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    Re: How Many Chronometers?
    From: Gary LaPook
    Date: 2009 Sep 16, 10:37 -0700
    As usual, George is right again (mostly.)  I will keep the watches is the freezer for a while longer but even the  short time period so far has shown a considerable change in the rates of the watches. The temperature in the freezer has been in the range of 1º F to - 10ºF, say an average of about -5º about 80ºF (45º C) lower than before. In the 10.3 hours that they have been in the freezer so far they have lost 1.5, 1.5 and 1.0 seconds corresponding to daily rates of -3.5, -3.5 and -2.3 seconds per day. Based on their performance in the past they should have each gained some small amount but that is lost in the imprecision of my reading of the watches compared to the WWV time signals, about one half second resolution. George predicted a change of rate of 7 or 8 seconds per day with this change in average temperature but the observed change in the short period so far is only about half of that but this might be masked by the imprecision of the readings also.

    Apache Runner provided a formula for the change in frequency of the watch crystal as:

    "Quartz crystals have the great advantage that they have very little temperature dependence.   Typically, they're fabricated to have a minimum sensitivity to temperature around 25 degrees C.

    As I recall, the dependence is roughly a quadratic, and goes like the square of the difference in temperatures - departures from 25 degrees C.   The coefficient is something like 0.04 ppm/(degrees C)**2

    So, at freezing, one might expect 25 ppm shift, which is 2 seconds per day - pretty significant, if I consider that my typical systematic drift is 0.1 seconds per day at standard temp's."

    Using this formula would also predict a change of rate of 7 seconds per day which hasn't happened so for but we will follow it for a while longer. Assuming that this formula is approximately correct, a change of average temperature of 5ºC would predict a change of rate of .09 seconds per day and a change of 10ºC would cause a change of .35 seconds per day.

    So I disagree with George to the extent that if the watches are kept in an insulated box, to limit the effect of diurnal changes in cabin temperatures, then the change in rate will only happen based on long term changes in ambient temperature, say on a cruise from the Caribbean to England. But, if the cabin is kept in a range of temperatures which are habitable for humans then the change of rates can be kept to a small number.

    And my advice for anyone wanting to use these watches for celestial navigation on an expedition across Antarctica is to duct tape them to your stomach under all of your clothes which will turn you into a temperature stabilizing "oven" for the crystals. Off course, prior to your expedition, you must determine their rates by wearing them taped to your stomach for some reasonable period of time.


