Talk:Coriolis force/Archive 1

"there is no real force acting on the object"... 'k, gotta explain something to me.

Any time a body's world line deviates from a straight line in whatever coordinate system one's using, a force has to be concocted to account for that. If we're fool enough to use polar coordinates, we have to come up with Coriolis forces. If we're fool enough to use a rotating coordinate system, we need to invent centrifugal forces.

But didn't general relativity do the same thing to gravity? Isn't, in fact, any "force" that operates in strict proportion to the mass of the affected body, imaginary - an acceleration term that can be eliminated by an appropriate change of coordinates?

Aren't Coriolis and gravity equally imaginary?


 * (William M. Connolley 20:26, 21 Feb 2004 (UTC)) I essentially agree with the above... Coriolis force appears as a result of co-ordinate transform. Gravity is equivalent to acceleration. OTOH, Coriolis does no work (being dead. Sorry, no, I mean: being orthogonal to the velocity) - could this be a criterion for it being "imaginary"? Or is that an arbitrary test? I notice several google-found web pages hedge their bets by describing Coriolis as imaginary, but putting imaginary in quotes to weaken it.

Section: is coriolis "fictitious"?
I've added a section to the page about the above. I'm not 100% sure about this - anyone who really knows general relativity (or coriolis) may care to correct.

To make things consistent, I've also cut some text from the article.

A minor point: I cut "(due to Newton's laws of motion)" - I don't think this is right even if coriolis is fictitious - its a kinematic effect.

Your description of GR is pretty accurate except for the bit about gravity not being a pseudo-force. In the context of GR, it certainly is. By the same token, the Coriolis effect should certainly be understood as a pseudo-force, in that it does not occur in inertial frames. -- Xerxes 20:58, 2004 Jul 26 (UTC)


 * (William M. Connolley 21:07, 26 Jul 2004 (UTC)) I think that might depend on what you mean by a force. But if you are saying that Coriolis is no more fictitious than gravity, that will do, since "everyone" knows that gravity is not fictitious...


 * [Owen Jones] 11:22 GMT+1 24 Sep 2004. I think all the talk of General Relativity (GR) is beside the point. In classical mechanics fictitious forces arise as a result of moving from an inertial frame to a non-inertial one, ie from the fixed frame of the stars to the rotating frame of the earth. With the advent of relativity we have moved from having one privileged set of non-inertial frames to every frame being equal, and this does complicate matters. The last section is correct, but I feel it should explain that fictitious is being used in a mathematical sense. One could almost read it and get the impression that it is wrong to call the coriolis force a fictitious force. In the wider scheme of things, perhaps we could do a page on mathematical appropriation of everyday terms to describe mathematical concepts. For starters there are differentiation and integration. What is so normal about a normal group? What is so irrational about irrational numbers? What is so fictitious about fictitious forces?


 * (William M. Connolley 18:31, 24 Sep 2004 (UTC)) Well, in wiki we can do "fictitious (natural language)" and "fictitious (precise)" but you can't do that in speech. But on the cor page, I'm not at all sure we are distinguishing the two meanings or need to. I wrote that bit: I'm happy to be corrected: but as far as I can see there is no physical reason to call coriolis forces fictitious. Thus the word is used in a maths and physics sense. I think it *is* wrong to call cor fictitious. As far as I can see, GR renders the distinction meaningless.


 * As to irrational numbers: thats a softball: they are irrational because they are not ratios (nothing to do with rational (mental state)). Perhaps you mean imaginary numbers? :-)


 * In fact there is one sense in which cor is imaginary: it does no work. But... who says that is the test?


