The Mysterious Coriolis Effect

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This page last updated on 02/28/2014.

Copyright 2001-2014 by Russ Meyer


Gaspard Gustave de CoriolisWhen I was in Junior High, I learned about the Coriolis effect in science class.  The Coriolis effect bends the path of wind (or ocean currents) into curves.  It's what makes hurricanes rotate like huge pinwheels.  It is caused by the rotation of the Earth.  That was pretty much the whole 8th grade science class description of the thing.  So, just exactly what is the Coriolis effect?  How does the rotation of the Earth cause it?  What is this thing scientists call the Coriolis force?

I have pondered the mysterious nature of the Coriolis effect since 8th grade, 29 years!  I've thumbed through numerous science books in a vain attempt to find a simple explanation.  I've discovered that science books either:

  • Tell you to take it on faith that the effect exists.  (Implying that it's too complex to discuss at the moment.  With a wave of the hand, the author walks right by.  Net result...no comprehension; the Coriolis effect is mysterious and inscrutable.)
     
  • Smother you with pages of complex calculations.  (Implying that it's too complex to describe with a simple model.  Net result...no comprehension; the Coriolis effect is mysterious and inscrutable.)

After years of head scratching, I finally figured it out for myself...no thanks to any of those science books!  I simply had a flash of insight one day.  I was in the shower watching the water swirl down the drain, pondering the Coriolis effect for the umpteenth time when it hit me!  Guess what I discovered...the explanation is really, really simple!  You know, I think a lot of those science books don't bother with an explanation because the authors don't really understand the Coriolis effect in the first place!  The other books, the ones with reams and reams of equations, seem to be written by authors that don't have an intuitive feel for the phenomenon...they only understand it on some mechanical level with a blizzard of equations.

An Example of the Coriolis Effect

Common, everyday, plain ol' wind provides a fabulous example of the Coriolis effect.  The pressure gradient between centers of high and low pressure causes most wind.  If the Earth didn't rotate, the wind would blow directly from the high to low pressure areas in a straight line.  However, since the Earth is actually rotating, Coriolis effects cause the wind to instead follow a curved path.  In the Northern hemisphere, the Coriolis effect causes winds to swirl counter-clockwise around low pressure centers and clockwise around high pressure areas.

 

The Rotating Earth

To understand the Coriolis effect you only have to appreciate one simple thing...on a rotating body, the velocity of any particular point on the body depends on the distance of that point from the axis of rotation.  Think of a bicycle wheel.  As it spins, you notice that a point on the hub moves around very slowly, but a point on the rim is going really fast.

That same thing happens on the Earth.  Someone standing on the equator is moving about 1000 MPH faster than someone standing at the North pole.  The guy at the equator has to circle the circumference of the Earth (24,901 miles) in one day.  He's got to hustle to make it!  The guy at the North pole only has to rotate around in a little tiny circle and he's got all day to do it.  (So he's going what...maybe 5 feet per hour?)

Now, let's just look at three little slices of the surface of the Earth.  We'll take a little circular strip from around the equator, another from around the North pole, and another from somewhere about half-way between (strips A, B, and C below).  Each of these little strips is like a Conveyor Belt.  Conveyor Belt A moves very slowly, belt C moves about 1000 MPH, and belt B moves at a speed somewhere in between...let's just say 500 MPH.

If you lifted these Conveyor Belts and set them next to each other, you'd see something like this:

 

Now, let's say you put a pistoleer on Belt A.  His task is to shoot at a target you've placed on Belt B, but only when the target enters his sights, directly opposite him.  What will happen to the bullet he fires?

______________________________________________________________________________________________________

Time 1:

______________________________________________________________________________________________________

Time 2, FIRE!:

______________________________________________________________________________________________________

Time 3:

______________________________________________________________________________________________________

Time 4, MISS!:

______________________________________________________________________________________________________

 

If you had been sitting at the target, watching the bullet, it would have looked like it angled away from you to the left, like this:

 

In fact, the bullet was going in a straight line, but you had a lot of speed and pulled away, putting significant horizontal distance between you and the bullet before it went by.  The very same thing happens when a bullet is fired from Belt C towards a target on Belt B.  The result looks like this (for the sake of brevity, I'm going to draw it in a compact way this time):

 

Just as before, if you had been sitting at the target, watching the bullet, it would have looked like it angled away from you, but this time to the right.  That's because the bullet was moving much faster to the right than the target, causing it to offset a significant horizontal distance to the right by the time it passed the target:

 

When you aim straight at something and pull the trigger, you don't expect your bullet to fly off to the left or right like this.  It's supposed to go where you point the pistol!  The thing making the bullets look like they are deflected is the speed difference between the target and the pistol.  By the time the bullet gets to where the target was, that speed difference has either carried the target out of the way or has moved the bullet way off to one side...it depends on your point of view.

The Coriolis Effect

This illustration with the pistol and target is exactly analogous to the Coriolis effect.  It's that simple.  In the original example of high and low pressure areas, the high pressure area is like the pistol and the low pressure area is like the target.  Air molecules are fired from the high pressure area to the low pressure area, but the points on the Earth where these pressure centers are stationed are moving at different speeds.  The air molecules actually miss the low pressure center and this sets up a rotating circulation.

