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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: Question Re: Position by Calculation
From: Lu Abel
Date: 2014 Jan 06, 14:31 -0800
Sean:

It would be exceeding rare to discover that two sights reduced using the NA tables would use the same Assumed Position.

A set of tables that would work for every tenth of a minute of dead reckoning latitude and longitude and of body GHA and declination (the things we need to reduce a sight) would be impossibly large.   Even HO229, the largest of the traditional sight reduction tables, doesn't do that.

The way to make sight reduction tables "concise" is to reduce the number of possibilities.   With the NA tables we do that by reducing accuracy to a full minute, not 0.1 minutes but, more important, using not a DR position but an assumed position that is (a) an exact number of degrees of latitude (ie, 00.0 minutes of lat) and (b) a longitude that makes LHA an exact number of degrees.

So if I had to reduce two different sights using the NA tables to get a fix, it's highly likely I'd use APs with the same latitude (they'd be different only if I were doing a running fix and even then only under rare circumstances) -- and highly unlikely I'd use the same longitude for the APs.   (The only circumstance that I'd have the same AP longitude is if the two bodies had the same exact number of minutes (down to tenths) in their GHA if both were either east or west of me, or with "complimentary" GHAs (ie, the two bodies GHA minutes added up to 60') if the bodies were on opposite sides of my meridian.

Hope this helps.

Lu

On 1/6/2014 12:57 PM, Sean C wrote:

I was just using my new Kolbe LTA to complete a fictitious sight reduction problem of my own creation. I was pleased with the result which was 4.5 nm away from the actual position. (Bear in mind I purposely threw in a little random error.)

However, as is my usual practice I also ran the numbers using other methods to cross check my results. As one might expect Rodger Farley's "Teacup Celestial" program produced a fix much closer to the actual position. But I was curious about which part of my original calculations contributed most to the error. Was it the limitations of the concise sight reduction tables or maybe a plotting error on my part or just the random error I threw in? (I did remember to *add in the refraction and other corrections to the "raw" sight data.)

So, I decided to work backwards and start by checking the plot. I figured I'd cross check it by using my azimuths and intercepts to calculate the fix directly, which brings me to my question: Can the method described in the "Position from intercept and azimuth by calculation." section of the Nautical Almanac be used when you have different APs for each sight, as is required when using the concise tables, or is it necessary to have one single AP?

I'm no mathematician (to be honest, most of this seems like voo-doo to me), but my intuition tells me the latter would be the case. I say this because I notice there is only one instance of an AP lat/lon in the equations. Also, when I tried it I got a longitude that was very close to the actual, but the latitude was even farther off.

Thanks in advance for any insights!

Regards,
Sean C.
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