Coriolis Effect

Coriolis Effect

Behavior of objects under the Coriolis effect

History

Significance of the Coriolis effect

Resources

The Coriolis effect occurs when, on a rotating solid body, an inertial (apparent) force acts on a body at right angles to its direction of motion when it moves towards or away from the axis of rotation. The Coriolis effect (also called the Coriolis force) is based on the laws of motion introduced world by Issac Newton (1642–1727).

Behavior of objects under the Coriolis effect

Within its rotating coordinate system, the object acted on by the Coriolis effect appears to experience a force that would deflect it from its path of motion. This force is not real, like the “centrifugal force” that also seems to act on objects that are stationary or following arbitrary paths in rotating coordinate systems. A force is exerted on an object moving towards or away from the axis of rotation in a rotating system, but only if that object is to maintain a fixed position or move in an arbitrary path relative to the rotating coordinate system.

One way to understand the Coriolis effect is to imagine an ant crawling from the outer rim of a horizontal rotating disc toward the center of the disk. At the rim, where it begins its journey, the ant is making a certain number of revolutions per second. Given its mass and its distance from the center of rotation, it has a certain angular momentum. As it moves toward the center, to retain that angular momentum it must increase its angular velocity—make more revolutions per second. One can see this effect when a spinning skater pulls their arms in closer to their body and spins more rapidly. But if the ant is to walk a straight line toward the axis, then it will continue to make the same number of revolutions per second (because every point on a straight line drawn on the disc from axis to edge makes the same number of revolutions per second). The ant’s feet must, therefore, exert a force on the surface of the record that is counter to the direction of rotation as it moves toward the axis. This force transfers angular momentum from the ant to the disc (which is, presumably, far more massive than the ant); since momentum is always conserved, the angular momentum lost by the ant is equal and opposite to that gained by the disc (or whatever the disc mechanism is attached to, such as Earth). In this case a force is indeed exerted on the ant, but it is exerted by the muscles of the ant’s own legs, acting through friction on the surface of the disc; it is not some mysterious “Coriolis force” coming out of nowhere. This is why the Coriolis force is said to be “not real.”

Now imagine that a toy cannon on the edge of the disc is fired toward the center. The cannon ball moves freely with respect to the rotating reference frame of the disc (unlike the ant, which pushes sideways with its feet to achieve straight-line motion in the rotating reference frame). The path traced by the toy cannon ball over the rotating disc will lag the path that it would have taken had the disc not been rotating. From a nonrotating point of view, say that of a person standing in the room, the surface of the disc will rotate out from under the path of the cannon ball as the cannon ball flies over the disc. From the point of view of the rotating surface, however, the cannon ball is accelerated by a mysterious force that acts against the direction of rotation. The cannon ball is not in fact being acted on by any force, but is simply following a path that is curved sideways from the point of view of the rotating frame of the disc. Again, the “Coriolis force” is seen to be “not real.”

The effects described above would act in reverse for an ant or cannon ball traveling away from the axis of rotation. They also work on the scale of a planet, an accretion disk of material falling into a black hole, or a galaxy.

History

The Coriolis effect was first described by Gustave-Gaspard Coriolis, for whom the effect is named. Coriolis (1792–1843) was a French mathematician and engineer who graduated in highway engineering. He was a professor of mechanics at the École Centrale des Arts et Manufactures and later at the École des Ponts et Chaussées. Coriolis studied the motions of moving parts in machines relative to the fixed parts. His special gift was for interpreting and adapting theories to applied mathematics and mechanics. Coriolis was an assistant professor of mechanics and analysis and later director of studies at the École Polytechnique in Paris from 1816 to 1838 where he gave the terms “work” and “kinetic energy” their scientific and practical meanings, which are still used today.

Coriolis authored several books. His first, Du calcul de l’effet des machines (On the Calculation of Mechanical Action ) was published in 1829 and discussed applied mechanics. He also wrote The´orie mathe´matique des effects du jeu de billiard (Mathematical Theory of the Game of Billiards ) in 1835, and his understanding of the motions of billiard balls was directly related to his study of other solid bodies like the planets and especially planet Earth. In 1835, he published a paper called “Sur les équations du mouvement relatif des systemes des corps” (“On the Equations of Relative Motion of Systems of Bodies”), which described the force later named the Coriolis effect. Publication of this paper changed the studies of meteorology (weather), ballistics, oceanography, and astronomy as well as mechanics. The Coriolis effect and other mechanical principles were also described in a book published in 1844 after Coriolis’ death and titled Traite´ de la me´chanique des corps solides (Treatise on the Mechanics of Solid Bodies ).

Significance of the Coriolis effect

The Coriolis effect is important to virtually all sciences that relate to Earth and planetary motions. It is critical to the dynamics of the atmosphere including the motions of winds and storms. In oceanography, it explains the motions of oceanic currents. Ballistics encompasses not only weapons but the motions of aircraft including launching and orbiting spacecraft. In the mechanics of machinery, rotating motors and other electrical devices generate instantaneous voltages (called Christoffel voltages) that must be calculated relative to the rotation. In astronomy, astrophysics, and studies of the dynamics of the stars, the Coriolis effect explains the rotation of sunspots and the true directions of light seen on Earth from the stars.

The Coriolis effect does not have any relationship to two other effects. For many years, geologists have used the Coriolis effect to suggest that right banks of rivers will tend to erode more rapidly than left banks in the Northern Hemisphere; this has been proven not to be true. Also, many people claim that the spiraling water in a sinks or toilet bowl drains in counterclockwise or clockwise motion depending on whether the drain is located in the Northern or Southern Hemisphere. This is not the case. The Coriolis effect related to Earth’s rotation is too weak to control fluid spiraling on such a small scale. Rather, the direction of drainage spiraling is determined by the shape of each individual container. In either hemisphere, North or South, one can observe drainage spirals that go either to the right or the left.

Resources

deFuentes, Sean. The Coriolis Effect. Melbourne, Australia: Hard Pressed Publications, 2004.

OTHER

National Aeronautics and Space Administration (NASA). “Rotating Frames of Reference in Space and on Earth.” September 22, 2004. <http://www-spof.gsfc.nasa.gov/stargaze/Srotfram.htm> (accessed October 23, 2006).

Gillian S. Holmes