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Bravais n\u00b01: November 2004:<\/strong><\/p>\n\n\n\n\n\n<\/div>\n\n\n\n\n\n
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A friend had told me about the conical pendulum experiment that Bravais had done 150 years earlier, saying that I should look into it because it had only been done once by Bravais himself and no one had reproduced it. It was simple: a conical pendulum placed on one of the Earth’s poles cannot rotate at the same speed in either direction<\/strong> because of the Earth’s rotation.<\/strong> I decided to make one in my workshop, empirically and without any documentation. Intuitively, I thought it would turn faster counter-clockwise because the Earth rotates in that direction in the northern hemisphere (based on the principle that someone walking in the direction of a moving train goes faster than someone sitting down or moving backwards)<\/p>\n\n\n\n\n\n<\/div>\n\n\n\n\n\n
All the information below is, as usual, given so that anyone who tries the same experiment can benefit from my mistakes by not reproducing them…<\/p>\n\n\n\n\n\n
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Stator made with three electromagnets arranged in a triangle. Wall-mounted. 0.24mm steel wire. Ruby wire guide. Measurements made by cutting a laser beam.<\/p>\n\n\n\n\n\n
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Result when the pendulum turns 20 hours counter-clockwise (CCW):<\/p>\n\n\n\n
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The average half-rotation time is 0.9131412 seconds, i.e. 1.8262824 seconds.<\/p>\n\n\n\n\n\n
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Result when the same pendulum turns 12 hours clockwise (CW):<\/p>\n\n\n\n\n\nWhere we see that the average of the half-rotation times is 0.9130998 second, or 1.8261996.<\/p>\n\n\n\n\n\n
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The difference between the two is 0.0000828 seconds.<\/p>\n\n\n\n\n\n
As I believed at the time that a conical pendulum should be faster if it rotated in the same direction as the Earth’s rotation, I took this experiment as a failure.<\/p>\n\n\n\n\n\n
All the other tests showed the same results, so I told myself that my pendulum was poorly constructed. Then my son was born, and I put the experiment on hold to move on to more important things.<\/p>\n\n\n\n\n\n
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September 2023<\/strong>: Bravais n\u00b02<\/strong><\/p>\n\n\n\n\n\nBack to the experiment, as I hate unfinished projects. <\/p>\n\n\n\n\n\n
<\/p>\n\n\n\n\n\n<\/video><\/figure>\n\n\n\n\n\nStator made with three electromagnets, arranged in a triangle and adjustable in spacing. Cardanic suspension taken from a laser level to which a 1 mm wire is attached. Measurements made by cutting a laser beam. The main thing this proto taught me was how difficult it is to build such a thruster, which causes undesirable elliptical oscillations.<\/p>\n\n\n\n\n\n
As the results remained more or less the same, I once again criticised the quality of my prototype and thought it necessary to increase the number of thrusters.<\/p>\n\n\n\n\n\n
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October 2023<\/strong>: Bravais n\u00b03 <\/strong><\/p>\n\n\n\n\n\n<\/p>\n\n\n\n\n\nResult when the pendulum turns counter-clockwise (CCW):<\/p>\n\n\n\n\n\nWhere we see that the average half-rotation time is 1.397278 seconds, or 2.794556 seconds.<\/p>\n\n\n\n\n\n
Result when the pendulum turns clockwise (CW):<\/p>\n\n\n\n\n\nWhere we see that the average number of half rotations is 1.397253 second, or 2.794506 second.<\/p>\n\n\n\n\n\n
The difference is 0.00005 seconds, slower counter-clockwise. This was not at all what I had hoped for: above all, this experiment proved that my prototype needed to be improved.<\/p>\n\n\n\n\n\n
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February 2024: Foucault n\u00b024 \/<\/strong> Bravais n\u00b04<\/strong><\/p>\n\n\n\n\n\nA Foucault pendulum \/ clock and conical pendulum combo.<\/p>\n\n\n\n\n\n
