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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Lunar distance measurement in ideal conditions: attainable accuracy.
From: Antoine Couëtte
Date: 2013 Jan 16, 02:35 -0800

Hello Bill,

Thank you very much for publishing your most recent Lunars.

It is true that Frank's On Line Calculator (OLC) does not indicate the sign of the approximate Longitude Error. However, for the second example, it indicates a mean angular error of -0.3' . Accordingly the Observed Sextant distance should have been greater by 0.3' ("remove an Error and add a Correction"). Since distances are increasing, and since your recorded value is too small, the time derived from your Sextant reading is going to be earlier that the actual one, hence a Eastern shift/error into your computed Lunar Longitude(s).

The Longitude Error sign could be easily implemented by Frank, but probably he has decided that the OLC current design (version 4) is OK for most applications. We should also notice that the current OLC Longitude error seems to display a value exactly equal to 30 times the Sextant Angular Error. This is not always very accurate and represents only a "best case" and could bring to over-confidence in Lunars. Actual Longitude error could be 60 times (or even more) times the Sextant Angular error, depending on the Lunar Geometry as Frank earlier explained, as under such cases the benefits of shooting Lunars will greatly vanish.

*******

To escape your questions about "leaving all values positive when calculating longitude error", I simply averaged your observations as follows:

1st averaged set : 04h34m01.7s with distance corrected for IE 57d13.93' , and

2nd averaged set : 05h35m46.7s with distance corrected for IE 57d33.60' .

Your 1st averaged set run on Frank's OLC gives : Error in Lunar 0.0' with Error in Longitude 0'4, from which we can guess that your angular error was 30 times smaller, i.e. only 0.013'.

If I run your first set on my software, I find that your Instrument reading corrected for IE should have been 57d13'985 (again within 0.1' of OLC value), hence a difference of 0.055' .... quite negligible here. Given the Distance rate of change of +19.3'/hour, this 0.055' difference in angular measurement equates to a clock error of 10.2 seconds of time, hence a Longitude determination error of 2.55' : quite an achievement !!!!

Your 2nd averaged set run on Frank's OLC gives : Error in Lunar -0.3' with Error in Longitude 10'2, from which we can guess that your angular error was 30 times smaller, i.e. 0.34'. If I run your first set on my software, I find that your Instrument reading corrected for IE should have been 57d34'012 (again within 0.1' of OLC value), hence a difference of 0.402' .... Given the Distance rate of change of +19.3'/hour, this 0.402' difference in angular measurement equates to a clock error of 1 minute and 15.8 seconds of time, hence a Longitude determination error of 18.95' : still an acceptable value.

It is interesting to see that under current circumstances, the actual Longitude Angular Error]/[Sextant Angular Error] ratio reaches a value of 47.2, therefore significantly greater that the standard value of 30 which seems to be the one being implemented into Frank's OLC.

*******

Dear Bill, Merci encore infiniment ...

Antoine

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