Talk:Coriolis force/Archive 5

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PLEASE HELP SOON

IVE GOT AN EXAM on this stuff in 2 days so please help. heres my question: I understand that the centrifugal force on a weight supported by a string being spun around is balanced by a centripital force (string tension). if the corlois force is real in the frame of a weight what force acts equal and opposite to stop the weight from slowing down?

Nice one i sat my exam with no help but i worked out what was going on. the corilos force is not balanced by a force but an acceleration:

there is a component of acceleration perpendicular to velocity.

the centripidal force + this other force which i will metion in my next installment which will be added when im less drunk.

P.S. thanks for nothing

—Preceding unsigned comment added by 84.67.74.110 (talk) 21:18, 23 January 2008 (UTC)

This is hardly a place to ask exam questions.... —Preceding unsigned comment added by 82.198.140.23 (talk) 14:45, 14 August 2008 (UTC)

Popular culture

This article really needs a "Coriolis effect in pop culture".I think most of the people know something about the consequenses of the coriolis effect from The Simpsons.

Do readers need to guess who Ascher Shapiro is and what exactly was the nature of his experiments? Whoever put this in, what were you thinking? 75.3.8.133 03:59, 14 June 2006 (UTC)

I put it in. I agree it's not good. Before it said something about how it was possible to observe the Coriolis effect in a laboratory tank "in theory". I wanted to make it clear that it is possible in practice, and has been done. I'll add more information. Rracecarr 09:21, 14 June 2006 (UTC)

I think it should have the Simpsons reference. It was the plot catylist behind an entire episode. Valley2city 20:12, 22 October 2006 (UTC)

I changed the wording of the Simpsons and X-files references in the "Draining bathtubs and toilets" section. I hope it's OK.

Nicer wording

"the magnitude of the Coriolis effect changes with the latitude and the speed of the air (and water)."

Couldn't that reasonably be changed to say "the speed of the fluid?"

Search4Lancer 17:29, 24 June 2006 (UTC)

Exactly why I came to this page. I think the entire first paragraph could be written much more simply. I came to the definition to find what the Coriolis effect is, and I am leaving it without knowing. 29 December 2008 —Preceding unsigned comment added by 87.198.128.158 (talk) 02:37, 29 December 2008 (UTC)

That language is no longer in the article. Instead of responding to a two-year-old complaint, consider starting a new topic at the bottom. Dicklyon (talk) 04:29, 29 December 2008 (UTC)

Draining bathtubs/toilets

The Coriolis effect DO HAVE a clear influence on rotation of flushing bathtubs, toilets and mud volcanoes (and magmatic volcanoes as well). However, velocity of fluid, just as the article says, needs to be taken into account. This means that if mud is very fluid, the spiral line clockwise (Northern Hemisphere, of course) almost dissapears. A recent volcano in the Eastern region of Congo, in Africa (Nyamuragira Volcano, north of Lake Kivu), shows also de Coriolis effect, since the lava flow was not very fast (in this case), as it is possible to see in satellite images from Google Earth. This volcano has two diferent lava flows: the southern flow shows deviation towards left (we should remember it is in the Southern Hemisphere) being a proof of the Coriolis effect. However, the northern flow looks like not being affected by the Coriolis effect, maybe because of topography: most of this flow is by the eastern wall of the Rift Valley, which avoids deviation towards the left, at least, in part of it. --Fev 00:06, 3 August 2006 (UTC). Seen from the top, a mud volcano has a similar shape than the Iceland low pressure system showed in the article's first image. However, the movement of mud is clockwise (from top to the bottom around), since it is, actually, similar to a high pressure system. Just this fact is the proof that the Coriolis effect determines deviation of a straight line due to Earth's rotation: deviation is the same either in high pressure systems than in low pressure systems (towards the right in the Northern Hemisphere and to the left in the Southern Hemisphere. --Fev 01:08, 3 August 2006 (UTC). --Fev 03:08, 3 August 2006 (UTC)

---You could say the Coriolis effect has an influence on rotation of flushing bathtubs, toilets, but the "force" is much smaller than other influences and is far from enough to affect the drain direction...It is a different story to mud volcanos in repect to the various influences. --Natasha2006 17:41, 31 July 2007 (UTC)

Ditto on the Draining of Bathtubs and Sinks

One can easily see when travelling the greater the rate of spin when further north for sinks and bathtubes. There are even demonstrations with properly-modified upside down 2-liter bottles at the equator to estimate the equator's location to within 100 meters. The rate of spin is even noticeably different between Atlanta and Cincinnatti. It was quite a shock when i finally realized why the drains always caught my attention and seemed really strange when i visited Cincinnatti. At first i thought the bathtubs were just made different or something, but then a sink really jolted my attention and i figured it out. I've been in enough hotel rooms to know.

—Preceding unsigned comment added by 216.186.158.98 (talk • contribs) 02:40, 18 November 2006

The above is your personal interpretation of your observations - and therefore is not allowed in the article as it is original research, see WP:NOR. Removed OR from page. --Vsmith 03:33, 18 November 2006 (UTC)

Please can someone amend the INCORRECT description that Coriolis Force has no effect on the water draining from sinks or bathtubs, it most certainly does has effect! I have people saying to me "but it says so in wiki" 213.235.52.66 14:12, 5 April 2007 (UTC)

It doesn't say that the Coriolis Force has "no effect". It says that the effect is so small that it doesn't affect the direction of rotation. This is true.

However, it is a good policy to not always trust a wiki. If something seems wrong, then it is a good idea to check out the references. The section on draining bathtubs refers to this article from the Berkeley Science Review, which is probably a trustworthy source. --PeR 22:03, 15 February 2007 (UTC)

OK, ignoring the flushing toilet example then because the flush maybe forced one way by toilet design flush system (the Simpson's simply chose a bad example and that article fails to see what the Simpson episode was trying to do, i.e a static draining bowl produces a rotation one way in one hemisphere and an opposite rotation in another) lets look simply at a circular bowl or even a bathtub. I have lived in both hemispheres and sat and shaved in many sinks and tubs. The draining water DOES UNDENIABLY rotate clockwise in the southern and anticlockwise in the northern. If it's not Coriolis Force that it attributing to this (you and the article state it is too small an effect to do it), what is?. Honestly I'd like to know. 213.235.52.66 14:12, 5 April 2007 (UTC)

Find a copy of "Butter side up!: The delights of science" by Dr. Magnus Pyke. There's a chapter on this subject that goes into great detail on experiments that were conducted to measure the coriolis effect at small scales- specifically draining water from specially constructed basins. The experiments involved allowing the water to stand for various periods of time and even covering the basins to keep off any drafts that could possibly impart a rotation to the water before opening the drain. Under laboratory conditions, water does go down a drain counter-clockwise in the northern hemisphere and clockwise in the southern hemisphere. Pointing to ordinary sinks and toilets, with water full of chaotic currents, drained after the water's only been alllowed to stand for seconds, then claiming that the coriolis effect has no bearing on which way the water will spin down the drain- that's BAD SCIENCE.

It's a conspiracy, obviously! They plant false information, telling us that water drains clockwise on the nothern hemisphere, to divert us from the obvious truth that Europe really lies on the southern hemisphere! This is to keep us from the fact that |Bielefeld is actually an island in the real North Sea! Sound reasonable, eh? —Preceding unsigned comment added by 80.134.46.76 (talk) 14:49, 5 May 2008 (UTC)

This article has too many errors

• First error: It looks like we should underestimate popular opinion. Popular opinion is based in the fact that, no matters the size of any rotating system on the Earth's surface, ALWAYS deflects in the same way according to the hemisphere where the movement takes place. This is valid for small whirling winds or mud volcanoes, for bigger tornadoes, for even bigger cyclones. Why we don't have exceptions to this rule?. We should remember than popular opinion is based on experience and this, in turn, derivates from physics laws. --Fev 23:47, 3 August 2006 (UTC)
• Second error: The Coriolis effect works also in high pressure areas, as it can be seen in the anticyclone article. It also works deviating normal track of hurricanes towards the north and eastward later.
• Third error: The article says the value of the Coriolis parameter, does vary with latitude, and that is due to the Earth's shape. It is not the Earth's shape but its rotation from West to East which is responsible for the Coriolis effect.
  • The magnitude of the Coriolis force is a function of the component of the speed of the object that is perpendicular to the earth axis. So, if the object is closer to the equator, the perpendicular component is smaller. This is dependent on the earth's shape; why should it be incorrect? Bob.v.R 01:08, 25 December 2006 (UTC)
• Fourth error: The Coriolis effect on Trade Winds (for example) does not stop at the Equator. When trade winds bring air masses near the low pressure belt around the equator they tend to climb up to a high altitude and deviate northwest first, then north and, finally, northeast. But people do not take into account that this movement of air masses from equator towards subtropical areas (opposite to Trade Winds) takes place at a high altitude and therefore, without clouds, a fact that makes keeping track of its movement less obvious. --Fev 00:27, 11 August 2006 (UTC)

• The winds go in the wrong direction on the picture of the Earth! They should be anticlockwise in the northern hemisphere, and clockwise in the southern! WolfKeeper 13:57, 25 August 2006 (UTC)
  • No Wolfkeeper, the picture is correct. A wind coming from the north will go to a region with higher local speed (eastward) of the surface of the earth, than the air particles themselves, therefor the path of this wind will be directed to the right (so: clockwise). Bob.v.R 00:59, 25 December 2006 (UTC)
• Remember a hurricane contains, in one, two kind of whirl-winds rotating in different directions: its base is formed by cold and dry air rotating clockwise (inner deviation towards the center of storm) and that makes, in turn, the climbing of warmer and moistener air climbing up with a deviation towards the left (also to the center of storm), counterclockwise. See the Cumulonimbus article, especially, the first and second images. --Fev 04:18, 19 December 2006 (UTC)

Wolfkeeper, the diagram that you removed represents (very schematically), the concept of inertial oscillations. The circles on that diagram are unrealistically large, but the diagram does give correctly the (theoretical) direction of inertial oscillations in the atmosphere. Read more about inertial oscillations in this article by the meteorologist Anders Persson.

Anyway, the phenomenon of inertial oscillations (especially as recognized in oceanography) could use an article of its own. The diagram is correct but with not enough explanation, it is easily misunderstood --Cleonis | Talk 15:03, 25 August 2006 (UTC)

Sauna question

Question??? When in a sauna and you throw some water on the rocks the heat reaches one side first and then rotates around the sauna. This is the coriolis force doing this isn't it?

Not from the earth's rotation, it's not. Not unless your sauna is several dozen miles across and takes several hours for the heat to travel from area to area. It's more to do with the way the convection currents move in your sauna. By moving the rocks, you can probably get it to go in the other direction. DewiMorgan 20:19, 11 May 2007 (UTC)

Frisbee deflection?

I was just curious if the strange path a frisbee takes while landing is related to Coriolis forces?

Most likely, there is not any relationship. First, time flying a frisbee is not long enough. Second, frisbee takes different turning sides while landing according to the person throwing it: with left-handed persons, frisbee turns around the opposite way as right-hand players. And third, wind direction is a more important fact in frisbee playing. --Fev 20:24, 14 September 2006 (UTC)

The answer above relates to the Coriolis effect by the Earth's rotation. But what about the Coriolis effect caused by the rotation of the frisbee? It will drag some of the air under it into rotation, and there may be some effect. Any answers to that one? −Woodstone 19:29, 3 October 2006 (UTC)

There is no coriolis effect caused by the rotation of the frisbee. The coriolis force only occurs if you are standing in a rotating system (such as the earth) while imagining that you are in an inertial frame of reference (ignoring earth's rotation). Since you are acknowleging that the frisbee is rotating, it cannot give a Coriolis force. The effect on the frisbee is caused by asymetric aerodynamic drag, and gyroscopic precession. --PeR 07:58, 9 November 2006 (UTC)

Diagram looks wrong

The picture of a ball rolling on a flat plate looks wrong. The transverse speed in the rotating frame of reference should be increasing with distance from the centre, but it seems to be moving in a semicircle.WolfKeeper 00:19, 25 November 2006 (UTC)

You mean this picture?

Ball rolling on a flat plate?

I believe the diagram is correct. The velocity is constant in the inertial frame, which should make the path in the rotating frame an Archimedean spiral. The first 90 degrees of this looks similar to a semicircle.

Initially the ball is in the center where the centrifugal force (as seen from the rotating frame) is zero, and only the Coriolis force is at play. As the ball moves further away from the center, the centrifugal force acting outwards will be counteracting the Coriolis force. --PeR 10:34, 26 November 2006 (UTC)

I'm not saying it's actually wrong, but the perspective view is unnecessary and makes it look like a semicircle.WolfKeeper 11:20, 26 November 2006 (UTC)

The shading on the lower "plate" should be rotating just as the shading on the upper "plate" is. I disagree with PeR's analysis of "centrifugal force" and "Coriolis force" - neither one of these is a force. Cbdorsett 05:21, 30 January 2007 (UTC)

Neither Coriolis or centrifugal forces are "real" forces strictly speaking. However, they are a mathematical concept that arise when working in a rotating frame as opposed to an inertial frame; and PeR correctly used the terms. I think the problem with the image is not the "semicircle" in the perspective view (whatever curve it actually is, it looks close to that), but the track in the plan view is a straight line. It would be better if the track in that view was curved, following the actual route of the ball. One thing to bear in mind, the transverse speed may be increasing, but that would not necessarily affect the angular velocity.--Nilfanion (talk) 16:58, 30 January 2007 (UTC)

Squirts of water from a fountain on a rotating rim

Is the animation Image:Rotating_fountain_coriolis_effect04.gif an option?

The above water spurt animation depicts "Coriolis Effect" very well and shows how objects moving in straight lines look like they are moving in very funny ways when viewed from a rotating reference frame. Sort of the "Big whoopy deal" of science. If you look at a motionless object from a moving frame, the object will appear to move. Shock! If you look at something from a rotating frame that is either still or moving in a straight line, it will be rotating, or not moving in a straight line. Double shock!

Sorry for the sarcasm. But, remember it is not those early observation that probably lead Coriolis to any breaking findings but the following:

Try to picture the water spurts as hard brass balls. Each ball is thrown up at different directions and viewed from a rotating reference frame. They return as if mysteriously affected by a non-measurable force. Out side that reference frame, we have the view that those brass balls are not being affected by a force because they are moving in a straight line. OK, funny effect, not worthy of force catalogue, it is not a force. Provided to show changing water to brass doesn't affect anything.

OK, now change that brass ball tosser to a brass ball slider on a pole. Drill holes into each ball and slide them onto a flexible but very low-friction fishing pole like rod. The rod is strung from the rim to the hub. Slide the balls up and down the rod. The rod could go all the way across to the other side of the rim.

The outside observer would see nothing spectacular. He/she would see balls moving in a spiral like pattern. Obviously being affected by forces that are acting on the balls.

The rotating observer would see a ball striving to move in a straight line. BUT! For some reason, the fishing pole was flexing as if the balls were putting a force on it. Why? Things tend to move in a straight line unless acted upon by an outside force, right?

We've already pointed out that the brass balls really are being acted on by outside forces, as the are observable from outside. One of the forces is the radial force that keeps the balls from accelerating off the disk (friction). The other must then be a tangential force and is causing the pole to bend/flex.

How do we calculate that force from an outside reference frame? We take stop action stroboscopic pictures and measure the distances the object has moved. Then calculate the forces needed to move the known mass that much, yeah gets kind of ugly and stinky real fast and doesn't give us much insight into the problem.

Or We could do it from the rotating reference frame and call that "mysterious force bending the fishing pole" the "Coriolis force". Now it is easy. It is what you'd expect a function of the brass ball's radial speed and the rotating speed of the disk, correct? And we quickly see the force is there because the ball needs to go from the slower hub speed to the fast rim speed, a real acceleration that can't be seen by the rotating observer.

Now that we've shown that Coriolis was indeed trying to calculate a "real force" we merely need to come to some agreement of what it really means. The Coriolis force is the force necessary for an object to move in a straight line on a rotating frame. The Coriolis effect is the effect observed by a rotating viewpoint on an object that isn't affected by a force. Most things will be in between those two pure phenomena. And there is now a real force involved that is cause by real things, and can be measured with spring scales and calculated and everything.

PS, the water spurt picture would benefit from some straight line in both reference frames showing the straight line motion. The line in one frame must be moving. (Same lines, ) Hopefully someone will modify it and add it to the main page, as well as make one with bending fishing poles.

Note: The measurable presence of fictitious Centrifugal or Coriolis Forces are the dead give away that you are in a rotating reference frame and why rotating reference frames are not part of Einstein's relativity theories.

Eric Norby 20:18, 23 May 2007 (UTC)

It is mathematically correct, and at 47 KB the size is reasonable. The current animation is mathematically wrong, and it is a whopping 213 KB

However, there is a disadvantage that both animations share. In the rotating fountain animation the motion of the squirts of water with respect to the rotating coordinate system needs both a coriolis term and a centrifugal term. Arguably, it is not an example of pure coriolis effect but an example of some sort of combined centrifugal/coriolis effect. --Cleonis | Talk 20:14, 30 January 2007 (UTC)

Huh? No, the fountain has both centrifugal and coriolis correct. The same thing happens in both pictures; just rotated. That's exactly what should be happening; nothing has been neglected (possibly apart from friction).WolfKeeper 17:40, 15 February 2007 (UTC)

I believe both pictures are correct. It would not be a good idea to make a picture of Coriolis effect without centrifugal force, because then the object wouldn't follow a straight line at constant speed in the inertial frame. File size is probably an important factor, and that might be a reason to prefer the "fountain" animation. (I'd love to see a real fountain built like that!) However, adding a "trace" to the water squirts would make it clearer that they move in straight lines in the first picture. This shouldn't add much to the file size. --PeR 22:16, 15 February 2007 (UTC)

In the rotating fountain animation, the motion with respect to a rotating coordinate system is described with a centrifugal term plus a coriolis term. I would like to argue the following: that is is a case of pure coriolis effect when in the equation of motion the terms that are not the coriolis term drop away against each other. Specifically: when there is a central force that is a harmonic force, then at all points in space the vector of the central force and the centrifugal term are equal in magnitude and opposite in direction. The distinction is illustrated with java applets by the meteorologist Brian Fiedler.

* Motion over a flat surface

* Motion over a parabolic surface

The main example of coriolis effect is meteorology: at all latitudes (except at the poles) a central force is present that is equal in magnitude and opposite in direction to the centrifugal term. Hence in meteorological calculations the centrifugal term drops away. In meteorological calculations, the centrifugal term is much bigger than the coriolis term, if it wouldn't drop out of the calculation, the centrifugal term would drown the coriolis term. --Cleonis | Talk 23:33, 15 February 2007 (UTC)

The "Force"

The title of this article declares the Coriolis force to be fictitious yet it is used in the article to explain things. --Eplack 16:09, 18 December 2006 (UTC)

Fictitious force is standard physics jargon for a force caused not by a physical source, but by a non-interial frame of reference. WilyD 16:40, 18 December 2006 (UTC)

The problem that Eplack points out is real.

In the article it is stated:

The force balance is largely between the pressure gradient force acting towards the low-pressure area and the Coriolis force acting away from the center of the low pressure. Instead of flowing down the gradient, the air tends to flow perpendicular to the air-pressure gradient and forms a cyclonic flow.

That is, currently the article is claiming that something non-physical (a non-inertial frame of reference) is counteracting a pressure gradient. That doesn't make sense. --Cleonis | Talk 16:29, 25 January 2007 (UTC)

In a non inertial frame of reference the coriolis force is a physical force.WolfKeeper 03:07, 25 February 2007 (UTC)

Ballistics

I've added a section about Naval gunnery into the section on ballistics as it is a famous "example" of the coriolis effect in action. The section is not my own work, but instead was inserted into the Battle of the Falkland Islands, where it is of questionable relevance. However, I felt it was interesting and well enough written to merit inclusion here. I hope you all agree with me. Getztashida 12:19, 25 January 2007 (UTC)

That section consists of a quote of undisclosed origin (possibly a copyvio), followed by a lot of original research. It should be removed, unless someone can provide references. What is needed is a reference to a scholarly article refuting the anecdotes. If no such article exists, then Wikipedia is not the right place to publish one. --PeR 12:03, 30 January 2007 (UTC)

I support removing the naval gunnery stuff. Relevancy is insufficient, and it's anecdotal. --Cleonis | Talk 13:13, 30 January 2007 (UTC)

Wind

I removed the following paragraph:

"If you where standing on the equator the wind should appear to be going to the right north of the equator or left which is south of the equator. The reason is because of the Coriolis effect. The air is changed by the amount of sunlight or radiation that hits the earth's surface and creates distinct wind patterns on the earth's surface."

The text seems to be saying the same thing that was explained in the preceding paragraph. I considered rewriting it, but concluded that there was nothing to be gained.

Cbdorsett 05:16, 30 January 2007 (UTC)

The Coriolis Force in Magnetism

The article entitled 'The Coriolis Force in Maxwell's Equations' [1] explains very clearly how the Coriolis force equation and the magnetic F = qvXB force equation are equivalent.

Rracecarr continues to delete this reference claiming that the author is a crackpot. Would it not be better if Rracecarr would actually read the article and put a bit of thought into the matter? It is highly presumptious of Rracecarr to think that electromagnetism is so well established that nobody could possibly demonstrate that the Lorentz force contains the Coriolis force on a microscopic scale.

The fact that Rracecarr chooses to instantly delete this reference and label the author a crackpot, does not reflect well on Rracecarr. It makes one wonder why he is so determined to censor this aspect of knowledge. It would have been more professional on Rracecarr's part if he might have contacted the author privately and pointed out exactly where the error in the derivation exists, if he is so convinced that the derivation is wrong. David Tombe 9th February 2007 (210.213.225.33 16:03, 9 February 2007 (UTC))

Hi David. Wikipedia has a policy against posting original research (WP:NOR). Your research is not only original, it flies in the face of a century's worth of scientific support for and acceptance of special relativity. That, however, doesn't really matter. My deletion is justified on the basis of the aforementioned Wikipedia policy alone. Rracecarr 16:15, 9 February 2007 (UTC)

Your deletion wasn't motivated in slightest by whether or not it contradicted Wikipedia policy. You were obviously upset by the contents and you didn't want anybody else to be thinking about the link between the Coriolis force and the magnetic Lorentz force. You didn't claim that you had deleted it because it contravened Wikipedia policy. You claimed that you had deleted it because the author was a crackpot.

Why not study it with an open mind? I think that you will soon realize that the Coriolis force is heavily involved in magnetism. If it contradicts Einstein's theories of Relativity then should we not be questioning Einstein's theories of Relativity? There are many people who disagree with Einstein's theories. Einstein's theories are notoriously controversial. They may well be accepted by the so called mainstream today, but I have no doubt that in the fullness of time they will truly be seen as crackpot theories. David Tombe 9th February 2007 (210.213.225.33 16:47, 9 February 2007 (UTC))

Whether it's right or wrong, it doesn't seem notable; in google I found only one link to the article from [2]. The rules say that Wikipedia has to contain notable points of view only.WolfKeeper 16:17, 9 February 2007 (UTC)

Hi again David. I won't deny that my personal motivation for deleting the content and reference you added was because it was wrong. However, neither my reason for deleting it, nor yours for posting it, are relevant. People edit Wiki articles for many different reasons. The WP:NOR policy doesn't care about editor motivation. Neither does the WP:3RR policy, of which you are now in violation, having added your content back in 4 times after deletion by 3 different editors.

On a separate note, I think you should consider the possibility that the so-called mainstream physics community is made up of a large number of very bright people. Could it be that they're right? Rracecarr 19:02, 9 February 2007 (UTC)

Hi Rracecarr. That last note of yours shows your appalling naivity. Is this what it all comes down to? You have been taught by the ruling physics party and you have been taught Einstein's theories of relativity. You have chosen to believe in them without question. You are obviously unaware of the enormous amount of dissent as regards Einstein's theories of relativity. Am I supposed to dismiss my derivation linking the Coriolis force to the Lorentz force simply on the grounds that you claim that the physics community is made up of a large number of very bright people? What sort of an argument is that to come out with? I challenge you to show me an error in the derivation. If you can't find an error, could it not be that it's right? David Tombe 10th February 2007 (202.69.162.228 03:19, 10 February 2007 (UTC))

It doesn't matter if your theory is right or wrong. The policy on Wikipedia is that you must get it published in a peer reviewed journal first. Please read WP:NOR --PeR 07:24, 10 February 2007 (UTC)

OK. Let's sum the matter up. The topic is Coriolis force. We are all agreed that in meteorology, oceanography and in many other situations, that the Coriolis force is fictitious. The controversy here has arisen over the suggestion that a real Coriolis force is involved in magnetism. OK, let's drop the issue of "Coriolis Force in Magnetism" since it obviously breaches Wikipedia's rules. I would have hoped that the suggestion of the connection might have sparked some interest. Unfortunately it was zealously opposed by people who's motives, I suspect, were not anything to do with Wikipedia's rules. It was much more likely that they were motivated by the need to protect Einstein's theories of relativity.

