MiniFoucault n° 23: technical data.

From the presentation at the “Foucault pendulum” symposium, Fort St Père, Brittany, 4 May 2024)

“And yet it turns!”

The model presented here is a small Foucault pendulum.

I preferred to show this one rather than another because its 19 centimetres exacerbate all the difficulties that can be encountered with large pendulums. What’s more, I originally designed it for permanent use by imposing constraints never seen elsewhere: an oscillation length limited to 2 centimetres, minimising the Coriolis effect. This was the price we had to pay to ensure its longevity. The few lines below describe the technical aspects of the pendulum, carefully avoiding any scientific references.

“It’s not just the length that counts…”

Foucault pendulum with oscillation maintained by an electromagnet powered by a 1.5-volt battery allowing three years of continuous use. The chassis is machined from a block of granite. The suspension block is a watchmaker’s lathe. The wire is a 0.18 mm D’Addario PL008 guitar string, the Charron ring is a printer spindle bearing and the magnet is a 5 mm rare-earth beast. The pendulum weighs 1.4 kilos and has an oscillation amplitude of less than 1.5°. Its length is 19 centimetres, but it is designed to be reduced to 15 centimetres without tools

The challenges:

To sum up, a large pendulum will happily tolerate design errors. A pendulum less than two metres long tolerates far fewer, and also requires a ‘Charron’ ring to reduce the elliptical effect induced by its small size. A pendulum measuring less than a metre is no longer forgiving. But for a pendulum measuring 20 centimetres, the scale of problems becomes logarithmic: reducing its length by just one centimetre doubles the number of problems to be solved each time. Hence the discreet charm of the thing..

Intrinsic problems :

This is a problem with twelve unknowns that are all related: botch just one and your pendulum will never swing. You therefore need to ensure that they can all be adjusted separately, for the most part without tools.

1) The rigidity of the suspension.

Vital in all cases, and a Cornelian issue when it comes to a free-standing pendulum. For the MiniFoucault, a thousandth of a millimetre of torsion in the chassis is enough to ruin the experiment for good. It is measured with a dial gauge.

2) The levels.

Three adjustment screws are perfect, four are unmanageable. This is the Ockham’s razor of stability: a chair with three legs will never be wobbly. They are measured by the bubble.

3) The direction of the wire.

It must be possible to turn it completely on itself. If a pendulum swings without rotating, turn the wire clockwise for 15 minutes. If the rotation doesn’t follow, the truth lies elsewhere.

4) The height of the wire.

It’s always better when it can be adjusted. In this case, the wire is just guided by the suspension but not clamped into it. The height is therefore adjusted by letting the wire slide through the suspension.

5) The direction of the suspension.

If the pendulum oscillates but still doesn’t turn, turn it clockwise for 15 minutes. If nothing changes, the truth is still elsewhere.

6) The length of the pendulum.

This is adjusted by unscrewing a lever that raises or lowers the suspension. It is never measured with a ruler, always with a clock.

7) The height of Charron’s ring.

Vital. There is no absolute rule that determines its height, but the wire should only caress it. It therefore depends on the amplitude of the pendulum’s swing. It is also adjusted by unscrewing another lever on the right. It is measured by feel.

8) Centring the Charron ring.

Vital.

9) Centring and rotation of the electromagnet.

Vital.

10) Centring the magnet.

Not very important, but so much fun.

11) The height of the magnet.

Not vital, but so practical. It can compensate for any change in the length of the wire.

12) Aerodynamics.

This problem is sneaky because it’s very discreet: a tiny post-it note stuck on the pendulum once wiped out the Coriolis effect for a week without me understanding anything. A bit of symmetry, for heaven’s sake.

Extrinsic problems:

1) Keep all magnetic material 20 centimetres away from the propulsion magnet.

2) Keep any non-magnetic electrically conductive material located under the propulsion magnet (copper, brass, bronze, aluminium, silver, etc.) 20 centimetres away from it to avoid any eddy currents.

That’s all there is to it. Other external phenomena such as the Earth’s magnetism, the proximity of a mountain, air currents, shocks and the precision of the launch can be considered insignificant. For example, a shock to the pendulum will cause it to make a figure 8 with its axis at the centre: it will stabilise very quickly if the amplitude is greater than Charron’s ring.

The setting protocol.

It’s easy to lose years of settings (yes, years!) if you don’t follow the correct method. This MiniFoucault went simultaneously into ellipse, backwards, stopped, got stuck and did only what it wanted for two months until the right adjustments were made. There’s only one rule to avoid getting lost: every modification must be archivable, reversible and provable.

So here’s how it’s done. There are eight columns on a sheet of paper. They show the date, the time, the direction of the stem, the direction of the wire, the angle of oscillation, the angle of any rotation and its direction, the height of Charon’s ring and the result. The data is recorded two or three times a day until the pendulum turns. For the rough adjustments, I record the angles in minutes for the sake of convenience. When the time comes to make fine adjustments, I’ll do it in degrees.

The measurement protocol.

It’s a simple time-lapse covering a month, with one long exposure photo taken automatically every hour. It is taken by a Raspberry running Debian with Allsky managing the shots.

Rotation time measurements.

These can be seen on the time-lapse and cover the entire period between 1 and 25 April 2024. There are 30 half rotations at an average of 18.4 hours, or 15 complete rotations at an average of 36.8 hours. At my latitude, MicroFoucault is therefore rotating 10% slower than it should.

What happens now?

This pendulum is installed in the Grenette café in Sion, where it runs continuously.

A few comparisons…

If we look at the Wikipedia list of all Foucault’s pendulums, the average length is 21 metres, with an average weight of 100 kilos and an average oscillation time of 9 seconds.

A recent list shows that there are 297 Foucault pendulums in the world, 10 of which are less than 2 metres long, and only 5 less than one metre…

MiniFoucault n°23 is the smallest public and permanent Foucault pendulum ever made. The four other experimental pendulums under 70 cm known to date were built by the following laboratories:

– H. Richard Crane, in 1981 (Department of Physics, Ann Harbor, Michigan), with a 70-centimetre pendulum(Am.J.Phys, Vol. 49, n°11, November 1981)

– D. Rae Carpenter and Richard B. Minnix (Department of Physics, Lexington, Virginia) in 1982 with a 50 cm pendulum(Phys. Teach. 21, 477-478 (1983)

– Haym Kruglak and S. Steele (Department of Physics, Kalamazoo, Michigan) in 1984, with their 25-centimetre pendulum(TPT, Vol. 21, # 7, Oct. 1983)

– D.B. Plewes (Department of Biophysics, Toronto, Ontario) in 2018, with his 65.4 centimetre pendulum (Rev. Sci. Instrum. 89, 065112 June 2018)