MicroFoucault n° 26: Trial and error and technical data. (Part 3)
11 September, midnight. EX-CE-LLENT! 16 hours for a half-revolution, or 32 hours for a full revolution. 4% error.
12 September: 13 hours, 29 hours for a complete revolution, i.e. 14% faster than it should be under my latitude (33h26).
Launch of a two-week long test without any external intervention.
Behind the scenes… The camera and Raspberry are at the top, and at the bottom is the PC with MicroSet recording the data.
15 September: Made his last complete revolution in 30 hours: 10% too fast, but improving nicely.
16 September: Made its last revolution in 30 hours: still 10% too fast.
17 September: Made last revolution in 32 hours: only 4% too fast!
18 September: Last revolution in 32 hours: excellent!
The four-day graph is extremely interesting because you can see that it evolves over the days:
You can see that the curve is getting flatter and flatter to the point where, if it continues like this, it should become much more linear and revolution times will soon fall below 10%. These curves may seem a tad anarchic and fluctuating, but they are a huge victory for such a tiny Foucault pendulum.
19 September: last revolution in 30 hours. Another 10% too fast.
20 September: 30 hours.
21 September: 32 hours.
22 September: 30 hours.
Example of the signature of a complete revolution:
27 September: end of test after 15 days:
…where we can see that it has made 24 half-revolutions, i.e. 12 complete revolutions out of 170 hours, which gives us an average of around 29 hours (instead of 33). You can also see that the amplitude of the balance gradually stabilises as the days go by. Here’s the video of these 15 days of testing:
…where you can see that this pendulum had a hidden admirer: a spider that came to look at it as the days went by! But if we note down the times when the pendulum is at 0° (midday), we get the following half-revolution periods:
This gives us a rounded average of 14 hours 30 per half-revolution, i.e. 29 hours per revolution: this micro pendulum turns too fast by 15% over 15 days of uninterrupted operation.
This result can easily be improved by continuing to fine-tune the settings to correct the pendulum’s travel between -70° and -20°, the point at which it spins too fast. Accuracy could then fall below 10%. But you have to know when to stop.
28 September 2024: It’s time to bring this experiment to a close, because it has lasted 5 months and others now need my measuring equipment and my time. I’m going to dismantle everything and finally put my kitchen and living room back in order, and the spider will have to find another nest, the one it’s been nesting in under the clock all this time.
The untamable: data acquisition .
How is its rotation measured?
An RPI HQ camera is connected to a Raspberry running Rasbian (Linux). The image-taking software is Allsky, which can be downloaded here: https://github.com/AllskyTeam/allsky. It’s astronomical software for taking pictures of asteroids, satellites, etc. As it’s summer, I’ve set it up as if it were at the South Pole, to make it think it’s night all day… The camera is timed to take a one-second image every hour to make a time-lapse. Allsky is also an Internet server that allows the position of the pendulum to be viewed live from any screen. A small reflector is glued to the pendulum, giving the white line in the photo. The whole thing is lit by a single LED and completely isolated behind black cloth. I’ll then insert a graduated scale into the time-lapse to keep track of the exact position of the pendulum hour by hour throughout the experiment, which could last a month.
How is the pendulum’s period of oscillation measured?
In one case, it is the contact of the wire against the Charron ring that triggers the timer, a MicroSet controller. It records each oscillation with an accuracy of one millionth of a second. As the amplitude of the pendulum is not the same according to its position, which changes constantly, the graph will show a recurring curve that is found at each half-rotation. This is the signature of the pendulum, which is completely different for everyone. In this way, we can measure the pendulum’s rotation time and its position at any given moment. Above all, this system can measure the centring of the Charron ring.
The image below shows 24 hours in the life of the MicroFoucault. Each peak shows a revolution of the pendulum. (The lines that cross the graph do not count: they are just bad contacts of the Charron ring)
From this we can deduce
- That it has rotated in 24 hours,
- that the peaks occur when the pendulum is on the X axis,
- that the bumps occur when the pendulum is on the Y axis.
In the other case, I use the impulse given by the electromagnet to trigger the timer. This formula is much more precise than the electrical contact of the Charron ring.
Why are all these measurements so time-consuming?
Because each adjustment has to wait 17 hours, half a rotation at my latitude, before its data is validated.
That’s the price we have to pay. And any scientific experiment must be reproducible. That gives us a minimum of 34 hours.
But if we wanted to be honest, we would have to redo each experiment in reverse to return to the original data: 34 hours, plus 17 to confirm the modification: 51 hours…
And if we wanted to be perfectly honest, we’d do the experiment on a full rotation to confirm the half-rotation. That gives us 102 hours….
In a nutshell: 4 days just to know what we’re talking about after the slightest adjustment. Multiply that by the number of modifications, and we’re no longer talking in days, but in months!
How do you centre the Charron ring and the electromagnet?
Both are centred by 4 screws placed in an X shape around the Charron ring on the one hand, and around the electromagnet on the other. Roughnecks often try to measure with a ruler, but this is more of a DIY exercise than anything else. Here’s the absolute way to be fair: a stopwatch that measures each oscillation to a millionth of a second. In my case, I use a MicroSet timer.
If you look closely at the graph below, you can see that before setting 1, every other measurement is shorter than the other. Setting 2 fine-tunes the final result.
Always start with the Charron ring, which is so difficult to adjust, and finish with the electromagnet. Allow between half a day and a full day of adjustment before you are satisfied with your work.