But dropping the issue about the Coriolis force in magnetism doesn't mean that matters to do with centrifugal force also need to be censored. There are clearly two existing schools of thought on whether or not real centrifugal force exists. There are plenty of official citations and articles which show us that real centrifugal force is involved in planetary orbital theory.

I will hence restore the point about the difference between fictitious Coriolis force and fictitious centrifugal force, but without mentioning anything about real Coriolis force. David Tombe 10th February 2007 (222.126.33.122 09:35, 10 February 2007 (UTC))

The WP:NOR policy applies to this as well. If, as you say, "there are plenty of official citations and articles which show us that real centrifugal force is involved in planetary orbital theory", then cite those.

[[3]]

[4] see equation (15)

There are two for a start.

Note that it is not sufficient that something is on the internet.

I thought there was a rule that you didn't need to produce a citation to back up a claim that an apple is a fruit. You so-called physicists shouldn't need a citation to show that centrifugal force is involved in the planetary orbit equation.

The publication has to be noteworthy (and preferably peer reviewed). As it is, your addition is certain to be removed. (I've already reverted you twice today, so I'm not going to do it again myself.)

In addition, you removed a rather large amount of text. It is usually better to discuss such changes on the talk page first, and try to achieve consensus before a drastic rewrite. --PeR 11:42, 10 February 2007 (UTC)

This is now quite ridiculous. You are demanding evidence for something that was in my applied maths notes at university. It can be found in any textbook about orbital mechanics and it can be found instantly on the wikipedia article on Orbital Mechanics. Centrifugal force is one of the two components in the differential equation that is used to solve planetary motion. Why should I have to prove something so basic? It's not going to be in a peer reviewed journal. The equation was around long before peer reviewed journals came into existence.

Have a look at this Wikipedia article Planetary orbit and scroll down to the section entitled 'Analysis of orbital motion'. Look at the last term on the right hand side of the very first equation. That is the centrifugal force. Any textbook will back this up. Try and get the conic section solution to planetary orbital theory without using centrifugal force and see how well you get on. David Tombe 10th February 2007 (210.213.229.36 12:12, 10 February 2007 (UTC))

In fact if you include the tangential terms (Coriolis force and Angular force) in the planetary orbital equation that are normally excluded on the grounds of Kepler's law of areal velocity, you will obtain the skeleton structure of electromagnetic theory. The solution in a multi-particle dielectric is almost certainly a sea of solenoidal double helixes. The Coriolis force and the Angular force combined is the Lorentz force. David Tombe 11th April 2007 (61.7.161.229 10:25, 11 April 2007 (UTC))

Question about the Coriolis force

If the Coriolis force is only supposed to be an artefact of the Earth's rotation, how come it's effects are visible when we look down on the Earth from above? (58.69.250.10 16:14, 21 February 2007 (UTC))

We interpret cyclones etc as being caused by the Coriolis force because we use the Earth as a reference frame. Looking at the Earth from space, there is no Coriolis force. In an inertial frame, cyclones are the result of real forces--as air that is already rotating (with the earth) converges, it rotates faster. Imagine a bucket of water sitting on a rotating turn table. If you pull a plug from a hole in the bottom of the bucket, the water will drain out, spiralling in the same direction as the table turns. The reason is that as the rotating water moves inward, it increases its rate of rotation to conserve angular momentum. But if you were a very small person living in the bucket, you might choose to use the bucket as a reference frame. In that case, you would not see any movement in the water before the drain was opened, and you would interpret the direction of the vortex as a result of the Coriolis force.Rracecarr 16:56, 21 February 2007 (UTC)

---

In general, the effect deflects objects moving along the surface of the Earth to the right of the direction of travel in the Northern hemisphere and to the left of the direction of travel in the Southern hemisphere.

Is this truly correct? If you start in the northern hemisphere and head south, your deflection due to the rotation of the earth will be to your right, and will not magically change when you cross the equator. If you're moving south, your deflection will still be to your right, even if you're in the southern hemisphere. However, every reference I can find on the web echo what is written here. Ziwcam 03:05, 24 February 2007 (UTC)

As you approach the equator though, the deflection goes to zero, due to the angle of the ground there being parallel to the rotation axis, so it's not like there's a sudden kink in your trajectory or anything, and yes, in the northern hemisphere you would be deflected to the right, and in the southern to the left.WolfKeeper 03:37, 24 February 2007 (UTC)

Ok, still having trouble envisioning how its always a certain (left or right) deflection in a particular hemisphere. If we launch a missle from 60°N 90°W, and it takes an hour to reach the equator, the earth will have rotated 15° beneath the missle, and so is 15° west (to its right) of its target (Putting it at 0°, 105°W). If that missile were to continue south, and spend another hour to reach 60°S, wouldn't it be another 15° westward (right) of its target, putting it at 90°S, 120°W)? (If this is better handled somewhere other than the talk page, let me know please.) Ziwcam 06:24, 25 February 2007 (UTC)

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Was the bucket of water on the table a good example? The water in it was actually rotating. A Coriolis effect is about apparent motion in a rotating frame of reference. The rotational effects in the ocean currents are more than apparent. They are relative to the background stars. Dr. Seaweed (203.189.11.2 14:33, 24 February 2007 (UTC))

Try this thought experiment. Manufacture a parabolic dish in the following way: pour resin that takes several hours to set in a slowly rotating dish. After the resin is set, pour water in that parabolic dish (dish still rotating at the original angular velocity). The water will redistribute itself into a layer with even thickness, much as the earth's atmosphere is equally thick everywhere. Now open a small hole in the parabolic dish some distance away from the center of rotation. Some water will immedately pour away through that hole, creating a local area of low water level. Surrounding water will tend to flow towards the low level area, but due to the coriolis effect all incoming water tends to be deflected into cyclonic flow around the low level area. Eventually all the water will flow out through the hole, but it will take a surprising long time. Whenever water moves down the water level gradient, it tends to be deflected to cyclonic flow again.

IN the atmosphere, whenever a low pressure area has formed, cyclonic flow develops, and of course that formation process is not apparent; because of the development of cyclonic flow, a low pressure area may persist for weeks, rather than days. --Cleonis | Talk 16:07, 24 February 2007 (UTC)

You are confusing the Coriolis force with real scenarios in rotating liquids. I'll give you a proper example of the Coriolis force. Suspend a bucket of still water above the north pole and then make a hole in the bottom of the bucket. The water in the bucket will not be partaking in the Earth's motion and it will be stationary relative to the background stars. The water will flow out through the hole radially without any curl at all.

From the perspective of observers standing at the north pole, the water in the bucket will uniformly rotate and complete one revolution in 23 hours and 56 minutes. That apparent rotation is the Coriolis force and it cannot be viewed from space.

Likewise with a Foucault pendulum at the north pole. It will not precess relative to the background stars and so it will appear to have a precessional period of 23 hours and 56 minutes relative to the surface of the Earth. That is the Coriolis force. It is artificial.

The spiral effects in the weather patterns (and in the oceans) can be viewed from space and so they must be caused by something other than the Coriolis force. Dr. Seaweed (203.189.11.2 02:59, 25 February 2007 (UTC))

Actually I didn't confuse what you claim I confused. I used the expression 'coriolis effect', but the expression 'coriolis effect' is very ambiguous; inadvertendly I wrongfooted you. I am accustomed to using the expression 'coriolis effect' in a meaning that is distinct from 'coriolis force', hence the babylonian confusion.

Clearly one should not attribute physical meaning to the coriolis term. However, quite a few people assert that the Coriolis term does influence the physics taking place. Usually, this is formulated as a conditional statement: "In a rotating frame of reference, the coriolis force causes the deviation." What is awkward about that is that the condition, the expression "in a rotating frame of reference", has no physical meaning. Being "in an inertial frame of reference" as opposed to being "in a rotating frame of reference" is not a physical thing, it is a point of view. Whatever point of view one happens to choose isn't physics.

The tabletop demonstration that I described is designed to help in tracking the forces that are at play. In the demonstation that I described, one will actually see the formation of cyclonic flow. In my opinion, in seeking physical understanding, the direct approach is to track the motion with respect to an inertial frame of reference. Tracking the motion with respect to inertial space has the advantage that the bewildering complexity of the centrifugal and coriolis terms is avoided.

The first meteorologist who recognized the physical effect that needs to be taken into account was William Ferrel, around 1850 (At the time, the work of Gustave Coriolis was unknown among meteorologists). Around 1900 meteorologists started to use the expression 'Coriolis effect' for what is taken into account in meteorology. As you point out, the choice to use the label 'Coriolis effect' leads to awkward discrepancies. I suppose that if one insists that that the expression 'Coriolis effect' is inappropriate in meteorology, then the next best thing would be to introduce the expression 'Ferrel effect', after the man who first recognized it. Either that, or one accepts that the expression 'Coriolis effect' is used in several different meanings. -Cleonis | Talk 11:03, 25 February 2007 (UTC)

So what causes this Ferrel effect then? (203.189.11.2 11:28, 25 February 2007 (UTC))

Think of the bucket as the earth. The water in the bucket rotates with the bucket. The water on the earth rotates with the earth. Repeat: water in the ocean, and air in the atmospere is rotating. Yes, the Coriolis effect is the result of a rotating frame of reference. For the ant in the bucket who sees a Coriolis force due to the rotation of the bucket, or the human on earth, who sees a Coriolis effect due to the rotation of the earth, the Coriolis force produces the swirling motion. Looking from outside, in either case, it is just convergence of fluid that is already rotating. Rracecarr 18:10, 25 February 2007 (UTC)

Exactly! Water in the Ocean is rotating with the earth and this is exactly why you are wrong. The Foucault pendulum at the poles only experiences Coriolis force for the very reason that it is not rotating with the earth. Because the atmosphere and the oceans are rotating with the earth we should expect no Coriolis force. Hence there must be an alternative explanation for the spiral effects in the weather patterns and in the ocean currents. Dr. Seaweed. (203.189.11.2 11:06, 26 February 2007 (UTC))

Not to unduly complicate things, but perhaps the article could be made more clear if we introduced the concept of a Hamiltonian frame of reference, which I understand moves with a moving particle. Raylopez99 22:27, 25 February 2007 (UTC)

Commenting on Dr Seaweeds proposal that something else than the Coriolis effect is causing the rotation of currents of in sea and of wind: Is it really these rotations that are visible from space, or rather thier patterns in e.g. clouds? —Preceding unsigned comment added by 194.103.185.14 (talk) 20:13, 21 October 2007 (UTC)

Coriolis Effects on Supertankers and Insects

I referenced the below and it was deleted by a user sans explanation. Please explain why. I have updated the supertanker reference to account for the opinion (not a fact) that Coriolis Effect is negligible. This doesn't mean it is not present nor corrected for, but in the opinion of an unnamed poster at the external link, it is not as significant as other effects (wind, current, etc). As for the insect cite, that's from a recent edition of Science. Several authors have specifically stated Coriolis effect on insects. Since Wiki posters probably cannot afford a subscription to Science like Daddy Warbucks I can, here is a Google link (one of many) that suggests the same thing: http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1013339

- === Insect flight === - Crane flys and moths correct for Coriolis effects when flying, using either their halterers or antennae, respectively, or they would crash to earth - - === Supertankers === - Supertankers have to correct for Coriolis effects when steering

Raylopez99 16:36, 24 February 2007 (UTC)

The force of e.g. the wind on a supertanker is hundreds of times bigger than the Coriolis force. For insects, the forces of random air currents are thousands of times bigger. The "Coriolis force" referred to in the articles has nothing to do with the rotation of the earth. Rather, it is in reference to fictitious forces generated by the rotation of parts of the insects' bodies. It is fine to include this, with an explanation, but just to say that the Coriolis force is important to insect flight implies to the casual reader that the rotation of the earth is important. Rracecarr 17:26, 24 February 2007 (UTC)

Thanks for the clarification, your edit is fine about Coriolis forces within the insect's rotating frame of reference. As for the supertanker, let's leave it out for now, though I do recall that Coriolis forces are present between front and back of a long tanker, but perhaps they are negligible Raylopez99 22:08, 25 February 2007 (UTC)

How the Ferrel effect explains the formation of cyclonic flow

I copy and paste from above:

So what causes this Ferrel effect then? (203.189.11.2 11:28, 25 February 2007 (UTC))

The physical mechanism that was first recognized by William Ferrel has a a number of aspects.

I will describe the Ferrel's line of reasoning for the example I mentioned earlier: a parabolic dish that is rotating slowly (about 10 revolutions per minute) in counterclockwise direction. To my knowledge, Ferrel didn't specifically discuss the parabolic dish example, but his line of reasoning applies perfectly in this example

Water is poured in the parabolic dish, with the dish rotating at the same angular velocity as when it was manufactured: the water will then redistribute itself into a layer with even thickness (this models the physics of the fact that the Earth's atmosphere has an even thickness.) Open up a small hole in the dish, some distance away from the main axis of rotation. A little bit of water will flow directly down that hole, creating a local area with a lower water level; surrounding water will tend to flow towards that low level area.

Let the center point of the parabolic dish be called the 'pole', and let the rim of the dish be called 'the equator' Let the counterclockwise direction be called 'east' and let the clockwise direction be called 'west'

• The water that is initially to the west of the low level area is pulled towards that area by the level gradient. Being pulled along, that water gains angular velocity around the main axis of rotation). Having gained angular velocity, that water climbs a bit higher up the incline of the parabolic dish. (Compare a car negotiating a curve on a banked circuit; the higher the velocity of the car, the stronger the tendency to climb up the embankment.)
  The pattern: water that is initially pulled in west-to-east direction tends to move subsequently towards the equator.
• The water that is initially to the east of the low level area is pulled towards that area by the level gradient. So the angular velocity (around the main axis of rotation) of that volume of water decreases. Having lost angular velocity, that water slumps down the incline of the parabolic dish.
  The pattern: water that is initially pulled in east to-west direction tends to move subsequently towards the pole.
• The water that is initially on the outside of the the low level area gets pulled towards that area, and in being pulled closer to the main axis of rotation its angular velocity increases. (Compare the example of an ice-skater who pulls her arms closer to her body, thus increasing her angular velocity.)
  The pattern: water that is initially pulled in equator-to-pole direction tends to move subsequently towards the east.
• The water that is initially on the inside of the the low level area gets pulled towards that area, and in moving away from the main axis of rotation its angular velocity decreases. (Compare the example of an ice-skater who after a couple of seconds of spinning extends her arms again. Extending her arms has the effect of slowing her angular velocity.)
  The pattern: water that is initially pulled in pole-to-equator direction tends to move subsequently towards the west.

The above combination of mechanisms comprises the line of argument of Ferrel. It explains the formation of cyclonic flow. Importantly, it explains why the tendency to develop into cyclonic flow is the same from all directions. One can refer to the entire set for all directions as the generalized Ferrel effect. I must emphasize that the expression 'Ferrel effect' has never been used. Ferrel made his discoveries around 1850, without any knowledge of the work of Gustave Coriolis. (In his papers, published in the 1730's, Coriolis had investigated energy conversions, Coriolis was interested in the efficiency of waterwheels, the amount of energy that any design of waterwheel can extract from water that moves relative to the waterwheel. There is no mention of the Earth's rotation in Coriolis' papers.) Around 1900, meteorologists started to use the label 'Coriolis effect' for the effect that they were taking into account in their calculations. --Cleonis | Talk 01:57, 26 February 2007 (UTC)

What you are basically acknowledging is that the spiral patterns in the ocean currents and in the atmosphere are actually caused by something other than the Coriolis force. I would agree with that.

Whether yours or Ferrel's explanations are adequate or not is another matter altogether. Dr. Seaweed (203.189.11.2 05:30, 26 February 2007 (UTC))

There are many ways to think about this. By far the easiest is to treat the Coriolis force as real for meteorological purposes. All other explanations are either equivalent to this (ie, produce in the end the same results), or wrong William M. Connolley 09:29, 26 February 2007 (UTC)

The Coriolis force is a fictitious effect as viewed from a rotating frame of reference. The spiral patterens in the weather are not fictitious. If you want to suddenly decide to treat the Coriolis force as being something real in meteorology, you are going to have to explain exactly how that can be so. Seaweed (203.189.11.2 11:12, 26 February 2007 (UTC))

This is an *old* discussion. Coriolis is a fictitious force in exactly the same way gravity is fictitious. Coriolis forces appear when you transform into rotating frames of reference. Within those frames you can treat them as real William M. Connolley 11:31, 26 February 2007 (UTC)

I would argue that Coriolis forces are "ficticious", but only if you use a Hamiltonian frame of reference (one that moves with a body). If you do so, there's Coriolis component, but it doesn't show up in the same way as an inertial frame of reference. How'se that for a synthesis, eh Dr. Bill? Seems we travel in the same circuit, quite by chance. Raylopez99 12:43, 26 February 2007 (UTC)

I would say that you have got it completely wrong. In Hamiltonian frames of reference there is no Coriolis force at all. The Foucault pendulum at the north pole tells us that the Coriolis force is a fictitious effect that only occurs on something that does not share in the motion of the rotating frame. Dr. Bill has also missed the point. The Coriolis force, when it occurs, may seem real to people in the rotating frame of reference. However, the rotational effects in the weather patterns and the oceans are viewed from more than just the rotating frame of reference. Hence they must be caused by something other than the Coriolis Force. Seaweed (203.189.11.2 13:01, 26 February 2007 (UTC))

Seaweed you seem all washed up, pardon my pun. First you claim that in a Hamiltonian frame of reference (which moves with a person, and thus is not inertial) tells us Coriolis acceleration is ficticious. Fair enough. But then you say there's no Coriolis force at all, which is contradicted by your further statement "may seem real". Which is it Weed? You can't have your Porphyra and Edith too. Why do hurricanes turn one way in one hemisphere as opposed to the other? Ιt's obviously a 'real' force, when viewed from a non-inertial frame. Thus the Foucault pendulum experiment shows that a "force" is present to twist the pendulum, at least until it gets to the equator, for the person in the non-inertial (Hamiltonian) frame of reference. Raylopez99 15:16, 3 March 2007 (UTC)

You didn't read what I said. I said that in a Hamiltonian frame of reference there is no Coriolis force at all. Show me where I said that Coriolis force is fictitious in a Hamiltonian frame. I said that Coriolis force is fictitious when it acts on the Foucault pendulum at the poles. The Foucault pendulum at the poles is not in a Hamiltonian frame because it does not partake in the Earth's diurnal motion. Dr. Seaweed (203.189.11.2 09:59, 23 March 2007 (UTC))

Sorry Weed but you left me even more confused than before. But this is a complicated field, and that's no LIE {group} (pun intended, see: http://www.amsta.leeds.ac.uk/Applied/news.dir/issue14.dir/art/review3.html Raylopez99 20:38, 25 March 2007 (UTC)

Coriolis is no more ficticious than other effects of inertia, Gravity, etc.

This article has a big problem. What's all this 'ficticious this' 'ficticious that' here as if all we have here is nothing more than an optical illusion? Is this a joke? Cause there is a real dynamic (Newtonoan?)effect that is called Coriolis force that does bend a rolling ball on a rotating "disc". The Coriolis force is nothing but inertia. And inertia is not branded ficticious in Wikipedia, so there is absolutely no reason whatsoever to brand Coriolis ficticious.

And what about that animation? It is not showing what happenes when a ball actually makes a curved path on a rotating disc and only shows what would happen if a ball rolls in a straight path. That is telling only half of the story. There are two things here:

1, A real bending of path of something (ball for instance) that is rolling on a rotating surface.

2, An apparent bending of a ball that is actually going in a straight line (= optical illusion)

The second one is the only one adressed here in this Wiki article. In order to achieve clarity we must realize that while the two have the same name, the physics is distinct. That (No. 2) one would happen only if the ball has sufficient initial acceleration that overrides the force coming from under it (from the rotating "disc"), like in a roulette, that would have led the ball to roll in whatever straight path it initially started. Only in that case is there an optical illusion in the eyes of someone attached to the rotating object that would cause a straight line appear to be bent. But otherwise there will be a real coriolis force that acts at the right angle to the initial would-be straight path and bends the rolling ball away from that expected straight path. And this is not an optical illusion but a real bending of the path of the ball (as seen from above (stationary frame) as well as seen while standing somewhere on the disc (rotating frame of reference).

Something must be done about this folks. Or perhaps it is better to create a separate wikipage titled "Coriolis force" (so that this one would remain only about one of the two things. Who decided to merge/redirect it all anyway? Benua 16:45, 26 February 2007 (UTC)

Nope. There is only one effect, not two. The Coriolis effect is the result of the Coriolis force, which is a fictitious force that arises in rotating frames of reference. Any motion can be analyzed from an intertial frame, in which case there is no Coriolis force, or from a rotating frame, in which there is a Coriolis force, which is termed "fictitious" because it's only there because of the chosen frame. The results are the same either way. All of which has nothing to do with the frictional force which causes a ball rolling on a rotating surface to follow a curved path. That is a real force is all frames, and is not a Coriolis force.

By stating that the Coriolis force is just inertia (you are essentially correct), and then that it causes a ball on a rotating surface to roll in a curve, in an inertial frame (you are wrong), you are contradicting yourself. Rracecarr 17:36, 26 February 2007 (UTC)

You are wrong. There is nothing ficticious about inertia. Otherwise it would have been noted there. See this mpeg where the ball DOES bend (seen from both frames): http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/crls.rxml Benua 17:53, 26 February 2007 (UTC)

See the mpeg yourself. When the camera is not rotating with the merry-go-round, the ball goes straight. Hold your finger or something on the screen as a reference to convince yourself of this. Please stop cluttering up this talk page. Rracecarr 18:10, 26 February 2007 (UTC)

What cluttering? Is the discussion page reserved for "serious" discussion of Coriolis insects only? Anyway I have seen the picture and the ball is affected by the rotation. Check this other coriolis deflection video: http://www.classzone.com/books/earth_science/terc/content/visualizations/es1904/es1904page01.cfm?chapter_no=visualization There are two issues here. Jury is still out.

You have both missed the point. Rracecarr is right in that the Coriolis force is only fictitious and it is an artefact of being in a rotating frame of reference. He doesn't seem to realize however that the rotational effects in the atmosphere and ocean currents are not fictitious and must be caused by something other than the Coriolis Force. George Smyth (203.115.188.254 09:37, 27 February 2007 (UTC))

No, it's not entirely ficticious. I actually disagree with the term 'ficticious' since it causes problems like these. It's a real effect caused by inertia. That's why the rotation effects occur in the atmosphere, due to inertia. I actually prefer the term pseudo-force. Pseudo implies it's real, but deceptive, in the case of coriolis it's inertia underlying the force, but the effects of the pseudo-force are as real as any force gets (arguably forces don't exist anyway, it's all potential energy, energy seems to be more fundamental.)WolfKeeper 09:53, 27 February 2007 (UTC)

This is not a matter of preference but a matter of how this force is commonly called in the physics literature. I have seen both terms used, but "fictitious force" is the most common. The usage seems to be interchangeable, so both terms could be mentioned in the Wikipedia article. --Itub 10:59, 27 February 2007 (UTC)

The point is that fictitious is a misnomer. If it was fictitious it wouldn't exist at all. On the other hand pseudo implies it's something pretending to be something else; in this case inertia. The centrifugal and coriolis pseudo forces are real and are due to inertia. Pseudo force is the term that Richard Feynmann used for example, he was generally reckoned to be a good physicist, to say the least.WolfKeeper 06:02, 1 March 2007 (UTC)

I admire Feynman and I agree that in retrospect fictitious forces may not be the best name for this forces. But the point is that in an encyclopedia we have to reflect common usage, rather than legislating ourselves which name is more "correct". I should also mention that it is normal for technical terms to have meanings that don't match exactly the common meaning of the word. In this case, "fictitious force" = "force that results from non-inertial frame of reference", not "force that does not exist". If you look at other technical terms you'll find that many of them are misnomers or don't seem to match common sense. Some examples: atom, reversible (thermodynamics), spontaneous (thermodynamics), aromatic (organic chemistry). --Itub 09:10, 5 March 2007 (UTC)

That is indeed what I am asserting, Wolfkeeper. You can't have a real inertia and a ficticious coriolis force. It is absurd. A ficticious force can't have a real effect. The second instance (optical illusion) may be considered ficticious, but in the first instance I mentioned, Coriolis force is not ficticious in this case because Wikipedia's own definition of ficticious is that it is an apparent force needed by an observer in non-inertial frame. So a real inertia with a real effect can't be ficticious. Benua 14:05, 27 February 2007 (UTC)

Ficticious forces are real - it's just a name. Well, in as much as any forces are real (debateable). But they're not different - the term ficticious force just refers to their origin (i.e. the non-inertial frame). WilyD 14:21, 28 February 2007 (UTC)

Why did Benua delete this quote?

