7 January 2011
After reading a survey which reported that 20% of Americans think the Sun revolves around the Earth[?], I undertook the challenge of building a Foucault Pendulum in my living room. These devices are often seen in science museums, swinging back and forth, slowly shifting their apparent plane as the planet rotates beneath it.
Clearly a momentum-based pendulum is not feasible in my living room. Research online found reports that a top-driven pendulum is subject to precessing into an elliptical path, an effect that can only be mitigated by being extremely long or through the use of various active-dampening techniques. No information could be found as to whether this limitation applied to a bottom-driven pendulum. Logically it would seem that the central magnet under the bob would tend to collapse any ellipse which formed.
Accordingly, I chose to build a bottom-driven pendulum. A surplus 30 lbs cannon ball from the war of 1812 seemed like a convenient bob. The whole thing was suspended form a door frame, which while not as tall as my ceiling, offered a firm anchor point from which to swing. A universal joint at the top allowed the pendulum to swing in any direction. Mechanical construction was quick and easy. Swinging on momentum alone, the pendulum would run for half an hour. Not enough to show your planet's rotation, but a promising start. Powering the system proved to be a greater challenge.
Problem #1: Ground
The simplest way to drive the electromagnetic coil is with a timer. The ubiquitous 555 timer chip[?] in monostable mode seemed like an easy answer. Unfortunately the first two chips I tried exploded with a puff of smoke during testing. After being unable to find anything wrong with the circuit design, I eventually traced the problem back to my new oscilloscope. Until recently I had been using an elderly two-prong scope from the 1960s. Just like a volt meter, one connected both a ground wire and a signal wire to the circuit and took a reading. However this piece of equipment had been thrown out by a relative (along with nearly all my other tools), so I had recently purchased a replacement oscilloscope. Unbeknownst to me this more modern device didn't float; its ground was tied to the third prong. So when I attached its ground wire to +12 volts, it caused the abrupt release of magic smoke.
Problem #2: Calibration
Once the timer was pulsing nicely, it was time to calibrate it with the pendulum. Measurements showed that half a swing took 1.3 seconds. I spent several hours trimming the 555's potentiometer, replacing resistors and tuning the circuit to match. It was impossible. Even though the 555's specs say it is 0.005% accurate, in reality its pulses were as punctual as the Space Shuttle's launch times. Maybe it was variability in the performance of my capacitor or resistors. In any event, the 555 is not a good choice for slow accurate pulses.
Problem #3: Milliseconds
Being a software engineer, the simple answer was to write "delay(1300)", upload it to an Arduino microcontroller and be done with it. Replacing the 555 with a Boarduino worked well. After a bit of calibration I found that a cycle time of 1319 milliseconds was virtually perfect. Unfortunately virtually perfect isn't perfect. After ten minutes the electromagnet and pendulum would drift out of phase of each other and the magnet started sapping energy from the pendulum instead of adding it. Clearly an open-loop controller wasn't going to work. I needed feedback from the pendulum.
Fortunately this was fairly simple. I glued a photoresistor to the magnet and programmed the microcontroller to be triggered by the darkness caused by the bob swinging past. A little bit of clever coding allowed the system to self-calibrate and handle changes in ambient light over the course of a day.
Problem #4: Compass points
Finally, the system was behaving perfectly. I started it going and left it swinging overnight. Unfortunately by morning the plane of the swings hadn't moved one bit. Were those 20% of Americans correct after all? Was the Earth actually motionless? Were the Foucault pendulums in those elitist museums all rigged in order to perpetuate the liberal myth of Galileo?
Well, not quite. It turns out that the universal joint at the top of the pendulum isn't ideal. The join is made up of two bearings that are rotated 90° from each other. Normally both joints are in motion, allowing the pendulum to swing wherever it wishes. However when the pendulum is swinging in one of the four compass directions only one of the two bearings is moving, and the other is motionless. In these cases the bearing in motion is experiencing kinetic friction while the motionless bearing is experiencing static friction (the latter being greater). This means that once the pendulum hits either of these two directions it becomes stuck in a rut, unable to escape.
Problem #5: Ellipses
A higher quality universal joint could solve the problem of being stuck at the compass points. However, in the mean time one should still be able to see some good movement between these two boundaries. Unfortunately starting the pendulum at a 45° angle revealed a more severe problem.
The swings started in a straight line, but soon devolved into an ellipse, which circularized, became an ellipse in the opposite direction, collapsed into a straight line 90° from the original, then devolved back through an ellipse, a circle, an ellipse, returning to the original swinging plane. A full cycle took around 10 minutes.
So there we have it. Like their top-driven counterparts, bottom-driven Foucault pendulums are also susceptible to precessing into an elliptical path. Various solutions exist to actively damp this out[?], but the trust that the pendulum is actually showing Earth's rotation would be broken. The only good solutions would be to either increase the length of the pendulum to the point where it is no longer possible to do at home, or else speed up Earth's rate of rotation to about 10 minutes per revolution.