Thoughts on Detecting Pendulums!

[John Doe 2Participant @johndoe2]

Worrying about the rise and fall times of a switching light source is surely irrelevant because the light source won’t be switched on and off in normal use.

But I have an idea which might be useful to improve detection. All the pendulum detectors so far have been beam-interrupting or proximity systems, triggered by a plate or magnet fitted near the bob of the pendulum.

Thinking about an instrument called a mirror galvanometer, or a spot galvanometer; how about instead fixing a small mirror to the pendulum pivot. Shine a small horizontal slit of light onto the mirror, and put a detector alongside the light source, both looking at the mirror – both source and detector in long tubes and also with horizontal slots, to avoid stray light triggering. And/or use a laser source. The reflected light beam from the mirror will move twice as fast across the detector than the speed that the pendulum moves at, which should improve switching accuracy ?

A mirror on the pivot will not affect the pendulum from air currents, or air turbulence, since it will barely be moving compared to the speed of the bob, nor will it matter if the pendulum bob moves in a slight ellipse, but the mirror will double the speed that the slit shaped light beam crosses the detector, which should improve the crossing accuracy ?

 

Another thought is: have the Earth’s magnetic and gravitational fields been considered ?  These might cause odd effects to a pendulum, depending on the relative orientation of the pendulum with magnetic and geographical north ?

[duncan webster 1Participant @duncanwebster1]

We’ve been down the mirrors route before, can’t remember the outcome but unless you use a well focused laser you’ll get light spread with a long path.

Someone cleverer than me can work out the effect of eddy currents in the bob from cutting the earth’s magnetic field. I suppose it must provide some damping, but I’ve never seen a clock with a non conducting pendulum bob. High density materials tend to be metals.

[duncan webster 1]

On duncan webster 1 Said:

[…] but I’ve never seen a clock with a non conducting pendulum bob. High density materials tend to be metals.

Oddly enough, Duncan … I have been looking at the possibility of using glass or stone: There are some useful-looking items around [the classic marble rolling-pin being one].

MichaelG.

[Robert Atkinson 2Participant @robertatkinson2]

Core drill cores immediately came into my mind. Clyindrical or disc with handy center hole…
Granite counter top makers must throw out lots of them.

[S KParticipant @sk20060]

Worrying about the rise and fall times of a switching light source is surely irrelevant because the light source won’t be switched on and off in normal use.

Pulsing the light source was used as an analogous substitute for interrupting a static beam since it allows accurate triggering of the scope during measurement of the sensor’s latency and jitter.

Any “worry” was about whether the light source itself has a fast rise/fall time, e.g. due to a slow phosphor, was because that would degrade accurate timing in the tests. In the end, I don’t believe it turned out to be an issue in my measurements.

Yes, the use of a mirror, a laser, and a longer optical lever-arm has been discussed in the past. This approach is used in recreations of the Cavendish gravity experiment, for example, but I haven’t been aware of its use with clock pendulums.

But I’ve repeatedly brought up the question of just how good does the timing need to be to be superior to the mechanical noise in a high-performance pendulum? About the best pendulum data I’ve seen is about 1 ppm RMS jitter in short-term period measurements. Now, those measurements were themselves made using break-beam or Hall effect sensors, so one has to be careful, but if 500-600 ps RMS noise in the electronic timing is adequate, then the simple break-beam approach is fine.

 

[S K]

On S K Said:

Worrying about the rise and fall times of a switching light source is surely irrelevant because the light source won’t be switched on and off in normal use.

…
But I’ve repeatedly brought up the question of just how good does the timing need to be to be superior to the mechanical noise in a high-performance pendulum? About the best pendulum data I’ve seen is about 1 ppm RMS jitter in short-term period measurements. Now, those measurements were themselves made using break-beam or Hall effect sensors, so one has to be careful, but if 500-600 ps RMS noise in the electronic timing is adequate, then the simple break-beam approach is fine.

 

Whether a factor is irrelevant or not depends on what the need is!

