Precision pendulum techniques

[SillyOldDufferModerator @sillyoldduffer]

Posted by John Haine on 24/03/2023 07:29:47:

Do you really need to do this? … it's the counter that converts frequency to phase (time) that needs synchronising to ntp surely? …

Yes that's right – I don't need to do what I described. It's the counter that needs synchronising, not pendulum.

I asked the question because my logic and solution both felt overcomplicated. Now I've explained my thinking, and seen the responses, I realise my approach was muddled, and it is overcomplicated. I fixated on using the clock's ability to predict bob position.

Martin got in first by asking 'Is it really necessary to synchronise the pendulum with the ref.', at which point my mental model collapsed because the answer is 'NO'.

Proof of the pudding is in the eating. Took me about 10 hours cursing to write and debug the code for my complicated approach that only set the clock with 0.025s. Abandoning that, the alternative took under 10 minutes to write and test – it's much simpler.

What it does now is:

• On receiving a set-clock command, the raspberryPi spins as before to get just past the next whole NTP second.
• The second value is sent as a UNIX timestamp to my clock, with microseconds zeroed.
• My clock loads the timestamp into the counter
• On the next beat, the counter is incremented by one period, and the result, also a UNIX timestamp, is sent back to the raspberry
• The raspberry calculates the difference between my clock's time stamp and NTP time. The difference is sent back to my clock which applies it as a correction to the counter.

Needs more work because the protocol makes no allowance for transmission and processing delays. I'm going to write code to test these further: the exchange over USB serial takes about 0.0002s, which can be compensated out, but I don't know how much the exchange time varies. It's not an exact constant.

Michael's got me thinking about sub-second accuracy. Hopefully the rebuild will improve my frisky pendulum – i's not supposed to be all of a twitch! Assuming I can get it to swing reliably, I plan to use the pendulum's compensated period to set a counter timer to generate a 1s NTP aligned pulse at the next second point. Say the clock ticks and increments the clock's counter to a value like 1679653264.750020 . That means the Arduino has to output a seconds pulse 0.24998s later. I propose to do that with another counter/timer, setting it with numbers in which the Arduino's oscillator frequency is calculated from the pendulum. Not sure how accurately it's possible to set the counter to multi-digit delays like 0.24998s. As the counter is binary, the worst case error might be horrible. If the method works at all, should be possible to generate 0.1s pulses in the same way.

Dave

[Michael GilliganParticipant @michaelgilligan61133]

No idea how good/bad the chip is … but I thought I would mention this, just advertised by the PiHut

**LINK**

Pi RTC (DS1307)

Very reasonably priced, and could come in handy

MichaelG.

.

Edit: data-sheet for the DS1307 chip

https://www.mouser.co.uk/datasheet/2/256/DS1307-99500.pdf 

Edited By Michael Gilligan on 24/03/2023 17:31:33

[SillyOldDufferModerator @sillyoldduffer]

Posted by Michael Gilligan on 24/03/2023 17:28:17:

No idea how good/bad the chip is … but I thought I would mention this, just advertised by the PiHut

**LINK**

…

It's about as accurate as a domestic quartz clock, so not bad. However, for a bit more money, modules using the DS3231 are 2ppm. A notch more accurate because the crystal is embedded inside the chip and is temperature compensated. About 3x the price of a 1307, Pi Hut sell them too.

[S KParticipant @sk20060]

Something I've been thinking about:

An "invertible" pendulum that has the same period hung either way (see my "precision gravity pendulum" project) has its centers of oscillation right at its pivots. This configuration should therefore result in a minimum of motion of the support structure and hence less energy loss, etc.

Achieving that balance is fairly easy to within say 0.1%, as long as you are willing to tune the pendulum's basic parameters. In the end, it wouldn't have to actually be invertible, it would just have to be balanced as such.

It may be worth considering, especially for attempts that would benefit from higher Q.

Edited By S K on 25/03/2023 00:38:49

[John HaineParticipant @johnhaine32865]

I'm not sure why the lateral force at the pivot should be minimised by doing this?

[Michael GilliganParticipant @michaelgilligan61133]

Posted by John Haine on 25/03/2023 09:56:17:

I'm not sure why the lateral force at the pivot should be minimised by doing this?

.

Maybe worth considering how the two versions would behave on a wheel-balancing machine at your favourite tyre depot.

MichaelG.

[Martin KyteParticipant @martinkyte99762]

If the invertable pendulum has an effective length l equal to the distance between the pivots then is it not effectively identical to a pendulum of mass m at length l. Why then would you say that the centre of oscillation is at the pivot.?

Certainly the centre of mass isn’t.
Regards Martin

PS I thought the point of it was to make the measurement of l easy so as to measure local gravity.

