Precision pendulum techniques

[Michael GilliganParticipant @michaelgilligan61133]

If I have missed some fundamental new-found truth in Ziemkiewicz's paper … please educate me!

Despite its good analysis, using modern terminology, it seems to simply be a recognition/assertion of the need to maximise ‘signal to noise ratio’ … or, as Harrison put it: the pendulum should hold dominion.

The numbers are [and thereby the engineering design is] irrelevant … what matters is that we maximise the ratio.

Harrison’s solution was ‘inspired’ and has in recent years come to be appreciated; but that need not preclude exploration of alternatives.

MichaelG.

[John HaineParticipant @johnhaine32865]

Posted by Mason Green on 28/02/2023 23:23:58:

Posted by John Haine on 28/02/2023 10:27:08:

Interesting that both the Shortt and Fedchenko pendulums have much higher Q and very small amplitude and are nevertheless significantly more stable. For a comparison (not showing Fedchenko) see page 72 of:

I'm sure the mechanical phase-locked loop, which provides negative feedback to the system, has a lot to do with it.

I find it extremely interesting that Ziemkiewicz's paper shows that the Harrison's pendulum period is accurately modeled by assuming the "random forces" acting on it follow a Maxwell-Boltzmann distribution. Thus the clock error behaves as a fractal, showing the system has long-term memory!

Essentially over a long period of time the pendulum is self-correcting despite the random forces acting on it.

–MG

I'm referring to the Shortt41 measurements analysed by Tom Van Baak – these were taken on just the master pendulum impulsed with some electronics designed so that it was free running – which it always was of course, it was the Synchronome slave that was frequency (not phase) locked to it. The Fedchenko was also free running.

I'm not sure to what a pendulum clock can "self correct" over a long term. At any instant it has a state completely determined by its history and what happens next depends on that state and how its environment behaves.

[SillyOldDufferModerator @sillyoldduffer]

Posted by John Haine on 01/03/2023 09:34:14:

Posted by Mason Green on 28/02/2023 23:23:58:

Posted by John Haine on 28/02/2023 10:27:08:

…

…

Essentially over a long period of time the pendulum is self-correcting despite the random forces acting on it.

–MG

…

I'm not sure to what a pendulum clock can "self correct" over a long term. At any instant it has a state completely determined by its history and what happens next depends on that state and how its environment behaves.

I understood Mason's comment to mean that pendulum period varies as it responds to changes in the environment, which can be compensated for, but also randomly, resulting in noise. A pendulum "self-corrects" in the the sense that many instabilities cancel out on average.

A 1 second mechanical pendulum, no matter how well made, does not deliver exact 1 second periods. Periods are always slightly different, but cluster around a median, like this example from my clock. The vast majority of beats are near the median, but a proportion are distributed either side, with extreme variations becoming increasingly rare. The steeper the peak the better – high Q – but, even if the pendulum is fully compensated, there is always some variation, or noise. Any frequency that''s not exactly average is noisy.

.

 

On average, the pendulum keeps time, but the period of individual beats vary. Deviations to the right tend to balance out deviations to the left over time. A well-made pendulum delivers good long-term stability by averaging out noise, even though the pendulum's short-term stability could be relatively poor.

Nonetheless, it's desirable to improve short-term stability as well. As I understand it Allan deviation measures and identifies the types of noise, so it might be possible to reduce or engineer them out. Worrying about noise is precision clock territory! An example: Invar is an Iron/Nickel alloy that doesn't change size as temperature varies. It's excellent for making pendulum rods. But looking closely at Invar rod clock performance shows Invar is far from perfect! When measured at high resolution, it turns out Invar is unstable at the molecular level, causing minute physical changes that change the pendulums period slightly. The instability can be reduced by heat ageing, but Invar isn't perfect, and maybe another material like quartz, might do better. But fundamentally, everything the clock is made of is a bit unstable.

Therefore, I don't agree with John's: "At any instant it has a state completely determined by its history and what happens next depends on that state and how its environment behaves". However the difference of opinion is tiny, because my version is: "At any instant it has a state almost entirely determined by its history and what happens next depends on that state and how its environment behaves"

Dave

 

 

Edited By SillyOldDuffer on 01/03/2023 11:35:05

[Martin KyteParticipant @martinkyte99762]

Posted by SillyOldDuffer on 01/03/2023 11:33:43:

Posted by John Haine on 01/03/2023 09:34:14:

Posted by Mason Green on 28/02/2023 23:23:58:

Posted by John Haine on 28/02/2023 10:27:08:

…

…

Essentially over a long period of time the pendulum is self-correcting despite the random forces acting on it.

