, wouldn't they fly off into space? Weather occurs in atmospheres which by definition is a fluid bound by gravity. = Watchwolf49z (talk) 15:17, 21 February 2013 (UTC)

Yes, so what? Martin Hogbin (talk) 16:58, 21 February 2013 (UTC)

Well ... it would improve the article if this was made more clear? = Watchwolf49z (talk) 18:03, 21 February 2013 (UTC)

What exactly needs to be made clear? We need to make clear that is one Coriolis force, which is an inertial force found only on rotating frames of reference, but it can appear in a variety of circumstances. Do you agree? Martin Hogbin (talk) 18:22, 21 February 2013 (UTC)

By the way, why do you mark your comments as minor edits they are just normal edits and if you mark them as minor some interested parties may miss them. Martin Hogbin (talk) 18:23, 21 February 2013 (UTC)

Well, that would depend on precisely what assumptions you're making, which aren't spelt out precisely enough to give a definite answer to the question. If you're assuming that the force of gravity on a body at rest on the surface of the Earth were somehow suddenly turned off, a more apt description for its initial motion would be "float off" rather than "fly off". In the rotating frame of the Earth the only appreciable force or pseudoforce initially acting on the body would be the centrifugal, which would produce an acceleration of only about 3.3cm/sec² at the equator. After 10 seconds a body starting from rest on the equator would have risen only about 1.5 m and be travelling at only about 1.1km/hr, almost vertically upwards relative to the surface of the Earth, and the Coriolis force on it would still be negligible. After 100 seconds it would still have risen only about 16.5 m and be travelling at about 11km/hr. At that speed, air resistance would be enough to start reducing its upward acceleration somewhat. Nevertheless, it would eventually pick up sufficient speed for the Coriolis force to produce a noticeable and gradually increasing drift to the west.

But as long as we're going to make counterfactual hypotheses—i.e. that a body is not subject to gravity—why should we assume that it starts from rest on the surface of the Earth? Suppose instead that it's propelled westward down the centre of a perfectly evacuated toroidal tube encircling the Earth's equator. Suppose that the centre of the tube is at a distance r from the centre of the Earth, and that the body is propelled at speed ω r, where ω is the angular velocity of the Earth's rotation. In the rotating frame of the Earth The body is subject to a vertically upward centrifugal force of ω² r and a vertically downward Coriolis force of 2 ω² r. The resultant downward pseudoforce of ω² r is exactly enough to prevent the body from "flying off" to the upper surface of the tube, and will keep it moving at speed ω r along the tube's centre. With respect to the distinction you are trying to draw between bodies "bound to the sphere" and ones "not bound" to the sphere, would this body count as belonging to the former or the latter category? And, more to the point, why would it belong to either one, rather than the other?

While I don't want to deny categorically that any such distinction can be drawn, I have to say that, like Martin Hogbin, I haven't the foggiest idea what it is that you're trying to make "more clear". Unless you're really able to make it more clear on this talk page, I don't think it would be possible for you to do so in the article itself.

David Wilson (talk · cont) 03:32, 22 February 2013 (UTC)

P.S. To forestall any quibbles that my toroidal tube example wouldn't work because of the Earth's motion around the Sun—or various other practical difficulties—I should acknowledge that yes, I realise that this would be so, and that I have simply ignored them.

David Wilson (talk · cont) 03:53, 22 February 2013 (UTC)

Intuitive explanation of the Coriolis effect

I made an edit 2/17/2014 by adding a paragraph to the intuitive explanation of the Coriolis effect. It was removed 6 days later by tentinator. I would like to be given a reason for its removal. The explanation I gave is intuitive, accurate, and easy to understand. A Thousand Clowns (talk) 02:30, 24 February 2014 (UTC)

The intuitive explanation is awful! I cannot understand it. There's a lot of jargon in it. The bottom line is that your rotational velocity of the earth declines as you move to the poles and vice versa. Thus, if you start at the equator, (which has the highest rotational velocity), because of conservation of momentum, as you move north (or south) you retain the eastward momentum you had at the equator. Meanwhile, the Earth beneath you is slowing down, so you will move to the east relative to the ground. When proceeding toward the equator, you have a small rotational velocity, thus as you move the Earth's surface under you appears to speed up, and you will move west relative to Earth's surface. If there's no objections, I will attempt to rewrite this section presently. Warren Platts (talk) 15:57, 30 March 2014 (UTC)

Many have gone before you to try for a better intuitive explanation. Note that it should not only explain the effect on North/South movements, but also for East/West, which is equally large (and preferably also for up/down). −Woodstone (talk) 16:52, 31 March 2014 (UTC)

Contradiction regarding vortex circulation in schematic figures

The photo showing the vortex over iceland says the vortex spins 'counter-clockwise', whereas the figure of the earth below, showing the vortex circulation patterns, shows vortices spinning clockwise on the northern hemisphere. One of the two must be wrong, apparently. — Preceding unsigned comment added by 131.188.166.21 (talk) 14:26, 14 April 2014 (UTC)

Both are correct. They occur in different circumstances. The first shows airflow caused by air pressure differences, the second the trajectory of a floating object in absense of driving forces. −Woodstone (talk) 16:16, 14 April 2014 (UTC)

I recommend making a note about this difference in the caption for the lower figure. Otherwise one has the initial impression that the figure is wrong. — Preceding unsigned comment added by MuTau (talk • contribs) 17:33, 6 October 2014 (UTC)

Coriolis force is not intuitive

The second sentence in the lead is quite correct. If an object is moving towards the centre, in the case of clockwise rotation, it will be deflected to the left. It's always to the left for clockwise rotation, no matter whether the object is moving towards or away from the centre of rotation. But for the case where it is moving towards the centre, the situation is counter intuitive. If it were simply a case of the observed deflection from a frame of reference that is rotating clockwise, then the deflection for an object moving towards the centre would be to the right. That's why I removed a few words from the first sentence. By all means restore if you think I am wrong, but I would like to hear some comments. 94.173.45.184 (talk) 18:42, 13 November 2014 (UTC)

I guess I'm not seeing the connection between your above argument and the phrase "when they are viewed" in the first sentence. IMO the phrase is important because when a moving object is viewed in a non-rotating frame, there is no Coriolis force. Even for an stationary observer watching a ball roll across a rotating table, if she does the mechanics in her stationary frame there still is no Coriolis force. I've reintroduced the phrase with some tweaking to make clear what is meant by "viewed". This is in line with every reliable source that says that the Coriolis force is an artifact of the rotation of the reference frame being used to describe the objects motion. Do you have a source that says otherwise? Perhaps the confusion is that the velocity that goes into calculating the Coriolis force is the velocity in the rotating frame and not the velocity in stationary frame? --FyzixFighter (talk) 15:10, 15 November 2014 (UTC)

Sorry, second thought here. I think I see your argument now, but I disagree with the statement that the deflection for an object moving towards the center would be to the right if it were simply a case of observed deflection from a frame of reference. For example, if we have an object moving with constant velocity in a straight line from some point on the rim to the center as seen in a stationary reference frame, then in a reference frame with clockwise rotation the initial velocity has a radially inward component as well as a tangential component in the counter-clockwise direction. The object then will be seen in the rotating frame to curve to its left (based on its velocity in the rotating frame) and eventually pass through the center. For me this is easier to seen when taken to an extreme, ie that of a very very small radially inward velocity as seen in the stationary frame. However in a clockwise rotating frame the object is seen to be moving counter-clockwise and slowly spiraling inwards. In the rotating frame the spiraling inwards is explained as the Coriolis effect deflecting the object radially inward, or in other words to the left relative to the objects mainly counter-clockwise velocity (as seen in that frame). --FyzixFighter (talk) 16:13, 15 November 2014 (UTC)

FyzixFighter, I'll use the case of firing a cannon from a rotating platform to illustrate my point. If a cannon is fixed on a rotating platform and then fired, the Coriolis force acts on the cannon ball as a natural consequence of conservation of angular momentum. However, if we are on a rotating platform and observe a cannon that is not on the platform, firing from the stationary ground below the platform, the situation is quite different. In the former case for a clockwise rotation and a cannon firing inwards to the centre, the deflection will be to the left as per the Coriolis force. In the latter case, the deflection will appear from the rotating frame to be to the right. My point was that a Coriolis force acts within a rotating system. Observation alone is not sufficient. We need more than just observation for a Coriolis force to occur. That's why I adopted a bear minimalist approach to the wording, in order to avoid these subtleties. Coriolis force is about everything being in the rotating system. Your amendment uses the idea that the Coriolis force occurs when the motion is described in a rotating frame. It might, but it might not. It depends on other factors as well. Best to leave it as I suggested in order to avoid such issues in the lead. Maybe these issues can be discussed in a special section. 94.173.45.184 (talk) 17:42, 15 November 2014 (UTC)

Sorry but I still disagree. In the latter case, the deflection in your latter case (a stationary cannon firing inwards observed from a clockwise rotating frame), I see the deflection due to the Coriolis effect being to the left relative to the cannonball's velocity in the rotating frame, mainly because in the rotating frame, the cannonball has a counter-clockwise component to its velocity along with the radially inward component. If the deflection where to its right, the cannonball would curve away from the center. Instead, the deflection is to its left and towards the center so that both the rotating observer and the stationary observer agree that cannonball crosses the center. To sum up the points and to see where we may disagree:

1. The initial velocity of the cannonball in the clockwise rotating frame has both a radially inward component and a counterclockwise tangential component
2. The cannonball follows a curved path so that it crosses the center
3. The deflection is to the left relative to the cannonball's velocity (if you were facing the direction the velocity vector points)

In your former case, a stationary observer doesn't see a Coriolis force and will see the cannonball follow a straight line once it leaves the cannon. Only in the rotating frame will an observer have to invent a fictitious force perpendicular to the ball's velocity to explain cannonball's motion in that frame.