    George Huxtable wrote:
    Gary wrote-
    "So I have decided to extend my experiment. I have just placed all thee
    watches in my freezer which is at -7º right now (along with the recording
    thermometer) and will see what the rates are after three weeks and I will
    report back then."
    Let me predict that Gary will then see all three watches losing about 7 or 8
    seconds a day (if he's talking about temperatures measured in Fahrenheit
    Quartz crystal frequencies do change with temperature, but not necessarily
    in a linear way. By choosing the way that the crystal is cut, it's possible
    to make its resonant frequency change parabolically with temperature, such
    that it's a maximum at a convenient ambient temperature (such as 25º C) and
    falls away either side, at temperatures that are higher or lower. This means
    that it's most constant over the range of ambient temperatures that a watch
    has to live in. (I understand that in some circumstances crystal oscillators
    can be made to give a point-of-inflection rather that a maximum frequency at
    that temperature, which can extend the useful temperature range somewhat
    But, as with any such parabolic variaition, once you get away from the
    optimum temperature, the dependence on temperature becomes more severe.
    In the freezer, Gary will be operating his watches at about 47ºC below their
    optimum temperature of 25ºC. Similarly, I would expect that if he operated
    them at 47ºC, above it, at 72ºC, if they will stand that (he may be
    understandably reluctant to try), then I would expect them to run similarly
    slow, 7 or 8 seconds a day.
    Wearing a watch on the wrist well help to keep its temperature up in the
    daytime, but won't help much if it's taken off at night, in many
    environments (such as small craft) that don't expect central heating. Nor
    will "wrapping the watch in blankets"; an inanimate object will derive
    little benefit from such attentions, much less than  Gary or I would. They
    will only delay changes in ambient temperature reaching the watch; but they
    will get to it in the end.
    Gary refers to the use of a "crystal oven", to compensate for changes in
    ambient temperature. Indeed, that's a viable technology, that I was using
    for precise time measurement, 40 years ago. The crystal is put into a little
    insulated housing containing a heating element and a temperature sensor,
    with feedback to keep the crystal's temperature constant. It's done that
    way, because it's so much easier to heat things above ambient temperature
    than to cool them below it. An operating  temperature is chosen that's
    higher than the environment is ever expected to reach (40ºC, say) and a
    crystal is chosen which has its optimum temperature to correspond. Such an
    oscillator has its own "warm-up" period, after switch-on, until the oven
    stabilises. This technique is seldom used for anything portable, unless
    unavoidable, because of the power consumption by the oven.
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message -----
    From: "Gary LaPook" <glapook@pacbell.net>
    To: <navlist@fer3.com>
    Sent: Wednesday, September 16, 2009 1:34 AM
    Subject: [NavList 9757] Re: How Many Chronometers?
    I remember when I first got involved with radios back in the '60s that I
    coveted a high end radio that had an "oven" to keep the oscillator crystal
    at a constant temperature to keep the radio frequency from drifting as the
    crystal changed temperature. I now think, however, that that was mainly "a
    self inflicted wound" due to the tubes (valves) in the radios having
    "heaters" to "boil off" electrons from the cathodes in order to make the
    tubes function which caused the radios to change temperature a lot and to
    run quite hot. The young guys won't remember waiting for a radio to "warm
    up" before it would start working but us old timers will remember the orange
    glow coming out of the back of the radio from the glow of the "heaters" in
    each tube. I clearly remember warming my hands on cold nights over the hot
    I now wonder if the much less extreme swings of temperature that would be
    expected in a wrist watch, or by a watch kept in an insulated box below
    decks, would make a large change in the watch crystals' resonant frequency
    affecting their rates in any significant way.
    So I have decided to extend my experiment. I have just placed all thee
    watches in my freezer which is at -7º right now (along with the recording
    thermometer) and will see what the rates are after three weeks and I will
    report back then.
    --- On Tue, 9/15/09, Werner Luehmann <wksj.luehmann@t-online.de> wrote:
    From: Werner Luehmann <wksj.luehmann@t-online.de>
    Subject: [NavList 9737] Re: How Many Chronometers?
    To: navlist@fer3.com
    Date: Tuesday, September 15, 2009, 10:21 AM
    Sorry Gary, wrong conclusion. The problem with quartz watches (or any quartz
    driven oscillator) is their temperature dependance. Only under a constant
    temperature you would get constant "rates". For example, in high class
    radios the quartz is kept at a constant temperature higher than the ambient
    temperature in order to ensure frequency stabilty. In wrist watches
    compensating electronic devices can be used. But this is expensive and not
    found in 17 Dollars pieces, if at all.
    So unfortunately this cheap solution doesn't work for us.
    B.T.W.: I have some nice digital (and not too cheap) stopwatches (made by
    German manufacturer "Hanhart") that elected to adjust their rates according
    to the year's season ;-)
     Am Dienstag, 15. September 2009 11:22:33 schrieb Gary LaPook:
    Based on our discussion, I became curious about the accuracy of digital
    watches and their suitability for use as chronometers so I went to my
    local TARGET store and purchased three identical watches for $17.00
    each, the cheapest that they had. I set them and let them run for a few
    days and, as I expected, they each had different rates. Based on this I
    labeled them "A", "B", and "C" in the order of their rates starting with
    the slowest. I then reset them to UTC at 0121 Z on May 28, 2009. I
    checked them against UTC from WWV eleven days later on June 8th and
    found that they were all running fast by 2, 4 and 7 seconds respectively
    and I worked out their daily rates as .1818, .3636, and .6363 seconds
    per day, respectively.
    On July 11th, 44 days after starting the test, the watches were fast by
    9, 17 and 28 seconds. Using the rates determined in the first 11 days
    the predicted errors would have been 8, 16 and 28 amounting to errors in
    prediction of 1, 1, and 0 seconds. If using these three watches for a
    chronometer we could average the three errors and end up with only a .66
    second error in the UTC determined by applying the daily rates to the
    three displayed times after 33 days from the last check against WWV
    which took place on June 8th.
    I determined new rates now based on the longer 44 day period of .2045,
    .3864 and .6363 seconds per day, respectively.
    On September 15th at 0800 Z (per WWV), 110 days after starting the
    test, I took a photo of the watches which I have attached. The photo
    shows the watches fast by 21, 41 and 69 seconds but by carefully
    comparing them individually with the ticks from WWV the estimated actual
    errors are 21.5, 41.8 and 69.0 seconds. Using the 44 day rates, the
    predicted errors are 22.5, 42.5, and 70 seconds giving the errors in the
    predictions of 1.0, 0.7 and 1.0 seconds which, if averaged, would have
    caused a 0.9 second error in the computed UTC after 66 days from the
    last check against WWV on July 11th.
    If, instead, I used the 11 day rates then the predicted errors would
    have been 20.0, 40.0, and 70.0 seconds which would result in errors of
    prediction of -1.5, -1.8, and 1.0 which, if averaged, would cause and
    error in the computed UTC of -0.6 seconds after 99 days from the last
    check against WWV which would have been on June 8th in this example.
    From this experiment it appears that fifty one dollars worth of cheap
    watches would give you a perfectly adequate chronometer.

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