#### Magnetic vs gravity impulsing

Bepi

The old dear synchronome seems to be much better at measuring time than I was expecting.

When I say measuring time here I mean intrinsically, with reference to its own internally produced noise. Then there are all those nasty explicitly time dependent potentials like temperature, pressure, celestial body attraction, etc, we'll take care of them later, here I am only concerned with the internally manufactured noise. The noise which would look statistically the same whenever you conduct the experiment. Correct me if I am wrong.

The ones who have looked at my previous post might have noticed that I added to the clock a magnetic impulsing system (MagImp) which seems to be working really well, if there is interest I can describe it in detail in another post.

It works well in the sense that I can reduce the impulse irregular period to the level of any other free fall period by carefully centering it in the sense of Airy's tangent rule. With MagImp the average power is somewhat reduced too, I got rid of the clock losses linked to the timing wheel operation, and I am always referring to stationary states at constant amplitude of when the clock ticks normally, I should say ticked. And with those losses we do without the associated noise too.

In the following I will show circular error free data where the amplitude stays the same for hours, within a few thousands of a degree, corresponding to a fraction of a microsecond of circular error.

With the following graphs I'll compare two runs, one with magnetic impulsing and the other with the old gravity escapement of a classic synchronome. The clock is always the same other than the missing drawing arm, I can switch from one impulsing scheme to the other in a matter of minutes on the same clock, the one I purchased a few months ago on Ebay for 280 pounds.

First set of plots refer to the classic escapement:

the second set of plots refer to the magnetic impulsing case:

Compare the second graph of both set first: the average period over the impulsing cycle vs time in hours. The average is different because the data were taken months apart and the calibration had been changed in the meantime, but we are not interested in the average, we are interested in the regularity of the clock. The y scale to contain all the measurements is roughly twice as big for the MagImp data, in fact over the experimental run the SD (standard deviation) of the MagImp data is 4.14 μs while for the gravity arm case the SD is 1.82 μs. The impulsing cycles are different, the MagImp cycle consists of 5 clock periods, the synchronome of 15, but the MagImp data have been averaged over the same number of periods, 15, before taking the SD, so the SD comparison is fair.

The circular error variation calculated from the amplitude (green points third graph) is shown in the red trace. In both cases the circular error contribution to the SD is negligible, a small fraction of 1 μs.

The real surprise is in the period within the cycle, first trace. The data show typical individual period amplitudes during the run. Those specific ones occurred at the end of the blue trace just below the second graph, in hours from the beginning of the run but they all look statistically the same.

Pay attention to the y scale in those graphs, always in s, the mechanical escapement induces ms size fluctuations around the power impulse, plus a mess after it, while the magnetic impulse induces a variation in the order of tens of μs, if any. The MagImp impulse was not optimized as well as it could but its amplitude deviations are nevertheless not bigger than the following free pendulum ones. You couldn't tell when the impulse occurred and it was only 60 to 70 ms long.

The regularity of a clock, even this fast scale regularity, is not just a matter of size of the fluctuations but also of their correlation properties, I'll test the autocorrelation function when I have time, but the fluctuations themselves are a prerequisite for errors and in the mechanical case they are almost 2 orders of magnitude larger. Did you ever look at the output of a clock timer like a Microset with a quartz clock as an input? It's frozen on the same period reading to the 0.1 μs figure. I don't have a Microset, I use what Luke Mester gives away for free and an Arduino based one, but the result is the same.

Since the SD we are talking about is the one of the averages over the whole cycle, 15 periods, what just said means that those large deviations of impulse duration occurring at and around impulsing are just as regular and reproducible as all the others.

I find this surprising and I would like to share it with all those people that fell speechless in front of these data too.

Disclaimer: In this document words importing the masculine gender shall be deemed and taken to include the feminine gender and the singular to include the plural and the plural the singular unless the contrary as to gender or number is expressly provided or unless the same is inconsistent with the context and where covenants are to be entered into by more than one person the same shall be entered into jointly.....

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Bepi

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