Like I said, all the sources I've seen are pretty clear in saying that the Coriolis force/effect is an artifact of describing the motion in a rotating frame. Whether you have rotation of objects or not relative to the stationary frame is irrelevant, it's all about whether or not the coordinate system/reference frame is rotating. Do you have sources that suggest otherwise? --FyzixFighter (talk) 18:21, 15 November 2014 (UTC)

Clockwise rotation. Cannon on the ground under the rotating platform, not participating in the rotation. Cannon fires ball radially inwards to the centre. People on the rotating platform will observed the cannon ball deflecting to its right and spiraling anti-clockwise into the centre point. No Coriolis force. Imagine a clock is painted on the ground directly below the rotating platform. The cannon ball goes from 12 o'clock to the centre, in a straight line. To people on the platform, that line will regress anti-clockwise like a clock hand moving backwards. The cannon ball will be moving away from them to the right.

Now consider a cannon fixed on the platform and firing ball radially at the centre. Coriolis force will deflect the ball to the left, and the ball will miss the target. Let me check out some references to see what I can find out regarding whether or not it's purely a matter of observation. 94.173.45.184 (talk) 18:41, 15 November 2014 (UTC)

Perhaps this is the issue. The Coriolis effect is not about transformation of the velocity vector from the stationary to the rotating frame. In the stationary frame, the cannonball has a constant radially inward velocity, while in the clockwise rotating frame the initial velocity is both radially inward and anti-clockwise - I guess you could call this right relative to the radially inward velocity, but this is not the Coriolis effect found in textbooks. The Coriolis effect is what causes the ball to spiral inward to the center, so that the path of the ball is initially anti-clockwise but curves to the left (relative to the velocity of the cannonball) until it hits the center so the path looks something like a deformed "C" in the rotating reference frame. Note that the left/right definitions we are using here and in the article are with respect to the cannonball's velocity and not with respect to any observer. --FyzixFighter (talk) 19:06, 15 November 2014 (UTC)

First hit on google http://www.merriam-webster.com/dictionary/coriolis%20force implies that it's about the rotating system and not about how it's observed. 94.173.45.184 (talk) 18:49, 15 November 2014 (UTC)

So what is the difference between saying it's about the rotating system and not about the rotating reference frame? --FyzixFighter (talk) 19:06, 15 November 2014 (UTC)

OK. Even Gaspard Coriolis himself didn't see it as an observational artifact. He was working on coordinate frames fixed in rotating systems. If it were only an observational artifact, then we wouldn't observe the Coriolis effects in the atmosphere from space. And consider the rim of a spinning gyroscope. If we subject it to forced precession, the rim velocity becomes radial to the forced precession axis, and a Coriolis force causes it to tilt at right angles to the forced precession. That is a real effect, not an observational artifact. My point is that the Coriolis force is more than just an observational effect. The Coriolis force is a product of conservation of angular momentum within a rotating system. That's why it's best to leave the wording in the lead in a bear minimalist form. By using the terms 'observe' or 'describe' you are implying that real effects such as atmospheric effects or gyroscopic effects, magically come about as a result of making observations from a rotating frame of reference. It's just not as simple as that. That's why I reduced the wording in the lead to the simple term "in a rotating frame of reference". Anyway, let's leave it for somebody else to decide. I'm glad that you are thinking about the matter and I hope that others will think about it too, because the sources are not consistent. 94.173.45.184 (talk) 19:57, 15 November 2014 (UTC)

Putting it all very simply, in the case of single particle motion, the Coriolis force is not just about how we observe the motion from a rotating frame of reference. It's about how we observe conservation of angular momentum from a rotating frame of reference. But you can't put that in the lead. That's why it's best to leave 'observe' or 'describe' out of the lead altogether, because it is misleading in the absence of the caveat about conservation of angular momentum. 94.173.45.184 (talk) 20:50, 15 November 2014 (UTC)

Actually, I'll try, but feel free to take out the clause about angular momentum if you are not happy about it. 94.173.45.184 (talk) 20:52, 15 November 2014 (UTC)

Just because the force is an artifact of the rotation of the frame doesn't mean that effect isn't real. Take your example of the cannonball fired from the cannon on the rotating platform. In the rotating frame the cannonball has no angular momentum, so in the rotating frame it looks like the momentum is not being conserved which is why we have to introduce fictitious forces (momentum conservation is just another way of saying F_net=ma=dp/dt) to explain why it misses. However, in the stationary frame the cannonball leaves the cannon with both a r-hat and a theta-hat component to its initial velocity. Once it leaves the cannon, it follows the projectile path expected for that initial velocity - no Coriolis force is needed to describe its motion. Both frames agree that the cannonball misses the target, but they don't agree on why. Conservation of momentum only holds in stationary frames so effects that are attributed to conservation of momentum/inertia in the stationary frame have to be attributed to fictitious forces in non-stationary frames.

To paraphrase John Taylor's "Classical Mechanics" pg. 350, both the Coriolis and centrifugal forces are at root kinematic effects, resulting from our insistence on using a rotating frame of reference. In a few simple cases, it is actually easier to analyze the motion in an inertial frame and then transform the results to the rotating frame. However, the transformation between the two frames is usually so complicated that it is easier to work all the time in the rotating frame and live with the "fictitious" Coriolis and centrifugal forces. --FyzixFighter (talk) 21:41, 15 November 2014 (UTC)

It's an artifact of a real effect as viewed from a rotating frame of reference. That real effect is the conservation of angular momentum relative to the inertial frame. It's the conservation of angular momentum aspect that we were missing out on, in the earlier part of the discussion. Hence, when the cannon on the platform fires, the man on the ground sees no Coriolis force. He only sees conservation of angular momentum with respect to the origin of the rotating frame. On the platform however, they only see a Coriolis force while conservation of angular momentum appears to have broken down. 94.173.45.184 (talk) 22:06, 15 November 2014 (UTC)

Yes, I would agree with those last three sentences. But also remember that momentum conservation is part of Newton's laws of motion. More generally, conservation of momentum (both linear and rotational) appears to be broken in any accelerated frame which is why introduce fictitious forces like the centrifugal and Coriolis forces. This is why the sources say the fictitious forces are artifacts of the rotation frame - they are added only to bootstrap Newton's laws to rotating frames, but in the preferred inertial frame they do not exist. As long as we are describing rotating systems from a stationary reference frame, we don't have to invoke a Coriolis force. --FyzixFighter (talk) 22:24, 15 November 2014 (UTC)

FyzixFighter, See your talk page. There is alot more to this topic than can be discussed here. 94.173.45.184 (talk) 10:22, 16 November 2014 (UTC)

"Analogy to Magnetism"

The magnetic force is not similar to a Coriolis force, there ist no analogy beyond the cross product. The cited paper is not reviewed, not even published! Meier99 suggested this analogy in the german-wikipedia-article as well [4], but it was reverted and the resut of the discussion between the members of the WikiProject Physics ist clear: No original research - and no reliable source. I have deleted it for the second time. Kein Einstein (talk) 14:04, 25 November 2014 (UTC)

Ther are some similarities. Like a charged particle in a magnetic field a particle or a particle moving under the influence of just the CF does no work. Martin Hogbin (talk) 17:10, 10 April 2015 (UTC)

Variation with lattitude

I have removed a section stating that the force is greatest at the poles because it is misleading. As the article states, the Coriolis force depends only on the velocity of the object and the angular velocity of the reference frame. The Coriolis force is therefore independent of position on the Earth's surface.

For an air mass constrained to move parallel to the Earth's surface the Coriolis force does cause a greater diflection near the poles, which is what the source says, 'The Coriolis deflection decreases as latitude decreases, until it is zero at the equator'.

Because of this complication, I do not think the added text is suitable for the lead. I might be added in an appropriate section of the body ofthe article, where there is room to explain in more detail. Martin Hogbin (talk) 17:07, 10 April 2015 (UTC)

Hello Martin, I think the information is both sourced and relevant. It is about the horizontal component of the coriolis effect been stronger near the poles. in the previous sentence it was making reference about movement along the surface, so I think it is implied that we are talking about the horizontal component and that we are not changing altitude (with respect to earth).

The effect is due to changes in linear speed on the reference frame (Earth's surface) at different latitudes. Caused by the fact that even though the angular velocity of Earth is constant the diameters of circles of latitude is different at different latitudes and so linear speed is maximum at the equator and minimum at the pole.

