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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
www.icareclinics.com
tsult@charter.net



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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