Precision pendulum techniques

All springs display hysteresis. I'm not talking about overcentre type things, just flexing within the elastic range. It's very small, but real. Cycling quickly within the elastic range will cause a spring to get warm. Google elastic hysteresis.

Well, yes, I'm sure all materials will exhibit some elastic hysteresis, but it would be very hard to measure any in a nice thin strip of well-tempered spring steel or beryllium copper, etc., and when flexed only slightly.

My query was whether the "spring" in a spring is actually beneficial at all to a pendulum, or whether it's a detriment that's only used because it's functional and convenient in other ways. I think the latter.

Anyway, the adverse effects of a spring are likely minimal compared to air friction (like maybe 1% of air friction), and the ancillary benefits (support and some anti-twist) are useful. Alternatives such as silk threads or knives have their own problems that are typically worse. But you still want a spring that presents as little interference with the motion of the pendulum as possible, including by being thin, narrow (including when split in two) and short.

It depends if you are trying to minimise the spring effect or use it to balance out other causes of period error.

Youngs modulus decreases with temperature so the restoring force of the suspension will also decrease with temperature. Shaped cheeks have been employed (notably by John Harrison) to create an additional control factor by shortening the effective length with increasing angular displacement and so balancing environmental changes with modified circular error.

Best if you realise and quantify at least in order of magnitude all the factors that effect the motion of the pendulum.

Agreed except perhaps the 'narrow' bit. I think of it this way: the bob of a perfect pendulum should always travel in a straight line. Real pendulums rarely do, instead describing an ellipse, shallower the better. Many reasons for deviations: air currents, earth tremors, building movement, impulse twisting or twanging the rod, unbalanced bob, brownian motion, vibration due to humans, molecular changes in the metal work (notably Invar), stress relief after temperature changes, frame not stiff enough, and probably many others, mostly small.

Some are easier to fix than others. Air currents in the room are a major risk, but easily avoided by encasing the pendulum. However, this causes new air-currents inside the case due to the bob stirring air in a confined space: these can be eliminated by evacuating the case so the bob swings in a vacuum. The vacuum also eliminates inconsistency due to buoyancy changing with barometric pressure.

A broad rather than narrow spring suspension is a fix because it tends to resist the bob and rod twisting sideways. If something deviates the bob, the spring will store energy from the torque and return it in the opposite sense to straighten the rod. Thus the minimum energy path (straight) is positively encourages by the spring, broader the better within reason. There's advantage in slotting a broad spring because the removed central slice adds weight and doesn't help keep the spring straight much.

Is it a fix or a problem? An issue with springs occurs when the impulse is misaligned with the bob. Then the impulse can torque-oscillate the spring resulting in the bob flying in the ellipse we're so keen to avoid! May not matter to other than perfectionists though, because the induced ellipse likely to be in phase with the period. The error is corrected by tweaking the rate in the normal way, and the pendulum owner probably won't notice (or need to care) that a small part of his rate error is caused by off-centre pulsing.

Deviation effects are much more obvious in my lightweight experimental pendulum clock than big ones. An advantage of building big, heavy and rigid in the time-honoured way is that such errors become proportionally less troublesome.

What fascinates me about precision pendulum clocks is the huge range of interacting design choices available. There isn't a simple black-and-white answer. Instead there are thousands of compromises to explore, where we find that the result can always be improved.

Pendulum development largely stopped a century ago because quartz-electronics provided better accuracy for less money and opened the door to even better methods. However, that change of course left amateurs with the highly tantalising prospect of being able to make the best pendulum clock ever. Difficult but not unrealistic, and packed with surprising interest.

Dave

The springiness of the suspension will change the period, I think it will reduce it. However I don't think it matters as long as it's constant. The effect will be very small. As Martin points out, the Young's modulus will reduce with temperature, but over the range we are talking about that will be a very small change, and as the spring is metal, it will get longer with temperature and so slow down the pendulum, but as the spring is very short this again will be very small. A potential downside is that the top of the pendulum is less rigid in the plane of swing, but if the impulse is applied at the right point, there is little or no force at the top.

