Wednesday, April 05, 2017

Tick

A common source of inaccuracy in timepieces is an error in the period of the device's tick, which causes the clock to run too fast or too slow. This is sometimes described in dimensionless units like parts per million or PPM: a one part per million error in a clock with a tick of one second is equivalent to an error of about thirty-two seconds each year, because there are approximately thirty-two million seconds in a year. One PPM is equivalent to a relative error of 0.000001 or 0.0001%.

More ticks per second - so each tick has a shorter period - are better. The shorter the period of the tick, the less important a relative error in that period is, because the smaller the error will be in absolute terms.

The inverse of the period of the tick is, of course, its frequency, what a scientist or engineer would measure in units of Hertz or cycles per second, but what horologists refer to as beats per second.

Rolex Oyster Perpetual Date GMT Master II Automatic Chronometer

My beloved Rolex GMT Master II wristwatch - originally designed by Rolex for Pan American flight crews on long haul flights - ticks at a frequency of eight beats per second: if you listen very carefully, for every second the second hand marks off, you can hear it tick eight times. That's the sound of the mechanical escapement and balance wheel - you can think of them as a kind of tiny pendulum - inside my Rolex, driven by a mainspring that is automatically wound every time I move my arm. Eight beats per second is pretty typical of a good mechanical watch. The mechanism, or movement, of the watch handles the translation of the 8Hz beat into the motion of all of the hands on the watch.

A one PPM error rate in my Rolex would equate to it being off about four seconds a year. In practice, no mechanical watch is anywhere near that good. Rolex aims for a few seconds a day, perhaps in the neighborhood of fifty PPM. Still, my Rolex is a certified Swiss chronometer, a test for stability, accuracy, precision, and reliability that can be traced back to the invention of chronometers for celestial navigation in the days of sail. My Rolex is perfectly adequate for navigating by sextant, should the need arise. Also, it doesn't need batteries.

Quartz watches work like this too. But instead of a mechanical escapement, they use the vibration of a quartz crystal, called an oscillator, driven by an electric current, to count off ticks. (The audible click you may hear in an analog quartz watch isn't the quartz crystal, which is vibrating much to fast to discern, but that of the electro-mechanical actuator of the watch that moves its hands.) The quartz watch movement exploits the piezoelectric effect: a minute electrical current applied to a quartz crystal causes it to vibrate at a known rate. (And vice versa: applying mechanical stress to a quartz crystal generates a minute electrical current. Physics!)

Todd Snyder Timex Mod Quartz Watch

The quartz crystal in my affordable yet oh so stylish Todd Snyder Timex Mod wristwatch vibrates at a frequency of 32,768 beats per second, 4,096 times more often than my Rolex. So the period of the Timex tick is a tiny fraction of that of my Rolex. A relative error in the period of the Timex tick would be far smaller in absolute terms than the same relative error in my Rolex. Which is why my Timex is typically going to be more accurate than my Rolex.

Even so, quartz crystals vary in their exact rate of vibration according to their temperature, which can vary widely in a wristwatch. My Timex may have an error rate of perhaps four PPM. In applications which require a higher degree of precise timing, a crystal oscillator may be embedded in an oven that thermostatically controls its temperature. Such oven-controlled crystal oscillators (OCXO) can be surprisingly small surface mount components.

Casio F-91W Quartz Digital Watch

The use of crystal oscillators as timing sources, or frequency standards, is ubiquitous. There is at least one crystal oscillator in every digital device you own. The accuracy, precision, and reliability of the oscillator in this US$10 Casio F-91W digital watch - that, plus its back is easily removed, giving access to its innards, and, of course, it's cheap as dirt and easily available - makes it a favorite amongst fabricators of improvised explosive devices (IED), or so I've read.

A rubidium atomic clock - an atomic clock is really an extraordinarily high precision oscillator - has a frequency of 6,834,682,610.904 beats per second. That astonishingly high frequency is why atomic clocks are so good: we are hard pressed to even measure a relative error in a period that short, except by comparing two atomic clocks. (Which, by the way, is one way in which time dilation in the Theory of Relativity has been experimentally verified.)

A cesium atomic clock has a frequency of exactly 9,192,631,770 beats per second. Why exactly? Because 9,192,631,770 beats of a cesium atomic clock is the definition of a second in the International System of Units.

And a strontium atomic clock - the most accurate timekeeping device ever constructed by humankind - beats at about 430 trillion times a second. It will lose a second perhaps every fifteen billion years. That's an error rate better than any number for which we have a name.

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