Sight Planning and the Star Fix

Fix Geometry and Crossing Angles

A celestial fix is only as good as the geometry of its intersecting lines of position. The crossing angle — the angle at which two LOPs intersect — determines how sensitive the fix is to small errors in each sight. Two LOPs crossing at 90° give the best possible fix: an error in either LOP shifts the fix position by only that error's length along its own line, with no amplification. Two LOPs crossing at 10° give a very poor fix: the same small error in either LOP shifts the position by a large distance perpendicular to the acute intersection.

The practical rule: for a two-body fix, aim for a crossing angle between 60° and 120°. For a three-body fix, ideal geometry is three LOPs at approximately 60° intervals — equivalent to choosing bodies at azimuths roughly 120° apart. At that geometry, each LOP bisects the angle between the other two, and the resulting cocked hat (the small triangle formed by three imperfect LOPs) is equilateral and minimally sized.

The cocked hat is almost always the result when three LOPs are plotted — the three lines very rarely pass through a single point. This is expected and normal. Random sighting errors, small timing errors, and residual corrections all ensure the LOPs form a small triangle rather than a perfect intersection. A small equilateral cocked hat — where all sides of the triangle are roughly equal and the triangle area is small — indicates consistent, unbiased sights and good geometry. A large or elongated cocked hat indicates a problem: either one sight is significantly in error, or the crossing geometry is poor.

Interpreting the cocked hat: the convention is to take the center of the cocked hat as the most probable position. If one of the three LOPs is from a body whose sight the navigator is less confident in — perhaps taken in a cloud gap or from a body near the horizon — that LOP should be given less weight in placing the fix. Some navigators prefer to use the most recently observed body's LOP (which requires the least advancing) as the primary reference and center the fix relative to it. In coastal waters where shoaling might lie on one side of the cocked hat, the prudent navigator takes the vertex of the cocked hat nearest the danger.

Poor geometry examples: three stars all in the east give LOPs running roughly north-south, nearly parallel, with very poor east-west definition. Three stars all at very high altitude (above 70°) produce LOPs that run in arbitrary and changing directions, often with poor accuracy due to the flatter geometry of the azimuth computation at near-zenith angles. The ideal star fix avoids both extremes: bodies between 20° and 60° altitude, spread around the compass in azimuth.

Planning a Twilight Session

Effective twilight star fix planning begins in the afternoon, well before darkness falls. The goal is to know, before going on deck, exactly which bodies to observe, in what order, in what approximate direction, and at what approximate altitude — so that the observation session can proceed efficiently during the narrow twilight window.

Step 1: Establish approximate DR position and time. Determine your dead reckoning position for the planned observation time (typically evening civil twilight, estimated from the almanac for your longitude). Note the date and the planned observation time in UTC.

Step 2: Use the 2102-D Star Finder or H.O. 249 Volume 1. For the 2102-D, set the transparent overlay for your latitude to align with the computed LHA Aries for the observation time. Read off the altitude and azimuth for all visible navigational stars and planets above about 15°. For H.O. 249 Volume 1, simply enter the table with LHA Aries and your latitude and read the pre-computed list of the seven best stars with their altitudes and azimuths.

Step 3: Select the bodies. From the list, choose three to six bodies that span a wide range of azimuths. Target bodies between 20° and 60° altitude for best accuracy. Include Polaris if you are in the northern hemisphere — it is a fast, easy latitude line. Consider including a planet (Venus, Jupiter, Saturn) if one is available at a good altitude and azimuth, as planets give bright, unmistakable sights.

Step 4: Write the plan. On a card (waterproof notepad or taped slip), list each body with: name, approximate altitude (set this on the sextant before going on deck), approximate azimuth (where to look), and any distinguishing features (color, brightness, nearby constellation). Order the list by altitude — lowest bodies first.

Step 5: Set a pre-dawn or evening alarm. The timing of evening civil twilight for your longitude is in the almanac's twilight tables. Set an alarm with enough time to be on deck, sextant in hand, at the start of the window. For evening twilight, beginning the session about 10 minutes before the tabulated evening civil twilight time — when the sky is still bright but the very brightest bodies are appearing — captures the best conditions.

Planets in the plan: if Venus or Jupiter is available, put it first in the observation order. These bright bodies are visible before most stars appear and the horizon is at its clearest. Taking Venus during early civil twilight gives an excellent first LOP with minimal horizon uncertainty.

Executing the Star Fix

With the pre-computed list in hand and the sextant ready, executing the star fix is a matter of disciplined technique applied efficiently within the twilight window. Every minute of the window is valuable, and experienced navigators develop a fluid routine that allows them to shoot four to six bodies before the horizon disappears.