 * (Owen Jones 21:59, Sep 26, 2004 (UTC)) I used to be a big fan of QM and GR as far superior to classical phsyics. But then I realised that for all but the most extreme problems (large velocity, large mass or small scale) classical physics is the rational choice. Also, the majority of people actually think in terms of classical mechanics (when you take a sharp corner in a car you feel a force), so I think it is fair to have it in wikipedia. I think it's important point that this isn't actually a force (I can't think how I would define a force, but for one there is no equal and opposite reaction force anywhere). I would favour something along the lines of


 * In physics the term 'fictitious force' is used when what appears to be a force is caused by being in an accelerating frame of reference. For example, the force you feel when taking a tight corner in a car is a fictitious force in this sense. This is not to say that the force is imaginary in any sense.


 * (William M. Connolley 22:12, 26 Sep 2004 (UTC)) But what is an accelerating frame of reference?


 * (Owen Jones 20:09, Sep 27, 2004 (UTC)) One that is accelerating with respect to the fixed frame of the stars is how it was originally defined.


 * (William M. Connolley 20:27, 27 Sep 2004 (UTC)) But thats "cheating": what is there in the laws of physics to priviledge this one frame of reference?


 * I am very new to Wikipedia, so do tell me if I should just get on with it and edit the page myself, instead of discussing it here first.


 * (William M. Connolley 22:12, 26 Sep 2004 (UTC)) Its very much up to you. But if something is a subject already discussed, talking on the talk page is usually a good idea. If (elsewhere) no one responds then just do it.


 * I don't quite follow: are you saying that it is wrong to call the coriolis force fictitious in a maths and physics sense because we should use GR instead of classical mechanics and in GR there are no fictitious forces because no frame is privileged as being the rest frame?


 * (William M. Connolley 22:12, 26 Sep 2004 (UTC)) Yes, except that "use GR" isn't meaningful. You can't just pick-and-choose your theory (well not if you really want to know what is going on). GR is the best theory going.


 * (Owen Jones 20:09, Sep 27, 2004 (UTC)) If you want to compute where a projectile that is fired vertically up from the surface of the earth will land, then you apply classical dynamics (which I think ends up using the coriolis effect). When I say 'use GR' or 'use CD' I mean apply that theory to obtain an answer. You could use GR to get an answer to this problem, but it would be much harder and would give almost the same answer as CD, precisely because CD is a very good approximation to GR. There are situations where you have to use GR to get an answer which tallies with observations, but you only meet them in very specialised situations.


 * As for irrational numbers, I know that there is a logical argument for why rational and irrational are used as they are, but when people say 'rational' they don't mean 'in ratio' they mean 'in reason', so although maths may not have appropriated the word it does use it in a different sense and can easily be misinterpreted.


 * (William M. Connolley 22:12, 26 Sep 2004 (UTC)) In maths, 'rational numbers' means 'in ratio'. Yes the word has other meanings in natural language, but so what?


 * (Owen Jones 20:09, Sep 27, 2004 (UTC)) What I was proposing was a page to explain some of the confusing terms used in maths. Just because 'rational' has a sensible explanation doesn't stop it from being confusing when first encountered. I admit phrases such as 'fictitious forces' are more confusing and really could have been chosen better.


 * (William M. Connolley 20:27, 27 Sep 2004 (UTC)) Oh, OK. Thats a fair enough idea. I misunderstood you.

Coriolis force: possible source of confusion
Coriolis force is a fictitious force, but there's a catch. Consider the pair 'centrifugal force' and 'centripetal force': in the setting of a pilot training centrifuge they are very much different. The centripetal force is a mechanical force, transmitted by fysical contact. The percieved centrifugal force is, if it is transmitted, equally strong for all particles of your body. Like having gravity around, as soon as you break fysical contact, you don't feel anything.  Imagine a rotating disk, very slippery, just a little bit of friction. An object attached to a rope is released, and it is slowly allowed to move away from the center of rotation. Each time the distance to the center of rotation is increased, the object is slipping for a while, until its angular velocity is once again synchronized with the rotating disk. In the inertial frame of reference, the acceleration vector is a function of spatial coordinates and the amount of angular velocity mismatch. In the rotating frame of reference the acceleration vector points in the "opposite direction", and there too it is a function of spatial coordinates and the amount of angular velocity mismatch. Both acceleration vectors are referred to as 'the coriolis force'. :-(  I'd say go for the inertial reference frame. In the inertial reference frame there is at first a mismatch in angular velocity. The friction force, although insufficient to provide immediate grip, causes the object to catch up and become synchronized. In the rotating reference frame there is at first a mismatch in angular velocity, that - seen from the rotating frame - looks like a spooky accceleration. Friction force slows that spooky motion down to zero velocity, and then the spooky acceleration is gone too. Cleon Teunissen 13:11, 29 Jan 2005 (UTC)