The maximum change in that linear speed increases as we approach the poles the derivative of the cosine of the latitude is 0 at 0 (equator) and reaches its maximum value at 90 or -90 (the poles) which means that the rate of change in linear speed at the surface when we change circles of latitude (going north or south) approaches 0 as we near the equator 5 degrees travelling north from there make the diameter decrease by 0.4% (1-cos(5)) while five degrees from a pole towards another increase the diameter by 8.72%.

If the surface travel is within a circle of latitude there is no horizontal effect with respect to the frame of reference as linear velocity remains constant along a circle of latitude. Regards.--Crystallizedcarbon (talk) 19:03, 10 April 2015 (UTC)

I agree that the information is sourced and relevant but I do not think it is that clear that you are talking about the horizontal component of the CF. To make it clear, as you have done here, takes more text which makes it a bit long for the lead. It is better to add new text to the body of the article anyway rather than add everything to the lead.

Why not add your bit to an appropriate part of the body ofthe article, wher oit can be explained properly? Martin Hogbin (talk) 19:38, 10 April 2015 (UTC)

Hello Martin, I will follow your advice and I promise to add a more detail description to the body to make sure it is clearly explained, but I hope you don't mind that I have also restored it to the lead (with small changes, It was written force by mistake, when it is just an effect and I also mentioned the horizontal component), as I think it is important and it will help the casual reader understand better the effect. Regards.--Crystallizedcarbon (talk) 22:08, 10 April 2015 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Coriolis force/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Submit to GAC for external validation, but looks good. Titoxd(?!? - cool stuff) 00:35, 16 July 2008 (UTC)

Substituted at 20:21, 2 May 2016 (UTC)

What can and cannot be ascribed to the Coriolis Effect?

In the light of the above remarks, I reproduce a (rather lengthy and wide ranging) discussion between Seattle Skier and Cruithne9 on this very topic on the 3753 Cruithne Talk Page. The entire discussion is pasted here (suitably formatted for easy reading), with the exception of a short section that was irrelevant to the Coriolis effect. The signatures have also been shortened to diminish the potential clutter. Seattle Skier’s crucial conclusion at the end of the discussion is highlighted in red (bottom of the page). Whether this is a generally accepted interpretation of the Coriolis Effect I leave to the experts in the field.

Comment by Cruithne9:

I notice that Seattle Skier has removed the comment I made some time ago that 3753 Cruithne's curious orbit (as seen from earth) is an instance of the Coriolis Effect. His reason is that it is "not relevant" to Cruithne. In a note to me on my Talk page he says "They are completely unrelated effects, other than the fact that both are seen in rotating reference frames, they have no other connection".

The Coriolis effect is a deflection of moving objects when the motion is described relative to a rotating reference frame. This rotating reference frame can be a turn table in your home, a rotating bowl of water in a laboratory, or the motion of water, air, or long-range artillery shells across the rotating earth’s surface. It also applies to the geographic paths seen to be taken by artificial satellites that orbit the earth, and it is a Coriolis “force” that keeps geostationary satellites above a “fixed” position on the earth’s rotating surface. The curious motion of the planets that intrigued the ancients, but are now known, thanks to Copernicus, Galileo and Newton, to be due to Coriolis effects caused by using the earth (orbiting round the sun) as the frame of reference. When the sun is used as the frame of reference the planets' motions are far more straight forward. The same can be said about Cruithne’s strange orbit, as seen from earth. But, from what I gather Seattle Skier says (unless I am completely misunderstanding his very brief remarks), it seems that Coriolis mathematics does not apply, or is inappropriate at some arbitrary altitude above the earth’s surface. I’m obviously missing a very fundamental principle here. As far as I understand the Coriolis effect, it applies as much to an ant on a turn table watching a fly fly straight across that turn table, as it does to our observations of the motions of the objects in our solar system using our rotating and orbiting earth as the frame of reference.

Could someone please clarify whether or not 3753 Cruithne's motion as observed from earth is an instance of the Coriolis Effect or not. I'm very curious to know the readship's opinion on this.

Reply by Seattle Skier:

You appear to be misunderstanding some basic physics here, such as the extent of what the Coriolis effect is and what it applies to, and you are thus misapplying it to cases which really have nothing to do with it. Take your statement that "it is a Coriolis “force” that keeps geostationary satellites above a fixed position on the earth’s surface." That is completely untrue: the Coriolis force ${\boldsymbol {F}}_{C}=-2\,m\,{\boldsymbol {\Omega \times v}}$ on a geostationary satellite is zero, because its velocity in the rotating frame is zero. In the rotating frame, it is entirely the centrifugal force ${\boldsymbol {F}}_{c}=-m\,{\boldsymbol {\Omega \times (\Omega \times r)}}$ which is nonzero and keeps the satellite in place versus plummeting downward, not the zero Coriolis force.

That is exactly correct. There really should not be any discussion about these thinngs here. As Seattle Skier says, it is all basic, and well-understood Newtonian physics. Martin Hogbin (talk) 19:15, 26 August 2015 (UTC)

Your next statement that the "curious motion of the planets that intrigued the ancients, but are now known, thanks to Copernicus, Galileo and Newton, to be due to Coriolis effects" is also completely untrue, although for different reasons than the prior statement. The "curious" apparent retrograde motion of the planets can be explained without any reference to Coriolis effects or to any fictitious forces at all, it is a simple case of geometry and does not even need Newton's laws or any physics at all to explain. See the diagrams in the 3753 Cruithne article which should make this quite clear. Similarly, the motion of Cruithne can be explained by simple geometry in the rotating frame as shown in the animated image File:Horseshoe_orbit_of_Cruithne_from_the_perspective_of_Earth.gif, without needing Coriolis effects or any physics at all.

Your statement that "I’m obviously missing a very fundamental principle here" appears to be quite true. Hopefully these examples provide some of the very simple explanation which you have overlooked, and will make it clearer where the Coriolis effect actually applies, and where it does not.

By the way, it is irrelevant what the readership's opinion on this is, because what is important for Wikipedia is that any information added to articles be verifiable in reliable sources (and also be correct!). There are no reliable sources which state that 3753 Cruithne's motion as observed from earth is an instance of the Coriolis effect, because that is simply not true.

Reply by Cruithne9:

Thank you for this extensive explanation. I will need to ponder over it for a while to let the implications sink in, particularly in the light of the remarks about the apparent motion of distant stars as seen from the rotating earth in the "Distant stars" section in the Coriolis effect article, which seems to suggest that "any" motion (which I would imagine would include objects with an apparent velocity of zero) observed from a rotating frame of reference can be referred to as a "Coriolis effect". (No reference is provided in that section, so I cannot check whether astronomers are comfortable with the term or not, and what they would apply it to, if the term is used by them.)

PS. I don't want this to sound as if I am arguing with you. I'm looking for information and enlightenment. So I hope you will bear with me here. As you say above, the Coriolis force is an entirely fictitious "force", as is the Centrifugal "force". Both effects can be explained in terms of simple geometry and physics. I therefore struggle with the dismissal of one fictitious force (the Coriolis effect) in favor of another fictitious force (the centrifugal force) to explaining the apparent behavior of a geostationary satellite. These comments probably sound ridiculous to you, but I would desperately like to know what types of motion viewed from a rotating frame of reference can and cannot be termed "Coriolis" effects.

PPS. I think I may have discovered why we seem to be talking at cross purposes. When an object moves over the earth's surface (and is partially or wholly detached from that surface) it seems to follow a curved path. For someone observing that curved motion, and who is unaware that the earth is rotating, it would seem as if the object is subject to a sideways force causing it to deviate from traveling in a straight line. One can calculate the force that would account for this motion, and call it a "Coriolis Force". But it is an entirely fictitious force. The formula you use applies to this situation, which is a special case of the Coriolis effect. When a straight-line motion across the solar system is viewed from our orbiting perspective, the path would also appear curved. The formula needed to calculate the "force" that might be responsible for that curved motion would be different from the one you present above. Things become mathematically horrendously difficult if the "real" motion is circular or elliptical round the sun. But that does not mean that the distorted motion as viewed from the orbiting earth is not an instance of the Coriolis "effect".

Cruithne's bean shaped orbit in the vicinity of the earth is not due to Coriolis Forces (or, let's say, it would be foolishness to calculate them, as they would be unique to Cruithne, and applicable nowhere else in the universe). But that does not mean that its motion as seen from earth is not an instance of the Coriolis Effect. I hope this makes sense.

Reply by Seattle Skier:

I will try my best to patiently re-explain things, as I've done this sort of thing many times in the past with students (I don't currently teach physics, but had to do so often in the past during several years of graduate work prior to my PhD and then several years working as research faculty after that). I apologize in advance if my comments seem snippy or curt, that is not my intent, but it is hard to convey tone properly in online writing. However, a real problem here is that you're just making up a lot of things out of thin air to fit your pre-existing beliefs, things which are not true, and some of this may be due to failing to read various statements carefully. Please be willing to read carefully and learn, while not clinging to your pre-existing beliefs about this subject. From your statements above:

"As you say above, the Coriolis force is an entirely fictitious "force", as is the Centrifugal "force"." I never said this in what I've written to you, you're putting words in my mouth. See above, I say "without any reference to Coriolis effects or to any fictitious forces at all", I do not ever say that the Coriolis force is an entirely fictitious force. The use of that term "fictitious" leads to a lot of needless trouble, perhaps it's best to call them pseudo forces or inertial forces instead, as they are very real effects in the rotating frame.