Stator made with nine electromagnets, arranged in a circle and adjustable in spacing. Measurements made by cutting a laser beam. Suspended by wire.<\/p>\n\n\n\n\n\nThis was a bad idea, as the experiment was bogus. The two systems work, but are not practical if you want them to coexist because you have to wind up the Charron ring to let the Bravais pendulum turn. So they have to be dismantled to make two separate objects.<\/p>\n\n\n\n\n\n
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September 2024: Bravais n\u00b05<\/strong><\/p>\n\n\n\n\n\n<\/p>\n\n\n\n\n\n
Prototype mounted on a laser-level gimbal and a 9-coil propeller assembly mounted in a circle. Failed.<\/p>\n\n\n\n
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October 2024<\/strong>:(Mini)Bravais n\u00b06<\/strong><\/p>\n\n\n\n\n\n50-centimetre pendulum, 5-kilo tin\/lead pendulum, suspended by a needle cardan joint. The propeller is mounted upside\/down: the electromagnet is located under the pendulum while the magnets are fixed at the bottom. Does not work efficiently enough for this type of experiment, as it tends to systematically make an ellipse after a period of use.<\/p>\n\n\n\n
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October 2024<\/strong>: Bravais n\u00b07<\/strong><\/p>\n\n\n\n\n\n<\/p>\n\n\n\n\n\n
This slowly led me to the seventh prototype: 9 star-shaped thrusters, home-made gimbal suspension (photo), 3.20 metre Invar wire, aluminium plate (Thorens TD160 turntable) with levels adjustable to a hundredth of a millimetre, 2 kilo brass balance. Laser measurements taking 2 samples per rotation, the beam being cut twice per revolution.<\/p>\n\n\n\n
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here’s the first result:<\/p>\n\n\n\n
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Eureka<\/strong>. Here at last is proof that my intuition was wrong and that my conical pendulums worked perfectly!<\/strong><\/p>\n\n\n\n\n\nYou can see on this graph that the pendulum spins counter-clockwise for 12 hours (the left-hand side of the image), that I then throw it in the other direction (the disturbance in the centre) and that it then stabilises and spins more rapidly<\/strong> clockwise for another 12 hours. The undulations are due to a continuous and recurring elliptical effect that disturbs the pendulum, but only their average counts.<\/p>\n\n\n\n\n\nBelow is the data for the pendulum rotating counter-clockwise for 20 hours:<\/p>\n\n\n\n\n\nAverage counter-clockwise half-revolutions: 1.757722 seconds<\/p>\n\n\n\n\n\n
And now the data for the pendulum turning clockwise 18.7 hours:<\/p>\n\n\n\n\n\nAverage hourly half-revolutions: 1.757608 seconds<\/p>\n\n\n\n\n\n
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Observation on 16 October:<\/strong><\/p>\n\n\n\n\n\n<\/div>\n\n\n\n\n\n
Average counter-clockwise revolutions<\/strong>: 1.757722 X 2 = 3.515444 seconds<\/p>\n\n\n\n\n\nAverage counter-clockwise revolutions<\/strong>: 1.757608 X 2 = 3.515216 seconds<\/p>\n\n\n\n\n\nAverage of hourly and counter-clockwise revolutions: 3.515330 seconds. This is the time it would take my pendulum to make one revolution at the equator, in either direction.<\/strong><\/p>\n\n\n\n\n\nDifference between anti-clockwise and clockwise revolutions: 0.000228 second.<\/p>\n\n\n\n\n\n
Percentage difference between a revolution at my latitude and one at the equator: 99.9967572%<\/p>\n\n\n\n\n\n
This gives a time difference of 5.6 seconds per day at my latitude, which is counter-clockwise and clockwise. This measurement, which is independent of the length of the balance wheel, must of course be confirmed by further experiments. <\/p>\n\n\n\n\n\n
The time had finally come for a Foucault\/Bravais combo.<\/p>\n\n\n\n\n\n
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November 2024: Combo Foucault (n\u00b028) \/ Bravais (n\u00b08<\/strong>)<\/p>\n\n\n\n\n\n<\/div>\n\n\n\n\n\n
One pendulum, two experiments.<\/p>\n\n\n\n\n\n
