[time-nuts] Q/noise of Earth as an oscillator

Tom Van Baak tvb at LeapSecond.com
Sun Jul 31 21:16:35 EDT 2016

Hal Murray wrote:
> It's energy loss in both cases.
> Is there a term other than Q that is used to describe the rate of energy loss 
> for things that aren't oscillators?

I've seen "energy dissipation" or "energy decrement".

Before Q was used to describe line width of atomic and optical clocks,
before Q was used to describe performance of simple harmonic oscillators and quartz crystals,
before or while Q was used to describe the ratio of reactance to resistance in a coil,
horologists that worked with precision pendulum clocks needed a way to characterize the amount of energy lost per period.

This was very important because the energy lost each swing (due to all forms of friction) had to be replaced in order to keep the pendulum oscillator running. And the timekeeping performance seemed to be related to how small or how consistent this energy was. I'm sure "decrement" was used before then, but I'm not well-read enough in science history to have any idea. Still...

What I do know is this abstract from a 1938 paper [1], written by an early time nut:

    ABSTRACT. The decrement of a pendulum falls slowly with the amplitude: hence the
    need for determinations based on small changes of angle. The resulting errors of observation
    lead to erratic values but not to systematic error. The result of measurements with a
    seconds pendulum enclosed in a case is shown by a smoothed curve, the departure from
    observed times being expressed by smoothing fractions, and a smoothing figure is a
    measure of this departure for the whole or part of the experiment. >From the decrement
    the rate of loss of energy is calculated. This 7 kg. pendulum with amplitude 53' dissipates
    a Board of Trade Unit (which serves a 70 w. lamp for 14 hours) in rather over 100,000
    years. Experiments with different pendulums are described by which the component
    losses due to suspension, rod, and bob are found. Suspension springs made from thin
    strip clamped in chaps dissipate large and variable amounts of energy compared with
    springs made from thick strip ground thin in the middle. The variable losses are associated
    with variable rates of the pendulum. The cylindrical case adds considerably to the air
    resistance. The measured loss due to a gravity impulse lever is little in excess of the
    computed loss from collision with the pendulum: for a seconds pendulum 1/2000 part of
    the free pendulum loss.

This article is also a favorite of mine because it talks about a "root mean square of a series of such fractions may be called the smoothing figure for the series, and its smallness is an indication of the confidence which may be placed in the result." -- a 1938 precursor of the two-sample variance, or Allan deviation.


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