From:                                         Bob Goethe

Sent:                                           November 16, 2017 9:34 AM

To:                                               'Carly and Bill'

Subject:                                     NASA: Bowditch (and the Navigational Triangle)


I think your 1995 edition will do just fine, Carly...though editions from 1977 or earlier tend ot be a bit more complete in their treatment of celestial navigation.


Indeed it is not divided into volumes.  1995 tried to get everything in a single volume.  So one of its strengths (it is more concise than earlier editions) is also one of its weaknesses (it is more concise than earlier editions).  1995, for instance, eliminates 100% of the tables that comprised vol. 2 in the edition from twenty years before.


But as I have said before, Bowditch is like an encyclopedia.  You tend not to read it from cover to cover, but to find something in the table of contents or index, and you read just that much.


Now, I downloaded a PDF of the 1995 edition, and I see on page 313 that they refer to "The Sight Reduction Tables" without telling you WHICH sight reduction tables they are using (e.g. Pub. 249, Pub. 229, Pub. 211, or what).


"Sight Reduction" – as you will learn in January – is all about solving the so-called "navigational triangle".  That is, you can imagine any celestial sight as involving a triangle on the face of the earth. 


·        One point is the North Pole (abbreviated as NP).  It never changes. 

·        Another point of this triangle is the approximate position where you think you are (you don’t know exactly where you are...which is why you are doing a sextant fix to begin with – but for now, just the approximate position will do.  We call this the "assumed position" and abbreviate it as AP

·        A third point is the spot on the earth where the sun (or planet, etc.) is directly overhead.  That spot is called the "Geographic Point" and is abbreviated GP.  The GP is constantly in motion.


Now, if you are dealing in a flat piece of paper, solving a triangle can be as simple as a2 + b2 = c2.  But on the surface of a sphere, nothing is that simple.


You know the latitude and longitude of the GP from the Nautical Almanac (though the Almanac calls these "GHA" and "Declination" – for reasons that are lost in the history of the English language).  It is constantly speeding across the face of the earth, but with your accurate watch plus the Almanac, you know where the GP is for every second of every day of the year.


You of course know that latitude and longitude of the AP.


By subtracting the longitude of the GP from the longitude of the AP, you get one of the angles of the navigational triangle.  We call this angle the "meridian angle" – abbreviated either as MA or as t.  This is the difference, in degrees of longitude, between the GP and the AP.


These are standard navigational abbreviations used throughout the English speaking world.  "t" has been used because old time navigators thought of angles and time as being strictly equivalent.  That is, since the sun moves precisely 15° from east to west in exactly 1 hour, you could talk of that movement either in terms of degrees of movement, or hours of movement, depending on personal preference.  Hence the abbreviation "t" for time.


So we know the length of two sides of the triangle, plus the included angle.  Having that, we can work out the length of the third side and the other two angles.


What we want to know is the size of angle Z and the length of the side of the triangle H.  Once we get those, we can work out our fix.





The main point here is that solving triangles on the face of a sphere (so called spherical trigonometry) is not straightforward.  The equations are complicated....and so people have come up with books of tables that do all the math for you...and these books are called "Sight Reduction Tables".  And there is not just one flavor of sight reduction tables, but two or three common ones, and dozens of less common ones.  Which tables you choose to use is partly determined by personal taste.  WE will be using Pub. 249.


Once you graduate from my class, you can do like lots of members of NavList do, which is to experiment with different sight reduction tables.


Bill, "NavList" is an online navigational community that Carly and I are both members of.  You can join by going to and clicking on the link to join.  I have elected to get all postings by email.  This is undoubtedly the leading online community for celestial navigation, probably not just of the English-speaking world, but of the whole world.


If you join, you need to enjoy what intrigues you, and what you understand...and forget about the rest.  As I told you both before, mastery in celestial navigation is feasible in a relatively limited amount of time.  Once you achieve mastery, then if you want to continue to be challenged, you can a) teach (which is the way I keep myself challenged), or b) start exploring progressively more obscure corners of the navigational art.


A number of NavList members were either airline pilots or navigators on US or British air force bombers...back in the pre-1992 days when aircraft came with little domes or windows in the roof where you could stick a bubble sextant to get sun and star sights.  Prior to GPS, if you wanted to fly across deserts or oceans, you needed to use celestial navigation or be prepared to die young.


In any case, some of the aerial navigators get discussions going on some topic I don’t understand, and I just delete those particular emails.


That Bowditch 1995 can talk of one edition of "The Sight Reduction Tables" without telling you which one they are talking about is probably indicative that the writer was thinking of US Navy vessels...which all have some version or other in a cabinet on the bridge (probably pub. 229 as of 1995)...and they all have the SAME version.  But that is not entirely helpful to us as civilian navigators. 



So what we are seeing here is the effect of GPS in this edition: their treatment of celestial navigation is a bit haphazard.  Parts of it are very good.  Other parts, less so.


No matter.  Here are the practical pieces of this for you.


1.     Your primary learning resource is Bob Goethe.

2.     Your secondary learning resource is Budlong, Sky and Sextant.

3.     You will use Bowditch 1995 as a tertiary reference guide.  There is no harm at all in having multiple versions of Bowditch on your shelf.  This is not uncommon for navigators, as different versions of Bowditch have different strengths and weaknesses.  I have both the 1977 and 2017 editions in hard copy, and a PDF of the 2002 edition (and now, of 1995).

4.     You will still encourage Bill and Judi to come out storm watching, and to bring you along the extra vol. 1 and vol. 2 that he picked up, and purchase them from him.  Vol. 2 contains, for instance, a table for calculating dip when Saltspring Island is in your way...and you don’t have a clear view of the distant horizon.  That is, some of these tables you will never use.  Others will be enormously useful depending on your situation.




Bob Goethe


"As I sail, I praise God, and care not."

            Luke Foxe, Arctic Explorer, 1634


I desire no more delight

Than to be under sail and gone tonight.

           Gratiano, in Act 2, Scene 6, The Merchant of Venice

           By William Shakespeare, 1596




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