 * The account above is not quite correct. Seen from the inertial reference frame: as long as there is a velocity component away from the center of the disk, the mismatch in angular velocity increases, because there isn't sufficient friction to do the necessary work immediately. As soon as the velocity away from the center stops, the angular velocity mismatch stops increasing. The friction force may not be enough to synchronize the velocities entirelyThis model approximates the problems in weather modeling. In weather modeling, using a stationary Earth together with the fictitious coriolis force is the best calculation strategy, of course. In the weather model the fictitious force is always doing work, the air currents are always deflected, inducing circulating flows. In the inertial reference frame the inertia is doing the work. Cleon Teunissen 14:54, 4 Feb 2005 (UTC)

I've decided to remove my comments from this page.
after reading this comment

>>>since radians are dimensionless. <<<

I decided you here need much more help than I can provide. I hoped to clarify things but instead can see it will just start argument.

Sorry for the inconvenience.

Please remove all record of my correspondence. I retract the material I presented and retain all copyright privileges and you or your group retains none.


 * When you posted, you agreed to license your edits under the conditions at Copyrights, which include the proviso that "you can never retract the GFDL license for the versions you placed here"... Marnanel 04:06, Apr 5, 2004 (UTC)


 * Indeed. And since radians *are* dimensionless, its clear who needs the help... though I'm not sure where you found the comment you refer to.

I suppose degrees, gradients, and percent slope, are dimensionless too! :rolleyes


 * (William M. Connolley 08:41, 2004 Apr 6 (UTC)) See: angle

2 px
I put two pictures in to illustrate two phenomena: atmospheric circulation causing prevailing winds, and rotation of storms. --wwoods 16:54, 8 Apr 2004 (UTC)


 * (William M. Connolley 17:24, 2004 Apr 8 (UTC)) Yes but... I don't much like the prevailing winds pic, its quite misleading as a pic of the actual circulation. Sometime I'm going to write the ferrel cell does not exist and I'll be in a stronger position then :-) Put it back if you must...


 * I'm not wedded to that picture, which I found on atmospheric circulation, but it seems like a reasonable subject for a picture. Can you find/make a better one? -wwoods 17:38, 8 Apr 2004 (UTC)


 * (William M. Connolley 18:40, 2004 Apr 8 (UTC)) That will be part of the ferrel cell page... I have a project for dynamically correct meteorology on wikipedia. But, its liable to be a slow process. Perhaps I'm being too picky. http://www.antarctica.ac.uk/met/wmc/circ.png might be a better picture... it shows the zonal mean meridional wind (admittedly from a climate model, not observations, but its a good climate model...). Or http://www.antarctica.ac.uk/met/wmc/circ1.png. See how much stronger the hadley cell is than the others... hmm, but it may not be a very good general-purpose pic.

Dimensions stuff that doesn't belong here
From the angle link " Note that angles are dimensionless, since they are defined as the ratio of lengths. " So how do the dimensions of R, theta and Phi in spherical coordinates aspire to the claim of being a dimension? Or are two of those a half ratio of the third???


 * (William M. Connolley 08:25, 2004 Apr 15 (UTC)) You're confusing "dimensionless" with "dimension".

Since the angle can be determined by dividing the arc length by the radius doesn't mean they are defined that way,


 * (William M. Connolley 08:25, 2004 Apr 15 (UTC)) but it does mean they *can* be defined that way, and that any other way must be consistent with that, and that therefore angles are dimensionless.

and it certainly doesn't mean they are dimensionless because the dimension of length is gone. They have now acquire the dimensional units of radians, degrees, or etc depending on which system you use.