'If the atmosphere moves with the Earth then there can be no Coriolis force in the atmosphere. This has been proved by the Foucault pendulum experiment. The precessional period of the Foucault pendulum changes from infinite to 24 hours as it moves from the equator to the poles. This means that the Coriolis force only operates to the degree to which the pendulum is not partaking in the Earth's motion. Dr. H R D Wheeler, Manchester (58.69.250.10 11:35, 27 February 2007 (UTC))

is there not a case to answer here?

• Apart from being original research, it's unverifiable because it's false. Those are the only problems I see. WilyD 14:53, 27 February 2007 (UTC)

Since when has the Foucault pendulum been original research? Everybody knows that the precessional period of the Foucault pendulum is infinite at the equator and 24 hours at the poles. Are we witnessing censorship here? Is WilyD frightened about something?

I'm frightened of bees - that's about it. WilyD 14:22, 28 February 2007 (UTC)

WilyD, I didn't know I was deleting anything when I replyed. In fact that quote by Dr. Wheeler raises an interesting point, because it means that line of argument alone proves the actual Coriolis force since it is the earth (and not every rotating thing like for eg. a ball or disc) that has an atmosphere around it that is rotating with it. Benua 18:51, 27 February 2007 (UTC)

Oh, well then those merely would have been good reasons for you to delete it. The statement is basically nonsense - the atmosphere no more "rotates" with the earth than does a pendulum. WilyD 18:55, 27 February 2007 (UTC)

With Rracecarr saying that the atmosphere does rotate with the earth and WilyD saying that it doesn't, I think we have a serious problem here. Rracecarr is actually correct on this point. If the atmosphere didn't rotate with the earth, there would be a powerful wind blowing. The Foucault pendulum rotates with the earth at the equator but not at the poles. This means that the Coriolis force only applies to the unentrained scenario. Hence the big question. What causes the spiral patterns in the oceans and in the atmosphere? It is cetainly not the fictitious Coriolis force. It must be something else. I think that alot of you need to go away and have a long hard think about all this. George Smyth (203.115.188.254 05:44, 28 February 2007 (UTC))

Well it's true, it isn't true in the way he means it, which is why he draws erroneous conclusions while doing his own, original research. The way in which the Foucault Pendulum and the Atmosphere rotate with the earth is the same, both rotate with the earth (after all, both are fixed to a point to first order) but neither is ridgedly fixed so. FWIW, the Coriolis force also acts inside the earth (which rotates with the earth) it's just that it's so much smaller than the intermolecular forces in the solid earth that its effect is entirely trivial. In any event, yes, I'll keep reverting nonsense and original research, especially when it contradicts every reliable source on the subject. WilyD 14:19, 28 February 2007 (UTC)

The Coriolis force is responsible for the rotation of cyclones. See Cyclone and Tropical cyclone, for example. Please don't change the article to state that there is any doubt about this fact, because there isn't. Rracecarr 08:06, 28 February 2007 (UTC)

If you are so sure about this, then how come we can view the spiral patterns from space? We can't view a precessing Foucault pendulum from space because it is fixed relative to the background stars.

'fraid not, that's only true at the pole. And you can indeed view a Foucalt pendulum from space.WolfKeeper 09:59, 28 February 2007 (UTC)

The cyclones are obviously rotating relative to the fixed background stars, and so this rotation cannot be a fictitious Coriolis effect. It must be something else. G Smyth (203.115.188.254 09:34, 28 February 2007 (UTC))

It can because the cyclones are not at the equator. The other factors involved include centrifugal force (i.e. more inertia) around the center of the cyclone, the pressure difference, and the coriolis effect.WolfKeeper 09:59, 28 February 2007 (UTC)

Wolfkeeper, So you are admitting then that it is only at the poles that the Foucault pendulum is fixed relative to the background stars. Good. That's what I have been trying to say too. As it moves towards the equator, its precessional period increases from 24 hours to infinite. This means that it only experiences Coriolis force to the degree that it is not rotating with the earth. At the equator, the Foucault pendulum is rotating with the earth and it experiences no Coriolis force. The cyclones do not rotate with the earth at any latitude and so they cannot experience a Coriolis force. You needn't try to bring centrifugal force to the rescue because it is a radial effect.G Smyth (203.115.188.254 12:02, 28 February 2007 (UTC))

No, you can either analyse this in a non rotating frame of reference, and in that case you get just the same rotating structures, because of the way the inertia of the air masses interacts with the pressure differences. If you wish to analyse this more simply, in a frame rotating with the earth, then you need to identify the effects on inertia due to the rotating reference frame and the coriolis and centrifugal pseudo forces appear. These pseudo forces have very real effects in a rotating reference frame such as the Earth. They are not fictitious in any normal sense of the word. For example Sherlock Holmes was a fictitious character, he never existed at all, but inertia is real, and pseudo forces which are a manifestation of inertia have real effects in such a frame.WolfKeeper 22:03, 1 March 2007 (UTC)

The facts are that Coriolis force as defined by this article cannot explain the rotational patterns in the weather. G Smyth (203.115.188.254 12:02, 28 February 2007 (UTC))

This article defines Coriolis force in accordance with all modern teaching. I cannot critize the Wikipedia definition of Coriolis force. It may not have been what Coriolis himself intended. He may have intended the 2mvXω to refer to motion in a vortex in hydrodynamics, but that is beside the point. The Wikipedia definition corresponds exactly to modern teaching. Ie., the Coriolis force is a fictious force that we observe on a moving object as observed from a rotating frame of reference. Eg. A bird flying overhead as we ride on a carousel.

I think that the problem that we are facing in this article is that the Coriolis force is being wrongly used to explain real effects in Hamiltonian reference frames such as in the oceans or in the earth's atmosphere. Perhaps the main article could be shortened to only defintions, and all the controversies surrounding meteorolgy and oceanography could be moved to a new controversial article on cyclones and ocean currents. Dr. Wheeler, Manchester (58.69.250.10 04:45, 1 March 2007 (UTC))

There is, in fact, no contraversy (at least, no evidence of one) - certainly not enough that we could cover it. WilyD 15:41, 3 March 2007 (UTC)

The Cause of the Spiral Effect in Cyclones

Rracecarr, It is not a verifiable fact that the rotational effect in the cyclones is caused by the Coriolis force. You admit yourself that,

(1) The Coriolis force is fictitious, (2) That the atmosphere rotates with the Earth. (3) That the spiral effects in the atmosphere are not fictitious because they can be viewed from space.

We also know from the Foucault pendulum experiment that the Coriolis force only acts on things that are not partaking in the motion of the rotating frame of reference, such as an aircraft or a missile flying above the earth's surface, or balls thrown over a children's roundabout.

You are imposing your own point of view here. You are asserting that the Coriolis force causes the spirals in the weather patterns. I changed it to the less assertive 'it is believed to cause'.

In fact, all the evidence suggests that the spiral effects are caused by another mechanism. George Smyth (203.115.188.254 08:25, 28 February 2007 (UTC))

• All the reliable sources assert that this is the case (if you're curious, many will also include derivations so you can see why). Your unique conclusion can't be used here because it can't be reproduced or confirmed by others. Instead of trying to convince poor Wikipedia editors, who shouldn't be trying to figure things out themselves anyways, why not submit your revolutionary theory to Nature? Nature publishes all kinds of wrong stuff, but is still considered a reliable source, or at least good for your CV - when this is done, you can cite the journal article and we can make an offhand mention about it somewhere in the article. Until then, our hands are tied - even if we wanted to include your novel conclusion, as Wikipedia is not a publisher of original research WilyD 15:05, 28 February 2007 (UTC)

I'm not sure if it my unique conclusion. I never studied meteorology or oceanography. I studied applied maths and I was merely reciting those orthodox teachings regarding the precessional period of the Focault pendulum. It is 24 sidereal hours at the poles. This means that a full Coriolis force on the Foucault pendulum is in operation at the poles. The precessional period is determined by the ω term in the Coriolis Force expression. Periods tending towards infinite as we approach the equator indicate partial entrainment.

We all know that both the atmosphere and the Earth's magnetic field are fully entrained with the earth's motion. I was surprised therefore to read that meteorologists and oceanographers are attributing the spiral patterns in the cyclones and ocean currents to the Coriolis force. I was merely concurring with the editor that mentioned the Hamiltonian frame.

But if this is the state of conventional wisdom and if that is wikipedia's policy to mirror that state, then I don't suggest that you change your article. A couple of days ago, I changed it to 'Believed to be', but somebody quickly changed it back to 'Is definitely'.

I thought that the purpose of the talk pages was to discuss these clashes of opinion.

Are you absoluely sure that it is the Coriolis force that causes the spiral effects in the ocean currents?

I suggest that you think about it at any rate. George Smyth (203.115.188.254 07:46, 1 March 2007 (UTC))

Thinking about it is not what's important. Find a reference disputing that the Coriolis force is not responsible for Hurricanes and the like and we can consider the point disputed. Until then, all we have is your own reasoning, which isn't any good. FWIW, it's fairly apparent to me that the Coriolis force should cause atmospheric torques - the atmosphere is not a rigid rotator - I'm not sure if this is obvious, but it's fairly easy to argue. The B field is same - both don't change much now because they're in a quasi-equilibrium state - where various effects balance, but local deviations (like hurricanes) still occur. WilyD 14:49, 1 March 2007 (UTC)

The B field is actually the answer, but then that is original research and so it can't be put on the main article. I tried to insert a reference a few weeks ago but it was instantly deleted along with all my other entries on centrifugal force. The Earth's magnetic field determines the circular nature in the weather patterns. The magnetic equation F = vXB is the Coriolis force. B = 2ω if B is vorticity and there is every reason to believe that B is vorticity. David Tombe (222.126.33.122 05:17, 2 March 2007 (UTC))

• If you still have the reference, I will read it - I mean, as soon as I've read the stack of papers my supervisor just dumped on me ;) WilyD 14:33, 2 March 2007 (UTC)

The reference essentially meant that the Coriolis force is responsible for the rotational patterns in the weather and the oceans, but not for the reasons described on the main article. The vorticity of the magnetic field gives rise to a real Coriolis force. The reference is [5]. There is a gap between the maths and the physics in conventional teaching. This gap results in the illogical attempts to explain a real effect with a fictitious force. David Tombe (203.87.176.3 16:32, 2 March 2007 (UTC))

To understand the Coriolis effect as taken into account in meterology, I recommend the work of the following two meteorologists: Anders Persson and Brian Fiedler.

Check out these two physlets that were developed by Brian Fiedler: (physlets are Java applets for demonstrating physics principles)

merry-go-round
inertial oscillations
(For a description of inertial oscillations as recognized in oceanography see this page from an online oceanography textbook

Brian Fiedler's physlets do not directly addres formation of cyclonic flow, but the inertial oscillations physlet does show crucial underlying physics. The inertial oscillations physlets presents the coriolis effect as taken into account in meteorology.

An illuminating article by Anders Persson that is available online as PDF document: The coriolis effect. Discussion of various aspects. Anders Persson shows how the coriolis effect as taken into account in meteorology is related to the Eötvös effect. In fact, in high performance meterological models, the Coriolis effect and the Eötvös effect are incorporated in the equations conjointly. Understanding the Eötvös effect is half the work in to coming to an understanding of the coriolis effect as taken into account in meteorology. --Cleonis | Talk 15:03, 6 April 2007 (UTC)

The Coriolis acceleration (vXH) occurs in hydrodynamics where H is vorticity. It occurs as a consequence of motion in a vortex. It can't be more straightforward than that. The question is simply, 'where are the vortices that cause the Coriolis force in meteorology and oceanography?' Their alignment must ultimately be traced back to the Earth's rotation. We know this because of the fact that the direction of rotation of these oceanic and atmospheric phenomena is determined by the direction of the Earth's rotation. We also know that the spiral patterns in the oceans and the atmosphere are real and not fictitious, and therefore the vortices that cause them must be real. We are not dealing with the fictitious Foucault pendulum scenario.

Kepler's law of areal velocity tells us that there are no large scale vortices in space as they have been sponged up by the magnetic field. The areal velocity term is identical in mathematical form to the Lorentz force. We must therefore look to the Earth's magnetic field as being the cause of the spiral effects in the oceans and the atmosphere. According to Maxwell, a magnetic field is a sea of tiny vortices aligned solenoidally.

The main Wikipedia article has only recognized the existence of fictitious Coriolis force as when something is viewed from a rotating frame of reference. It then attempts to explain certain natural phenomena such as the spiral effects in the oceans and the atmosphere in terms of this fictitious effect, when the explanation actually lies in the real Coriolis force of hydrodynamics. David Tombe 11th April 2007 (61.7.161.229 09:01, 11 April 2007 (UTC))

You guys seem to be arguing science, which in my opinion doesn't belong on an article talk page. There is another article Tornado#Rotation that says the Coriolis effect is not responsible for the spin direction, contradicting this article. Couldn't someone just find a textbook or something that settles the question and put in the citation with a superscript? Orthografer 15:42, 19 August 2007 (UTC)

Define cyclone. A tornado is small-scale relative to the earth and the Coriolis effect's influence is proportionally not much stronger than other meteorological phenomena - which can cause it to spin "the wrong way" if strong enough. With water flowing out of a sink, Coriolis is negligible compared to other factors. With a tropical cyclone (much bigger than a tornado), the storm always rotates in the direction Coriolis makes it - as is true of any other similar scale large scale event. The argument above seems to stem from "Coriolis is fictitious". It is not a real force, but a consequence of working in a rotational frame as opposed to an inertial frame.--Nilfanion (talk) 17:40, 19 August 2007 (UTC)

It's just that the second sentence of the cyclone article says that a tornado is a cyclone. Orthografer 21:14, 20 August 2007 (UTC)

I've added the modifier large to the word cyclones to bring it into agreement with the tornado article. Rracecarr 21:19, 20 August 2007 (UTC)

Edit by Ian Strachan

Today's edit by Ian Strachan seems to be in good faith and may bring additional clarification. It is however clumsily formulated, repetitive and not a real improvement as it was inserted. If better developed it may add to the article. For now I think it is better to revert. −Woodstone 20:56, 12 April 2007 (UTC)

Fatal flaw in David van Domelen's attempt at explanation

Woodstone has added a link to a webpage by David J. Van Domelen that presents an attempt at providing an explanation for the coriolis effect.

Unfortunately, this attempt contains a fatal flaw, that is illustrated with the stereographic image

Van Domelen writes:

Consider being on a rotating sphere with no gravity. An observer who is glued to the sphere throws a ball straight to the "east" on the globe, in the direction of rotation. Since there are no forces on the ball, it will travel in a straight line, the tangent line shown in Figure 2 at t=0.

Time passes, and the ball continues on its straight line. But the observer is attached to the globe and moves around to a new position. At this new position, the observer's definition of the "east" direction has changed, and is no longer the same as it was at time t=0. The ball is no longer traveling on the observer's "east" line, and, in fact, seems to have drifted off to one side. If the globe is spinning slowly enough that the observer can't feel the spin, then the natural conclusion would be that some mysterious force pushed the ball off course, sending it drifting away from the axis of rotation more quickly than it would go if it were still heading the "correct" easterly direction.

Similarly, if the observer throws a ball to the west at time t=0, it will seem to have been forced inward towards the axis of rotation because the "west" line has moved.

Stereographic image. Look at the image with crossed eyes to obtain the stereo-effect.
Blue line: motion predicted by Coriolis formula for air mass (initially) moving in east to west direction.
Red line: great circle that is tangent to latitude line; represents trajectory of ballistically moving object.

When a ball is thrown towards the east, its motion will proceed along the great circle. To the observer glued to the sphere (the sphere rotating underneath the trajectory of the thrown ball) there will be an apparent deflection of the ball to the right, which is in fact the observer's trajectory curving away to the left.

The blue line represents the motion that is predicted by the Coriolis formula:

${\vec {a}}_{C}=-2\,{\vec {\omega }}\times {\vec {v}}$

When mass (such as a volume of air mass) has a velocity in western direction, it is deviated to the north of the latitude it starts from. That is what the Coriolis formula describes, and that is what need to be explained.

The attempt at explanation by Van Domelen breaks down for a ball that is thrown towards the west. Again the red line, the great circle tangent to the latitude that the ball is trown from, gives the trajectory of the ball. To the observer glued to the sphere (the sphere rotating underneath the trajectory of the thrown ball) the ball will appear to proceed less fast to the equator than it actually does. The point is: there is no way that the observer glued to the sphere will see the thrown ball move north of the latitude it was thrown from; a great circle that it is tangent to a latitude line proceeds towards the equator, both in west-to-east and in east-to west direction.

It is difficult to guess how Van Domelen has managed to overlook the flaw. He seems to have ignored the fact that he is dealing with a sphere instead of with a disc, and consequently failed to take into account that objects that are thrown always move along a great circle, but even so his construction doesn't work for a disc either. --Cleonis | Talk 12:03, 12 May 2007 (UTC)

A pity. It looked so nice. But the formula talks. This still leaves us without an intuitive explanation. Could you devise one? −Woodstone 12:45, 12 May 2007 (UTC)

Implicitly the intuitive explanation is already in the current article. I am in favor of making it more explicit.

Animation 1
Object co-rotating on a very shallow parabolic dish. Due to the slope of the dish, the object is subject to a centripetal force. This centripetal force provides the amount of force required to remain co-rotating with the dish.
If a momentary force causes the object to rotate around the central axis slower than co-rotating motion, the object will slide down the incline.

Animation 2
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 ellipse-shaped trajectory.

Left: the motion as observed from the inertial point of view. The gravitational force pulling the object toward the bottom (center) of the dish is proportional to the distance of the object from the center. This force causes the elliptical motion.
Right: the motion as seen from a co-rotating point of view. In this frame, the inward gravitational force is balanced by the outward centrifugal force. The only unbalanced force is Coriolis, and the motion is an inertial circle.

In the article the following correct observation is made:

In a manner of speaking, the Earth represents such a turntable. The rotation has caused the planet to settle on a spheroid shape such that the normal force, the gravitational force, and the centrifugal force exactly balance each other on a "horizontal" surface. (See equatorial bulge.)

The parabolic dish's shape deviates from perfect flatness due to its rotation. (A resin was poured, and a rotation of about 6 revolutions per minute was maintained while the resin hardened.) The Earth deviates from perfect spherical shape due to its rotation. The equator is about 20 kilometers further away from the Earth's geometrical center than the poles. Seen in that way, moving towards the equator is going uphill, and moving towards the poles is to slide downhill, in analogy with frictionless motion over the surface of the parabolic dish.

Air mass that has no velocity relative to the Earth is subject to a centripetal force that sustains the co-rotating motion, analogous to what is shown in Animation 1. When air mass acquires a velocity in east-to-west direction, it is circumnavigating the Earth's axis slower than the Earth itself. When circumnavigating the earth's axis slower than co-rotating motion, the air mass will slide down the incline: the air mass will move towards the nearest pole, and that effect is what the Coriolis formula is designed to describe! --Cleonis | Talk 19:30, 12 May 2007 (UTC)

It's a start. The coriolis force makes a mass moving west move towards the closest pole indeed, but this has nothing to do with the shape of the earth. It would also happen on a perfect sphere or a cube spinning around two opposite corners. The coriolis force vector pointing straight inward to the axis has a horizontal component towards the pole. You are making it unnecessarily complex by involving the frictionless disk. However, the question is to make this understandable without using the formula. −Woodstone 20:26, 12 May 2007 (UTC)

I guess to you it looks unnecessarily complex. The purpose of the analogy is reduction of complexity; instead of jumping straight to the terrestrial physics, an intermediate step is presented, the rotating dish. You seem to indicate that you believe that the parabolic-dish and oblate-Earth analogy doesn't hold good. --Cleonis | Talk 21:17, 12 May 2007 (UTC)

The analogy is ok, but unnecessary for explanation. Also the frictionlessness is an unnecessary complication. The formula shows that for an object moving west, the coriolis force will point inward towards the axis. The vertical component cannot be acted upon (ground resists), the remaining component is north (on the northern hemisphere). Van Domelen's picture number three shows this quite correctly. Only his explanation at picture two is misleading. Better might be along this line: the object moving west stays behind on the rotation giving the effect that is sinks below the horizon from the rotating observer. However, there I get stuck. How does it look to the moving airmass? How is it pressed to the ground? −Woodstone 22:15, 12 May 2007 (UTC)

There are two completely different phenomena at involved here. I think they should be kept separate. Trying to explain both at the same time will only confuse the reader.

First: Why doesn't the centrifugal force cause everything on earth to slide towards the equator? Answer: The earth isn't round. (Turntable analogy). This has nothing to do with the centrifugalCoriolis force.

Second: What causes the Coriolis force? Answer: Motion in a rotating frame of reference. This can be explained without involving either gravity or the centrifugal force.

The text by Domelen (quoted above) offers two different metaphors explaining the cause of the Coriolis force. (Paragraphs 3.1 and 3.2.) The error that he makes is to say that one of them only applies to north/south movement, and the other one to east/west movement. In fact, both apply all the time. If you try to derive the Coriolis force from just one of them you will not get the "2" in the formula.

--PeR 20:03, 13 May 2007 (UTC)

The phenomenon that needs to be explained is the phenomenon where Van Domelen's attempt at explanation breaks down. When a ball is thrown, or when a huge cannon fires a shell over a distance of tens of kilometers, the hurled object moves along a great circle that is tangent to the latitude the object was thrown/fired from. However, air mass that is (initially) moving in east-to-west direction doesn't move along a great circle, instead it turns to the north. In my opinion, the article should present the explanation why air mass and thrown objects move so differently. The statement 'the coriolis force is caused by motion in a rotating frame of reference' does nothing to explain that: both the thrown object and the air mass are moving in the same rotating frame of reference. --Cleonis | Talk 20:51, 13 May 2007 (UTC)

Exactly. The northward deviation from a great circle (as seen from an inertial frame) cannot be explained by any statement about the Coriolis force, because it has nothing to do with the Coriolis force. It falls under the first of the two different phenomena that I listed above. --PeR 21:58, 13 May 2007 (UTC)

That doen't seem a correct statement. The formula shows quite clearly that the horizontal component of the Coriolis force is always perpendicular to the movement and the size does only depend on the movement speed (at fixed rotation speed and latitude). So movements to the west (north) of certain speed cause a Coriolis force to the north (east) of a fixed size. The formula is clear; what we are looking for is an intuitive understanding of why it happens. −Woodstone 22:31, 13 May 2007 (UTC)

Yes. The Coriolis force is always perpendicular to the direction of movement. This is quite well explained by the sum of the two metaphors that van Domelen gives. My statement above concerns a system as seen from an inertial frame. (The discussion about great circles only applies in an inertial frame. Then there are no fictitious forces.)

A bullet that is fired horizontally, due west, so that it has zero velocity with respect to the center of the earth, will fall straight toward the center of gravity, and land north of the latitude that it was fired from. The equatorial bulge has been greatly exaggerated in the picture.

The main source of confusion here appears to be that it seems counterintuitive that a bullet that is fired due west can land north of the latitude that it was fired from. This, again, is due to the shape of the Earth. I've made a picture to try to explain this. Imagine that a bullet is fired from a high tower, horizontally and due west with a speed that makes it stationary with respect to the center of the earth. From the point of view of a rotating reference frame, this bullet will be deflected to the north. In an inertial reference frame it will fall straight towards the center of the earth. In both cases it will land north of the latitude of the tower. The explanation in the inertial reference frame is that the tower was built perpendicular to the surface of the earth, which is not the same as "away from the center of gravity".

