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Re: Digital watches for use as a chronometer
From: Gary LaPook
Date: 2010 Sep 14, 17:35 -0700
From: Gary LaPook
Date: 2010 Sep 14, 17:35 -0700
Here is the photo. gl On 9/14/2010 3:06 PM, Gary LaPook wrote: > A year ago in September 2009 we discussed using cheap digital watches > as chronometers in the thread "How many chronometers?" I described an > experiment I was doing using three cheap ($17.00 each) watches to > determine how useful they would be as a chronometer. ( I have provided > links to some of my posts in that discussion below.) > > The experiment has continued now for almost a year and this is an > update to the prior posts. > > Since I had modified the test conditions temporarily to see what > effect very cold temperatures would have on the rates of the watches, > I had to restart the experiment on September 18, 2009, 360 days ago. > The three watches, "A", "B", and "C" were, respectively, 7, 31 and 60 > seconds fast at that point. I had computed their daily rates to be > .1919, .3737 and .6263 seconds per day respectively. The watches are > kept in a cabinet with a minimum-maximum thermometer (see photo) and > the temperature range was 62.5° to 82.4° F ( 16.9° to 28.0 °C.) > > I have checked the watches on five occasions by comparing them with > the radio time signal from WWV and estimated the time to the nearest > half second. Using the daily rates, I predicted what the accumulated > errors should be and compared them with the actual error and the > difference would have been the error if relying on the predicted > errors for navigation. > > The first occasion was on November 13, 2009, 56 days after the start. > In the format for A, B, and C in seconds: actual error; predicted > error; difference. > > A = 17.0/17.7/-.7: B = 52.0/51.9/ .1: C = 95.0/95.1/ -.1 > > Averaging these differences equals -.2 > > > December 31, 2009, 104 days: > > A = 26.5/27.0/ -.5: B = 70.0/69.9/ .1: C = 124.0/125.1/-1.1 > > Averaging these differences equals -.5 > > March 16, 2010, 179 days: > > A = 41.0/41.3/-.3: B = 97.0/97.9/ -.9: C = 172.5/ 172.1/ .4 > > Averaging these differences equals -.3 > > June 23, 2010, 278 days: > > A = 61.5/60.3/1.2: B = 134.0/134.9/ -.9: C = 232.0/234.1/ -2.1 > > Averaging these differences equals -.6 > > September 13, 2010: > > A = 79.0/76.1/2.9: B = 164.0/165.5/ -1.5: C = 281.0/285.5/ -3.5 > > Averaging these differences equals -.7 > > Evaluating this data shows that the greatest difference between > predicted time and actual time was 3.5 seconds after 360 days which > would result in less than one minute of longitude error in almost a > year. So using any one of these watches as a chronometer would provide > sufficient accuracy for celestial navigation. > > Averaging the three readings resulted in a maximum difference of .7 > seconds which would provide a longitude to an accuracy of less than > one-quarter of a minute. > > So it appears that if the watches can be kept in the cabin where the > temperature can be maintained at a comfortable temperature for the > occupants, 17° to 28° C, that these three $17 watches are all you need > for a year of voyaging without recourse to a radio time signal. > > gl > > Check out these previous posts: > > > http://www.fer3.com/arc/m2.aspx?i=109724&y=200909 > > http://www.fer3.com/arc/m2.aspx?i=109757&y=200909 > > http://www.fer3.com/arc/m2.aspx?i=109766&y=200909 > > http://www.fer3.com/arc/m2.aspx?i=109824&y=200909 > > http://www.fer3.com/arc/m2.aspx?i=109825&y=200909 > > http://www.fer3.com/arc/m2.aspx?i=109847&y=200909 > > http://www.fer3.com/arc/m2.aspx?i=109894&y=200909 > > http://www.fer3.com/arc/m2.aspx?i=109942&y=200909 > > > >