However, as I said you need more help here than I can provide.


 * (William M. Connolley 08:25, 2004 Apr 15 (UTC)) Then why don't you go away and stop being "helpful"?

Bye! I hope you don't get your dimensionless radians confused with your dimensionless degrees. :rolleyes

Taylor-P theorem
(William M. Connolley 22:32, 29 Sep 2004 (UTC)) I'm happy with the theoretical T-P theorem. I'm somewhat unhappy with the way its used in the article, because its very vague as to whether this occurs (a) usually (b) almost never or (c) somewhere in between. I also don't know what Ro<<1 and Re>>1 mean in oceanic terms - we really ought to say, typically. I do rather doubt that there is anywhere in the ocean where the entire vertical column moves as one... but possibly its true away from the upper/lower boundaries?

Hi.

yes, it's of limited applicability in the open ocean. It comes into its fore in certain industrial flows (of which I am totally ignorant), limnology, and astrophysical fluid dynamics. Rather than argue here, I'll amend the article... What should go here and what should go into Taylor-Proudman theorem?

Robinh 07:24, 30 Sep 2004 (UTC)

Mach is inappropriate
(William M. Connolley 22:14, 21 Nov 2004 (UTC)) I don't think the Mach stuff belongs here. It should be in inertia.

Foucaults pendulum and fictitious force
Historically, Foucault used the pendulum to prove once and for all that the Earth is rotating. So, what assumptions under this proof have been challenged by general relativity?

In general relativity space-time is part of the physical world, energy is carried away from pulsars orbiting each other, the energy is carried away in the form of propagating deformations of space-time, usually called gravity waves.

Space-time is sensitive to direction of motion. Once motion is started, zero-curvature space-time is transparent only to a continuation of that motion in a straight line. Direction of motion is conserved, and this is valid for a pendulum too.

Around a non-rotating mass the distribution of space-time deformation is spherically symmetrical. However, according to general relativity, the gravity around a rotating mass has such an interaction with the universal space-time, that in the neighbourhood of the rotating mass the direction of space-time is affected too. Gravity Probe B has been build to verify that prediction of general relativity. The theoretical physicists expect that the gyroscopes onboard Gravity Probe B will be affected due to moving through space-time with the property that is also called gravitomagnetism. The expected deviation is 42 milliseconds of an arc over the course of a year.

That gives an indication of the error in the pendulum experiment when set up to show the Earth is rotating. Apart from the gravitomagnetic correction, general relativity confirms that the pendulum experiment provides proof that the earth is rotating.

So, is it possible to create circumstances in which there is a space-time geometry related centrifugal force, and a space-time geometry related coriolis force? I think Einstein's money would have been on the hypothesis that a hollow cylinder, sufficiently massive, and spinning sufficiently fast, would have inside a deformation of the geometry of space-time with properties that are the exact couterpart of the fictitous forces. How fast would be fast enough? Probably the wall of the cylinder would have to approach the velocity of light very, very closely. Cleon Teunissen 10:55, 3 Feb 2005 (UTC)

Coriolis effect on masses falling in mine shafts
Cleon Teunissen 08:37, 4 Feb 2005 (UTC) The following text had been inserted in to the 'is coriolis force fictitious? section by 82.77.126.23
 * I just want to add that Coriolis Force is also visible for masses that fall in mine shafts. The falling masses will tend to move to the east side of the pit, as compared to the vertical of the place. The most important effect is at the Equator.

I have moved this remark to the discussion page, because it is a comment; it starts with 'I just wanted to add [...] The comment disturbed the coherency of the existing text. Cleon Teunissen 08:37, 4 Feb 2005 (UTC)

The coriolis effect, inertia, fictitious force, and doing work.
Cleon Teunissen 11:50, 4 Feb 2005 (UTC) Inertia is resistance to a change in velocity. It is analogous to the behavior of a conducting wire with a coil with self-inductance in it. As voltage is applied, the change in current induces a counter-voltage, opposing the change in current. So inertia is a force, but not as we know it.

