Foucault's Pendulum Recreation for Physics Project

[Tom.G]

re. spherical vs flat support

I've wondered about that - though not needed to so far. However, I'd be a little wary - whenever the pivot travelled, it would then be on a slope.

The idea was that a spherical support would cancel out any imperfections over a rotation cycle and keep the center of the bob path fixed over the excitation device ('electrostatic motor'), at least on average.

p.s. Could you post a photo of the contraption?

 

[lesaid]

Could you post a photo of the contraption?

Here goes - hopefully it won't be too large for the forum ...

I have more design details - if anyone wants to try to put something like this together and would like more detail, please let me know.

From top left, clockwise
1. The pivot assembly. White 'blob' is polymorph that holds the china platform in place and prevents the pivot from sliding off it. Frame is made from pieces of brass bar cross section 13x3 mm, soldered together with the aid of a small blowtorch. Don't look too closely at the solder quality - I'm used to a soldering iron, not a blowtorch for soldering! Assembly was done with the aid of lots of (now charred) temporary wooden jigs and clamps. The support bar is made from two lengths of bar, one perpendicular to the other, to form a 'T' cross section. This was the stiffening required to remove lissajous figures, after which the pendulum worked. Shaft is 3 mm brass rod, joined with M4 hex standoff nuts with bar soldered into the ends, and with M4 threaded brass rod to provide height adjustment. The ruby probe is one of these : http://www.renishaw.com/shop/Product.aspx?Product=A-5000-7808.

2. The bob, slung on an M4 threaded brass hook screwed into a hex nut on the bottom of the shaft. below is the card marked off in 'hourly' intervals.

3. The base, underneath the card. The driver electrode is screwed into an acrylic sheet, and (not visible) attached to a screened EHT lead going to the power supply. The reason for the long bolt is to get the action point well away from the feeder. Initially, with an unscreened feeder and a short bolt, the pendulum would tend to swing in line with the feeder cable! The bob is a brass-encapsulated lead clock weight with a bolt and domed nut glued to the bottom, matching the driver electrode.

4. The pivot assembly on its own, showing the pivot point. the probe is screwed into an M2 hexagonal nut, which in turn is screwed on to an M2 bolt whose head is soldered to an M4 nut that joins the frame pieces.

This is the schematic from which I constructed the whole thing. The attachment of the ruby probe to the frame is not quite the same as the final device, but otherwise it is accurate.

 

[sophiecentaur]

The axes don't rotate. Their directions were tied to the orientation of the pivot bar whose flex was causing the problem.

The simplest Lissajous figures are generated with totally independent X and Y inputs (two separate generators with different phases or frequencies). Actually, two nominally independent High Q oscillators can 'see' each other through all sorts of electrical paths and you can get interaction (beating) between them. In this case, there has to be some coupling between the two oscillators because they are connected to the same beam support. The Q factor is only in the order of hundreds or a few thousand (?). Displacement in one direction (particularly when you have a single supporting rod / beam can cause a displacement in the other direction. Twisting the beam can cause it to shorten. If there is any asymmetry in the support, a change in length can cause an offset in the position of the pivot in the line of the beam. (This will depend on the rigidity of the supports, of course) It would be pretty easy to force this to happen by using a low modulus, asymmetrical support. In your case, you improved things by increasing stiffness, which reduced the coupling. The clincher, I think, is when the lissajous figures have maximum deviation (possibly almost a straight line in one direction) and then it changes to another direction every cycle (walking through) - showing that the energy has left one mode and gone to the other one - and back again. It's quite possible that your arrangement has always been good enough to eliminate this beat over the operating time of the pendulum so my idea may just not be relevant. If you were to sort the oscillation in the direction of the axis, was there any oscillation induced across the beam? That would have to be due to coupling but only if the beam were not being rotated by the earth, of course and the gyroscopic effect came in.

 

[lesaid]

The simplest Lissajous figures are generated with totally independent X and Y inputs (two separate generators with different phases or frequencies). Actually, two nominally independent High Q oscillators can 'see' each other through all sorts of electrical paths and you can get interaction (beating) between them. In this case, there has to be some coupling between the two oscillators because they are connected to the same beam support. The Q factor is only in the order of hundreds or a few thousand (?). Displacement in one direction (particularly when you have a single supporting rod / beam can cause a displacement in the other direction. Twisting the beam can cause it to shorten. If there is any asymmetry in the support, a change in length can cause an offset in the position of the pivot in the line of the beam. (This will depend on the rigidity of the supports, of course) It would be pretty easy to force this to happen by using a low modulus, asymmetrical support. In your case, you improved things by increasing stiffness, which reduced the coupling. The clincher, I think, is when the lissajous figures have maximum deviation (possibly almost a straight line in one direction) and then it changes to another direction every cycle (walking through) - showing that the energy has left one mode and gone to the other one - and back again. It's quite possible that your arrangement has always been good enough to eliminate this beat over the operating time of the pendulum so my idea may just not be relevant. If you were to sort the oscillation in the direction of the axis, was there any oscillation induced across the beam? That would have to be due to coupling but only if the beam were not being rotated by the earth, of course and the gyroscopic effect came in.

