Thursday, December 10, 2020

Checking Sight Reduction With CelestialTools.exe

CelestialTools.exe is a free PC program that solves many problems in cel nav and other areas. It was written by the late Stan Klein, navigator, teacher, and friend. It was written for USPS students and instructors, but Stan decided to share it with the public several years ago and ask us to host it, which we were happy to do.  It is a wonderful tool for learning cel nav, especially with regard to one unique function it includes called "SR Methods and Fix." Download celestial tools and its manual.

Below is the graphic menu to the program (Windows only). The function at hand now is far left of the middle row.

 Figure 1 Splash screen index.  (Click any image for a better view.)

Here is the motivation for this note. A student working a sight reduction using the NAO Sight Reduction tables got the wrong answer, and submitted this form for us to check. This is one of the Starpath work forms, available online as blank forms. The instructions and examples are in a separate book.

We are happy to make such checks for our students, but we try to encourage them to use CelestialTools as it is a way to find mistakes much faster than waiting for our response. This note here is just a reminder about how this works. You can use it to check any type of sight reduction.

 Figure 2. An NAO form with wrong data.

This has the wrong answer. Recall that a sight reduction means we start with Lat, LHA, and dec and end up with Hc and Zn. Here we have Lat = 45N, dec = N 19º 23.9', and LHA = 327.  We can find the right answer with the "SR Methods and Fix" tool, shown below, by selecting a direct computation called here "Law of Cosines."

Enter LHA = GHA and use Lon = 0. Enter dec and Lat and then choose your sight reduction on the right and click it.  Then you have to study the output carefully to see what the individual steps of the solution should be—although this does not really apply to the Law of Cosines solution.

 Figure 3 The right answer by direct computation.

This gives the answer of Hc = 52º 34.9' and Hc = 122.3, which is not what was found by the NAO table form shown above because it was not filled out correctly.

Now we look at the option called NASR (Nautical Almanac Sight Reduction) which is these days more commonly called the NAO sight reduction tables, standing for Nautical Almanac Office of the USNO.

 Figure 4. The NAO solution (called here NASR).

Referring back to Figure 2, we see that he got the parameter A correct (22º 39'), but then failed to round it properly to 23 in Box 2. The bar in box 2 is a reminder to round these values. Then when transferring the data for F, he changed the 59 to a 39, and so carried on with A = 22 and F = 39 when this should have been A = 23 and F = 59.

Below is the result using wrong input, which was actually extracted properly, followed by the table showing the right values.

 Figure 5. NAO Table selection showing student's wrong entry.

 Figure 6 Right data from NAO tables.

When these values are used to complete the process the NAO results are Hc = 52º 35 and Hc = 122.3, which is within 0.1' of the best solution. This agreement is better than average. The NAO solution will generally be right on Hc to within ± 0.4' and will usually have the right Zn to a tenth or two.

We encourage everyone who is practicing with sight reduction of Pub 249, Pub 229, NAO or even more exotic older tables to have a look at this tool. It will save you a lot of time.

Here for reference is the same sight reduction done by Pub 229 and then by Pub 249.

 Figure 7. Pub 229 solution details.

 Figure 8. Pub 249 solution details.  In our cel nav course we interpolate the d-corr in 249, so we may differ by a tenth or two on Hc. He follows the official rules and rounds the declination.

Capt. Petar Cumbelic, PhD said...

The Nautical Almanac has published the so-called NAO sight reduction tables every year since 1989 and attributes the authorship to Admiral Davis. It is actually a plagiarism of my Nautical Tables PRW that I published 20 years earlier, ie in 1969. American Practical Navigator Bowditch quotes my charts from the 1974 edition. Here is a link to my website: www.pcumbelic.com

David Burch said...

Thank you for your interesting note. The NAO tables are the work of Admiral Thomas Davies then, among other duties, head of the Navigation Foundation and Dr. Paul Janiczek, who I believe was head of the US NAO at the time. There were also modifications after a year or two made based on the work of Alan Bayless of the USPS, who also published a modified set of the tables.

Your excellent website seems a thorough history of this question, including the responses from both the US and UK NAO offices as to why they do not believe there was plagiarism involved, which you openly include. Nevertheless, there is, as you note, a striking similarity between the table samples you show in your article, so we are only left with the arguments made by the two agencies and the reviewers they used.

We do believe that this NAO type of table is the best backup for a computed solution, so if you have created one like this earlier on then you are to be congratulated. If we had access to the full set of your tables as they existed in 1980 we could make a more thorough assessment.

David Burch said...

I might note that the "NAO Tables" were actually first published not by the Nautical Almanac, but rather as a commercial set of tables called Concise Tables for Sight Reduction by Thomas D. Davies, published and copyrighted by Cornell Maritime Press in 1984. These tables yield the same intermediate values and final values cited in the two examples you give, and they are laid out in the same format.