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I am supposing that by length, you mean the effective pendulum length for constant periodic time, would be increased by 0.2% where g increases from 9.80 to 9.81 N/kg.
On 2015, May 15, , at 12:06, brian whatcott <betwys1@sbcglobal.net <mailto:betwys1@sbcglobal.net>> wrote:
Bernard,
I replicated your value for Q given the following assumptions which I presume you made:
1) the effective pendulum length l is obtainable from Period = 2.Pi. root(l/g)
yes
2) The value for g at Trinity is 9.8 N/kg.
yes, however in my method it “cancels”. [except for the length, which changes little (0.2%) as the change is ~ delta (g)/2 ]
For a lossless pendulum, the kinetic energy max would equal the potential energy max.The pendulum amplitude is 55mr.
3) The maximal value for pendulum energy occurs at the potential energy max.
? is ~ constant, and I understand your reasoning, which I used. BTW, there’s a web site that gives the E for M, g, A,and T; and the speed at BDC!
While it is certainly the case that a pendulum maintained at constant amplitude has its losses made good by the escapement, the potential energy calculated using Woodward's method necessitates an assumption about how the dissipation occurs - if I postulate a pivot point with great horizontal compliance, then the potential energy calculation which depends upon the bob's (reduced) ascension would be reduced, which would have an obvious effect in reducing the value of Q calculated for a given escapement energy contribution.
4) Infinitely rigid (support), lossless pivot
Not necessary as the drive “cancels” all the dissipations.
If I choose instead the moment where angular displacement = 0 mr
and an escapement increment has occurred, the maximal KINETIC energy is calculated by adding half the escapement energy to the peak potential energy (the other half of the escapement's energy contribution being dissipated as the bob returns to a 0 angular displacement.) This changes the value for Q but only slightly.
Similarly, the amplitude of this clock varies: today (friday) it is 47 mr which has a much more distinct effect on the value of Q obtained.
Yes, only v. ~ 17% high now.
Doug has shared his reservations about 'free-wheeling' the Trinity clock gravity arms. It would be hard to disagree. As to continuous measurement of Q: this could be achieved by continuously monitoring the decay of energy between escapement contributions - but this is not something that you have done, as far as you have described it, so it is not quite a 'continuous' method that you have outlined. You mentioned Doug's "Measuring Amplitude Velocity and Q. I wonder if this is available on line at all?
I assume the Q was measured as a decay over “some” time with the pendulum moving the gravity arms only, which is likely a problem. This is because I only know of two persons(1) who've used the “bc” continuous Q measurement method, which finds the Q at the running amplitude instead of an average.
/snip/
Moreover, in the Cambridge vicinity, g runs 9.81
See http://www.bgs.ac.uk/products/geophysics/landGravity.html for N52.33 W0.0
None of this explains the large difference between your value and that provided for Dr Hunt.
I notice that no estimation of the effect of suspension pivot rigidity in space is given, other that a speculation about wind-driven deflection of the tower.
Brian W
[I see that Doug S Drumheller - Sandia emeritus and Hugh Hunt at Cambridge are both on your copy list. It would be interesting if they care to contribute.]
(1) Drumheller, Douglas Measuring Amplitude, Velocity, and Q HSN 2012-4 The author describes an improved version of the "bc" method w/ an example.
And B. Mumford who has incorporated it in one of his software versions accompanying the MicroSet.