Precision pendulum techniques

[Martin KyteParticipant @martinkyte99762]

Absolutely Duncan. The Shortt free pendulum is the timekeeping element in the combination and in MG’s set up that is replaced with the atomic clock which is then the timekeeper. The slave clock is perfectly redundant. It’s interesting as a piece of control engineering, that I will grant, but a clock in its own right it isn’t.
regards Martin

[S KParticipant @sk20060]

I noted about 6 microseconds RMS noise in the ~1.5 second period of my (genuinely) free pendulum. I don't know if this is good or bad, but I did see that the CERN dude's clock has what appears (casually) to be a little higher noise.

Anyway, I think the noise can be reduced further. I did move my counter and its fan away from the pendulum, since it was causing a LOT of extra noise, and I should be even more careful about that kind of thing (my oscilloscope was also nearby, and I didn't move that). I also learned I had to be careful where and when I walk or move around it.

A few other ideas I've had include traffic noise transmitted through the earth, my refrigerator if it's running (it's somewhat nearby), random air movement (it's not in a case), and perhaps even acoustic noise. I should go around and turn everything off before I look at it again. I should also measure it at 3AM and compare it to noon-ish, and see if there's a difference.

If it is anthropogenic (e.g. traffic), then I've also wondered if some mechanical isolation would help. I had presumed that any isolation such as rubber under the base would hurt by sapping the pendulum of energy, however minutely, but I could try something quick and dirty to see what happens.

I did think of doing a spectrum analysis, but as there's no impulse mechanism, I can't record for very long. My photodetector is at the end of the swing so I get a full period per pulse instead of two pulses per swing, meaning that it's only in range for maybe an hour. I guess I could put a broader flag on it so it's in range longer.

What other causes of reducible noise are seen?

As for what is "fair", e.g. is it fair to discipline a pendulum off a cesium fountain, if you feel happy and occupied with your time spent in a hobby, that's fair enough.

[John HaineParticipant @johnhaine32865]

Posted by S K on 05/03/2023 08:30:02:

I noted about 6 microseconds RMS noise in the ~1.5 second period of my (genuinely) free pendulum. I don't know if this is good or bad, but I did see that the CERN dude's clock has what appears (casually) to be a little higher noise.

…..

Based on what I'm seeing at the moment 6us is pretty good. The clock at CERN has some form of electromagnetic impulsing, not unlike a Synchronome I would guess though it is hard to find any details of how it works except in Czech, and it's quite likely to have significantly higher noise.

You have to understand where he's coming from – his day job is time and frequency and horology is a hobby, so for a bit of fun he has disciplined a pendulum oscillator in his office to exact time, just as one might an OCXO. This is what "my" Prof. Robertson attempted to do in 1925 except "exact" time was GMT as kept by Shortt-Synchronomes and only available once per day.

[SillyOldDufferModerator @sillyoldduffer]

Posted by S K on 05/03/2023 08:30:02:

I noted about 6 microseconds RMS noise in the ~1.5 second period of my (genuinely) free pendulum. I don't know if this is good or bad, but I did see that the CERN dude's clock has what appears (casually) to be a little higher noise.

Anyway, I think the noise can be reduced further….

If it is anthropogenic (e.g. traffic), then I've also wondered if some mechanical isolation would help. I had presumed that any isolation such as rubber under the base would hurt by sapping the pendulum of energy, however minutely, but I could try something quick and dirty to see what happens.

I did think of doing a spectrum analysis, but as there's no impulse mechanism, I can't record for very long. …

Good to see SK being sucked into the Time Nut Club!

FFT first, yes but to get enough data it will be necessary to impulse the pendulum. Not difficult, but one is left wondering how much noise is due to the impulses, and how much is due to the pendulum! Various sources already mentioned, such as traffic and air movement, but also the knife-edges cutting into the plinth and twisting because the alignment isn't perfect. The tripod probably vibrates because it isn't perfectly rigid, and like as not the floor it's stood on is bendy too.

High-precision clocks are often located in solidly built cellars, or deeper. I believe the BIPM clocks are 24 metres below ground to minimise surface vibration. Another way is to isolate the platform by digging a trench around it, say 300mm wide by 1500mm deep.