Trying to get my head around the implications of what you said ...

In this case, there has to be some coupling between the two oscillators because they are connected to the same beam support.

that makes sense, in principle. In this case though, the difference in 'flexibility' must be huge. In one direction, a relatively thin (3 mm) brass bar is bending over a six inch or so length - I was able (with the aid of a microscope) to estimate the spring constant quite easily. In the other direction, a displacement requires compressing the bar lengthways and/or distorting a pretty robust wooden beam to which the bar was clamped.

The behaviour I was seeing is exactly as described in https://en.wikipedia.org/wiki/Lissajous_curve under the subheading "Application for the case of a=b", though to complete a whole cycle took 58 minutes. If the swing was started off circular, that is the pattern it settled into. The stable directions did not move - the pattern stayed the same, including its orientation, right through the decay over five cycles or so. If I recollect rightly (can't do this experiment any longer having stiffened the bar!), if the swing was started as a straight swing half way between the two 'straight swing' directions, it would become elliptical and develop into the same pattern as if it had been started as a circular swing. Intermediate initial swing directions produced two stable swings that were not perpendicular - the angle depending on the direction of the initial swing. In all cases, the 'straight swing' directions, once established, did not move at all.

A quick calculation gives a Q of just over $10^5$, based on a swing period of 2.2s and a decay constant of about $1.33 * 10^{-5}$ - which I still find unbelievably high (if I've got it right!).

I tried modelling this behaviour in two different ways, using the measured spring constant, and predicting the frequency of oscillation for the measured spring constant, and a dramatically higher value. Calculating the elapsed time for the two frequencies to drift out of phase and back, through a whole cycle, came to 36 and 38 minutes for the two methods. I think this is close enough to the experimental 58 minutes to support the models, given the sensitivity of this system and the simplifications (one method involved modelling a longer pendulum such that the movement at the original pivot point matched the measured flex in the bar - the other was through setting up equations of motion and using eigenvalues to find the frequency).

I am practising newly learned skills here, so being a little wary of making silly errors, but these results seem to me to make sense.

I am wishing now that I had taken the time to try to measure the spring constant of the stiffened version of the bar before mounting it back into the pendulum. I suspect that flex would have been too small for me to detect.

I am thinking that the reason the swing decays into a small circular motion before finally stopping, is perhaps because the direction with the larger swing will decay faster than that with the lower swing, so the ratio of amplitudes of swing in the different directions might approach 1 as the amplitude approaches zero? Or perhaps it is due to transfer of energy, and if this system could run for 24 hours instead of 6, I might see a cyclic behaviour. Not sure how I tell which behaviour I'm seeing?

But now, since the fix, if I start with a circular swing - it just decays into smaller circles until, hours later, it finally comes to rest.

Learning a lot with this project!

 

[sophiecentaur]

@lesaid From what you say about your setup, the mods you did have reduced or eliminated the problem so perhaps you needn't worry about this.
It would not be too hard for you to retro fit a similar arrangement to your original. It struck me that a rigid plate, mounted on a round bar, with rubber each side, would give two different values of swing period and if you fix the rod at one end only, that would provide the coupling from one mode to the other. There are many alternative arrangements that you could probably incorporate in your setup. Perhaps a 'wedge' of resilient material, mounted diagonally, could provide some coupling.
Just to reiterate my point: if you start the oscillation in just one plane and the other mode starts up significantly within less than a few hours, then there must be some coupling. The Wiki article doesn't discuss coupled oscillations, afaics and that is another level of difficulty. With coupling, the amplitudes of each component change, according to the coupling coefficient.

 

[lesaid]

Thank you for those ideas - this project is spawning off things to think about in every direction! Pity I've got to move my focus primarily to my scheduled studies after this weekend - but I'll keep on at this in the background. I'm building up a growing list of things to explore!

I am not giving up yet on a simple drive with no electronics - I'm going to do a bit more on the electrostatic approach before moving to magnets. But - a question. It seems that the pivot assembly and the support bar experience a mutual force, whether they both have a charge at the same potential, or when just one is charged and the other is grounded. I presume the latter is because of induced dipoles.

So - it seems to me that two conductors each with the same charge will repel each other slightly less than Coulomb's law would predict, as induced dipoles in each conductor should add a small attractive force into the mix. And if the charges are opposite, they should attract slightly more than the prediction as both forces will now be attractive and should add together.

I haven't heard of this before so I suspect I'm wrong. But does this make sense?

If so, might be interesting to try to measure the discrepancy with a torsion balance or similar. I'll also have a go at trying to calculate what those forces should be, though I'm not sure yet how to work out the forces between charged bodies that can't be approximated as point masses! I suppose I need to start by understanding the charge distribution through and on the surface of the body. Perhaps I need to get through the 'Maxwell' part of my course first!

A work-around for this problem on the pendulum was suggested by someone else - to put the 60 Gohm resistor in the pendulum shaft just above the bob - so the entire upper shaft and pivot assembly can be grounded. Then all electrostatic forces at the pivot have to disappear.