"Both effects can be explained in terms of simple geometry and physics." Not true at all, where did you get this idea? Simple geometry cannot explain or derive either the Coriolis or centrifugal force, you must use physics in a rotating frame to derive them. But as I stated, simple geometry CAN easily explain the apparent retrograde motion of the planets and the motion of 3753 Cruithne, without needing any physics. This is the most fundamental issue that you are having, by failing to understand this key point. You're trying to turn problems which need only simple geometry into physics problems, when they are not.

"I therefore struggle with the dismissal of one fictitious force (the Coriolis effect) in favor of another fictitious force (the centrifugal force) to explaining the apparent behavior of a geostationary satellite." As the equations show, the Coriolis force is dismissed in this case because it is ZERO. The centrifugal force is not dismissed because it is non-zero. That is it. There is nothing to struggle with. The Coriolis force turns out to be zero in this case, so it is not relevant to the behavior of a geostationary satellite.

"but I would desperately like to know what types of motion viewed from a rotating frame of reference can and cannot be termed "Coriolis" effects." The only types of motion are those for which the Coriolis force ${\boldsymbol {F}}_{C}=-2\,m\,{\boldsymbol {\Omega \times v}}$ is nonzero. Anything else does not involve Coriolis effects. And anything which can be explained using simple geometry (not requiring physics) is definitely not an example of the Coriolis effect either. These are the 2 key points for clearing up this misunderstanding.

"remarks about the apparent motion of distant stars as seen from the rotating earth in the "Distant stars" section in the Coriolis effect article, which seems to suggest that any motion (which I would imagine would include objects with an apparent velocity of zero) observed from a rotating frame of reference can be referred to as a "Coriolis effect"." Where did you get that idea from reading that section? Does it state that ANY motion observed from a rotating frame of reference can be referred to as a "Coriolis effect"? No, it does not say that. That section (which is somewhat confusing, totally unreferenced, and probably worthy of deletion) is entirely about the spinning motion of stars around the poles (see the circumpolar star article for more info on this). And as the equations in that section show, by the 3rd line the Coriolis term completely vanishes and the total ${\boldsymbol {F}}_{f}=m\,{\boldsymbol {\Omega \times (\Omega \times r)}}$, which is only a centrifugal (centripetal) force with no Coriolis component remaining (there is no ${\boldsymbol {\Omega \times v}}$ term left). Therefore there is no Coriolis effect in the simple circumpolar rotational motion of the stars. The last line of that section says exactly as much ("therefore recognizable as the centripetal force that will keep the star in a circular movement around that axis"). Since there is no Coriolis effect in that motion, that section really does not belong in that article, and I may delete it after further thought on the matter.

"Cruithne's bean shaped orbit in the vicinity of the earth is not due to Coriolis Forces . . . But that does not mean that its motion as seen from earth is not an instance of the Coriolis Effect" Your first statement is true, the second one is false. The first statement implies that it is NOT an instance of the Coriolis effect. The bean-shaped motion relative to the Earth is derivable from simple geometry alone without needing any physics or Coriolis or whatever, and the animated image File:Horseshoe_orbit_of_Cruithne_from_the_perspective_of_Earth.gif demonstrates this derivation nicely. Please don't go looking to desperately call it a Coriolis effect, when it's just a simple geometric effect caused by the relative orbits of Earth and 3753 Cruithne around the Sun.

Reply by Cruithne9:

You present the image File:Horseshoe_orbit_of_Cruithne_from_the_perspective_of_Earth.gif as a sort of "proof" that Cruithne's bean-shaped motion relative to the Earth is derivable from simple geometry, and geometry alone, without needing any physics or Coriolis "forces" or whatever. But exactly the same can be said of all the following examples of the Coriolis effect taken from the following clips in the Coriolis effect article:

In the inertial frame of reference (upper part of the picture), the black ball moves in a straight line. However, the observer (red dot) who is standing in the rotating/non-inertial frame of reference (lower part of the picture) sees the object as following a curved path due to the Coriolis and centrifugal forces present in this frame.

Object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been released in such a way that it follows an elliptical trajectory.
Left: The inertial point of view.
Right: The co-rotating point of view.

and this animation clip of a cannon ball being fired from a rotating platform.

In each case the motion seen by an observer on the rotating non-inertial frame of reference can be explained even more obviously, simply, and in its entirety, by geometry, without recourse to any physics, or related sciences, than your example of Cruithne's orbit, when viewed from an inertial (stationary) frame of reference. I see absolutely no difference between your example of the File:Horseshoe_orbit_of_Cruithne_from_the_perspective_of_Earth.gif and the examples given in the Coriolis effect article (and other sources) of the "genuine" instances of the Coriolis effect.

Furthermore, if I understand you correctly, you maintain that the formula for the magnitude of the Coriolis Force, ${\boldsymbol {F}}_{C}=-2\,m\,{\boldsymbol {\Omega \times v}}$, defines the Coriolis effect. But consider this situation. A spot of light from a laser pointer is moved at a uniform speed, in a straight line across a rotating turntable (the spot of light does not need to move across the center of the turntable). If the surface of the turntable is light-sensitive, the spot will leave a trail on the surface which is curved to exactly the same extent as the trail left by a ball rolled across the turn table at the same velocity. It is difficult to conceptualize a real physical force that will have such a profound effect on a spot of light. Now move the spot of light in an ellipse across the turntable. The ellipse’s dimensions are a scale model of Cruithne’s orbit around the sun, with the turntable’s axle in the position of the ellipse’s “sun”. It is timed so that the ellipse is completed in exactly the same time as one rotation of the turntable. A bean shaped trail will be formed on the turntable, which is a miniaturized version of the orbit of Cruithne as seen from earth. If you acknowledge that this is an instance of the Coriolis effect, then the one we see in the sky must also be due to the Coriolis effect resulting from our orbit round the sun.

More on the Coriolis effect (continued)

Although I have no idea of how much of this discussion should be continued on the Talk pages of Wikipedia, because, much of this discussion could be resolved very quickly and efficiently through a face-to-face interaction, and then posted on this page in a few sentences, I feel I have to respond to some of the comments you have made.

Firstly, all of the texts explaining the Coriolis effect, including the Wikipedia article on the subject, start with the example of a rotating turntable or carousel, across which a pencil line drawn with a ruler (by a person outside the turntable) or balls tossed across the carousel either by a person on the carousel or by a person outside the carousel seem to follow curved trajectories when viewed by the person on the carousel.

Consider a rotating carousel (or merry-go-round), which, seen from above, is rotating clockwise. We will call the person on the carousel the “rotating” person, and the one on the ground outside the carousel as the “stationary” person. Any ball thrown across the carousel by either person follows a straight line as seen by the stationary person. But the rotating person will always see a curved trajectory. From the rotating person’s point of view it therefore seems that there is a force that acts (horizontally) perpendicularly to the ball’s motion to cause it to deviate from the Newtonian straight-line motion. This in not a real force, but an artefact of the observation relative to a non-linear rotating reference frame. (This is a direct quote form a Physics text book. The Wikipedia article on the Coriolis effect calls it a fictitious force, as do several other sources at my disposal). The entire effect can best be explained in terms of simple geometry, which, in your terms, if I understand you correctly, means that it is NOT an instance of the Coriolis Effect.

Where a “real” force comes into play (and cannot be explained in terms of simple geometry) is if the rotating person tries to move from point A to point B on the rotating carousel. If point A is close to the center of the carousel, and point B is near the periphery, then, if this person sets out in what he imagines is the shortest distance between the two points, he ends up to the left of his target. In order to reach point B he has to exert a sideways acting force to move him more and more to the right as he moves outwards towards B. On the carousel he will have traced a straight line trajectory, but according to the stationary person on the ground outside the carousel he will have moved along a curved path which can only have been caused by a sideways force. This force (or acceleration) is indeed real, because it required the expenditure of energy from both the rotating and stationary observers’ points of view. Is this the only instance of the Coriolis effect you would recognize as such?

If the turntable and carousel examples provided in all the introductions to the texts on the Coriolis effect are genuine, prototypical instances of the Coriolis effect then, by extension, any Newtonian motion beyond the carousel, viewed by the rotating individual, will also subject to Coriolis effects. Thus a ball thrown away from, or beyond, the carousel’s rim will also follow a curved as seen from the carousel. Indeed if it stays in the air for several turns of the carousel it will appear to follow an outwardly spiraling trajectory. In all cases the motion can be explained in terms of simple geometry from the point of view of the stationary observer. But if Newtonian motion across the carousel is correctly described as Coriolisean by the rotating observer, then the motion beyond the carousel must also be due to the Coriolis effect. It then ineluctably follows that motion observed from our orbiting earth of the planets and other objects in the solar system are also affected by the Coriolis effect. The fact that the complicated motions observed from earth are best resolved by translating them into the motions that would be seen by an individual in a stationary position in relation to the sun does not negate the fact that from the earth these motions are due to Coriolis effects, even though the stationary observer would ascribe them to simple geometry. The Coriolis effect does not exist for a stationary observer. But they are very real for an earth-bound observer unaware that (s)he is on a huge 3 x 10⁸ km diameter carousel centered on the sun.

