The Coriolis Force

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Coriolis Effect

Recall that we demonstrated the consequences of the pressure gradient force using a two-compartment water tank. In that setup, water flowed directly from high pressure to low pressure in a short amount of time. On smaller scales, like when you let the air out of a balloon, air behaves similarly, moving directly from areas of higher to lower pressure. But on the much larger scales of high and low-pressure systems, things get more complex—air doesn’t flow directly toward the low pressure. For example, a hurricane is a low-pressure storm – air doesn’t immediately flow to the center but “spins” around the storm center.

OK, you're probably asking, “What’s happening here?” The answer lies in the Coriolis force, an “apparent” force that comes into play because of the Earth’s rotation. As our planet rotates eastward, this force influences the movement of air over large distances. Named after the French engineer and mathematician Gustave Coriolis, the Coriolis force wasn’t originally tied to Earth’s rotation. Coriolis discovered it while studying the rotation of machine parts, but it turned out to be key in explaining how air moves in our atmosphere.

So, how does the Coriolis force come into play in the atmosphere? Let's consider two points at the same longitude, one at latitude 40 degrees north (we'll call Point N) and the other at 20 degrees north (Point S). 

Because the latitude circle at 40 degrees north is noticeably smaller than the latitude circle at 20 degrees north, Point S must move eastward faster than Point N because it must travel a greater distance around the equatorial circle during one 24-hour revolution of the earth. Indeed, Point S moves at approximately 900 miles per hour, while, at 40 degrees North latitude, the eastward speed of Point N (and all other points at 40 degrees north) is about 800 miles per hour. For the sake of reference, the eastward speed at the North Pole is zero.

Peculiar things happen when points on the earth's surface move at different speeds as the planet rotates on its axis. Suppose a projectile is launched directly northward from the equator toward latitude 40 degrees north. The projectile retains its great eastward speed as it starts its northward journey. With each passing moment, the northward-moving projectile moves over ground that has an eastward speed less than its own. In effect, the projectile surges east ahead of the lagging ground below.

To an observer on the launching pad, the projectile appears to swerve to the right as a natural consequence of our spherical, rotating earth.

Launching the projectile from north to south results in a similar rightward deflection relative to the observer on the launching pad at 40 degrees north. The projectile, by retaining much of its original eastward speed of about 800 miles an hour, moves progressively over the ground with faster eastward speed. In effect, the projectile falls behind the ground below, lagging increasingly to the west. To the observer on the launching pad at latitude 40 degrees north, the projectile again appears to deflect to the right. The bottom line is that no matter what direction the observer launches the projectile, the deflection will always be to his or her right in the Northern Hemisphere.

Now that we've seen how the Coriolis force causes deflection in the Northern Hemisphere, let's apply the same logic to the Southern Hemisphere, where the Earth's rotation has the opposite effect. I can make similar arguments for the Southern Hemisphere by first noting that if an observer in space looks “up” at the South Pole, the sense of the Earth's rotation appears to be clockwise, which is the opposite of the counterclockwise sense an observer gets while looking “down” at the North Pole. You can contrast the two in this animation, showing each perspective. Thus, deflections due to the Coriolis force in the Southern Hemisphere are to the left of the observer.

I've used an object moving north-south to demonstrate the impacts of the Coriolis force because I think it's the easiest to visualize. But, rest assured, Coriolis deflections to the right in the Northern Hemisphere (left in the Southern Hemisphere) occur regardless of the direction of motion. Coriolis deflections even occur for objects moving due east or due west, but I'll spare you the explanation (it's more abstract and harder to visualize than the north-south case).

Coriolis Force Effects (and Myths)

I emphasize that the Coriolis force is not a true force in the tradition of gravity or the pressure gradient force. It cannot cause motion. Rather, it is an apparent effect that simply results from an object moving over our spherical, rotating planet. The Coriolis force does not discriminate, either. Indeed, no free-moving object, including wind and water, is exempt from its influence. Given enough time, the Coriolis force causes air to move 90 degrees to the right of its initial motion caused by the pressure-gradient force.

However, the magnitude of the Coriolis deflection depends on several factors. These factors depend on 1) the latitude of the moving object, 2) the object's velocity, and 3) the object's flight time. Its impact on air movement is clear because air moves over long distances for long periods of time. But, what about the impact of the Coriolis force on shorter events that happen on smaller scales? You may have heard that the Coriolis force determines the rotation of water swirling down a drain, or perhaps you've heard that the Coriolis force has a big impact on sporting events (like a baseball thrown from the pitcher's mound to home plate). Are these things true?

To begin to answer these questions, let's see how these three factors impact the magnitude of the Coriolis force:

• the magnitude of the Coriolis force increases with increasing latitude (closer to the poles) and is zero at the equator.
• the magnitude of the Coriolis force increases with increasing velocity of the object (or air parcel)
• the magnitude of the Coriolis deflection increases with increasing flight time (for the velocities typically observed in nature, a flight time of minutes to hours is typically required to observe any deflection at all)

So, what's the upshot of these factors? Well, you typically cannot observe the Coriolis deflection of water emptying from a drain (the speed is too slow, and the time is too short), for starters. This is also true of water swirling down a toilet bowl. Water circulates in a certain direction because the basin is designed to move water in that direction (as is the case for toilets), or the swirling water is simply residual motion left over from filling the basin. Sorry, Simpsons! The Coriolis force only becomes noticeable over long distances or extended periods of time—like in atmospheric circulation patterns, ocean currents, or large-scale storms.

I point to these specific examples because they are often misunderstood in popular culture. Many online videos claim to show the Coriolis Effect via water draining out of a basin, such as this video taken in Equatorial Kenya (4:09 minutes).

Video: The Equator Water Experiment (4:09)

This “experiment” has numerous problems (like using a different bowl in each case, for example), but the water draining from these small bowls occurs over too short a time for the Coriolis force to have a noticeable effect. Furthermore, at very low latitudes (right near the equator), remember that the magnitude of the Coriolis force is practically zero! Such video demonstrations are full of nonsense and bad science.

What about objects that move faster? I'll spare you the math, but let's see what the Coriolis force does to a 100 mph fastball thrown from the pitcher's mound to home plate at Citizen's Bank Park in Philadelphia, Pennsylvania (near 40 degrees North latitude). At that speed, it takes the pitch about 0.4 seconds to reach home plate. Using these values, the Coriolis deflection is only 0.39 millimeters (0.015 inches)! That's far too small for anyone to see with the naked eye (or for any hitter to try to account for). That is why pitchers must rely on different grips and spins to fool hitters. How about a bullet fired at a long-distance target from a competition rifle? If we assume we're at 40 degrees North again, a bullet traveling 800 meters per second over a distance of 1,000 yards (0.57 miles) would have a flight time of 1.14 seconds and a Coriolis deflection of just 2.22 inches.

The “take-away” point here is that although the Coriolis force affects all free-moving objects, these effects can be really small (perhaps undetectable), unless the speeds are very great or the travel time is long. Atmospheric motions with respect to the climate have the advantage when it comes to the latter because air moves over long distances for long periods of time.