JoNo's Pendulum

Well, I am sure you know why the surface is dimpled...

Also, in the same vein, the Tubercles along the edge of a (humpback) whale flipper serve a similar purpose - and make the whale flipper one of the most efficient 'wings' on the planet! AND they just grow them, without any Aerodynamic schooling...

Man's attempt...

Edited By Joseph Noci 1 on 22/08/2023 15:17:16

Perhaps not at 'any' price, but it really is worth it if you insist on playing with pendulums!

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Yes of course, Jo, or I wouldn’t have mentioned it

… What I don’t know is how relevant it would be at “pendulum speeds” … whatever those might be.

MichaelG.

Anyone know what the ideal ratio of long axis to short axis for the oblate spheroid bob is? It scales at about 2:1. And what is a 'football shape with pointy ends'. I'd expect the oblate spheroid to be a football (US version, rugby ball to Brits)

Anyone tried British Library for Matthys book?

Michael, it depends on what the Pendulist is wishing to achieve. Vacuum tops it all, and then shapes and dimples are moot.

I have some odd 'standards' or limits I wish to abide by, and I feel using a vacuum is not allowed. So if the aim remains to achieve really good performance, then it is very relevant indeed. Since losses in air amount to over 90% of pendulum loss of mechanical energy, assuming a decent pivot, any % gained in reducing air resistance is a boon.

Those Tubercles on the whales flipper are working at very low speeds and have been shown to increase efficiency ( by measuring lift) by anything up to 30%! The problem is quantification by amateurs and amateur methods and tools...Since my main field is aerodynamics I have a very good feel for this, but at these low speeds it is very difficult indeed to quantify - hence my pedantism on trying to find a reliable, quantifiable, repeatable method of measuring Q. Most folk want high q to be able to eventually 'measure' tides - I want Hi Q so I can measure aerodynamic effects and the effect on Q.

I would propose that it is a straight oblate spheroid, but with a missle nose type tip so that the air is separated cleanly rather than compressed and then squashed aside - but how long is a point, and where around the oblate does it start...I think just a point will do better than none.

As to ratio - I have seen proposed ( I am digging to find the reference again..) that the ellipse should fit inside a Golden Rectangle = Golden Ellipse

Thanks for your wisdom, Jo

I knew about golf-balls … but they move fast

I knew about shark-skin … but that moves through water

I had missed-out on the whale flipper.

MichaelG.

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P.S. __ for anyone interested:

https://www.startribune.com/obituaries/detail/0000362412/

Edited By Michael Gilligan on 22/08/2023 16:57:01

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I agree on the first part of that, Duncan … but not the second:

**LINK**

https://www.dimensions.com/element/american-football

MichaelG.

My initial attempt at controlling to a fixed amplitude has met with some success and promise.

I used the angle ( = amplitude) of the pendulum as given by my angle sensor as reference, phase shift that sinusoid by 90deg and feed that to the coil driver, and control the level of that voltage so that the level of the voltage from the angle sensor remains constant.

A block diagram of the electronics:

A Sine generator generates a sine wave at 5KHz and feeds a 600ohm-600ohm transformer which drives the differential angle capacitor sensor. The pickup sensor of said device is buffered and feeds a synchronous detector, driven by a reference Sine from the sine generator. The resulting DC output is amplified differentially and filtered. This resulting voltage is a representation of the pendulum angle since the senor is fitted to the pivot.
This 0.5Hz sine wave feeds an ADC read by the Nucleo processor, for later processing.

The 0.5Hz also feeds a 90deg phase shifter. The shifted phase is required since the pendulum drive is via a drive coil atop the pendulum, above the pivot, and is fed with a sine wave drive per swing, all the time. The 90deg shift ensures that the sinusoidal drive voltage is at its peak when the pendulum is at BDC, and minimum when the pendulum is at the extremes of swing. There are no impulses, just a good sine wave drive, and I hope this will result in almost no pendulum perturbation.

The driving voltage level is maintained within a closed gain control loop - the pendulum angle sinusoid feeds a Peak detector, which generates a DC voltage equal to the peak of the voltage of the pendulum swing extremes. This DC voltage controls a voltage Gain Controlled amplifier. The input to the amplifier is the 90deg phase shifted sinusoid, and the output is that sinusoid, level controlled , to ensure that the pendulum swing angle is maintained. An increase in angle( amplitude) increases the Peak detector output and the VGA gain is reduced, reducing the drive sinusoid voltage to the pendulum drive coil. Reduction of swing is a reduction of the DC output of the Peak detector, causing an increase of Gain in the VGA, and increased drive to the pendulum coil.