I know that you have said above that this nonsense, but you have not explained why it is nonsense, nor given any examples of when and how the Coriolis effect applies. For instance, are you suggesting that the turntable and carousel examples used in all the texts explaining the Coriolis effect are simply “lies to children” (to quote Terry Pratchett)? What would your interpretation of these examples be? In the “Visualization of the Coriolis effect” section of the Coriolis effect article in Wikipedia a puck of dry ice is slid across a bowl of spinning water. This puck follows an elliptic track (as seen by a stationary observer) across the parabolically curved surface of the rotating water in the bowl (although it bounces back and forth off the rim of the bowl). The Coriolis motion as recorded by a camera mounted on the rim of the rotating bowl is uncannily reminiscent of the orbit of Cruithne as seen from earth.

Unraveling the Coriolis effect (continued)

I have tried my best to come to grips with your understanding of the Coriolis Effect. I have also re-read all the texts at my disposal on the subject. The result is that several things bother me about your exposition of the Coriolis Effect. Firstly you jump from one frame of reference to the other (i.e. from the “rotating” frame of reference to the “stationary”, and vice versa) without warning, or explaining why the one takes precedence over the other in one circumstance and not the other. Obviously when discussing the Coriolis effect both must be described side by side, equally weighted, to explain how the one is represented in the other frame of reference. To me all instances of the Coriolis Effect are simple examples of uncomplicated Newtonian motion when seen by the “stationary observer”, who can then apply some simple geometry to derive what that motion will look like from the rotating individual’s point of view. Things are a little bit more complicated for the person on the rotating platform. If that person assumes that when an object moves from A to B it should, according to Newton’s Laws, follow a straight line unless acted on by an external force. Thus when an object in his world follows a curved trajectory it must be acted upon by a force which he calculates can be derived from the formula ${\boldsymbol {F}}_{C}=-2\,m\,{\boldsymbol {\Omega \times v}}$.

Object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been released in such a way that it follows an elliptical trajectory.
Left: The inertial point of view.
Right: The co-rotating point of view.

But now consider the diagram which appears in the Coriolis Effect article of an object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been released in such a way that it follows an elliptical trajectory. If the rotating person applies the formula to the motion of this object (as seen from their perspective), assuming that it would be moving in a straight line were it not for the “Coriolis Force”, derived from his formula, he would obtain the wrong result for the motion he sees. They would need to know what a “stationary” person sees: portions of an elliptical trajectory, and apply the Coriolis formula to that motion to explain what they see. Without that knowledge, to which they might not be privy, the motion seems inexplicable, and not governed by the Coriolis formula. (I know that you will maintain that the Coriolis formula is still in force, but in order to establish that, you have to move your frame of reference, in which case it is probably easier to use simple geometry to predict the object’s motion across the rotating frame of reference, which, if I have understood you correctly, ensures that it is no longer an instance of the Coriolis effect.)

You mention that when $v$ in the formula is zero then the Coriolis Force must be zero as well, and the phenomenon cannot be stated to be an instance of the Coriolis Effect (because it is the force that defines the Coriolis effect). But consider the following situation. An object moves in a straight line at uniform speed right across a rotating turntable, from one rim to the other. It does not cross the center point of the turntable. The velocity of the object is adjusted so that it crosses the rim (onto the turntable) at the same point as where it leaves the turntable a short while later. The track of the object on the turntable forms a loop. At the point on the loop nearest the center of the turntable, the object is, for an instant, stationary with respect to the turntable – its velocity is exactly the same as the angular velocity at that point on the turntable. Thus, for that instant in time, $v$ is zero, and the Coriolis Force is zero. So, for a moment the Coriolis effect is suspended, which sound very much like the contention that when a missile is shot vertically upwards and its velocity slows to zero at the apex of its flight, the force of gravity acting on it is zero.

I hope you understand my concerns, which I, furthermore, hope are not due to unjustified prejudices.

Reply by Seattle Skier:

This reply addresses both what you've written above, and your August 4 post on my talk page. Please understand that this will be my final comment on this topic, as I definitely don't have the time to continue this discussion any further. Sorry about closing it off, but you seem quite stubborn about this subject, which is frustrating for me and not enjoyable to deal with, and in some cases you also try to extend the scope of my comments too far beyond what I've actually written. I realize by now that whatever I say is unlikely to shift your views closer to the limits of what professional physicists consider to be Coriolis effects (versus the vast broad overextension that you prefer where Coriolis effects are seen everywhere in all situations that could be viewed in a rotating frame). So we'll just be going in circles here (!) if we continue this.

Key points to remember to unravel and understand the Coriolis effect:

• Only the most simple (trivial) examples used to demonstrate the Coriolis effect can be solved using simple geometry. In general, to solve any problem, physicists prefer to use the most simple description / method / frame of reference which gives a valid solution, so if you can solve a problem with simple geometry or by physics in the stationary frame, then great, do it that way, and don't bother using the rotating frame or Coriolis. You're confusing trivial demos which can be used to demonstrate what the Coriolis effect is (some of the simplest cases from the turntable / carousel demos) with problems which actually require using Coriolis effects in a rotating frame for their solution. The simple demos are great for an educational purpose, because they can be solved in both the stationary frame and the rotating frame.
• Real non-trivial examples of the Coriolis effect can NOT be solved by simple geometry, nor can they be solved in the stationary frame. It is simply not practical or possible to solve for the motion of the winds in the atmosphere, long distance artillery shells, Foucault pendulum, or various other classic real-world examples, using simple geometry or the stationary frame. These problems can only be handled in the Earth's rotating frame, leading to Coriolis effects. These are the cases that professional physicists would normally refer to as examples of Coriolis effects.

Returning to the original issue at hand here: in order to include anything in Wikipedia, it must be verifiable in reliable sources. There are no reliable sources which state that 3753 Cruithne's motion as observed from earth is an instance of the Coriolis effect (nor the motion of any other astronomical bodies), and so it can not state that in the article. Thanks.

Reply by Cruithne9:

Thank you very much. That makes it a it a lot clearer and understandable, and I am happy to close the discussion.

Cruithne9 (talk) 09:34, 26 August 2015 (UTC)

Seattle Skier, You have explained the physics very well here. Your opinion would be most welcome on the centrifugal force page. The physics there is now correct but there is so much disinformation and confusion about the CF that I think we need to address it in some way.

what is this section about distant stars? it makes no sense physically.

this section about the coriolis effect and distant stars seems to make no physical sense. in my opinion, it is bogus. — Preceding unsigned comment added by 63.172.27.2 (talk) 19:04, 13 August 2015 (UTC)

I've deleted the section on distant stars, as the Coriolis term vanishes entirely and there is only a centripetal term, so the apparent motion of distant stars really has nothing to do with the Coriolis effect as that term is commonly understood. I had been thinking of doing this deletion for the last few weeks based on an ongoing discussion about the motion of 3753 Cruithne which had also been included in this article, but which I deleted. --Seattle Skier (talk) 06:35, 25 August 2015 (UTC)

I am not sure if the section ought to be in the article but it would have been correct had is started, 'in the rotating reference frame of the Earth'. Martin Hogbin (talk) 08:14, 25 August 2015 (UTC)

That is correct. The Coriolus effect provides a centripetal fictitious force on distant objects, when one enters a rotating frame and observes these distant (formerly static) objects. The fixed stars a great example of this. They go around you, and a fictious force is needed to explain their motion, and that force must be a centripetal one, since they are accelerating in an inward direction, by moving in a circle. There is of course a outwardly-directed (fictitious) centrifugal force m ω v too, but the Coriolis force is exactly twice as large (see that 2 in front of the Coriolus term?) and it wins out. I don't know why you think the Coriolus effect vanishes, Seatle Skier. You have an m, you have a ω, you have a v and so you have a Coriolus -2 m ω v directed inward by the right hand cross product rule, since ω and v are orthogonal, and inward along r is the direction the cross product points. SBHarris 01:12, 26 August 2015 (UTC)

Hello @Sbharris: I think Coriolis is meant to explain the apparent deflection of moving objects in a rotating frame of reference. The calculations and result seem mathematically correct and make sense, but the end result is only a centripetal force, as it should be. While this shows that the formula works correctly in this case, there is no deflection other than just the resulting fictitious centripetal force. I think that it is easier not to use Coriolis to explain that force. The mathematical calculations are interesting, but since there is no additional deflection component to explain (only a centripetal force) and since the section contents were contested and there are no sources I think it is best to remove the information pending the result of this discussion. Maybe it could be rewritten to say that the Coriolis formula also holds in the case of (almost) static objects relative to the center of the rotating frame of reference, like the stars seen from Earth, as in that case it only yields the centripetal component needed to explain its apparent circular motion. Do you agree? --Crystallizedcarbon (talk) 06:50, 26 August 2015 (UTC)

The Coriolis and Centrifugal forces enable you to use Newton's laws (unchanged) in a rotating reference frame. They explain any kind of motion in such a frame.

