MicroFoucault n° 26: Trial and error and technical data. (Part 1)

Diary of attempts to train a small wild animal…

6 May 2024, first attempt:

The wire guide is a watch bearing ruby. The upper Charron ring is made of bronze (friction, 6 mm) and the lower of copper (eddy current, 15 mm inside). The balance wheel is a rolling ball weighing 261 grams. The whole thing has taken the place of the MiniFoucault between my kitchen and living room, which disturbs it a lot but gives me the enormous advantage of having it permanently in front of me.

It wobbles, but doesn’t turn despite all my attempts to adjust it. Failed.

Test #2:

Modification n°1, the upper Charron ring is now half the size, in bronze (friction, 3 mm)

Modification n°2, the lower Charron ring is made of aluminium (eddy current brake, 25 mm)

Modification no. 3, the balance wheel. It is now a 700 gram petanque ball suspended by a magnet.

Modification n°4, addition of a pointer to avoid parasitic oscillations.

Oscillates, spun anarchically one day, sometimes in the right direction but too quickly, then stopped. Semi-failure.

Test no. 3:

Modification n°1, the lower Charron ring. It is now made of aluminium (friction: a 2’5″ silicon hard disk 20 mm inside placed on another 3’5″ aluminium hard disk 25 mm inside).

Oscillates, but does not rotate. An abject failure.

Test #4:

Modification n°5, the suspension: a chuck in place of the clamping clips.

Modification no. 6, the thread guide: turned upside down and re-adjusted.

Modification n°7, the Charron ring: re-tightened and better fixed than before.

Modification n°8, the ball attachment: no more magnet or needle, but fixed by a rod and a mandrel.

Change n°9, the bottom magnet is now pressed against a 5mm threaded rod. Height-adjustable.

Modification n°10, the propeller: concentric centring rings for amplitude measurements.

Oscillates, sometimes turns in the right direction and then stops. Semi-failure.

All my settings are perfect and it still doesn’t work: could it be that I’m learning to be more-than-perfect?

Test n°5

Modification no. 11, Replacement balance wheel: cast lead, turned, drilled and copper-plated. (6 hours of electrolysis!!!) This balance wheel is now non-magnetic, three times heavier (2.171 kilos) and its centre of gravity is lower.

Modification no. 12, the length, now 12 centimetres.

State of the lead ingots before machining: various scraps melted in a ceramic bowl…

Worked (badly) for a few hours after a few days of adjustments, then stopped its revolution to oscillate for 12 hours on the same plane before breaking the wire.

A complete failure, but it doesn’t matter because things are getting interesting.

Test no. 6

Modification n°13, modification of the balance wheel, replacement of the broken wire, shortening and rebalancing. Fitted a cascade of magnets.

Modification no. 14, fitted a ruler to measure the heights of the stem, suspension and Charron ring. Vital for adjustments.

Modification n°15, the installation of a prism to check the direction of oscillation. A magnificent piece of optics that had been lying around my workshop for 20 years, much more precise than a laser beam. It’s not pretty at all, but so practical! From now on, a five-minute wait will be enough to see and measure the pendulum’s rotation.

Modification no. 16: reduction of the lower Charron ring (with eddy currents). This is the price we have to pay to avoid any further wire breakage. We’re bordering on the limits of physics here: can the Coriolis effect still act with an amplitude of 7.5 millimetres? My dream is to one day be able to eliminate the upper Charron ring (mechanical, frictional) and keep only the lower one.

Change no. 17: the length, up to 10 centimetres.

Another failure…

A practical note on the length of the pendulum. You can’t measure it with a ruler because you can’t know exactly where its centre of gravity is. So I measure the time taken to make one period and then use the following formula: T=4⋅√L:g⋅K(sin(θ:2)) where k is the full elliptic integral of the 1st kind. Not knowing how to calculate, I’ll simply here: https://www.123calculus.com/pendule-simple-page-8-20-455.html to do the dirty work for me. My pendulum, which lasts 0.732 seconds, measures 13.3 centimetres. So far so good.

…Except that if I lower the Charron friction ring by one millimetre, the pendulum will swing 2 thousandths of a second faster. So it’s safe to say that this is a double pendulum. So far so good. However, if I surreptitiously remove the lower copper Charron ring (Foucault’s brake), the amplitude will increase by one millimetre and the time will then be 0.686 seconds, or the length of an 11.7 centimetre pendulum.

All this to say that at this level, the tiniest adjustment produces gigantic effects and that it will truly be the purest of coincidences if this pendulum ever works.

Test no. 7

Modification no. 18, installation of lateral reinforcements to avoid any risk of lateral torsion. Not a pretty sight.

