{"id":5135,"date":"2024-09-03T14:11:44","date_gmt":"2024-09-03T14:11:44","guid":{"rendered":"https:\/\/www.betrisey.ch\/microfoucault-n-26-tatonnements-et-donnees-techniques-part-2"},"modified":"2025-01-28T08:18:05","modified_gmt":"2025-01-28T08:18:05","slug":"microfoucault-n-26-tatonnements-et-donnees-techniques-part-2","status":"publish","type":"page","link":"https:\/\/www.betrisey.ch\/en\/microfoucault-n-26-tatonnements-et-donnees-techniques-part-2","title":{"rendered":"MicroFoucault n\u00b0 26: Trial and error and technical data. (Part 2)"},"content":{"rendered":"\n<div style=\"height:27px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>3 September 2024:<\/strong> It has slowed down a little, but is still 20% too fast on the last revolution. (third day)<\/p>\n\n\n\n<p><strong>4 September:<\/strong> The experiment has become extremely stable over 4 days and will no longer provide me with any new information.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1001\" height=\"687\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfoucault6.jpg\" alt=\"\" class=\"wp-image-3964\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfoucault6.jpg 1001w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfoucault6-300x206.jpg 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfoucault6-768x527.jpg 768w\" sizes=\"auto, (max-width: 1001px) 100vw, 1001px\" \/><\/figure>\n\n\n\n<p>So it&#8217;s time to modify it with new parameters&#8230;<\/p>\n\n\n\n<div style=\"height:27px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-center\"><strong>Trial 12<\/strong><\/p>\n\n\n\n<div style=\"height:27px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>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?<\/p>\n\n\n\n<p>One potential culprit could be an off-centre pendulum.<\/p>\n\n\n\n<p>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.)<\/p>\n\n\n\n<p>Another could be due to the harmonic vibrations induced by the Charron ring. How can we tell?<\/p>\n\n\n\n<p>For example: what happens if I gently place a one-gram rifle pellet (5.5mm, calibre .22) on the Y axis of the balance?<\/p>\n\n\n\n<p>This was done at 7.25am.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"668\" height=\"525\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/plomb1gr-1.png\" alt=\"\" class=\"wp-image-3978\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/plomb1gr-1.png 668w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/plomb1gr-1-300x236.png 300w\" sizes=\"auto, (max-width: 668px) 100vw, 668px\" \/><\/figure>\n<\/div>\n\n\n<p>The effect of placing the shot at 7.25 am can be seen very clearly in the time data:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"991\" height=\"683\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/plomb.jpg\" alt=\"\" class=\"wp-image-3999\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/plomb.jpg 991w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/plomb-300x207.jpg 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/plomb-768x529.jpg 768w\" sizes=\"auto, (max-width: 991px) 100vw, 991px\" \/><\/figure>\n<\/div>\n\n\n<p>But we can see that the pendulum resumed its normal course an hour and a half later, exactly as if nothing had happened. <\/p>\n\n\n\n<p><strong>5 September:<\/strong> the previous day&#8217;s lead experiment can be seen here:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"997\" height=\"688\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfouc7.jpg\" alt=\"\" class=\"wp-image-4001\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfouc7.jpg 997w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfouc7-300x207.jpg 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfouc7-768x530.jpg 768w\" sizes=\"auto, (max-width: 997px) 100vw, 997px\" \/><\/figure>\n\n\n\n<p>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.<\/p>\n\n\n\n<div style=\"height:27px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-center\"><strong>Trial 13<\/strong><\/p>\n\n\n\n<div style=\"height:27px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>9:37: Another &#8216;hot&#8217; 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&#8217;s hoping.<\/p>\n\n\n\n<p>11am, 12pm, 1pm, 2pm, 3pm&#8230; failure. Cuisantissime failure. The pendulum has stopped, and is even moving backwards a little. I don&#8217;t understand it any more.<\/p>\n\n\n\n<p>4pm: The susceptible has decided to go back, and in the right direction&#8230;<\/p>\n\n\n\n<p>8 p.m.: All&#8217;s well&#8230;<\/p>\n\n\n\n<p><strong>6 September: <\/strong>8 o&#8217;clock: the pendulum made its half-revolution during the night.