Easiest, in this case, is not to use a rotating reference frame but to use an inertial (non-rotating) reference frame. In that case it is all very easy. There is no force acting on the stars, so they therefore keep still. Martin Hogbin (talk) 19:07, 26 August 2015 (UTC)

I agree with you Martin, I also agree with Seattle Skier that to explain the apparent motion of the stars from our point of view here on Earth it is easier to just use simple geometry.--Crystallizedcarbon (talk) 19:42, 26 August 2015 (UTC)

From our point of view here on Earth, fixed stars rotate on the night sky

It is not geometry, it is physics. What do you mean by 'from our point of view here on Earth'? Martin Hogbin (talk) 22:01, 26 August 2015 (UTC)

Hello Martin: All roads do lead to Rome, but when I go there I prefer to fly by plane . Assuming that the stars are fixed with respect to Earth (Expansion of the universe, rotation around the sun, etc. are negligible) and since the Earth is rotating at an angular velocity of roughly 361º per day. From our point of view here on Earth, when we look at the night sky, the fixed stars seem to be rotating with that same angular speed around Polaris (for the northern hemisphere). As demonstrated above, you can use Coriolis and centrifugal forces to calculate their path speed etc. but what I mean is that is not the only way or the simpler way to do so. It is easier to explain their motion without the use of physics or forces. You can use Geometry (its mentioned in the introduction of the article), the formula for angular velocity and some simple trigonometry. Regards. --Crystallizedcarbon (talk) 07:33, 27 August 2015 (UTC)

Geometry and physics

Yes, of course you can use trigonometry to calculate the stars' positions relative to the Earth if we take it that the Earth is rotating with respect to the stars but that is not the problem. The problem is one of physics. We have to explain why the stars do not change their positions. In an inertial reference frame that is trivially easy. Ignoring all the things that you mention above, there are no forces acting on the stars, therefore by application of Newton's first law of motion, every star 'either remains at rest or continues to move at a constant velocity, unless acted upon by an external force'. Having done the, trivial, physics in this inertial frame, we can then do some simple geometry to calculate the stars' positions relative to a rotating Earth at any time. That is exactly what you suggest.

The problem arises if when we try to do the physics in the rotating reference frame of the Earth. In that frame, the stars are moving in circles but there are no forces acting upon them. How can we explain this? Newton's first law tells us that, without a force acting upon them they should continue at constant velocity (in a straight line), but they do not do this they move in circles. We cannot use Newton's laws in a rotating frame unless we invent some extra (inertial) forces. In this case we need to use the centrifugal and Coriolis forces. We can then do all Newtonian mechanics in exactly the same way as if we were in an inertial frame so long as we add in the two inertial forces.

In this particular case, we all agree that it is much simpler to do the physics in an inertial frame and then, if we wish, use simple geometry to calculate the result in a rotating frame. There are cases though where this is not the best approach. For example, as Seattle Skier mentions above, it would be very difficult to calculate the motion of the atmosphere in a cyclone in an inertial frame. It would also be very unnatural because we generally consider wind velocity to be with reference to the Earth's surface, not some (non-rotating) inertial frame. generally it is best for those studying elementary physics to work only in inertial reference frames until they get a good understanding of Newton's laws.

I do agree that this may not be a good example for this article unless all the above is very clearly explained. Martin Hogbin (talk) 09:26, 27 August 2015 (UTC)

I agree with your conclusions @Martin Hogbin: I think we only have a minor semantics difference. In the definition of this particular problem we state the assumption that the position of the fixed stars with respect to Earth is fixed. Personally, I don't see a need to invoke Newton's first law to reaffirm that they remain fixed, or for that matter why the Earth is rotating at a constant angular velocity, etc... so, like you, I think that this simple problem is easier to solve without the use of physics or Coriolis, just geometry. I agree with you that if you want to "do the physics in the rotating reference frame of Earth", then you need Coriolis but I don't see a practical application for doing so in this particular case, other than to show that the formula does works and Newtonian mechanics still apply in that reference frame. In my opinion I think that should be out of the scope of the article. Regards.--Crystallizedcarbon (talk) 11:42, 27 August 2015 (UTC)

In my opinion, we do need to explain why the fixed stars remain fixed and why the Earth continues to rotate at a fixed rate. You may consider these things obvious but you are underestimating the huge advance that Newton made to our understanding. In the millennia before Newton nobody had a clear idea of why some things moved and others did not. Newton's laws of motion and gravitation explained the motions of celestial bodies and things on Earth in a few simple laws. Anyone who asks the question of why, when, and how, things move needs only to apply Newton's laws to get an answer (for evErything up to and including the Moon landings).

There is no doubt that to explain the motion of the stars it is easiest to work in an inertial frame. The use of a frame rotating with the Earth is just an academic excersise to show how to do physics in a rotating frame of reference but please bear in mind that that is exactly what this article is about. When working in an inertial frame, which is always recommended for beginners, Coriolis and centrifugal forces do not exist. What would you say to having Centrifugal_force#An_equatorial_railway, which is pretty much the same question, in this article. Martin Hogbin (talk) 12:16, 27 August 2015 (UTC)

I like physics and I admire Newton. Since this seems like a slippery slope leading to a math vs physics argument and since I agree with your conclusion that the use of Coriolis in this case is an academic exercise, I am happy to just agree with you.

As far as the example that you mentioned I don´t think it should be part of the Centrifugal force article either as it is unsourced. As it is worded, even ignoring Coriolis it is easy to show that the train would not fly upwards. The reaction force from the track on either frame of reference counters the sums of the forces exerted on it (Fixing its value on one frame does not make too much sense to me). The centrifugal force generated in that frame of reference moving at that speed is orders of magnitude less than gravity (Geostationary orbit is at 35,786 kilometers above the equator). So even ignoring Coriolis there would be a resulting downward force that would be countered with a reaction from the track and the train would not fly.

If we can find references from reliable sources, I think it might be a good idea to include a similar example in the Eötvös effect section. Our train would be slightly heavier than when it was at rest, illustrating that in that case Coriolis points downwards and that there is no lateral deflection while travelling through the equator. If the train was travelling at the same speed but in the opposite direction it would be slightly lighter than when at rest. On the inertial frame the train of the example has no centrifugal force, so it is slightly heavier than when moving along at 361º per day along with the Earth (as it would be at rest on Earth) and still slightly heavier that if it was travelling in the opposite direction. In that case its angular velocity in the inertial frame would be double so its centrifugal force would increase proportionally to its square further counteracting gravity. Do you think it is a good idea? can you find sources for any similar example?--Crystallizedcarbon (talk) 18:58, 27 August 2015 (UTC)

I am looking for a source for the equatorial railway, although it could be said that it is a routine calculation.

The example does say, 'the upward reaction force from the track and the force of gravity on the train remain the same, as they are real forces'. We could, for example, place a digital weight sensor under the track to measure the reaction force. The value indicated must be the same in all frames. There is no part of current physics that allows a digital readout to display a different values when viewed from different reference frames. Maybe this point should be made clearer in some way.

Your proposal is a little confused. You say, 'In that case its angular velocity in the inertial frame would be double so its centrifugal force would increase'. In an inertial frame there is never any centrifugal force (or Coriolis force), whatever the motion of an object. Martin Hogbin (talk) 08:32, 28 August 2015 (UTC)

Let me try to clarify the example. From a non rotating frame point of view (looking at the train from a fixed point in space with respect to the center of the earth and, to make it simpler, ignoring that it is in orbit around the sun, rotation of the milky way, expansion of universe etc.):

• On the first case the train would be still from that point of view, with Earth rotating bellow it, and only gravity and the reaction from the track moving bellow it (we ignore drag) would act on the train.
• On the second case when the train is stopped at a point on the surface of Earth's equator, it would be seen from that fixed point of view in space to be rotating around the center along with the rest of the planet at 361º per day. that does generate a very small centrifugal force that counters gravity and makes it's weight at rest 0.31% lighter than in the previous case. From that that fixed point of view in space there is of course no Coriolis effect associated to the rotation of Earth.
• When the train travels in the opposite direction then it would be seen from that fixed point of view as travelling in a circle at 722º per day and therefore it generates more centrifugal force (also no earth related Coriolis in that case).

If the train could travel fast enough (ignoring air drag that would probably melt it) there would be a point at which it would levitate and start to orbit the Earth due to that centrifugal force. (as a curiosity and if it helps illustrate the example, in the first case in which the train is riding through the equator towards the west the people on board would see the sun still at the same azimuth and when travelling in the opposite direction relative to Earth day and night cycles would happen twice as fast for the travelers). I hope I was able to make it clearer. Regards.--Crystallizedcarbon (talk) 10:18, 28 August 2015 (UTC)

It may also be worth mentioning that there is a point at which the Eötvös effect reverses. It can be also illustrated with the example: If the train travelling west would increase its velocity beyond 361º per day in that direction with respect to Earth, it would gain back its centrifugal force (in the opposite direction) and would start becoming lighter. If it doubled its speed it should recuperate its "at rest" value and any additional increase would keep making it "lighter" until the point in which it would start to orbit the Earth. Regards.--Crystallizedcarbon (talk) 10:45, 28 August 2015 (UTC)

You say above, 'From a non rotating frame point of view...'. I take this to mean, 'in a non-rotating reference frame'. You do not mention any other reference frames so I presume that all your cases are measured in this inertial (non-rotating) reference frame.