Inertia is related to the physics concept of 'work'. If a car accelerates, you are negotiating inertia, the car's kinetic energy is increased (in the reference frame that is co-moving with the part of Earth where the car is driving around). If the car brakes then this kinetic energy can be regained, and some electric cars do just that. During deceleration of an electric car, the inertia is exerting a force, driving the generators, charging the cars battery system. The inertia is doing work.

When you are negotiating a curve, momentum is transferred from one direction of motion to another. You withdraw from the x-direction account and deposit in the y-direction account. The centripetal force, when working perpendicular to the direction of motion, provides the leverage to effectuate the transfer, but after the books have been balanced and the total kinetic energy is calculated it looks as if it hasn't done work.

So, whenever inertia manifests itself, it is doing work.  Fictitious forces would, if they would exist, always do work. It is impossible for a fictitious force to not do work. Cleon Teunissen 11:50, 4 Feb 2005 (UTC)

How do inertial flow meters work?
I have been reading the explanations of the principles of inertial flow metering. The tutorial on the website of Micro Motions offers extensive explanation.  External link: the Micro Motion tutorial The flow operating principle is explained for both the curved tube version and the straight tube version. As far as I can tell, the operation of these flow meters is based on the phenomenon of precession, not on the coriolis effect. Precession has a torque and a angular velocity as input, and it results in a torque. It is calculated with a vector cross product.  The coriolis effect has as input angular velocity and a component of a velocity away from the hub of rotation. It needs a cosine to be calculated, hence the vector cross product. The output of a coriolis calculation is a force, not a torque. The inertial flow meters designed by Micro Motion use sensors that pick up effect due to torque. Cleon Teunissen 08:38, 6 Feb 2005 (UTC)


 * On second thoughts: it doesn't really matter. The coriolis effect and precession are two manifestation of a single underlying dynamics, I guess. Cleon Teunissen 09:32, 6 Feb 2005 (UTC)


 * Third thoughts: the curved tube mass flow meter operating principle can be understood as precession or as coriolis effect, depending on what aspects are emphasized. The straight tube mass flow meter is just wonderful engineering thinking, and its all coriolis effect. Cleon Teunissen 08:33, 7 Feb 2005 (UTC)

Animation available
Image:Corioliseffectanimatie.gif, from de. Duk 02:02, 7 Feb 2005 (UTC)


 * Hi Duk, I know that animation, I saw it in the dutch wikipedia 'coriolis effect' article. In this animation there is no friction at all, so in this animation it's 100 % coriolis effect. But in the case of a 100 % coriolis effect there is no noticeble manifestaton of inertia. When there is friction between the rotating disk and the object on it, then the object is accelerated, and then inertia manifests itself. So I think an animation that would incorporate fricton would be even better. Cleon Teunissen 08:42, 7 Feb 2005 (UTC)

In all reference frames the physics is the same
I think any phrasing like: "the coriolis force appears as a result of coordinate transform." should be avoided, that phrasing doesn't represent a physics fact. Take the example of the electric car designed to charge its battery system when it decelerates with respect to a larger mass. In the inertial reference frame, the car decelerates from top speed to zero, recharging batteries; the inertia of the car is doing work.  In the reference frame that is co-moving with the car, the large object that the car is firmly resting on decelerates with respect to the car. The car has been switched to braking, and a force pushing in a forward direction is doing work, charging the cars batteries.  In both reference frames the same physics is going on; in both frames the manifestation of inertia is acting in the same direction, doing the same amount of work. In both reference frames, the forward acting force only acts when the car is braking, and the amount of forward force is at all times exactly proportional to the level of braking.<BR> Changing the coordinate system doesn't change the physics, it's only that sometimes, after a coordinate transform, one of the forces involved gets a different name. --Cleon Teunissen 14:47, 8 Feb 2005 (UTC)

The formula for the coriolis force
the previous formula was:
 * $$2m\left(\mathbf{v} \times \mathbf{\omega}\right),$$

I replaced that with the formula I found in the french wikipedia coriolis article
 * $$\vec{F}_C=2m(\vec{v_r} \times \vec{\omega})$$

where the arrow above the symbol indicates vector quantities, m is mass, $$\vec{v_r} $$ is the component of the velocity in the radial direction, and $$\vec{\omega}$$ is the angular velocity of the coordinate system.

