Talk:Coriolis force

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Why the negative sign?

Just an innocent question. Why is there customarily a negative sign in the equation for Coriolis acceleration and force?

${\boldsymbol {F}}_{C}=-2\,m\,{\boldsymbol {\Omega \times v}}$

It could be got rid of by reversing the order of ${\boldsymbol {\Omega }}$ and $v\,$ Then the direction of Coriolis force could be defined by the right-hand rule. Just wondering why it is normally written this way. --Chetvorno^TALK 11:50, 18 June 2015 (UTC)

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)

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.

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: [1]
• Ametlla de Mar: [2]
• Tarragona: [3]
• Hospitalet del Infante (Tarragona): [4]
• Vinaroz: [5]
• El Grao de Castellón: [6]
• Valencia: [7]

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)

Expect that this point is made above but I am too lazy to read all the way through it.

So I am making the point briefly in its own section. I am not at all happy to accept that either the Coriolis force or the centrifugal force is a non-force. I write as an engineer who must consider real forces, such as those which might result in the bursting of a rotating machine, or which might stress the casing of a centrifugal pump, but who may happily and safely ignore anything which does not exist, or which may exist in only a metaphysical sense. If a force is of significance in a practical case, then it must be defined in such a way that its reality is properly acknowledged. It makes no sense to me to define a force, and then say it is a non-force, or, as in the preceding section, to speak of a force when the observed motion depends precisely on the absence of any such force, and is properly described strictly in accordance with Newton's first law (unaccelerated motion in a straight line relative to an inertial frame).

Here is a better approach to the C force which acknowledges it in cases where it exists, and excludes it where it does not: The Coriolis force is the force required to constrain a moving mass to move in a straight line relative to a rotating frame of reference. For example, if a body is constrained to move radially on a rotating turntable, a lateral (tangential) force must be applied. Convention might require that we say that the C force is actually the reaction to the force so defined - others others can argue about that. If a moving body is not so constrained (as in the case of clouds moving in a cyclone), it is obvious and pleonastic to say that no lateral force exists (the motion is unconstrained). The observed lateral acceleration must then be explained without recourse to a force which simultaneously exists and does not exist. Such an explanation can be given by deducing that the observed motion (i.e. acceleration without a force) is observed with respect to a rotating frame, and then applying Newton's first law.

Similarly we can define a real centripetal force as a force required to constrain a mass to move in a circular path, and the centrifugal force is then the reaction to the centripetal force. Such a reaction is experienced by our bodies while in a cornering car. 1 Oct 2015

I have returned to this after having read some more of the contributions above, but still find I have not sufficient energy to give the entire discussion proper critical consideration. I will add two further points however. (1) Many internet sources discuss the "Coriolis Effect" (this is also the title of the present article), which avoids the problem of a force which does not exist, and merely seeks to explain the movement of, for example weather features, in terms of the rotation of the earth. This is commendable, and raises no objections. (2) The question of whether the Coriolis "force" exists is entirely a matter of giving precedence to either a rotating frame, or an inertial frame. In the first case it is a real force (from that point of view), in the 2nd case it does not exist (from that point of view). Thus it appears that those who write of it as a non-force are making an implicit and unstated assumption about their preferred frame of reference. However, the choice of the point of view that gives the C force reality must be seen as unsatisfactory, since there is no way of measuring such a force, and its existence must remain mystifying and metaphysical. Better to say plainly that it does not exist (and therefore need not be discussed) unless, that is, it is defined in the way I have suggested above (constrained radial motion on a rotating system).