In your first case you are correct when you say the only forces are 'only gravity and the reaction from the track'.

In the second case we are still doing our calculations in the inertial (non-rotating) reference frame so there is no centrifugal force. It makes no difference what the train is doing, it could be in a giant centrifuge, there is no centrifugal force when you are working in an inertial frame. It is still the case that the forces are 'only gravity and the reaction from the track'.

The third case has the same mistake. I am not sure how I can say this any more clearly. When you are working in an inertial reference frame, the Coriolis and centrifugal forces do not exist. It makes no difference what a body is doing, it can be going in a straight line or going rapidly in circles but there is never any centrifugal or Coriolis force. Martin Hogbin (talk) 11:14, 28 August 2015 (UTC)

To an observer on the rotating Earth, both satellites appear stationary in the sky at their respective locations.

The only centrifugal component that is not present in that frame is the one associated to Earths rotation. The centrifugal force that I refer to is the one generated from the circular path of the train in that frame. From that fixed point of view in Space with respect to Earths center on the image in the right you can see a satellite in a geostationary orbit. The force that is countering gravity in that frame is the centrifugal force generated from the satellite rotating at the same angular velocity as Earth (same as the train when is at rest with respect to Earth's surface). That centrifugal force that makes everything at rest on the surface of the Earth lighter is keeping the satellite in orbit at that altitude where gravity and the centrifugal force are matched.

I see I used the term centrifugal force incorrectly, you can reword the example in terms of centripetal force or change centrifugal force in that inertial frame for centrifugal force in a frame rotating along with the train for the second and third cases. on the second case when the train is at rest on Earth you would get the centrifugal force from Earth's rotation and in the third case when the train travels eastward you would get an increased centrifugal force as that frame rotates at a higher angular velocity. In all cases there would be no Coriolis effect as the train is still within each of the frames and the previously exposed conclusions would hold.--Crystallizedcarbon (talk) 11:57, 28 August 2015 (UTC)

Yes, in all cases where you put yourself in a frame where the train does not move, you have no Coriolis force. But in a frame where the train does move, you certainly do. The solution is not to simply refuse to visit such frames, as we're trying to describe the physics of rotating systems, where you don't always get your choice. In many real life problems you are stuck on the surface of the Earth, and you can't easily translate to the frame of something moving east or west. In any case, whether or not it's easier to put yourself on the train, is irrelevant. We're interested in the physics of forces on things what DO move (in the observer's frame). Simple examples are trains and ships as seen from the water or embankment, and there the Eötvös effect is merely the normal component of the Coriolis force/acceleration. That article has some nice illustrations, and at least one good source.

Even easier problems are where you have an object at a distance, not moving with respect to you, and you start spinning. In such a case the object moves about you in a circle. If you are to describe this in Newtonian terms, you need a source for the centripetal force, and the centrifugal force does not provide it. So you are left with Coriolis. That is why this simple situation should be a part of the Coriolis article. Those objects moving in circles might as well be the stars. They could be anything that wasn't moving before you started spinning and put yourself in a rotating frame.

To put it bluntly, from the surface of the Earth, the stars go round and round in circles. In Newton's physics they need a force to do that, and you keep deleting the section that describes what that force is. SBHarris 02:10, 29 August 2015 (UTC)

Hello @Sbharris: my problem with the example is that while you need Coriolis to explain tangible effects on Earth in meteorology oceanology long range ballistics etc. You do not need Coriolis to explain why the stars rotate. Your example: If you are rotating and look at a fixed object it seems to turn around you, is in my opinion a great way to explain why the stars seem to rotate around us. The article already explains in the introduction, referring to Coriolis and the centrifugal force, that "They allow the application of Newton's laws to a rotating system. They are correction factors that do not exist in a non-accelerating or inertial reference frame.". Maybe if a source can be cited and if there are no objections a short phrase could be added after it in line with "As an example, Coriolis provides the missing centripetal force term needed to cause the apparent rotation from our point of view of relatively fixed objects like the stars, allowing us to continue to use Newton's laws form our rotating frame's point of view".--Crystallizedcarbon (talk) 20:27, 29 August 2015 (UTC)

Yes I think you have got it. In your deleted section you said, 'The force that is countering gravity in that frame is the centrifugal force generated from the satellite rotating at the same angular velocity as Earth'. That is completely incorrect. In the inertial frame there is only gravity acting on a satellite. That provides the necessary centripetal force to maintain it in its circular orbit. If there were a centrifugal force acting outwards and balancing gravity then there would be no net force on the satellite and it would continue in a straight line out of orbit.

The idea of a centrifugal force acting on objects that move in a circle is an extremely common and very compelling misconception. That is why many teachers at an elementary level simply say that there is no such thing as centrifugal force. Until you get on to rotating reference frames, which would only be at undergraduate level physics, you can completely do without centrifugal (or Coriolis) force. Martin Hogbin (talk) 12:38, 28 August 2015 (UTC)

Agreed. I think that if it is properly worded and sourced it might be a positive contribution to the Eötvös effect section. Regards--Crystallizedcarbon (talk) 13:23, 28 August 2015 (UTC)

I will look for some good sources on the subject. Do you have any suggestions on how the wording can be improved to make the underlying physics as clear as possible to the general reader. Martin Hogbin (talk) 16:23, 28 August 2015 (UTC)

Great! I think together we should be able to do it. I will post a first draft here during the weekend for you and any other interested editor that may want to join us to review complement and add sources and if we find it useful we can move it to the article.--Crystallizedcarbon (talk) 16:53, 28 August 2015 (UTC)

I am working on an animation to help illustrate it. I expect to have it done by tomorrow.--Crystallizedcarbon (talk) 20:47, 29 August 2015 (UTC)

Here is the animation to help illustrate the example:

(Moved to the example section bellow)

(I hope it does not make anybody dizzy)I will add the text later.--Crystallizedcarbon (talk) 08:43, 30 August 2015 (UTC)

They are a bit fast. Which frames to you suggest that we analyse these examples in? Martin Hogbin (talk) 16:56, 30 August 2015 (UTC)

Intuitive explanation for Coriolis vertical deflective effect on westward and eastward moving objects (Eötvös effect)

I have created a new section for the example and moved here the image: here is the first draft

An intuitive example to understand the Eötvös effect:

Lets imagine that we have a train that travels through a frictionless railway line along the equator, and that when it is in motion it travels at the necessary speed to complete a trip around the world in one day. We will examine the Coriolis effect in three cases:1. When it travels west, 2. When is at rest and 3. When it is travelling east. We will look at this cases from our rotating frame of reference on Earth first and check it against the fixed inertial frame of a point on outer space above the North pole (see image):

1. The train travels toward the west: In that case it is moving against the direction of rotation so in on Earth's rotating frame the Coriolis term will be pointed inwards towards the axis of rotation (down) this additional force downwards should cause the train and those on board it to be heavier while moving in that direction.

• If we look at this train from our fixed non rotating frame on top of the center of the Earth, we see that it runs at such a speed that it remains stationary as the Earth spins beneath it, so the only force acting on it in this case would be gravity and the reaction from the track. So this force is greater (by 0,34%) than the force that the passengers and the train experience when at rest relative to Earth and therefore rotating along with it. That difference is exactly same and is an intuitive way to understand the Coriolis term on the previous paragraph.

2. The trains comes to a stop: From our point of view on Earth's rotating frame the velocity of the train is 0 so the Coriolis force is also 0 and therefore the train and it´s passengers recuperate their usual weight

• From the fixed inertial frame of reference above Earth, the train is now rotating along with the rest of the Earth. 0,34 percent of the force of gravity provides the centripetal force needed to achieve that circular motion on that frame of reference. The remaining force, as could be measured by a scale, would make the train and its passengers "lighter" than in the previous case.

3. The train changes direction and travels towards the East. In this case as it is moving in the direction of Earth's rotating frame, so the Coriolis term will be directed outward from the axis of rotation (up) this upward force would cause the train to seem lighter still than when at rest.

• From the fixed frame of reference on space the train travelling east will now be rotating at twice the rate as when it was at rest and therefore the amount of centripetal force needed to cause that circular path increases leaving less force from gravity to act on the track. this is what the Coriolis term accounts for on the previous paragraph.
• As a final check we can imagine a frame of reference rotating along with the train. such frame would be rotating at twice the angular velocity as Earth's rotating frame. the resulting centrifugal force component for that imaginary frame would be greater. since the train and it's passengers are at rest within it, that would be the only component in that frame explaining again why the the train and the passengers are lighter as in the previous two frames.

Earth and train

This also explains why high speed projectiles travelling west get deflected up and when they are shot east are deflected down. This vertical component of the Coriolis effect is called the Eötvös effect

Please let me know if you think it is clear and easy to understand intuitively. About the image, I think it is a good idea to slow it down, it will look a bit choppy as I had to make each frame with four layers each so there are only 16 frames, but now is probably to hard to look at without getting a bit dizzy. I will take care of it tomorrow.--Crystallizedcarbon (talk) 20:56, 30 August 2015 (UTC)

 Done The animation is now slowed down to 4 frames per second.--Crystallizedcarbon (talk) 09:56, 31 August 2015 (UTC)

The first two cases are are a common undergraduate physics problem and should be easy to find sources for. The third case might be harder.