Air flowing into a low pressure system from the North misses the low pressure center because that low pressure center is carried further East by the time the air gets there.  Air coming from the South again misses the low pressure center because the air itself has been carried further East by it's greater speed.

This illustrates why air circulates counter-clockwise around low pressure centers.  By making a few more drawings, it becomes clear why air circulates clockwise around high pressure areas; it's also easy to see why those circulation patterns are reversed in the Southern hemisphere (lows circulate clockwise, highs counter-clockwise).  Try drawing a few diagrams and see for yourself.  Ah, the mysteries of Coriolis effect revealed at last!

Of course the pistol model is pretty crude.  In the real world, the air molecules don't just get fired at the low pressure center once; their course is continually modified as they swing around the pressure center.  It's as if the pistoleer gets a chance to catch the bullet and re-fire it moment by moment.  This produces a nice, spiraled path for the air molecule.

Air directly East or West of the low pressure center experiences no Coriolis effect because both the low pressure center and the air itself are moving at the same speed (they're on the same Conveyor Belt).  You would think the air would fall directly into the low pressure center, right?  In the real world it doesn't do that, it continues the original curved course.  This is because when air mass arrives at a station exactly East/West, it still has significant Northerly/Southerly momentum.  This momentum carries the air mass past the East/West position.  It swings to a position North/South of the East/West line, and the Coriolis effect again takes hold.

Note that the degree to which the bullet (or air mass) is apparently deflected depends on the speed difference between the pistol and the target.  If the speed difference is high, the bullet will appear to deflect sharply.  If the speed difference is low, the bullet will only seem to be deflected a little.

An Interesting Phenomenon

Just as described in the previous paragraph, the greater the speed difference between two points on the Earth, the greater the Coriolis effect.  If you calculate the speed of the surface of the Earth at different latitudes, you find that it is related to the cosine of the latitude, like this:

Note that the actual equation for the surface speed of the Earth in miles per hour for a given a latitude is:  (circumference of the earth in miles / 24 hours) * COS(latitude) = (24901/24) * COS (latitude) = 1037.5 * COS(latitude)

However, the magnitude of the Coriolis effect is dependant on the speed difference, so lets see how the speed changes with latitude.  This speed difference is actually related to the sine of the latitude.  Below is a graph depicting this:

On this second chart, notice the difference in speed between adjacent latitude belts.  The speed difference is small at the equator (0) and quite large near the pole (90).  This means the Coriolis effect is small at the equator and increases to a maximum near the poles.  So, one can expect wind to flow in nearly straight lines from high to low pressure near the equator.  Near the poles, you would expect to see much more significant curvature of the wind streams.  Hmmmm...that's an interesting result.

Now consider this satellite image of a large low pressure system over North America:

Large low pressure systems are often not circular in shape.  In the Northern hemisphere they typically resemble a gigantic number 9.  Notice the humongous low pressure system in the middle of the photo...it looks like a big 9.  This is caused by the difference in the amount of Coriolis effect across different latitudes.  The Coriolis effect is smaller in the Southern part of the low pressure system, so the air mass is bent less and travels in a straighter line.  North of the low pressure center, the air mass is bent more strongly by the greater Coriolis effect felt at that latitude.  The air mass follows a tighter curve.  This gives rise to the characteristic 9 shape.  Small low pressure systems that do not span a wide range of latitudes are typically more round in shape, as you would expect.

The Coriolis Force

The Coriolis effect affects every moving object on the surface of the Earth.  Whenever scientists and engineers have to deal with objects moving over the surface of the Earth, they have to consider Coriolis effects.  For example, Coriolis effects have to be taken into account when firing artillery.  If you didn't account for it, the 2000 lb shells from your battleship would fall harmlessly into the sea while your smarter, Coriolis-effect-aware opponent blasted the stuffin's out of you.  So, this issue comes up frequently and it's important.

The only problem is, in the raw, it's awkward to take Coriolis effects into account during calculations.  So, scientists and engineers came up with a handy, easy-to-compute shortcut for accounting for Coriolis effects.  They call it the Coriolis force.  It's a fake force...it doesn't really exist.  It just makes stuff like like artillery trajectory calculations easier to do and more accurate.  Specifically, the Coriolis force is:

Fc = 2MΩV sin(Θ)

Where:     Fc = Coriolis force in the horizontal plane
                M = Mass of the object
                Ω = Angular velocity of the Earth (360 degrees per 24 hours)
                V = Velocity of the object over the surface of the Earth
                Θ = Latitude in degrees

Notes:

  • The Coriolis force acts at a right angle to the direction of motion of the object.  It pushes the object to the right in the Northern hemisphere and to the left in the Southern.
  • There is also a vertical component to the Coriolis effect.  It varies with the cosine of the latitude, but that is beyond the scope of this article.

When calculating the trajectory of the wind, an ocean current, or an artillery shell, this force is applied like any other force acting on the mass.  It neatly accounts for the effect of the rotation of the Earth on the apparent trajectory of the mass.

This force was originally defined by Gaspard Gustave de Coriolis, a French mathematician, in 1835, after whom the Coriolis effect is named...of course.