The point that I'm trying to make is that the shape of the earth acts to cancel the centrifugal force. This article is about the Coriolis force. It would be better if the two issues were kept more separate. --PeR 06:09, 14 May 2007 (UTC)

There is another factor, and it is not clear whether you have taken it into account. Let an object be at rest on the surface of the Earth, say at 45 degrees latitude. If all of the Earth's mass would be concentrated in a single point, and still exert exactly the same gravitation on the object (treat the object as supported by a massless shell) then where is that point? In the case of a non-spherical body this point does not coincide with the geometrical center.

For example: for an object located on the equator, the amount of gravitational attraction from the Earth that it experiences would be the same if all of the Earth's mass would be concentrated in a point ten kilometers away from the geometrical center. Taking a specific location as an example: Nairobi, the capital of Kenya is very close to the equator. For an object in Nairobi the center of the Earth's attraction is located on the line from the Earth's geometrical center to Nairobi (and so on for all other longitudes).

A bullet that is fired (from midlatitude) is not attracted to the geometrical center, but to a point several kilometers away from the geometrical center. This reduces any effect that could possibly make the bullet land north of the latitude it is fired from.

Anyway, all that is negligable stuff compared to what is described by the Coriolis formula. The ground track of a satellite cannot move to the north of a latitude that the ground track is tangent to, because the ground track follows a great circle. But air mass that starts in east-to-west direction just keeps getting deviated to the right, until eventually it flows in south-to-north direction, tens kilometers north of the latitude it started from, etc, etc. --Cleonis | Talk 22:06, 15 May 2007 (UTC)

(reset indent) Not sure what you mean. The effect that I describe is certainly not negligible compared to the Coriolis effect. It is equal to it, except that, as you point out, gravity is not necessarily directed towards the exact center of the Earth everywhere. I'll put numbers to the calculation to exemplify: Let's assume that the tower is located at a lattitude of 45 degrees north, where the difference between common and geocentric latitude $\alpha =0.003395\,\mathrm {rad}$. I've taken the Earth's radius at that latitude to be $r=6367\,\mathrm {km}$, the acceleration of gravity $g=9.80665\,\mathrm {m/s^{2}}$ and the rotational speed to be $\omega =0.00007292\,\mathrm {rad/s}$. (These numbers are based on figures that I found here in Wikipedia.)

From a rotating reference frame: The tower is point exactly "up". A bullet is fired due west with a velocity $v=328.3\,\mathrm {m/s}$. It is deflected by the Coriolis force, $a_{C}=2\omega v\sin(45^{o})=0.0339\,\mathrm {m/s^{2}}$. The bullet lands north of the latitude it was fired from.

From an intertial persepctivne: The tower points at an angle alpha = 0.003395 radians relative to the local direction of gravity. A bullet is fired due west so that its velocity is exactly zero. The acceleration of gravity has a northward component equal to $a_{g}=g\sin(\alpha )=0.0333\,\mathrm {m/s^{2}}$. The bullet lands north of the latitude it was fired from.

The difference between the two numbers is less than 2 % ($a_{C}\approx a_{g}$). The error can be attributed to the effect that you describe, and other errors in the input data. It should be pointed out that the Coriolis acceleration is much larger for a bullet than for an air mass (due to the higher speed). The reason why an air mass is deflected a longer distance is that distance is acceleration times time squared, and a bullet falls to the ground within seconds while an airmass moves over the course of days. --PeR 20:45, 18 May 2007 (UTC)

Visitor from a distant [medical] discipline. The [Coriolis] phenomena shows an uncanny likeness to the physiologic [systolic] rotation and [diastolic] counterrotation of the mammalian heart. Performance of the living heart is traditionally imaged and measured in long and short axes in a standard [echocardiogram]. Center reference of the heart is an echo dark solid irregular lump of shaped collagen [central body of the heart]. Said reference understood as center has a long [Robert Hooke] axis and a short(Pierre LaPlace] axis. Myocardial muscle cells (Macro-Myocardium, Micro-Cardiomyocyte) have been grouped in the literature in many ways, perhaps the most relevant to physics and Coriolis motion is seen in the work of [Torrent-Guasp]. Oblique variants of these two vectors are legion and readily imaged as bands or strings of interconnected cardiomyocytes moving around a center body beholden to Coriolis forces. Anatomists and physiologists have pondered the wringing and unwringing effect in a single phased beat of the heart for a very long time. In my limited understanding of the material, it appears that boundary physics likely represents an initial foothold in appreciation of generation of [torque] and [countertorque]within the heart muscle [myocardial mass] against incoming and outgoing [blood] [mass]. Measured on the [echocardiographic]long axis, muscle mass probably turns 15-30 degrees in systole, then 15-30 degrees back in diastole, blood mass much more. Volumetric and time derivatives of this phenomena are well described in the medical literature by [Frank/Starling] methods. Computational imaging of a heartbeat based on immersed boundary methods was first described at the [Courant Institute].--Lbeben (talk) 01:22, 25 July 2008 (UTC)

How ballistic motion proceeds if it gets enough time

I copy and paste from the thread above:

It should be pointed out that the Coriolis acceleration is much larger for a bullet than for an air mass (due to the higher speed). The reason why an air mass is deflected a longer distance is that distance is acceleration times time squared, and a bullet falls to the ground within seconds while an airmass moves over the course of days. --PeR 20:45, 18 May 2007 (UTC)

Animation 1
The black dot represents a balloon that is being swept along with air mass that has a velocity relative to the Earth's surface, and no atmospheric pressure gradient is present. The pattern of motion of the air mass is called 'inertial oscillation'.

Animation 2
The groundtracks of a formation of four satellites with a common orbit that is tilted with respect to the plane of the equator. Period of the orbit: 2 Earth days.

Let me get this straight: what is it that your are claiming here? How will air mass move around? (in the case of air mass that is not subject to a pressure gradient force.)

The rotating globe in the animation on the right represents the rotating Earth, and the black dot represents a balloon that is being swept along with air mass that has a velocity relative to the Earth's surface, and no atmospheric pressure gradient is present. The motion of the black dot is described by the coriolis formula. (In order to keep the number of animation-frames manageble, the following adjustment has been made: at 30 degrees latitude, the actual period of inertial oscillations is about 14 hours; in the animation the depicted period is exactly one half of the Earth's rotation period. Other than that the depicted motion is a true rendering of what the coriolis formula describes. Due west is deviated to the north, due north is deviated to the east, due east is deviated to the south, due south is deviated to the west, and so on. )

I'd like to know from you whether you recognize that animation 1 represents inertial oscillations correctly.

You suggest that the bullet does not have enough time to be deflected northward. It is very easy to give an object in ballistic motion enough time: shift to thinking about satellite orbits!

Animation 2 shows the motions of a formation of four satellites. The four satellites are in the same orbit, which is tilted with respect to the plane of the equator. The period of the orbit is two Earth days. This period of two Earth days results in the following: the velocity of the satellites' groundtrack with respect to the Earth is comparable to the velocity of air mass with respect to the Earth's in Animation 1.
For calculating the motion of the groundtrack with respect to the rotating coordinate system only the angular velocity of the satellite counts, not its altitude, so the case of a satellite is perfectly comparable to the case of a bullet that has been fired. Only the satellite orbit lasts a long time.

Both in animation 1 and in animation 2 there is a point in the cycle where the object moves tangent to a latitude line. In animation 1 the motion proceeds to the north, in animation 2 the motion proceeds to the other hemisphere

I'd like to know from you whether you recognize that animation 2 represents the ground tracks of the satellites correctly.

Do you recognize that the inertial oscillations remain close to the same latitude, and that ballistic trajectories, when given enough time, will proceed to the opposite hemisphere? --Cleonis | Talk 17:07, 20 May 2007 (UTC)

The example with the balloon is not very realistic. Without pressure gradient any velocity would quickly dampen out and no circles would be observed. −Woodstone 22:01, 20 May 2007 (UTC)

I notice that you gave no knowledge of meteorology. As a starter, I recommend the following article by the meteorologist Anders Persson: [The coriolis effect] (PDF-file 780 KB)

In the atmosphere, inertial oscillations are rare, because the right circumstances rarely occur, but its counterpart in water is recognized as quite a common phenomenon in Oceanography. In Persson's article inertial oscillations of a mass of ocean water are described, and a diagram with probe positions is presented (The probe is non-anchored buoy that continuously transmits its position). In the depicted measurement run, strong persistent winds on 25 july give a body of water mass a velocity of 25 to 30 cm/s in eastward direction. The measurement run plots the inertial oscillation from 25 july to 29 july, and the plot shows very little dampening of the inertial oscillation. In the atmosphere, friction is even less than in the seas.

Once they are whipped up, inertial oscillations continue for many cycles, lasting days if not weeks. (In the animation the motion keeps cycling, that is to keep the number of frames of the animation manageble. Of course actual inertial oscillations do decay.) --Cleonis | Talk 16:46, 21 May 2007 (UTC)

To make a better comparison: Try making an animation where the ballistic trajectory starts out in the same position as the air mass, and with the same horizontal velocity (due west). To give the bullet enough time, give it a very high vertical component of velocity. (Note that "vertical" here means "perpendicular to the surface of the Earth". At 30 degrees latitude that's about 10 arc minutes north of "away from the center of the Earth".) Plot the ground track (as projected using the above definition of "vertical") of both the air mass and the bullet. See how they both curve the same way? (The comparison isn't perfect because there's also a Coriolis effect due to the vertical movement, which is much larger than the horizontal one. For very small vertical speeds you get almost identical ground tracks.) Note that the bullet never crosses the equator. It comes crashing down into the Earth at a latitude grater than or equal to 30 degrees north, regardless of its initial vertical velocity. --PeR 22:29, 20 May 2007 (UTC)

Unfortunately, the comparison that you offer is worse. The large vertical (perpendicular to the local surface) velocity is an extra factor that obscures the view.

The purest comparison is the following thought experiment. If an object can slide around perfectly frictionless over the surface of a perfect sphere, how will it move if the object has a velocity? This is commonly referred to as the 'ice-hockey puck on an ice-planet setup'. The puck-on-an-icesphere setup has been extensively covered by James Mcintyre:

Coriolis force and non-inertial effects

Mcintyre's website features a number of animations.

Animation 2, showing satellite groundtrack serves a dual purpose, it also depicts the puck-sliding-on-an-icesphere scenario.

As you mention, in the bullet-shot-almost straight-towards-the sky setup, the view is badly obstructed by the the fact that the much larger vertical velocity component gives rise to a coriolis term component that is larger than the effect that you seek to explain.

The puck-sliding-on-an-icesphere setup has the following in common with air mass sliding over the Earth's surface: in both cases gravity confines the motion to motion parallel to the surface. That is the key element, gravity confines the motion to motion parallel to the surface.

It is not clear why keep trying to explain the Coriolis formula in terms of motion of a bullet, when a much purer representation is available. --Cleonis | Talk 16:59, 21 May 2007 (UTC)

The cyclonic flow fields visible from an inertial frame are caused by the frictional forces in the atmosphere. It is similiar to the relationship between centripetal motion and centrifugal force. If the object is not exhibiting centripetal motion in the non-inertial frame it is experiencing a real centrifugal force. For instance the car seat pushes on you to force you to follow the car in the turn. So as the air flows it encounters air that has a different speed based on its position relative to the earth. Frictional forces in the air accelerate the new air (from the current). For instance, if the atmosphere were truly rigid with respect to the earth, then the air at higher altitude has to be moving at higher speed (omega cross r). If an air current is moving inertially north (without any graviy forces) it will climbe in altitude relative to the earth's surface (but in a straight line relative to an inertial observer). Since it is a higher altitude it needs to be flowing laterally at a higher speed to match the nieghboring air. The shear forces then accelerate the flow laterally causes the cyclonic winds. The inertial observer would see a curved trajectory for the ball in the turntable illustration if the turntable put a frictional force on the ball. The inertial observer would see a curved trajectory for the ball and thus cyclonic like trajectoris. The answer is frictional forces just like real honest to goodness forces cause coriolis accelerations (as seen by the inertial observer) as cause centripetal accelerations (the rider going around the curve in a car.(Mangogirl2 00:36, 9 August 2007 (UTC)

In formation of cyclonic flow, friction plays a very minor role

I copy and paste from the thread directly above:

The cyclonic flow fields visible from an inertial frame are caused by the frictional forces in the atmosphere. Mangogirl2 00:36, 9 August 2007 (UTC)

To a good first approximation, friction is negligable in the motion of air masses. Of course, the high end computermodels do take it into account, as friction dissipates some of the energy of air mass that is in motion relative to the Earth. But - for example - in the formation of cyclonic flow friction is a much smaller factor than pressure gradient force and the Coriolis effect. --Cleonis | Talk 22:05, 10 August 2007 (UTC)

Maybe I was a little loose with the term friction but it takes inertially observable accelerations (due to forces) to curve the trajectory of the airflow. The cyclonic flows visible from an inertial location are due to the forces created by the air that it is being flowed into in order to match the flow conditions. Coriolis effects can only be seen from a rotating frame. the analoagy with the ball on the disc still applies. Unless the turntable exerts some type of force on the ball, its trajectory is straight for the inertial observer and so it will be with air currents. and centrifugal force.I am not talking about the earth sruface atmoshphere friction but rather the shear forces encountered when a current interacts with non-current air. Shear forces will tend to drive the two flows to the same conditions. So as the current flows north it encounters air that is moving east at greater speed than it was. This will cause the flow to deflect when the current intersects with air that has already accelerated to the current speed to stay over one spot on the earth. I would assume the confusion is arising over the fact the low is moving and accelerating relative to the inertial observer but not to the earth bound observer. So the observed motion relative to the low must be summed with the inertial motion of the low to get the wind motion observed by the inertial observer.Mangogirl2 02:46, 11 August 2007 (UTC)

For instance look at Figure 6-12. http://www.eng.warwick.ac.uk/staff/gpk/Teaching-undergrad/es427/Exam%200405%20Revision/TheWinds-b.ppt#270,6,Slide 6

This picture is from an inertial observer,  it looks to me like the wind direction is fixed inertially and it is the earth moving under it.  Event the captions says this.  Thus, Coriolis is not deflecting the wind trajectory for the inertial observer but only for the earth bound observer. Mangogirl2 03:07, 11 August 2007 (UTC)

Estuarine Salinity

I beleive the Coriolis effect is reponsible for a north/south salinity gradient in estuarine environments. Can someone expand upon this. —Preceding unsigned comment added by 219.89.21.37 (talk) 00:04, 13 September 2007 (UTC)

Offhand I don't see how the Coriolis Effect is a direct influence on estuary salinity gradients, especially if it is considered preferential to North/South gradient vectors. There are reportedly many estuary paradigms, so I am curious what data supports your proposal. Many estuaries are more or less static, such as the Texas Laguna Madre, so the motion wrt to the Earth surface is small. Nevertheless a Wikipedia article states the Laguna Madre has a gradient resultant from the weather. Good question, though. 158.81.13.147 (talk) 22:03, 18 December 2007 (UTC) Sorry, forgot to sign again. L Coyote (talk) 22:06, 18 December 2007 (UTC)

The Visuals are Inadequate to Visualize Deflection of Air From High to Low Pressure

The purpose of this entry is not to debate alternative explanations/mechanisms for the direction of deflection of the atmosphere, or the actual path/velocity of particles in a rotating reference frame, as posited by others in the forum.

If it is assumed that the Coriolis Effect does determine the cyclonic/anticyclonic movement of air, at least for purposes of this entry, it seems that it should be possible to pose a concise model/explanation, ideally with a visual aid, that demonstrates the observed movement of air around highs and lows. The current discussion, and the well-known "Merry-Go-Round" and "Dallas-to-Minneapolis" analogies are woefully inadequate with regard to atmospheric dynamics. For example if one goes in the opposite direction in the "Dallas-to-Minneapolis" analogy, from Minneapolis to Dallas, the movement of the air appears to be deflected to the left, which is opposite to what is observed. A more in-depth discussion addressing this point might seem inane to some, but might be very helpful to others less knowledgeable on the subject.

Hypergolic 04:29, 19 October 2007 (UTC)

What about east-west movement of wind?

How does the explanation of coriolis force resulting from the rotation of the Earth explain the rightward deflection of a wind in a perfectly east-west pressure gradient, or a south-north pressure gradient? (In the Northern hemisphere) Sancho 16:01, 8 November 2007 (UTC)

It is not the pressure gradient that causes the effect, but the velocity of a parcel of air. Initially, the parcel starts moving down the gradient. Explanations going straight to inertia are very tricky. Explanation using the formula is very straightforward. Consider the local coordinate system as described in the article, with axes (east, north, up). Assume a latitude of φ = 45^o, so that sin φ = cos φ = ½·sqrt(2). Then a parcel of air moving east west at unit speed has a velocity vector (-1, 0, 0). Use of the formula shows a Coriolis acceleration of a factor ω·sqrt(2) (which is positive) times the vector (0, 1, -1). The last acceleration coordinate pushes the air against the ground, where it cannot move further. The first two coordinates show an acceleration due north: to the right of the movement due west. You can exercise the south-north case yourself. −Woodstone 17:00, 8 November 2007 (UTC)

Yes, this makes sense, but explanations that chock up this coriolis force to an analogy with a a ball moving across a spinning disc lose the ability to explain the right-ward deflection of air that starts to move down an east-to-west or south-to-north gradient. Sancho 17:27, 8 November 2007 (UTC)

Actually I do not agree with your calculation. I haven't completely checked it, but the way I see it is more clear to define the axes with respect to the earths rotation axis. Then it immediately also becomes clear that for pure west-east flow there is no radial velocity component, and therefore there can be no Coriolis force. Also the horizontal red arrows in figure 13 should be removed and the '45 degrees arrow' should be drawn smaller. 82.171.21.253 (talk) 03:42, 11 January 2009 (UTC)

The Coriolis acceleration is not only related to radial movement. Also movements with or against the rotation generate it. Only movement parallel to the rotation axis does not. The shown coordinate system was chosen to allow easy discarding of the vertical components, which are meteorologically less relevant. A pure east-west movement of unit speed has components (−1, 0, 0) and the Coriolis acceleration according to the mathematical formula is (0, 2sin φ, −2cos φ). So indeed there is a component north and a component down (for positive phi). Using a coordinate system with z parallel to the rotation axis (x east, y perpendicularly inward to axis) would have a rotation (0, 0, 1), east-west movement (−1, 0, 0) and Coriolis acceleration (0, 2, 0), or horizontally inward to the axis, which could be decomposed again to north and down, just as before. −Woodstone (talk) 12:45, 11 January 2009 (UTC)

Thank you Woodstone, I understand it now. I was thinking in 2D while it's a 3D problem. 130.89.79.243 (talk) 13:46, 14 January 2009 (UTC)

Woodstone, a concise derivation of the Coriolis acceleration indicates that it is the tangential deflection of a radial motion. There can be no Coriolis force acting on an east-west motion.

In fact a rotating frame of reference only superimposes an apparent circular motion on top of the existing motion. The only fictitious force that can ever exist is when the rotating frame is angularly accelerating, in which case we can observe an apparent angular acceleration.

To get a Coriolis force, we must look to a non-circular Keplerian orbit. There we will see a real Coriolis force in action as the radial motion gets deflected tangentially.

It is a lack of Coriolis force in the atmosphere which actually causes the tangential deflections in a cyclone, and it is a tightening and slackening of centrifugal force which causes the radial deflections of the east-west air movements. David Tombe (talk) 15:11, 13 January 2009 (UTC)

David, your claim that east-west motion does not generate a Coriolis acceleration is in contradiction with the formula given in the article. In the paragraphs above I just filled in the numbers into the formula and the effect comes out. Actually, the size of the C-acceleration is equal for any horizontal orientation. That's why inertial circles arise. If you maintain that the well known and documented formula is false, that would be original research. −Woodstone (talk) 15:24, 13 January 2009 (UTC)

Woodstone, the formula as it is presented in this article, and in many textbooks is silent on the issue. The derivation of acceleration in polar coordinates involves the same mathematical principles as the derivation for the formula in question, and it explicitly states that the Coriolis force must be in the tangential direction. The derivation in relation to rotating frames includes that same restriction if you follow it from first principles very carefully line by line. David Tombe (talk) 15:47, 13 January 2009 (UTC)

You may disagree with the formula, but it is not silent on east-west movement. The formula is a vector formula expressed for a rotating frame of reference. It is independent of the coordinate system used in that frame of reference, be it rectangular, polar or cyclindrical. The vector Ω × v is perpendicular to Ω and v and has size equal to the product of the sizes of Ω, v and the sine of the angle between them. So it is only zero if either &Omega or v are zero of are parallel. As consequence, any non-zero east-west speed (not on the equator or the pole) generates a Coriolis acceleration. −Woodstone (talk) 20:08, 13 January 2009 (UTC)

Woodstone, yes I can see that. But if you follow the derivation through carefully, you will see that the formula is only valid if the velocity term is in the radial direction. This factor has been overlooked. There is no point in continuing to draw attention to a formula without being mindful of any restrictions of application that are rooted in the derivation of that formula.

Coriolis force is unequivocally a tangential force, just as centrifugal force is unequivocally a radial force. This comes through very transparently when we expand the general acceleration vector into polar coordinates. We see that Coriolis force is always in the tangential direction. The Coriolis force and the centrifugal force can never double up in the same direction. David Tombe (talk) 02:57, 14 January 2009 (UTC)

David, please re-read the part of the article which discusses the formula Ω × v, which discusses this in detail. In particular, consider that the Coriolis force is linear in both Ω and v. -- The Anome (talk) 09:41, 14 January 2009 (UTC)

Anome, yes on the face of it the Coriolis expression does not appear to restrict which direction v must be in. But when we use calculus to derive the Coriolis expression, the result clearly states that Coriolis force is a tangential force. This implies that it is only the radial component of the velocity that is important. That is a standard textbook result, but admittedly that derivation is not done in conjunction with rotating frames of reference. It is only done in connection with the Kepler problem.

If we do the derivation as per in rotating frames of reference, we don't use calculus directly. We start with a vector triangle. At that stage of the derivation, the velocity can be in any direction. But then we have to consider the limit as the sides of the triangle tend to zero. Only then do we get the desired expressions. In doing so, the velocity in question becomes unequivocally radial, and the Coriolis term becomes unequivocally tangential. This latter point is overlooked.

At any rate it is not my intention to continue with this argument. I was merely responding to an anonymous who made what appeared to be a legitimate concern which I supported. It turns out now that that anonymous has changed his position and is happy with the article as it is, and so there is no point in me debating the matter any further, because it has all been debated before.

But perhaps you do recall a citation that was supplied by SBHarris in about May 2008. It hinted at how the deflection of east-west motion was in actual fact very like a tightening or slackening of centrifugal force. Whoever that author was, he should be more bold about following his instincts because I would say that he was absolutely correct. I've lost that reference but it will be somewhere in the archives.David Tombe (talk) 05:30, 15 January 2009 (UTC)

The intuition that the Coriolis, centrifugal and Euler forces are deeply interrelated is exactly right, but not perhaps in the way you are thinking. Instead of being separate (pseudo) forces, you can view them as merely convenient names for the individual additive terms within the equation for the single composite pseudo-force that appears to be generated when we transform Newton's equations of motion from an inertial frame into a rotating reference frame. See rotating frame of reference for the complete derivation. -- The Anome (talk) 09:30, 15 January 2009 (UTC)

Hi David

You say:

Only then do we get the desired expressions. In doing so, the velocity in question becomes unequivocally radial, and the Coriolis term becomes unequivocally tangential.

Your statement refers to the angular component of acceleration in polar coordinates:

${\boldsymbol {a}}(t)={\ddot {\boldsymbol {r}}}=\left({\ddot {r}}-r{\dot {\theta }}^{2}\right){\hat {\mathbf {r} }}+\left(r{\ddot {\theta }}+2{\dot {r}}{\dot {\theta }}\right){\hat {\boldsymbol {\theta }}}$

According to the tangential component of this acceleration, what sometimes is called the Coriolis term $2{\dot {r}}{\dot {\theta }}$ is tangential, in agreement with your remark. However, this term is not what is meant by the words Coriolis force from a Newtonian vector mechanics standpoint. Rather, the term $2{\dot {r}}{\dot {\theta }}$ is what is often called the "generalized Coriolis force" in Lagrangian mechanics. The technical adjective "generalized" is inserted in the Lagrangian picture to emphasize that the Newtonian force is not the same thing. That is, you are arguing about the "generalized Coriolis force" while the article is about the Newtonian vector force, a different kettle of fish.

