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    Watches as chronometers
    From: Gary LaPook
    Date: 2011 Mar 25, 01:44 -0700
     This is an update on my experiment using three cheap digital watches
     as a chronometer. See below for prior reports and methodology.

    Two more sets of data have been obtained.
    In the format for A, B, and C in seconds: actual error;
    predicted error; difference.


    December 30, 2010, 435 days since the start:

    A = 101/95.4/5.6: B = 203/204.3/ -1.3: C = 347/350.7/-3.7

    Averaging these differences equals +0.2

    March 25, 2011, 551 days:

    A = 119/112/7: B = 234/236.4/ -2.4: C = 399/404.5/ -5.5

    Averaging these differences equals -.3

    So after 551 days, about a year and a half, the worst
    single error is 7 seconds making an error of 1.75 NM
    in longitude at the equator. Using the average of the
    three watches results in about a 0.3 NM error in longitude.

    gl


    Prior posts:

    -----------------------------------------------------------------

    see:
    http://www.fer3.com/arc/m2.aspx?i=113872&y=201009

    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



       
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