A (Hopefully) Simple Explanation
of the
Coriolis Force *
* and the centrifugal force, along the way

Dave Van Domelen
Kansas State University
Physics Education Research Group

Last revised 1/13/08

Abstract
 Most people have heard of the Coriolis force, but not many really can say they understand it. Most existing explanations require an intuitive understanding of angular momentum, which is no help at an introductory level. This piece is an attempt to explain the Coriolis force without invoking any equations or complicated concepts.

Introduction and Motivation

At some point in their lives, most people hear about the Coriolis force, whether in reference to weather patterns, sea currents or, most prosaically, which way water flows down the sink. Unfortunately, while many have heard of it, few understand it well enough to explain it without resorting to vector equations. And textbooks will generally either go straight to the equations, or not really explain it at all.

First, a bit of terminology. The Coriolis force is actually only part of the overall effects of being in a rotating system, a result of how the math was worked out. So I'm generally going to talk about frame effects rather than Coriolis in specific, because the distinction between what parts are or aren't Coriolis is sometimes confusing and not really important for this explanation.

So, what to do? This article intends to develop a means of explaining the Coriolis effect (and the overall frame effects) to people who haven't yet grasped angular mechanics. This explanation relies on linear quantities and uses rotational concepts infrequently.

The Basic Premises

There's really only three things that really need to be established right now, although there will be a few other concepts that will creep in later when we cover rotating spheres.

1. Newton's First Law in component form - Objects in motion stay in motion unless acted on by an unbalanced (or "net") force. A vector component of velocity will not be changed by a force perpendicular to that component. In other words, if you shoot something north, an eastward-directed force won't change the speed at which that thing goes north.
2. Assumption of "firm ground" - We tend to think of our point of view as being somehow special, or at least stable. "Forward" should stay forward, and anything that alters that must be the fault of some force or another. For instance, if we throw a ball forward, it will start to go downward as well, and we say this is due to the force of gravity.
3. Frames of Reference - And here's a really important bit. The assumption above can break down when the ground under our feet is actually moving. So be sure to read this page before you move on!

Two-Dimensional Frame Effects

Okay, let's start out simple. Why does standing on a rotating object cause mysterious forces to appear? The short answer is that our assumption of firm ground is incorrect, and what we consider to be "forward" or "to the left" changes as we spin around. For the long answer, click here.

Frame Effects on a Sphere

Now, without worrying about exactly why things stay on a sphere (a mix of gravity and the ground stopping you from falling too far), we tackle the more complicated task of looking at the Coriolis and centrifugal forces on the surface of a rotating globe like the Earth.

• Movement on a Globe - Before looking at a spinning globe, it's a good idea to take a moment to consider how things move on a sphere that isn't spinning, because this can cause some weirdness on its own.
• North-South Deflection - A bit more straightforward than East-West deflection, a simple matter of how the speed of the ground below a moving object changes as it moves towards or way from the equator.
• East-West Deflection - This is a lot harder to explain, and is the reason this is my third major stab at explaining the Coriolis force...the previous two times both had flaws (although the second one's flaws took nearly a decade to be pointed out).

Putting It All Together

Now that the basics have been covered, what is it good for? Keep in mind, though, that on the Earth, the maximum acceleration due to Coriolis and centrifugal forces will each be about 1/300th the strength of gravity. So if there's any other forces involved that are comparable to gravity (like friction between your feet and the ground), there's a good chance frame effects will wash out.

• Weather - The first time you heard the term "Coriolis force" was probably in reference to masses of swirling air forming weather patterns. Unfortunately, the Coriolis force is only a part of why air moves the way it does, but I'll at least try to explain one mystery here.
• Navigation and Aiming Issues - If you're traveling far enough, or shooting an artillery shell far enough, you have to worry about frame effects too.
• Water Going Down The Sink - While experiments in the 1960s1,2 showed that if you're really careful about eliminating "noise" factors you do indeed get water going down the drain different directions in the Northern and Southern hemispheres, it's not likely to happen in your sink at home.
• Spin On A Space Station - In freefall or zero gravity situations, you can spin a ship or station to simulate gravity. But when you do, frame effects become an issue. And here, frame effects force could be quite big compared to other forces you encounter, unlike on Earth.

Acknowledgements

Thanks to the readers of the Usenet newsgroups alt.fan.cecil-adams and misc.education.science for asking the questions which inspired the author to devise an explanation for the Coriolis effect. Thanks also to Donald Shabkie, who pointed out the importance of the Coriolis effect to aviators after seeing the original explanation online, to Steven Carson, who pointed out the references in Nature, and to Cleon Teunissen who pointed out some problems with the second version and inspired me to take another whack at the problem. Finally, work on the earlier versions of this explanation was supported in part by NSF grants NSF GER-9553460 and NSF DUE-9396205.

Notes:

1. Shapiro, 1962, Bath Tub Vortex, Nature, v 196, pp 1080-81 (Northern Hemisphere)
2. Trefethen, et.al., 1965, The Bath Tub Vortex in the Southern Hemisphere, Nature, v 207, pp 1084-85
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