Several key differences between the generalized force and the Newtonian vector force are:

1. The generalized Coriolis force is present in every frame of reference; the Newtonian Coriolis force is present only in a rotating frame of reference and vanishes in an inertial frame.
2. The generalized Coriolis force always enters the tangential component of acceleration; the Newtonian Coriolis force is the vector cross product of particle velocity and the rotation vector, and so can be in a variety of directions that depend upon the particle velocity vector direction.
3. The generalized Coriolis force actually is not a vector at all, and is tied to the particular coordinate frame chosen for the Lagrangian analysis: it always is in the tangential direction of the chosen polar coordinate axes, whatever the physical forces may be; the Newtonian Coriolis force is a true vector and is used in Newton's laws expressed within the rotating frame just like a real force.

I believe you recognize these differences, but have not recognized that you are making valid points about the generalized Coriolis force, while everyone else and the article are based upon the Newtonian Coriolis force.Brews ohare (talk) 16:04, 15 January 2009 (UTC)

Anome and Brews, I think the whole issue here is that there are two topics. There is,

(1) The Kepler Problem

(2) Fictitious forces

I have no quarrel at all with any of the physics in the Kepler Problem. But I have a quarrel with fictitious forces. As far as I am concerned, only the Euler force can ever be fictitious.

The way I see it is, that the terms that would properly be used in the Kepler problem have been stolen by the topic of 'fictitious forces'.

That's it in a nutshell. There's nothing further that I can constructively add to the Coriolis article here, within the context of how that force is understood as being a fictitious force. I think the article has got it completely wrong. The correct Coriolis force appears in the Kepler problem. But as you can see, Brews is objecting to the use of that term in the Kepler problem.

I discussed the terminology issue on the talk page of 'Kepler's Laws'. While Bo Jacoby was willing to call it the Coriolis force on his own talk page, he was not willing to support me on the issue on the 'Kepler' talk page.

So the points have been made. I don't think that we can take the matter any further.

I should however add that the generalized Coriolis force that Brews is talking about IS the Coriolis force. There is no other Coriolis force. It occurs when a powered wheel converts a rotational motion into a translational motion. David Tombe (talk) 04:56, 16 January 2009 (UTC)

David: You can adopt the view for yourself that the generalized Coriolis force is the Coriolis force, and the Newtonian vector Coriolis force is not, but you cannot then treat the generalized Coriolis force as though it were a true vector and a Newtonian force. You have to stick with the Lagrangian viewpoint consistently. You are not willing to do that, so I have to disagree with your approach.

As you love to do, you bring up an example that is supposedly very everyday, and just drop it there. Like a cat expects its master to recognize the merits of animal remains deposited at the doorstep. I suppose that your "conversion" of rotational to translational motion refers to what happens with an automobile tire. However, the connection to Coriolis force remains obscure, as this conversion is readily analyzed in an inertial frame, and no Coriolis force (in the Newtonian sense) appears anywhere in the analysis.

Alternatively, one could handle the matter entirely from a Lagrangian view point and introduce the generalized Coriolis force. Whether that would clarify your views, and what implications you would draw from this form of analysis, I do not know. Brews ohare (talk) 06:41, 16 January 2009 (UTC)

Do we need an article on the generalized Coriolis force, as distinct from the generally understood Newtonian use of the term? A Google search for "Lagrangian Coriolis term" suggests that this might be a better name. -- The Anome (talk) 12:13, 16 January 2009 (UTC)

Brews, As regards the horizontally rolling wheel, I was looking at the horizontal deflection of all vertical motion in the wheel. But on second thoughts, I now realize that that it is a radial centrifugal force and not a Coriolis force. So we can forget about that. David Tombe (talk) 05:52, 17 January 2009 (UTC)

Vector Product

Regarding, "The Coriolis force should not be confused with the centrifugal force given by (the vector or "cross" product)[m/omega x [ omega x r ]]," is that vector product incorrect by a minus sign? It has been many years, OK, decades, since vector calculus class, but I get the result of that equation as written in the article to be centripetal force. Obviously the absolute value is equal to the complementary force. I am assuming the omega vector to be positive in the counter-clockwise direction.

Otherwise the article is superb and accurate, in my opinion (disclaimer: which is based on having majored in undergrad physics when Reagan was president.)

And thanks for elucidating the Coriolis effect on cyclones and why the hurricane turns counter-clockwise, yet the inertial circle is clockwise (for positive latitudes.) To me, now, an oversimplified analagous visual concept is like that of many very small gears coupled to and surrounding a single flywheel--the direction is opposite. —Preceding unsigned comment added by L Coyote (talk • contribs) 18:25, 11 December 2007 (UTC)

Signature - Vector Product

Sorry for omitting the signature; still on the learning curve. L Coyote (talk) 18:43, 11 December 2007 (UTC) Did that do it?

Coriolis effect does occur in long narrow containers (e.g. bathtubs)

The effect is seen in my bath each time and that's what science is all about - observation.

I believe the usual opinion that the effect is too small to be noticeable is due to ignoring the contributory influence of the journey most of the water takes in travelling along the long axis of the bath. Also my bath is aligned north-south which would also tend to reinforce the effect.

I will wait for comments or discussion before editing the main article.

Johnmuir (talk) 15:03, 1 January 2008 (UTC)

I tend to agree. The few admittedly unscientific experiments I did in my sink on the northern hemispere indicate a clear preference for turning left. A numeric example I added to the article a while ago, but was removed later, indicates that under reasonable assumptions the Coriolis force is about 0.01% of the pressure gradient. Small, but not impossible to have effect. Note that for example the tidal force is also about 0.01% of gravity, which clearly has effect. −Woodstone (talk) 16:09, 1 January 2008 (UTC)

I would disagree. My understanding is that the effect is so small that motion within the water (due to getting in or out of the tub, how you were splashing before you got out, etc.) would have a greater influence. If someone wants to let their tub sit for 30 minutes, then pull the plug, and repeat this 10-20 times, then we might have scientific evidence of the influence of the Coriolis Effect. I do like the authors awareness of N/S vs E/W orientation, and the value of a long tub to increase the effect. Lee (talk) 17:29, 1 January 2008 (UTC)

The length of the basin surely has effect, because it gives more time for the force to act. The orientation should not matter, since the Coriolis forces are the same size, regardless of (horizontal) direction of flow. −Woodstone (talk) 18:12, 1 January 2008 (UTC)

It has been done with a scientific experiment, but it involved leaving the water to stand for a week or something, and numerous other safeguards. For most normal sinks, the shape of the sink and any remaining eddies in the water swamp any other effect.

Please give a link to this paper, otherwise that's just hearsay. Johnmuir (talk) 06:30, 2 January 2008 (UTC)

Well I certainly have observed this over my last 20 or so baths. Every time the water went anti-clockwise and as I read in the bath there was little or no turbulence or prior vortices. Can I ask any readers to give their own observations on this? Does anyone have contrary experiences? Please do not argue by external references - only by your own observations. (I'll wait a week so that we can gather some statistically valid results - happy bathing ;-) Johnmuir (talk) 22:09, 1 January 2008 (UTC)

By all means try it with lots of different sinks, but editing the article based on this would violate WP:OR- (User) WolfKeeper (Talk) 00:28, 2 January 2008 (UTC)

Ah! That seems to be a problem, but an understandable point of view. OK, I'll look for published research results. Bye the way my whole point on this was actually the difference between (round) sinks and (long) baths - please see above.

I would still be interested in hearing personal experiences though. That's still valid. Please contribute your observations! [User:Johnmuir|Johnmuir]] (talk) 06:28, 2 January 2008 (UTC)

Your enthusiasm is great. However, with all due respect, a bather's empirical observation provides little scientific value and therefore does not warrant edits to the page. If you are truly passionate about this topic, get any college-level textbook on "classical mechanics," which should explain the physics in great detail. By the way and for what it is worth, my bathtub is oriented northwest-southeast and appears to drain in random directions, often changing the direction of rotation in mid-drain. L Coyote (talk) 20:17, 2 January 2008 (UTC).

(Sheepish grin ;-) Umm, I checked out all the links I could find and it looks like my bathtub has a drain which tends to twist the exiting water in one direction. OK, I was barking up the wrong tree but thanks to all for being very polite about it. Johnmuir (talk) 08:08, 3 January 2008 (UTC)

Chemical Coriolis effect

This article on Chemical and Engineering News [6] discusses the formation of helical crystals, with a direction which has been attributed to the Coriolis effect. It is an interesting example that occurs in a very small scale (of the order of 1 cm), but on a long time scale (weeks). Are there any objections to adding it as an example to the Wikipedia article? --Itub (talk) 10:43, 9 January 2008 (UTC)

Interesting. I would like to see a more in-depth explanation of the phenomenon. The Coriolis effect acts only on things that move. Presumably a crystal forming is quite stationary. So I don't get it. Rracecarr (talk) 15:16, 9 January 2008 (UTC)

The crystal doesn't move, but it grows by accretion of molecules or ions from the surrounding solution. At the microscopic scale, these molecules are moving constantly, and if this explanation of the phenomenon is correct, their movement should be slightly biased due to the Coriolis forces. I'll try to find a more detailed discussion. --Itub (talk) 15:46, 9 January 2008 (UTC)

I couldn't find anyone discussing this phenomenon in detail, other than the original article, which says: "Our best hypothesis for this unusual effect simply involves the Coriolis force operating on a bubble of air which becomes trapped under the lattice of crystals of 46; slow evaporation of the solvent through the crystal roof propagates the helix. Nevertheless, if this were the only factor involved, it is clear that this effect would have been previously observed". They repeated the experiment three times in the Northern hemisphere, always obtaining a right-handed helix, and four times in the Southern hemisphere, where they obtained a left-handed helix three times and a right-handed helix once. Hardly a proof beyond reasonable doubt, but intriguing. The article has been cited 25 times, but none of them seem to discuss this phenomenon. I searched for articles about Coriolis effect and crystallization, and found some, but all of them talk about centrifuges, certain metallurgical processes, or crystallizing under microgravity (e.g., in a rotating space station). Nothing about crystals being influenced by the rotation of Earth, except one that talked about the orientation of crystals at the bottom of a dried lake if I understood correctly. --Itub (talk) 16:22, 9 January 2008 (UTC)

My guess is that the orientation of the helix is influenced by the initial rotation of the fluid, caused when the liquid is poured into the beaker. Presumably, the direction of the helix is determined when the first crystal seed is formed, and this may well happen within the time it takes for the liquid's angular momentum to dissipate. Given that the same person is always performing the experiment in the northern hemisphere, and a different person is doing it in the southern hemisphere, the results quoted above seem quite likely. The Coriolis effect would be several orders of magnitude smaller than the random forces due to impacts of solvent molecules, so I don't see how it could possibly affect anything. - At any rate, the scientists themselves call the Coriolis theory "speculation", so it can hardly be encyclopedic. --PeR (talk) 18:59, 9 January 2008 (UTC)

Coriolis Effect in Wave Power?

Ocean Wave Power in WP is entirely attributed to wind. Is that correct? Is Coriolis already incorporated into wind physics or is there a secondary effect that acts directly on the ocean in a manner that can be described as a physical (pseudo) force? Is my question just another example of a mistaken reference frame problem, or is there more to ocean waves than wind and Bernoulli? Tidal effects being excluded, we would need a solid reference, either yes or no. 100TWdoug (talk) 04:16, 25 March 2008 (UTC)

Cyclones vs. Inertial Circles

As I read through this article, it became increasingly clear that cyclones and inertial circles move in opposite directions (counterclockwise and clockwise, respectively, in the northern hemisphere). Why? I was unable to find an explanation in the article. Perhaps it is there, but if it is, it is buried. It should be more prominent. Most of the ideas related to coriolis force are pretty intuitive, but this discrepancy between cyclones and inertial circles needs explaining.

Is it that the air moving into a low-pressure area is all moving in inertial circles that are tangent to the cyclone? And that the direction of air flow at the outer edge of the (forming) cyclone then determines its chirality? So in other words, inertial circles act like a ring of gears surrounding a central gear turning in the opposite direction? If so, that's a complicated idea that needs to be explained in detail -- it really ought to have its own section.

I don't know the details here; I'm no expert and this is just guesswork, so if someone who knows a little more about the topic could step up to the plate, that would be helpful. Solemnavalanche (talk) 15:48, 4 April 2008 (UTC)

Inertial motions are called that because that is the way things move when they are subject to no external forces. Any particle moving on the northern hemisphere with no external force applied will move in a clockwise circle because the Coriolis force turns it to the right. In a hurricane, there are external (pressure gradient) forces. Rracecarr (talk) 20:06, 4 April 2008 (UTC)

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 ellipse-shaped trajectory.

Hi Solemnavalanche,
the terrestrial inertial oscillations are analogous to the inertia circles over the surface of a (very shallow) parabolic dish. The animation on the right is also in the article. Also important: (but not mentioned in the article, I believe) inertial oscillations are not eddies. If for example a group of wheather balloons would be swept along with a body of air mass in inertial oscillation, they would move pretty much in unison, they would not revolve around each other. (I really should make an animation showing that)

The force of gravity (red), the normal force (green), and the resultant force of those two (blue). The resultant force provides the required centripetal force.

The force of gravity (red), the normal force (green), and the resultant force of those two (blue). The resultant force provides the required centripetal force

The website of the MIT fluid dynamics lab shows some cool pictures and movies. There is a webpage about constructing a parabolic dish/turntable and subsequently a webpage about motion over the surface of a (shallow) parabolic dish

If you would use a flat turntable then any low-friction object resting on it would simply drift wide and it would drop over the edge. If the Earth would be perfectly spherical, but nonetheless rotating, then low-friction object resting on the Earth would drift towards the equator. However, the Earth isn't a perfect sphere. The Earth was formed from a protoplanetary disk. Gravity tends to contract matter into a sphere, but because of the rotation the contraction did not proceed all the way to a perfect sphere. The process is perfectly analogous with manufacturing a parabolic dish. In the case of the Earth the oblateness gives rise to a centripetal force, and at every latitude the amount of centripetal force that is provided is just the amount that is necessary.

So the way to visualize the cause of the terrestrial inertial oscillation is to use the analogy with the motion over the surface of the parabolic dish, which is a more straightforward case.

Once you understand the terrestrial inertial oscillation you understand the terrestrial coriolis effect, for the terrestrial inertial oscillation is the purest case: no pressure gradient force is present and no pressure gradient force builds up.

Inertial oscillation of air mass is very rare, but inertial oscilation of large sections of ocean water are common. The amplitude of the inertial oscillation is usually in the order of several kilometers. Inertial oscillation of water mass can be started by winds, blowing in the same direction for some days on end. --Cleonis | Talk 09:44, 10 April 2008 (UTC)

Let me also explain the origin of the expressions 'inertia circle' and 'inertial oscillation'. Imagine a tiny accelerometer mounted inside the puck that is sliding frictionless over the surface of the parabolic dish. Now, an accelerometer that is falling will read zero acceleration; giving in to gravity corresponds with a zero reading of any accelerometer. When a puck is sliding down the incline of the parabolic dish it's giving in to gravity. When a puck climbs up the incline, slowing down in the process, it's giving in to gravity. All the time, sliding around frictionless over the surface of a parabolic dish the effective gravity will be perpendicular to the local surface. In that sense the motion component parallel to the local surface of the parabolic dish can be regarded as inertial motion.

In the case of the motion of the puck over the surface of the parabolic dish the centripetal force can be thought of as absorbed in the geometry of the surface. This is why some authors describe the motion of the puck as 'not subject to an external force' --Cleonis | Talk 11:45, 10 April 2008 (UTC)

The Low Pressure Cyclone over Iceland

Does anybody looking at the picture of the low pressure cyclone over Iceland on the main page remotely believe that a very real spiral effect like that could be caused by a fictitious force? David Tombe (talk) 12:41, 21 April 2008 (UTC)

Fictitious force. - Eldereft ~(s)talk~ 17:14, 21 April 2008 (UTC)

I'm sorry but that was not an answer to the question. The question is the Coriolis equivalent to the Newton's bucket question. The spiralling effect in cyclones can be viewed from outer space and so the effect is more than just fictitious. David Tombe (talk) 11:05, 26 April 2008 (UTC)

Terminology

Why is this article called the Coriolis effect as opposed to the Coriolis force? What's wrong with using the term force?

Will we soon be talking about Newton's second law of motion as "Effect = mass X acceleration"?

Will police forces soon be referred to as "police effects"?David Tombe (talk) 07:50, 26 April 2008 (UTC)

If you read the introductory paragraph, you will find the term "Coriolis force" defined, and there's a redirect from that page to this article. An I'm feeling lucky Google search for "Coriolis force" leads to this page, and the number of Google hits are about the same for the two. (Slightly more for "effect"). Sometimes there are two good alternatives for an article title, and then it is best not to change back and forth. --PeR (talk) 09:34, 26 April 2008 (UTC)

Why are you complaining about not using the term "Coriolis force", when you are the one who removed it from the introduction? I have now restored it (twice). --PeR (talk) 12:22, 26 April 2008 (UTC)

PeR, There's other ways of doing it. The existing introduction contained some inaccuracies. You cannot claim that the deflection is only 'apparent' when it is clearly visible from outer space.

Sometimes it is only apparent, but we have to cater for the general situation and so we cannot have the word apparent in the introduction. David Tombe (talk) 14:06, 26 April 2008 (UTC)

"Apparent" means "visible". --PeR (talk) 16:09, 26 April 2008 (UTC)

An example of how the word 'apparent' is used in physics is in the expression apparent retrograde motion of planets. For example, we know that the actual motion of Mars is a keplerian orbit. From the Earth's point of view there is additional motion to that keplerian orbit: as seen from the Earth Mars is in retrograde motion from time to time. The additional motion is categorized as apparent motion. The keplerian orbit is accounted for in terms of physics taking place, the apparent motion is accounted for in terms of being an artifact of mapping Mars' motion purely from the Earth's perspective.

One can refer to the setup that gives rise to the apparent retrograde motion as 'retrograde effect'. Using the expression 'retrograde effect' in such a way would not be wrong. On the other hand, it would obviously be absurd to use an expression such as 'the retrograde-pushing force'; there is no such force.

The expression 'Coriolis force' is an unfortunate misnomer; there is no Coriolis force. What is taken into account in Meteorology is Coriolis effect. --Cleonis | Talk 19:11, 26 April 2008 (UTC)

Personally, I've never seen a force, so I wouldn't know what a 'real' force is. ;-)- (User) WolfKeeper (Talk) 19:23, 26 April 2008 (UTC)

PeR and Cleonis, The cyclones can be viewed from space and so they are real effects. They are not merely apparent effects.

PeR, You want to keep that term 'apparent' in the introduction because you want to deny everything that is real. Based on your comments on the centrifugal force pages, it is clear that you are steeped in fictitiousism. You can't stand facing up to the reality of the centrifuge and the fact that it must be a real effect. You are trying to spread the nonsense that everything is only fictitious and relative.

The spiral cyclones are a case in point. They are clearly a real phenomenon but you want to pretend that they are simply a illusion arising from a fictitious force.

[Copied from my talk page, where David ignored it] The Coriolis force is a fictitious force: it only ever exists if you are looking at the world from a rotating coordinate system. I'm sorry it doesn't make sense to you that, in the inertial frame, cyclones form without the Coriolis force, but that's the fact--in that frame, it's just pressure gradient force and inertia. A useful law for understanding the formation of cyclones in the inertial frame is the conservation of angular momentum.Rracecarr (talk) 15:23, 27 April 2008 (UTC)

The Coriolis force is a real force in hydrodynamics. It becomes real when the maths is applied properly. The maths only makes any sense when the v and ω terms are physically connected. That would be the case when an element of a fluid moves in relation to the larger body of a fluid which is rotating as is the case with the entrained atmosphere and oceans. David Tombe (talk) 06:44, 27 April 2008 (UTC)

Your opinion sounds like OR to me. Got any refs that point to notable sources?- (User) WolfKeeper (Talk) 06:47, 27 April 2008 (UTC)

Wolfkeeper, have you ever followed the derivation through? Do v and ω apply to the same particle or not?David Tombe (talk) 09:02, 27 April 2008 (UTC)

The v applies to the particle, but the w refers to the frame rotation.- (User) WolfKeeper (Talk) 16:38, 27 April 2008 (UTC)

Wolfkeeper, the ω term applies to exactly the same particle that the v term applies to. Sudy the derivation carefully.David Tombe (talk) 06:33, 28 April 2008 (UTC)

Coriolis effects appear when you do a frame transformation from an inertial frame of reference to a rotating frame of reference. The rotating frame of reference rotates with angular velocity of w. Nothing, I repeat nothing needs to be physically rotating at angular velocity w.- (User) WolfKeeper (Talk) 07:45, 28 April 2008 (UTC)

For example, it might take a mass at (1,0,3) moving in a straight line with velocity (5,0,7) at time 10, and transform it to a reference frame w that is rotating at 2 rad/s around the y axis (we'll assume the inertial reference frame and rotating reference frame have a common origin and axes at time zero). If I've done the arithmetic right, the transformed point will now be at point (-0.09, 0, 3.16) moving with velocity (2.3, 0, 6.41) at time 10. If you do the maths at several points in time, you will find that the curve is anything but straight ;-) (or circular for that matter). The coriolis and centrifugal accelerations apply within the rotating reference frame, and from the point of view of that frame, explains the strange curve you get.- (User) WolfKeeper (Talk) 07:59, 28 April 2008 (UTC)

Wolfkeeper, I have studied these matters in depth for years. Here is a weblink which I dug up on google which provides the derivation that we are talking about. http://www.kwon3d.com/theory/rotsys/rotfrm.html The ω does indeed ostensibly apply to the angular velocity of the rotating frame of reference with respect to the inertial frame. But when we go to the infinitessimal limit for calculus purposes, we obtain exactly the expression that we obtain when we do a direct differentiation on the position vector. Those two components reduce to exactly the two perpendicular components of the velocity of the particle. It is not possible that the meaning could be anything different than that. In the infinitessimal limit, the ω term becomes the angular velocity of the particle, and the v component becomes the radial velocity. Hence you can apply those equations to the space elevator because the object in question co-rotates and there is real centrifugal force. No need for a velocity term in the rotating frame. It is already catered for impicitly in the ω term.

Common sense alone should tell you that Coriolis deflections can only be east-west. A tangential motion would always be deflected outwards.

I'm not saying that any of this should go in the main article. All I am saying is that fictitious centrifugal force should take a back seat in the article. The current wording is fine, as per modern textbooks, but it shouldn't be up front as the flagship for what centrifugal force is all about. David Tombe (talk) 10:53, 28 April 2008 (UTC)

David Tombe, nobody is arguing that cyclonic motion does not occur or that kids cannot fly off the merry-go-round. Please stop putting words in our mouths. Your refusal to inform yourself of the clearly elucidated term "fictitious force" is beginning to resemble tendentious editing. Please carefully consider your arguments and your rhetorical style. Consensus can change, but it seems to be currently strongly in favor of terminology and analysis in line with the usages of the physics community. - Eldereft ~(s)talk~ 07:33, 27 April 2008 (UTC)

Eldereft, So what exactly is your point? Are you saying that it is all just an artifact which is only viewable from a rotating frame of reference? If not, then what exactly has been your problem with my edits?David Tombe (talk) 09:00, 27 April 2008 (UTC)

The current opening sentence of the Coriolis effect article

Currently, the opening sentence of the Coriolis effect article reads as follows:

The Coriolis effect is an apparent deflection of moving objects from a straight path when they are viewed from a rotating frame of reference.

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 ellipse-shaped trajectory.

This animation is a schematic representation of video images that are available on these fluid dynamics labs pages

The animation shows a puck sliding frictionless over a very shallow parabolic dish. The rim of the parabolic dish is marked with quadrants. The trajectory is ellipse-shaped. The right side of the animation pattern shows the motion pattern as seen from a co-rotating point of view.

Transforming the motion pattern to a co-rotating point of view has removed the overall circumnavigation, and what remains is the eccentricity of the trajectory. Obviously the eccentricity is not fictitious.

The motion pattern associated with the eccentricity is called an 'inertia circle'. Note that there are two cycles of the inertia circle for every cycle of the overall circumnavigation.

