Online Astronomy eText: Background Physics: Motions and Forces
Coriolis Effects
(also see The Rotation of the Earth and Fictitious Forces)

      As the Earth rotates to the East, any object not attached to it will seem to drift to the West. This is why the stars, Sun, Moon, and planets all rise in the East, and set in the West. Their motion is, in a sense, an optical illusion, a mirror image of the motion which we actually have. Similarly, there are effects which act on objects near the surface of the Earth, which are not so obvious as the rotation of the sky, but which can be directly verified by careful observation. These effects can be explained in terms of an 'imaginary' force, called the Coriolis force (after Gustave Coriolis, a French engineer and mathematician, who showed that such a force could be used to allow the use of the ordinary laws of motion in a rotating reference frame), and as a result, the effects are referred to as Coriolis effects.
      The nature and size of the Coriolis effects depend upon where you are. If you are near the Pole, the axis of the Earth's rotation is nearly vertical relative to your Horizon, and as things spin around in the sky, they move nearly horizontally. Similarly, the Coriolis effects are almost completely horizontal. But if you were near the Equator, where the Earth's axis of rotation is nearly horizontal, things spinning around the sky would move nearly vertically, and the Coriolis effects are almost completely vertical. At in-between latitudes, the stars rise and set at an angle to both the vertical and the horizontal, and there are both vertical and horizontal Coriolis effects. In general, as you move toward one of the Poles, the horizontal Coriolis effects grow, and the vertical ones shrink, whereas if you move toward the Equator, the horizontal effects shrink, and the vertical ones grow.

The vertical effect (predicted by Newton)
      The vertical Coriolis effect was actually predicted by Newton, when he discovered the laws which govern the motions of things throughout the Universe. As we move around the Earth, we have some speed (locally 870 mph to the East), and if no force were to act on us, we would move in a straight line, with that speed, without any change. But as the Earth rotates, we have to move along a circle (our parallel of latitude) to stay on the surface of the Earth. Since this is not a straight line, we need a force which points toward the center of that circle (toward the axis of rotation of the Earth) in order to not float off into space, and spiral away from the ground beneath us. As a result, the force of gravity, which we usually think of as just holding us on the Earth, actually has to do two things: hold us on the Earth, so that we don't drift away, and also squeeze us into the ground. It is only the latter effect which causes us to feel heavy, and if part of the force of gravity is 'used up', keeping us on the ground, then the remainder of the force, the part which produces our 'weight', will appear to be less than usual.
      If we were at the North Pole, we wouldn't going anywhere, so no force would be required to hold us on the Earth, and our weight would be equal to our true gravitational weight. But if we went towards the Equator, our motion around our parallel of latitude would be faster and faster, so we would need more and more force just to keep us on the ground (up to 1/3 of one percent of our weight at the Equator), and we would therefore seem to weigh less and less, even though our true weight would always be just about the same. This is the phenomenon experienced by astronauts in orbit, which makes them feel weightless. Their speed is so great that all of their weight is used up just keeping them in orbit, so there is nothing left to squeeze them downwards. You can experience this feeling yourself by jumping off a building. While you are falling, all your weight is used in making you fall, so you feel weightless until you hit the ground. Of course, you can tell that you are falling by looking at the ground, so you know that you aren't really weightless, but for an astronaut in orbit, the speed around the Earth is so great that the round shape of the Earth makes the ground "fall" away from him just as fast as he is falling, so it doesn't actually look like he is falling.
      Since, at the Poles, you wouldn't be going anywhere, and the force required to hold you on the ground is zero, and the apparent pull of gravity is the actual pull, things would have a weight, and would fall, in exactly the way that they really do. But near the Equator, you are going around at over 1000 mph, about 1/3% of your gravitational weight is used up just holding you on the ground, and you would seem to weigh, and to fall, only 99 2/3% as much, and as fast, as at the Poles. Careful laboratory measurements can easily show that this is correct.
      To see how this works, suppose that you lie down, and let someone put a 300 pound lead weight on top of you. Regardless of where you are, the weight would weigh 300 pounds. At the Poles, where none of the weight is 'used up' keeping it on the ground, you would feel 300 pounds pressing down on you. At the Equator, where 1 pound would be 'used up' keeping the weight going around the Earth, instead of off into space, you would only feel 299 pounds pressing down on you. The actual weight is the same, but you would feel a difference of 1 pound, because of the vertical Coriolis effect. This difference produces, somewhat surprisingly, a remarkable result. At the Equator, the Earth bulges out by 1/3% of its radius, or 12 miles, compared to the Poles. The rocks beneath the Earth's surface feel the full weight of the rocks above them, if they are below the Poles, but only 99 2/3% of the full, true weight, if they are near the Equator, and they are more compressed below the Poles, so that they take up less room, and less compressed near the Equator, so that they take up more room. The effects of this compression depend upon the response of the rocks to differences in weight, and cannot be easily predicted, but over 300 years ago, Newton was able to show that, insofar as the rocks inside the Earth are 'elastic' (springy), or behave like a fluid (able to move according to what forces act on them), the Earth would bulge out by 1/3% of its radius at the Equator. It took nearly 200 years after Newton for measurement techniques to become precise enough to show, to a reasonable degree of accuracy, that the actual shape of the Earth is close to the predicted shape, but that is indeed the case.