Some problems require the clock to be moved geographically. Some sea-side locations move enough with the tide to cause trouble, and micro-gravitational changes have been blamed on ground water moving tidally – some types of rock are full of water.

Practically I'm stuck with my home, and it's not good for this. Best I can do at the moment is a windowsill, which is mechanically stable and convenient, but the temperature varies. When the clock is working properly, I shall move it under the stairs and order visitors to tread lightly!

I have rubber feet under my clock, but they're a compromise. The benefit is they help to isolate the clock from a moving house; the disbenefit is they reduce Q by soaking up energy from the pendulum.

I've hit compromise problems repeatedly whilst trying to design my clock. For example, I know:

1. a spherical bob is aerodynamically better than a cylindrical bob, but also that
2. a heavy bob is better than a light one.

Which leaves an awkward question: will my pendulum improve if I reduce the weight of it's cylindrical bob to make it aerodynamic, or do the two effects cancel each other out, and it's not worth bothering? Maybe chamfering the ends of a cylinder would be a good compromise – I don't know.

The recent high vs low amplitude debate is another example. Harrison, a genius, described a high-amplitude system which no-one adopted, but has since been found to work. Everyone else built clocks with low-amplitude pendula, which also work extremely well. Is one system better than the other? I think the truth is that the high-amplitude approach solves one set of problems whilst creating another, and so does low-amplitude. Neither is perfect. As there isn't a simple clear winner, yer pays yer money and yer takes yer chances. However, I vote for low amplitude clocks because they're easier to make!

Dave

[Michael GilliganParticipant @michaelgilligan61133]

I am posting this NOT as a criticism of the book [for that is a one-of-a-kind master-work], but just as a word of warning.

Accurate Clock Pendulums by Robert J. Matthys : ISBN 0-19-852971-6

is currently selling for £100 plus

It was published in 2004, and at that time the rear fly-leaf stated:

Robert J. Matthys was a Senior Research Engineer at Honeywell, Inc., from 1952 to 1987. He has spent thirty-seven years designing a wide variety of hardware and instrumentation in the fields of electronics, optics, acoustics, mechanics, and photography. In addition, he has spent nine years designing and testing pendulums of various kinds, along with their electronic drive systems and servos, both pulsed and continuous sine wave. He lives in Minneapolis, Minnesota.

It remains an excellent book to have on the shelf, and dip-into, but the content does appear to be a tidied-up version of his notebooks and much of it is [inevitably] dated.

I doubt we shall ever see anything to replace it … and it is probably essential ‘prep’ for anyone experimenting with pendulums … but do be aware of what you are buying.

MichaelG.

[John HaineParticipant @johnhaine32865]

It is indeed a useful book. Sadly out of print, my copy came via an Amazon retail partner and has a US Library of Congress stamp on the contents page!

 

Certainly didn't cost me £100 or $…

Edited By John Haine on 09/03/2023 14:14:37

Edited By John Haine on 09/03/2023 14:15:34

[S KParticipant @sk20060]

Traditional clock making involves a lot of black magic and superstition, and unresolved questions. Just look at the question of how often to impulse, for example. In the "Electric Clocks" book, it was, colorfully, "shall it be little and often or the occasional square meal?" I don't think that's been fully resolved.

I've been wondering if superstition still influences the "heavy pendulum = better" notion, too. For an ideal pendulum the mass does not matter, while a canonical number might be for around a 14 lbs bob in practice. But if one is striving for a near-ideal pendulum anyway, is adhering to this canon still valid?

The "near ideal" pendulums in discussion here all include being completely detached from any mechanical clock train, with its friction and inertia to overcome, so less weight is needed. They include other anti-friction elements such as being in a partial vacuum and friction-free electromagnetic impulsing, so again less weight is needed.

What is left? A small amount of frictional losses due to residual air resistance and in the spring? Is the canonical ~14 lb bob really needed anymore? Are there some advantages to be gained from a lighter shaft and bob, or is more still always better?

[Michael GilliganParticipant @michaelgilligan61133]

Posted by John Haine on 09/03/2023 14:13:17:

It is indeed a useful book. Sadly out of print, my copy came via an Amazon retail partner and has a US Library of Congress […]

.