An exact description of the motion pattern of the inertia circle is given by the Coriolis term:

$Coriolis\;term\quad 2{\vec {\omega }}\times {\vec {v}}$

Note that the Coriolis term is correct for all directions, no dependency of the direction of the motion. The Coriolis term describes the acceleration of the object with respect to the rotating system.

Here is why I present this discussion: Which of the current Coriolis effect article editors regards the motion pattern of the animation as an example of the Coriolis effect? I think it is a prime example of Coriolis effect.

The animation depicts circumnavigating motion. But the openingssentence of the current version only speaks of object that are moving in a straight line. Why this awkward confinement to motion (with respect to the inertial coordinate system) along a straight path?

The eccentricity in the trajectory is not fictitious. As seen from a co-rotating point of view the eccentricity shows up as inertia circles. The inertia circles are described by the Coriolis term. It follows that in particular circumstances, such as in the example depicted in the animation (circumnavigating motion over the surface of a parabolic dish) the Coriolis term provides an efficient description of an effect that is not fictitious. --Cleonis | Talk 14:42, 27 April 2008 (UTC)

What change do you suggest? .."apparent deflection from the path they would otherwise follow..." ? Rracecarr (talk) 15:11, 27 April 2008 (UTC)

To answer your question, the animation is a very good depiction of the Coriolis effect. Rracecarr (talk) 15:19, 27 April 2008 (UTC)

Rracecarr, sorry for not replying on your talk page but I lost track of all the replies I had to do. Anyway, the problem with both the centrifugal force page and the Coriolis force page is that neither properly take into account the fact that these are real effects.

Let's deal with Coriolis first. There are effects that are attributed to the Coriolis force that are clearly not fictitious because they can be viewed from outer space. That is why I reworded the introduction. The key points that I removed were the word 'apparent' and the idea that the Coriolis force is only ever observed from a rotating frame of reference.

I've tried to explain to you that the centrifuge is a real effect and that the heavier particles are pushed to the edge by the centrifugal force.

The maths which you use is correct in its form, but you have unanchored it from the physical reality that it is rooted in. Those rotating frame formulae begin with the idea of a particle in motion. The position vector is differentiated with respect to time. This introduces an angular velocity term ω which is as much part of that particle's motion as the velocity v.

Hence, for those equations to have any meaning, the velocity v and the angular velocity ω must be physically connected as in the case of hydrodynamics. Oceans and atmosphere are hydrodynamics, and all movements of elements of these fluids are still physically connected to the angular velocity ω of the entrained oceans and atmosphere. Hence these effects are real, as can be seen from outer space.

You however are fixated on a fictitious application of these formulae which would apply if a bird were to fly over a children's roundabout.

I was trying to improve both of these pages, but I am being obstructed by a group of editors who clearly don't know very much about these matters, but have nevertheless decided to close ranks to ensure that they are the only group to be alloweed to have any input into these pages.

FyzixFighter and PeR for example have decided that they will delete every entry that I make. This kind of behaviour will lead eventually to administrative intervention.

Wolfkeeper has tried to fudge the whole issue by taking real centrifugal force away altogether to a new page and call it reactive centrifugal force, when in fact it is the centriptetal force that is the reactive force.

When your group has got a deeper knowledge and comprehension of these issues, then you will be in a position to edit. But at the moment, your are merely engaged in team vandalism, either out of ignorance, or out of a misplaced belief that you are ready to be editing encyclopaediae articles on these topics.David Tombe (talk) 06:57, 28 April 2008 (UTC)

Reply to Rracecarr on Angular Momentum

Rracecarr, you mentioned angular momentum to me. If Coriolis force is purely fictitious as in non-contact situations when something moves over a rotating frame of reference, we don't need to concern ourselves with conservation of angular momentum because the entire effect is an illusion.

The reason that you have to bring conservation of angular momentum into your hydrodynamical scenarios in the atmosphere, is because the effects are actually real.

You seem to be arguing to me that fictitious effects become real because of conservation of angular momentum. That is not a logical argument. David Tombe (talk) 11:04, 28 April 2008 (UTC)

What you don't seem to understand is that the way you explain things depends on the reference frame you view them from. You seem to have some interest in electromagnetism--a magnetic field in one frame transforms to an electric field in another, so one person's magnetic force is another's electric force. Just because the Coriolis force is important in the dynamics of a cyclone in a rotating frame does not mean that "Cyclones are caused by the Coriolis force, period, I'm not listening, LALALALALLALALALA...". The effects that are caused by the Coriolis force in one frame are due to other forces in an inertial frame (in this case, pressure gradient forces and inertia). Rracecarr (talk) 13:30, 28 April 2008 (UTC)

RRacecarr, I'm fully aware that other forces are involved in cyclones. But if the Coriolis force was purely fictitious then it couldn't interact with the real forces.

A purely fictitious Coriolis force occurs when an object flies overhead a rotating turntable. But in no way can it interact with the real forces going on on the turntable.

The cyclones are cyclonic which means that some real force must be involved that is connected with the Earth's spin. David Tombe (talk) 14:12, 28 April 2008 (UTC)

It is called conservation of angular momentum. As air moves inward, it's rate of spin (initially matched to that of the earth) increases, creating a whirlpool effect. Rracecarr (talk) 14:28, 28 April 2008 (UTC)

RRacecarr, I know all about it. But if the Coriolis force was a purely fictitious artifact then it wouldn't react in any way with the hydrodynamics of the atmosphere. Can you not see that there must be a real dimension to the Coriolis force, just as the centrifugal force can cause diffusion in a solution in a centrifuge.David Tombe (talk) 14:45, 28 April 2008 (UTC)

The physics are always the same, regardless of the frame of reference. The mathematical representation of the physics is different between an inertial and a rotational frame of reference. In the inertial one there are just terms of pressure gradients and inertia explaining all physics. In a rotational frame additional terms are needed to obtain a correct description, including the Coriolis force. −Woodstone (talk) 18:55, 28 April 2008 (UTC)

Woodstone, I have been arguing exactly that point. The physics doesn't change simply by changing to a different reference frame.

So what force causes the cyclonic effect in the cyclones? Whatever it is, it is real.David Tombe (talk) 08:23, 29 April 2008 (UTC)

It's inertia. But in the rotating frame of reference it appears as 2 pseudoforces in the equations of motion.- (User) WolfKeeper (Talk) 08:43, 29 April 2008 (UTC)

Wolfkeeper, if it's a fictitious force then it can't cause a real effect. The effect is either real or it isn't. It doesn't matter which reference frame we view it from. David Tombe (talk) 11:54, 29 April 2008 (UTC)

The current opening sentence of the Coriolis effect article (part 2)

I copy and paste from above:

What change do you suggest? .."apparent deflection from the path they would otherwise follow..." ? Rracecarr (talk) 15:11, 27 April 2008 (UTC)

To answer your question, the animation is a very good depiction of the Coriolis effect. Rracecarr (talk) 15:19, 27 April 2008 (UTC)

I suggest the following description:
In the case of circumnavigating motion sustained by a centripetal force the Coriolis effect is at play whenever the object is not in concentric uniform circular motion.

Animation 1
Object co-rotating on a very shallow parabolic dish. Due to the slope of the dish, the object is subject to a centripetal force. This centripetal force provides the amount of force required to remain co-rotating with the dish.

Animation 2.
Object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been nudged away from concentric motion. As a consequence, the puck has a velocity with respect to the rotating system.

Animation 1 represents a case without Coriolis effect. There is no velocity relative to the rotating system. The trajectory is circular motion, co-rotating with the rotating system.

Animation 2 represents the case where the puck has been nudged. The motion pattern is an ellipse-shaped trajectory. This ellipse-shaped trajectory has in cyclic sequence the following processes: the centripetal force pulls the puck closer to the central axis of rotation, increasing the puck's velocity. At some point the puck's velocity has increased so much that it "overshoots" the center, and the puck starts climbing up the incline again. Climbing up the incline the puck's gravitational potential energy increases, and its rotational kinetic energy decreases; it slows down, and at some point it has slowed down so much that the centripetal force pulls it back to the central axis again, etc etc.

As seen from a co-rotating point of view the motion pattern follows an inertia circle. The inertia circle is the eccentricity in the ellipse-shaped orbit. The inertia circle is an oscillation. Gravitational potential energy transforms into rotational kinetic energy and back again.

Summerizing:
- A necessary, but not sufficient condition for Coriolis effect is presence of a centripetal force.
- In the presence of a centripetal force (sustaining circumnavigation), there is no Coriolis effect when the motion is concentric uniform circular motion.
- In the presence of a centripetal force (sustaining circumnavigation), Coriolis effect is at play when the object has motion with respect to the rotating system.

If you would remove the centripetal force you would remove the Coriolis effect altogether. --Cleonis | Talk 20:59, 29 April 2008 (UTC)

I don't know what you're talking about, Cleonis. Does Coriolis effect mean something different to you than the effect of the Coriolis force (e.g. does Coriolis effect mean inertial circles)? Because obviously, the Coriolis force exists whether or not there's a centripetal force. A puck sliding over a spinning (flat) merry-go-round experiences the Coriolis force (and centrifugal force), and there is no centripetal force. The only thing is, the puck has to move to experience the Coriolis force, so eventually it will fall off the edge--no orbits like the ones in your animations are possible. But to me, that does not mean there is no Coriolis effect. I interpret Coriolis effect as it is described in the article--an apparent deflection. You are right that other forces, both real and pseudo, besides the Coriolis force can cause deflection from straight line motion, and I think there's probably a way to word the intro better. But I don't think you've found it yet. Rracecarr (talk) 14:43, 30 April 2008 (UTC)

Cleonis, the Coriolis force occurs when an entrained radial motion occurs. The atmosphere co-rotates with the Earth. If we have a radial motion of atmosphere relative to the the main body of atmosphere, we will get a Coriolis force in the tangential direction and it will be real. David Tombe (talk) 13:00, 30 April 2008 (UTC)

Hello David, what I can say is that I endorse it when edits by you are reverted by other editors. Judging from what I've read from you so far I don't think you even understand yourself.

I recommend that you set up a website of your own. On your own website you can present your views just the way you want. I'm not kidding; I have done that myself, I have set up a website of my own. A link to my website is on my User page.
--Cleonis | Talk 14:10, 30 April 2008 (UTC)

RRacecarr, There are certainly other forces involved that perhaps dominate the cyclones. And as you say, conservation of angular momentum becomes very important .

In my view, the Coriolis force only acts as a decider. Once the cyclonic direction is determined, the other effects dominate.

But to even act as a decider in terms of direction, it still has to be real. This is all hydrodynamics, and the Coriolis force expression is found in all the hydrodynamics of Laplace, Bernoulli, Euler, and Maxwell. Even Coriolis himself used it in relation to hydrodynamics. It is a real force in hydrodynamics.

It becomes fictitious only when we detach the moving particle physically from the rotating frame. Fictitious examples would be a missile flying over the surface of the Earth or a ball moving in a straight line over a rotating roundabout as viewed from the roundabout. In these scenarios, the deflection has got no real effect on anything. The cyclonic direction of cyclones could not be caused by such a fictitious Coriolis force. David Tombe (talk) 19:03, 30 April 2008 (UTC)

I will explain this not because I think you'll be convinced (that would be overlooking a mound of empirical evidence) but because I get a kick out of explaining it. Imagine a bucket of water hanging from a cord and spinning, as in Newton's bucket example, say clockwise. The bucket spins at a constant rate for a long time, so that the water inside is in solid body rotation (its surface will be dish shaped, but we don't care about that). Now, pull a cork out of a small hole in the bottom of the bucket (which keeps spinning at the same rate as always). What happens? As the water drains out of the hole, a clockwise whirlpool forms, with water spiraling toward the hole and finally flowing out. Why is the whirlpool clockwise? Because the water is spinning clockwise, as a parcel of water moves toward the drain, it begins to rotate faster, due to conservation of angular momentum. As an annular ring of water shrinks toward the drain, its initial rate of spin is amplified, just like an ice skater spins faster when she pulls in her arms. That is how you explain it in an inertial reference frame--no Coriolis force. But if you want to analyze the motion from the reference frame of the bucket (imagine a video camera attached to the bucket, spinning with it, looking down at the surface of the water), then there is no initial rotation. In this frame, the water is originally at rest. Yet nonetheless, when the cork is pulled, a clockwise whirlpool forms. In this frame of reference, the whirlpool spins clockwise because of the Coriolis force--as a parcel of water moves radially inward, it is subjected to a Coriolis force which deflects it toward the left. To recap: inertial frame--NO Coriolis force, just conservation of angular momentum causing a whirlpool; bucket frame: Coriolis force causes whirlpool. This is exactly analogous to a cyclone in the atmosphere. When a low pressure center forms, it is as if someone has "pulled a plug". Air flows inward toward the "drain" and a spiral flow forms. In the earth frame, the Coriolis force causes the spin. In the frame of the fixed stars, it is just conservation of angular momentum. The air in the atmosphere was already spinning with the earth (think bucket) so as it flows inward, its rate of spin is amplified. Rracecarr (talk) 20:31, 30 April 2008 (UTC)

Cleonis, thanks for the opportunist criticism. It's always easy to criticize somebody when they are arguing with alot of people all at once. It's nice to keep the majority sweet isn't it?

Theoretically of course, you could have backed me up. Whatever your reasons, your ultimate conclusion that the deflection is real, was the same as my conclusion. But rather than back me up, you opportunistically decided to distance yourself from me and let the majority know that you were against me too.

I could have criticized you too. When I read your statement

A necessary, but not sufficient condition for Coriolis effect is presence of a centripetal force.- In the presence of a centripetal force (sustaining circumnavigation), there is no Coriolis effect when the motion is concentric uniform circular motion,

I knew immediately that you were talking total poppycock. But I decided to keep quiet about it. However, since you have decided to criticize me publicly, I will now state my view on your theories.

Coriolis force doesn't need centripetal force. You are talking total nonsense.David Tombe (talk) 19:22, 30 April 2008 (UTC)

RRacecarr, I agree with your explanation above. But at the end of the day, we still have to answer the question about whether or not the Coriolis force in the bucket frame is a real effect or an apparent effect. I say that it is a real effect. It is a hydrodynamical application of the v times ω.

I'm trying to get you to see the difference between hydrodynamical applications of this maths, and applications that involve only particle motion where the particles have no physical connection with the rotating frame. In the latter case, the Coriolis force is purely fictitious.

This is a good introduction. It gives interesting history about Laplace's tidal equations. But the contentious bit that stuck out when I read it was the word 'apparent'.

It is obvious to me that the cyclonic effects are more than just apparent.

Let's take the special case of the tornado. We know that it is not the Coriolis force, as per the Earth's rotation, that causes these tornadoes. We know that water can swirl out of a sink with a random spin direction independent of the Earth's Coriolis force.

But the majority of tornadoes are cyclonic. This tells us that the Earth's Coriolis force must be decisive in determing the direction of spin for the tornadoes (but not for water running out of a bath sink).

The Coriolis force in Tornadoes can be compared to a slight nudge in one direction on a ball balanced at the top of a hill in unstable equilibrium. But even to play this minimal role, it must be real. David Tombe (talk) 06:09, 1 May 2008 (UTC)

Copied from above: "But at the end of the day, we still have to answer the question about whether or not the Coriolis force in the bucket frame is a real effect or an apparent effect."

In the bucket frame, the Coriolis force is as real an effect as any other. It's called "fictitious" or "pseudo" or "apparent" because it does not exist in an inertial frame.

Fluid particles are still particles. Fluid dynamics is just particle dynamics with a very large number of particles (too large, admittedly, to be solved exactly). There is no fundamental difference between the Coriolis or centrifugal force acting on a single particle and that acting on air in the atmosphere or on fluid in a centrifuge. (Rracecarr)

Rracecarr, it's the 'many particles' in hydrodynamics that is exactly what makes the big difference. It means that a fluid element is bonded to the main rotating body of fluid, and that's what makes the deflection real. The deflection is only 'apparent' in particle dynamics when the particle in question is physically unconnected with the rotating frame.

I think that your problem is that you have ignored the finer details that are implicit in the derivations of the Coriolis force in both hydrodynamics and in particle dynamics. If you were to pay attention to those details, you would see that the v in Coriolis force is the radial v of the actually body that is rotating.

But putting all the maths aside, you must know that the spin direction in cyclonic behaviour is real, and that it has been triggered by the Coriolis force associated with the Earth's rotation. David Tombe (talk) 09:54, 2 May 2008 (UTC)

To exist in physical sense versus to exist in mathematical sense only

I copy and paste from above:
If you would remove the centripetal force you would remove the Coriolis effect altogether. --Cleonis | Talk 20:59, 29 April 2008 (UTC)

I don't know what you're talking about, Cleonis. Does Coriolis effect mean something different to you than the effect of the Coriolis force (e.g. does Coriolis effect mean inertial circles)? Because obviously, the Coriolis force exists whether or not there's a centripetal force. [...] Rracecarr (talk) 14:43, 30 April 2008 (UTC)

An object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been nudged away from concentric motion. As a consequence, the puck has a velocity with respect to the rotating system.
In the equation of motion for motion with respect to the co-rotating coordinate system the Coriolis term (2ωv) provides an exact description of the object's motion.

Formation of cyclonic flow. Air mass that is flowing from east to west is circumnavigating the Earth's axis slower than the Earth, hence it tends to be pulled closer to the center of rotation.

It is necessary to distinguish between to exist in a physical sense, and to exist in an abstract, mathematical sense only. Gravitation exists in a physical sense; if gravitation would not exist celestial bodies such as planets, stars, neutron stars etc. would not exist. Inertia exists in a physical sense; when two objects collide, shattering each other, the kinetic energy that is involved in the collision is due to the inertia of the objects, the larger the inertial mass of the objects, the larger the kinetic energy that is involved.

Now for an example of a factor, used in physics, that does not exist in a physical sense.
In engineering, when calculating properties of electric circuits with capacitors and inductors it is customary to also use an imaginary current in the calculations. By adding this non-existent current the calculation can be handled faster. That imaginary current "exists" in a mathematical sense, but not in a physical sense.
Likewise the Coriolis term in the equation of motion "exists" in a mathematical sense only.

Describing the Coriolis effect as : 'the effect of the Coriolis force' is a phrase without physical meaning, for the "Coriolis force" does not exist in a physical sense.

Identifying energy conversions

The science of physics, and especially the science of dynamics, is in identifying energy conversions. For example the case of a compressed gas that expands and moves a piston. Then potental energy is converted to mechanical energy. Whether you map the motion of the expanding gas and the piston in an inertial coordinate system or in a rotating coordinate system is arbitrary: the physics is in the energy conversion.

In the case of the motion pattern depicted in the animation the pattern of energy conversion is back and forth from potential gravitational energy to rotational kinetic energy. It does not matter whether you map the motion of the object and the dish in an inertial coordinate system or in a rotating coordinate system: the physics is in the energy conversion process, not in the mapping.

The motion pattern depicted in the animation presents the simplest, purest case. Given the example, the next step is to identify the energy conversions taking place. That particular pattern of energy conversions constitutes the physics of the Coriolis effect.

Perfectly fitting for Meteorology

Note that defining the Coriolis effect in this way slots in seamlessly with Meteorology. The terrestrial Coriolis effect that is taken into account in meteorology is an effect that is equal in magnitude for all directions of air mass flow.

Air mass that is flowing from west to east is in a sense "speeding", it's circumnavigating the Earth's axis faster than the Earth's rotation, and due to its inertia it tends to swing wide. Air mass that is flowing from east to west is circumnavigating the Earth's axis slower than the Earth's rotation, so it tends to be pulled closer to the Earth's axis. That (along with all other directions of flow) is what is taken into account in Meteorology --Cleonis | Talk 08:24, 2 May 2008 (UTC)

I believe I understand you. You have fundamentally the same misconception as David Tombe--that there is a real "Coriolis effect" which is somehow different from that produced by the Coriolis force term in the equation of motion in a rotating frame of reference. There isn't. Rracecarr (talk) 13:15, 2 May 2008 (UTC)

RRacecarr, your mind is totally closed to all reason. You can see with your own eyes that the Coriolis force in hydrodynamics is real. You need to go back to first principles and examine the derivation of the transformation equations. Never let the maths drift away from the physics that it originally applies to.

Then you will see that Coriolis force only applies to the radial velocity of an element of a co-rotating fluid.

For a fictitious Coriolis force, we need to consider a totally disconnected particle motion, say above a rotating roundabout. But even then, I'm beginning to think that the apparent deflection, albeit that it certainly appears like a Coriolis force, is not technically a Coriolis force. David Tombe (talk) 13:40, 2 May 2008 (UTC)

Pure consequence of transformation

The idea reflected above that the Coriolis force only acts on co-rotating objects is false. The Coriolis force is purely a consequence of the coordinate transformation. A passing meteorite viewed from a coordinate system fixed to Earth is subject to the same Coriolis force as atmospherical particles. −Woodstone (talk) 14:20, 2 May 2008 (UTC)

Woodstone, A passing meteorite is not physically connected and the effect will be fictitious. The atmosphere is a hydrodynamics issue. You are not living in the real world if you think that the cyclonic direction of the cyclones is only an illusion. Coriolis force in hydrodynamics is a real effect. Have you ever thought about going back to first principles and deriving the equations and noting the meaning of the terms at each stage of the derivation. David Tombe (talk) 16:21, 2 May 2008 (UTC)

As said before, the physics is always the same. The forming and direction of cyclones is physical. It can be explained (derived) by writing the hydrodynamic equations in an intertial frame without any appearance of Coriolis force. It can also be explained in a rotational frame, with a Coriolis force appearing (and a centrifugal term). These are just the same equations, but transformed to the rotating frame. The Coriolis and centrifugal terms are introduced by the transformation. The results of the calculation are always the same and will show the cyclone. The cyclone is real. The Coriolis and centrifugal forces are artifacts of the transformation and therefore called fictitional. −Woodstone (talk) 16:37, 2 May 2008 (UTC)

Woodstone, OK, so we are agreed that the effects are real. When these effects are described in a rotating frame of reference, we use the Coriolis force.

In that case, your concept of 'fictitious' is not the same as Rracecarr's. Your concept of fictitious is that it is a mathematical expression that doesn't exist in the inertial frame.

Rracecarr's concept of fictitious is that the actual effect is only 'apparent' in the rotating frame.

Would you agree with me then that we could remove the term 'apparent' from the introduction, since we are now agreed that the effect is real?David Tombe (talk) 07:19, 3 May 2008 (UTC)

Mathematics of rotational effect

the forces that are at play in the case of a curved surface.
Red: gravity
Green: the normal force
Blue: the resultant force.

Animation 1
An object moving frictionlessly over the surface of a very shallow parabolic dish.

Animation 2
The eccentricity an of ellipse-shaped trajectoty represented as an epi-circle on a circle.

For the sake of completeness I'd like to present mathematical proof that in the case presented in the animation the motion with respect to the co-rotating coordinate system is exactly a circle. This proof applies only for the case of using a co-rotating coordinate system. In meteorology the rotating coordinate system that is used is always the co-rotating coordinate system.

The motion of the puck over the surface of the (very shallow) parabolic dish is caused by the presence of a centripetal force. The cross section of the surface is a parabola, hence the centripetal force is proportional to the displacement, which results in a harmonic oscillation. The motion of the puck can be decomposed into two perpendicular harmonic oscillations. The following parametric equation of the position as a function of time describes the motion of the puck:

${\begin{aligned}x&=a\cos(\omega t)(1)\\y&=b\sin(\omega t)(2)\end{aligned}}$

Notation:

$a$ is half the length of the major axis

$b$ is half the length of the minor axis

$\omega$ is 360° divided by the duration of one revolution

This parametric equation provides a complete description, it accurately describes the position and velocity and acceleration at each point in time. When a and b are equal the trajectory is circular, when they are unequal the trajectory is ellipse-shaped.

Proof that the motion with respect to the co-rotating coordinate system follows a circle:
The parametric equation can be rearranged as follows:

${\begin{aligned}x&=\left({\begin{matrix}{\frac {a+b}{2}}\end{matrix}}\right)\cos(\omega t)+\left({\begin{matrix}{\frac {a-b}{2}}\end{matrix}}\right)\cos(\omega t)\\y&=\left({\begin{matrix}{\frac {a+b}{2}}\end{matrix}}\right)\sin(\omega t)-\left({\begin{matrix}{\frac {a-b}{2}}\end{matrix}}\right)\sin(\omega t)\end{aligned}}$

Animation 2 represents this rearrangement geometrically.