 

[SPW]

(I apologise if this is the wrong area to post)
Hello everybody

I am planning on building my first Focault Pendulum(As a physics projject for school) and I have a few questions. I am going to purchase a cable(it needs to be smooth and friction-less around 7 feet), I also am going to need to purchase a bob (around 2-3lbs). Now my first question is where can i buy these items? Online has only a few varieties and I do not like my options.

Also what would be the best way to suspend this cable from my ceiling in order to have it rotate 360 degrees without friction causing it to slow?

I was also thinking of purchasing a donut magnet and installing it at the top as a kicker (possibly with an iron collar); if there is too much friction/wind resistance and my pendulum would stop after 2 hours.

Any help, advice, questions, are all appreciated thank you very much for taking the time!

Brad

Hi, one of the easiest ways to obtain a low friction pivot for your project is to use a universal joint. They are available in very small sizes for around £10 - £12. You can also use a solid bar instead of string/cord for greater accuracy.

 

[lesaid]

Hi, one of the easiest ways to obtain a low friction pivot for your project is to use a universal joint. They are available in very small sizes for around £10 - £12. You can also use a solid bar instead of string/cord for greater accuracy.

Hi! Thanks for joining in!

Actually - I am using a solid bar for exactly that reason - I found it a great improvement on a cord! My pivot is a ruby bearing sitting on a hard platform - if you scroll up a few posts, you'll find photographs :) With a shaft of only about a metre, I didn't think any kind of 'ordinary' joint would be good enough.

What I have now works very nicely - shows the Foucault effect over up to six hours while it decays (unpowered). Currently looking at how to implement an electrostatic driver.

Edit : Sorry - misunderstood - you were replying to the first post in the thread? Ignore my comment if it isn't relevant!

 

[SPW]

To obtain a low friction 360degree pivot you could use a Universal Joint. These can be bought for around £10. Another possibility is to use a Neodymium magnet. Both of these solutions would also allow you to use a metal rod instead of string, which would be more accurate. I hope this is useful.

S.P.W.

 

[SPW]

Hi again, if you want run the experiment for 24hrs you could use an escapement, such as is used to keep an analogue clock ticking. Depending on how good you are at woodwork, they're quite simple to make. Google "escapement animations". Alternatively, you could adapt "the perpetual pendulum" which uses magnetic induction to give your pendulum a kick. It's not that complicated. It uses a couple of coils. 1 to discharge the current at just the right time & the other works like an electromagnet to give the kick. Here's a model & curcuit diagram. http://www.bowdenshobbycircuits.info/swinger.html

Hope that's inspired you. Keep your thread updated, I'd love to see the finished project.
S.P.W.

 

[lesaid]

Hi again, if you want run the experiment for 24hrs you could use an escapement, such as is used to keep an analogue clock ticking. Depending on how good you are at woodwork, they're quite simple to make. Google "escapement animations". Alternatively, you could adapt "the perpetual pendulum" which uses magnetic induction to give your pendulum a kick. It's not that complicated. It uses a couple of coils. 1 to discharge the current at just the right time & the other works like an electromagnet to give the kick. Here's a model & curcuit diagram. http://www.bowdenshobbycircuits.info/swinger.html

Hope that's inspired you. Keep your thread updated, I'd love to see the finished project.
S.P.W.

This project is highly inspiring :)

My aim is to have this experiment run for a complete rotation - which at my latitude is about 29 hours - somewhat longer than a 'day'. If it will run perpetually, I just might use it as a 'laboratory clock' just for fun! But I'm not there yet!

I don't think I can use any kind of 'escapement' mechanism - the point of this is to demonstrate the Foucault effect, which requires that nothing explicitly pushes or pulls the pendulum in any way other than very precisely along the radius of swing. Magnetism certainly can provide that kick, though I'm trying to avoid it. Partly just for the challenge, and to try something I haven't seen talked about before, I want to try to get a 'kicker' working that doesn't require any electronics beyond a power supply. So I'm trying to use electrostatic repulsion rather than magnetism for the driver.

I would like to see that circuit - but I get 'page not found' when I click your link.

Not doing anything more on the pendulum for a day or two though. Next step is to solve the problem mentioned in post #41 and requires a resistor that I have had to order. It will be sometime next week probably before I get it (100 G-ohm 20 kV). Replacing the 60 G-ohm one with a higher value, since I'll be putting it into the pendulum shaft just above the bob. The bob alone will have a considerably lower capacitance than the whole pendulum assembly, so I think I need a higher value resistor to get a similar time constant. In the meantime, I'm trying to figure out and analyse the exact causes of the problems from #41.

If (no! when !) if finally works properly and completes a full cycle, I'll upload details here for you to see :)

 

[SPW]

Hi, I put "perpetual swinging pendulum" into Google and in the results the web page is "bowdenshobbycurcuits". Hope that helps. There's a circuit diagram a bit further down the page. Another possibility if you want to cheat: have you seen those toys you can get in £1 shops? They've got a tiny photovoltaic cell & the magnetic gubbins inside. You might be able to bastardise one?

S.P.W.

