One More Round with the Coriolis Force

Part 1. Odd and Humorous Beliefs

Kevin T. Kilty

On Friday, October 17, 2003, I sat with four other faculty members at lunch. All of them were trained in various disciplines in science, engineering, or science education. We were talking about a new idea that one of my colleagues and I have about teaching high-school mathematics, but I became aware of a subconversation at the other end of the table where a very intelligent computer science professor was telling the science education professor that water spirals down a toilet because of the Coriolis force. I was stunned, and interjected that it does so for no such reason. The science educator was not buying his argument either, and the two other faculty members had no opinion on the subject. They sort of shrugged their shoulders as if to say, "I've not thought about this at all."

This was very distressing. I often hear all sorts of nonsense, myths, superstitions, and invalid arguments about the Coriolis force and its effects, some of which I'll repeat here, but this incident made me realize that some pseudoscience is extremely difficult to combat, because its proponents are well educated people promoting ideas that they have never thought through carefully.

The Coriolis force

First, let me make clear that there is a Coriolis force which results from the rotation of the Earth on its axis, and which affects objects that move on, under or over the Earth's surface, ship's gyroscopes and the flight of long-range artillery projectiles, for example. There are also Coriolis-like forces which appear in rotating mechanical contraptions, but which have nothing to do with the Earth's Coriolis force--torque converters and childrens' tops, for instance. This Coriolis-like force is what balances a top against gravity as it precesses around its pivot. From this point on I am speaking only of the Earth's Coriolis force.

Second, let's not become embroiled in an argument about whether the Coriolis force is a true force or just an acceleration. This distinction does not matter, because from one perspective it behaves just like a real force, and from another it obviously results from a rotating frame of reference. Thus, I will use the word "force" to describe it. The real problem with the Coriolis force is that people learn about it in a superficial manner. The typical college junior physics student encounters it briefly in a week of lecture about accelerated frames of reference. Most science teachers know almost nothing about it at all, and neither do most engineers, except for mechanical engineers involved in advanced dynamics. A geophysicist may study it in more depth if he or she is a fluid dynamicist, but otherwise Stommel and Moore describe how practically everyone learns about it:

"Clutching a teacher's hand they are guided over the narrow gangplank between the resting frame and the earth's rotating frame. Once safely aboard [the earth's frame] many are glad to accept the idea of Coriolis force, confident that it is derived rigorously. Some prefer never to look over the side again."

In summary, the Coriolis force is a strange and complex thing, about which many people have obtained misinformation. They likely do no further thinking about it and remain ignorant forever more. Well, let's have another look over the side of the gangplank.

Odd and humorous beliefs

Nearly everyone believes something weird about the Coriolis force. For example, nearly everyone believes (incorrectly) that the Coriolis force makes water go down a drain clockwise in New Mexico and anticlockwise in New Zealand. The protagonist New Zealander in the movie "The Quiet Earth," for example, says he knows he has entered a different universe because water keeps going down the drain hole the wrong way. Who among us ever even notices which way the water drains, let alone that it drains the wrong way some particular morning? This same belief extends to all sorts of draining motions, as, for example, the direction that whirlwinds, tornadoes, and water spouts rotate.

These beliefs persist among scientists and laymen alike, including some of my colleagues. Isaac Asimov, the well regarded science writer, wrote, "In the end, [even dish water down a drain], winds, and currents move in large circles, clockwise in the northern hemisphere and counterclockwise in the southern hemisphere... concentrated more tightly [this circulation] becomes a hurricane, still more tightly a tornado."

Other beliefs about the Coriolis force include:

It controls the spiral of water going down a toilet, as I mentioned in my introduction.

It causes train wheels and rails to wear preferentially on one side.

It causes artillery shells to drift noticeably to the right after only 200 meters of flight. Long range artillery shells are most definitely affected by the Earth's Coriolis force, but not shells or bullets on short flights.

It causes rivers in the Northern hemisphere to erode their right hand bank more severely (Baer's Law).

Penguins and lost polar explorers tend to turn in circles because of it. A student once told me that his junior high science teacher had the class wander around blindfolded to demonstrate this.

It is the reason for rotation and tearing of tectonic plates.

It causes certain crystals to grow in spirals.

It alone causes the intense boundary currents known as the Gulf Stream and the Jet Stream.

It causes a rattleback toy to turn oppositely in the two hemispheres. The Hubbard Scientific Physics (1993) catalog of scientific supplies advertises a rattleback, and the ad states that the rattleback will spin oppositely in the southern hemisphere. The obvious implication is that Coriolis force causes it to spin so. Did anyone ever simply do the experiment? Probably not.

Rules to guide arguments

Before examining each of these claims in turn, let's assemble a list of rules about the Coriolis force. Although I have an excellent explanation about the origin of Earth's Coriolis force that does not require calculus, most analyses do not need an explanation about its origin. The facts on this list, plus a few additional calculations, should serve to demolish most silly arguments.

First, a Coriolis force occurs only when a frame of reference rotates, and is apparent only within the rotating frame.

Second, a Coriolis force occurs only when something has motion with respect to the axis of rotation within this rotating reference frame.

Third, the Earth's Coriolis force has a consistent sign within each hemisphere of the Earth. Any effect blamed on this Coriolis force must have consistent behavior within each hemisphere.

Fourth, the magnitude of the Coriolis force is proportional to the rate of rotation of the reference frame and the velocity of the thing that moves within the reference frame. That is, per unit mass, CF = 2omega U where U is the velocity, and omega is the rate of rotation (angular velocity). Actually both omega and U are vectors and the product involved is the vector cross product. But I will ignore such formalities here.

Fifth, on a spherical surface, like the Earth, the Coriolis force along the surface varies from a maximum value at the poles to a minimum at the equator. This results from the changing orientation of Earth's surface with respect its rotation axis.

Sixth, we often describe the Coriolis force of the Earth as always being to the right of motion in the Northern Hemisphere and to the left in the Southern Hemisphere. But this is for horizontal motion only. If there is vertical motion, there is additional Coriolis force that can't be described as being to the right or left. In the Northern Hemisphere a rising body feels a Coriolis force toward the southwest and a falling one feels a force toward the northeast.

Seventh, the Coriolis force, acting as it does at right angles to velocity, can accelerate a mass, but does no work on it. It cannot provide a source of energy.

A numerical aid for any discussion is that of a measure of Coriolis force compared to whatever force is needed to produce an observed motion or what force a motion implies. Because the observed motion in most cases follows a curved path, the force needed to maintain the curved motion is a centripetal force, which, per unit mass, is CPF = U^2/L. U, once again, is the velocity of whatever is moving, and L is the radius of the curved path this thing takes. A very useful quantity is the ratio of this force to the Coriolis force. What results is R_o = U/(2Lomega), a dimensionless group of parameters known as the Rossby number. In the case of the Earth, omega is 2pi radians of rotation in 86,400 seconds, which is roughly omega = 7 times 10^(-5) sec^(-1).

In the next issue of The Citizen Scientist, Kevin Kilty will examine the alleged effects on his list one by one. Editor.

References

Henry M. Stommel and Dennis W. Moore, An introduction to the Coriolis Force, Columbia University Press, 1989.
Isaac Asimov, What is the Coriolis Effect? Science Digest 69, 82-83, 1971.
I. Amato, The Curling Crystal Club, Science News 135, 124-125, 1989.
Anon., Coriolis force for continents, Science News 101, 215, 1972.
Anon., Do slabs rotate as the earth turns? Science News 125, 358, 1984.
Albert Einstein, Die Naturwissenschaften, 14, 1926.