Sight reduction tables: HO 229 and HO 249
1The lesson in plain words
Tables replace the formulas. Enter with whole degrees of latitude, LHA and declination, then correct for the declination minutes. HO 229 is precise; HO 249 is quicker.
Why tables
Before calculators, and still as the backup when electronics fail, navigators used precomputed tables. They solve the same triangle for whole degrees of latitude, LHA and declination. That is why you choose an AP: its latitude is the nearest whole degree to the DR, and its longitude makes LHA a whole degree. The almanac gives GHA and Dec; the tables give Hc and Z.
HO 229
Pub. No. 229, from the US National Geospatial-Intelligence Agency (NGA), is published in Britain as NP 401. It has six volumes, each for a band of about 15° of latitude, and covers every declination. Choose the same name page when latitude and declination have the same name, contrary name when they differ. It gives Hc to 0.1′, the change d for 1° of declination, and Z to 0.1°.
HO 249
Pub. No. 249 (NP 303 in Britain) was made for air navigation. It gives Hc to the nearest minute and Z to the nearest degree, and it is quicker to use. Volumes 2 and 3 cover all latitudes but only declinations 0°–29°: Sun, Moon, planets and many stars. Volume 1, for selected stars, is computed for an epoch, now 2025, and used for about four years either side.
Same sight by HO 229
Latitude 17°, LHA 320°, declination 22°, contrary name: tabulated Hc 34°43.8′, d −40.0′, Z 133.5°. For the 8.1′ of declination: −40.0 × 8.1 ÷ 60 = −5.4′. Hc = 34°38.4′, the same as by formula. Z between 22° and 23° of declination, interpolated, is 133.6°.
Naming Zn
Table Z is measured from your elevated pole: north in north latitude, south in south latitude. This differs from the calculator formula’s north-referenced Z. North latitude: LHA over 180°, Zn = Z; under 180°, Zn = 360° − Z. South latitude: LHA over 180°, Zn = 180° − Z; under 180°, Zn = 180° + Z. The rule is printed on the pages: check it every time.
2Key data
- HO 229 (NP 401)
- Hc to 0.1′, Z to 0.1°; six volumes; every declination
- HO 249 (NP 303)
- Hc to 1′, Z to 1°; Volumes 2–3 for declinations 0°–29°
- HO 249 Volume 1
- Selected stars; epoch 2025, used about four years either side
- Worked by HO 229
- 34°43.8′ + (−40.0 × 8.1 ÷ 60 = −5.4′) = 34°38.4′
- Zn, north latitude
- LHA > 180°: Zn = Z; LHA < 180°: Zn = 360° − Z
- Zn, south latitude
- LHA > 180°: Zn = 180° − Z; LHA < 180°: Zn = 180° + Z
3Key points
- 1
Tables need whole-degree latitude and LHA: choose the AP to make them so.
- 2
HO 229: Hc to 0.1′, all declinations. HO 249: Hc to 1′, quicker; Volumes 2–3 stop at 29°.
- 3
Correct the tabulated Hc for the declination minutes with d: here −5.4′.
- 4
Turn Z into Zn with the rule for your hemisphere and LHA.
4Frequent mistakes
Wrong: Enter the tables with your DR longitude and interpolate for the odd minutes of LHA.
Right: Choose the AP longitude so that LHA is a whole degree. The tables are built for that.
Wrong: Use the same-name page because the tables use positive values only.
Right: Latitude N with declination S is contrary name. The wrong page gives an Hc that is far too high.
Wrong: Any edition of HO 249 Volume 1 will do.
Right: Volume 1 is epoch-based. Use the current epoch edition or HO 229. Volumes 2–3 are an alternative only for declinations within 0°–29°.
5Practice case & exam keys
At 17°N in the mid-Atlantic, your calculator and plotter are dead. You have this year's Nautical Almanac and HO 249 Volume 2. The Sun's declination is S22°. Can you still reduce a morning Sun sight, and how precise will the result be?
Show the answer
Yes. Volume 2 covers latitudes 0°–40° and declinations 0°–29°, so the Sun at S22° is in range. Choose an AP that makes latitude and LHA whole degrees, use the contrary-name page, correct Hc for the declination minutes and turn Z into Zn. Hc is rounded to 1′; that is table resolution, not a guarantee of one-mile accuracy.
Exam keys
- AP: whole-degree latitude; longitude chosen so that LHA is whole.
- HO 229 (NP 401): Hc 0.1′, Z 0.1°. HO 249 (NP 303): Hc 1′, Z 1°; Volume 1 stars, epoch 2025.
- Correction for declination minutes = d × minutes ÷ 60.
- N latitude: LHA > 180° Zn = Z, else 360° − Z. S latitude: LHA > 180° Zn = 180° − Z, else 180° + Z.
Finish this unit
When you've read it, answer three questions. Get all three right to finish the unit; opening the page alone doesn't count.
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