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    Re: How Many Chronometers?
    From: Tom Sult
    Date: 2009 Sep 15, 06:22 -0500

    looks to me like $17 would give a perfectly adequate chronometer,
    especially when compared to early chronometers of sea faring days.
    Thomas A. Sult, MD
    IntegraCare Clinic
    On Sep 15, 2009, at 4:22 AM, Gary LaPook wrote:
    > 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.
    > gl
    > >
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