The horizontal effect: The Coriolis Effect
      In addition to this effect, due to the vertical part of the rotational effect, there is a horizontal effect, which is usually explained by describing the motion of a pendulum.
      If you set a pendulum to swinging, the only forces normally acting on it are the force of gravity, which is downwards, and the force of the string supporting the pendulum bob, which is up and to the side. These two forces define a vertical plane, and if no other forces act on the pendulum bob, the pendulum should swing back and forth in this plane without veering to either side of the plane.
     If you set a pendulum up like this at the North Pole, you can see that it does always swing in the same way by comparing the direction of swing to the direction of the stars. It will continue to swing back and forth between the same (stellar) directions, without any change, as long as there is no twisting due to the string or its support. But because the Earth is rotating, the stars seem to gradually turn towards the West during the day, and so the pendulum, keeping the same position relative to the stars, seems to also swing to the West. In reality, neither the stars nor the pendulum are swinging to the West. The Earth is simply turning to the East underneath them. But if we "forget" this, then the motion of the stars and the pendulum seem perfectly real. Pendulums set up to demonstrate the Earth's rotation in this way are called Foucault pendulums, after the first man to do this.

The force of gravity and the tension along the line between the pendulum and its support define a plane (the plane of your screen, as you view this). The motion should be strictly back and forth, only in that plane.

If viewed from above, the motion is along a straight line. At the Pole, we can align the motion with a star, and the pendulum would always move along the line toward the star; meanwhile, the Earth is rotating to the east, under the pendulum.

If we use the rotating Earth as our reference frame, the star appears to move to the west; so the pendulum, maintaining its alignment with the star, appears to move to the west, as well. This illusion, created by using the rotating frame of the Earth as our reference, is the Coriolis effect of our rotation.

The University of Illinois' WW2010 site has an interesting, albeit all too brief movie of this effect, showing children on a playground merry-go-round rolling a ball back and forth (the Quicktime version is recommended, for quality and an audio commentary). The clockwise motion of the merry-go-round mimics the effect of the Earth's rotation, as seen at the South Pole. As seen from above, the ball moves in a straight line, from one child to the next; but in the rapidly rotating frame of the children, the ball does some very strange things.

     At the Poles, the pendulum seems to turn to the West once each time that the Earth turns under it, or every 23 hours 56 minutes. At the North Pole, where East is to your left and West is to your right, the pendulum turns around to the right. At the South Pole, where East is to your right and West is to your left, the pendulum turns around to the left. At other latitudes, the speed at which the pendulum appears to turn is different, because the top of the pendulum is being dragged around the Earth with the building that it is attached to, and so the situation is not as simple as at the Poles, but the direction of turning is still the same: to the right in the Northern Hemisphere, to the left in the Southern Hemisphere. Close to the Poles, the rate of turning is close to once a day, and the rate decreases as you approach the Equator, until it disappears completely at that location.
      In the case of the vertical Coriolis effect, as discussed above, there were two types of results:

(1) Laboratory Experiments: Things seem to fall slower and weigh less, the nearer the Equator the laboratory is.
(2) Global Results: The Earth bulges at the Equator by 1/3% (12 miles radius).

      Similarly, there are two types of horizontal results:

(1) Laboratory Experiments: Things thrown horizontally veer off to the right in the Northern Hemisphere, and off to the left in the Southern Hemisphere, faster near the Poles, and slower near the Equator, so that Foucault pendulums gradually rotate to the right in the Northern Hemisphere, and to the left in the Southern Hemisphere, faster near the Poles, and slower near the Equator.
(2) Global Results: The circulation of the atmosphere and oceans, and local weather patterns, have consistent effects due to the rotation of the Earth. In the Northern Hemisphere, winds circle around low-pressure zones counter-clockwise, and around high-pressure zones clockwise. In the Southern Hemisphere, winds circle around in the opposite direction.