–MG

…

I'm not sure to what a pendulum clock can "self correct" over a long term. At any instant it has a state completely determined by its history and what happens next depends on that state and how its environment behaves.

I understood Mason's comment to mean that pendulum period varies as it responds to changes in the environment, which can be compensated for, but also randomly, resulting in noise. A pendulum "self-corrects" in the the sense that many instabilities cancel out on average.

A 1 second mechanical pendulum, no matter how well made, does not deliver exact 1 second periods. Periods are always slightly different, but cluster around a median, like this example from my clock. The vast majority of beats are near the median, but a proportion are distributed either side, with extreme variations becoming increasingly rare. The steeper the peak the better – high Q – but, even if the pendulum is fully compensated, there is always some variation, or noise. Any frequency that''s not exactly average is noisy.

.

On average, the pendulum keeps time, but the period of individual beats vary. Deviations to the right tend to balance out deviations to the left over time. A well-made pendulum delivers good long-term stability by averaging out noise, even though the pendulum's short-term stability could be relatively poor.

Nonetheless, it's desirable to improve short-term stability as well. As I understand it Allan deviation measures and identifies the types of noise, so it might be possible to reduce or engineer them out. Worrying about noise is precision clock territory! An example: Invar is an Iron/Nickel alloy that doesn't change size as temperature varies. It's excellent for making pendulum rods. But looking closely at Invar rod clock performance shows Invar is far from perfect! When measured at high resolution, it turns out Invar is unstable at the molecular level, causing minute physical changes that change the pendulums period slightly. The instability can be reduced by heat ageing, but Invar isn't perfect, and maybe another material like quartz, might do better. But fundamentally, everything the clock is made of is a bit unstable.

Therefore, I don't agree with John's: "At any instant it has a state completely determined by its history and what happens next depends on that state and how its environment behaves". However the difference of opinion is tiny, because my version is: "At any instant it has a state almost entirely determined by its history and what happens next depends on that state and how its environment behaves"

Dave

Edited By SillyOldDuffer on 01/03/2023 11:35:05

Therefore, I don't agree with John's: "At any instant it has a state completely determined by its history and what happens next depends on that state and how its environment behaves". However the difference of opinion is tiny, because my version is: "At any instant it has a state almost entirely determined by its history and what happens next depends on that state and how its environment behaves"

Do you mean that if the noise is White noise the no long term feature of the noise can be inferred from the current state, in effect the pendulum has ‘forgotten’ past history noise but retains some imprint of recent disturbances?

regards Martin

[John HaineParticipant @johnhaine32865]

Yes, I see your point – "depends on how the environment and the system parameters behave" might be more accurate?

[Clive SteerParticipant @clivesteer55943]

I think noisy might be averaged out in a linear system, but because of circular error, there is a degree of non-linearity so would noise get "rectified" and produce a timing offset.

CS

[Martin KyteParticipant @martinkyte99762]

• Posted by Clive Steer on 01/03/2023 12:12:44:

I think noisy might be averaged out in a linear system, but because of circular error, there is a degree of non-linearity so would noise get "rectified" and produce a timing offset.

CS

Well yes, but the point I was making and questioning was any past disturbance that is averaged out, is effectively ‘lost’ information and cannot form part of the current state. (In fact I was asking Dave is that what he meant). Of course anything that is biased on the distribution curve will form part of the current state.

Is that not what the AV curve shows with the negative slope to a minimum as larger sampling frames ‘forget’ past history.?

regards Martin

Edited By Martin Kyte on 01/03/2023 12:30:27

[duncan webster 1Participant @duncanwebster1]

Looking a John's links from yesterday, in the Schott clock, the support of the suspension spring is really rigid, a large copper tube bolted to the wall (no doubt brick or stone) and a very substantial brass structure on to to support the actual suspension. Reproducing this with something stood on a table would not be easy.

Turning to John's impulse problem, the Brillie clock had a curved bar magnet running inside a coil so the it could impulse equally either side of centre, synchronome et al gravity likewise. I suggested recently that a Fedchenko type coil could be made to switch polarity on centre, or a really way out scheme would be an aluminium vane running through a linear motor (which is only 3 coils). All of these need to know which way the pendulum is swinging, but not difficult with some electronics

[John HaineParticipant @johnhaine32865]

A very interesting article in the latest HSN included this plot.