Quartz crystals are effectively a mass on a spring, and they keep very good time, similarly balance wheels in chronometers. I think the mass on spring system is independant of amplitude, and so isochronous (as long as the spring is linear)

The best things to read about suspension springs are Philip Woodward and Kenneth James. PW wrote some articles in HSN that also reference James, HSN 1998 No. 5 and 2001 No. 4. A chap called Alan Emmerson has looked at solving the exact equations for a compound pendulum on a spring suspension, it is a horrendous problem and the answer is of little practical interest. As far as I can make out one of the main conclusions is that there is an additional pendulum mode where it rotates around a transverse axis at a frequency determined by the moment of inertia and the spring rate and dimensions.

Watch and chronometer balance wheels have carefully designed "terminal curves" to make them isochronous. Philip Woodward also looked at the theory of this and wrote a 6 part article in HJ.

Compared to springs, pendulums are easy!

I remember Dick Stephen doing some measurements on suspension springs Vs small ball races for pendulum suspension and concluding that there wasn't much to choose between them - the frictional losses in the ball race were comparable to the hysteresis loss in a spring. I don't know whether he published any results - he was certainly writing on & off for HJ and ME at the time.

I found this paper on elastic hysteresis in steel, dated 1912. The effect is small:

The difference of length to be measured is not more than one hundredth of the total variation of strain, and on apiece 4 inches long amounts to but 1/50000 inch, so that the measurement is a very delicate one, an error of one-millionth of an inch in absolute length being equivalent to 5 per cent, in the result. The test piece was loaded to 10 tons per square inch and oscillated at 120Hz - much faster than clock pendula.

I doubt it matters. Any evidence hysteresis effects time-keeping? Sure it will cause the spring to lose a little energy, but nothing is 100% efficient. I think it's a molecular effect, see list below.

Be useful to create a scaled list of things that cause pendulums to misbehave.

My guess for my geologically stable quiet part of the world, most serious first, unfortunately without numbers:

• Non-rigid frame and loose connections absorbing energy
• Unstable pendulum rod: one that bends, twists, stretches, sensitive to wet, decomposes etc
• Impulse faults
• Excessive amplitude
• Draughts
• Suspension faults - misalignment, high friction, asymmetry, too many degrees of freedom etc
• Uncompensated Temperature changes
• Aerodynamic effects inside the case - turbulence, drag
• Uncompensated Barometric changes
• Man-made Vibration
• Seismic effects
• Molecular effects
• Atomic effects

Any comments?

Dave

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Three disruptive comments, from a sedentary position:

1. your list looks like a good start … it could take a lifetime to quantify and rank the entries
2. please excuse the pedantry, but I think we need to note the distinction between effect and affect
3. possibly irrelevant, or possibly fundamental: Time is not what it was … so are we chasing the recorded performance of the best existing pendulum clocks, or the Caesium second ?

MichaelG.

By "narrow," I meant the net width of the spring material, not the spacing between springs in a two-spring configuration. So, using two of the thinnest, shortest and narrowest springs (spaced apart appropriately) that can hold the weight and not permanently deform under abuse, etc., are likely to be best.

It's clear that a lot of clock-making black magic is in trying to balance one unavoidable adverse effect against another opposing adverse effect. But I'm not patient enough to fuss with all that. I just want to do a respectable job based on good materials and straight-forward techniques, maybe with a touch of artistic flair, and hopefully get decent results.

• Relativistic space-time effects. There is no such thing as "time" as a stand-alone feature of the universe. There is only unified space-time. My "time" and yours are necessarily different, and it doesn't even make complete sense to speak of time as a discrete thing. So what does your pendulum even measure, really? 😛🙃

Apologies for affect and effect; I hit those rocks every time. Can't do nine sevens, or righty tighty / leftie loosie either.

