The Horizon and Altitude
Every Celestial Sight Starts at the Horizon
The Visible Horizon vs. the True Horizon — Dip
The true horizon is the great circle exactly 90° below the zenith — horizontal in the strictest geometric sense. The visible horizon is the line where sea meets sky as seen by the observer. Because the observer is elevated above the water, the visible horizon is actually below the true horizontal. This angular difference is called dip.
Dip exists because the Earth curves away beneath you. The higher your eye above sea level, the further the visible horizon and the greater the dip. The formula is: Dip (minutes of arc) ≈ 0.97 × √Height of Eye (feet), or approximately 1.76 × √Height of Eye (meters). At a typical eye height of 9 feet (2.7 m), dip is about 2.9 arcminutes; at 16 feet it's about 3.9 arcminutes.
Dip is always subtracted from sextant altitude (Hs) as part of the correction sequence. Because the visible horizon is below the true horizontal, your sextant reading is larger than it would be if measured from the true horizontal. Correcting for dip brings the reading down toward the true geometric value.
Dip is tabulated in the front inside cover of the Nautical Almanac, under 'DIP', as a function of height of eye in feet and meters. It's one of the first corrections applied.
Measure your height of eye carefully before a passage and write it in your sight reduction workbook. A few feet of difference in eye height changes dip by a meaningful amount. Standing on the coach roof to take sights versus kneeling in the cockpit can easily change your dip correction by 1–2 arcminutes — directly affecting the accuracy of every sight.
Dip can be affected by abnormal refraction near the horizon in unusual atmospheric conditions (temperature inversions, extreme cold over warm water). In these conditions, the visible horizon may appear at an unexpected altitude and your dip will be anomalous. If you notice the horizon looking strange or 'wavy,' treat your altitude observations with caution.
An observer's eye is 9 feet above sea level. The Nautical Almanac gives a dip correction of −2.9'. How is this applied to the sextant altitude?
Why does a higher eye height produce a larger dip correction?
Altitude Corrections — Index Error, Refraction, Parallax, and Semi-Diameter
Index error (IE) is an instrument error that arises when the index mirror and horizon mirror are not perfectly parallel when the sextant reads zero. It is found by setting the sextant to 0° and looking at the horizon — if the direct and reflected views of the horizon don't form a perfectly straight line, an IE exists. IE is applied before all other corrections: Hs corrected for IE → apparent altitude (Ha). IE can be on-the-arc (subtracted) or off-the-arc (added).
Refraction is the bending of light as it passes through the Earth's atmosphere. The atmosphere is denser near the surface, bending light upward (toward the observer) so that bodies appear higher than they actually are. Refraction is always a subtractive correction — it makes raw altitudes read too high. Refraction is most severe near the horizon (up to about 34 arcminutes at exactly 0° altitude) and diminishes rapidly above 10°. Above 20° it's typically less than 3 arcminutes. Never take sights below 10° if you can avoid it; refraction becomes unpredictable near the horizon.
Parallax is the difference between the altitude as seen from the center of the Earth (the geometric position used in the almanac) versus the altitude as seen from the observer's location on the surface. For stars and planets, parallax is negligible — too small to matter. For the Sun, parallax in altitude (PA) is small but significant, about 0.1 arcminutes maximum. For the Moon, parallax is large — up to 61.5 arcminutes — because the Moon is so close. The Moon's parallax correction is called HP (Horizontal Parallax) and must be carefully applied.
Semi-diameter (SD) applies to the Sun and Moon because they have visible discs. A sextant measurement is made to the upper or lower limb (edge), not the center. The SD correction converts the limb measurement to the center. For a lower limb observation, SD is added (the center is higher than the lower edge); for an upper limb observation, SD is subtracted. SD values for the Sun and Moon are tabulated daily in the almanac.
The Nautical Almanac combines refraction, parallax, and semi-diameter for the Sun into a single 'Total Correction' table on the inside front cover, entered with apparent altitude and lower or upper limb. For the Moon, a more elaborate two-step correction applies. Stars and planets use a separate correction table that accounts only for refraction (and small parallax).
Atmospheric refraction makes celestial bodies appear _______ than they actually are, so refraction is always a _______ correction.
Why is the Moon's parallax correction much larger than the Sun's?
Observed Altitude (Ho) — Walking Through the Correction Sequence
The goal of all corrections is to produce the observed altitude (Ho) — the altitude of the center of the body as it would appear from the Earth's center, in a vacuum, with a perfect instrument. This is the value that matches what the sight reduction tables calculate. Getting there from the raw sextant reading requires a careful, sequential chain of corrections.
Step 1 — Apply Index Error (IE): If IE is on the arc (instrument reads too high when set to zero), subtract IE. If off the arc (reads too low), add IE. Result: apparent sextant altitude.
Step 2 — Apply Dip: Subtract the dip correction for your height of eye (always subtractive). Result: apparent altitude (Ha), sometimes called 'altitude above the sea horizon corrected for dip'.
Step 3 — Apply altitude corrections: For the Sun, use the combined altitude correction table with Ha and upper/lower limb. For stars and planets, use the stars/planets correction table. For the Moon, apply the two-part correction (main correction plus additional correction using HP). The result of all corrections applied to Ha is the observed altitude (Ho).