Can’t recall exactly when I bought mine, brand new … but it was somewhere between 2004 and 2007
[ by which time it was being sold at a reduced price by the BHI ]

MichaelG.

[duncan webster 1Participant @duncanwebster1]

Even if your clock is bolted to a robust wall, there are always going to be external factors like heavy vehicles going by, or even teenagers banging doors. Heavy pendulum will be less affected. I suspect windage effects are less for heavy as well as the mass/surface are is higher, but that's just a gut feel.

Edited By duncan webster on 09/03/2023 15:10:30

Edited By duncan webster on 09/03/2023 15:11:07

[John HaineParticipant @johnhaine32865]

Good questions. It all depends…

As to bob mass, a larger bob mass is better at resisting small unwanted forces which are part of the impulse, for a given aerodynamic loss factor. These small forces could be variation in the impulse itself or noise, for example from the clock train. On the other hand a larger bob mass makes the clock more susceptible to noise transmitted through the suspension point (e.g. seismic noise). Depending on the noise processes at work, there's probably an optimal bob mass, but absent specific noise data it's impossible to calculate.

Regarding impulse frequency. The two extreme examples are the Shortt and Fedchenko, impulsing once per 30 seconds or once per second respectively. The Fedchenko is significantly more stable and is electromagnetically impulsed while the Shorrt was mechanical (albeit magnetically triggered).

Both those examples work in vacuum so barometric error is absent. The influence of buoyancy without a vacuum is reduced in proportion to the ratio of air to bob density which favours a denser bob, frequently heavier. A Harrison-type clock has a rather low Q and high amplitude and has to be impulsed every swing to make its barometric compensation work. It is pretty stable, though an order of magnitude or so less than the Shortt/Fedchenko. My feeling is that barometric compensation is still not well understood.

If impulsed near the top I'm rapidly being persuaded that a light and flexible rod is undesirable as it easily supports unwanted modes at lowish frequencies that have quite high Q – so you need to impulse near the bob. Thin rod has lower air resistance = higher Q. But the Harrisonites will say that air resistance and low Q is good!

You pays your money and takes your choice…

[S KParticipant @sk20060]

Posted by duncan webster on 09/03/2023 15:10:13:

Even if your clock is bolted to a robust wall, there are always going to be external factors like heavy vehicles going by, or even teenagers banging doors. Heavy pendulum will be less affected. I suspect windage effects are less for heavy as well as the mass/surface are is higher, but that's just a gut feel.

I think what you are arguing is that the pivot would move due to an upset, but that the bob would be relatively undisturbed because it's more massive. But that's not really true unless the mount or hinge or shaft is flexible. If it's rigid, as one tries for, the bob would necessarily be disturbed too. So while I see an intuitive argument in there, I'm not sure intuition is sufficient.

Also, the surface area to mass argument is certainly a fact, but if we are talking vacuum, then it's irrelevant.

My argument is that the closer the pendulum is to ideal (fully detached, vacuum, etc.), the less the mass of the shaft and bob matters. And then one wonders if there are hidden advantages to a lighter pendulum, or to a different form factor for the pendulum.

For example, I think the light, thin shaft / heavy bob arrangement is substantially about coping with air resistance. If that's not a factor, then a solid bar pendulum is just as good. In fact, the last of the gravity pendulums adopted simply a solid quartz rod as the pendulum.

 

Edited By S K on 09/03/2023 15:45:12

[S KParticipant @sk20060]

Posted by John Haine on 09/03/2023 15:32:39:

As to bob mass, a larger bob mass is better at resisting small unwanted forces which are part of the impulse, for a given aerodynamic loss factor. These small forces could be variation in the impulse itself or noise, for example from the clock train. On the other hand a larger bob mass makes the clock more susceptible to noise transmitted through the suspension point (e.g. seismic noise). Depending on the noise processes at work, there's probably an optimal bob mass, but absent specific noise data it's impossible to calculate.

It sounds fair to assume that the variation in impulse energy would be proportional to the energy. So a pendulum needing less energy per swing would see proportionally less variation in the impulse energy as well. And then a smaller, lighter pendulum would generally require less energy input, correct? (I mean, if not, give a nuclear kick to a tiny, light pendulum and see what happens.) So perhaps it's a wash, or maybe even in favor of lighter given your second point?

