JoNo's Pendulum

I suspect the confusion over Q is caused by clockies insistence on calling the time for the pendulum to swing from one side to the other the period, whereas real engineers would call the period the time to get from extreme left back to extreme left, ie the time for one complete cycle. Wkipedia's definition is per radian, and one engineer's cycle is 2PI radians, which is where Alan (Philip Woodward) gets the 2PI. John Haine at 12:24 pm seems to be totally awry, as exp(-1) is 0.3678, not 0.6321

If I take my reasoning and using clockie definition of period then :

Q=swings to 61%*(2*PI)

Q=swings to 50%*4.5324

Q=swings to 36.79%*PI

Q=swings to 21%*2.013

which agrees with some of the figures JoNo is quoting

Edited By duncan webster on 16/08/2023 18:11:57

Edited By duncan webster on 16/08/2023 18:18:59

Edited By duncan webster on 16/08/2023 18:22:03

Rawlings in 'The Science of Clocks and Watches', spends Chapter 4 on 'Dissipation of Energy by a Swing Pendulum'. He addresses the amount of energy needed to keep a pendulum swinging, but doesn't relate it to Q, which was new to clocks when he wrote circa WW2. Rawlings measures the decay of an actual pendulum and graphs it, Then from the graph he derives an equation that's a close match to the curve. The formula uses e (Naperian Log) and a constant of 16.6e10-5 per second; "chosen to make the curve pass as close to the squares as possible".

The 3rd Edition of Rawlings (1993) was updated and annotated by several up-to-date contributors, notably D A Bateman, who introduces Q. He mentions Drop until 50%, then x 4.53 as a way of estimating Q and explains that it and Joe's other values derive from the Naperian Log part of the equation. which assumes the pendulum exhibits 'damped harmonic motion', in much the same way as an early spark transmitter. DAB extends the maths in Appendix 2 'The Linear Theory of Vibration', which finishes with:

• The logarithmic decrement leads to an easy rule of thumb for measuring Q.
• Then: Q = πn/ln2 = 4.532n (approx) and
• With the low frequency of a second pendulum, this may entail waiting for an hour or more , but the calculation could hardly be simpler.

But I suggest there are several ways in which the formula could give wobbly results! For example, when a pendulum swings through a tiny arc, how accurately can the observer judge when 50% decay has occurred? And does he know that his pendulum is following 'damped harmonic motion'.

Unless the measurement is made very carefully in the same way by all parties, I think it unwise to get excited comparing the Q of other folks pendula. However, when the same method is applied consistently by the same operator, Q is useful as a way of checking whether a modification has improved or made a pendulum worse worse.

As a self-check, if the values of Q measured in the same run at 21%, 36%, 50% and 63% are wildly different, it's likely that the operator is doing it wrong, or that the pendulum is wonky, or both!

My method of deriving Q from a bandwidth formula has other problems. It assumes that the values of a large set of frequencies are normally distributed. This way of obtaining Q doesn't assume a logarithmic decay, which is just as well because my pendulum is being impulsed: definitely not 'damped harmonic motion'. And I'd expect the Q of a powered pendulum to be different from the Q of the same pendulum left to lose energy naturally. Nonetheless Bandwidth Q is meaningful to me because exactly the same method is applied every time I log new data, and I can trust it in my context. It's not necessarily useful to anyone else unless they use the same method.

Measuring is hard!!!

Dave

Oops! Quite correct Duncan. Told you to trust Woodward.

I think SOD is confusing drop BY and drop TO

Edited By duncan webster on 16/08/2023 18:46:19

John,

From your post -

An/A0 = exp(-n*pi/Q), where n is number of periods. So if ln(An/A0) = -1, then Q = n*pi.

So An/Ao = exp(-1) = 0.6321. Count cycles until amplitude is 63.2%, multiply by pi.

your formula gives..... exp(-1) = 0.3678 ? Which would then follow that :

Count cycles until amplitude is 63.2% 37% , multiply by pi.

What have I missed ?

edit - Duncan beat me to it!!!   NOW it is clear!  I could not understand  what was presented at all...

Edited By Joseph Noci 1 on 16/08/2023 19:06:18

If the formulae is scientifically derived , it is unlikely to give 'wobbly' results. Claiming that is does or can, and defending that by blaming the wobble on slackness on the part of the observer in taking measurements is hardly a defence... If you cannot take accurate, or repeatable measurements you need to question why you are doing this in the first place. The formulae will not lie if the data is sound.

