MicroFoucault n° 26: Trial and error and technical data. (Part 2)

3 September 2024: It has slowed down a little, but is still 20% too fast on the last revolution. (third day)

4 September: The experiment has become extremely stable over 4 days and will no longer provide me with any new information.

So it’s time to modify it with new parameters…

Trial 12

The dips on the Y axis are where the pendulum turns fastest. If I can fill them, the total rotation time will be slower and the pendulum more accurate. Where do they come from, and how can I eliminate them?

One potential culprit could be an off-centre pendulum.

Another could be a tiny oscillation of the frame on the Y axis. (The X axis, on the other hand, is held firmly between the two walls.)

Another could be due to the harmonic vibrations induced by the Charron ring. How can we tell?

For example: what happens if I gently place a one-gram rifle pellet (5.5mm, calibre .22) on the Y axis of the balance?

This was done at 7.25am.

The effect of placing the shot at 7.25 am can be seen very clearly in the time data:

But we can see that the pendulum resumed its normal course an hour and a half later, exactly as if nothing had happened.

5 September: the previous day’s lead experiment can be seen here:

You can see that it had no influence on the speed of revolution of the pendulum, which still turned in 26 hours instead of 33. A semi-failure, then. Removing the lead.

Trial 13

9:37: Another ‘hot’ experiment: fitting an external reinforcement to the Y axis, a large block of marble placed at the back of the pendulum. The graphs should show in 4 hours whether the dips are due to torsion of the frame in this axis. Here’s hoping.

11am, 12pm, 1pm, 2pm, 3pm… failure. Cuisantissime failure. The pendulum has stopped, and is even moving backwards a little. I don’t understand it any more.

4pm: The susceptible has decided to go back, and in the right direction…

8 p.m.: All’s well…

6 September: 8 o’clock: the pendulum made its half-revolution during the night.

Observation: fitting the external reinforcement has no effect on the pendulum’s speed of revolution. Caramba, missed again.

Another observation: the pendulum always turns at the right speed EXCEPT WHEN IT’S IN THE Y AXIS: it then turns 40° in an hour, which is four times too much.

If I can eliminate the hole in the Y axis, I’ll have a very accurate Foucault pendulum.

Test 14

8.30 a.m.: I place two small vials of mercury on the pendulum chuck in the hope that the mercury will dampen the parasitic harmonic oscillations. One can dream…

8h40… Total failure after just ten minutes!

9.18am: One of the vials of mercury is placed a little lower down, directly on the balance wheel.

4.30pm: Failure. The pendulum does not turn at all. The vial of mercury is removed.

7 p.m.: The pendulum turns. Suspension wire rotates 15′ clockwise.

7 September 2021: The dip has also moved 15′ clockwise. The problem was simply there: the wire was the cause.

Test 15

7 September 2021: I made a centring system for the electromagnet, a test pattern graduated in degrees and a revolution test pattern calibrated for my latitude and graduated in hours. Assembling the system, centring the Charron ring and the electromagnet. Very nice.

Launched at 6pm and running perfectly. I’m very happy with my brand new rotation indicator:

8 September: Made its half-revolution in 14 hours, still 20% too fast. The time curve is very clean and completely different from that of last week. The speed of revolution is twice as fast between -10° and 90° where the curve is at its lowest and the amplitude at its highest. So I need to smooth out the whole part of the curve that is below 0.381129 seconds. Understanding and solving this problem will be the programme for the coming weeks.

You can see here that we might be satisfied with the accuracy of this pendulum if we take the duration of a complete revolution, but not if we look at it hour by hour. This is because the places where the pendulum is moving forward are balanced by those where it is lagging behind, the average of the two giving us the illusion that things aren’t going so badly.

I distinguish three degrees of quality in a Foucault pendulum:

degree 1: it turns in the right direction, but no more. The speeds of revolution are exotic, but you can still call it a Foucault pendulum as long as Coriolis is directing it.

2nd degree: it rotates in the right direction, and each total period of revolution is within 10% (slower or faster) of what it should be. It’s a good Foucault pendulum.

3rd degree: it turns in the right direction, and each hour is within 10% (slower or faster) of what it should be. It’s an excellent Foucault pendulum.

8 September: Manufacture of two shock absorbers, one with three 100-microlitre drops of mercury placed in a star and another with three 50-microlitre drops. They are designed to dampen the harmonic oscillations induced by Charron’s ring.

Midnight: the 50-microlitre shock absorber is fitted to the balance wheel.

9 September, 8.30 am: No noticeable difference, either with or without the damper. The second mercury damper (100 microlitres) is fitted on top of the other.

10.50am: Total failure, no pendulum rotation at all. Back to square one, and removal of the top damper (100 microlitres) to leave only the first.

10 September: Exactly the same as yesterday. No noticeable difference, with or without shock absorber.

7.50am: Removal of the 50 microlitre mercury damper. Fitted 16 mm copper eddy-current Charron ring. Unsuccessful: amplitude too small.

8.30 am: Installation of a 26 mm copper eddy current Charron ring. Another failure. A good amplitude, but … no more revolution.

3pm: Installation of a 40mm aluminium Charron eddy current ring.

8 p.m.: Another dismal failure.

9pm: Removal of the lower Charron ring, which was useless anyway.

11 September: 6.45am, rotation of the suspension by 45° CCW (counter-clockwise) to move the error zone to 00 degrees south.

4 p.m.: The kid’s doing really well! He’s suddenly decided to give us a magnificent curve that’s twice as flat with a much more constant speed of revolution. I don’t understand a thing about it, but it works: I don’t understand any more!

This page is too long again: the rest is here