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Design and manufacture of a mobile ring eliminating the elliptical effect of a short Foucault pendulum. This is not a Charron ring but a self-centring floating ring<\/strong>: it consists of two discs with different internal diameters, placed under the pendulum and free to move in all directions. The magnet brushes against the smaller ring at the end of each oscillation, moving it by a tenth of a millimetre each time. As a result, the ring is always perfectly centred, the elliptical effect is well and truly damped and the system is much more precise than a Charron ring.<\/strong><\/p>\n\n\n\n\n\nPrinting of a thruster assembly with 9 coils arranged in a circle for the Bravais and a central coil for the Foucault (photo taken when it came out of the 3D printer), as well as a box enabling the ‘Foucault’ \/ ‘Bravais’ function to be selected using a simple switch.<\/p>\n\n\n\n
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1 November 2024:<\/strong> Launch of the ‘Foucault’ version of the tests, which should take 2 weeks to record.<\/p>\n\n\n\n\n\nFirst results: here is the time signature of the Foucault pendulum over 6.7 days:<\/p>\n\n\n\n\n\n…where you can clearly see the difference with all my other Foucault pendulums: there are no longer the recurring undulations that used to show the position of the pendulum. The variations seen here are due to the floating ring. They are aberrant from a horological point of view, but beneficial for the course of a Foucault pendulum.<\/p>\n\n\n\n\n\n
Here is the video of the Foucault pendulum:<\/p>\n\n\n\n\n\n<\/video><\/figure>\n\n\n\n\n\nIf we break this film down frame by frame, we can see that the times of the 20 half-revolutions are 16, 17, 16, 17, 17, 16, 16, 17, 16, 16, 17, 16, 16, 17, 16, 16, 17, 16, 16 and 17 hours. <\/p>\n\n\n\n\n\n
The times of the 10 complete revolutions are therefore 33, 33, 33, 33, 33, 32, 33, 32, 33 and 33 hours.<\/p>\n\n\n\n\n\n
The total time of these 10 revolutions is 328 hours<\/p>\n\n\n\n\n\n
The average of the 10 revolutions of this Foucault pendulum is therefore 32.8 hours. At my latitude, it should have taken 33.13 hours. This pendulum therefore turned 1% too quickly over a period of 16 days.<\/strong><\/p>\n\n\n\n\n\n <\/strong>In short, this is the most accurate of all my Foucault pendulums: it indicates my latitude with an error of 70 kilometres to the north.<\/p>\n\n\n\n\n\n<\/div>\n\n\n\n\n\n
17 November 2024<\/strong>: <\/p>\n\n\n\n\n\nTest No. 1: the Foucault is stopped, and the Bravais is launched while keeping the same self-centring floating disc.<\/strong><\/p>\n\n\n\n\n\n<\/div>\n\n\n\n\n\n
24 November 2024:<\/strong> Findings<\/strong><\/p>\n\n\n\n\n\nThe results of the new tests confirm those of October. The graph is completely different because of the floating ring, but the result is the same: the pendulum turns faster clockwise than anticlockwise.<\/p>\n\n\n\n\n\n<\/div>\n\n\n\n\n\n
Here are the 18-hour averages for the counter-clockwise pendulum:<\/p>\n\n\n\n\n\nAnd the 24-hour averages for the clockwise pendulum:<\/p>\n\n\n\n\n\nFrom which we can deduce that:<\/p>\n\n\n\n\n\n
The average of the counter-clockwise rotating pendulum is 1.772608 seconds per half rotation, i.e. 3.545216 seconds per rotation.<\/p>\n\n\n\n\n\n
The average of the clockwise rotating pendulum is 1.772498 seconds per half rotation, i.e. 3.544996 seconds per rotation.<\/p>\n\n\n\n\n\n
The difference between the two is 0.000220<\/p>\n\n\n\n\n\n
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Test 2: launch the Bravais under the same conditions for confirmation, first anti-clockwise for 24 hours, then clockwise for 24 hours. All while keeping the same self-centring floating disc.<\/strong><\/p>\n\n\n\n\n\n<\/p>\n\n\n\n\n\n
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27 November 2024<\/strong><\/p>\n\n\n\n\n\nResult of throwing the pendulum back and forth for 20 hours. Important note: it snowed and my pendulum, which is attached to a roof beam, descended slightly because of the weight of the snow: the rotation time is therefore significantly different from that in test No. 1<\/p>\n\n\n\n\n\nHere are the 10-hour averages for the counter-clockwise rotating pendulum:<\/p>\n\n\n\n\n\nAnd those of the 9-hour clockwise rotating pendulum:<\/p>\n\n\n\n\n\nFrom which we can deduce that:<\/p>\n\n\n\n\n\n