Transforming the equation to a co-rotating coordinate system is straightforward, and results in the following parametric equation:

${\begin{aligned}x&=\left({\begin{matrix}{\frac {a-b}{2}}\end{matrix}}\right)\cos(2\omega t)\\y&=-\left({\begin{matrix}{\frac {a-b}{2}}\end{matrix}}\right)\sin(2\omega t)\end{aligned}}$

The circular motion with respect to the co-rotating coordinate system is called an 'inertia circle'.
The radius of the inertia circle is (a-b)/2
Notation:
radius of the inertia circle: r_s
velocity relative to the rotating system: v_rot
The velocity v_rot of the motion along the inertia circle follows from the relation v=ωr
The acceleration of the motion along the inertia circle is given by a = 2ω²r_s. This is equivalent to a = 2ωv_rot

This proves the following:
When the centripetal force is a harmonic force, and the object has a velocity relative to the rotating system, then the eccentricity in the ellipse-shaped trajectory shows up as a perfectly circular motion with respect to the co-rotating coordinate system. In the equation of motion for the co-rotating coordinate system this inertia circle is described exactly by the Coriolis term.

Of course, this exact match applies only for the case of a co-rotating coordinate system. When the parabolic dish was manufactured it was rotating at a specific angular velocity, and thus the curvature of the surface was tuned to a particular angular velocity. The effect is described exactly by the Coriolis term if and only if the rotating coordinate system is co-rotating with the tuned parabolic dish.

When meteorologists are saying that the Coriolis effect is involved in the formation of cyclonic flow they refer exclusively to the case of using a co-rotating coordinate system. In other words, in meteorology it goes without saying that the expression 'rotating coordinate system' refers to the coordinate system that is co-rotating with the Earth. --Cleonis | Talk 13:07, 3 May 2008 (UTC)

The Current State of Knowledge

The current state of knowledge about Coriolis force is so flawed that it makes it impossible to have a decent article on the topic here on wikipedia. The current state of knowledge is based on the idea that the Coriolis force is a fictitious effect which is viewed from a rotating frame of reference. This idea is extrapolated from the transformation equations for a rotating frame of reference.

A term appears in these equations which is velocity dependent and deemed to be the Coriolis acceleration.

It is then assumed that a Coriolis force will act on anything with velocity as measured relative to a rotating frame of reference.

This concept is then applied to moving streams of air in the atmosphere and used to account for their deflections.

In actual fact, if the derivation of the transformation equations is scrutinized properly, we can see that the Coriolis term specifically means the tangential acceleration on a co-rotating radial motion. The maths tells us nothing about how this situation may occur in practice.

Moving air currents do not conform to this situation unless they are restrained to radial motion. But in a cyclone, the air currents are not restrained to radial motion and so a Coriolis force only occurs to the partial extend that these air currents are made to co-rotate with the larger body of atmosphere. The spiral effects which are very real and visible from space, are a consequence of the partial Coriolis force which the atmosphere as a whole applies to the moving air currents in order to try to keep them co-rotating. David Tombe (talk) 08:56, 10 June 2008 (UTC)

David, have you ever wondered why the Sun, after rising at a certain angle, then starts rising less fast, then around midday stops rising and starts setting? Yes, that's the Coriolis effect. On the Northern hemisphere it curves to the right (left down south). Do you think the rotation of the Earth exerts a real force on the Sun? −Woodstone (talk) 12:56, 10 June 2008 (UTC)

The current state of knowledge about Coriolis force is so flawed that it makes it impossible to have a decent article on the topic here on wikipedia. Fortunately or (possibly for David) unfortunately, the wikipedia only tries to capture the current stat of knowledge...- (User) WolfKeeper (Talk) 14:52, 10 June 2008 (UTC)

Woodstone, Spherical geometry in observational astronomy has got nothing at all to do with the Coriolis force. The Coriolis force doesn't remotely enter the question.

All the celestial objects trace out a circle in the sky due to the Earth's diurnal rotation. That is not Coriolis force. You are making the mistake of confusing a superimposed tangential artifact motion with a tangential deflection of a radial motion. They are two different things. Only the latter is Coriolis force. The 23 degrees tilt of the Earth along with latitude are the major deciders on matters to do with sunrise and sunset angles.

On your specific question, the Earth's rotation exerts no force on the Sun under classical theory unless we start looking at the negligible torque effects associated with the assymetry of the Earth's shape. And those would be truly neglible. David Tombe (talk) 16:33, 10 June 2008 (UTC)

You keep confusing the different frames of reference. In the frame of reference fixed to Earth and co-rotating, the Sun is deflected from continuing to rise indefinitely by applying the (fictitious) Coriolis force. And furthermore, the Coriolis force is by no means limited to radially moving objects. −Woodstone (talk) 17:27, 10 June 2008 (UTC)

No Woodstone, I am not confusing any reference frames. You are confusing Coriolis force with the circular motion which is superimposed on stationary objects as viewed from a rotating frame of reference. The former is a tangential deflection of a radial motion. The latter is a tangential sueprimposition.

There is no Coriolis force involved in observational astronomy. David Tombe (talk) 15:02, 17 July 2008 (UTC)

Eötvös effect,

Interesting addition to the article. Brews ohare (talk) 19:43, 10 June 2008 (UTC)

Cannon on a turntable

The figures in this section need fixing. The x and y axes are out of proportion. Since the graphs are depicting a trajectory, it is important that the horizontal and vertical axes be scaled the same. Rracecarr (talk) 19:03, 13 June 2008 (UTC)

The scales in Figure 3 are in scale, using the same units on x and y axes. The scales on x- and y-axes in Figure 4 are labeled, although not on the same scale: without complete prescription of all the parameters (which is pretty useless anyway), this figure is just of qualitative value: it shows that the angle is steeper for faster rotation. I added to the caption to alert the reader to the scales. Brews ohare (talk) 03:19, 14 June 2008 (UTC)

No, the axes are not scaled the same in Figure 3. They are scaled differently. The x-axis is stretched relative to the y-axis, making for a confusing figure. Similarly, the larger discrepancy in the scaling of the axes in Figure 4 is also confusing. Why not upload correctly scaled versions of the figures? Rracecarr (talk) 00:45, 15 June 2008 (UTC)

What exactly is made confusing by the very slight scale distortion in Figure 3 (now Figure 4)? Brews ohare (talk) 01:12, 16 June 2008 (UTC)

The fact that the blue line is clearly not an arc of a circle makes it less apparent that it is the same blue line shown in the other figure. The shapes of the trajectories are wrong due to the distortion. Slightly wrong, but still wrong. I don't understand your resistance. It cannot be difficult to make the slight changes. Why not make the figures as good as they can be, rather than stopping short of that? Rracecarr (talk) 13:37, 16 June 2008 (UTC)

I've changed the figures; the angle of launch is more meaningful than the rate of rotation when interest is focussed upon successful trajectories. (Other variables just change the time scale, not the appearance of the plot.) Circular curve in Figure 4 is the trajectory of the target, not the cannonball. Brews ohare (talk) 16:02, 16 June 2008 (UTC)

Yes, but, once again, it's not circular (it looks elliptical, erroneously). The inset panel in Fig 4 has unequally scaled x and y axes. Thanks for fixing Fig 5--it's much better now (though it's still not perfect--the x-axis is slightly stretched relative to the y-axis). Fig 4 needs a similar fix.Rracecarr (talk) 17:45, 16 June 2008 (UTC)

I have replaced this figure Brews ohare (talk) 23:34, 16 June 2008 (UTC)

Nice. Rracecarr (talk) 17:27, 17 June 2008 (UTC)

Evaluation using a determinant

A wikipedia link is provided that describes how the cross-product is related to a determinant. In my opinion, for those who know about it, this addition is helpful, and for those who don't, they can either look at the link or just read on. There is no need to penalize those well versed, nor those who would like to become so. Brews ohare (talk) 03:13, 14 June 2008 (UTC)

Figure 2

Figure 2: Coriolis effect causing apparent deflection of ball.

I tried to increase the size of this picture in several ways, and ended up with a kludge. Specifying pixel number doesn't affect the size. Also, to me the deflection appears to be to the left, although it was originally captioned to be a rightward deflection. Please take a look at this. Brews ohare (talk) 21:50, 15 June 2008 (UTC)

Yes, the deflection is to the left. Two comments: 1) should probably mention that the centrifugal force also acts to deflect the ball--it is not Coriolis alone. 2) At least in my browser, the figure caption does not show up anywhere near the figure. Why not just keep the small version? Rracecarr (talk) 15:08, 16 June 2008 (UTC)

I'd prefer to see the picture better, and to avoid a long thin display of the caption. Brews ohare (talk) 16:10, 16 June 2008 (UTC)

Agreed, that would be better. However, having the caption separated from the fig is even worse, IMO. Rracecarr (talk) 17:41, 16 June 2008 (UTC)

Tossed ball on carousel

This set of diagrams is completely correct, as can be determined by examination of the trajectories in the inertial frame. Just look at the vectors connecting the ball to (i) the thrower of the ball, and (ii) the center of rotation. Please take some time to think about this issue. Brews ohare (talk) 13:42, 19 June 2008 (UTC)

BTW: The trajectories from the camera point of view are in agreement with the other diagrams in the various articles on the carousel. The trajectory from the ball-thrower's perspective is not discussed in these articles, but can be arrived at very easily by drawing the inertial frame trajectory, placing equally spaced time points on the trajectory and joining them to the equally spaced time points on the periphery. The vectors are nearly parallel, indicating a simple straight back and forth of the ball for the ball-tosser.

Of course, the figures were generated mathematically, not by a graphical method.

It is not possible for the camera and the ball-tosser to have the same perspective, because the ball-tosser is in accelerated motion compared to the center of rotation. That acceleration adds other forces to his frame of reference. Brews ohare (talk) 13:50, 19 June 2008 (UTC)

Diagram is wrong. The tosser and camera are fixed relative to each other. The trajectories they record can differ only by translation and orientation. I don't know where your program is wrong, but wrong it is.Rracecarr (talk) 15:19, 19 June 2008 (UTC)

Your mistake may be that you're ignoring the rotation of the tosser, and calculating the trajectory as if the tosser were moving in a circle without changing direction at all (which of course is not the situation).Rracecarr (talk) 15:25, 19 June 2008 (UTC)

Right on! ::I propose to reinstate the diagram with the tosser's perspective deleted: how about that?? Brews ohare (talk)

Sounds great. Rracecarr (talk) 15:38, 19 June 2008 (UTC)

Done. Brews ohare (talk) 16:30, 19 June 2008 (UTC)

The article says

Figure 7 illustrates a ball tossed from 12:00 o'clock toward the center of a counterclockwise rotating carousel. On the left, the ball is seen by a stationary observer above the carousel, and the ball travels in a straight line to the center, while the ball-thrower rotates counterclockwise with the carousel.

If the ball is thrown by a person rotating with the carousel, then it has an additional component of motion to the left in Fig 7. Shouldn't the rotating person be just another observer and the thrower be standing on the ground at 12:00 o'clock?

--Bob K (talk) 15:46, 31 January 2009 (UTC)

Frequent remark

In this long discussion, one can notice that there is a frequent remark about the fact that (roughly) "if Coriolis is fictitious effect, why then can we see the result in certain cases (atmospheric events) from a external absolute point of view".

I pondered on that (because I stumbled on the same remark alone) and think Diag N° 13 is misleading. It gives the impression (view from above) that we are dealing with an external and non mobile view (newtonian frame), which is not true : the red arrows representing Coriolis force is ONLY valid if we are moving with earth (like a geostationnary satellite) so it is a non-newtonian frame.

I wonder whether a note could be added on this.

Besides, the red arrows of Fig 13 may induce people into thinking that the Coriolis force is the same everywhere around which is not true. It could be said somewhere that we represent schematic forces. It may sound like details but they are not.

The article seem to lack a clear addition about why we can see concrete and massive "effects" (nice spiraling clouds) of the Coriolis effect even when we are observing things from a Newtonian frame.

Newtoon —Preceding comment was added at 19:41, 12 July 2008 (UTC)

It's because the term 'fictitious force' is a misnomer. Fictitious forces are real, but they're not real forces; they're really inertia acting when the frame is accelerating (in this case rotating). Some people prefer the term 'pseudo force' for that reason.- (User) Wolfkeeper (Talk) 02:49, 28 October 2008 (UTC)

As regards centrifugal force, some people might argue that it's the other way around. Inertia is the manifestation of centrifugal force in an inertial frame referenced to cartesian coordinates, with centrifugal force being a real outward radial force.

The situation as regards Coriolis force is more tricky because Coriolis force is usually confused with the tangential superimposition that is observed when any motion is viewed from a rotating reference frame. The existing 'rotating frames' theory of Coriolis force does not explain the cyclonic behaviour in the atmosphere. We need the hydrodynamical approach to Coriolis force to explain that. And as everybody can clearly see, the effect is real because it can be viewed from space. David Tombe (talk) 20:14, 28 October 2008 (UTC)

You're really very out of your depth here David.- (User) Wolfkeeper (Talk) 23:11, 28 October 2008 (UTC)

No Wolfkeeper, the authors of the article are totally out of their depth. They are trying to explain real atmospheric phenomena using the concept of illusion in a rotating frame of reference. The proper home of Coriolis force is hydrodynamics and not rotating frames of reference. What did Coriolis himself have to say on the matter? David Tombe (talk) 13:49, 29 October 2008 (UTC)

You are so very confused. The coriolis effect is a term that appears in the equations of motion when you do a coordinate transformation of Newtons laws of motion from an inertial frame into a non inertial frame. They are derivable from, and part of Newtonian mechanics. It's not an illusion, it's real.- (User) Wolfkeeper (Talk) 14:52, 29 October 2008 (UTC)

It's like the parable of the blind men and the elephant. If you grab it by the body, it's inertia. If you grab it by the ear, it's coriolis effect, if you grab it by the leg, it's centrifugal effect, if you grab it by the tail it's centrifugal effect (polar coordinate) etc. etc. The name of the elephant is inertia.- (User) Wolfkeeper (Talk) 15:29, 29 October 2008 (UTC)

Wolfkeeper, we all know about those transformation equations. But not so many have actually scrutinized the derivation. Coriolis force is indeed a real force, but it only actually occurs in certain circumstances. Rotating frames of reference do not create a Coriolis force. We either need to have vorticity in space, or else we need to apply an actual tangential force to a radial motion, such as would occur on water in a radial pipe on a rotating turntable.

If we merely observe an event from a rotating frame of reference, then all we will get is a circular motion imposed on top of the already existing motion. Coriolis force is not involved in such a scenario. David Tombe (talk) 15:42, 29 October 2008 (UTC)

You need to grab it by the ear, not the body. You're still grabbing it by the body or the tail; and exclaiming 'there's no more to this Elephant!'. Grab it by the rotating reference frame.- (User) Wolfkeeper (Talk) 15:53, 29 October 2008 (UTC)

And how do you grab hold of a rotating reference frame without involving co-rotation? David Tombe (talk) 18:25, 29 October 2008 (UTC)

No corotation is required; the equations are entirely derived from, and equivalent to, Newtons equations. Why on earth would they be in any way constrained in this bizarre way of yours???????- (User) Wolfkeeper (Talk) 05:15, 30 October 2008 (UTC)

Wolfkeeper, the equations are derived with reference to a point that is fixed in a rotating frame of reference. David Tombe (talk) 10:57, 30 October 2008 (UTC)

No, go to the bottom of the class, oh you're already there. The point is moving with a speed. The speed is also transformed.- (User) Wolfkeeper (Talk) 15:59, 30 October 2008 (UTC)

The coordinate transform takes (positionVector, speedVector)_inertial -> (positionVector, speedVector)_rotating, and you can follow the maths derivation and it does this successfully. This is not an inductive proof. It's the same level of certainty as 4+1=5.- (User) Wolfkeeper (Talk) 16:03, 30 October 2008 (UTC)

Wolfkeeper, the derivation is identical mathematically to the derivation of the expression for acceleration in polar coordinates as referenced to the inertial frame. It simply focuses on a point that is fixed in a rotating frame of reference. David Tombe (talk) 18:33, 30 October 2008 (UTC)

The transformation equations have speed in them, and there are no constraints on it. Why on earth would anyone bother with a coordinate transformation that wasn't fully general?- (User) Wolfkeeper (Talk) 00:11, 31 October 2008 (UTC)

They do have those constraints. And I have also asked why we need to bother with them at all. David Tombe (talk) 01:31, 31 October 2008 (UTC)

There are no such constraints; your idea of how it works would make it a pointless waste of space. It's not.- (User) Wolfkeeper (Talk) 02:05, 31 October 2008 (UTC)

I agree with Wolfkeeper about the generality of the derivation. More complete remarks on this same question are found at Talk: Centrifugal force. Brews ohare (talk) 17:01, 31 October 2008 (UTC)

This kind of garbage has no place in the wikipedia at all. It's unsubstantiated OR on David Tombe's part, that additionally, nobody else agrees with.- (User) Wolfkeeper (Talk) 18:31, 31 October 2008 (UTC)

I was just about to direct the discussion there. Rotating frame transformation equations only have any meaning for co-rotating particles. That is built into the derivation. David Tombe (talk) 17:43, 31 October 2008 (UTC)

Conservation of Angular Momentum

Conservation of angular momentum is a consequence of the fact that gravity is a central force. The Coriolis force is not a central force, so does that mean that we should expect a breakdown of the conservation of angular momentum when the Coriolis force is active? Some of the theories relating to atmospheric effects seem to have been depending on the fact that conservation of angular momentum always holds true. David Tombe (talk) 08:08, 15 November 2008 (UTC)

I believe it's correct that angular momentum in a rotating reference frame is NOT a conserved quantity. Of course, that doesn't interfere with it being conserved in the same situation when evaluated in an inertial frame. It may still be useful in some situations to treat angular momentum as being approximately conserved; I'm not sure what atmospheric theories you're referring to. Dicklyon (talk) 20:41, 16 November 2008 (UTC)

Dick, angular momentum in a cyclone is either conserved or it's not conserved. Which is it? David Tombe (talk) 23:01, 16 November 2008 (UTC)

Angular momentum is a conserved quantity in Newtonian mechanics. It is also conserved in rotating reference frames, since none of the centrifugal effect, the coriolis effect nor does a spatial rotation alter it.- (User) Wolfkeeper (Talk) 01:05, 17 November 2008 (UTC)

Certainly angular momentum of a cyclone is conserved. Whether it is also conserved in a rotating frame is not a question I have pondered. Either David or Wolfkeeper may be right and I hope to learn which. Sources? Dicklyon (talk) 15:29, 17 November 2008 (UTC)

Wolfkeeper, Angular momentum is a conserved quantity in Newtonian mechanics because Newton's law of gravitation is a central force. See Kepler's second law in Kepler's laws of planetary motion. Once we introduce a tangential force, the situation then changes. Coriolis force is a tangential force. David Tombe (talk) 11:08, 17 November 2008 (UTC)

Conservation of angular momentum is not a consequence of the fact that gravity is a central force. Conservation of angular momentum also holds in electromagnetism, even though magnetism is not a central force. Conservation of angular momentum holds in a more general context than classical mechanics or classical electromagnetism. Conservation of angular momentum is more fundamental than classical mechanics or E&M. Conservation of angular momentum is violated in a rotating frame, but that's not surprising, because many laws of physics are violated in a rotating frame. Newton's third law is violated in a rotating frame, because the Coriolis force has no Newton's-third-law partner. Conservation of momentum is violated in a rotating frame, since any violation of Newton's third law also leads to nonconservation of momentum.--76.167.77.165 (talk) 03:30, 1 December 2008 (UTC)

76.167.77.165, I don't know how you reason that out. If there is a tangential force then there will be no conservation of angular momentum. Conservation of angular momentum is a consequence of there only being a central (radial) force acting. In electromagnetism, conservation of angular momentum will break down in any situation that involves a non-central force. The F = qvXB force and the -(partial)dA/dt force are both non-central forces. At least we're agreed that Coriolis force is a non-central force, and so when it acts, we must have a breakdown in the law of conservation of angular momentum. There were edits further back on the discussion page where editors invoked the conservation of angular momentum in tandem with the Coriolis force in relation to cyclones. David Tombe (talk) 12:23, 2 December 2008 (UTC)

It might be helpful to examine Noether's theorem, which as I understand it, says that conservation of angular momentum is a consequence of rotational symmetry. Also see Angular momentum. Brews ohare (talk) 16:06, 6 December 2008 (UTC)

Brews, I looked at Noether's theorem. The only thing that I can conclude is that he is referring to the spinning of a body about a symmetry axis, in which case angular momentum will be conserved. But that is just another way of saying that there will be no induced tangential forces. If there are induced tangential forces, then angular momentum will not be conserved. This can happen when objects are spun on an asymmetrical axis. See the rattleback. David Tombe (talk) 12:05, 15 December 2008 (UTC)

multiple references to Ascher Shapiro and bathtubs, etc.

There are two references to Ascher Shapiro, and I think the number of references ought to be zero, since he's not particularly notable in connection with this article, and anything he did as an educational demonstration in the 20th century could not have been groundbreaking work, since the Coriolis effect was understood centuries before. I think the multiple mentions of bathtub drains, etc., should be condensed into one area of the article, rather than appearing in two completely different places.--76.167.77.165 (talk) 03:34, 1 December 2008 (UTC)

WP:SOFIXIT. Dicklyon (talk) 03:47, 1 December 2008 (UTC)

Coriolis acceleration in the inertial frame of reference

Consider tangential acceleration defined by $\scriptstyle r{\ddot {\theta }}+2{\dot {r}}{\dot {\theta }}$. It has two components. There is a Coriolis component and an angular acceleration component. And let's choose an inertial frame of reference. And let's consider an elliptical Keplerian orbit.

I can see both an angular acceleration by virtue of the tangential speed increasing and decreasing cyclically. I can also see a Coriolis acceleration by virtue of the radial direction of motion continually deflecting tangentially. The two effects cancel out mathematically in magnitude and direction, leading to conservation of angular momentum. But they are both clearly visible individually nevertheless.

Can anybody think of any other scenario in nature where two mutually cancelling accelerations can still be physically observed, apart from in a couple where torque results? David Tombe (talk) 09:52, 29 December 2008 (UTC)

Take a look at Rotating_spheres#General_case. Brews ohare (talk) 02:01, 30 December 2008 (UTC)

Brews, that doesn't really address the issue. It's a simple question. In an elliptical Keplerian orbit, can you observe the fact that the tangential speed varies? I can. Can you observe the fact that the radial motion is rotating? I can. The sum of these two accelerations is zero, which is why we have conservation of angular momentum, yet we can still observe these two accelerations individually. Can you think of another example in nature where this state of affairs occurs and where a couple is not involved? David Tombe (talk) 06:04, 30 December 2008 (UTC)

Rotating_spheres#General_case has these features:

• Angular momentum is conserved
• The Coriolis force takes on an arbitrary value and sign between fixed limits; it may balance the centrifugal force or overcompensate it depending upon the required centripetal force for the chosen rate of rotation.
• The example assumes a constant rate of rotation, but not a particular value. Brews ohare (talk) 15:15, 30 December 2008 (UTC)

• No torque is involved Brews ohare (talk) 15:15, 30 December 2008 (UTC)

Brews, Thanks anyway, but that wasn't what I had in mind because the centrifugal force is a radial force. The Coriolis force which you are talking about above is a radial Coriolis force, and in my books, no such thing exists.

I was looking purely at the tangential situation in a Keplerian elliptical orbit. There is no net tangential force, hence conservation of angular momentum. Yet, we can still see the two individual components of tangential force in operation. This matter is of great significance on a number of counts.

(1) It shows that Coriolis force can exist in the inertial frame when vorticity is present.