 

[SPW]

One way around it, and the way it was demonstrated before our new fangled tech, was to hang the bob inside a London monument (don't know which one). It was around the height of Nelson's Column. It actually doesn't matter about the swing rate, it will always come back around to its starting point over 24hrs... It's fun to get these sorts of projects working...

S.P.W.

 

[lesaid]

Well - if it is the Foucault effect, it would be a bit more than 24 hours - but yes. The really fun challenge (for me) is to make that work with a pendulum around a metre long, rather than the height of a tall monument! That is what requires huge attention to detail. Mine takes about 29 hours to go around, which is about right for my latitude - though it won't do it all in one go until I get a driver working without screwing up the Foucault behaviour. I have to restart it every five or six hours.

If I have to use magnets for a driver, I'd be thinking perhaps of a single photocell under the bob at the centre of the swing, with a nearby LED to provide some light. It would trigger when the edge of the bob passed over it on its way towards the centre of the swing - and after a timed delay, could deliver its 'kick'.

 

[Tom.G]

Hi, I put "perpetual swinging pendulum" into Google and in the results the web page is "bowdenshobbycUrcuits". Hope that helps. There's a circuit diagram a bit further down the page. Another possibility if you want to cheat: have you seen those toys you can get in £1 shops? They've got a tiny photovoltaic cell & the magnetic gubbins inside. You might be able to bastardise one?
S.P.W.

The "bowdenshobbycUrcuits" link in the above quote should be "bowdenshobbycIrcuits"

The link in your post #60 (http://www.bowdenshobbycircuits.info/swinger.html) has an "L" on the end. If you drop the "L" and use http://www.bowdenshobbycircuits.info/swinger.htm it works.

Hope it helps.

 

[lesaid]

The "bowdenshobbycUrcuits" link in the above quote should be "bowdenshobbycIrcuits"

The link in your post #60 (http://www.bowdenshobbycircuits.info/swinger.html) has an "L" on the end. If you drop the "L" and use http://www.bowdenshobbycircuits.info/swinger.htm it works.

Hope it helps.

got it - thanks!

Not quite the same kind of pendulum though as I'm working on.

Might be a fun challenge to modify that design to decrease its current load - see how far one can reduce it to maximise battery life. Quite a lot of scope I think.

 

[SPW]

The "bowdenshobbycUrcuits" link in the above quote should be "bowdenshobbycIrcuits"

The link in your post #60 (http://www.bowdenshobbycircuits.info/swinger.html) has an "L" on the end. If you drop the "L" and use http://www.bowdenshobbycircuits.info/swinger.htm it works.

Hope it helps.

Sorry about that Tom. The perils of high speed typing on an iPad. In my defence, the U&I are next to each other & spellchecker doesn't understand when you connect words without spaces. Lol...

 

[Nidum]

Pneumatics . A tiny suction or blowing vent on centre line . Activated when bob is just off centre . No electromagnetics in near vicinity of bob at all .

 

[lesaid]

Pneumatics . A tiny suction or blowing vent on centre line . Activated when bob is just off centre . No electromagnetics in near vicinity of bob at all .

Interesting idea :)

Still need sensor electronics though, and some actuator to provide a puff of air. A lot would depend on just how perfect the cylindrical symmetry of the bottom of the bob is - might work on mine! And of course on the symmetry of the puff of air.

The beauty of the electrostatic approach though, which none other that I have thought of can match (if it works!), is that the sensing of the bob's position, the triggering of the push and the push itself is done by a simple spark with no electronics, timing or complexity. All it should need is an appropriate DC supply voltage, and a suitable, resistive discharge path from the bob to ground.

 

[SPW]

Pneumatics . A tiny suction or blowing vent on centre line . Activated when bob is just off centre . No electromagnetics in near vicinity of bob at all .

Nice idea but difficult to pull off without deflecting the pendulum. I still think a simple escapement would work provided the whole unit is hung underneath a universal joint. Tricky one.

 

[lesaid]

Nice idea but difficult to pull off without deflecting the pendulum. I still think a simple escapement would work provided the whole unit is hung underneath a universal joint. Tricky one.

I can't imagine what kind of escapement could work here, given that the pendulum needs to be able to swing equally in any direction without any influence to favour one direction over another. Escapements (so far as I am aware) are only used where the pendulum is swinging in a single plane, such as a clock. Can you elaborate on how it would work?

Edit : just realized what you're talking about - an escapement driving the pendulum in a single plane, but the whole plane, escapement and all, rotating under a universal joint. So - it would essentially be a double pendulum - the lower one just like a clock in principle, and the upper one being a free, non-driven pendulum under a universal joint. That sounds complex to figure out !

Would an analogy be a child on a seat attached to a single rope, that can swing any way, and on a seat that can rotate in any direction. The child keeps the swing going by swinging his legs in the direction he happens to be facing in. This induces a swing in the whole system which is able to rotate any way. Is that a reasonable way of thinking of it?

Need to think about it - not a clue how that kind of system might behave!

 

[SPW]

I can't imagine what kind of escapement could work here, given that the pendulum needs to be able to swing equally in any direction without any influence to favour one direction over another. Escapements (so far as I am aware) are only used where the pendulum is swinging in a single plane, such as a clock. Can you elaborate on how it would work?