A critical discipline: work the corrections in this exact sequence every time. Write each intermediate value down. Skipping to the total correction without checking intermediate values makes it impossible to find errors later. A simple form with labeled rows — Hs, IE, Ha, Corr, Ho — keeps every sight organized and auditable.
For Sun sights, the Nautical Almanac's combined correction table (inside front cover) does refraction, parallax, and semi-diameter in one step. Enter the table with apparent altitude (Ha) and lower or upper limb designation. The combined correction for a lower limb Sun sight at 30° altitude is about +14.8' — a significant number you don't want to forget.
Upper limb Sun sights are unusual (lower limb is standard) but legitimate. When taking an upper limb sight, the combined correction table gives a smaller number (roughly SD less than lower limb), and the correction is still applied algebraically. Mark your sight record clearly as UL or LL to avoid applying the wrong correction.
In the correct correction sequence, what is 'apparent altitude' (Ha)?
A navigator takes a lower limb Sun sight. Hs = 42° 15.3'. IE = +1.8' (off the arc). Dip (HoE 10 ft) = −3.1'. Altitude correction (lower limb, Ha ≈ 42°) = +15.2'. What is Ho?
Using Altitude to Determine Latitude Directly — The Noon Sight
The noon sight — observation of the Sun at Local Apparent Noon (LAN) — is the oldest and simplest celestial latitude calculation. At the moment the Sun crosses the observer's meridian, it reaches its maximum altitude for the day. No hour angle exists because the body is due north or south; the geometry is purely vertical.
The formula is: Latitude = 90° − Ho + Declination (when the Sun is between the observer and the equator). More precisely, you need to consider the relative positions of the observer and the Sun:
If the Sun is to the south of the observer (most common in northern latitudes): Lat = Dec + (90° − Ho), where Dec is north-positive. If the Sun is to the north of the observer (rare — requires being in the tropics with the Sun overhead or north): Lat = Ho − (90° − Dec). If the observer and Sun are on opposite sides of the equator: Lat = (90° − Ho) − Dec.
The noon sight requires no chronometer — only a sextant and the almanac page for today's declination. The navigator tracks the Sun's altitude as it approaches noon, advancing the sextant drum as the Sun climbs, until the Sun 'hangs' momentarily at its peak and begins to dip. That maximum altitude reading, fully corrected for IE, dip, and altitude corrections, is Ho. The calculation takes about 30 seconds.
As a daily discipline, the noon sight combined with a morning Sun line gives a running fix — the most common celestial position-fixing routine on a passage. The morning sight establishes a line of position that is advanced along the course line to noon; the noon sight crosses it, producing a fix. This two-sight running fix has guided ocean sailors for centuries.
To find LAN before it happens, calculate it from the almanac: LAN occurs when GHA of the Sun equals your longitude (in degrees west). Convert the GHA at the nearest whole hour to the time of meridian passage using the almanac's 'Mer. Pass.' column. The result gives LAN to within a minute or two, letting you be at the sextant and ready ahead of time.
What makes the noon sight simpler than other celestial calculations?
An observer in the northern hemisphere takes a noon sight. Ho = 55° 22.4'. The Sun's declination is 18° 14.2' N (Sun is south of the observer). What is the observer's latitude?
Summary
Dip is the angular difference between the visible horizon and true horizontal, caused by the observer's height above sea level — always subtracted from sextant altitude.
The correction chain from sextant altitude (Hs) to observed altitude (Ho) is: apply IE, subtract dip to get apparent altitude (Ha), then apply altitude corrections for the specific body.
Refraction always makes bodies appear higher than they are — it is always a subtractive correction; avoid sights below 10° where refraction becomes large and unpredictable.
Parallax is significant only for the Moon (up to 61.5'); semi-diameter corrections apply when observing the upper or lower limb of the Sun or Moon.
Observed altitude (Ho) is the fully corrected altitude used in all sight reduction — it represents the body's center as seen from the Earth's center, in vacuum.
The noon sight (LAN) gives latitude directly from Ho and declination alone, with no sight reduction tables and no chronometer required.
Key Terms
- Dip
- The angular depression of the visible horizon below the true horizontal, caused by the observer's height above sea level. Always subtracted from sextant altitude.
- Sextant Altitude (Hs)
- The raw altitude reading from the sextant arc and drum before any corrections are applied.
- Apparent Altitude (Ha)
- Sextant altitude corrected for index error and dip. The intermediate value between Hs and Ho.
- Observed Altitude (Ho)
- The fully corrected altitude of a celestial body — corrected for IE, dip, refraction, parallax, and semi-diameter. Used directly in sight reduction.
- Refraction
- The bending of light as it passes through the Earth's atmosphere, causing celestial bodies to appear higher than their true position. Always a subtractive correction.
- Index Error (IE)
- Sextant instrument error resulting from misalignment of the index and horizon mirrors when the arc reads zero. Can be positive (on-arc, subtract) or negative (off-arc, add).
- Parallax
- The difference in apparent position of a body as seen from the observer's location versus the Earth's center. Negligible for stars; significant for the Moon (up to ~61.5').
- Semi-Diameter (SD)
- Half the angular diameter of a celestial disc (Sun or Moon). Applied when the observed limb (upper or lower edge) is sighted rather than the center.
- Local Apparent Noon (LAN)
- The moment when the Sun crosses the observer's meridian and reaches its maximum daily altitude. A noon sight at LAN gives latitude directly without sight reduction tables.