Member postings for S K

A true Gaussian (a "bell curve" ) has infinite tails, which you wouldn't want, so it would need to be a modified one that starts and stops with zero force. Perhaps a modified Gaussian-like profile without the infinite tails is not perfect for this, but it has got to be pretty close. You want it to start almost imperceptibly, grow smoothly to a peak, and then decline back to zero in the same way.

P.S., that darned insertion of a winking smiley when you type " followed by ) is so irritating!

Edited By S K on 11/03/2023 22:35:43

If I may make a point ("you can't!" says a voice from the peanut gallery), I'd like to draw a line ("again: can't!" ) between pure math ("Math? Ha! Any so-called consistent formal system can't prove it's own consistency!!!" ) and reality ("Hahaha, you and everything you think of as real is all just a holographic projection on the surface of a black hole - and even that is just a computer simulation!" ), ... wait, I forgot my point ("GROAN!" ). Oh, never-mind! ("Mind? As in 'free-will?' Lol, you haven't heard of super-determinism, have you..." ) 🙃

Edited By S K on 11/03/2023 21:17:19

Would "rigid" apply to the character of someone who insists that the word "rigid" must be banned, and those using it excoriated, except if we are talking about an imaginary world of abstract ideas? 😛

Right, but that's exactly why the frame rocks as the pendulum does, as SOD observed (Newton). Anyway, enough pedantry for me.

I think electromagnetic impulsing is the way to go for higher control and precision, but I've wondered how modern techniques could apply to traditional approaches. So:

In a mechanical impulsing design such as in the Synchronome, a weighted roller applies force to an anvil on the shaft. The profile of the force is determined by several factors, such as how close the tolerance is at the beginning of the force (e.g., does it strike the anvil with an initial shock or very gently) and the profile cut into the anvil, etc.

But what if you applied the force with a servo through a load-cell or capacitive measurement or some other force-monitoring system. With electronics to monitor the force, a profile such as a pseudo-Gaussian force curve could be applied. This would avoid sudden shocks to the pendulum that could cause vibration.

For electromagnetic impulsing, I've thus far only seen a more-or-less digital approach: The coils are simply turned on and off via a digital signal, with little other control except timing and sometimes magnitude. But a proper electronic filter could soften the blow in a more controlled fashion. Or, even better, a DAC and associated circuitry could implement an arbitrary programmable force curve.

Either way, it's not clear to me that anything much different than a pseudo-Gaussian is worthwhile, but being able to control it at a fine level sounds interesting and possibly beneficial.

Does this make sense?

Off topic, but you are saying that Hooke's law = Newton's third? Or that Hooke's is the one that applies here, not Newton's?

Every pendulum support will move (Newton had something to say about it). The only question is by how much. I presume you have set it up to amplify the motion? Have you calculated the amount of motion right at the pendulum, and for a more realistic amplitude?

I've wondered about how pendulum length affects performance. Matthys claimed that shorter pendulums have higher Q, but without explanation, and that's about all I've seen on the subject.

A longer pendulum is slower, and can move over a shallower angle while still covering enough distance at its bottom to fit in your measurement apparatus. My guess is that it should encounter lower losses at the hinge and in air due to these factors, though a longer shaft would induce some additional losses too. I'm not sure it matters much if you are going to have a partial vacuum and a shallow swing on a low loss pivot, though.

Edited By S K on 10/03/2023 20:18:50

Hi John,

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

Thanks.

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

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

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

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

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?

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

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?

It leaves you Totally in the Wrong (capitalized!) until you submit to the proper terminology! Lol.

OK, so I made one of the all-time most notorious mistakes in my calculations: I accidentally mixed metric and English units! 🙄

It didn't change the result much, but it definitely changed the error propagation calculation. After another trial with more care and a bit of other tuning, and of course correcting the error, I found:

g = 9.7964 +/- 9x10^-4 m/s^2

The RMS noise on my period measurements also dropped to 5.5 us.

So I gained 2 significant digits to 5 digits (by the skin of my teeth), mostly by correcting the error. The measurement remains identical to the National Geodetic Survey's computed estimate within my error bars.

I think my next step is to calculate how much altitude I'd have to gain before I could find a repeatable change in period. That way I can see how good it is as an "invariable" pendulum - one used for relative g measurements (e.g. after calibration at a site where g is know to high precision), rather than absolute g measurements.

Edited By S K on 06/03/2023 22:00:26

Just an aside, as it slightly irritates me: What's with the "Precision Event Timer" talk, capitalized and all like it's a Very Real Thing!?

The long-accepted term for such a device is "time to digital converter" or TDC. 😉

(In a prior career ages ago, I designed a TDC with 500 ps resolution.)

Edited By S K on 06/03/2023 21:20:35

Why not an A-frame design like my free pendulum used? You (mostly) only need rigidity in one direction anyway, and an A-frame is likely to be better than most vertical-only supports.

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.