"Getting Around The Coriolis Force"
David J. Van Domelen
The Ohio State University
Physics Education Research Group
The Coriolis "force": most people know about it, but
few understand it. A simple explanation not requiring an intuitive
understanding of angular momentum is provided. Scales over which the
Coriolis Effect is relevant are also discussed.
1.0 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.
Of course, most physics textbooks which deal with angular
kinematics will have the following equation relating the Coriolis force to an
object's mass (m), its velocity in a rotating frame (vr) and the
angular velocity of the rotating frame of reference (w):
FCoriolis = -2 m (w x
The text will then either explain the Coriolis force in
terms of angular quantities such as conservation of angular momentum, or will
use the Coriolis force to illustrate the angular kinematics. Unfortunately, most
of us are not comfortable with angular mechanics. It would not be an
exaggeration to say that some students dread it. Nor can we expect students to
enter the classroom understanding the Coriolis force. Hence, whether using
physics to explain the phenomenon or using the phenomenon to explain the
physics, students are shaky on both sides of this
So, what to do? This article intends to
develop a means of explaining the Coriolis effect to people who haven't yet
grasped angular mechanics. The explanation relies on linear quantities and uses
rotational concepts infrequently.
2.0. The Basic Premises The following
principles are needed before starting the body of the explanation:
Premise 2 is probably the easiest for
students to accept, since you can draw on a globe to demonstrate that an inch is
15 degrees of longitude at one latitude and 30 degrees at another. Having a ball
or globe on hand for the explanation is generally helpful. Premises 1 and 3
require some science background, however, but should be acceptable to students
in mechanics courses.
- Newton's First Law in component form - Objects in motion stay in motion
unless acted on by an unbalanced force. A vector component of velocity will
not be changed by a force perpendicular to that component.
- Spherical Geometry of the Earth - X degrees of longitude gives you
different distances between longitude lines (in miles or kilometers) at
different latitudes, plus a few additional results of being on a sphere which
will be detailed later.
- Gravity - Objects under the influence of Earth's gravity will fall towards
(and thus orbit) the center of mass of the Earth.
- Force - In one way of looking at it, a force is anything that causes a
mass to accelerate in one's frame of reference. However, most people think of
force as "something doing something to something". The Coriolis effect is a
force in the first sense, but not in the second sense: nothing is actually
pushing or pulling on anything, the acceleration is due to the fact that the
observer is moving in a circle. From this point on, the Coriolis effect will
not be directly called a force, even though that's how it's normally
3.0. Explanation of the Coriolis Effect While
all Coriolis-based deflection can be explained using rotational concepts, a
linear explanation is simpler if you separate the effects into those in the
north/south direction and those in the east/west direction. The deflection of
objects moving north and south can be explained without invoking centripetal
acceleration, as we see next.
3.1. I Feel The Earth Move Under My Feet: North/South
Motion Note first that all points on the Earth have the
same rotational velocity, w (they go around once per
day). Also, places at different latitudes have different linear speeds. A point
near the equator may go around a thousand miles in an hour, while one near the
North Pole could be moving only a few dozen miles in an
Normally, objects in contact with the ground travel
the same speed as the ground they stand on. As a result, the Coriolis effect
generally doesn't have a noticeable effect to people on the ground; the speed of
the point you're standing on and the speed of the point you're stepping onto are
too close for you to tell the difference. Or, looking back at the Coriolis
effect equation above, if the velocity relative to the rotating frame (the
Earth) is zero, so is the Coriolis effect.
However, when an
object moves north or south and is not firmly connected to the ground (air,
artillery fire, etc), then it maintains its initial eastward speed as it moves.
