Celestial navigation

A hobby

Learning to fly and flying cross country tours I became more and more curious about how did our ancestors find their route before the radio age. My interest turned soon to celestial navigation and bought my first sextant. Since being completely landlocked, it was an aircraft sextant, a Link A-12, perhaps from the last year of WWII or just after it, that I had to recondition,  and now it is fully operational and surprisingly accurate. Since then I have learned a lot, made few hundred fixes while travelling, with all kind of celestial bodies, done a lot of "lunars" (yes, a marine sextant was purchased too and put in an operational condition) and I am always trying to find new areas to discover and challenging problems.

And meantime, just because the best learning is by doing, I have created some things that may be worth sharing here. 

Dreisonstok reprint

To be battery free some kind of paper based solution is needed for sight reduction. The precomputed tables are huge to carry so I turned to the shorthand methods. I have checked out some, and found  the Dreisonstok (H.O. 208) method interesting, but the original fifth edition was very inconvenient for me: the rules were awkward and I did not like the ordering of Table I.

So I decided to regenerate my own arrangement:

• Table I is in Latitude order. One can print only those latitudes that she/he is interested in. And for multi body fixes with the same assumed position this is a better arrangement.

• Tabel II is extended with an aid for interpolation

• Rules are simplified and incorporated onto each page, you don't need to memorize them.

• Latitude range is extended, varies from 0° to 76°.

I find this method very accurate (with interpolation it gives Hc with  0.1'  and Z with 0.1° accuracy in most cases), easy and straightforward to calculate, though not being the fastest. I am in doubt about anyone could use it effectively in the air (especially in its original form), but for stationary observations for a hobbyist it is excellent.

Later I have added some tables for calculating refraction, dip, dip short, motion of observer and motion of body and similar transformations and a detailed description, so it can be used with any almanac without the need for additional tables.

The booklet is in A5 size format, easy to carry and use in small places too.

Reorganized Dreisonstok table (PDF, 1.6 MB)

(After creating my first version of this table, I learned that there were some alternatives in the past that fined the original method: for example the Hughes' tables for sea and air navigation / compiled by L.T. Comrie.  or Letcher's book: the Self-contained celestial navigation with H.O. 208. I did not have access to them, they may have more clever improvements or rules. The German F-Tafel is something similar too. In the 1961 edition Norie's Nautical  Tables  the Alt-Az table is almost the same, although it requires separate secant and tangent tables to be used. They may be worth a try too.)

Flat Bygrave

The RAF Bygrave slide rule was a very interesting development in the early 20th century for speed up aerial celnav calculations.  It provides approximately 1' accuracy at a very good speed at that era. An exhaustive description of the device form Ronald W.M. van Riet can be found here: PositionLineSlideRules.pdf. 

The originals are very rare, but many replicas are reported. Building a replica is not impossible, but requires skills and time. (Printable scales for building a replica can be found in Robert Stuart' s post.) For those who just want to check out the work with this device, Gary LaPook invented a flat version that he describes in his blog. Gary's version cuts the scale by halve: the 0° to 180° scales were reduced to 0° to 90°, and as a consequence the original rules had to be altered and a special solver sheet might be necessary to use.

My version is very similar to Gary's, except it covers the whole 0° to 180° range.  This let us to use the rules described in the original manual. The scales are "slide rule like", non overlaping for easier reading. The cotangent scale doesn't fit on a sheet this way, but printing on both side, one can turn it over if runs out of the scale.

Download the traditional flat Bygrave (PDF, 1.2 MB)

The original manual can be downloaded from NavList, although the rules are printed onto the base (cotangent scale) too. The azimuth rules in the original manual work nice for visible bodies (bodies over the horizon) only, they had to be extended for negative altitudes and great circle distance calculations.

For those who would like to check it out, some instructions to print:

• Print the cosine scale on a A4 transparency film.

• Print the cotangent scales on normal A4 paper: print pages 2-3 on both side with flip on SHORT edge, optionally print pages 3-4 on both side with flip on SHORT edge. That way it's easy to turn over the cotangent scale if necessary.

• A good quality printer is highly recomended! To check the print accuracy: set the index (cos) at 44°49' (ctg), the two marks at 88°40' must match.

On can play with an online Bygrave emulator too: Traditional Bygrave Emulator or Gary's version Flat Bygrave Emulator.

Lunarists' Kit

Finding the local time and/or longitude by the help of lunar distance observation is still a great fun and can give you the proof of  your skills and knowledge! However it needs good understanding of the problem, can be done easily and one can analyze the result on-line by the help of Frank Reed's web app.

But how was it done long before computers and calculators? 

Warning! Follows the hardest way among the hard ways!

William Chauvenet's lunar clearing method was first published in the mid of the 19th century when chronometers were already affordable and widely used on ocean going ships, and the importance of the lunar distance observation declined to a role of a crosscheck for the chronometer.  Chauvenet's method was the last lunar distance clearing method published in Bowditch. Lunars were almost never used at sea in this period, and the Almanacs dropped the lunar distance tables in the early 20th century. Chauvenet's method is more laborious than other manual methods, but is well documented  and provides amazing accurate results. We compete with GPS today, so we may vote for this.

1. Chauvenet's tables for correcting lunar distance observations. (PDF, 2.5 MB)
   Printable A5 booklet on 76 pages, including all the necessary log and trig tables as well.

2. Excel worksheet for checking calculations. (XLSX,  550 kB)
   A worksheet that calculates a clearing process exactly as should be done on paper, displaying all the intermediate results and values as well. It is good for crosschecking manual calculations.

3. Lunar Distances Almanac for 2024 (PDF, 900 kB)

Lunar Distances Almanac for 2023 (PDF, 900 kB)

Lunar Distances Almanac for 2022 (PDF, 900 kB)

This almanac follows their 19th/20th centuries form. Not just lunar distances are printed but the proportional logarithms as well, making manual calculations somewhat easier, and all data that are required for Chauvenet's method. Additional Almanac is not needed. A4 size approx 80 pages.