Not to kick sand in your face, but it seems that in order for your automated
turn-over device to work, as well as to accurately measure the time
intervals, you would need a means to determine when the sand quits flowing.

Correct. It's not unlike a zero crossing detector. The period
of the sand flowing cycle is only 0.000278 Hz (1/hour).

Possibly an accelerometer or microphone, with the added benefit of being
able to hear the close-in phase noise.

I wasn't planning on it but an optical detector sampled by a
sound card might also give a pleasant audio signal as well
as a data source from which the end-of-sand point can be
determined with greater accuracy.

I admire your dedication to monitoring the hour long periods of the sand
timer so diligently. Truly a time-nut!

You now all see why the hourglass is on top of the H-maser.
Issues of installation, environment, reliability, instrumentation,
gravity, data analysis, noise, stability and long-term frequency
drift are very similar for both clocks.

And given the sand inside, it's also a ... quartz crystal oscillator.

/tvb



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