The calculation of the coriolis force must be designed in such a way that it produces a force that is tangent to the circle. Therefore, the velocity vector that is used as input for the vector cross product must be the radial component of the velocity

It appears the that $$$$ markup doesn't have a boldface version of /omega, therefore I copied the notation with the arrows above the symbols. --Cleon Teunissen 18:31, 9 Feb 2005 (UTC)

Alistair B. Fraser
External link: Alistair B. Fraser's 'bad coriolis' webpage <BR> In the current article on the coriolis effect the above site is referred to. It is a webpage by Alistair B. Fraser, who has committed himself to debunking bad meteorology, bad physics teaching, bad science in general.

Alistair B. Fraser writes in answer to a question: "It is true that the Coriolis force does no work." In answer to another question he writes: "[...] the magnitude of the Coriolis force on an object is independent of the direction in which that object is traveling." And to another question: "No, I don't mean the Coriolis effect. [...] I am referring to the Coriolis force."

Now, I have written that when the coriolis effect is involved the manifestation of inertia is always doing work, and so on. So what's up? I suddenly realized what exactly Alistair B. Fraser is referring to. Roughly, there are three sorts of situations to consider:
 * 1) an object is resting on a rotating disk, and there is so much friction that the object is guaranteed not to slide. Calculation of motion is straightforward then.
 * 2) an object is resting on a rotating disk, and it has some grip, it is somewhat constrained, but it's not enough to prevent the object from "lagging behind" if the object is moved in a direction away from the hub. That's tricky to calculate.
 * 3) an object is in motion close to a rotating disk but there is no actual contact. That is once again straightforward to calculate, just adding vectors.

Everything I write is about the second situation. The second situation is what applies in for example the case of the movement of masses of air in meteorological modeling.

The things that Alistair B. Fraser write fall into their proper place when it is recognized that he is talking about the third situation. For example, Alistair B. Fraser writes about a turntable on a desk and carefully moving a pencil in a line that is straight with respect to the desk while the turntable is rotating. <BR> Imagine a hovercraft above a very large rotating disk. The hovercraft makes several passes over the rotating disk, and everytime the hovercraft is just coasting; straight-line inertial motion. On the underside of the hovercraft there is a device that releases a drop of ink every second. Then all the tracks are seen to be curvilinear. So, if there is no interaction between the disk and the object, if they constitute two independent systems, then, according to Alistair B. Fraser, the coriolis force is causing the hovercraft to move in curvilinear motion all the time. Another claim of Alistair B. Fraser about the independent systems situation is that the magnitude of the coriolis force is independent of the direction of the object's motion in the inertial coordinate system. And since there is no contact between the object and the rotating disk, no work is being done, of course. --Cleon Teunissen 16:08, 7 Mar 2005 (UTC)

Major rewrite march 8th 2005
I did a major rewrite and rearrangement of the article. The exposition at the beginning is aimed at paving the way for understanding the role that the coriolis effect plays in atmospheric motions. Probably, most people will look for information on the coriolis effect in the context of atmospheric phenomena. The first sections treat the basics. As the article goes on, the discussions gradually become deeper and more specialized.

I'm considering to move this talk page to Talk:Coriolis_effect/archive1, because the current length of this talk page approaches or has already exceeded 32K. Now, after this major rewrite, might be just the time for it. --Cleon Teunissen 10:31, 8 Mar 2005 (UTC)