The average of the counter-clockwise rotating pendulum is 1.7726269 seconds per half rotation, or 3.5452538 seconds per rotation.<\/p>\n\n\n\n\n\n
The mean of the clockwise pendulum is 1.7725676 seconds per half rotation, or 3.5451352 seconds per rotation.<\/p>\n\n\n\n\n\n
The difference between the two is 0.0001186<\/p>\n\n\n\n\n\n
The average between the two directions of rotation is 3.5451925 seconds. This is the time it would take for my pendulum to make one revolution at the equator, in either direction.<\/strong><\/p>\n\n\n\n\n\nAverage between counterclockwise (CCW) and clockwise (CW) revolutions: 0.0000593 seconds.<\/strong><\/p>\n\n\n\n\n\nThat’s 50 millionths of a second from the result of test n\u00b01.<\/p>\n\n\n\n\n\n
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3rd December 2024. <\/strong><\/p>\n\n\n\n\n\nTest 3: Bravais launched under the same conditions, first counter-clockwise for 18.6 hours, then clockwise for 19.2 hours. Always keeping the same self-centring floating disc. Only the temperature has changed.<\/strong><\/p>\n\n\n\n\n\n<\/div>\n\n\n\n\n\n
Here are the averages for the counter-clockwise rotating pendulum:<\/p>\n\n\n\n\n\nAnd those of the clockwise rotating pendulum:<\/p>\n\n\n\n\n\n<\/div>\n\n\n\n\n\n
From which we can deduce that:<\/p>\n\n\n\n\n\n
The average of the counter-clockwise rotating pendulum is 1.772803 seconds per half rotation, i.e. 3.545606 seconds per rotation.<\/p>\n\n\n\n\n\n
The mean of the clockwise pendulum is 1.772721 seconds per half rotation, or 3.545442 seconds per rotation.<\/p>\n\n\n\n\n\n
The difference between the two is 0.000164<\/p>\n\n\n\n\n\n
The average between the two directions of rotation is 3.545524 seconds. This is the time it would take for my pendulum to make one revolution at the equator, in either direction.<\/strong><\/p>\n\n\n\n\n\nAverage between counter-clockwise (CCW) and clockwise (CW) revolutions: 0.00016 seconds.<\/strong><\/p>\n\n\n\n\n\n<\/div>\n\n\n\n\n\n
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8 December 2024<\/strong><\/p>\n\n\n\n\n\n7th test<\/strong>:<\/p>\n\n\n\n\n\n<\/div>\n\n\n\n\n\n
All of the above experiments were performed with the thruster engaged and the pendulum grazing the self-centring floating ring.<\/strong> <\/p>\n\n\n\n\n\nFor the experiment to be truly pure, the thruster would have to be used only to keep the pendulum rotating at a constant amplitude and free of any eccentricity before being switched off to let the pendulum rotate by its inertia alone.<\/p>\n\n\n\n\n\n
This should answer three questions:<\/p>\n\n\n\n\n\n
A: What is the disruptive influence of the thruster and the self-centring floating ring on the pendulum stroke?<\/strong><\/p>\n\n\n\n\n\nB: What is the CW and CCW travel of the pendulum when the thruster is switched off<\/strong>?<\/p>\n\n\n\n\n\nC: What are the differences between the travels of the maintained and free pendulums?<\/strong><\/p>\n\n\n\n\n\n<\/div>\n\n\n\n\n\n
Here are three counter-clockwise<\/strong> throws, followed by three cuts in the thruster power supply.<\/p>\n\n\n\n\n\n…where we can clearly see that the maintained pendulum grazing the self-centring floating ring rotates at an average of 1.772804 seconds per half rotation, or 3.545615 seconds per revolution. Once it is free, however, its course becomes slower and very stable, maintaining an average of 1.773315 seconds per half rotation, or 3.546630 seconds per revolution.<\/p>\n\n\n\n\n\n
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Here are three clockwise<\/strong> launches, followed by three cuts in the thruster’s power supply.<\/p>\n\n\n\n\n\n…where we see that the maintained pendulum grazing the self-centring floating ring is now rotating at an average of 1.772757 seconds per half rotation, or 3.545514 seconds per revolution. On the other hand, once free, its course becomes slower and very stable, maintaining an average of 1.773257 seconds per half rotation, or 3.546514 seconds per revolution.<\/p>\n\n\n\n\n\n