Generated in a spreadsheet by having a small random variable that can be + or – added to a running sum in each row. 10 runs each with a different starting seed. If you look at any single run it may tend towards zero at some point but later will diverge away and may come back again. Over a long period if you look at the rms "error" from zero over all the runs it grows as the square root of the number of runs. Many clock errors are like this, there is no tendency to "cancel out" over a long period.

[Mason GreenParticipant @masongreen60104]

From Ziemkiewicz's lecture on YouTube:

YouTube Link

His analysis reveals the pendulum period error is not a simple gaussian random walk, but rather follows a Maxwell-Boltzmann distribution:

YouTube Link

"Interestingly the error function is a fractal that resembles the trajectory of Brownian motion… further details reveal it is not pure Brownian motion, individual "jumps" are slightly correlated"

"pendulum has a memory"

His previous paper is also an interesting read:

"Numerical analysis of grasshopper escapement"

But, a wise man once told me to never waste my time trying to convince anyone of anything on an internet forum, lol.

[John HaineParticipant @johnhaine32865]

Another wise man said that in physics models should be as simple as necessary but no more. The paper you quote from explicitly says:

"On the other hand, long-term effects originating from environmental
changes of temperature, pressure etc. [21] are not explored here."

(page 2 LH column about half way down). Harrison's main achievement was to create a system that was nearly insensitive to barometric pressure which is a random variable that can easily cause errors of seconds per year and do not cancel with time. To do this it was operated at a point where a number of factors were in equilibrium and reduced its sensitivity to other influences, including torque variations and arguably support vibration. Ziemkewicz's research is interesting but omits vital factors.

[Mason GreenParticipant @masongreen60104]

Posted by John Haine on 01/03/2023 15:24:00:

Another wise man said…

And your point is? Your sound very defensive and reactive here.

Take the time to watch the lecture in its entirety and digest the two papers without your ego getting in the way.

But alas, it appears you already know everything there is to know on the subject. ha!

I'm out.

[Joseph Noci 1Participant @josephnoci1]

Come now Mason….let's all play nicely here – its about 'time'…

Never found John's ego an impediment to sound discourse at all – he does like to chase the science and thats good…

This thread is great and has stimulated thought in many folk – lets keep it that way.

[SillyOldDufferModerator @sillyoldduffer]

Posted by Mason Green on 01/03/2023 14:26:33:

From Ziemkiewicz's lecture on YouTube:

YouTube Link

His analysis reveals the pendulum period error is not a simple gaussian random walk, but rather follows a Maxwell-Boltzmann distribution:

YouTube Link

"Interestingly the error function is a fractal that resembles the trajectory of Brownian motion… further details reveal it is not pure Brownian motion, individual "jumps" are slightly correlated"

"pendulum has a memory"

His previous paper is also an interesting read:

"Numerical analysis of grasshopper escapement"

But, a wise man once told me to never waste my time trying to convince anyone of anything on an internet forum, lol.

Not really a question of conviction, more about me gripping the point and how the hypothesis might make a difference to what I'm doing. If I've learned anything from my experiments it's that clock stuff is hard to measure AND difficult to understand. Misled myself on many occasions, and am probably doing it now!

No disrespect to Professor Ziemkiewicz, but looking critically at his conclusions:

• 'Grasshopper escapement is the most accurate clock mechanism'. Maybe the most accurate mechanical mechanism, but not proven its the most accurate, yet! Harrison's fiendishly clever ideas look excellent to me, but no one pursued them. None of the world's best pendulum clocks used the system, though it' true recent examples have done well. I emboldened mechanical because it's not necessary for a pendulum to have an escapement at all, and there's a strong case that no escapement is best.
• The Lego clock is impressive in it's way, but it's full of noisy mechanical imperfections. Although indicative, they may be confusing the conclusions.
• 'Recording the clock sound is an easy and accurate way of measuring it's speed'. Up to a point, but the pendulum itself is silent. The acoustics are generated by the escapement, which isn't exactly synchronised with the pendulum. (I don't believe the pendulum was measured relative to the noises off.)
• 'Great care needs to be taken…' Absolutely! For example I could claim my graph evidences a Maxwell-Bolzmann distribution and have a few even more convincing examples. Only problem is, I'm pretty sure my skewed graphs are due to over-impulsing. The curves look Brownian, but aren't. Looking at other data reveals my clock has a correlation between the degree of skew and impulse power.
• 'The rate at which environment entropy is increased is directly linked to the clock accuracy; very lossy system (e.g. large pendulum amplitude) can be the most accurate.' An interesting observation, but again 'not proven' I think. For example, on my clock, over-impulsing can do horrible things to the pendulum without damaging the time-keeping in the long-run. The reason I suspect is large amplitudes work provided they're consistent, not just because they're big. Small consistent amplitudes work too.

