From left to right: Mike Town, Ph.D. candidate, University of Washington; John Bird, Ph.D., FBIS, P.Eng, York University; R. Allan Baker, Sonoma State University
A Foucault Pendulum at the South Pole was determined to have a period of 24 hours, ± 50 minutes. The acceleration due to gravity, g, was determined to be 9.85 ms-2 ± .03 ms-2. The rotation of the Earth was in a clockwise direction if looking down from above the South Pole.
A Foucault Pendulum appears to rotate in time with respect to the floor it is swinging above. However, because of the way it is suspended it will not twist so any rotating is being done by the floor and the floor is attached to the Earth so it is the rotation of the Earth that is being observed.
The pendulum will travel in a circle relative to the floor a distance of (360ºSin f in 24 hours, where flatitude. The latitude at Sonoma State University is 38º20’ so the pendulum will subtend an angle of 223º in 24 hours, i.e., it has a period of 38 hours, 45 minutes. At the equator the latitude is 0º and (360)Sin0 = 0, the pendulum will not appear to rotate at all but only swing back and forth remaining in the same plane relative to the floor. At the South Pole the latitude is 90º and (360)Sin90 = 360º so the pendulum will make one complete revolution in one day. This makes sense because the Earth rotates once on its axis every 24 hours and the South Pole marks the Earth’s axis of rotation (± 10 meters due to the precession of the Earth).
The South Pole is an excellent place to build a Foucault Pendulum and observe the rotation of the Earth but its environment poses a number of unique challenges. When this pendulum was made the temperature was —90ºF and the physio-altitude was greater than 11,000 feet (atmospheric pressure approximately 660 mB). It was decided to build the pendulum in the stairwell of the new station that was under construction, out of the way of traffic, out of the wind and ice and other elements. Also, the enclosed stairwell is 6 stories high and would allow for a long pendulum. A longer pendulum arm will have greater angular momentum, less air resistance, and the amplitude of its arc will decay more slowly.
Construction on the Foucault Pendulum began by measuring out a length of guy wire 33 meters in length. A hole was drilled through a length of 2x4 through which the pendulum’s wire was fixed in such a way that it would have freedom of movement in all directions. The 2x4 was then fixed to the top of the stairwell and the wire suspended down into the stairwell. At the bottom of the stairwell a 25-kilogram weight was suspended from the wire approximately 5 centimeters off the floor. After waiting for the weight to stop spinning and come to rest the Foucault Pendulum was ready to operate.
Operation and data acquisition:
The weight (bob) of the pendulum was released from an angle and the pendulum was started. At the apex of the arc a mark was made on the floor corresponding to a pointer on the bottom of the bob every 20 minutes for 24 hours. There was no mechanism for keeping the pendulum swinging and the amplitude decayed within a couple of hours so it had to be restarted periodically over the 24 hour period.
Calculations and conclusions:
If the period of the pendulum was 24 hours then it should subtend an angle of 15º every hour. Intermediate measurements and calculations were made to verify this. By measuring the lengths of 3 sides of an equilateral triangle formed by the swinging pendulum over a 20 minute period and using the Law of Cosines to calculate the angle subtended in that time period it was determined that the earth rotated in a clockwise direction, relative to looking down at the South Pole, 5º every 20 minutes as expected.
By timing the period of the arc made by the swinging pendulum and using the equation a value for the acceleration due to gravity was calculated. T was measured to be 11.5 seconds, L was measured to be 33 meters so g was calculated to be 9.85 ms-2 ± 0.03 ms-2. Since the pendulum’s period is independent of the weight of the bob this experiment was performed with a variety of weights until one was found that gave consistent results.
Notes and other fun stuff:
Standing on the bottom of the world the Earth spins backward relative to the direction it spins in the Northern Hemisphere (however, water still spins down the drain in the same random direction). Our first attempt with the pendulum showed the Earth spinning backward from what was expected. We didn’t notice this at first because we’re all from the Northern Hemisphere and are accustomed to the earth spinning in an anticlockwise direction. We then realized that from our frame of reference the earth should be spinning clockwise so we had to modify the pendulum. At an altitude of 11,000+ feet we think a bit more slowly.
The opening picture shows the three of us kneeling next to the pendulum with the weight hanging in a vertical configuration. The air resistance against this weight caused the pendulum itself to rotate. This gave us spurious results for our first attempt. Later we fashioned the weight so that it was hanging horizontally to the plane of the floor and we got results consistent with what was expected.
Our second attempt showed the earth rotating in the proper direction but at an angular velocity twice what is expected (i.e., 12 hour days instead of 24). We suspected some kind of government conspiracy but decided to make a further modification and try it again. Our last attempt showed that the earth spins on its axis once every 24 hours, as expected. (We were somewhat disappointed that we did not uncover a government cover-up).
It is stinkin’ cold at the South Pole and the air is very thin. After hiking up 5 flights of stairs at 11,000 feet we had to stop and rest. While we were resting we got cold soaked from the extreme temperature so we had to go back down and warm up. While the "beer can" is enclosed it is not heated and its ambient temperature is the same as the outside temperature. For our second attempt we walked up the stairs a bit more slowly and rested for a shorter period of time and were able to begin construction on the pendulum. After several trips up and down five flights of stairs the pendulum wire was finally suspended and the rest of the construction could be performed at floor level. Even then we had to go in and warm up approximately every 10 minutes. On average, it takes 6 times longer to do things at the South Pole than it does anywhere else in the world.
It was difficult to make the pendulum swing in a plane instead of an ellipse. After several attempts with various techniques of holding the bob and dropping it we always got some kind of ellipse instead of a plane. This adds to our error because it is more difficult to locate and mark the pendulum arc’s apex. A way to do it is to suspended the bob by tying it off with a piece of string and letting it settle, then burn through the string. The bob would then drop without any outside force and swing in a plane. Since it is against the Antarctica Treaty to have any open flames at the South Pole we could not do this. After much practice Mike Town got very adept at dropping the bob so that it arced in a plane.
We have demonstrated a physical phenomenon confirming that we are on the axis of rotation of the Earth. Although the result matches our hypothesis and nothing new has been discovered, we have placed ourselves among the stars, and standing beside Galileo in recognition of our planet as a rotating sphere floating in the heavens. We have thus enhanced our own understanding of our place in the Universe. The South Pole Foucault Pendulum is still in place and periodically one of us will go out and start it swinging and take further data to refine our findings.
[Note: this page was originally published on Al Baker's former page on the Sonoma State University web site in 2001; I have adjusted the HTML slightly and removed the dead links--Bill]