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Celestial navigation

Sight reduction – the position line with the Nautical Almanac and Pub. 249

Celestial navigation the paper-and-pencil way – just without the pencil. You look up every value yourself in the Nautical Almanac and in Pub. 249; NauticTools2 is the form: it does the sums, shows for every line where the value comes from, checks each entry on request and draws the position lines on a plotting sheet.

• Nautical Almanac
• Pub. 249, volumes 2 and 3
• Sun, moon, planets, stars
• Polaris, noon sight, compass check
• Check and automatic
• Plotting sheet

What is sight reduction?

It is working out a position line with tables instead of trigonometry. Because Pub. 249 only contains whole-degree latitudes and local hour angles, you do not work from the DR position but from an assumed position (AP) close to it: latitude to the whole degree, longitude chosen so that the local hour angle LHA comes out in whole degrees. For this position the tables give the computed altitude Hc and the angle Z. The difference from the observed altitude Ho is the intercept – the number of nautical miles from the assumed position to the position line, towards or away from the body.

When do you need it?

• With tables on board: if you carry the Almanac and Pub. 249, you can work a position line without a calculator – the app only replaces the paper form.
• Checking your own working: with “Check” every line shows ✓, ≈ or ✗. You find the mistake yourself – the app only tells you where it is.
• A form to fill in by hand: printed blank on A4 landscape, for working at the chart table.
• Understanding the method: “Automatic” fills in all table values, so you can follow every step before looking them up yourself.

The five steps of the form

1. Observed altitude Ho

   Sextant angle Hs, index error, dip and the correction for sun, moon, planet or star from the Almanac give Ho – rounded to whole minutes, because Pub. 249 works in whole minutes.

2. Position of body and ship

   GHA for the whole hour and the increment for minutes and seconds, declination from the Almanac. Latitude to the whole degree (working lat), longitude chosen so that LHA comes out in whole degrees.

3. Computed altitude Hc

   In Pub. 249 with working lat, declination (whole degrees, same or contrary name) and LHA: Hc, d and Z. Table 5 corrects Hc for the minutes of declination; Z becomes the azimuth Zn.

4. Compare altitudes

   Intercept = Ho − Hc, in nautical miles. Ho greater: Closer, towards the body; Ho smaller: Away.

5. Plot

   Assumed position, Zn and intercept – ready for the plotting sheet.

Worked example

All forms

• Sun, moon, planet, star sight: the position line; for the moon with HP and second correction, for the planets with the additional correction, for the stars with SHA. The 57 navigational stars of the Almanac are available.
• Polaris sight: latitude from the pole star with the Polaris tables (a0, a1, a2).
• Noon sight: ship's noon from meridian passage and arc to time, then latitude from the noon altitude.
• Compass check: the sun's Zn from Pub. 249 against the compass bearing – compass error and deviation.
• Plotting sheet: two or three saved sights, run on with the log or with course and speed over ground, and the fix.

Pub. 249 included

Volumes 2 and 3 of Pub. 249 (latitudes 0° to 89°, declinations up to 29°) are included as a book, as is Table 5. A button in the form opens the right page and marks row and column. Reading off the value and entering it is still the navigator's job – just like the printed book next to the form.

Check and automatic

Check compares every entry with the value that should be in the Almanac and Pub. 249 and shows ✓, ≈ or ✗. Tap an ✗ to see the expected value. Automatic fills in all table values; switch it off again and your own values return. Both are switches – working by hand is and remains the normal case.

Almanac and tables for practice

If you want to work the examples with your own tables, the practice data is available free as PDF from TheNauticalAlmanac.com (source of all the links below). The examples in NauticTools2 are dated 18 October 2026 – for them you need the 2026 Almanac, Pub. 249 volume 3 (latitude 48°) and Table 5.

• Nautical Almanac: 2026 (6.8 MB) · 2027 (6.9 MB) · earlier years: 2020, 2021, 2022, 2023, 2024, 2025
• Pub. 249: Volume 2 (latitudes 0°–39°, 4.7 MB) · Volume 3 (latitudes 40°–89°, 4.2 MB) · Volume 1, Selected Stars, epoch 2025 (58 MB)
• Table 5: Correction to Tabulated Altitude for Minutes of Declination (40 KB)

Source: All files come from TheNauticalAlmanac.com and are hosted there, not by NauticTools2. Pub. 249 is published by the US NGA.
For practice only: The linked almanacs and tables are offered here solely for practising and working through the examples. Their publisher expressly rules out their use for navigation – on board you need an official Nautical Almanac. Volumes 2 and 3 and Table 5 are already included in the app.

Printable record

Every form can be printed filled in or saved as a PDF, on one A4 landscape page: sight data and the five steps with the source of every value. The plotting sheet prints the chosen sights, the drawing and the fix on one A4 portrait page.

View the sun sight example record as PDF ›

View the plotting sheet example record as PDF ›

Things to watch out for

• Almanac for the right year: GHA and declination only apply to the year printed.
• Same or contrary name: if latitude and declination have the same name (both north or both south), use the same-name side of Pub. 249, otherwise contrary. Mixing them up gives a completely wrong Hc.
• Assumed position, not DR: the intercept is laid off from the assumed position, not from the DR position – otherwise the position line is off by the difference.
• Stars with high declination: Pub. 249 volumes 2 and 3 go up to 29° declination. Stars beyond that need volume 1 (Selected Stars), which is not included.

How it works in NauticTools2

1. Choose the form

   At the top: sun, moon, planet, star, Polaris, noon sight, compass check or plotting sheet.

2. Sight data

   Date and time (UT), DR position, log, course and speed over ground.

3. Enter the values

   Block by block, as on paper. Coloured labels show where to look: Almanac, Pub. 249, Table 5 – or the app works it out.

4. Save, plot, print

   Saved sights can be chosen on the plotting sheet. The form prints filled in or blank, on A4 landscape.

Frequently asked questions

What is Pub. 249?

A set of tables published by the US NGA (Sight Reduction Tables for Air Navigation). For an assumed position they give Hc and Z – you look them up instead of working the trigonometry.

Do I need a Nautical Almanac?

Yes, you enter the values yourself as on paper. If you just want to see the method, let “Automatic” fill them in.

Why work from an assumed position?

Because Pub. 249 only contains whole-degree latitudes and local hour angles. The assumed position is therefore on a whole-degree latitude, and its longitude makes LHA a whole number.

What do Closer and Away mean?

If Ho is greater than Hc, the position line lies that many miles towards the body (Closer), otherwise away from it (Away).

Related tools

• Fix from 2 or 3 altitudes – the same task, with the app working everything out
• Noon latitude and sun-run-noon fix – latitude from meridian passage
• Compass check – compass error from the sun's azimuth, fully computed
• Sextant altitude corrections – from Hs to Ho