Monday, February 2, 2015

The Coriolis force and a bit of equatorial flimflam

Got by Mail from Jearl Walker


You have spent a lifetime on a rotating planet but the only frequent and obvious clues about the rotation are the apparent motion of the Sun during the day and the stars and Moon during the night. Otherwise, the rotation is not noticeable. However, there is one common feature that you probably have heard about. Because of the rotation, water will swirl in the counterclockwise direction when draining from a bathtub in the Northern Hemisphere and in the clockwise direction in the Southern Hemisphere. Right at the equator, on the line separating the two hemispheres, the water will drain without swirling.

coriolis force on earth

Here is a video proof of these draining results … well, the video seems to prove them and with stunning ease. The demonstrator first drains water from a small tub placed right on the equator, marked with stones as you can see. There is no swirling. Then she moves the demonstration a short distance south of the equator, and the water drains with clockwise swirling. Finally she moves the demonstration a short distance north of the equator, and the water drains with counterclockwise swirling.

However, what you see in the video is at best a magic trick and at worst a scam. Before I explain the video, let me set you up about the physics of a strange effect due to Earth’s rotation.

Because we rotate along with the ground, there seems to be a force called the Coriolis force that can cause a deflection in material (such as water) that moves over Earth’s surface. The deflection occurs because the speed of the ground around Earth’s rotation axis differs with latitude. The speed is greatest at the equator. If you stand there, you, the ground, and the air are moving eastward with speed of about 1000 miles per hour (1600 kilometers per hour) around a huge circle every 24 hours. If you stand at a higher latitude, you will travel eastward around a smaller circle every 24 hours, so the speed is less. The greater the latitude, the slower the eastward speed.

Suppose you had a very slippery ice lane that extended northward from, say, the middle of the United States. Send an ice puck northward along the center of the lane. When you release it, the puck has a certain speed northward --- say, 5 meters per second. It also has a large eastward speed because of Earth’s rotation.

As the puck moves northward, its eastward speed does not change because it is not attached to the ground but the eastward speed of the ice lane beneath it, which is attached to the ground, steadily decreases. If we watched this process from space, we would see that the center of the lane fails to keep up with the puck as they both move eastward. However, from the ground view, we interpret the situation differently --- the puck would seem to be deflected to the right, away from the center line and toward the right side of the lane. This would be strange because there is no apparent force causing the deflection. That imaginary force is the Coriolis force.

This rightward deflection is easier to see on a rotating merry-go-round instead of a sphere:

If the merry-go-round rotates counterclockwise, the strange deflection is rightward. Clockwise rotation gives a leftward deflection. In the Northern Hemisphere, there is rightward deflection on flowing air and water. In a large storm system, such as a hurricane, air flowing toward the low pressure center (eye) from any direction is deflected rightward, setting up a counterclockwise rotation. In the Southern Hemisphere the deflection is leftward and the storms swirl clockwise.

According to popular belief, the same deflection and swirling should occur in a draining bathtub. However, any Coriolis deflection of the water moving toward the drain is so tiny that the turbulence already in the water dominates the drainage, and it can cause swirling in either direction. If you give the water near the plug a clockwise swirl with your hand and then pull the plug, the water will drain while swirling clockwise. A counterclockwise swirl with your hand results in a counterclockwise swirling. If you let the water stand for a while, the turbulence can die out and then you might have a shot at seeing the Coriolis effect. For a large tub, the water needs to be undisturbed for at least a day.

How does the woman pull off the Coriolis scam? She uses a small tub with only a bucket-full of water, puts it on the equator, and then leaves the water undisturbed for a while to get rid of any turbulence. When she pulls the plug, the water flows directly to the drain and out. Then she moves the demonstration to the south. The Coriolis force and deflection are zero exactly on the equator. At the new location they are so tiny that they can be approximated as being zero and absolutely cannot affect the water drainage.

So, how does she get the anticipated clockwise swirling? She pours in the water on the left side of the tub so that it swirls clockwise around the tub. The swirling near the surface and side walls quickly decreases but the swirling near the center remains. A few seconds later, after she pulls the plug, the swirling becomes apparent, especially when she throws in the floaters near the top of the swirl.

When she moves the demonstration to the north side of the equator, she pours in the water on the right side of the tub so that it swirls counterclockwise. It is still swirling that way when she pulls the plug and throws in the floaters.

Who thought of this trick? I don’t know but I bet it was a physics student who knew about the Coriolis force from class and who needed some extra money from the tourists.

My favorite demonstration of the Coriolis force is already at the FCP site. A man pours tea from a container into a cup while standing on a rotating platform. From practice the man has learned to anticipate the strange deflection of the falling tea stream so that he has the cup in the correct position to catch the tea. Moreover, he can catch the tea while spinning in either direction. This man has an intuitive feel for the Coriolis effect.

When bullets or artillery shells are fired over a long range, Earth’s rotation during the object’s flight must be taken into account. Here is a video that shows the effect on rifle shots at targets at a distance of 1000 yards (914 meters). When the target is directly eastward, the bullets hit higher than center (bull’s eyes) because Earth’s rotation toward the east moves the target downward during the flight. Shooting westward, the bullets hit low.

If you have the time, here is a 1960 movie about frames of reference that move relative to each other. I remember very little about my high school days (far too much teenage angst clouds my memory), but I distinctly remember this movie. In fact, it was probably one of the reasons I went into physics.