Modification n19, fitting of a second optic for adjustment.

Modification n°20, installation of a mechanical Charron ring under the pendulum (two hard disks) to prevent parasitic oscillations.

Worked for a few hours before stopping. Semi-failure.

Test no. 8

Modification n°21: elimination of the mechanical Charron ring under the pendulum.

Erratic and unpredictable behaviour. Failed.

10 August 2024, modification no. 22, raising the Charron ring by 0.5 millimetres. It works!

12 August: A short-focus camera is installed above the pendulum. Outraged, he decides to act like a diva and stop filming: he’s really starting to deserve his name…

13 August: L’Indomptable suddenly decides to start shooting again. Camera on at 8.43am.

14 August: 16:00. The camera is exchanged for one with a longer focal length. L’Indomptable runs like clockwork.

15 August: First data received on revolution times, which are about 15% too fast on average. The revolution speeds are quite different depending on the position, so all that’s left to do is wait and record continuously: days, weeks… From now on, I’ll be making modifications ‘on the fly’ to see the differences. Some may stop the pendulum’s revolution, others may speed it up or slow it down…

16 August: 16:30: The Charron ring rises by 1 mm, without touching the pendulum. The pendulum rotates too fast. (rotation in 24 hours instead of 33 hours: 40% too fast)

19 August: 8.40 am: The Charron ring descends by 1 millimetre to the same values as on 15 August. Delay.

20 August: 9:00 am: the Charron ring is raised by 3 mm, the time display is centred and reset to zero, and the time intervals are changed (3593000 milliseconds instead of 3600000).

21 August: 8.00 am. Pendulum very accurate on half a rotation. To be confirmed over the next few days.

22 August: 9.50 am. The time for a complete revolution is 32 hours: 5% too fast. E-xce-llent!

23rd August: 12h00. All is well. Installation of a probe, a timer and a computer to record each oscillation to a millionth of a second.

24 August: 27% too fast revolution over the last 2 days. Years of experience in building Foucault pendulums mean that I’m by far the most qualified to say that I don’t really understand anything.

28 August 2024: Here are the recordings of 8 days of rotations:

…Where it turns out that it has made a total of 8 complete revolutions that are accelerating faster and faster: successively 30, 28, 23, 25 to then stabilise at 20, 20, 20 and 20 hours.

Interesting.

I’m referring here to a phenomenon that is often observed: the running-in of the suspension wire, having often seen clocks that didn’t work for a few days start up by themselves without any external intervention. The rest promises to be fascinating. In this experiment, I’m not trying to make it work as well as possible: I’m provoking every possible error to learn how to get round them. In this way, what is learnt here will be used to understand the whole.

Test n°9

29 August 2024: 1pm. Receipt of data from a rotation.

Here is the time graph for a complete revolution of the Indomitable, showing that it has accelerated again: 19 hours for one rotation. You can also see that a rotation is made up of two half-revolutions, as shown in the diagram below.

Start of measurement: 18 hours

Peak n°1: 19 hours

Trough n°1: 23 hours

Peak n°1: 5 hours

Trough n°1: 8 hours

This gives us the following geographical positions:

Put into a spreadsheet, these 3050 data give us the following gentle symmetry:

Trial 10

29 August: 2pm: Charron ring moved 1 millimetre higher.

7pm: failure. The pendulum stopped turning after 5 hours. The Charron ring moved 3 millimetres lower.

Failure. The pendulum stopped in the middle of the night. Charron ring moved 2 millimetres higher.

30 August: 12 o’clock. Everything seems to be working. A new probe is made for more precise measurements, and connected to the computer.

9pm. The pendulum’s revolution is stopped again. Failure.

Trial 11

31 August: I make a (fabulous) measuring device that allows me to:

1) to centre the Charron ring precisely and directly,

2) to centre the electromagnet and the magnet precisely and directly,

3) instantly compare the two at the flick of a switch,

4) tell me the maximum possible height of the Charron ring,

5) measure the Charron and/or electromagnet periods to one millionth of a second,

6) and thus save me weeks or months of trial and error and approximation.

11 o’clock: launch of the pendulum. Stabilisation of the stroke.

12 noon: camera and measurement software launched.

2 September: Here is the graph of 2 days of revolutions. It’s clear that it’s very clean.

If I take the data for a complete revolution and put it in a spreadsheet…

…and round off this graph…

…I can deduce that the pendulum spun 28% too fast on the first day and that the amplitude peaks occur exactly when the pendulum is swinging on the Y axis. So I’m going to let the pendulum swing a few more days to confirm all that.

This page is getting too long, but if you really want to know what happens next, just click here.