There's another thought that may be pertinent: the finding that smaller pendulums (and oscillators in general) tend to have higher Q. So a tiny quartz crystal can have a Q of order 10^6, for example. Perhaps this also tempts one to prefer smaller, lighter pendulums?

[Martin KyteParticipant @martinkyte99762]

Posted by S K on 09/03/2023 16:12:57:

Posted by John Haine on 09/03/2023 15:32:39:

As to bob mass, a larger bob mass is better at resisting small unwanted forces which are part of the impulse, for a given aerodynamic loss factor. These small forces could be variation in the impulse itself or noise, for example from the clock train. On the other hand a larger bob mass makes the clock more susceptible to noise transmitted through the suspension point (e.g. seismic noise). Depending on the noise processes at work, there's probably an optimal bob mass, but absent specific noise data it's impossible to calculate.

It sounds fair to assume that the variation in impulse energy would be proportional to the energy. So a pendulum needing less energy per swing would see proportionally less variation in the impulse energy as well. And then a smaller, lighter pendulum would generally require less energy input, correct? (I mean, if not, give a nuclear kick to a tiny, light pendulum and see what happens.) So perhaps it's a wash, or maybe even in favor of lighter given your second point?

There's another thought that may be pertinent: the finding that smaller pendulums (and oscillators in general) tend to have higher Q. So a tiny quartz crystal can have a Q of order 10^6, for example. Perhaps this also tempts one to prefer smaller, lighter pendulums?

The impulse has only to make up for the losses doesn’t it. So notionally in a vacuum a heavy bob could be no more lossy than a light one.
If the stored energy in the bob is the signal and disturbances are the noise then a more massive bob has a higher signal to noise ratio. (I think that’s what John was saying)

Regards Martin

[SillyOldDufferModerator @sillyoldduffer]

Posted by S K on 09/03/2023 14:45:47:

Traditional clock making involves a lot of black magic and superstition, and unresolved questions. …

Not sure I completely accept with the Black Magic and superstition conclusion! My reading shows the old guys had a high level of understanding and many of their ideas make good sense.

Unresolved questions is fair cop though, and some of them are being explored in my experimental pendulum project. In it I've mostly ignored accepted wisdom to see what can be done with modern technology and a fresh look.

The clock is in line with your ideas: no connection to a going train, no escapement, intended to run in a semi-vacuum, free-standing, light-weight, and an unusual approach to compensation, which includes a whiff of machine learning.

My 40g bob is about 150 times lighter than the usual 6kg. The rod is also light-weight, a 250mm length of 2mm diameter carbon-fibre rod. Works well enough for me to persist with the experiment, though there are many open questions.

The clock impulses the bob with a micro-controlled electromagnet, making it easy to try different impulse strategies. I can confirm that my light pendulum, Q about 9500, keeps better time when gently impulsed on every stroke, compared with giving it a more powerful kick every 'n' beats. Don't believe I've proved that's a universal truth though. It's possible a heavy bob on a pendulum with higher Q would do better with occasional impulses: Shortt's Q was about 100 times better than mine. It's also possible my light-bob is too light. I may be demonstrating that light bendy rods go twang and disturb the bob when kicked hard. In other words impulse power depends on a relationship between the weight of the bob and how stiff the rod is. Maybe!

State of play at the moment is a rebuild. Although results were promising, I couldn't get the clock to run reliably within 100mS of NTP, and better.

An important change is to the suspension. I started by using the rod as a spring, that is no suspension at all. Worked well enough to show that Carbon-fibre rod is humidity sensitive, moisture almost certainly effecting matrix elasticity rather than the fibre, and low Q. So I switched to a conventional steel spring suspension, which delivered much higher Q, but had to be levelled carefully. Too simple and poorly made, and I hoping better construction will reduce the amount of noise on the pendulum's frequency. Several other improvements suggested by the forum in hand too.

It's a very interesting subject, quite easy to get moderately good results by dispensing with an escapement, but after that improving by successive orders of magnitude is tough going. Tricky to identify the causes of misbehaviour at the microsecond or faster level, and also pinning down why the pendulum sometimes wanders off average during longer runs for no apparent reason. Months of fun!