Certainly not saying the whole idea is hopelessly wrong, far from it, but to be convinced it's proven, I think we need more evidence that all the other possibilities have been eliminated?

Dave

[Martin KyteParticipant @martinkyte99762]

Just to defend the old gentleman a little as far as I see it:-

Harrison’s ideas were never really understood at the time, he was understandably secretive and what he did write was not clearly expressed.

The Sea Clocks were a dead end as far as longitude was concerned with the development passing to the Watch. H4 etc. which certainly was developed.

The RAS was never really completed and certainly never fully adjusted.

The Adjustment of the suspension cheeks for Grasshopper pendulum clocks was time consuming.

I’m happy to be corrected on anything above, I’m certainly no expert, but I have to confess a fondness for our Mr Harrison.

Not really disputing anything else apart from the implied criticism that what he did was not followed up because it was in some way erroneous.

regards Martin

[S KParticipant @sk20060]

I watched the whole video with interest (without the patience to work through his main paper). It's thought provoking, but some of it is contrary to hundreds of years of experience, and other bits (like invoking fractals) raised doubts (but I'm not enough of an expert to say exactly why).

I think I'd stick to high Q and minimal impulsing at BDC as the most likely path to success.

Edited By S K on 01/03/2023 17:15:09

[S KParticipant @sk20060]

I have two simple questions about pendulums:

1) Given a typical disk-shaped bob, why is the vertical position (as typically seen in grandfather clocks) considered superior (e.g., "higher Q" ) to the same disk oriented horizontally (e.g., in my gravity pendulum)? One advantage of the horizontal position is that there's no possibility for a misalignment of the bob's angle of attack. It does push the mechanism out further, but what of Q?

2) To adjust a pendulum's period, a small weight is often added along its shaft. Sliding a weight (not adding a weight) lower on the shaft (closer to the bob) tends to slow it down because it moves the center of oscillation further down, while sliding it closer to the hinge tends to speed it up by moving the COO upwards. Leaving aside the mechanical issues, is there any reason why it's disadvantageous to increase the weight's effect further by moving it above the hinge (or below the bob)?

Thanks.

 

Edited By S K on 01/03/2023 17:13:21

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Martin Kyte on 01/03/2023 16:42:21:

[…]

Not really disputing anything else apart from the implied criticism that what he did was not followed up because it was in some way erroneous.

.

Forgive me, Martin … I’ve been out and have not yet read this page of posts thoroughly

To help me catch-up … can you point me to that implied criticism, please

MichaelG.

[SillyOldDufferModerator @sillyoldduffer]

Posted by Michael Gilligan on 01/03/2023 17:12:26:

Posted by Martin Kyte on 01/03/2023 16:42:21:

[…]

Not really disputing anything else apart from the implied criticism that what he did was not followed up because it was in some way erroneous.

.

Forgive me, Martin … I’ve been out and have not yet read this page of posts thoroughly

To help me catch-up … can you point me to that implied criticism, please

MichaelG.

If it was me pointing out that no-one else built one, it was an observation rather than a criticism.

I'm often struck by the number of times the same idea occurred at about the same time across the world. Hooke has a claim to inventing the pendulum clock as well as Gallileo. Newton and Liebniz ditto calculus, Swan & Edison light bulbs, Wheatstone, Morse and other telegraph systems, many experimenters working on wireless before Marconi, and the one thing I'm sure of is that Alexander Graham Bell didn't invent the telephone! Given the amount of talent that went into developing pendulum clocks, it's surprising no-one picked up on Harrison's idea. Possibly no-one else thought of it, more likely they did, but minimising disturbance seemed more promising.

Dave

[Martin KyteParticipant @martinkyte99762]

Posted by SillyOldDuffer on 01/03/2023 18:00:42:

Posted by Michael Gilligan on 01/03/2023 17:12:26:

Posted by Martin Kyte on 01/03/2023 16:42:21:

[…]

Not really disputing anything else apart from the implied criticism that what he did was not followed up because it was in some way erroneous.