Edited By Martin Kyte on 25/03/2023 12:46:39

Edited By Martin Kyte on 25/03/2023 12:48:52

[S KParticipant @sk20060]

I was in error – not sure what I was thinking.

There is at least one configuration that does have zero influence on the stand: a type of pendulum with an infinite period. But that's not very practical for a clock.

Edited By S K on 25/03/2023 17:05:36

[BazyleParticipant @bazyle]

I don't think there has been any mention of humidity, perhaps ignored because bad weather goes along with low pressure, but does anyone try to seal their case and put desiccant into it? Perhaps the effect is too small to matter.

[Martin KyteParticipant @martinkyte99762]

Posted by S K on 25/03/2023 17:01:50:

I was in error – not sure what I was thinking.

There is at least one configuration that does have zero influence on the stand: a type of pendulum with an infinite period. But that's not very practical for a clock.

Edited By S K on 25/03/2023 17:05:36

Don’t sweat it I jump to false conclusions all the time but then those who never dream up daft ideas never come up with anything new. The trick is identifying the daft idea with a spark of brilliance in it. Realising why a daft idea is daft is useful too. Viva le daft idea. (Nothing to do with Vauxhalls)

regards Martin

[SillyOldDufferModerator @sillyoldduffer]

Posted by Bazyle on 25/03/2023 17:22:30:

I don't think there has been any mention of humidity, perhaps ignored because bad weather goes along with low pressure, but does anyone try to seal their case and put desiccant into it? Perhaps the effect is too small to matter.

Duncan Webster was going to try and calculate how much humidity changes air density. Might cause an error by altering the bob's buoyancy. He's not reported back, so maybe the maths is horrible. None of my books worry about humidity, but they all agree removing air is a good thing.

Wooden pendulum rods are sometimes used because they don't change length much with temperature. Although wood is humidity sensitive, I've not seen it mentioned directly, through Grimthorpe recommends keeping church tower pendulums well ventilated, not boxed in.

When I used carbon-fibre as a combined spring/pendulum, it was markedly sensitive to humidity. However, the effect disappeared when I fitted a steel spring. I'm pretty sure humidity affected the spring of the plastic matrix, but not the length of the rod, which is controlled by the carbon fibre innards. Same might happen to wooden-rods, which run with the grain, where humidity might alter diameter much more than length. Changing the diameter of a pendulum rod wouldn't make much difference to the period.

As far as I know, what humidity does to pendula is still mysterious, but any effect on metal rods must be tiny.

Dave

[Martin KyteParticipant @martinkyte99762]

Well if you increase the water molecule content of air it becomes less dense so buoyancy will decrease. How the viscosity changes is another question.

regards Martin

[John HaineParticipant @johnhaine32865]

I had a look at this recently though haven't worked it out thoroughly. Water vapour does reduce air density and given the RH, pressure and temperature one can compute the density, and hence make allowance for the effect on drag though neglecting viscosity. But IIRC when Tom Van Baak analysed the Clock B results there was no obvious correlation of rate with RH.

[SillyOldDufferModerator @sillyoldduffer]

Posted by Martin Kyte on 25/03/2023 18:24:07:

Well if you increase the water molecule content of air it becomes less dense so buoyancy will decrease. …

regards Martin

What exactly happens to buoyancy is complicated because relative humidity varies with temperature, and less obviously with pressure. Do humidity and temperature cancel out or add? One of my graphs captured temperature and RH% marching nicely together but in the opposite sense:

But notice the curves aren't an exact match, and other examples are more jumbled. I think this example is unusually close because air-pressure happened to be falling steadily at the time, no jerks. I don't know what a graph of air density or viscosity would look like!

Dave

PS.  Any american's reading this?   In the UK 'buoy' is pronounced 'boy', whereas the US say  'boo-ee'.  How is 'buoyancy' pronounced in the USA?  'boo-ee-ancy' sounds very odd to me! 

Edited By SillyOldDuffer on 26/03/2023 11:19:49

[Martin KyteParticipant @martinkyte99762]

Hi Dave it’s absolute humidity that determines the density. Basically molecule counting. As a water molecule is less massive than an O2 or an N2. Using the ideal gas law with temperature and pressure constant for the same number of mixed molecules the density reduces. It also reduces with increasing temperature with increasing divergence at higher temperatures with different absolute humidities. Temperature variations seem to be the bigger factor in density than humidity.
regards Martin

[Michael GilliganParticipant @michaelgilligan61133]

I recall, from my time in the ‘Environmental Engineering’ test-house, that Humidity is one of the trickier things to monitor/measure/control … many commercial devices are of questionable accuracy.