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Conclusion:<\/strong><\/p>\n\n\n\n\n\nThe powered pendulum rotates in 3.545615 seconds CCW and 3.545514 seconds CW, a difference of 0.00010 seconds.<\/strong><\/p>\n\n\n\n\n\nThe inertial pendulum rotates in 3.546630 seconds CCW and 3.546514 seconds CW, a difference of 0.00011 seconds<\/strong>.<\/p>\n\n\n\n\n\nThe powered pendulum is faster, less accurate, but can be tested over very long periods. The inertial pendulum is slower, more accurate but cannot be tested for more than half an hour before forming an ellipse. <\/p>\n\n\n\n\n\n
Both demonstrate the Earth’s rotation.<\/p>\n\n\n\n\n\n
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21 December 2024, 8th test.<\/strong><\/p>\n\n\n\n\n\n<\/div>\n\n\n\n\n\n
“The enemy is the ellipse<\/em><\/p>\n\n\n\n\n\nThe course of a conical pendulum inevitably ends up in an ellipse, distorting all measurements. Bravais therefore made pages of mathematical corrections to correct this elliptical effect and thus obtain a usable result. Instead, I chose to circularly constrain the travel of the powered pendulum, which is thus accelerated by a thousandth of a second per rotation, in both directions.<\/p>\n\n\n\n\n\n
The 8th test was therefore carried out in automatic mode: pendulum powered for 5 hours, power cut for 10 minutes, then pendulum powered again for another 5 hours, then power cut for 10 minutes… and so on for 8 days. The propelled pendulum guarantees stable revolutions, free from any elliptical effect. When the power is cut off, it continues its course cleanly for ten minutes by its inertia alone.<\/p>\n\n\n\n\n\n
The automatic mode allows measurements to be taken without any external intervention for an unlimited number of clockwise or anti-clockwise rotations.<\/p>\n\n\n\n\n\n
Result: the inertial pendulum rotates in 3.546592 seconds CCW and 3.546436 seconds CW, a difference of 0.00015 seconds.<\/p>\n\n\n\n\n\n
<\/p>\n\n\n\n\n\n
Conclusion from the total of the 8 trials: The revolutions of the pendulum are always slower counter-clockwise and faster clockwise, confirming the hypothesis made by Bravais in 1851<\/strong>.<\/p>\n\n\n\n\n\nThe<\/strong>differences between counterclockwise (CCW) and clockwise (CW) revolutions during the 8 experiments were as follows:<\/p>\n\n\n\n\n\n2 November 2004, with a 0.83-metre pendulum: 0.00008 seconds <\/p>\n\n\n\n\n\n
21 October 2023, with a 1.93 metre pendulum: 0.00005 seconds<\/p>\n\n\n\n\n\n
16 October 2024, with a 3.06 metre pendulum: 0.00022 seconds<\/p>\n\n\n\n\n\n
7 November 2024, with a 3.12 metre pendulum: 0.00022 seconds <\/p>\n\n\n\n\n\n
27 November 2024, with a 3.12 metre pendulum: 0.00011 seconds <\/p>\n\n\n\n\n\n
3 December 2024, with a 3.12 metre pendulum: 0.00016 seconds<\/p>\n\n\n\n\n\n
8 December 2024, with a 3.12-metre pendulum: 0.00010 seconds (powered), 0.00011 seconds (inertial).<\/p>\n\n\n\n\n\n
21 December 2024: 3.12 metre pendulum: 0.00015 second (inertial).<\/p>\n\n\n\n\n\n
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Suspensions of the Foucault\/Bravais combos 28\/8 (point), 29\/9 (wire) and 30\/10 (gimbal):<\/p>\n\n\n\n\n\n<\/p>\n\n","protected":false},"excerpt":{"rendered":"
Bravais n\u00b01: November 2004: A friend had told me about the conical pendulum experiment that Bravais had done 150 years earlier, saying that I should look into it because it had only been done once by Bravais himself and no one had reproduced it. It was simple: a conical pendulum placed on one of the […]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-5150","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/pages\/5150","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/comments?post=5150"}],"version-history":[{"count":2,"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/pages\/5150\/revisions"}],"predecessor-version":[{"id":5152,"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/pages\/5150\/revisions\/5152"}],"wp:attachment":[{"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/media?parent=5150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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