Edit : just realized what you're talking about - an escapement driving the pendulum in a single plane, but the whole plane, escapement and all, rotating under a universal joint. So - it would essentially be a double pendulum - the lower one just like a clock in principle, and the upper one being a free, non-driven pendulum under a universal joint. That sounds complex to figure out !

Would an analogy be a child on a seat attached to a single rope, that can swing any way, and on a seat that can rotate in any direction. The child keeps the swing going by swinging his legs in the direction he happens to be facing in. This induces a swing in the whole system which is able to rotate any way. Is that a reasonable way of thinking of it?

Need to think about it - not a clue how that kind of system might behave!

Don't forget that the pendulum does not deviate from a left to right plane, not in some kind of figure of 8 pattern. It's the Earth that rotates, so provided the top pivot rotates freely around 360degrees an escapement, preferably spring wound shouldn't affect the outcome. I've been thinking about the electromagnet, electrostatic or pneumatic approaches, which would potentially deviate the natural course of the pendulum. Any induction, however small, would surely have to be at the top of the system. You've really given me something interesting to ponder anyway. Good luck & let us know what transpires... PS: a grasshopper escapement causes nominal resistance.

 

[lesaid]

Don't forget that the pendulum does not deviate from a left to right plane, not in some kind of figure of 8 pattern. It's the Earth that rotates, so provided the top pivot rotates freely around 360degrees an escapement, preferably spring wound shouldn't affect the outcome. I've been thinking about the electromagnet, electrostatic or pneumatic approaches, which would potentially deviate the natural course of the pendulum. Any induction, however small, would surely have to be at the top of the system. You've really given me something interesting to ponder anyway. Good luck & let us know what transpires... PS: a grasshopper escapement causes nominal resistance.

A question - in the 'escapement' scheme - would the escapement itself form the bob of another pendulum swinging from the universal joint, or would it be held rigid, unable to move in any way other than to rotate about the vertical axis?

If the latter, what does the swinging pendulum achieve? How will the torque at the universal joint (in relation to the rotating frame of reference that is the earth) differ from what it would be if it was simply an inert weight being suspended - such as a heavy horizontal bar - under the universal joint?

If it does swing, I'm not sure how to start analysing the likely motion!

This is indeed making me think - and I'll let you know how the project develops.

 

[SPW]

A question - in the 'escapement' scheme - would the escapement itself form the bob of another pendulum swinging from the universal joint, or would it be held rigid, unable to move in any way other than to rotate about the vertical axis?

If the latter, what does the swinging pendulum achieve? How will the torque at the universal joint (in relation to the rotating frame of reference that is the earth) differ from what it would be if it was simply an inert weight being suspended - such as a heavy horizontal bar - under the universal joint?

If it does swing, I'm not sure how to start analysing the likely motion!

This is indeed making me think - and I'll let you know how the project develops.

Yes, you're spot on. The escapement assembly and pendulum would be fixed & only rotate around a vertical axis. This should not make any difference to the progression as the Earth rotates. Although it appears to draw a figure of 8 as it progresses the pendulum does actually trace a straight line. If you think about it an advance of 1 degree equates to -1 degree at the opposite end of the swing, I can jot down the equations for you if you'd like, it's all to do with the conservation of angular momentum.

 

[lesaid]

Yes, you're spot on. The escapement assembly and pendulum would be fixed & only rotate around a vertical axis. This should not make any difference to the progression as the Earth rotates. Although it appears to draw a figure of 8 as it progresses the pendulum does actually trace a straight line. If you think about it an advance of 1 degree equates to -1 degree at the opposite end of the swing, I can jot down the equations for you if you'd like, it's all to do with the conservation of angular momentum.

I'd be interested in the equations.

I have to say I'm still struggling to see, in that scenario, what difference it makes whether what is attached to the universal joint is a pendulum or a fixed bar that doesn't swing. In each case, there will be a minute torque (relative to the rotating Earth frame) applied to the universal bearing. I'm obviously missing something in my intuition!

By the way - the current version of my pendulum (which is free swinging - not driven) works well and displays the expected Foucault effect - but does not do figure of eights - it swings in a long, very thin, ellipse that is close to a straight swing, and that never changes shape, other than, when it decays to a few percent of its original amplitude after five hours or so, the ellipse gradually becomes more circular. And the 'bearing' at the top doesn't rotate. It could, easily - but it is the swing that rotates (relative to earth) - not the bearing at the top. Otherwise my bearing wouldn't be able to show more than a small amount of rotation without colliding with its supports

Fascinating!

 

[Herman Trivilino]

By the way - the current version of my pendulum (which is free swinging - not driven) works well and displays the expected Foucault effect - but does not do figure of eights - it swings in a long, very thin, ellipse that is close to a straight swing, and that never changes shape, other than, when it decays to a few percent of its original amplitude after five hours or so, the ellipse gradually becomes more circular.

How are you releasing the pendulum to get it started?

 

[lesaid]

How are you releasing the pendulum to get it started?