Dave

[S KParticipant @sk20060]

Posted by Martin Kyte on 09/03/2023 17:01:20:

The impulse has only to make up for the losses doesn’t it. So notionally in a vacuum a heavy bob could be no more lossy than a light one.
If the stored energy in the bob is the signal and disturbances are the noise then a more massive bob has a higher signal to noise ratio. (I think that’s what John was saying)

Regards Martin

To make up for losses, a pendulum has to be lifted, and a heavy pendulum takes more energy to lift than a light one, right? Take half the mass off a heavy pendulum and the same impulse will give it twice the kick, right? So then the question is does a 2X heavier pendulum have twice the Q (meaning it needs to be impulsed half as often or half as much), and I don't think the answer is yes.

John made the point that a heavy pendulum is more sensitive to environmental disturbances than light ones. I'm not positive I follow that yet, though.

Edited By S K on 09/03/2023 17:24:34

[John HaineParticipant @johnhaine32865]

Posted by S K on 09/03/2023 17:23:33:

Posted by Martin Kyte on 09/03/2023 17:01:20:

The impulse h….

To make up for losses, a pendulum has to be lifted, and a heavy pendulum takes more energy to lift than a light one, right? Take half the mass off a heavy pendulum and the same impulse will give it twice the kick, right? So then the question is does a 2X heavier pendulum have twice the Q (meaning it needs to be impulsed half as often or half as much), and I don't think the answer is yes.

John made the point that a heavy pendulum is more sensitive to environmental disturbances than light ones. I'm not positive I follow that yet, though.

Edited By S K on 09/03/2023 17:24:34

Why lifted? It has to be pushed sideways. The push only has to supply the amount of energy lost since the last push which is a function of the loss factor not the mass. If you had bobs of the same shape and size but different densities, they would all have the same loss factor and need the same impulse if running at the same amplitude. Their Qs however would be different, greater in proportion to the masses. Like an LC circuit, if you have a given series loss resistance and increase the inductance and reduce the capacitance, for the same current at resonance the power dissipated is the same though the Q can be much higher.

I don't think I quite said that a heavy pendulum is more sensitive. It is more sensitive to lateral support vibration but less sensitive to impulse noise. A denser pendulum is less sensitive to barometric variation.

Edited By John Haine on 09/03/2023 17:38:09

[S KParticipant @sk20060]

Posted by John Haine on 09/03/2023 17:37:16:

 

Why lifted? It has to be pushed sideways.

 

No, it has to be lifted. The "side-ways" force that you happen to apply at bottom dead center is really just to lift it at the end of the swing. (So yeah, potential and kinetic energy is exchanged, but you do have to lift the pendulum!)

If it was true that a 2x heavier pendulum had 2x the Q, then if my 1.5 lb pendulum was increased to 15 lbs, the Q would go from 18,000 to 180,000? Is that sort of relationship real? If you stopped impulsing Big Ben it would rock for a week?

My reply to the impulse noise was that a lighter pendulum needs less impulse energy and the noise of the applied energy would scale as well.

Edited By S K on 09/03/2023 17:51:29

[S KParticipant @sk20060]

Hmm, after some further thought: With an equal swing, the potential / kinetic energy is twice as much if the pendulum's mass is twice as much. The reduction in energy per swing is proportional to 1/Q. All else being equal (that's quite stretch!), double the mass should provide double the Q. Given that density is finite (except for a black hole), this could only happen in a hard vacuum.

The impulse energy needs to make up for the 1/Q loss. Double the mass means about double the Q (in a vacuum, all else equal). Therefore, since the mass is doubled (need twice the energy to lift the pendulum) but Q is also doubled (which alone means you need to apply an impulse half as often or half as much), the amount of energy per swing needed is constant and is only related to the losses in the pivot or elsewhere.

If not in a vacuum, then heavier bobs should do better since air resistance grows slower than bob mass. This is almost the only reason that a heavier bob is better (leaving aside environmental disturbance for the moment since it's so complicated).

If in a vacuum, the impulse only has to counter the hinge friction, and so it's not clear to me that bob mass matters at all aside from basic practical issues.

Edited By S K on 09/03/2023 19:30:46

[Martin KyteParticipant @martinkyte99762]

I still don’t agree with your lifting argument SK unless I’m misunderstanding what you are saying.

