In 1835, French engineer-mathematician Gustav-Gaspard Coriolis described a phenomenon of bodies moving in a rotating frame of reference. He showed that an object in said reference will undergo an apparent deflection from its intended path, and that this 'Coriolis' effect must therefore be considered when attempting to apply Newtonian laws of motion to rotating coordinate systems. Ostensibly, such an object curves, when in actuality this is not the case. One can observe the Coriolis effect most easily when examining an object in a longitudinal path of motion from a fixed frame of reference. On earth, for example, an object moving along a north-south path will undergo an apparent westward deflection while in the northern hemisphere, and eastward deflection while in the southern hemisphere. There are two reasons for this: 1) the rotation of earth is eastward, and 2) at the north and south poles tangential velocity to the earth is essentially zero, but as one approaches the Equator, said velocity increases attaining a maximum at the equator. In other words, things attached to the earth move faster at the equator than they do at the poles.

Therefore, if one were to fire a projectile from the equator toward the North Pole, its path would be deflected toward the east. If that projectile were fired from a point at North Pole to a point on the equator directly south of the North Pole, an observer in a non-inertial frame of reference would see a deflection to the left. This type of displacement occurs regardless of which direction one might fire the projectile. There are three things to consider about a Coriolis deflection: 1) motion of the object, 2) motion of the coordinate system, and 3) and the longitude of this system. The Coriolis effect is also noticeable when one drops an object (ignoring wind, air friction, etc.) toward the earth. This object will always land east of its radial path toward the target directly beneath it.

Many believe that some mysterious ‘Coriolis force’ causes this deflection. The Coriolis force is fictitious, much like its cousin centrifugal force. It is perceived by an observer outside the rotating frame of reference. In a non-inertial frame of reference, the motion of an object appears to undergo acceleration without any applied force, but how can this be if we know that F = ma? There is no force acting on the object, yet it appears to accelerate. Solving for a, therefore yields nonsense:

0 = ma

a = 0

It is therefore necessary to apply to this situation an equation that describes an inertial force. As it turns out, the scalar quantity by which the object misses its 'intended' target is given by:

s = wvt²

where w equals the angular speed, v equals the difference in the velocities of the points between which the object passes. The displacement, s, is perpendicular to vector v, and the acceleration of the mass is:

a_cor = 2 wv

The Coriolis effect has applications in astrophysics, stellar dynamics, meteorology, physical geology, oceanography, and atmospheric dynamics, but it is especially applicable to toilets-or so we thought. We will be studying the Coriolis effect through observation of a toilet-like apparatus.

In a common household drainage system, we do not have the benefit of huge inertial forces and large time scales. Everything is smaller, and the Coriolis deflection, which incidentally can be described as a vector quantity of acceleration, is barely as big as a few microns per second squared. In an ordinary sink, this deflection could only reverse a spin of about one rotation per day. In other words, there will not be any visible deflection due to the Coriolis effect unless the water in the vessel is stationary or barely moving.

Since the dawn of time, man has yearned to know which way liquids drain and why, yet he has been led astray by fallacies concerning toilet-drainage. This leads to my question what are the common misconceptions about the Coriolis Effect and how can I employ scientific experiments to clear them up and show the world the truth? Also, what really makes liquids drain the way they do in our bathtubs and kitchen sinks? We shall solve this mystery so that the world can finally be at peace.

In a carefully controlled environment within the Northern Hemisphere, water will drain counterclockwise. I will attempt to control the variables such as temperature, frictional effects with the walls of my drainage device (a highly technical apparatus consisting of a bucket and a funnel), and waiting several hours before draining in order to reduce pre-existing spin. We will attempt to discover whether we can defy the Coriolis effect through manipulation of the liquid.

While watching water spin down a toilet, one admires the spectacular dynamics of flushing-mechanics at work. It's like being inside joy, as if joy were something tangible. It is this awe that has driven us to study the Coriolis Effect. How did we proceed to do this? Doubtless, it is a story worth telling.

Fate was against us that night as we attempted to conceive a home-made toilet, but we persevered, knowing that our journey of much experimentation and data collection had to begin with that first crucial flush. We knew that if we could build it, people would come from the outlying suburbs of Tualatin to enrich themselves with knowledge about the fantastic mystery of the Coriolis Effect. We needed a bucket, and yes, a funnel in order to realize our dreams. We cut a hole in the bottom of the bucket, attached the funnel to the bucket with the finest waterproof tape that $3.49 can buy, corked the opening at the bottom, filled the apparatus with water, and celebrated our masterpiece of toilet-engineering. However, the success of the device was fleeting. The sleek cylindro-conical design was not prepared for the contingency of leakage. The tape had failed us and water leaked out of the device like the tears of those who had assembled it. We thought that perhaps we had used the wrong kind of tape, so we tried others. Each one failed more spectacularly than the last. Then came our savior: all we needed was caulk. Caulking the base provided a watertight seal worthy of Swiss craftsmanship. We were ready to begin.

