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» Online Classroom   » Celestial Navigation   » Public Discussion of Cel Nav   » Using NAO tables for low sights in CelNav book

Author Topic: Using NAO tables for low sights in CelNav book
John Pinto

 - posted May 07, 2021 10:24 AM      Profile for John Pinto           Edit/Delete Post 
The explanation for low sights in the CelNav book is a little confusing(page 193).

The steps referred to appear to be the long instructions (which are not the same step numbers as the short instructions) but the text does not indicate that. Maybe it should be specific as to which steps it is referring to.

Maybe the Short Instructions should have a note indicating they are not all appropriate for low sights and that the long instructions should be followed with the low sight changes.

What is most confusing is how to handle Step 9. An example would help here. There are no low sight worked examples on pages 194-195.

When you calculate 180-Z2 (I think we can assume that will be an angle greater than 90) to put in row 2 for Z2, do we ever change the sign it was assigned in step 7? (Which was set ignoring the sign of F).

From: Orlando
David Burch

 - posted May 07, 2021 11:11 AM      Profile for David Burch           Edit/Delete Post 
If you can please provide a specific sight to be reduced then we can go over it and compare to a precise solution.


From: Starpath, Seattle, WA
John Pinto

 - posted May 09, 2021 05:13 AM      Profile for John Pinto           Edit/Delete Post 
Are there any examples or exercises in the book which would be low enough to have a negative F value to use with the NAO SR tables?
From: Orlando
John Pinto

 - posted May 09, 2021 08:05 AM      Profile for John Pinto           Edit/Delete Post 
I think my confusion is because there are 2 rules for F regarding Z2 in the instructions on page 193. One dealing with F>90 and one where F is negative.

Low altitude instructions say to ignore the sign of F until step 13.

Step 7 says Z2 is to be treated as negative if F>90 (I’m assuming we are ignoring the sign of F in this step)

In the low altitude instructions it says to change Z2 to 180-Z2 if F is negative and to remember that the original Z2 has a sign (I’m assuming the original sign referred to is from step 7 where we were ignoring the sign of F).

What happens when F>90 and F is negative? Or is that impossible?

If it is impossible then the sign of Z2 will always be positive when F is negative and in that case 180-Z2 will also be positive between 90 and 180. It also means we don’t need to be concerned about the original sign of Z2 when F is negative since it will always be positive.

From: Orlando
David Burch

 - posted May 09, 2021 10:15 AM      Profile for David Burch           Edit/Delete Post 
Can you please provide a sight reduction where this issue comes up and we will look at that specific one. Thanks.
From: Starpath, Seattle, WA
John Pinto

 - posted May 10, 2021 09:33 AM      Profile for John Pinto           Edit/Delete Post 
I'm not sure it is possible to have F both negative and its absolute value to be greater than 90. Does anyone know? Or are those mutually exclusive cases?

I tried a few low altitude sights but the negative F is always pretty small. But maybe I am not picking the correct example to make a large negative F value.

I don't want to keep searching for a sight reduction example for a case that can't occur.

From: Orlando
John Pinto

 - posted May 19, 2021 01:07 PM      Profile for John Pinto           Edit/Delete Post 
I picked up a copy of Davies original pamphlet that introduced this particular sight reduction method. He makes no mention of negative F value rules. I believe he was ignoring what he considered to be impractical sights.

Does anyone know where these negative F value rules in the NAO SR tables came from?

From: Orlando
David Burch

 - posted May 19, 2021 03:41 PM      Profile for David Burch           Edit/Delete Post 
As you have noted above, the source of these instructions is Page 193 of the book Celestial Navigation: A Complete Home Study Course.

Here is a sight you can practice this with. We call it a horizon sight, namely you simply time the sunset and call it Hs upper limb = 0º 0'.

Date July 4, 2021, UTC = 4h 25m 00s
DR: 30N, 140W
WE =0, IC = 0 HE = 6 ft.
Hs UL sun = 0º 0.0'

This will get you a negative F. Note the instructions are special for this case, as you have noted, but they will work.