What we are trying to establish here is the scientific soundness of the formulae, not people's pendulums or measurement methods.

Your emboldened paragraph above is key, but also key is to know that the pendulum that you are playing with is of useful quality ( not Q, but appropriate workmanship, design concepts, accepted pivots concepts, etc) and that you are in the ball park with practical Q values. There is no point chasing 1sec/year if your pendulum Q is 2000. If the real Q value is 15000 or 17000 is irrelevant, either is good, and so is 12000...

Q is not the Final Cut , but it gives the user a warm feeling that he can continue to the next phase.

ALSO, you state :

. And I'd expect the Q of a powered pendulum to be different from the Q of the same pendulum left to lose energy naturally.

I don't agree = Q is Q - you cannot improve the Q by 'powering' the pendulum - put it in a vacuum, a better pivot, etc, yes, but then Q will be the new Q and nothing else.  In an LC oscillator , if you remove the amplifier around the resonant cct, and hit the LC cct with a pulse, and measure the ringing decay, that will give a representation of Q. Adding the amplifier to make it oscillate only puts back the energy lost in the decay, and maintains oscillation. The Q certainly did not change.

The capacitive angle sensor I made for this is ideal for amplitude measurements. I digitise the sinusoid ( to 16bits) and log it all the while - the decay of swing is seen clearly in the overall plot, and a curve fit to the peaks shows a decay level wherever you want , against number of swings at that point. You would be hard pressed to measure more accurately than that I would guess..

Edited By Joseph Noci 1 on 16/08/2023 19:23:36

Edited By Joseph Noci 1 on 16/08/2023 19:25:53

Edited By Joseph Noci 1 on 16/08/2023 19:31:34

Of course this all depends on Q being constant, i.e. not affected by amplitude. I'm not sure this is a valid assumption, but my knowledge of very low speed aerodynamics is extremely lacking. Q will almost certainly be affected by whether the door of the clock case is open or closed. It's easier to push the air out of the way with the door open I think.

It would be interesting to take multiple readings during a run down test and see if Q changes.

I'm surprised what I said is controversial, hey ho such is life!

My point is three-fold: the formula is an approximation; it assumes the test pendulum exhibits damped harmonic motion; and results depend on the ability of the observer to measure amplitude accurately, which is hard. (Of all the ways discussed on the forum I'd expect your capacitive system to be the most accurate because it eliminates the human element!) I suggest this combination of factors creates a situation in which forum members report different values of Q.

Although the Q formula we're discussing is scientifically derived, it's simplified. Many others are in the same boat: Ohms law doesn't apply to substances with negative resistance, and it only applies to DC or pure resistances; Newton's Laws are inaccurate at very high-speeds and below Atomic scale; the standard pendulum formula is a simplification, only accurate over small arcs.

I absolutely agree Q isn't the final cut!

I disagree that Q is Q. In electronics, there is unloaded Q, loaded Q and coupled Q. An electromagnetically impulsed pendulum, or one attached to an escapement, are both loaded. More importantly, a mechanical system has more disturbances than an LC circuit. As Duncan says, opening the door of a pendulum case alters Q because the air eddies around the bob will be different. Impulsing also disturbs the pendulum mechanically, in an extreme case by whipping the rod. Therefore, so I'd expect my pendulum kicked by a single pulse to have lower Q than it would with a well-adjusted sinusoidal drive.

So I see Q-factor as a useful guide rather than an absolute measurement.

When your pendulum is running and logging data, it will be easy to calculate Q from bandwidth periodically. Try it and see how it compares with my results and the lost energy calculation. Whatever it is, I'll be amazed if your pendulum doesn't keep better time than mine.

I suspect we're only disagreeing about the size of the Q ball-park! One thing I've learned in my pendulum adventure is that measuring anything to do with precision clocks is tricky.

Dave

I disagree that Q is Q. In electronics, there is unloaded Q, loaded Q and coupled Q. An electromagnetically impulsed pendulum, or one attached to an escapement, are both loaded.

But that's the point. Q under the measured condition will not/should not change - loaded Q measured again must be the same ( or close) or else your measurement was poor.

