Very interesting approach Joe!

Sinusoidal drive was used in a couple of clocks by Ned Bigelow in the US. He used a moving magnet design with a large number of turns on his coils. This gave a high transduction coefficient "K" which allowed him to connect the pendulum as the resonator in a simple oscillator circuit – in effect he had a resonant circuit with the Q of the pendulum. IIRC "K" is the volts/m/s as well as newtons/ampere – same value different units. I looked at using a similar approach with my design but K is very small so the impedance would be swamped by the circuit parasitics. Do you have any measurements for your drive arrangement? I did consider using sinusoidal drive in the way you are proposing and still might, so looking forward to seeing your results.

On the suspension, the arrangement you have for the trunnion bearing makes it hard for the pendulum to hang truly vertical "back and forth" as there will be some friction between the bar and vees (yes, I know I use a similar arrangement!). IIRC the maximum hanging angle is something like arcsin(coefficient of friction), it's in Matthys' book. Doug Bateman simply has a flat surface on the "brackets" so the pendulum can roll to verticality. Or one could use ball bearings to reduce friction but also constrain the pendulum back-and-forth.

This sort of post does nothing for my inferiority complex! Loads of good ideas, extra well-made, and Joe is another one who must work at least twenty times faster than me.

Disappointing results from the accelerometer were predictable, but good to see it tried, especially in a pendulum design that allows that sort of experimentation. Though I like sensors inside the bob, I worry about wires flapping about inside the rod and adding friction where they exit at the top. (Causing much more friction than the knife-edge?)

May be worth adding a humidity sensor. Although almost completely insensitive to temperature change, my samples of solid Carbon Fibre rod were humidity sensitive. I believe humidity acts on the matrix and alters its elasticity. If running the pendulum for a long time shows anomalies, humidity might be the cause. (In the UK humidity varies a lot: I've no idea how much it changes on a Namibian sea-shore!)

Can't wait to see how it performs.

Dave

PS Poor Joe. After resisting the pendulum bug for ages he's caught it badly. Worst case of pendulitus I've ever seen. Welcome to the dark-side…

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.

Philip Woodward, in his book.. My Own Right Time, page 17 gives…

Q = 2Pi x (total vibrational energy / energy lost per period)

which he says can be proved that Q = Pi /(loge 2) x the number of periods (double swings) the pendulum takes in decaying to half amplitude.

pi / loge 2 = 4.53.

His pendulum came out with Q = 14,000 (approx)

Edit… Loge is exponential logarithm

Alan

Edited By Alan on 16/08/2023 13:21:13

Yes, the rule here is "always trust John Haines." 😉

Aaaand I misspelled John Haine. Sorry.

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

I think SOD is confusing drop BY and drop TO

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