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"987\" height=\"659\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfouc8.jpg\" alt=\"\" class=\"wp-image-4032\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfouc8.jpg 987w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfouc8-300x200.jpg 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfouc8-768x513.jpg 768w\" sizes=\"auto, (max-width: 987px) 100vw, 987px\" \/><\/figure>\n\n\n\n<p>Observation: fitting the external reinforcement has no effect on the pendulum&#8217;s speed of revolution. Caramba, missed again.<\/p>\n\n\n\n<p>Another observation: the pendulum always turns at the right speed EXCEPT WHEN IT&#8217;S IN THE Y AXIS: it then turns 40\u00b0 in an hour, which is four times too much.<\/p>\n\n\n\n<p>If I can eliminate the hole in the Y axis, I&#8217;ll have a very accurate Foucault pendulum.<\/p>\n\n\n\n<div style=\"height:27px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-center\"><strong>Test 14<\/strong><\/p>\n\n\n\n<div style=\"height:27px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>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&#8230;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"867\" height=\"1024\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/mercure-867x1024.jpg\" alt=\"\" class=\"wp-image-4037\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/mercure-867x1024.jpg 867w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/mercure-254x300.jpg 254w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/mercure-768x907.jpg 768w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/mercure-1301x1536.jpg 1301w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/mercure-1734x2048.jpg 1734w\" sizes=\"auto, (max-width: 867px) 100vw, 867px\" \/><\/figure>\n\n\n\n<p>8h40&#8230; Total failure after just ten minutes!<\/p>\n\n\n\n<p>9.18am: One of the vials of mercury is placed a little lower down, directly <strong>on<\/strong> the balance wheel.<\/p>\n\n\n\n<p>4.30pm: Failure. The pendulum does not turn at all. The vial of mercury is removed.<\/p>\n\n\n\n<p>7 p.m.: The pendulum turns. Suspension wire rotates 15&#8242; clockwise.<\/p>\n\n\n\n<p><strong>7 September 2021:<\/strong> The dip has also moved 15&#8242; clockwise. The problem was simply there: the wire was the cause.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>Test 15<\/strong><\/p>\n\n\n\n<p><strong>7 September 2021: I<\/strong> 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.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"938\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/coil-centerer-1024x938.jpg\" alt=\"\" class=\"wp-image-4061\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/coil-centerer-1024x938.jpg 1024w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/coil-centerer-300x275.jpg 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/coil-centerer-768x703.jpg 768w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/coil-centerer-1536x1406.jpg 1536w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/coil-centerer-2048x1875.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>Launched at 6pm and running perfectly. I&#8217;m very happy with my brand new rotation indicator:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2358\" height=\"1851\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/image.jpg\" alt=\"\" class=\"wp-image-4070\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/image.jpg 2358w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/image-300x235.jpg 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/image-1024x804.jpg 1024w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/image-768x603.jpg 768w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/image-1536x1206.jpg 1536w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/image-2048x1608.jpg 2048w\" sizes=\"auto, (max-width: 2358px) 100vw, 2358px\" \/><\/figure>\n<\/div>\n\n\n<p><strong>8 September:<\/strong> 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\u00b0 and 90\u00b0 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.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"997\" height=\"685\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfouf9-3.jpg\" alt=\"\" class=\"wp-image-4130\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfouf9-3.jpg 997w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfouf9-3-300x206.jpg 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfouf9-3-768x528.jpg 768w\" sizes=\"auto, (max-width: 997px) 100vw, 997px\" \/><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"821\" height=\"758\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfoud9.png\" alt=\"\" class=\"wp-image-4162\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfoud9.png 821w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfoud9-300x277.png 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfoud9-768x709.png 768w\" sizes=\"auto, (max-width: 821px) 100vw, 821px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-video\"><video height=\"500\" style=\"aspect-ratio: 610 \/ 500;\" width=\"610\" controls src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/microfouc9.mp4\"><\/video><\/figure>\n\n\n\n<p>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&#8217;t going so badly.