Nautical Almanacs and Sight Reduction Tables

The Nautical Almanac

The Nautical Almanac is an annual publication produced jointly by the US Naval Observatory (USNO) and HM Nautical Almanac Office (HMNAO). It is the foundation document of celestial navigation — without it, sextant angles are merely numbers with no connection to the surface of the Earth.

The almanac is organized into three main parts. The daily pages form the bulk of the book: two facing pages for each day of the year, listing the positions of celestial bodies for every whole hour of UTC (Universal Time Coordinated). The left-hand page covers the Sun and Moon; the right-hand page covers the navigational planets (Venus, Mars, Jupiter, Saturn) and Aries (the reference point of the stellar coordinate system). For each body and each hour, the almanac lists GHA (Greenwich Hour Angle) and Dec (Declination) — the two coordinates that fully describe where the body is in the sky at that moment.

The star pages (white pages near the back) list the SHA (Sidereal Hour Angle) and Declination of 57 selected navigational stars. These values change only slowly over the year, so stars are listed once per three-day period. To find the GHA of a star, you add the star's SHA to the GHA of Aries at the time of observation — a simple and elegant system.

The increments and corrections pages (yellow pages at the back) allow interpolation for minutes and seconds of time between the whole-hour tabulations. If you observed the Sun at 14h 23m 41s UTC, you use the daily page for 14h and then the increments table for 23m 41s to find the precise GHA and Dec at the exact moment of your sight.

Additional tables in the almanac cover the equation of time (the difference between apparent solar time and mean solar time), the semi-diameters of the Sun and Moon (needed for limb corrections), and the Moon's Horizontal Parallax (HP) — a value unique to the Moon that changes daily and is required for the Moon's parallax correction.

Sight Reduction Tables

Sight reduction tables are pre-computed sets of values that convert the inputs of a celestial sight — your assumed latitude, the body's Local Hour Angle (LHA), and its Declination — into two outputs: the computed altitude (Hc) and the azimuth (Zn). These two values define the line of position.

The two most widely used sets of tables are HO 229 (Sight Reduction Tables for Marine Navigation) and HO 249 (Sight Reduction Tables for Air Navigation). HO 229 covers the full range of latitudes from 0° to 89° and provides values accurate to the nearest 0.1 arcminute — the standard for marine celestial navigation. HO 249, originally designed for aerial navigation, provides values accurate to 1 arcminute and is organized for faster entry, making it popular with yachtsmen who find HO 229's six-volume set cumbersome. For most yacht navigation, the 1-arcminute precision of HO 249 is entirely adequate — it corresponds to roughly 1 nautical mile of position accuracy.

Both tables are entered with three arguments: Assumed Latitude (aLat), LHA (Local Hour Angle — the angle from the observer's meridian westward to the body's hour circle), and the body's Declination. The assumed latitude is rounded to the nearest whole degree for HO 229; HO 249 requires integral LHA as well. The navigator chooses an assumed position (AP) — a latitude and longitude close to the DR position — that satisfies these rounding requirements.

From the table entry, you extract Hc (the altitude the body would be at if you were at the assumed position) and Z (the tabulated azimuth angle, which is then converted to Zn, true azimuth, using a simple rule based on hemisphere and hour angle). The difference between Hc and the observed altitude Ho — the intercept (a) — is the key quantity for plotting the line of position.

HO 249 Volume 1 is a special case: it is designed specifically for selected stars, listing the seven best stars to observe from any latitude at any sidereal hour angle. It calculates Hc and Zn directly without requiring a separate Dec argument, making it particularly fast to use for a round of star sights at twilight.

The Complete Sight Reduction Workflow

Sight reduction follows a fixed sequence of steps. Each step takes a specific input and produces a specific output. Learning the sequence as a procedure — rather than trying to understand every formula simultaneously — is the most effective way to gain competence. The understanding follows naturally from practice.

Step 1 — Record the sight. Note the sextant altitude (Hs) and the UTC time of the observation. Record both immediately — time errors of even 4 seconds introduce about 1 NM of longitude error in a Sun sight.

Step 2 — Apply corrections to Hs to get Ho. From Hs, apply: Index Error (IE) — the calibration error of your sextant; Dip — the correction for eye height above sea level, which lowers the apparent horizon; Altitude correction — accounts for atmospheric refraction (always bending the body upward) and, for the Sun and Moon, the semi-diameter correction (upper or lower limb). The result is the observed altitude (Ho) — what you would have measured from the center of the Earth with no atmosphere.

Step 3 — Extract GHA and Dec from the almanac. Using the UTC time of the sight, look up the body's GHA and Dec from the daily pages, then apply the increments correction for the minutes and seconds.

Step 4 — Choose an assumed position and calculate LHA. Select an assumed latitude (whole degree nearest your DR latitude). Choose an assumed longitude to make LHA = GHA − Assumed Longitude (west) a whole number of degrees. LHA is your local hour angle — how far the body has moved west of your meridian.

Step 5 — Enter the sight reduction tables. With assumed latitude, LHA, and Dec, look up Hc (computed altitude) and Z (tabulated azimuth angle). Convert Z to true azimuth Zn using the appropriate hemisphere rule.

Step 6 — Calculate the intercept. a = Ho − Hc (in arcminutes). A positive intercept means the body is closer to you than your assumed position (the LOP is drawn toward the body, i.e., toward the azimuth). A negative intercept means the body is farther away. Each arcminute of intercept equals 1 nautical mile.

Step 7 — Plot the LOP. On the chart (or plotting sheet), mark the assumed position. Draw a line in the direction of Zn. Measure the intercept distance (in NM) toward or away from the body along this azimuth. Through the intercept point, draw a line perpendicular to the azimuth — this perpendicular is the line of position.

Electronic Sight Reduction

Electronic calculators and software can perform the entire sight reduction computation — from Ho, UTC, and body name to intercept and azimuth — in seconds, completely eliminating the arithmetic steps and table-lookup process.

Dedicated celestial navigation calculators such as the Celesticomp V and the NavStar were designed specifically for celestial navigation. They contain the full nautical almanac database and perform all sight reduction computations internally. The navigator inputs the body name, UTC, Hs, IE, and eye height; the calculator returns the corrected Ho, Hc, Zn, and intercept. These devices are robust, low-power, and work independently of any internet or GPS signal.

Smartphone applications have largely supplanted dedicated calculators for many sailors. Apps such as iNavX, the Celestial Navigation App (CN App), and LtCalc perform full sight reduction and almanac lookups. Most can also run the entire computation from raw Hs to plotted intercept. Some include an artificial horizon mode for practice. The principal concern with smartphone-based sight reduction is battery life and water resistance — a waterproof case and a power bank are essential companions.

The case for learning manual tables first is not simply traditionalist sentiment. Working through the tables by hand builds a precise mental model of what each step is doing and why. When an electronic result looks wrong, the navigator with table experience will recognize the anomaly and be able to identify the source of the error — wrong limb, wrong time, wrong body. The navigator who has only ever used a calculator often cannot. Furthermore, all electronic devices can fail. On an offshore passage, the ability to complete a sight reduction with a pencil and a book remains the deepest level of navigational redundancy.

The recommended learning sequence is: (1) master the full manual workflow with paper forms and HO 249; (2) introduce a calculator or app to check your manual results; (3) use electronic tools routinely at sea while maintaining the ability to revert to manual methods.