So I see Q-factor as a useful guide rather than an absolute measurement.

I guess that's what I said? But it does not help if the method and maths are not consistent - If you want to see if your pendulum Q is in the useful range, compared to other useful 'good' pendulums, then you need to take measurements that give compatible data...

Perhaps when pendulum Q is quoted, folk need to indicate the method as well for apples to be compared. But I think this is somewhat pedantic - Most folk will understand what a run-down Q of Xthousand means....You are probably on your own if you choose different methods...

Me, I'm mostly on my own in this anyway - I have little notion of what I am doing - I am good at devising appropriate technologies to apply and use for test and measurement, but with my good data in hand I am somewhat lost with what to do with it!

What I am aiming for is along these lines - 

The angle sinusoid , which so far proves to be very stable and environmentally immune, feeds a very fast comparator ( 5us propagation delay, 7ns rise and fall time) to give me a sq wave, switched at the sinusoid's zero cross. This sq wave is fed into the TDc7200 TDC chip ( Time to digital) on the stop input. The start input is fed with a 1hz pulse from my pretty stable and accurate GPSDO. The TDC gives me the delta, down to the nearest 2ns.  With TIMELAB I can get ADEV directly from this data.

The angle sensor sinusoid zero cross is at BoB BDC and observing that point, and the comparator switching, referenced to the GPSDO 1hz, all on a scope, shows a jitter around that point of less than 200ns. This alleviates any issues related to opto-slot sensors and light shielding vanes, etc.. - there are none!

The pendulum drive - this is my nemesis right now but, - The angle sensor peaks are at the ends of the swing, BDC is the sinus zero point, so the drive current to the drive coil is displaced 90deg. The Nucleo takes the angle sensor sinus, and generates a drive sinus, 90deg shifted, of 'appropriate' amplitude, via a 16bit DAC, to the coil. The idea is to control the pendulum amplitude (not rate) either via that drive sinus amplitude or a combo of amplitude and phase relationship to the angle sensor sinus, both controlled ONLY by the running computation of energy loss each cycle, and NOT referenced to any time control pulse, ie, the pendulum is free running, with only lost energy being replaced. If temp and pressure and humidity compensation can be applied as well, and if the free running pendulum is stable, then I can adjust time with the balance weights, and finally just gear the pendulum time up or down to match the rest of the world's time...

post far to long - no-one reads such dissertations!

Edited By Joseph Noci 1 on 16/08/2023 21:36:59

What do you mean by multiple readings Duncan? At which points?

Low speed aerodynamics are difficult - there is a glaring scarcity of scientific data at such low Reynold numbers - sub 10, even below 3 or 4...In aircraft wings design I worked with numbers up in the R10,000, for fighter jets, down to R1000 or so for small UAV's - there are few software tools that model correctly below R10. There are toold for liquid flow in pipes..

What is valid though, and contrasts with aircraft wings, is that laminar flow is not a Bob's friend. When the air sticks close to the bob, at low bob velocities, it causes the glove of air attached to the laminar layer to be dragged along, instead of being pushed aside. That artificially increases the perceived size of the bob in terms of frontal air area, and therefore drag. Cylinder bobs standing up are bad - flying saucer bob horizontal are almost as bad, vertical are quite good. Rugby balls are very good, but MUST be aligned in swing, else much worse than most. Balls are a reasonable compromise, better than cylinders.

Turbulent airflow is , as in aircraft, just bad and causes wobble of the bob. Also, a problem that aircraft don't have, the air pushed aside, now turbulent, is not displaced far away and the returning bob rides through old turbulence on its return trip..

perfection would strive to have a rugby ball shape, polished mirror finish, so that laminar flow is encouraged, with a small ring around each nose of the ball ( position and size of ring critical, or course), called a trip - as the airflow reaches nice laminar conditions, the trip breaks that flow so that the air detaches from the bob surface and flows smoothly past the bob.

This is used on aircraft as well, esp really fast ones, to break the air from the wing - friction is reduced , sometimes up to 30%, lift can be increased by up to 15-20%, and during high angle on attack, stall can be delay by 4-5degrees. all for a piece of wire...

Edited By Joseph Noci 1 on 16/08/2023 21:57:13

.

I admit that much of what you wrote went way over my head …

But those few words are ‘music to my ears’

.

MichaelG.

