Q&A: The Coriolis Force

Question: You’ve mentioned the Coriolis force is a few recent posts. I’m not sure I totally understand how it works. Could you please expand on that topic? — Several Readers, Earth

Answer: Certainly. The Coriolis force is a consequence of Earth’s rotation. It’s not a real force, like gravity or friction or tension in a rope, but it’s effect is the same since it causes a moving mass to change its direction of motion. The Coriolis force is an inertial effect caused by differential rotation speed of Earth’s surface.

The graphic shows the path of a mass (m) projected to the north (or south) from the equator. Because the Earth is rotating, that projectile has an eastward speed of 1038 mph even before it is launched. It maintains this eastward speed as it moves to the north (or south) where points on the Earth’s surface are moving to the east more slowly. This causes a point on the Earth’s surface to move west relative to the projectile, and the projectile to deflect to the east. It is as though the projectile is feeling an eastward force equal to:

FC = 2m(Ω×v) where

Ω = the angular speed vector
v = the tangential velocity vector
Ω×v = the vector cross-product

FC is what physicists call a fictitious force because it arises in a rotating frame of reference where acceleration modifies the usual laws of motion. It’s similar in cause to the centrifugal force you experience on merry-go -rounds and other rotating amusement park rides.

French mathematician Gaspard Gustave Coriolis’ (1792-1843) figured out the mathematics of FC. His most famous paper was entitled “On the equations of relative motion of a system of bodies,” and an earlier paper was called “On the principle of kinetic energy in the relative motion of machines.” Coriolis is credited with extending the concepts of work and energy to the rotating reference frame and applied his research to machines such as waterwheels.

One example of the Coriolis force has been observed at least as early as 1651. Military officers noticed that in artillery practice their cannon balls always landed to the right or left of where their calculations predicted. Their observations were correct, but their calculations were not allowing for FC. Cannon balls are shot over long enough distances that, while they are in the air, the Earth rotates beneath them. Once the military had the formula for FC it was possible to achieve far greater accuracy.

Intercontinental ballistic missiles (ICBMs) can be launched on a trajectory that takes them over the North Pole. These trajectories experience an FC that varies in direction as the missile’s path transitions from northward to southward. The calculations are complex, but easily done by computers. Modern ICBMs can be accurate to within 100–400 meters, depending on the model and launch platform.

Ocean currents like the northward-flowing Gulf Stream are also affected by FC. Part of its deflection to the east is a results of continental land masses, but there is also a component caused by FC. In both the Atlantic and Pacific, there are large gyres that rotate clockwise in the northern hemisphere and counter-clockwise in the southern hemisphere in response to FC. Check out this map.

But the most immediate impact that FC has on all of us is through large weather systems. Low pressure systems rotate counter-clockwise north of the equator and clockwise south of the equator. High pressure systems do the opposite. It’s not the same rotation as ocean gyres, because of the air flow direction into and out of lows and highs.

And finally, here’s one thing that FC does not affect: the flow of water down a sink or toilet drain. You may hear about this in popular media, but it’s been totally debunked. If the water in your drain seems to obey this “rule” it’s by chance, and governed more by residual water motion or the geometry of the drain.

Next Week in Sky Lights ⇒ Beach Mushrooms

Q&A: How Fast Earth Spins
Beach Mushrooms

2 comments on “Q&A: The Coriolis Force”

  1. Coriolis Force brings flashbacks. 50 years ago, I was teaching air navigation at the Air Force Academy.

    The stars can be used to determine your location on earth using a sextant to measure the star’s angle above the horizon. In an aircraft there is no visible horizon to use as a reference point. Aircraft sextants have a bubble similar to that in a carpenter’s level. The aircraft sextant’s bubble is deflected by Coriolis force. The position correction we made was 3 nautical miles to the east.

    1. I did not know of the Coriolis force acting on bubbles, but it makes perfect sense. Of course, the force actually acts on the fluid in the bubble level (which has more mass than the bubble of air). So the fluid would shift as expected in response to the force, and the bubble would move in the opposite direction. Thanks for the additional insights!

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