I'm chasing the recorded performance of the best existing pendulum clocks, and what ever I build has to depend on a pendulum too.

As to SK and the nature of time, it's remarkable time is measured so incredibly accurately even though no-one understands what it is!

Dave

Well my time varies at random, but keeps exactly in step with my pendulum. That's my truth and I'm sticking to it (as a certain prince of the realm said)😂

Edited By duncan webster on 01/04/2023 22:52:25

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Ah - but, they can only measure ‘time’ so accurately because they have defined it [as being the thing they can measure accurately] … very convenient.

MichaelG.

Ah the old nature of reality question. Who knows what anything is ‘really’. All we have is what our senses and sensors tell us. Back to Plato and the cave. We get a little further with instrumentation in as far as building spectrometers allows us to agree what we mean by Yellow for example but still we cannot be sure that what I ‘see’ as yellow is the same as what you see. Past and Future are emergent from conscienceness but the equations don’t differentiate and can run both ways. All we can do is trust our instruments and leave the rest to the philosophers cos it ain’t physics.
regards Martin

Edited By Martin Kyte on 02/04/2023 09:31:38

Edited By Martin Kyte on 02/04/2023 09:32:43

Somewhere I read that the very latest atomic clocks can detect the difference in time running at head height compared to foot height due to gravitational time dilation. Whether your feet or your head gets older first I can't recall!

Edited By david bennett 8 on 06/04/2023 20:36:22

Not quite, but I believe it's close enough for my purposes.

All power supplies are noisy, some worse than others. Even the best mains powered supplies are vulnerable to muck arriving over the line - switching transients, solar activity, distant lightning strikes, radio signals, mush generated by appliances. Many sources: motors with faulty suppressors, unfiltered VFDs, and - very common - switch-mode power supplies.

The latter are wonderfully power efficient, but difficult to suppress properly. Too cheap models just dump spikes on both input and output. Better made units are much cleaner, but still electrically noisy. For most applications noise below a certain level doesn't matter, but for others it does.

Audiophiles claim to be able to hear switched mode noise on their amplifiers, discuss! More to the point, noise spikes on the power supply can upset communications systems, computers, and sensors. It's possible that electrical noise on the supply to a beam-break IR sender and IR receiver could cause slightly early or late detects. So with a 1 second pendulum a poorly decoupled sensor might report 1.0000, 1.0000, 1.0003, 1.0000, 0.9999, 1.0000, 0.9997 In the example, the mean is 1.0000s, with ±0.3mS noise, but spikes could bias away from the mean, hence it's good to problematic noise.

Actually, in my set-up, which has a noisy pendulum, ie the period varies, I don't have any evidence, yet, that power supply noise is the cause. Power is from a reasonably clean wall-wart USB PSU via an Arduino's regulator, and the sensor electronics are decoupled. No obvious difference running the pendulum with a linear power supply (which I have available).

In the event switched mode power was confirmed to be causing period noise, the obvious first step is a linear power supply. In the unlikely event the sensor was so sensitive that a linear supply upset it, batteries are as low noise as power gets. A battery is on the cards already - not to clean up the power supply, but trickle charged to keep the clock going during power cuts.

The most likely cause of my clock's noisy period is its faulty suspension and whippy rod. They have to be fixed before I look for anything else.

Dave

If you are that worried about psu noise you would have to make sure you were using the battery voltage direct, ie not through a regulator. And if using a trickle charger not have it on permanently but eg 7 hours on, 7 hours off so that you can compare any anomalies for coincident with the charger, and not use a sub multiple of 24hrs to progressively move through day/night variations, and use a prime number of time units.

Dave, glad to see you have this well in hand. I was concerned the noise was making it hard to differentiate clock noise from test noise, but de-coupling sensor electronics resolves that.

dave8