SK’s query about how good the timing of an individual pendulum swing needs to be is a good example.   Not much for ordinary pendulum clock purposes, where the timing and rate are determined by averaging the total of many swings.   Averaging hides many sins, but provided errors balance each other out, who cares?

Well I do.   My goal is to build a pendulum clock at least as good as a Shortt-synchronome, this to be achieved by exploiting cheap electronic and other modern techniques not available to Mr Shortt!    Despite promising results, no coconut so far.  The devil is in the detail, and the more accurate a clock needs to be, the more difficult those details become.   Things irrelevant to building an ordinarily respectable pendulum clock suddenly become serious roadblocks when 1000x accuracy improvements are required.

One example is errors caused by disturbing the bob.   The bob should be protected from draughts in the room, but tightly boxing the pendulum causes turbulence inside the box.  How bad is the chaos?  Only way to find out is to measure individual swings accurately.

Shortt fixed the turbulence and draught problem by running the synchronome in a vacuum.   A good solution, but challenging for me.

The bob is disturbed by many other factors,  Shortt found a problem with Invar rods, later found to be because although the alloy has a wonderfully low temperature coefficient of expansion, it is also rather unstable at the molecular level.  The instability is so small it needs a highly accurate pendulum to reveal it!  Cure: use a particular member of the Invar family that’s least unstable, and age it for a few years  before use.   My problems are less exotic, notably my dubious build quality, where the construction might be too mobile!

The easiest way to detect bob problems is to measure individual swing times.   I’ve detected:

• Bob flying in an ellipse, rather than straight (mostly fixed by levelling, and using a flat spring suspension)
• frequency dropping in jerks due to suspension slippage (design error)
• Over impulsing problems:  (set-up error)
  • The rod going ‘twang’
  • period disturbed unduly
• Ambient light issues (screen required)
• Apparent bob problem actually caused by IR internal reflections (design error, blacken shiny surfaces and add slits.)
• Poor choice of break beam module. (didn’t confirm an assumption)

Current state of play is that my per-swing measurements are telling me loud and clear that something is still wrong.  More work needed.

Once my pendulum is beating and being measured satisfactorily I need accurate per swing measurements to calculate the temperature and air-pressure correction coefficients.   They depend on accurate statistics, not just averages, of per swing pendulum timings plus long term start-finish data.   Garbage in, garbage out – when statistics are being gathered, the data needs to be as good as I can get it, because of the way the I’m tacking the ultra-high accuracy problem.   If it sounds unnecessary to other clockmakers, I’m not surprised – as far as I know the Duffer clock is unique.   Also unproven!

Dave

 

[John HaineParticipant @johnhaine32865]

A mirror plus laser was used for example in Pierre Boucheron’s measurements on a Shortt vacuum pendulum still under vacuum at NIST which turned out to have an attached mirror and glass port.  This was in the 60s or 70s I think? Revealed that the pendulum could detect tides.  Also I believe used by the “Harrison Project” in testing Clock A.

[duncan webster 1Participant @duncanwebster1]

Pressure and temperature change fairly slowly, so why can’t you use average period over say 100 swings? The ambient change in <2 minutes must be too low to measure.

[Michael Gilligan]

On Michael Gilligan Said:

On duncan webster 1 Said:

[…] but I’ve never seen a clock with a non conducting pendulum bob. High density materials tend to be metals.

Oddly enough, Duncan … I have been looking at the possibility of using glass or stone: There are some useful-looking items around [the classic marble rolling-pin being one].

MichaelG.

Marble has a density of 2.7 te/cu.m, steel is 7.8, tungsten is 19.2. I can’t imagine any advantage from loss of eddy currents out weighing the extra dsrg an buoyancy effects of using a lighter material

[S KParticipant @sk20060]

Averaging destroys the number I’m looking for.

Most people are interested in data acquired over long time periods to quantify stability, e.g. how far off is it over days, months or years? After all, that’s what’s most important for tasks like navigation or general timekeeping. And if you are only interested in relatively long time periods, then the precision in measuring each swing is not terribly important, as imprecision there effectively gets averaged-out over time.