Preparation on deck: arrive on deck five to ten minutes before the window opens. Allow your eyes to dark-adapt. Have the observation card at hand. Set the sextant to the altitude of the first planned body. Check the index error. Have a recording notebook and pencil (not a pen — saltwater destroys ink) ready, and a red-filtered flashlight to preserve night vision.

Finding the body through the telescope: point the sextant in the expected azimuth direction, set to the pre-computed altitude, and scan slowly. On a moving vessel, keep the eye piece steady against your brow. For a brighter star or planet, you will see it immediately. For a fainter second-magnitude star, scan gently — ±3° to 5° from the expected altitude and ±5° in azimuth covers reasonable pre-computation errors. Once the body is in the field of view, bring it to the horizon using the micrometer drum.

The sight itself: rock the sextant gently from side to side to find the vertical. Bring the body's lower limb (or center for a star) to kiss the horizon at the nadir of the rocking arc. At the precise moment of tangency, call 'mark' to a partner reading the watch, or press the stopwatch button while your partner reads the sextant. Record the time (to the nearest second of UTC) and the sextant reading immediately — before moving on to the next body.

Speed and sequence: after recording the sight, immediately set the sextant for the next body on the list, pivot to the new azimuth, and take the next sight. A practiced navigator can complete a sight, record it, and be set up for the next body in 60 to 90 seconds. Four bodies in 10 minutes is routine; six bodies in 15 minutes is achievable with good planning.

Averaging multiple sights: if the window permits, taking two or three shots of the same body in rapid succession (within 60 seconds) and averaging the altitude and time reduces individual sight errors significantly. With six planned bodies, shooting each twice requires about 20 minutes of window — possible in high latitudes where twilight lingers, less feasible in the tropics where twilight is brief.

Recording format: a standard sight log records: body name, sextant reading (Hs), watch time, and any notes (cloud obstruction, rough sea state, confidence level). A clean, complete sight log makes the reduction work below straightforward and preserves a record of observation quality for later review.

Plotting the Fix

With sights recorded, the navigator moves below to reduce them and plot the resulting LOPs. For a multi-body twilight fix, all sights are reduced to lines of position, each advanced or retarded to a common fix time, and then plotted on the working chart or plotting sheet.

Reducing the sights: each sight is worked through the standard process — apply sextant corrections to get Ho, compute LHA for the body, enter sight reduction tables with LHA, declination, and assumed latitude to get Hc and Zn, find the intercept (Ho − Hc), plot the AP, draw the intercept along the azimuth, and draw the LOP perpendicular to the azimuth at the intercept distance. This process is identical regardless of whether the body is a star, planet, or the Sun.

Advancing sights to a common time: in a 15-minute observation session, sights taken at the beginning and end of the window need to be advanced (or retarded) to a common fix time. This is done exactly as with a running fix: the AP and LOP are shifted in the direction of the vessel's course by the distance run between the sight time and the fix time. For a 15-minute session at 8 knots, the maximum advance needed is 2 nautical miles — small enough that many navigators accept all twilight sights as simultaneous without significant error. At slower speeds or in shorter windows the approximation is even better.

Plotting and the cocked hat: with three to six LOPs on the plotting sheet, the navigator examines the resulting triangle or polygon. A small, compact triangle indicates consistent sights and good geometry. A large or irregular polygon suggests one or more outlier sights. The navigator identifies any LOP that does not pass near the intersection of the others, investigates that sight (timing, body identification, reduction arithmetic), and either corrects or discards it.

The navigator's judgment — where is the fix? The center of the cocked hat is the standard most probable position (MPP). However, the navigator applies professional judgment informed by the observation context. A sight taken in a brief cloud gap may be less reliable than one taken from a clear horizon. A sight on a body very near the horizon may be less reliable than one at 40°. Sights taken near the end of the window, when the horizon was beginning to blur, may be less reliable. The navigator weights the LOPs by confidence and places the fix accordingly — not slavishly at the center of all LOPs, but at the most credible position supported by the preponderance of the evidence.

Comparing to DR: once the fix is plotted, compare it to the vessel's dead reckoning position for the same time. A consistent difference between fixes and DR over multiple days indicates a systematic current or a persistent DR error (leeway, speed error). A large single-day discrepancy may indicate a DR error from a course change that was not logged, or may indicate a celestial fix error. The navigator examines both possibilities before accepting a large correction to the DR track.

Recording the fix: note the fix time, the bodies used, and the fix position in the log. Note the size of the cocked hat (e.g., 'cocked hat 2 NM equilateral') as a quality indicator. A record of fix quality over the passage gives the navigator a calibration of their technique and the conditions.