(2) But it contradicts the idea that there is no vorticity in the gravitational field. The zero curl result for gravity follows directly from the fact that the angular momentum is conserved. So we have a problem in gravitational theory. But at any rate, the picture backs up my earlier assertion that Coriolis force only exists where vorticity exists. David Tombe (talk) 02:12, 31 December 2008 (UTC)

Hi David:

Well, this is a bit beyond me I guess. First, I suppose that no vorticity of gravitational field means curl(grad(1/r)) = 0? Isn't that a tautology? Brews ohare (talk) 03:42, 1 January 2009 (UTC)

Brews, basically it means that in an elliptical orbit there is both Coriolis force and vorticity, despite the zero curl of the gravitational field which is based purely on the radial component, and the assumption that there is only a radial component. The vanishing of the tangential component is strange in that it vanishes mathematically, and sufficiently to ensure conservation of angular momentum. But the two individual tangential components are still very much active and they give rise to Coriolis force, angular acceleration, and vorticity in an inertial frame of reference. David Tombe (talk) 09:10, 3 January 2009 (UTC)

So the gravitational force is not proportional to grad (1/r) ? That's news. Brews ohare (talk) 14:16, 12 January 2009 (UTC)

Brews, the radial component of gravity satisfies that relationship. But there is obviously a tangential component of gravity which has been written out of the analysis. You can see it with your own eyes in a non-circular Keplerian orbit. David Tombe (talk) 13:00, 13 January 2009 (UTC)

New article on generalized Coriolis force

Copied from above discussion:

Do we need an article on the generalized Coriolis force, as distinct from the generally understood Newtonian use of the term? A Google search for "Lagrangian Coriolis term" suggests that this might be a better name. -- The Anome (talk) 12:13, 16 January 2009 (UTC)

It would be nice to have such an article. Something of this sort is sketched out in the Wiki article Mechanics of planar particle motion. Here is a google book search. See for example: Handbook of Industrial Automation, Introduction to Mechanics and Symmetry and Principles of Quantum Mechanics. Robotic manipulators are a major source for such work, which relies heavily on computer modeling using the Euler–Lagrange equations. Brews ohare (talk) 15:48, 17 January 2009 (UTC)

Brews, I haven't looked into this fully yet. But off the top of the head, Lagrangian mechanics is all about conservation of energy. There are no energy terms associated with forces of the form vXH, were v and H are independent (H is vorticity).

Can you show me what a Lagrangian Coriolis force looks like? There is an interesting section in Goldstein where he purports to derive a Lagrangian for the electromagnetic vXH force. But the result A.v is actually more accurately for the centrifugal force, where H is the angular velocity, and where v and ω are not independent. It would apply to the magnetic force on a current carrying wire as opposed to the vXH force in EM induction.

At any rate, I will eagerly await this new article on Coriolis force because I would like to learn more about it. David Tombe (talk) 07:06, 18 January 2009 (UTC)

Take a look at the references and Wiki articles already linked just above. Brews ohare (talk) 10:19, 18 January 2009 (UTC)

The three inertial forces

The three inertial forces mentioned in the main article all appear as real forces in the inertial frame of reference in an elliptical, hyperbolic, or parabolic Keplerian orbit. There have been two separate disputes going on which can be simultaneously resolved by comparing them side by side. In the Kepler's laws of planetary motion article, these three forces are recognized to be real but their names are denied. In the centrifugal force and Coriolis force articles, these three forces are deemed to be fictitious and their names are promoted in that context, and that is despite the fact that it is not the context in which Coriolis himself originally conceived the effect which bears his name.

Something is going to have to be done with this article. My advice is to begin by paying closer attention to the distinction between situations in which the moving object is totally free, and situations in which the moving object is co-rotating. Paying attention to that distinction will be the first step in remedying the problem and bringing this article into harmony with Kepler's laws.

It should eventually become understood that it is all one single topic, and that the only one of the three inertial forces that can ever actually be fictitious is the Euler force. David Tombe (talk) 16:40, 30 January 2009 (UTC)

Woodstone, Regarding your reply on your talk page, I now see exactly what your argument is. I had a prolonged argument about this matter on the talk pages of centrifugal force. You think that a stationary particle, as viewed from a rotating frame of reference, traces out a fictitious circle. Correct. But you also think that this fictitious circle can be mathematically accounted for in terms of a combination of centrifugal force and a radial Coriolis force.

Despite the fact that there is indeed some backing for this argument in the literature, I have made it clear that I am strenuously opposed to the idea. I did also point out that most reliable textbooks only concentrate on worked examples that involve co-rotating situations, and indeed evidence was provided in relation to Goldstein's 'Classical Mechanics' that a considerable degree of revisionism in relation to attitudes towards centrifugal force had appeared in the 2003 edition.

The correct theory is to be found in the Kepler's laws of planetary motion talk page. But the problem there is that there has been an attempt to block any correlation between the equations that are listed there, and the equations that are listed in fictitious forces articles. You can read that debate yourself and also on the talk page of user Bo Jacoby, just to educate yourself on the degree of opposition which is encountered when trying to apply the names, centrifugal, Coriolis, and angular, to their rightful terms in the Kepler problem.

If you see the point that I am making, you will see that a Coriolis force can only be in the tangential direction. As such, there is no Coriolis force acting on the stars, as viewed from the rotating Earth, or on a cricket ball flying over a rotating roundabout. In order to get Coriolis force, we need to have a constrained co-rotating radial motion, such as we observe in a non-circular Keplerian orbit, and such as can be contrived by mechanical means, or indeed in the case of the vXH force in electromagnetism.

This is a factual error. The Coriolis force is perpendicular to the speed (in the rotational frame) and the rotation axis. For a tangential movement of speed v=−Ω×r as seen of a star over the equator at position r (distance R), the Coriolis force −2mΩ×v is radially inwards and of size 2mω²R. The centrifugal force −mΩ×(Ω×r) is also radial, but outwards and of size mω²R. The result is radially inwards of size mω²R. You will readily recognise this as the force leading to a circular movement at radius R and period ω. Hope this clarifies the situation. −Woodstone (talk) 12:21, 1 February 2009 (UTC)

I will finish with one simple question. Yesterday, you said that the Coriolis effect can be observed from the inertial frame. I would agree with that, providing that we actually have a Coriolis force force to be observed. Do you still stand by what you said yesterday on that point?

If you do still stand by what you said yesterday, then I'm sure you will see my point that meteorological deflections are real and can be observed from outer space, whereas deflections of unconnected free projectiles can only be observed from within a rotating frame of reference. David Tombe (talk) 05:47, 1 February 2009 (UTC)

Woodstone, I notice you didn't answer the key question which relates to the legitimacy of FyzixFighter's reversions of my edits. If you had stood by what you said yesterday, that the Coriolis force can be observed in the inertial frame, you would have reverted FyzixFighter on my behalf.

On the other point, you are overlooking the derivation of the Coriolis force term. I can see quite clearly what you are saying. But there are hidden restrictions in that expression which are implied by the derivation. The derivation is done more carefully in the Kepler problem, and you can see in the equations in the section below this, that the Coriolis force is always a tangential force. So long as you continue to turn a blind eye to this restriction, as all others here do too, you will never fully comprehend the Coriolis force. There is no such thing as a radial Coriolis force. On the Kepler page, they accept those equations, but they deny the names of the terms. David Tombe (talk) 12:51, 1 February 2009 (UTC)

David, the Coriolis effect is more loosely defined than the Coriolis force. In an inertial frame there is no Coriolis force, but the effect of cyclones forming is still there and is caused by straight inertia. And there is nothing special about meteorological effects compared to other consequences of rotational frames. By saying that there is never a radial component in the Coriolis force, you just deny the universally accepted mathematical formula. Any such conclusion must be seen as WP:OR in wikipedia. −Woodstone (talk) 13:13, 1 February 2009 (UTC)

Woodstone, you can't write it off as plain inertia. Those effects can be seen from space. So clearly the cause is more complicated than simply a deflection as viewed from a rotating frame of reference.

And I have pointed to the error. Coriolis force is indeed something more complicated than has been described in this article, and it is purely tangential. And to say that it is tangential contrary to the apparent freedom that it is afforded in 'fictitious force' chapters of textbooks, is not original research when it is based on accepted theory surrounding the Kepler problem. That why I wrote out the Kepler equations in the section below.

It all boils down to two branches of physics/applied maths in which the right hand doesn't know what the left hand is doing. My interest in all of this has always been through the Kepler problem, so maybe that knowledge is indeed original research as viewed from the domain of fictitious forces. But I also examined the derivation of Coriolis force doing it the 'rotating frames' way. I pointed out many times that that derivation is based on a vector triangle which when it shrinks to zero (in the calculus sense), the velocity that gives rise to the Coriolis force has to be radial. The derivation in 'fictitious forces' and the derivation in the Kepler problem are ultimately the same derivation.

That's why I suggest that we forget about about it. I thought I could have highlighted the issue by pointing out simple facts such as that the cyclones are visible from outer space, but that doesn't seem to work. David Tombe (talk) 15:20, 1 February 2009 (UTC)

Reply to FyzixFighter regarding the Kepler problem

You restored a statement which said that the inertial effects can only be observed from rotating frames of reference. Yet we can observe the cyclones from outer space. And Woodstone has even admitted that we can observe Coriolis effects from the inertial frame of reference. So something is wrong somewhere. That's what I'm trying to sort out. It would be much more helpful if you would come and discuss your views on the talk page before making reversions.

This is a very tricky issue and I'm trying to get it tidied up. I'm going to bring in the equations from the Kepler problem to help sort it out. David Tombe (talk) 08:27, 1 February 2009 (UTC)

Here are the Kepler equations,

Radial equation

${\ddot {r}}=-GMr^{-2}+r{\dot {\theta }}^{2}$

Tangential equation

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

Those equations apply to any object in motion in a gravitational field. Coriolis force is either there or it is not there. It is there in an elliptical orbit and it keeps turning the direction of the radial motion.

You cannot create a Coriolis force from a rotating frame of reference. The Coriolis force, as envisaged by Laplace and Coriolis is a real hydrodynamical force. It's role in meteorology is an interesting area of investigation. But we are getting absolutely nowhere at the moment, because of an insistence to push some misinformed view about fictitious forces. David Tombe (talk) 08:37, 1 February 2009 (UTC)

No, the statement I reinstated said that the "forces", not the effects, vanish in the inertial frame. A statement that is backed up by every classical/analytical mechanics textbook out there when discussing the inertial/fictitious/pseudo- forces. Real forces are those forces which appear in $\sum F$ in Newton's second law $\sum F=m{\ddot {\vec {r}}}$ (which is really the constant mass case of the general definition of force as the partial derivative of momentum with respect to time, but let's ignore this for the moment since mass is a constant in the Kepler case). All planetary orbits satisfy the vector equation $-{\frac {GMm}{r^{2}}}{\hat {r}}=m{\ddot {\vec {r}}}$, so no additional forces are required. This is true for other phenomena as well; an inertial observer can explain the motion in cyclones and planetary orbits with simply Newton's second law and the traditional forces. It is only an observer in a non-inertial frame that must add in additional forces for F_net=ma to still hold true within the rotating frame.

The inertial forces are not real forces but are purely kinematic consequences of bootstrapping Newton's 2nd Law to apply to non-inertial, specifically rotating, frames. All reliable sources agree with such a statement. I have seen no source that states that the centrifugal, Coriolis, and Euler pseudo-forces are real forces that exist in the classical, Newtonian, inertial frames. --FyzixFighter (talk) 09:27, 1 February 2009 (UTC)

FyzixFighter, there is no point in taking this discussion any further because you have just done exactly what user Bo Jacoby did. You have stated the radial planetary orbital equation and hidden the centrifugal force term. The full radial equation is written above, but for reasons which we may never fully establish, you have decided to hide the centrifugal force term which constitutes an important aspect of solving the equation in order to get the conic section solution. Bo Jacoby did the same thing. You can read the debate on his own talk page. And when I tackled him on the matter, he tried to deny it. He said that he hadn't hidden the centrifugal term. And after a while, the centrifugal term emerged again as if he had never hidden it.

While this attitude continues, there is no hope whatsoever of discussing the Kepler problem in a rational fashion. The only thing that made the Kepler article easier to deal with was the fact that the full equations were there prior to my arrival, and the argument that ensued was only over the issue of attempts to deny the names of the terms in those equations. On the centrifugal force article, you in particular spared no effort to keep the full equations off the page. And now that the full equations are on this page, you have calmly ignored them, and re-written the radial equation, minus the centrifugal term, just as Bo Jacoby tried to do on his own talk page.

It is impossible to conduct a rational scientific debate when people first try to deny equations that are in the textbooks, then try to deny that the textbooks really mean what they say, and when it reaches the stage that certain equations can no longer be denied, to deny the names of the terms in the equations, and then finally to simply re-write the equations with the controversial terms dropped out.

I'll leave you guys to think about it for a while. But it would appear that the authors of this article still don't know what Coriolis force is. David Tombe (talk) 12:43, 1 February 2009 (UTC)

I'm sorry you don't want to rely on reliable sources, and instead insist that your original research be the basis of the article. It is not me saying that the Coriolis force and the other inertial forces vanish in the inertial frame, it is every reliable sources that says it. As wikipedia is based on reliable sources, so says the article. From my perspective it is because you refuse to accept reliable sources, and instead rely on your own original thoughts and interpretations, such as the restriction that the Coriolis force can only be tangential, that has caused the impasse. You are welcome to try the standard dispute resolution avenues if you feel you've been dealt with unjustly. --FyzixFighter (talk) 18:01, 1 February 2009 (UTC)

FyzixFighter, you hid the centrifugal force in your equation above. The full equations are listed further up, but you hid the centrifugal force. That says it all. You cannot face up to the facts. Likewise, you are deliberately ignoring the fact that the Coriolis force must be in the tangential direction. Those are the roots of the problem.

There are two textbook topics which are self contradictory. Fictitious forces/rotating frames seems to have gradually given way to the idea that the Coriolis force can be in any direction. I have clearly shown where the derivation means that this is not so. You can call it original research if you like. But I am backed up by another chapter in the textbooks which treats Coriolis force in conjunction with planetary orbits, and it is explicitly clear that the Coriolis force is a tangential force and that everything to do with extrapolating rotating frame transformation equations to non-co-rotating situations is a total nonsense.

And we don't need to even go into any maths at all. We can all see that cyclones are visible from an inertial frame of reference. Yet you are still trying to say that the Coriolis force which causes the cyclonic effect is only observable in a rotating frame of reference. You will never be able to correct your understanding of this subject until you wake up to the reality that there is something seriously wrong with this present article.

You restored statements which say that the Coriolis force is only observed in a rotating frame. Yet you can see with your own eyes that that is not true as regards meteorology. When you and the others face up to that fact, we will be able to make some progress on getting a proper understanding about what is really happening in cyclones. It is not the simple Coriolis force that you think. It is a much more complex hydrodynamical interaction involving actual tangential force from the main body of the atmosphere being unable to totally restrain moving currents of air in a co-rotating radial motion. David Tombe (talk) 18:58, 1 February 2009 (UTC)

David, I am beginning to think that you are mixing up the expression of Newtonian mechanics in polar coordinates with expression in a rotating frame of reference. These are completely different things. I do not have the time now to precisely point this out. Think about it. −Woodstone (talk) 21:30, 1 February 2009 (UTC)

Woodstone, That's the whole point. They are not different. For the rotating frames of reference transformation equations which are the subject of this particular article, there is a derivation which is based on the principle of considering the motion of a particle relative to a point on a rotating frame of reference. The derivation involves setting up a vector triangle. The sides of the triangle are (1) origin to stationary point on rotating frame, (2) Stationary point on rotating frame to the moving point in question, and of course (3) Origin directly to moving point.

At that stage of the derivation, the moving point is free to move in any direction, and that is the source of all the confusion. As regards (2), the velocity is then deemed to be the velocity relative to the rotating frame, and as such it would appear to be free to be in any direction. This is the velocity which appears in the final coriolis force term, and hence you are under the impression that since the velocity appears to be free, that the Coriolis force can be in any direction.

However, when we go to the next stage of the derivation, we have to shrink the triangle to infinitessimal size for the limits, as per calculus, in order to get the final expressions. The centrifugal term then becomes purely radial, and it applies to the fixed point on the rotating frame. As a corollary, the Coriolis force term becomes purely tangential.

Moving on to polar coordinates, this is just a different approach to deriving exactly the same mathematical expressions, but without any specified context. Coriolis force comes out, unequivocally and explicitly to be a tangential force, and that is acknowledged when these expressions are used in the Kepler problem.

So basically, the rotating frame transformation equations are correct when applied to particles that are co-rotating in the rotating frame. As far as Coriolis force is concerned, that means undergoing a constrained radial motion.

Unfortunately in recent years, some textbook authors have let the rotating frame transformation equations become unanchored from the restrictions which are inherent in the derivation, and Coriolis force has been let loose to act in any direction. This is a very bad mistake in modern physics.

I know you will immediately rush to wikipedia's rules about 'no original research'. But what I am doing is pointing out how the right hand doesn't know what the left hand is doing. I am not doing original research. I am pointing out how planetary orbital theory contradicts some notions that are currently held about fictitious forces.

Hence when it comes to meteorology, we have a constrained co-rotating atmosphere and we have a basis to involve Coriolis force of a kind, albeit that that basis is not yet fully understood. But with free projectiles flying over roundabouts, there is no Coriolis force involved at all, because there is no constrained radial motion. The apparent deflection as viewed from the roundabout is a tangential superimposition. It is not a Coriolis force.

You cannot say, as you did above, that polar coordinates and rotating frames are two totally unrelated topics. They are not. The maths is identical in each case. The problem arises because scholars of rotating frames of reference have overlooked the restrictions inherent in the maths as regards its application to their field of interest.

The net result is that your introduction here contains distinct factual errors which are manifestly obvious for many people to see. It is wrong to state that Coriolis force only occurs in rotating frames of reference. We can see it in elliptical orbits, relative to the inertial frame, and we can see it in the cyclones from an inertial frame.

There is something seriously wrong with an article which claims that Coriolis force causes the cyclonic behaviour in the atmosphere, but can only be observed from a rotating frame when everybody can see it from an inertial frame.

Coriolis force is a very definite effect which is clearly not understood by the authors of this article David Tombe (talk) 07:30, 2 February 2009 (UTC)

David says:

Unfortunately in recent years, some textbook authors have let the rotating frame transformation equations become unanchored from the restrictions which are inherent in the derivation, and Coriolis force has been let loose to act in any direction. This is a very bad mistake in modern physics.

This is not the place to point out very bad mistakes in modern physics. Write it up, get it published in an academic journal, and then, if you still have time what with all the fame and fortune that comes with revolutionizing a scientific discipline, come back here and put it in the article, with a citation.

For years, you have been pointing to cyclones, and the fact that you can see them from an inertial frame, as evidence that Coriolis effects exist in inertial frames. So answer me this: Have you ever seen water spiral down a bathtub drain? Do you attribute that to the Coriolis force? If you do, you are wrong--there are any number of citations refuting that idea. If you don't, if you realize that it's just conservation of angular momentum as the slow rotation of the water in the tub is amplified as it moves toward the drain, then you should have no problem understanding cyclones from outer space. As slowly rotating air moves inward, its rotation is amplified. No Coriolis.Rracecarr (talk) 15:56, 2 February 2009 (UTC)

RRacecarr, Neither the water spiralling out of a bathtub drain, nor cyclones on the large scale involve fictitious Coriolis force as it is understood in this article. Furthermore, where conservation of angular momentum is involved, Coriolis force cannot be involved. Conservation of angular momentum can only occur where no tangential forces are acting. Coriolis force and conservation of angular momentum are incompatible.

You are exactly right: Coriolis and conservation of angular momentum are incompatible. In the rotating frame, angular momentum is not conserved, and the rotation of cyclones is explained by the Coriolis force. In the inertial frame, there is no Coriolis force, and the rotation is explained by conservation of angular momentum. Two different explanations of the same phenomenon. Each is correct in its own reference frame.Rracecarr (talk) 18:06, 2 February 2009 (UTC)

The problem then becomes a matter of discovering what is the real explanation for the large scale cyclones in the atmosphere. Well the effect is cyclonic, so it involves the Earth's rotation. A Coriolis force would be necessary to prevent cyclonic behaviour, but clearly the atmosphere does not provide sufficient Coriolis force on elements of itself to constrain radial flows of air in a radial path into depressions or out of anti-depressions. The end result is complex. It involves a partial applied Coriolis force, applied by the atmosphere on moving elements of itself. There will also be Coriolis force acting at intermolecular level due to vorticity in the molecules, and so there will be large scale vorticity anyway, even without the Earth's rotation. The Earth's rotation is an extra effect which sets the direction of the vorticity.

Wow. Just wow.Rracecarr (talk) 18:06, 2 February 2009 (UTC)

The bathtub drain is an example that doesn't involve the initial cyclonic aspect of the Earth's rotation. It is pure hydrodynamics, and Coriolis force is a real hydrodynamical force that comes into play where sinks and inter-molecular vorticity are involved. That's how Laplace and Coriolis envisaged the vXH force (H being vorticity).

But I'm not going to touch the main article now. There is no need for an edit war over this. I was merely trying to remove a few incorrect sentences without actually contradicting what it says in the textbooks. But if you want those sentences in, then so be it. David Tombe (talk) 16:54, 2 February 2009 (UTC)

Rracecarr, How can you have a breakdown in the conservation of angular momentum in the rotating frame if it is conserved in the inertial frame?

I don't think we're going to be able to reach any agreement on this and I've said I'm not going to edit the Coriolis page any more.

But ironically, there are actually some areas of agreement to be found where least expected. We are both agreed that Coriolis force, as per this article, is not involved in tornadoes or in the water swirling out of a bathtub. Interestingly most tornadoes are cyclonic whereas the water swirling out of a bathtub is not cyclonic. We are even agreed on that extra twist to the issue.

It is in there that you will find the clues. Basically, Coriolis force in the hydrodynamical sense, as conceived by Coriolis himself, is behind all these vortex phenomena. The Earth's rotation adds a cyclonic dimension in the larger phenomenon such as cyclones and tornadoes.

Check out our areas of agreement and I think you'll then realize what my point has been all along. David Tombe (talk) 05:01, 3 February 2009 (UTC)

Angular momentum in a rotating frame "breaks down" if you don't include the proper fictitious forces. If you do include them, you can still make sense of the angular momentum, but it is not conserved, as the Coriolis force applies a torque. From an inertial frame, the physics behind a drain vortex and that behind a cyclone are exactly the same. And in neither case is there a Coriolis force. Rracecarr (talk) 16:04, 3 February 2009 (UTC)

Rracecarr, I can see now that you have a different opinion than I do as regards what actually constitutes the Coriolis force. You seem to link the Coriolis force with the fictitious tangential superimposition that is observed from rotating frames of reference. In the two examples which you have given above, I can clearly see a real Coriolis force in both of them. As the fluid moves, it gets deflected at right angles. Let's look at the drain, since we are both agreed that the Earth's rotation is not involved. As the water swirls into the sink, its angular acceleration is increasing. But there is an equal and opposite Coriolis acceleration. That real hydrodynamical Coriolis force is clearly visible. All inward radial motion is deflected in the tangential direction, opposite to the direction of the angular acceleration. That is real Coriolis force. The angular acceleration and the Coriolis force cancel each other out mathematically, and hence angular momentum is conserved. But the two forces are still both physically present and clearly visible. It's just as per Kepler's law of areal velocity in non-circular orbits. That's where the real Coriolis force lies. That is the hydrodynamical Coriolis force that Coriolis himself was talking about in 1835.

Your article here is about the wrong effect. It's about some fictitious circular motion that gets superimposed when when we observe a motion from a rotating frame of reference. And your explanation above about angular momentum being conserved using the right fictitious forces was not very convincing. You'd need to explain that in more detail.David Tombe (talk) 17:42, 3 February 2009 (UTC)

Sorry if you don't think it's convincing, but it's the truth. In an inertial frame, angular momentum of a closed system, like linear momentum, is conserved. In a non-inertial frame, that is not true.Rracecarr (talk) 19:27, 3 February 2009 (UTC)

David do you really think that after filling about a megabyte of talk page at Centrifugal force that you can present the same tired arguments here, to any different effect? Everybody else here understands what this article is about, what it's always been about, and it's not a polar coordinate thing, it has never, ever been about that. You're simply wasting your, and everybody else's time.- (User) Wolfkeeper (Talk) 04:59, 4 February 2009 (UTC)

RRacecarr, you are overlooking the fact that in hydrodynamics, conservation of angular momentum can involve a real Coriolis force that is mathematically cancelled by a real angular acceleration. They cancel mathematically, but they are still both present physically and can be easily observed even in a kitchen sink where no cyclonic effect is present.

I think that once you grasp the idea that Coriolis force, as per Coriolis himself, and as per how it was originally intended to apply in meteorology, is not the same thing as the fictitious effect which you have in mind. I can't figure out how you are expecting to dabble with real angular momentum using fictitious effects in a rotating fame of reference, unless it's all about some kind of fictitious angular momentum. But we don't need to go into all that. David Tombe (talk) 05:26, 4 February 2009 (UTC)