I am simply holding the bob in my fingers, at a point roughly half way up to minimise the initial oscillation of the bob around the hook that supports it (about four hertz as near as I can judge by guesswork), pulling it back and with ordinary care, letting go with my fingers. Usually, I get it into a pretty straight swing at the first attempt - if not, at most two or three attempts is enough. Then I let it swing for five minutes to settle down, and then rotate the base slightly to align the appropriate indicator on the 'clock' card with the initial swing direction. (won't be able to do that alignment when the pendulum is being driven though, as it would misalign the diver electrode).

I have never needed to bother with burning threads and such, or be too paranoid about precision of release. I am wondering if that is because my setup seems not to have significant coupling between different swing directions, so the initial ellipse is stable and doesn't turn into lissajous figures. But that is guesswork. Is the burning threads technique a workaround required to overcome asymmetries and/or flexing in the system?

What I do have to be careful of, is how far back I pull the bob - too far and the pivot travels slightly across the platform. This doesn't matter for a 'free swing', but would also cause the driver to misalign.

It also matters that the pivot assembly is symmetrical - otherwise when pulling the pendulum back, it tends to rotate.
edit : symmetrical vertically - so the CofG is close to the pivot point in all directions. Having a rigid pendulum rather than a cord helps with this too.

Although the driver at the moment tends to suppress the Foucault effect - it instead rotates the swing to a preferred direction - using the driver, it can be started simply by switching on the driver, and giving the pendulum a tiny nudge. It takes an hour or so, but the driver will gradually build up the amplitude itself into a good swing. Then turn off the driver and the Foucault effect takes over.

 

[lesaid]

I'd be interested in the equations.

I have to say I'm still struggling to see, in that scenario, what difference it makes whether what is attached to the universal joint is a pendulum or a fixed bar that doesn't swing. In each case, there will be a minute torque (relative to the rotating Earth frame) applied to the universal bearing. I'm obviously missing something in my intuition!

After further thought ... a suspended solid bar will only rotate (relative to the earth) if the static friction in the pivot is low enough that the torque applied by the Foucault effect can overcome it. If that were easy, nobody perhaps would bother with pendula. So - in your 'escapement' type of model - with a 2d pendulum suspended from a universal joint and constrained only to rotate around the vertical, and not itself swing - each quarter swing will provide a much higher torque than the static bar would, due to the coriolis force. Over a complete cycle, those torques would sum to exactly the same as the solid bar, but individually could be high enough to overcame the static friction in the bearing. Essentially the same idea as mentioned in an early post - adding 'noise' (or in this case, nearly cancelling coriolis forces) to reduce apparent friction. The universal joint would be constantly rotating back and forth slightly with each swing, staying in motion.

Is that a reasonable intuitive view of the reason why, in your scenario, a pendulum would do better than a solid bar?

I would like to calculate what the effective torque applied to a given pendulum due to the Foucault effect would actually be - interesting to compare it to the performance of a good universal joint (if those figures are available). Not sure how to do that though - and haven't yet tried. Another thing for the 'to-do' list !

In the design I'm working with, I think it is different. There is no torque applied by the swing to the pivot - the swing can go equally easily in any direction, regardless of the orientation of the pivot. So the pivot does not itself rotate and static friction becomes irrelevant (as regards rotation around the vertical axis).

I wonder if, for the same reason - that the universal joint approach would tend to cause the rotation to be slower than ideal, as sliding friction would also be in play, hindering the Foucault rotation.

Does that all make sense?

 

[SPW]

The pendulum would have to be a solid bar. When bolted firmly to an escapement it becomes the vertical pivot. The horizontal bearing being the other one. The oval trace will form as the pendulum exerts a rotary force on the horizontal bearing (which would probably have to be a large flat plate.

I've been looking into the equations and as the pendulum reaches the end of the swing it has Potential Energy. Then, as it begins to swing back it has Kenetic Energy. These cancel each other out. You can then use the mass of the bob, acceleration under g and the sin of the angle to calculate latitude etc. I will send you the equations but my iPad is limited at writing them, so I'll put them on paper & photograph them...

 

[lesaid]

The pendulum would have to be a solid bar. When bolted firmly to an escapement it becomes the vertical pivot. The horizontal bearing being the other one. The oval trace will form as the pendulum exerts a rotary force on the horizontal bearing (which would probably have to be a large flat plate.

I've been looking into the equations and as the pendulum reaches the end of the swing it has Potential Energy. Then, as it begins to swing back it has Kenetic Energy. These cancel each other out. You can then use the mass of the bob, acceleration under g and the sin of the angle to calculate latitude etc. I will send you the equations but my iPad is limited at writing them, so I'll put them on paper & photograph them...

By a solid bar in my previous post, I was meaning not a pendulum at all - say something like a weightlifters barbell, suspended in the middle from the universal joint. Then, in a frictionless environment, it's moment of inertia alone would cause it to exhibit rotation I think. But I think this doesn't happen because no bearing we can make will be 'that' symmetrical and frictionless.

I was thinking about how the coriolis force acting sideways on 2d 'escapement' pendulum suspended from the universal joint might just make the Foucault effect apparent. It's interesting, though it feels a very complicated way of doing it. Are you thinking of building such a device yourself?