You should get from the NAO tables and the special instructions Hc = - (0º 43') at 297.4º

[The exact value is -42.4' at 297.1º]

Ho = -52.0'

thus your LOP from this horizon sight is a = 9' A 297, plotted from 30N, 140º 8.8'W

... and of course, all this needs to be checked, but that is what i get on a first pass.

From: Starpath, Seattle, WA
David Burch

 - posted May 19, 2021 04:57 PM      Profile for David Burch           Edit/Delete Post 
PS. on another topic, thanks for your valuable notes on the on the GPS backup book. We are working on that now... we face the standard challenge of index error v. index correction and watch error v. watch correction, and the best algebra of how to do ±, etc.
From: Starpath, Seattle, WA
John Pinto

 - posted May 19, 2021 08:36 PM      Profile for John Pinto           Edit/Delete Post 
I’ll work it up David using both your rules and those in the NA.

I will also attempt it using Davies original rules to see the difference if any.

I still would like to know where the negative F rules came from as they are not in Davies original pamphlet “Concise Tables for Sight Reduction”.

Besides your book and the LTA, similar instructions for handling a negative F are in the NA.

I’m guessing someone (maybe Davies?) agreed to extend Davies original rules from his pamphlet to handle this extreme case. Probably when it was incorporated into the NA. I’d love to know more about the background to that extension.

Looking forward to the updated backup GPS book.

From: Orlando
David Burch

 - posted May 19, 2021 09:38 PM      Profile for David Burch           Edit/Delete Post 
I have not looked at the NAO instructions in the NA for decades, but will take a look tomorrow when I get to work.

It is not a surprise they are in the LTA, as we (Starpath) publish that book by Geoffrey Kolbe, and when doing so we encouraged the author to add that set of tables to it, to make it a one book solution.

Here is a quote on the history of these tables as I know it from our Celestial Navigation textbook:

"The NAO tables were the invention of Admiral Thomas Davies and Dr. Paul Janiczek, then Head of the Astronomical Applications Department of the US Naval Observatory They were originally published as the Concise Tables for Sight Reduction by Cornell Maritime Press. This type of tables is referred to as “concise,” or “compact” tables, as opposed to the full form tables such as Pub. 229 and 249, which are referred to as “inspection tables,” since they require fewer steps."

"Forerunners of these short tables were the Ageton Tables (Pub. 211) and the Dreisenstock Tables (Pub. 208). The Ageton Tables were included in Bowditch, Vol. 2 (editions prior to 1985) but not included in later editions, perhaps because they are now in the Nautical Almanac. Both Ageton and Dreisenstock are long out of print. US Power Squadron courses on celestial switched to the new NAO tables shortly after they were published, with the help of USPS National Education Director Dr. Allan Bayless, who had published his own version of the tables called Compact Sight Reduction Tables."

"Admiral Davies was aware of the Starpath work form (Form 106) for the NAO tables and suggested at the time that it be included in the Nautical Almanac, which was agreed upon by the US NAO. The almanac, however, is a joint publication with the British NAO, and at the time they did not want to include any forms in the almanac, so this was dropped. In 2006, there was a change of heart in the UK, and a single-column work form does now appear in the almanac for these tables. It is better than none, but it remains valuable to keep a Starpath form for these tables in the almanac, since it takes you step by step through the process with no further instructions required."


Not mentioned in this was a long research paper by Allen Bayless where he investigated, as I recall, the limits of the tables, as well as resolving some accuracy issues. We likely still have this in our library, but I do not for now know where. It also could be that his paper is the primary source of the low sight solution, but I cannot recall these details now. We have always supported the horizon sight as a simple method of emergency navigation and would have pursued that with any new solution. We were working on that long before the NAO tables emerged in 1989.

I might also note that Stan Klein's Celestial Tools module called "SR Methods & Fix" has the step by step solutions for NAO tables as well as others. He calls them NASR. He was in touch with Bayless, so I would guess he has the low sights included.... And realized this moment writing this, that it might be worth looking at his Help file that we also host at that page. Note too on that page that Stan had made such a resource for our N(x) tables—the world's shortest sight reduction tables.