Would you agree that a perfect loss free pendulum once set swinging at some amplitude will continue to swing indefinitely exchanging kinetic energy for gravitational potential energy. That’s just conservation of energy.
Reality adds losses so it’s clear that the impulse must balance the losses. Impulsing at the centre of the swing adds to the kinetic energy that has been lost and restores the amplitude.

When you say doubling the mass requires double the energy to lift the bob (which is true) that is already available from the similarly doubled kinetic energy of the bob at centre. So I contend that impulsing merely has to balance the losses.

Rereading your post I realise that maybe that is what you are saying if so all well and good and I shall shut up for a bit.

regards Martin

[John HaineParticipant @johnhaine32865]

Posted by S K on 09/03/2023 19:16:02:

Hmm, after some further thought: With an equal swing, the potential / kinetic energy is twice as much if the pendulum's mass is twice as much. The reduction in energy per swing is proportional to 1/Q. All else being equal (that's quite stretch!), double the mass should provide double the Q. Given that density is finite (except for a black hole), this could only happen in a hard vacuum.

The impulse energy needs to make up for the 1/Q loss. Double the mass means about double the Q (in a vacuum, all else equal). Therefore, since the mass is doubled (need twice the energy to lift the pendulum) but Q is also doubled (which alone means you need to apply an impulse half as often or half as much), the amount of energy per swing needed is constant and is only related to the losses in the pivot or elsewhere.

If not in a vacuum, then heavier bobs should do better since air resistance grows slower than bob mass. This is almost the only reason that a heavier bob is better (leaving aside environmental disturbance for the moment since it's so complicated).

If in a vacuum, the impulse only has to counter the hinge friction, and so it's not clear to me that bob mass matters at all aside from basic practical issues.

Edited By S K on 09/03/2023 19:30:46

In a vacuum there are still the issues of impulse noise and support vibration – the first is reduced by more mass, the second by having less mass.

[S KParticipant @sk20060]

Posted by Martin Kyte on 09/03/2023 20:01:35:

Rereading your post I realise that maybe that is what you are saying if so all well and good and I shall shut up for a bit.

regards Martin

Yes, we are in agreement.

My motivation for this discussion was the notion that mass becomes relatively unimportant as a pendulum comes closer to ideal, i.e., "free," in a vacuum, etc. I still think that's mostly true.

I'm presently thinking about my next project, which would use a spring hinge rather than knife blade pivots, and actually keep time. No vacuum, though. Given the price of brass these days (howls of pain!!!), I'm sweating how much weight I need.

Edited By S K on 09/03/2023 20:32:52

[Martin KyteParticipant @martinkyte99762]

However the amount of stored energy of the system will determine the response rate and decay time from disturbances effectively integrating non random noise so knowing the characteristics of non random noise will help in choosing a suitable Q would it not. (Just thinking aloud here feel free to shoot me down in flames anyone). It possibly may also affect how disturbances are coupled into the system. Seismic events that are close to resonance will be more strongly coupled that those far from resonance for example. So picking a suitable Q may optimise cumulative errors in timekeeping.

As I said I’m really just thinking aloud so feel free to put me right if I’m barking up the wrong tree (or even just barking&#129396

regards Martin

[Michael GilliganParticipant @michaelgilligan61133]

Posted by S K on 09/03/2023 20:30:16:

[…]

My motivation for this discussion was the notion that mass becomes relatively unimportant as a pendulum comes closer to ideal, i.e., "free," in a vacuum, etc. I still think that's mostly true.

[…]

.

If I may throw a thought into the mix …

Another way of looking at high Q is simply that it represents low Damping.

Your musings about in vacuo performance feel more intuitively obvious when expressed that way.

MichaelG.

[duncan webster 1Participant @duncanwebster1]

To add a finale to SK's lifting suggestion, putting energy in does make the bob lift higher than it would have done (at the extreme of swing), but a given amount of energy (ie that lost since the last impulse) will lift a heavy pendulum less than a light one. It will therefore increase the amplitude of a light bob more than a heavy one, and so reduce the period more. If you're impulsing every swing I don't suppose it matters.

[S KParticipant @sk20060]

Hi John,

Would you have a recommended magnet-wire gauge for these applications?

Thanks.

[Author]

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