<\/p>\n\n\n\n<div style=\"height:27px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color has-link-color wp-elements-0abd16d43f12f7d9753fe172e7f95350\"><strong>I distinguish three degrees of quality in a Foucault pendulum<\/strong>:<\/p>\n\n\n\n<div style=\"height:27px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color has-link-color wp-elements-58689d61edd2d75dff89aec41ced2a29\"><strong>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. <\/strong><\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color has-link-color wp-elements-2a773dd4b2d4a64523b53df8e9edfd9b\"><strong>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&#8217;s a good Foucault pendulum.<\/strong><\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color has-link-color wp-elements-9eddfef760a768bc9c08744cdbc13fca\"> <strong>3rd degree: it turns in the right direction, and each hour is within 10% (slower or faster) of what it should be. It&#8217;s an excellent Foucault pendulum.<\/strong><\/p>\n\n\n\n<div style=\"height:27px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><strong>8 September<\/strong>: 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&#8217;s ring.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"998\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/mercure-1-1024x998.jpg\" alt=\"\" class=\"wp-image-4097\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/mercure-1-1024x998.jpg 1024w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/mercure-1-300x292.jpg 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/mercure-1-768x749.jpg 768w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/mercure-1-1536x1497.jpg 1536w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/09\/mercure-1.jpg 2022w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>Midnight: the 50-microlitre shock absorber is fitted to the balance wheel.<\/p>\n\n\n\n<p><strong>9 September<\/strong>, 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.<\/p>\n\n\n\n<p>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.<\/p>\n\n\n\n<p><strong>10 September:<\/strong> Exactly the same as yesterday.  No noticeable difference, with or without shock absorber. <\/p>\n\n\n\n<p>7.50am: Removal of the 50 microlitre mercury damper. Fitted 16 mm copper eddy-current Charron ring. Unsuccessful: amplitude too small.<\/p>\n\n\n\n<p>8.30 am: Installation of a 26 mm copper eddy current Charron ring. Another failure. A good amplitude, but &#8230; no more revolution.<\/p>\n\n\n\n<p>3pm: Installation of a 40mm aluminium Charron eddy current ring. <\/p>\n\n\n\n<p>8 p.m.: Another dismal failure.<\/p>\n\n\n\n<p>9pm: Removal of the lower Charron ring, which was useless anyway.<\/p>\n\n\n\n<p><strong>11 September<\/strong>: 6.45am, rotation of the suspension by 45\u00b0 CCW (counter-clockwise) to move the error zone to 00 degrees south.<\/p>\n\n\n\n<p class=\"has-vivid-red-color has-text-color has-link-color wp-elements-3b3e158cca253254d113f0298800fb31\">4 p.m.: The kid&#8217;s doing really well! He&#8217;s suddenly decided to give us a magnificent curve that&#8217;s twice as flat with a much more constant speed of revolution. I don&#8217;t understand a thing about it, but it works: I don&#8217;t understand any more!<\/p>\n\n\n\n<div style=\"height:27px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-center\">This page is too long again: the rest is <a href=\"https:\/\/www.betrisey.ch\/en\/microfoucault-n-26-tatonnements-et-donnees-techniques-part-3\">here<\/a><\/p>\n\n\n\n<div style=\"height:27px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>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&#8217;s time to modify it with new parameters&#8230; Trial 12 The dips [&hellip;]<\/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-5135","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/pages\/5135","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=5135"}],"version-history":[{"count":2,"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/pages\/5135\/revisions"}],"predecessor-version":[{"id":5213,"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/pages\/5135\/revisions\/5213"}],"wp:attachment":[{"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/media?parent=5135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}