This is just an application of Newton's First Law. An object moving east
continues going east at that speed (both direction and magnitude remain the
same) until something exerts a force on it to change its velocity. Objects
launched to the north from the equator retain the eastward component of velocity
of other objects sitting at the equator. But if they travel far enough away from
the equator, they will no longer be going east at the same speed as the ground
The result is that an object
traveling away from the equator will eventually be heading east faster than the
ground below it and will seem to be moved east by some mysterious
"force". Objects traveling towards the equator will eventually be going more
slowly than the ground beneath them and will seem to be forced west. In reality
there is no actual force involved; the ground is simply moving at a different
speed than its original "home ground" speed, which the object
Consider Figure 1. Yellow arrow 1 represents an
object sent north from the equator. By the time it reaches the labeled northern
latitude, it has traveled farther east than a similar point on the ground at
that latitude has, since it kept the eastward speed it had when it left the
equator. Similarly, green arrow 2 started south of the equator at a slower
eastward speed, and doesn't go as far east as the ground at the
equator...seeming to deflect west from the point of view of the ground.
3.2. Well, It Used To Be East: East/West Motion In
explaining how the Coriolis effect acts on objects moving to the east or west,
it helps to turn off gravity for a moment. Don't worry, we'll turn it back on
later, just be sure to put the lid back on your coffee.
Consider being on a rotating sphere
with no gravity. An observer who is glued to the sphere throws a ball straight
to the "east" on the globe, in the direction of rotation. Since there are no
forces on the ball, it will travel in a straight line, the tangent line shown in
Figure 2 at t=0.
Time passes, and the ball continues on its
straight line. But the observer is attached to the globe and moves around to a
new position. At this new position, the observer's definition of the "east"
direction has changed, and is no longer the same as it was at time t=0. The ball
is no longer traveling on the observer's "east" line, and, in fact, seems to
have drifted off to one side. If the globe is spinning slowly enough that the
observer can't feel the spin, then the natural conclusion would be that some
mysterious force pushed the ball off course, sending it drifting away from the
axis of rotation more quickly than it would go if it were still heading the
"correct" easterly direction.
Similarly, if the observer
throws a ball to the west at time t=0, it will seem to have been forced inward
towards the axis of rotation because the "west" line has
Now to turn gravity back on. Gravity pulls objects
towards the center of mass of the Earth, which means it cannot change an
object's velocity in the directions perpendicular to up and down. In other
words, it won't change the east/west or north/south components of an object's
Figure 3 shows a slice through the
Earth so that east points out of the page. The thick arrows show the directions
that eastbound and westbound projectiles would seem to go as a result of the
Coriolis effect in the absence of gravity. The eastbound projectile (red, upper
horizontal arrow) would seem to drift away from the axis, while the westbound
projectile (green, lower horizontal arrow) would seem to drift towards the axis.
Both of these lines have been split into components, with one component being
"up/down" and the other being "north/south." Gravity will act against any "up"
components, and the presence of the ground will act against any "down"
components, so projectiles will stay within the light blue
As a result of gravity pulling down on
objects and the ground holding them up, the remaining effect of the Coriolis
effect on objects heading east or west is to deflect them to the north or south.
In the northern hemisphere, objects heading east are deflected to the south, for
example. The Coriolis effect "pushes" them away from the axis, and gravity pulls
the object back down to the ground so that the remaining effect is an apparent
"push" to the south.
It's worth noting that this effect is
weakest at the equator, since there's no north/south components to "great
circle" motion moving east or west along the equator. And, of course, it's also
weakest at the poles, since there's no meaningful east or west motion. It turns
out that this effect is strongest at mid-latitudes.
4.0. Putting It Together: Low Pressure
Systems Now we've explained how things moving towards
the poles curve to the east, things moving away from the poles curve to the
west, things moving east curve towards the equator and things moving west curve
towards the poles. In other words, air (or anything else) moving freely in the
northern hemisphere deflect to the right, air moving freely in the southern
hemisphere deflect to the left. And this is what the result of the vector cross
products in the Coriolis effect equation says as well, in its mathematical
What does this mean for, say, weather systems?
Take, for example, a low pressure center, where there's less air than in the
area around it. If there's less air in one place than in the surroundings, air
will try to move in to balance things out.
Air starting at rest with respect to
the ground will move towards a low pressure center. Such motion in the Northern
Hemisphere will deflect to its right, as shown in Figure 4. However, the forces
which got the air moving towards the low pressure center in the first place are
still around, and the result will be a vortex of air spinning counter-clockwise.
Air will try to turn to the right, the low pressure system will try to draw the
air into itself, and the result is that air is held into a circle that actually
turns to the left. Without the Coriolis effect, fluid rushing in towards a point
could still form a vortex, but the direction would either be random or depend
solely on the initial conditions of the fluid.
