Three-Bearing Fix and the Cocked-Hat Triangle

TL;DR — A fix is the intersection of two or more simultaneous LOPs; when three LOPs are used and they do not meet at a single point, the resulting triangle is called a cocked hat, and the vessel's most probable position is plotted within it. Bowditch Ch. 7 §701

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What the Rule Says

Lines of Position and the Fix

A line of position (LOP) is a line along which the vessel is known to lie at a given moment, derived from a single observation. Bowditch Ch. 7 §701 A fix is established by the intersection of two or more LOPs taken simultaneously. Bowditch Ch. 7 §701 The key word is simultaneously — all bearings must be taken at the same instant, or as close to it as practicable, so that the vessel's motion between observations does not introduce error.

When only two LOPs are available, their intersection gives a fix, but there is no independent check on the accuracy of either bearing. A third LOP provides that check. In practice, three simultaneous compass bearings to three charted objects are plotted on the chart. Each bearing is drawn as a line through the charted position of the object, in the direction of the reciprocal bearing (i.e., from the object toward the vessel). Ideally, all three lines converge at a single point — the fix.

The Cocked Hat

In reality, small errors in compass reading, chart accuracy, or the observer's technique almost always prevent three LOPs from meeting at a single point. Instead, they form a small triangle. This triangle is called the cocked hat. The name is traditional and universally recognized in practical navigation.

The size and shape of the cocked hat are diagnostic:

• A small, compact triangle indicates good agreement among the three bearings and suggests a reliable fix. The navigator plots the vessel's position at the center of the triangle.
• A large triangle indicates significant error in one or more bearings, a poorly chosen set of objects, or a systematic compass error. A large cocked hat demands investigation before the position is accepted.
• An elongated triangle often points to a single bad bearing — the outlier LOP can sometimes be identified by re-observing the suspect object.

The convention for placing the position within the cocked hat is to use the center of the triangle as the most probable position, unless there is a navigational hazard nearby, in which case the navigator uses the corner of the triangle closest to the hazard as the assumed position — the conservative, safety-biased choice.

Selecting Objects for a Three-Bearing Fix

The geometry of the chosen objects directly affects fix quality. For a two-LOP fix, the ideal angle of cut between the two LOPs is 90°. For a three-LOP fix, the ideal angular separation between successive objects is approximately 60°, which distributes the three LOPs evenly around the compass and produces a compact, equilateral cocked hat when small errors are present. Poor geometry — objects clustered within a narrow arc — produces LOPs that cross at shallow angles, making the cocked hat large and elongated even when individual bearings are accurate.

Charted objects suitable for bearing fixes include fixed aids to navigation such as lighthouses, daybeacons, and other structures whose positions are precisely known. A red triangle daybeacon on a piling, for example, marks the starboard side of a channel returning from sea and is charted with a precise position. Light List — Daybeacon — Triangle (Starboard-Hand) Such aids are reliable LOP sources because their charted positions are surveyed and maintained.

An articulated light — a floating tower restrained by a sinker on the seabed — holds its position more accurately than a moored buoy and is therefore a more reliable bearing target. Light List — Articulated Light A conventional buoy, by contrast, swings on its mooring and should be used for bearings only when no fixed aid is available.

Relationship to the Running Fix

When three simultaneous LOPs are not obtainable — for example, when only one charted object is visible — the navigator may resort to a running fix. In a running fix, the first LOP is advanced along the DR track to the time of the second observation, and the intersection of the advanced LOP with the new LOP is the running fix. Bowditch Ch. 7 §702 A running fix is explicitly less accurate than a fix derived from simultaneous LOPs. Bowditch Ch. 7 §702 The three-bearing fix, using simultaneous observations, is therefore the preferred method whenever three suitable objects are available.

A special case of the running fix using a single object is the doubling-the-angle technique: two relative bearings are taken to the same object, and the distance run between the two observations equals the distance to the object at the time of the second bearing. Bowditch Ch. 7 §703 This is a useful technique when only one charted object is visible, but it still produces a running fix — less reliable than a three-bearing simultaneous fix.

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Why It Matters on the Exam

OUPV and Master 100 GT written examinations test the three-bearing fix and cocked hat from several angles:

1. Definition questions. Candidates must know that a fix requires two or more simultaneous LOPs Bowditch Ch. 7 §701 and that a cocked hat is the triangle formed when three LOPs do not converge at a single point.

2. Position placement within the cocked hat. The exam frequently asks where to plot the vessel's position when a cocked hat is present. The standard answer is the center of the triangle. The safety-biased exception — using the corner nearest a hazard — is also tested.

3. Fix vs. running fix. Candidates must distinguish a fix (simultaneous LOPs) from a running fix (advanced LOP). Bowditch Ch. 7 §702 Confusing the two is a common error. A three-bearing fix taken at the same moment is a fix; three bearings taken sequentially without advancing the earlier LOPs is not a proper fix.