And a note that it may not be productive to compare the original version of the Concise Tables with later ones, as they eventually appeared in the NA, as there were improvements made, i believe in content as well as instructions.

From: Starpath, Seattle, WA
John Pinto

 - posted May 20, 2021 04:54 AM      Profile for John Pinto           Edit/Delete Post 
I did the reduction using the method in your textbook and the method in the NA. Both come out as you indicated.

But again the F value is pretty small. So it does not answer my original question as to whether the F value for a horizon sight could ever be large, like -91°, which would make the sign of Z2 be negative as well.

Interestingly using Davies pamphlet you get the same value for Hc but positive as he did not have a rule to make it negative for a negative F.

Zn using his pamphlet comes out to 299° which shows further its limitations with low sights.

But Davies instructions do mention to record the sign of F but after that never uses the sign of F for any further rules in his pamphlet. So he must have realized it could be negative but did not pursue its implications further in his pamphlet.

I’ll look in the help file for the software.

I’d be interested in reading anything Dr. Bayless wrote regarding his updates to Davies work especially anything regarding these low sight rules. Maybe he already addressed my question about large negative F values?

From: Orlando
John Pinto

 - posted May 20, 2021 04:58 PM      Profile for John Pinto           Edit/Delete Post 
David I read the help file in Stan’s program but the only comment he has about low sights is that he sets a lower limit of the NASR Ho value to -59.9’.

So I wrote Stan an email regarding the realistic possibility of large negative F values when doing horizon sights of the Sun and if he had ever encountered such cases when testing his program.

If he responds I will update this discussion. Thanks!

From: Orlando
David Burch

 - posted May 20, 2021 09:16 PM      Profile for David Burch           Edit/Delete Post 
Very sorry to have to tell you but Stan died several years ago. He was a talented and generous person who had made a tremendous contribution to marine navigation education, including an invaluable review of our Hawaii by Sextant book. We had been hosting his CelestialTools program for him for quite a while before then, because it was not getting much circulation from within the USPS setting he originally wrote it for.

Returning to Bayless, who was a key player in these tables: You might check your local Interlibrary Loan as this book is in 6 US Libraries:
Compact sight reduction table : modified H.O. 211, Ageton's table by Allan Bayless. Used copies are very expensive... and it might not have the answers you want. I was referring to a typed manuscript he sent me that I think was different from this, but I am not sure. This was all about 32 years ago. In Seattle an ILL request is $5.

From: Starpath, Seattle, WA
David Burch

 - posted May 20, 2021 09:26 PM      Profile for David Burch           Edit/Delete Post 
Another place where you can almost certainly get your answer about these tables is an online discussion group called the NavList, which you can reach as http://fer3.com/arc/

Post your question there and you will get tons of answers very shortly. The list goes back many years and is fully searchable. There are many experts there on the history of cel nav, and all aspects of it. Stan was an active member. Some members of that group like these tables, others don't, so you should get an interesting response.

From: Starpath, Seattle, WA
John Pinto

 - posted May 21, 2021 02:40 AM      Profile for John Pinto           Edit/Delete Post 
So sorry to hear of Stan’s passing. I will check out that discussion board. Thank You!
From: Orlando
John Pinto

 - posted May 21, 2021 08:02 PM      Profile for John Pinto           Edit/Delete Post 
On the NavList site so far the only case that appears to generate a large negative F (-179°) is a Polaris site at 1° South of the equator at lower culmination (LHA=180) with a large HE. Not very realistic.

I’m still asking on the NavList site if anyone can think of another more realistic case where say F= -100°

But if that Polaris sight is the only one where F is a large negative value then I think we can safely say for the NAO SR tables: if F is negative then realistically its absolute value will always be less than 90 and therefore Z2 will be positive before doing the Z2=180-Z2 substitution step.

From: Orlando

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