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Re: [Phys-L] Trinity Pendulum Q

Hugh,
It was tantalizing to see the responses to your pointer for data on a Trinity clock restart for October 2009, in connection with seeking a value for Q.
Though the various determinations of a restart Q were scattered (from ~1000 to 2000) they
all were remarkably lower than the Q values found earlier for free decay of the pendulum.
Why? If a small but constant fraction of the available energy is lost at each decay cycle, then during restart, not only that loss needs to be made good, but the remainder of the escapement's contribution is all that remains to increase the amplitude. This seems like a plausible reason for the discrepancy between the decay Q and the recovery Q.
I was particularly taken with Bernard's sharing of a method using the transit time of a narrow vane at peak pendulum velocity on successive cycles as tokens for kinetic energy and energy loss per cycle (in the form of the square and the difference of successive squares) though it was not difficult to see that the mechanization of this fine idea introduced two discrepancies which led him to a somewhat high dynamic value for Q. I was curious to understand how Drumheller found a way to compensate the peak velocity value in the face of decreasing amplitude, where more of the slower swing was included. I was interested to hear of Rawling's Q estimator - using the cycle count to half amplitude - which naturally led to a review of the multiplier between time to half life Tsub hl and exponential time constant tau.
This was pertinent to the very snappy response to your note which Bernard offered (within the hour?) where from a decent exponential model and a reasonable value of time constant of ~26 minutes for the October 2009 recovery data to which you alluded, he "Qestimated" (cute!) a value Q~1000 whereas I show it closer to Q=1633 using his time constant, and Q=1566 using my similar model and Rawling's estimator. Even Donald Polvani's carefully computed value Q=2100 is far below your value for Q during decay (Q=5441).
I notice that Doug Bateman keeper of the Westminster clock (aka Big Ben) alluded to a high Q value of the unloaded undriven pendulum there. Though he objected to your calculation of Q including all losses (not least the fly clutch) I saw that simply as a comparable calculation to Bernard's original citation of a text problem which also did the very same inclusion of all system components (though one supposes there was no lossy vane involved in the text example).
Finally, I should again say thanks to the contributors to this thread for providing a week of harmless computation for me: - Matlab, NLReg (Non linear Regression Analysis by Sherrod) and the old TI Scientific just didn't know what hit them!

Sincerely
Brian Whatcott

On 5/18/2015 1:10 AM, Hugh.Hunt wrote:
Dear Brian,
I'm glad we agree!
You might find this interesting to ponder:
In 2009, October clock change, rather than putting it back one hour it was advanced by 23 hours. This meant that the free decay of the pendulum was even slower, because the gravity arms were lifted off the pendulum. But the interesting question is the restart. The exponential curve that shows the swing amplitude getting back to normal surely tells us something about the drive?

<http://trin-hosts.trin.cam.ac.uk/clock/?menu_option=�; data&from=� 25/10/2009&channel=�amp&channel2=�0&to= �25/10/2009&xmax=�2&skip=� 0&ymax=�54&ymin=�37>

Food for thought.

Best wishes

Hugh





On 18 May 2015 4:57:49 am brian whatcott <betwys1@sbcglobal.net> wrote:

Thank you for responding, Hugh. Your working clarified that the cause of
Bernard's rather high value for the Q of the Trinity Pendulum was his
use of the escapement energy contribution at each cycle as about 0.0029
j in lieu of the 0.0038 j which would be needed to maintain a Q value as
low (!!) as your free decay Q value. This escapement energy
contribution value was evidently derived from a Trinity Clock site
mention of the Denison gravity arms weighing 50 grams each and
descending 3 mm.
Your note was also a useful reminder of Denison's use of an
air-brake ('fly') with a lossy friction clutch to cope with the varying
clock drive needed during the year while maintaining a sensibly constant
impulse to the pendulum, and as important, eliminating the escapement
skip not uncommon in tower clocks prior to 1860.
Thanks again
Brian Whatcott

On 5/17/2015 12:21 PM, Hugh Hunt wrote:
> Dear Bernard, Doug, Brian
>
> I'm very interested in your calculations. I am Keeper of the Clock at
> Trinity and Rick Lupton, who wrote the report, was my student.
>
> The pendulum free decay (without drive) can be see here t clock change
> <http://trin-hosts.trin.cam.ac.uk/clock/?menu_option=data&from=26/10/2008&to=26/10/2008&width=700&channel=amp&&xmax=1&skip=0&ymin=32&ymax=53.6>
>
>
> Note that the decay is nicely exponential. The width of the plot is
> one hour, so the decay is from 53.6mrad to 29.8mrad in about 3050 seconds
> Using the usual definition of Q from where it derived (Quality Factor
> for resonant circuits) then A2/A1 = exp(- zeta w T )
> where A1 and A2 are two amplitudes separated by time T for a damped
> oscillator with resonance frequency w (rad/s)
> The Damping Factor zeta = 1/(2Q)
>
> So A1=53.6 A2=29.8 T=3050 s w = 2*pi/3 for our 3s pendulum
> (half period = 1.5s)
> gives zeta = 0.0000919 or
>
> Q = 5,441
/snip/