Whilst pondering this, I’ve just found some interesting notes, here: **LINK**

https://www.processsensing.com/en-us/blog/effect-of-temperature-and-pressure-on-rh%20.htm

MichaelG.

[Martin KyteParticipant @martinkyte99762]

**LINK**

The above link may be useful and there are references to viscosity too.

The graphs are in terms of relative humidity and temperature but I guess that’s because it’s a far easier thing to measure.
regards Martin

[S KParticipant @sk20060]

I made some progress towards a spring-hinged pendulum (for yet-yet-yet another arduino-based clock), but now I have some doubts.

The spring is from 0.004" (0.1mm) beryllium copper. I wanted to make it simple and robust, so it's a single piece spring that is 13/16" (~20mm) wide.

Now, looking at it and comparing notes with other pendulum designs, I think it's too wide. This may be especially true since I intend on a much lighter weight of 2 lbs, compared to the 14 lb or so bobs that seem common. It's already mounted on one side to chops, so it would be hard to trim it any smaller at this point, neatly anyway.

What do folks here think?

[S KParticipant @sk20060]

Buoy is frequently pronounced more like "boy" here, but tinged with "buoy" (our English is so sloppy), and buoyancy is most frequently pronounced sounding like "boy" as well, maybe with a slight tinge of "buoy" too.

[Martin KyteParticipant @martinkyte99762]

Posted by S K on 29/03/2023 21:50:30:

I made some progress towards a spring-hinged pendulum (for yet-yet-yet another arduino-based clock), but now I have some doubts.

The spring is from 0.004" (0.1mm) beryllium copper. I wanted to make it simple and robust, so it's a single piece spring that is 13/16" (~20mm) wide.

Now, looking at it and comparing notes with other pendulum designs, I think it's too wide. This may be especially true since I intend on a much lighter weight of 2 lbs, compared to the 14 lb or so bobs that seem common. It's already mounted on one side to chops, so it would be hard to trim it any smaller at this point, neatly anyway.

What do folks here think?

Punch a slot down the middle of the suspension strip. Wide is good as it’s more stable but losing a portion of the middle will reduce the spring rate and leave the chops as made.

regards Martin

[SillyOldDufferModerator @sillyoldduffer]

Posted by Martin Kyte on 30/03/2023 08:01:44:

Posted by S K on 29/03/2023 21:50:30:

…The spring is from 0.004" (0.1mm) beryllium copper. I wanted to make it simple and robust, so it's a single piece spring that is 13/16" (~20mm) wide.

Now, looking at it and comparing notes with other pendulum designs, I think it's too wide. …

What do folks here think?

Punch a slot down the middle of the suspension strip. Wide is good as it’s more stable but losing a portion of the middle will reduce the spring rate and leave the chops as made.

regards Martin

Wot Martin said.

Not long ago I tried to find out if there was any science behind suspension-spring elasticity, length and width, and failed to find any. Probably been studied, but I couldn't find it.

My gut feel is the exact details don't matter much. The spring only needs to be strong enough to take the weight and wide enough to inhibit twisting. Length: long enough to provide restoring action, but short compared with the rod.

Both extremes have been used in real Pendula: from rods suspended by silk threads, with no spring action at all to pendula where the entire rod is a spring. Most use a short wide spring strong enough to support the bob, which is usually heavy. The exact dimensions vary.

With luck someone will be along with a better answer!

Dave

[S KParticipant @sk20060]

Posted by Martin Kyte on 30/03/2023 08:01:44:

Punch a slot down the middle of the suspension strip. Wide is good as it’s more stable but losing a portion of the middle will reduce the spring rate and leave the chops as made.

regards Martin

How might I do that? It's just a thin strip hanging in space from the chops. I can't think of a clean way to cut a slot in it at this point.

[Martin KyteParticipant @martinkyte99762]

I have to admit to not noticing that you had fixed the chops I was assuming you had just made the bits. However you could make a simple punch and die set. Slot milled in a couple of bits of steel and a punch to suit with the whole thing pinned together to align. Much as you would do when punching holes in a spring steel suspension. It can be made of mild steel as it won’t get much use.

regards Martin

[duncan webster 1Participant @duncanwebster1]

Can't you use a piercing saw on beryllium copper?

[S KParticipant @sk20060]

I think it would have to be stabilized somehow, like clamped between sacrificial metal.

I think I'll just use it as-is. At least it should be robust, as I had wished when I initially laid it out. I'll make a better-thought-out Version 2 if I get that far.

It does lead me to wonder "why a spring?" in the first place. I had thought the springiness was irrelevant, and that the goal was just to act as a pivot. But this strip is springy enough to have an influence on the pendulum vs. my knife-edges. Is there more to the spring being a spring than providing a pivot?

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