But whether from the Shortt or Clock B, or one of the amateur efforts, I’m wishing for for the Standard Deviation in the period over relatively short time periods (too short for temperature and tides, etc., to mess with it), e.g. for 1000 swings.

I found the following quote from a paper by Duncan Agnew concerning the Fedchenko clock: “The uncertainty in the impulse from the clock is stated to be 7 × 10−6s.” I’m not positive how to interpret this statement, but if that’s the S.D. of the period, then it’s merely in line with amateur efforts.

 

[duncan webster 1]

On duncan webster 1 Said:

Marble has a density of 2.7 te/cu.m, steel is 7.8, tungsten is 19.2. I can’t imagine any advantage from loss of eddy currents out weighing the extra dsrg an buoyancy effects of using a lighter material

I know, Duncan … it was simply an observation; I wasn’t trying to impress or persuade anyone.

MichaelG.

[S K]

On S K Said:

…..And if you are only interested in relatively long time periods, then the precision in measuring each swing is not terribly important, as imprecision there effectively gets averaged-out over time.

……

 

Well, maybe not.  It depends very much on the nature of the variations.  You can’t separate what the variation in each reading is due to the pendulum itself or the measuring device, and how the standard deviation builds up can be very different.  Pendulums apparently exhibit flicker noise and the rms deviation grows without limit with number of measurements.  A much better measure is Allan Deviation, which computes  a sort of “standard deviation” for different timescales and plots them on the same graph.  The shape of the graph allows you to separate out observational errors and “real” variations.  Lots of good explanations and examples on the “Leap Second” website.

[S KParticipant @sk20060]

Perhaps theoretically the “RMS deviation grows without limit,” but I wouldn’t expect it to be a serious concern over practical time scales. And if one still believed that, why use a pendulum to measure time? At some point between now and the heat-death of the universe it would be infinitely wrong!

And of course you can’t separate “the pendulum” from the measurement apparatus. But a pendulum with a few kg mass, with a near perfect pivot, in a vacuum, mounted in that proverbial remote castle basement, should have incredibly low noise, far better than the 7 × 10−6s figure mentioned for the Fedchenko unit (which was in a vacuum and mounted in a controlled subterranean vault).

I just can’t imagine that a good several-kg pendulum would not benefit from lower-noise timing instrumentation. But can any benefit be measured? I’d imagine using a Hall effect device, then the Sharp, then my sensor, should show improvements.

Also, I understand the more universal nature of Allan deviation, but the problem is that most plots I’ve seen start at longer time-scales than strictly period-to-period (e.g. they might start at 1000 seconds and extend to days, etc.).

At the moment I’m primarily interested in the shortest-term fluctuations in the period. In fact, if a delineated ascii file or spreadsheet of periods from a “run down” experiment (e.g. for measuring Q) is available, please point me to it.

 

 

[John HaineParticipant @johnhaine32865]

I think you’ll find quite a few over on the HSN site. https://groups.io/g/Horological-Science-Newsletter/topics

[John Doe 2Participant @johndoe2]

Another thought:

A single beam break is subject to inaccuracies. Systems which need very accurate timing often have a series of pulses to enable synchronisation, not just one single pulse.

So how about having a series of vertical black and white bars on the beam-break plate, and have the computer read the whole “word” as it passes, and a subroutine to establish a more accurate timing event from several edges rather than just a single edge.

This would also allow measurement of the pendulum speed as well as its position, which might help establish shorter term variations in timing as well.

[S KParticipant @sk20060]

Yes, I’ve imagined lining up a bunch of them. Going further, it’s not inconceivable that a short scale or grating could be focused on and digitized along each swing. Or break out the laser interferometer as in LIGO, etc. Our pendulums are sensitive enough to detect gravity waves, right? 😉

[S KParticipant @sk20060]

Deleted due to an error, sorry.

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