I would not use the word 'fictitious'. It is not necesary because the Coriolis force 'is' an inertial/fictitious force. Using the word again could suggest that there are two Coriolis forces; one real one and one fictitious one.

It is better to use 'frame of reference' rather than 'point of view'. POV is a not a clearly defined technical term so might be open to incorrect interpretation. Perhaps we could say that it would be natural in many cases for a person on the surface of the Earth to use a frame of reference rotating with the Earth. Martin Hogbin (talk) 08:11, 31 August 2015 (UTC)

I think they are both good points. I have made both of the changes to the text above. --Crystallizedcarbon (talk) 10:08, 31 August 2015 (UTC)

It is important to make clear what frame of reference we are working in and to distingusih between what is experienced by a traveller and the physics. In every case, what is experienced by the traveller is the same in every frame of reference. How this is explained by the physics depends on the frame of reference in which you are working. Martin Hogbin (talk) 10:24, 31 August 2015 (UTC)

Yes, that is what I tried to do by subdividing each of the three cases using bullets. In each case we use first Earths rotating frame. the next bullet is the inertial frame and in the third case we added an extra bullet for a frame rotating along with the train. I have added some extra text to that bullet point to try to clarify that we are using a different frame in that case. Regards.--Crystallizedcarbon (talk) 11:01, 31 August 2015 (UTC)

I have changed the text to try to further clarify the different frames used.--Crystallizedcarbon (talk) 11:19, 31 August 2015 (UTC)

Hello @Martin Hogbin: Please feel free to improve it however you see fit it to make sure it is both accurate and intuitive. Regards. --Crystallizedcarbon (talk) 20:24, 31 August 2015 (UTC)

Can I suggest that we start with my wording in the Centrifugal force article. Martin Hogbin (talk) 11:46, 1 September 2015 (UTC)

Sounds good to me, feel free to edit the text above.--Crystallizedcarbon (talk) 13:00, 1 September 2015 (UTC)

Earth and train

I propose using this slower version of the animation. I slowed it down to two frames per second, I think it may be easier to watch and understand. --Crystallizedcarbon (talk) 12:25, 2 September 2015 (UTC)

Hello @Martin Hogbin: I have changed the example according to your recommendations. I think I made very clear the frame used for each case. The third point of the third case may or may not be necessary. Any feedback would be apreciated.--Crystallizedcarbon (talk) 16:37, 3 September 2015 (UTC)

•  Comment: Another very interesting point from this example is that if the westward train moves any faster, the downward Coriolis component (Eötvös effect) starts diminishing. When the train doubles its speed it completely disappears (as the train would be rotating in the inertial frame at the same speed as Earth but in the opposite direction) so it would need the same amount of centripetal force as when at rest. Any further increase of speed would make it seem lighter. Do you think it is worth mentioning that Eötvös effect only "works" up to a certain westward speed. Can it be sourced? --Crystallizedcarbon (talk) 16:37, 3 September 2015 (UTC)

I don't think it needs a source, other than WP:CALC. But this effect is more than just increased weight-- it's decreased weight also. Obviously the increased weight from the Eötvös effect reaches a max when the train reaches the speed of the rotating Earth as seen in the inertial frame: at that point, Eötvös effect has simply undone any existing centrifugal "lightening," and now that full gravity acts, that's all the increased "heaviness" you can get. However, going in either direction from that speed, makes it lighter symmetrically whichever way it goes, and this effect continues until it is in orbit and is weightless, and if you go faster in either direction, even has to be held down by the rails, increasing its outward acceleration without limit as you keep increasing velocity. SBHarris 05:41, 4 September 2015 (UTC)

Graph of the force experienced by a 10 grams object as a function of it's speed moving along Earth's equator (as measured within the rotating frame). (Positive force in the graph is directed upward. Positive speed is directed eastward and negative speed is directed westward).

Right, I agree with you. I created this graph to explain the force experienced by a 10g object due to its speed along the equator. The parabola is explained by the centripetal force needed to keep its circular motion on the inertial frame, and the reason that is not centered in the axis accounts for the fact that we measure the speed and its effects within Earth's rotating frame. I think the graph will also be a good complement to the example, and I will add it to the Eötvös effect article as well.--Crystallizedcarbon (talk) 09:09, 4 September 2015 (UTC)

If the current version is OK with everybody I will add it to the article tomorrow and we can continue to make improvements there. --Crystallizedcarbon (talk) 08:36, 5 September 2015 (UTC)

Hello @Martin Hogbin: I have added the example to the article, feel free to insert additional references to it if you want. This afternoon I will probably insert a couple more. --Crystallizedcarbon (talk) 09:41, 6 September 2015 (UTC)

Apparent deflection

The Foucault's Pendulum shows it is an apparent deflection towards the left in the northern hemisphere and towards the right in the southern hemisphere. Movement of pendulum is set in a straight direction (let's say, from south to north) which is kept, by inertia, in the same direction as long as the pendulum moves. However, pendulum will push down a small ball from the circle every half an hour if we previously set 24 little balls on the outside circle separated, therefore, by 15 sexagesimal degrees of angular separation. Every hour, the moving pendulum will push down two little balls (one going north to south and the other coming the other way around) and, therefore, the pendulum will throw down the 24 balls in half a day, that is, in 12 hours. And the reason for this is not a deflection of the pendulum (since it keeps its original direction as far as it moves) but a consequence of the rotation movement of the Earth. The center of the circle where balls are set gives a complete turn every 24 hours (since it moves along the parallel of latitud of this exact point), but every point (and ball) on the outside circle gives two complete turns every 24 hours (one around the parallel of latitude of each ball and another around the center of the circle). This is the reason why all the 24 little balls are thrown down in 12 hours: pendulum moves, apparently, 15º per hour to the left going north to south and another 15º coming the other way around, also to the left. The only exception to this rule is when the center of the pendulum's circle is at one of the Earth's poles because, in this case, all the little balls are located at the same latitude because it's a parallel of latitud around the pole (remember that a parallel of latitude is a minor circle around the pole).

In sum, deflection of the pendulum to the left on the northern hemisphere (and to the right in the southern one) is apparent because it is caused, not by a deviation of the pendulum's direction itself, but by the rotation movement of the Earth. I think these ideas should be revised and included in this page. --Fev 22:43, 20 September 2015 (UTC) — Preceding unsigned comment added by Fev (talk • contribs)

Coriolis effect and Geography

This article is maybe OK from the standpoint of Physics (many phormulae and other atracting considerations), but it is awful from the point of view of Geography. Two examples:

1. The article says: As a result, in tornadoes the Coriolis force is negligible. On the contrary, it is very strong and, besides, it is not a force, but an effect of the Earth's rotation movement. In Geography, moving of objects such as air masses must take into account its length, width, AND HEIGHT, being this last dimension the real reason why wind speed in a tornado is so high. So, it is impossible to reduce the Coriolis effect to a plane of rotation.

1. The article also says: Contrary to popular misconception, water rotation in home bathrooms under normal circumstances is not related to the Coriolis effect or to the rotation of the earth. This statement is not referenced because it is FALSE. As well as tornadoes, bathroom toilets use Coriolis effect to accelerating flushing down of water: it is like a water tornado and moves the same way as toilets do (counterclockwise in the Northern Hemisphere). Deflection of air and water masses is toward the left on the Northern Hemisphere and to the right on the southern one, regardless of the object's size, let's say, a bathroom toilet OR the Mediterranean sea, where all the ports are closed to the left (seeing from the coast) and open to the right, to avoid coastal current that is counterclockwise (like the Baltic sea and others). Some examples on the western Mediterranean as they are seen in Google maps:

• Barcelona: [5]
• Ametlla de Mar: [6]
• Tarragona: [7]
• Hospitalet del Infante (Tarragona): [8]
• Vinaroz: [9]
• El Grao de Castellón: [10]
• Valencia: [11]

And the geometry of these examples has nothing to do with prevailing winds (westerlies at this latitude) — Preceding unsigned comment added by Fev (talk • contribs) 11:22, 25 September 2015 (UTC)

The Coriolis force that is due to the rotation of the Earth is negligible within a tornado itself but the direction of rotation of a tornado is determined by the rotation in the larger air masses from which it forms and this rotation is due by the Coriolis force (or the rotation of the Earth, if you prefer).

There is a force deflecting the water draining from a basin, just as you say, but it is negilgible compared with the effect of other factors such as any residual rotation from the filling, or the plumbing. Martin Hogbin (talk) 10:37, 26 September 2015 (UTC)

A commentary on this 2 statements

The two statemens are not referenced and are wrong. Nothing is negligible regarding effects of the rotation movement of the Earth. But I don't like to go on with this discussion and, therefore, I quit. Sincerely --Fev 00:53, 27 September 2015 (UTC) — Preceding unsigned comment added by Fev (talk • contribs)