The RMS current in the drive coil is 0.14mA when the loop is stable. The angle sensor Peak to Peak voltage output for a 2 deg total pendulum swing is 2 volts PP. This voltage varies by less than 0.2mV over 3 hours with the loop stable.
The drive voltage from the coil driver is 1.2V PP, and feeds the 10ohm coil via 3000ohm series resistance.

The Peak detector output is summed with the output from a 16bit DAC. The DAC output will be used to provide a voltage offset to the VGA, causing an increase or reduction of the swing amplitude. The intention is to perform temp/pressure/humidity compensation is software, and to feed corrections via the DAC to the VGA.

Presently there is no microprocessor control at all. There is a Time to Digital convertor that measures the time in nanoseconds from the rising edge of a 0.5Hz reference pulse from my GPSDO, and the rising edge of the pulse from the pendulum BDC sensor ( an opto interrupter). This will be used to Phase lock the pendulum to the GPSDO 0.5Hz pulse initially, by control of the DAC, breaking the Peak detector loop. When phase locked to the GPSDO reference, the uP will
log the variation of DAC control voltage to maintain lock, as well as logging Ambient temp, pressure, Humidity, bob temp, and rod temp.

I hope to find a way to implement some sort of amplitude compensation using all that data as reference input, at which point the pendulum will be released again and be free running, with only the amplitude loop controlling it, and the uP performing environmental corrections only.

The phase shifter is also able to be voltage controlled. If the amplitude control of the coil drive voltage does not achieve the control required ( since period is largely independent of amplitude) then the VGA loop will control amplitude, and the DAC will be used to adjust the drive voltage phase, allowing a lag or lead drive voltage to slow or speed up the swing.

A lot of electronics and a lot to experiment with....quite enjoyable.

Starting some logging now to see how the phase lock to GPSDO performs, and now that the ADC is in place, I want to do a few run-down swings to try calculate Q...

Some photos of the the growing electronics.

Edited By Joseph Noci 1 on 29/08/2023 00:06:05

Reference the above whale flipper link Jo, I couldn’t resist chipping in with this…

…the leading edge of a dragonfly wing.

Apparently, for whales, the tubercles provide swifter manoeuvrability. That would be handy for a dragonfly too.

And how about the leading and trailing edges of a pendulum rod with a suitably shaped (elliptical) cross section?

By the way, that’s brilliant work you are doing Jo!

Sam

Absolutely amazing how Nature builds structures that challenge and overwhelm all man's scientific methods! That wing is gossamer thin and as strong as steel, but weighs nothing...Nice photo Sam.

I have/had all sorts of ideas for the bob and rod - as you are suggesting, but modelling such concepts is difficult and at pendulum velocities, involves lots of guesswork and many assumptions. To obtain definitive results an approach would be to use a functional, stable pendulum, and then make such a rod, for example, and see its effect on the performance. The problem is always, digging out the delta from all the other delta's - temp, humidity, etc. A road to Hell...and it takes a long time...

Edited By Joseph Noci 1 on 29/08/2023 07:22:31

Really interesting system Joe. A couple of questions.

How do you filter the signal from the synchronous detector? There was a long debate in HSN between Matthys and Bigelow about the significance of any phase shift in the sinusoidal drive oscillator loop. Bigelow used a very simple oscillator circuit where the pendulum was the resonator, using a single op-amp and (zener?) diodes to limit amplitude. The op-amp GBW was 1 MHz, so there was a small excess phase shift at 0.5 Hz which meant that the impulse wasn't quite in phase with the pendulum. Bigelow thought that this was insignificant, Matthys was concerned, I think there's a whole chapter in his book that reflects this debate.

I'm also interested in how you achieve the 90* phase shift needed for the pendulum drive, at 0.5Hz!

I've wondered about sinusoidal drive for my clock, but not having a proportional angle sensor would probably mean having to phase-lock a digital system and synthesising the sine wave.

John,

The Sync detector filter is a low pass with cutoff @ 1KHz. The angle sensor runs at 5KHz, so 1KHz cutoff is OK and the phase shift on that signal is very low in the 0.5Hz domain.

I read in detail the Bigelow texts re his oscillator, also the details in Matthuys - studied and modelled his circuits in Simulink, etc, but I believe the concept and approach is flawed - clipped sine wave will always cause perturbations - The 'thermal' analogue multiplier has interesting potential - rids signals of some noise issues, but not sure it is worth the effort. In addition, that concept provides no means of adjusting phase if in error/needed.