      On a non-rotating Earth, if there were a region with lower than normal air pressure, winds would blow so as to carry air into that region, filling it with more and more air, until pressures were normalized. But because of the Coriolis effect, winds blowing into such a region tend to circle around it, allowing the low pressure to persist for some time. In fact, if the winds reach high enough speeds, a separate effect, called the Bernoulli effect, can actually intensify the low pressure, causing the winds to try to push in even more. But because they are rotating around the low pressure zone, if the winds push in closer, they will have to speed up, just like an ice skater pulling in their arms spins faster. In this way, the Coriolis effect transforms the initially random energy of the winds into an organized, and in some cases, remarkably fast motion (e.g., hurricanes).
      There are similar effects in the general circulation of a planet's atmosphere. Because the Sun provides more heat near a planet's Equator than near its Poles, warm air tends to rise at the Equator, cold air tends to sink at the Poles, and a general circulation tends to arise where warm air carries heat towards the Poles, and cold air carries a lack of heat towards the Equator. If the planet were small enough, there could be a single circulation pattern like this, but even on the Earth there is too much space to cover, and three circulation patterns emerge. Near the Equator and the Poles, surface winds blow towards the Equator and upper atmosphere winds blow towards the Poles, in Hadley cells, while at in-between latitudes, the winds blow in the opposite directions, in Ferrell cells.


Diagram of Hadley and Ferrell cells.

Near the Equator and the Poles, air moves toward the Equator at the surface, and toward the Poles at altitude. At mid-latitudes, air moves toward the Poles at the surface, and toward the Equator at altitude.

      If the Earth were not rotating, the wind circulation would be essentially North and South, but because of the Coriolis effect, winds veer somewhat to the right of their original direction in the Northern Hemisphere, and to left, in the Southern Hemisphere, producing "normal" wind circulation patterns such as these:


Coriolis Effects on Atmospheric Circulation
North-South motions veer to right in Northern Hemisphere, to left in Southern Hemisphere

      On Jupiter, and other fast-rotating planets, the Coriolis effect is so strong that North-South winds (of the sort on the left) are transformed into East-West winds (of the sort on the right) that are so fast that the difference in motion from regions that blow mostly to the East or mostly to the West can exceed 1000 miles per hour. Needless to say, at the boundary between such regions, very powerful storms are created. The Great Red Spot is one such storm.

Although the Coriolis effect causes motions over large distances and times to noticeably deviate from straight-line motions, motions over small distances and times, such as the motion of water in a bathroom sink, toilet bowl, or tub, are not affected, because the rotation of the Earth is too slow and its effects too small in comparison with the motions involved, to have a significant effect. For a humorous and informative look at wrong-headed applications of the Coriolis effect, visit Alistair Fraser's Bad Coriolis page.

Summary
      Someone at the surface of the Earth sees phenomena, called Coriolis effects, as a result of the Earth's rotation.
      The vertical effect is an apparent reduction in the force of gravity as we move from the Poles to the Equator, and a resulting change in the rate of fall of objects; but actually, the force of gravity is approximately the same at every latitude, and if anything is greater at the Equator than at the Poles, because of the excess material wrapped around the bulge of the Equator.
      The horizontal effect is an apparent veering to the right or left of a straight-line path by an object moving horizontally; as viewed from space, the object is actually moving in as straight-line a path as possible, given the curvature of the Earth's surface.
      In other words, Coriolis effects can be viewed as an illusion caused by the rotation of the Earth, rather than real phenomena. They appear perfectly real to an observer moving with the Earth's rotation, but illusory to an observer viewing the motion from a reference frame fixed in space.

Further Topics
      There is a whole class of phenomena, such as Coriolis effects, which could be explained by forces which produce the observed effects; since the effects are illusory, the forces invoked to explain them are also illusory. We refer to such forces as
fictitious forces; in the case of the Coriolis effect, this fictitious force is called the Coriolis force. To an observer in space, not taking part in the rotation of the Earth, the Coriolis force and its supposed effects do not exist; but to an observer on the ground, the effects seem perfectly real, and may be explained by this apparently real force.
      (more coming "soon" -- an explanation of inertial and accelerated frames of reference; fictitious forces, including the Coriolis force and the force of gravity; and more diagrams, to better explain the topics above)

(A further discussion of some of the topics covered here (or to be covered later) can be found at The Science of Physics.)