I meant what John H posted above, which clearly shows that Q is not constant, so for consistency across different penduli we should stick to an agreed percentage run down.

I'm awaiting your ultralow speed wind tunnel to optimise bob shape. Mine's cylindrical, axis vertical. Next one will be rugby ball passing into large diameter air cored drive coils. I wish I understood magnetic circuit design!

Don't exist...With all the associated compromises, these sorts of tests are normally done in water with dye injection, and then they try to extrapolate to air and compensate for viscosity, etc - Most times you get as accurate an idea by blowing your pipe smoke into the clock case and watching the smoke.

A neat way is also to have a smoky flame from below, and orient the bob vertically for a rugby ball bob, for example, with the smoke hitting center of bob point. Video the smoke/air flow to capture the vortex, and play back slowly and compute the air speed from the distance traveled by the smoke in 1 sec, etc. Use a hotter flame for faster, or cooler for less..and then clean up the mess.

Edited By Joseph Noci 1 on 17/08/2023 10:38:48

I once worked on machines which ran in high vacuum. Despite very high velocity, the Reynolds numbers were very low. Inspection department were keen to use water flow testing on some components as it was a lot easier than messing about with vacuum. As a fairly junior engineer I was despatched to Lucas factory in Burnley to tell them as little as possible about what was a sensitive project. When I told their boffins what the R number was, the meeting wrapped up immediately, they stated that using a fluid whose density was orders of magnitude higher than real life had no chance of success. Lucas at that time were big into gas turbine combustion systems, so they had a lot of expertise. Due to catastrophic management the company no longer exists. I did get a tour round the works, where they had amongst other goodies an old submarine in use as a pressure test chamber, and an enormous reciprocating compressor used to pump it up/down, can't remember which.

Why would the vertical vs. horizontal orientation of a same-shaped bob matter? I've always wondered why saucer shaped bobs hang vertically, when that requires the alignment to be perfect, while horizontal has no alignment problems.

Sorry for the belated response - problem with these topics sometimes - they pop off the stack so quickly and then are forgotten till news is worthy of publishing again...

In a pendulum where local air is becoming the limiting factor, bob shapes play a significant role. A vertical saucer presents the same aerodynamic shape while swinging in an arc ; when fitted horizontally, the air flow over the top will tend to break away from near midway on the upper surface and becomes turbulent in the bob's wake. That increases drag, induces wobble, and the bob has to return through that still turbulent air. The air on the bob underside suffers similarly, except slightly reversed and somewhat reduced - the leading edge section has increasing angle of attack with air breakaway, and the resulting turbulent air washes over the trailing edge. We are talking of VERY small effects here, but significant when you are trying for short of Shortt performance.

Rawlings (in The Science of Clocks and Watches) discusses bob shape in Chapter 4 (Dissipation of Energy by a Swinging Pendulum), and DA Bateman adds a useful section in which 'The objective was to discover which shape would give the lowest air resistance for a given volume, and hence the largest Q for a given mass and density.'

In short:

• The bob should be made of a high density material such as Tungsten
• Swinging inside a case reduces Q compared with swinging in open air
• in DAB's comparative experiment
  • A 3:1 cylinder was worst - Q=1845
  • Next up, a sphere - Q=2946
  • Best performer, a 2:1 parabolic spindle - Q=3375

My pendulum has a mild-steel cylinder bob, not a good shape and it might rust, but I plan to swing it in a partial vacuum. As my ancient vacuum pump only gets down to about 600mb, I might try to improve the shape by rounding the ends into a "cylinder with hemispheres".

Cylinders are easier to make and balance than other types, which is a practical advantage.

I guess Joe's bob shape isn't the absolute best possible. However, still hot stuff - better than a sphere, and much better than my cylinder.

I don't think Rawling's mentions polishing. I'd expect a highly polished bob to perform better than a rough one.

Dave

From Matthys:

Matthys's BoB..

So mine does have 'pointy' ends, but is not a smooth curve - the idea being that the first face angle is a 'trip' to prevent any laminar flow.

I presume you have Matthys' book - it is good reading in moments of despair.

Sadly not - last time I found one for sale it was too expensive. Ought to look again, I'm often in despair! Zero progress today on anything.

Dave

.

Whilst certainly not an aerodynamicist … I might ponder upon the not-so-humble golf-ball

MichaelG.