You said -

The op-amp GBW was 1 MHz, so there was a small excess phase shift at 0.5 Hz which meant that the impulse wasn't quite in phase with the pendulum.

Did you mean impulse? I guess so, since the clipped sine is more 'impulsive' - What I have tried to implement is really a 'pure' sine, at least as pure as the pendulum swing, with the coil current always in tune with the pendulum position and velocity - it can never differ, only the lead/lag can differ by changing the 90deg phase shift, and that is the ideal control point input.

The op-amps I used are 2MHz GBW, except for the differential instrument amp after the Sync detector - that is 500KHz. However, any build up of phase shift become unimportant as the 90deg shifter can be adjusted to shift by the amount needed to lock the loop. The peak detector voltage is monitored and that will stabilize while the final PID loop ( too be implemented still!) controls either to VGA gain, or the phase shifters setpoint.

OP amp choices are always a trade-off - I want really low noise and really good input offset performance, but that tends to oppose higher GBW, so overall system compensation is the way to go..

My 90Deg shifter is purely analogue right now - an all pass filter with 90deg point set at 0.5Hz. I will most likely implement this digitally - either a FIR all-pass or Hilbert transform - for concept testing right now the analogue all pass works just fine! It will have shift drift due to the tempco of the C's in the filter, but I believe all tempco's can be compensated for at system level, ie, an overall temp compensation, rather than compensating each circuit element.

If you want details of the angle sensor, I am happy to give my drawings and circuits - Do you have a desktop CNC router? Easy then to make the capacitor elements with FR4 PCB.

Drool! Pure porn. I can't wait to see how it works in practice.

Dave

Thanks Jo.

This was the original single frame (best of the bunch snapshot). Hence the loss of definition.

And the branch was swaying in the breeze.

Good luck with the pendulum.

Sam

Did a few runs today and logged data to calculate Q - Not impressive, but I think definitive.

The Processor reads data from - Angle sensor (sinusoid), Angle Peak detector, and all the temperature sensors, humidity and pressure. The angle and peak detectors are sampled at 200Hz and can be logged at 200Hz, 100Hz, 50Hz, 20Hz and 10Hz. 200Hz fills large files fast...

With the pendulum running and the control loop stable, the drive voltage to the drive coil was then disconnected and the pendulum angle data logged at 50Hz.

This plot is 2-1/2 hours of data at 50Hz. The data was analysed at the points where the amplitude had fallen by:

61% - Q = 12000

50% - Q = 12400

31.8% Q = 14514

50Hz data log of pendulum sinusoid amplitude over time: 

It is interesting that the Q increases with extended run-time. The amplitude of the swing at the start was 2deg full swing - Q seems to increase usefully with reduced swing angle. I will try another run with a 1.5deg full swing angle from the start to see if this is so.

The sine wave from the angle sensor looks good, sampled at 200Hz. The sample artifacts at 50 Hz are quite clear in the posted examples below. The 200Hz sampled waveform will be used to generate the digital 90deg phase shift to the coil drive, in due course.

200Hz sampling and logging

50Hz Sampling

With the 'knife-edge' pivot and efforts I put in on the Bob format, etc, I would have thought I should achieve a better Q than it appears, although my expectations are/were biased by what others have been saying they have achieved - I will placate myself somewhat in the belief that the Q figures bandied about have been very much over-estimated in light of the recent discussions on ways to calculate Q and methods to do so.. I think the method I used is definitive and is very repeatable and should enable quantitative evaluating of the effects of modifications and alterations to the system.

Edited By Joseph Noci 1 on 29/08/2023 22:53:20

Incorrect use of words...

This plot is 2-1/2 hours of data at 50Hz. The data was analysed at the points where the amplitude had fallen [by]:

61% - Q = 12000

50% - Q = 12400

31.8% Q = 14514

Meant to say :

This plot is 2-1/2 hours of data at 50Hz. The data was analysed at the points where the amplitude had fallen [to]:

That looks like ‘text book’ stuff, Jo

… you will likely be a cited reference for future investigators

MichaelG.

Thank You, Michael.

However, I am at the limit of my bounds on this - I don't know what to do next - so putting the Pendulum to sleep for a while!

Please don’t let it sleep until you have tested with different start angles, Jo

You have a rig which obviously works and there is a wealth of information to be discovered

… just grab more data for now !!

MichaelG.

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Footnote:

Data become information when we understand them.

Edited By Michael Gilligan on 30/08/2023 09:07:48