First, we needed to test the assumption that water will always drain with an anti-clockwise spin in the Northern hemisphere. To do this we set up two trials. The first required allowing the water to settle for several hours before allowing it to drain. This was in order to eliminate pre-existing spin. We placed a small piece of buoyant material in the water so that we might observe spin more easily than we would by watching only the water.

For the second trial, we wanted to test whether the effect could be defied. So we set the water in the apparatus spinning in a clockwise fashion. The results of these experiments appear in the data section.

Finally, many people believe that the curvature in the path of the water is a result of a 'Coriolis Force'. Adhering to Newtonian Laws of Motion, we must, however, conclude that these people are wrong. How do we prove it through experimental data? It is the contention of the educated physicist that the Coriolis force is fictitious, much like its cousin centrifugal force. It is perceived by an observer outside the rotating frame of reference. Theoretically, if the earth were not rotating, water would drain from the bucket from gravity radially toward the center of the earth without causing any spinning effects, but since the earth does rotate, it causes a slight deflection. We knew that if we could show that there was no real acceleration, then, by F = ma, there could be no real force. So what we decided to do us suspend the bucket with rope above the floor and affix it to a rotating device. We attempted to get the entire combined mass of toilet and water spinning counterclockwise at the same rate so as to see whether this acceleration really existed. This, as the reader will see, proved to be a waste of time.

The result of the first experiment was successful, as we were able to observe the small mass we placed in the water rotating in an anti-clockwise direction. As the water drained to the level of the funnel, the distance the object was from the center of the bucket decreased and the object underwent an apparent acceleration until it was flushed out the bottom. We tried this multiple times, each time receiving similar results. There was, however one unexpected result of this experiment. After several trials, the object we were using underwent sedimentation, falling through the water as it was simultaneously flushed out of the apparatus. We assumed this was because the material must have been semi-porous, becoming saturated with water and eventually dense enough to lose its buoyancy. We believe that because of its increased density, the object was less affected by the spinning water. This was apparent because while it was falling through the water, it did not seem to rotate with the water, but rather follow a vertical path downward straight toward the opening. We attempted to recreate the fluke, but never quite observed the same result. From this we concluded that either: 1) there were clockwise currents beneath the surface of the water that hadn't died down before we did the experiment which were able to cancel out the natural counterclockwise rotation of the object and make it appear as if it were falling vertically, or 2) as an object undergoing sedimentation in a draining system becomes denser, the Coriolis effect approaches negligibilty. The latter would seem more reasonable, since objects with greater mass have greater inertia. One would get a similar result if they dropped, say, a brick down towards the funnel.

Shortly thereafter, we set up another experiment in which we 'stirred' the water in a clockwise direction. We had hypothesized that the Coriolis effect would be unable to reverse this pre-existing spin. After trying this a few times, our qualitative results showed that we were indeed correct. The water consistently left the device with a noticeable clockwise spin in each trial.

Next, we determined the flow-rate in order to see if slowing it down or speeding it up affects the speed of the spiraling effect. Here is the process by which we determined it, factoring in error:

(For collected data, see data.txt)

We surmised that reducing the size of the hole in the funnel by half would reduce the flow-rate by half. The size of the diameter of the hole in the funnel is 2.5cm give or take 2mm. Therefore: see data2.txt

It turned out that we were mostly right, but in fact the flow-rate undergoes a deceleration as the amount and pressure of the water decreases. Our attempts to measure this negative acceleration were very inconsistent and we were forced to throw away this data. So for our purposes, we assumed that it was a linear relationship. It turned out that reducing the size of the opening reduced the amount of spin. We tried to measure this difference quantitatively by placing a floating object at a certain distance from the side of the bucket and measuring the time it took to make one full rotation, but we encountered a problem with this. The floating material was 'sucked' toward the center of the bucket, and we were left with an accelerating object instead of one moving at a constant speed. However, qualitatively, it was obvious that the spin had slowed.

When we tried to debunk the Coriolis force, we encountered only minimal success. By rotating the entire system, we had not modified the intended frame of reference. We realized that the observer, not the apparatus, would have to be rotating about the bucket in order to observe non-acceleration. We with our feeble minds did not know how best to accomplish our desired results, so what we did was walk around the bucket while observing the floating material within. Then we could tell somewhat that there was no real acceleration.

Unfortunately, we made mostly unsuccessful attempts to gather quantitative data. We believe that the reason we were unable to gather the data that we wanted could have been because there were chaotic phenomena at work, such as imperceptible currents beneath the surface of the water affecting its drainage or frictional effects with the walls of the bucket and cone. The reason we chose this shape was that it was symmetrical, but it could be imperfect. Another possibility is that there are reliable means by which to calculate hard data that are beyond our current conceptual understanding of physics; as the Coriolis effect may work differently in 2-plane geometry than it does in 3-plane geometry. Besides the rotational forces, we also would have had to consider gravity and its effect on the experiments.

