Re: [Phys-L] Trinity Pendulum Q

[Bernard Cleyet <bernard@cleyet.org>]

On 2015, May 24, , at 08:04, brian whatcott <betwys1@sbcglobal.net> wrote:

> It was tantalizing to see the responses to Hugh Hunt's 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. (I calculated 6094 for the decay on that same morning! )
> 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.

This convinces me that recovery time-constant is not a valid method of determining running clock Q.  A valid method (The correct origin of Q is in an article in the Horological science Newsletter.) is the half power frequency method, which I mentioned earlier.  Another is the directly measured drive energy and the indirectly measured pendulum energy.   As I wrote previously I’d performed half power and decay methods with a v. ~ comparable result.   

However, the numerical model does confirm the asymmetric TCs in recovery from above and below equilibrium.  Incidentally, I suspect using time constant to describe non-linear oscillator behaviour is invalid, and some positive function of the non-linearity.  We are dealing w/rather high Q oscillators, so OK?  This is also what I found in the case of E*T (adiabatic invariance).  

>  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.

Note:  D. Drumheller in HSN-2012-4 informed that amplitudes only are sufficient for Q calculation by the bc method, as there is a cancelable common factor.  (not accurate for low Qs)


> 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.

Is this an invitation for a copy?  I suggest all interested subscribe;  the British version also, which I haven’t "afforded”.


> 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  and exponential time constant tau. This was pertinent to the very snappy response to Hugh's 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 Hugh 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 Hugh's 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 Hugh's 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).

or Gate Keeper’s clock. 

> 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