I can solve the equations of a 2d pendulum - I'm finding a 3d one somewhat harder! My modelling so far hasn't been of the Foucault effect itself. It has been purely about getting the pendulum swing truly independent of its direction and free of Lissajous patterns. I have simply assumed that when successful, the Foucault effect will appear - and that seems to be what has happened :)

 

[Nidum]

This is getting silly . The whole point of a Foucault's pendulum is that it's swing is not greatly influenced by the Earth's rotation .

Anything added to the system which puts coupling between the pendulum action and the rotation of the Earth will cause the pendulum swing to start tracking the rotation of the Earth .

The principle of design is to minimise the coupling - ideally to zero . Not possible in practice but can certainly be reduced to a very low value .

There are only one calculation of any relevance to Foucault's pendulum design . This relates the relative influence between any coupling torque tending to rotate the plane of swing of the pendulum and the resistance of the pendulum action to any such rotation .

 

[sophiecentaur]

I was thinking about how the coriolis force acting sideways on 2d 'escapement' pendulum suspended from the universal joint might just make the Foucault effect apparent. It's interesting, though it feels a very complicated way of doing it. Are you thinking of building such a device yourself?

Isn't it the fictional Coriolis Force that causes the Foucault effect in the first place? The problem with supplying energy to maintain the pendulum is that it has to be totally 'unbiased', and any force must be directed to the centre of the swing. You have to be absolutely sure that it is not introducing any perturbation. It would be possible to introduce a force along the length of the suspension to supply energy which would satisfy this requirement (a bit like the way you can work yourself up when standing up on a swing. You do 'dips' at the appropriate time by bending your knees. The same could be achieved with a solenoid, moving the bob up and down in the right phase. A 1kg battery could probably supply enough energy for a 24+ hour operation, if the Q is as high as has been measured.

 

[lesaid]

I like that idea! though challenging perhaps for a home DIY-er to fabricate!

Pulling the bob up with a solenoid also perhaps leads to the same kind of challenges as all the other schemes, to get things adequately symmetrical - getting the solenoid force to act very precisely along the length of the pendulum for example. And in my case - brass rod bends a little and so the pendulum shaft is not absolutely straight. If the vertical stress on the shaft is changing each time the bob is 'pulled' - it might momentarily flex the pendulum shaft in the plane of its bend, introducing another asymmetry. However we approach it, the challenges are analogous I think :)

In the post you quoted, I was speculating on how SPW's idea might also show the Foucault effect, for all that it looked awkward. Perhaps I didn't word it well.

I've done a little experiment to look at the strength of the electrostatic force between chunks of brass rod of the same kind as the pivot frame is built with. Just to get some evidence to compare with calculations. I was astonished, that in a simple torsion balance made from dangling a rotating electrode made from brass bar off a length of fine harpsichord wire, very close to a matching static electrode, a 9V battery is enough to bring the two electrodes together! I am this evening, exploring the electrostatic forces in practice, using a handful of 9V batteries in series to generate different voltages, offset grounds and so on. Whereas I had expected to need hundreds or thousands of volts. Little wonder that the 6-10 kV used in the pendulum was influencing the orientation of the pivot piece! Measuring the deflection by looking at the movement in the reflection of a little LED laser off of the moving electrode, shone on to a sheet of paper.

So electrostatics demonstrations don't always need high voltages ! And pendulum pivots don't want them!

 

[SPW]

No I'm definitely not going to attemp the challenge. I'm strictly a paper & pencil physicist, but it was an interesting proposition. I am unsure what part of the Faucault effect you are trying to model? In the real world there will be slightly different outcomes due to the imperfections of whatever system you choose eg: the centre of gravity shifts depending on width of the bob. In an ideal system, with a perfect bearing, directly above the north/south,pole, in a vacuum etc, the standard equations hold true. As do the calculations for arc seconds at specific latitudes. The coriolis effect is due to your frame of reference.

In a body rotating with angular velocity

, a particular point with position vector

has a velocity

given by

In fact for any vector

(not necessarily a position vector) fixed in a rotating body,

Thus for unit vectors

,

and

, directed along the

(east),

(north) and

(upwards) axes fixed on the Earth's surface (see figure 1), we have

Figure 1: The directions of the

,

and

axes for a point on the Earth's surface with latitude

.Another more accurate way of measuring the effect in a physical system is with a gyroscope. You could bastardise a hard drive but be careful as most spin at 7,200rpm. Set in a gimbal parallel with the Earth? The effect would be small but measurable. A time lapse app would help.

As a thought experiment, imagine a man in a box traveling at a constant velocity in 0g. What would happen if a pendulum was 'hung' from the top (as judged from the man's point of view, who would feel the bottom was directly opposite from the vector of travel)?

 

[lesaid]

Thanks for those equations. I found the reference for them here https://www2.warwick.ac.uk/fac/sci/physics/intranet/pendulum/derivation/. Those equations were part of the introduction to that paper. The paper goes on to derive the rotation period of a Foucault pendulum, and which I will enjoy working through. Thank you.

I am unsure what part of the Faucault effect you are trying to model?

Not sure what you mean - the Foucault effect is what it is - 'parts' of the effect?