The eye of a
hurricane is a clear example of fast winds bent into a tight circle, moving so
fast that they can't be "pulled in" to the center. The very low pressure at the
center of the hurricane means that there is a strong force pulling air towards
the center, but the high speed of the wind invokes the Coriolis effect strongly
enough that the forces reach a kind of balance. The net force on air at the eye
wall is a centripetal force large enough to keep the air out at a given radius
determined by its speed.
5.0. Other Results and Non-Results "Fine," you
may say, "that explains storms. But what about water going down the sink?" In
fact, this question is a good "hook" for getting students interested in the
Coriolis effect in the first place.
Because the Earth's
angular velocity is so small (360 degrees per day, or about 7 x 10-5
radians per second), the Coriolis effect isn't really significant over small
distances (As equation 1 shows, high velocity also can make a difference, but
for the purposes of this paper small distance-high speed effects will not be
considered). So, what things are likely to be affected by the Coriolis effect in
a large way?
5.1. Up In The Air Just looking at a weather system on
the nightly news gives one example that has already been addressed. Large
weather systems feature masses of air and moisture that travel hundreds of miles
and can have wind speeds reaching over a hundred miles an hour in the worst
Another example of a quickly moving object in the
sky which covers hundreds of miles is an airplane. All pilots need to have
familiarity with the effects of the Coriolis effect, since airplanes can reach
speeds much higher than even the fastest hurricane winds. Over the course of a
several hour trip, an airplane could be deflected by a significant amount if the
pilot didn't compensate for the Coriolis
Long-distance artillery may or may not be another
example of something requiring a Coriolis correction. I've seen some papers that
say it's negligible compared to the Magnus force (a result of the fact artillery
shells spin), and others that claim it is important on its
So, fast things moving over great distances can be
significantly affected by the Coriolis effect. But what about the sink?
5.2. Water Going The Wrong Way Down The Sink In a
kitchen sink, of course, speeds and time scales are much smaller than hours and
miles. Water rushing down a drain flows at speeds on the order of a meter per
second in most sinks, which are themselves less than a meter wide.
Qualitatively, there doesn't seem to be much chance for deflection.
Quantitatively, putting these numbers into Equation 1 results in an estimated
change in rotation of only a fraction of a degree per second, and a very small
fraction at that...less than an arc-second (1/3600th of a degree) per second
over the course of the entire draining of the sink, ignoring additional effects
caused by conservation of angular momentum and the like. Under extremely
controlled conditions, this can cause water to flow out of a container
counter-clockwise in the northern hemisphere and clockwise in the southern
hemisphere, but your kitchen sink is not so controlled. Things like leftover
spin from filling the sink (even when the water looks still, it's rotating
slowly for a long time after it seems to stop), irregularities in the
construction of the basin, convection currents if the water is warmer or colder
than the basin, and so forth, can affect the direction water goes down the sink.
Any one of these factors is usually more than enough to overwhelm the small
contribution of the Coriolis effect in your kitchen sink or bathtub. Research in
the 1960s showed that if you do carefully eliminate these factors, the Coriolis
effect can be observed1,2.
Water in the sink
doesn't go far enough to trigger a noticeable north/south deflection. Most
often, it simply spirals down the sink the way it went into the sink, and the
same is true of things like the famous "demonstration" of the Coriolis effect
shown at tourist traps along the Equator (especially since east/west deflection
is absent!). Maybe there's a conspiracy to manufacture right-handed sinks in the
Northern Hemisphere and left-handed sinks in the Southern Hemisphere? In any
case, don't blame it on the Coriolis effect unless your sink is the size of a
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 above explanation online, and to
Steven Carson, who pointed out the references in Nature. Finally, work on this
paper was supported in part by NSF grants NSF GER-9553460 and NSF DUE-9396205.
- Shapiro, 1962, Bath Tub Vortex, Nature, v 196, pp 1080-81 (Northern
- Trefethen, et.al., 1965, The Bath Tub Vortex in the Southern Hemisphere,
Nature, v 207, pp 1084-85
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