The water not only moved right to left, but also radially downward towards the center of the earth, as demonstrated by this picture (green dye illustrates the general tendency of the currents).

We were, however, able to show that the common pre-conceived notions about the Coriolis effect are not always true. Namely, the idea that things will always drain in a counterclockwise direction in the Northern Hemisphere, and the contention that a force acts to deflect the path of an object moving in a rotating frame of reference. We showed that, with a little sleight of hand, we could get the water to drain any way we chose, and that if one is willing to walk around a bucket like an idiot, they can see that the Coriolis force is a fictitious one. This would have been observed much more easily on a merry-go-round, but we lacked this foresight.

Lastly, we determined that the one thing that affects the direction of drainage on this small a scale is not the rotation of the earth, but the initial spin the liquid is given. There is an easy way of observing this: 1) one must go to a sink, 2) turn on the water, 3) place his hand between the flowing water and the sink deflecting the water toward the northwest region if the sink. The water will begin to drain clockwise. Toilets can drain either way regardless of their longitudinal location. Their drainage is most largely affected by the way in which the toilet was manufactured. Tiny jets that release the water are angled and determine the direction of the spin.

Though in a sink or bathtub, the Coriolis effect can be manipulated, on larger scales it must be taken into account. For example, a pilot flying a plane from Mexico to Canada must make a slight westward course correction in order not to land many miles east of his intended target. Weather patterns are also largely determined by the Coriolis effect as well. It is the reason that hurricanes (which appear in the Northern Hemisphere) and typhoons (which appear in the Southern Hemisphere) have opposite spins.

The most important thing that we learned from doing these experiments is that real-world physics is many times more complex than that which we do in our class. We are curious to know how to do the physics that would actually get us results in our situation. Though it is humbling to not fully understand what is going on, these feelings of inadequacy serve to develop curiosity and an impetus that makes us want to learn more.

Bartlo, Joseph. "Coriolis and Centrifugal Forces." [Online Available] http://meteorology.miningco.com/library/weekly/aa081298.htm. November, 1998.

Domelen, Dave Van. "The Coriolis Effect." [Online Available] http://www.physics.ohio- state.edu/~dvandom/Edu/coriolis.html. November, 1998.

Emerson, Ryan. "The Bowl." [Online Available] http://www.esm.psu.edu/htmls/graduate/remerson2.htm. November, 1998.

Fraser, Alistair B. "Bad Coriolis." [Online Available] http://www.ems.psu.edu/~fraser/Bad/BadCoriolis.html. November, 1998.

Geerts, B. and Linacre, E. "The Coriolis effect revisited." [Online Available] http://camille-f.gsfc.nasa.gov/912/geerts/cwx/notes/chap11/coriolis.html. November, 1998.

Giancoli, Douglas C. Physics. USA: Prentice Hall International, 1980.

Gold, Dale & George, Jenny. "The Coriolis Myth." [Online Available] http://www.jgeorge.com/coriolis.html. November, 1998.

Heimbaugh, Jason R. "Tyson Debunking the Coriolis Force." [Online Available] http://www.urbanlegends.com/science/coriolis/coriolis_force_tyson_debunking.html. November, 1998.

Renyck Heather J. "The Coriolis Effect." [Online Available] http://www.iup.edu/~ttwkhab/lowpress/CORIOLIS.HTM. November, 1998.

Wills, Jamal. "Coriolis effect (Coriolis force)." [Online Available] http://www.millennial.org/~jwills/GIG/C/Coriolis_effect_Coriolis_force_.html. November, 1998.

1. Science/Coriolis Force A site dedicated to urban myths with several fluid mechanical descriptions of the Coriollis effect
2. The Drain Site The home of a world-wide experiment to test the hypothesis of the direction the fluid will drain
3. Coriolis Effect Defintion of the Coriolis term and is uses
4. The Coriolis Effect: A Simple Explanation Another definition of Coriolis Acceleration with some discussion on drains
5. Coriolis and the Atmosphere Description of the Coriolis Effect on wind
6. The Coriolis Force Home of four animated gifs showing Coriolis force
7. Coriolis Force: An Artifact of the Earth's Rotation Includes a video of Coriolis effect on merry-go-round
8. Bad Coriolis Description of a PBS special perpetualting the Coriolis Myth and tips for doing it yourself
9. The Bowl  Shows the true angled inlets of the toilet bowl
10. Algorithm, Incorporated / Algorithm, Inc. - Science! - The Coliolis Force Newtonian description of the Coriolis Force
11. Scientific American: Ask the Experts: Physics Answers by several scholars on the Drain problem