But I am not actually trying to model the Foucault effect itself. I am interested in what it takes to get a pendulum 'ideal enough' to be able to display the Foucault effect reasonably accurately for a 24 hour cycle on a 'desktop' scale. Which is why I started with a lump of metal hung off a piece of string (which was never going to work!), and have been analysing and solving each problem one-by-one until the Foucault effect appears. I don't want to make the 'perfect' pendulum - I want to find out what is 'good enough', and prove it in practice (hence the iterative approach rather than simply building the best I can immediately).

I would really like to model, for example, the effect of a slightly misaligned driver - where the 'kicker impulse' has a small tangential component to it. So I can find out analytically, how accurate the driver alignment needs to be and just what effect it has on the whole system. But so far, the resulting messy mathematics has defeated me. Perhaps because I haven't yet looked at Lagrangian mathematics, which, from what I have read, is useful in this kind of problem. Related to that - in practice, in my electrostatic driver, the spark jumps slightly before dead centre, and the repulsive impulse will be strictly radial - not directly in line with the swing. Will that impulse tend to widen, flatten, or not affect the shape of the ellipse? I have a hunch that it 'might' flatten it, but having a hard job working that out!

(Motivation is to practise newly learned physics and mathematics skills as well as experimental techniques - I am currently studying the subject)

the centre of gravity shifts depending on width of the bob.

does it? I don't see why (assuming the bob is hanging plumb and cylindrically symmetrical) and the bob doesn't change shape over time! The centre of gravity will shift as the pendulum swings - otherwise the thing wouldn't swing! But the restoring force due to gravity surely has to be radial, and unable on its own to introduce a torque around the vertical axis.

Another more accurate way of measuring the effect in a physical system is with a gyroscope. You could bastardise a hard drive but be careful as most spin at 7,200rpm. Set in a gimbal parallel with the Earth? The effect would be small but measurable. A time lapse app would help.

I don't think I'll attempt that - sounds too challenging for a home DIY project, to get the system precise enough. But why should it be more precise than a pendulum? I haven't looked at gyroscopes, but I'd have thought it easier (at least, outside of a professional laboratory) to set up a very precise pendulum?

As a thought experiment, imagine a man in a box traveling at a constant velocity in 0g. What would happen if a pendulum was 'hung' from the top (as judged from the man's point of view, who would feel the bottom was directly opposite from the vector of travel)?

I don't think the man would 'feel' anything and the pendulum would not swing - the whole system would be in free fall with no forces of any sort acting relative to the box? The man should be unaware of any travel and should not be able to 'feel the bottom'. For that, there would have to be an external force accelerating the box. But if you meant the box was accelerating in a straight line rather than at constant velocity, then the pendulum would swing in a constant plane that would not rotate. There would be no Foucault effect.

 

[SPW]

My apologies, I did indeed say "constant velocity"! Thank goodness for peer review. I apologise for any misunderstandings. It has been many years since I studied these things. However, I have only offered ideas and opinions in an attemp to help or provoke thought. I will be careful to reference any papers in the future. The joy I find in physics is seeing the realisation in my childrens' eyes when things fall into place, no matter how small. They have been raised to ask why or how. I may have assumed you were not as advanced as you are, again I apologise. With respect, I am a little confused; you have said that it was the challenge of making a device to impulse a force on a short pendulum but have also mentioned Langrangrian mathematics and modelling the tangential effects of electrostatic impulses. I have not researched this but I can only offer an opinion. I can remember coveriing double pendulums. I admit I did not know enough to fully comprehend it at the time. Although with fiendishly complicated mathematics it can be done; in reality it remains chaotic (due to the infinity of possible variables) Your proposal, if I have understood, will produce a very, very complicated set of equations, similar to those of the double pendulum, but remain experimentally chaotic. I would most definitely need to spend many months working on such a project, and need help from someone wiser than myself. Even Einstien needed Hilbert.

All the best
S.P.W.

 

[lesaid]

No problem :) I'm no expert - I'm an undergraduate student (later in life) studying mathematics and physics. I'm feeling my way along with newly learned skills, and know exactly the joy of things falling into place that you mentioned !

I am not sure whether the maths I need is in fact that complex, if I tackle it in the right way. I have not yet studied Lagrangian mathematics, but have read that it is helpful for these kinds of problems.

I have been simplifying the maths by treating the motion of the pendulum as a horizontal ellipse with a restoring force due to gravity - otherwise ignoring the vertical components. Where I have a problem is when I add in 'radial' forces centred on a point slightly offset from the 'origin' - i.e. a misaligned driver. It would be useful to know how precise the alignment needs to be!

I am wondering whether a path integral along a section of the ellipse covering the significant part of the impulse might let me find the overall direction of the bob's acceleration due to each impulse. By comparing that with the direction of the elliptical path over the same region, I think I should be able to find whether the impulse tends to flatten or broaden the ellipse. I shouldn't need to derive specific equations of motion for this - just look at an impulse on a point mass traveling around a 'generic' ellipse. Don't know if that's a good way of doing it, but I'll explore it.

But this is now a background thing for me - my regular studies have to take precedence now term has started :)