NavList:

Gentlemen:

Some of you now have gone to great lengths to put on the records of this lists the mathematical background of the NA table sight reduction.  Thank you. There is no doubt that the method works.

However, that was not the issue. At issue were the specific advantages of this method. Is it particularly brief, easy, accurate, fast - in other words truly concise as its name claims?

You might want to read the following article:

http://www.oceannavigator.com/January-February-2003/Sight-reduction-methods-compared/

It compares the most popular sight reduction methods.About the NA table method its says:

The advantages of the NASR method are: It uses only one book and      requires no interpolation, and the pages are organized by increasing latitude, facilitating multiple reductions from the same assumed latitude. This method's disadvantages include: It requires an AP for table entry and plotting and requires dual entries of two different tables.

Exactly! BTW: the necessary tables cover at least 36 pages. About evaluating the strict formula the article says:

This is the only method that does not require tables to determine the intercept and azimuth. Like all other methods, a Nautical Almanac is required to determine the LHA and declination of the observed body. This method utilizes the trigonometric functions found on most scientific calculators to produce a computed altitude and an azimuth angle. These are easily converted to an intercept and true azimuth. This is a quick and easy method of sight reduction that plots from the DR position. The disadvantage of this method is that it requires an electronic calculator involving numerous key strokes providing the opportunity for error.

Almost correct. Except, of course, you do need a table, the cos-table, in written or electronic form.

The article does not include the hav-DONIOL - it probably was not known at the time. However, it is clear that it has the same advantages as the strict formula because it is a version of it using the haversine in stead of cos / sin. You an easily construct it since hav(angle) = sin^2(angle/2). It  covers only 2 pages.

And more: There is no confusion re: sign rules, and there is just a single multiplication for finding Hc. Also, as Geoffry says, you will never be lost in log-land. Finally, you can easily do it by hand as opposed to evaluating the strict formula which requires 3 multiplications.

I have included the NA sight reduction worksheet by the Royal Navy and G. Rudzinski's hav-DONIOL worksheet. The difference is striking.

After reading the entire article and considering all this you may ask yourself which method is truly concise?

As for the azimuth: There is now a very simple graph that can be used with any method. You will find it and the hav-DONIOL worksheet on this list's document g29725. You may also look at my worksheet at g30071.

H

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Attached:

NASR worksheet, Royal Navy

hav-Doniol , G. Rudzinski,  Dec 21, 2014, g29725,