NavList:

This is an update to this previous post. The experiment has now been going on for 415 days and I checked the errors of the three watches again on December 28, 2010. The measurements are:

In the format for A, B, and C in seconds: actual error; predicted error;
difference.

A = 101.0/95.4/5.6; B = 203.0/204.3/ -1.3; C = 347.0/350.7/ -3.0.

Averaging these differences equals 0.4 seconds.

The worst error was 5.6 seconds which would only result in a 1.5 minute error in longitude. Averaging all three results in an error of 0.4 seconds which would cause an error in longitude of 0.1 minutes of longitude, about 600 feet.

Not bad for $51.00 worth of watches after 415 days.

gl

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Prior post

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.navlist.net/m2.aspx?i=109724&y=200909

http://www.navlist.net/m2.aspx?i=109757&y=200909

http://www.navlist.net/m2.aspx?i=109766&y=200909

http://www.navlist.net/m2.aspx?i=109824&y=200909

http://www.navlist.net/m2.aspx?i=109825&y=200909

http://www.navlist.net/m2.aspx?i=109847&y=200909

http://www.navlist.net/m2.aspx?i=109894&y=200909

http://www.navlist.net/m2.aspx?i=109942&y=200909

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