 

.

Forgive me, Martin … I’ve been out and have not yet read this page of posts thoroughly

To help me catch-up … can you point me to that implied criticism, please

MichaelG.

If it was me pointing out that no-one else built one, it was an observation rather than a criticism.

I'm often struck by the number of times the same idea occurred at about the same time across the world. Hooke has a claim to inventing the pendulum clock as well as Gallileo. Newton and Liebniz ditto calculus, Swan & Edison light bulbs, Wheatstone, Morse and other telegraph systems, many experimenters working on wireless before Marconi, and the one thing I'm sure of is that Alexander Graham Bell didn't invent the telephone! Given the amount of talent that went into developing pendulum clocks, it's surprising no-one picked up on Harrison's idea. Possibly no-one else thought of it, more likely they did, but minimising disturbance seemed more promising.

Dave

I didn’t think you were being critical. Just wanted to gently say something on Harrison’s behalf. It’s so easy for posts to get a little misunderstood by future readers and I think the quality of the threads that your clock has generated certainly deserves to become a reference. It’s been the most interesting thing on the forum for years.

best regards Martin

Actually I should really have said the potential criticism  implicit in the wording. Shows how hard it is to actually say what you mean. If we were Lawyers it would be unambiguous but also probably unintelligible except to other Lawyers.

Edited By Martin Kyte on 01/03/2023 19:49:05

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Martin Kyte on 01/03/2023 19:42:47:

[…]

Actually I should really have said the potential criticism implicit in the wording. Shows how hard it is to actually say what you mean. If we were Lawyers it would be unambiguous but also probably unintelligible except to other Lawyers.

.

Thanks for the clarification, Martin

… Only just seen it, on my return from a St David’s Day recital by the local ladies chorus.

I rather feared that you had mis-read my comment at the end of the previous page.

All’s well that ends well … Mr Harrison retains his rightful position !!

MichaelG.

.

Edit: ___ For the benefit of those future readers of these pages; I think it is worth linking

https://soptera.files.wordpress.com/2013/10/csm-translation.pdf at this point.

Edited By Michael Gilligan on 01/03/2023 20:52:09

[S KParticipant @sk20060]

That document is interesting.

After wading through (sometimes) politely-expressed but numerous long-standing grievances (what is it with old-time clock experts and their in-fighting? Or even modern ones – hehe.), we find that a pendulum in vacuum is some sort of over-balanced perpetual motion machine that can't be used to tell time! Air friction is a life-saver!

I guess geniuses are often "special."

 

Edited By S K on 01/03/2023 22:32:39

[duncan webster 1Participant @duncanwebster1]

My interpretation is that Harrison found really ingenious ways of managing temperature and air density variations. More modern astronomical clocks use low temperature coefficient materials, and get away from density variations by running in vacuum. Add the ability to very accurately control amplitude and Harrison techniques are no longer appropriate.

Those like me who only want to know what time it is to a reasonable accuracy can stick to low coefficient pendulum rod and controlled amplitude. And no I'm not going to define reasonable.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by duncan webster on 02/03/2023 15:26:52:

[…]

And no I'm not going to define reasonable.

.

You don’t need to, Duncan …”The man on the Clapham Omnibus” defines reasonable

MichaelG.

[S KParticipant @sk20060]

I wonder what master-level clocks would have evolved to today if pendulums were still the most precise time-keeping technology?

I'd presume all the last developments prior to quartz oscillators (controlled vacuum, low COE materials, high-Q, small amplitudes, decoupled pendulums, etc.) but with electromagnetic drive and electronic measurement and compensation techniques much as folks here are playing with.

I'm still wondering how a synchronome-style mechanical gravity-impulsed drive compares to electronic drive. Certainly the best of the historical mechanical ones are still amongst the best of all. But I have to imagine that electronic drive can be made better due to the lack of friction if nothing else.

My next project will be a clock of sorts (probably still just a pendulum, with everything else electronic), but as I would not be aiming for ultimate accuracy, I've been toying with the idea of making a mechanical drive for it as a steam-punk flourish. Therefore, I've been wondering what a modern interpretation of that would look like. For example, electronic triggering is an obvious improvement over a mechanical counting wheel. And perhaps a servo might reset the drive weight rather than an electromagnet? Any other ideas?

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