4. Geometry and object selection. Questions may describe a scenario with objects poorly separated in bearing and ask why the resulting fix is unreliable. The answer relates to shallow angles of cut producing a large, elongated cocked hat.

5. Radar as a fix source. Marine radar provides range and bearing to a target, which together constitute a direct fix. Bowditch Ch. 13 §1301 A radar range (arc of position) crossed with a visual bearing is a common two-LOP fix technique. Radar ranges generally produce more accurate LOPs than radar bearings at short to moderate ranges, because radar bearing accuracy is limited by antenna beamwidth.

6. Aid identification. Exam scenarios may describe the aids used for bearings. Knowing that a red triangle daybeacon marks the starboard side of a channel returning from sea Light List — Daybeacon — Triangle (Starboard-Hand) and that a fixed light (F) burns continuously Light List — light-characteristic (F) helps candidates correctly identify the objects in a scenario and confirm they are charted, fixed references suitable for LOPs.

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Common Pitfalls

Pitfall 1 — Treating sequential bearings as a simultaneous fix. If you take three bearings one after another over 90 seconds while the vessel is making way, the LOPs are not simultaneous. The vessel has moved between observations. The result is not a true fix; it is an approximation that introduces position error proportional to speed and elapsed time. To obtain a true three-bearing fix, take all three bearings as rapidly as possible, or use a technique such as noting the time of each bearing and applying a small correction for vessel movement.

Pitfall 2 — Always plotting at the center of the cocked hat regardless of hazards. The center-of-triangle rule is the default, not an absolute. When a shoal, reef, or other hazard lies near the cocked hat, the navigator must assume the worst-case position — the corner of the triangle closest to the hazard. Plotting at the center in that situation is a seamanship error and a likely wrong answer on the exam.

Pitfall 3 — Accepting a large cocked hat without investigation. A large cocked hat is a warning, not just a nuisance. Candidates sometimes treat any cocked hat as acceptable and simply plot the center. The correct response to a large triangle is to re-examine the bearings, check for compass error, and consider whether the objects were well-separated in bearing.

Pitfall 4 — Confusing a running fix with a three-bearing fix. A running fix advances an earlier LOP to the time of a later observation. Bowditch Ch. 7 §702 It is explicitly less accurate than a simultaneous fix. Bowditch Ch. 7 §702 Do not describe a running fix as equivalent in reliability to a three-bearing simultaneous fix.

Pitfall 5 — Using a buoy as a primary bearing reference. Buoys are not fixed — they swing on their moorings. An articulated light is a more accurate position-keeper than a moored buoy. Light List — Articulated Light Fixed structures such as lighthouses and daybeacons are preferred bearing targets.

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Quick Check

Q1 — What is a line of position (LOP)?

A line along which the vessel is known to lie at a given moment, based on a single observation. Bowditch Ch. 7 §701

Q2 — What is a fix, and what distinguishes it from a running fix?

A fix is the intersection of two or more LOPs taken simultaneously. Bowditch Ch. 7 §701 A running fix is obtained when LOPs cannot be taken simultaneously; the first LOP is advanced along the DR track to the time of the second observation, making it less accurate than a simultaneous fix. Bowditch Ch. 7 §702

Q3 — What is a cocked hat, and where do you plot the vessel's position within it?

A cocked hat is the triangle formed when three simultaneous LOPs do not converge at a single point. The vessel's most probable position is plotted at the center of the triangle. When a navigational hazard lies near the triangle, the position is plotted at the corner of the triangle closest to the hazard — the conservative, safety-biased choice. Bowditch Ch. 7 §701

Q4 — What does a large cocked hat indicate, and what should the navigator do?

A large cocked hat indicates significant error in one or more bearings, poor object geometry (shallow angles of cut), or a systematic compass error. The navigator should re-observe the bearings, check for compass error, and verify that the chosen objects are well-separated in bearing before accepting the position. Bowditch Ch. 7 §701

Q5 — Why is an articulated light preferred over a moored buoy as a bearing target?

An articulated light is restrained by a sinker on the seabed and holds its position more accurately than a moored buoy, making it a more reliable reference for an LOP. Light List — Articulated Light

Q6 — How does radar contribute to a position fix?

Marine radar provides range and bearing to a target, which together constitute a direct fix. Bowditch Ch. 13 §1301 A radar range crossed with a visual bearing is a common two-LOP fix technique.

Q7 — What is the doubling-the-angle technique, and what type of position does it produce?

The doubling-the-angle technique uses two relative bearings to a single object; the distance run between the two observations equals the distance to the object at the time of the second bearing. Bowditch Ch. 7 §703 It produces a running fix — less accurate than a simultaneous fix from multiple objects. Bowditch Ch. 7 §702