Visual Piloting — Three-Bearing Fixes and Danger Bearings

TL;DR — A fix is the intersection of two or more simultaneous lines of position (LOPs); three simultaneous bearings produce a triangle of error that reveals plotting accuracy. A running fix, obtained by advancing an earlier LOP along the DR track, is inherently less accurate than a simultaneous fix and must be treated with appropriate caution.

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What the Rule Says

Navigation by Piloting

Marine navigation encompasses four primary methods: dead reckoning, piloting, celestial, and electronic. Modern practice combines all four, with electronic navigation as the principal real-time reference and the others serving as cross-checks. Bowditch Ch. 1 §101

Piloting specifically is navigation by reference to landmarks, aids to navigation, and soundings. It is the primary method employed in confined waters, where dead reckoning alone is insufficient and electronic positioning may be obstructed by terrain or interference. Bowditch Ch. 1 §103 This makes visual bearing work — the foundation of three-bearing fixes and danger bearings — the dominant skill set whenever a vessel is operating near the coast, in harbor approaches, or transiting channels.

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. A fix is the intersection of two or more LOPs taken simultaneously. Bowditch Ch. 7 §701

The critical word is simultaneously. When two LOPs are taken at the same instant, their intersection is a true fix — the vessel's position is at that point, subject only to the accuracy of the observations and the plotting. When a third simultaneous LOP is added, the result is almost never a perfect point. Instead, the three lines form a small triangle called the triangle of error (also called a cocked hat). The size and shape of that triangle tells the navigator how much confidence to place in the fix and, crucially, which side of the triangle to favor when a hazard is nearby.

The Running Fix

A running fix is obtained when LOPs cannot be taken simultaneously. The procedure is to advance the first LOP along the DR track to the time of the second observation; the intersection of the advanced LOP with the new LOP is the running fix. Bowditch Ch. 7 §702 The running fix is explicitly less accurate than a fix from simultaneous LOPs, because any error in the vessel's speed, course, or set and drift during the interval between observations is carried forward into the advanced LOP. Bowditch Ch. 7 §702

Bearings to a Single Object — Doubling the Angle

When only one charted object is visible, a running fix can still be obtained if the relative bearing to that object changes substantially between two observations. The doubling-the-angle technique uses two relative bearings: when the second relative bearing is exactly double the first, the distance run between the two observations equals the distance from the vessel to the object at the moment of the second bearing. Bowditch Ch. 7 §703 This is a special case of the running fix and carries the same limitation — it is less accurate than a simultaneous multi-object fix.

Constant Bearing, Decreasing Range (CBDR)

Compass bearings are also the canonical tool for detecting risk of collision. If compass bearings to an approaching vessel remain constant while the range is decreasing, risk of collision exists. Bowditch Ch. 7 §704 This principle underlies the concept of a danger bearing: a navigator pre-plots a bearing to a charted object such that, as long as the observed bearing remains on the safe side of that pre-plotted value, the vessel is clear of a hazard. If the bearing crosses the danger bearing, the vessel has moved into the danger zone.

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Why It Matters on the Exam

OUPV and Master 100 GT written examinations test visual piloting heavily because it is the foundational skill for operating in the coastal and inland waters where these license holders work. Expect questions in the following categories:

1. Identifying a fix versus a running fix. The exam will present a scenario and ask whether the result is a fix or a running fix. The distinguishing criterion is simultaneity. Two or more LOPs taken at the same time produce a fix. Bowditch Ch. 7 §701 Any scenario where the first LOP must be advanced along the DR track before it can be crossed with a second LOP produces a running fix, which is less accurate. Bowditch Ch. 7 §702

2. The triangle of error from three simultaneous bearings. When three simultaneous compass bearings are plotted and they do not intersect at a single point, the resulting triangle of error is normal and expected. The exam may ask what the triangle indicates (plotting or observation error, or both) and where to place the vessel's position when a hazard is present. The conservative answer is always to assume the vessel is on the side of the triangle closest to the hazard. This is consistent with the principle that cumulative navigational errors must be checked against fixes whenever possible. Bowditch Ch. 23 §2301

3. Doubling the angle on the bow. The exam tests whether candidates know that in the doubling-the-angle technique, the distance run between the two bearings equals the distance off the object at the second bearing. Bowditch Ch. 7 §703 A common question format gives you the first relative bearing, the second relative bearing (double the first), and the distance run, then asks for the distance off at the second bearing. The answer is simply the distance run.

4. Danger bearings and CBDR. Questions on danger bearings often appear in the collision avoidance context. The underlying principle is that a constant compass bearing with decreasing range indicates risk of collision. Bowditch Ch. 7 §704 A danger bearing pre-plots this logic onto a charted hazard: the navigator assigns a bearing to a landmark such that the hazard lies on one side of that bearing line. Monitoring the observed bearing against the danger bearing provides continuous situational awareness without requiring a full fix.

5. Piloting as the primary method in confined waters. Exam questions sometimes ask which navigation method is primary in confined or restricted waters. The answer is piloting — navigation by reference to landmarks, aids to navigation, and soundings. Bowditch Ch. 1 §103 Electronic navigation may be unavailable due to terrain or interference, and dead reckoning alone is insufficient in confined waters. Bowditch Ch. 1 §103

6. Sources of navigational error. Navigational errors arise from instrument error, observation error, plotting error, computation error, and the assumption that the vessel has maintained the planned course. Cumulative errors must be checked against fixes whenever possible. Bowditch Ch. 23 §2301 The exam may ask a candidate to identify which type of error is introduced by a specific action — for example, advancing an LOP along an assumed DR track introduces error if the vessel's actual speed or course differed from the planned values.

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Common Pitfalls

Confusing a fix with a running fix. Candidates frequently call any two-LOP intersection a "fix." Remember: if the LOPs were not taken simultaneously, the result is a running fix, and it is less accurate than a simultaneous fix. Bowditch Ch. 7 §702

Misapplying the doubling-the-angle rule. The rule states that the distance run between the two bearings equals the distance off at the second bearing. Bowditch Ch. 7 §703 Candidates sometimes confuse this with the distance off at the first bearing, or attempt to apply the rule when the second bearing is not exactly double the first.

Treating a large triangle of error as a valid fix. A large triangle of error signals significant observation or plotting error. Bowditch Ch. 23 §2301 Candidates should not simply place the vessel at the center of a large triangle and proceed; the correct response is to take additional bearings and resolve the discrepancy before proceeding in confined waters. Bowditch Ch. 1 §103

Ignoring CBDR in a danger bearing context. A danger bearing is only useful if the navigator is actively monitoring compass bearings. If the bearing to the landmark is constant and the range is decreasing, the vessel is on a collision course with the hazard — the same principle that applies to vessel-to-vessel collision avoidance. Bowditch Ch. 7 §704

Assuming electronic navigation eliminates the need for visual piloting. Electronic positioning may be obstructed by terrain or interference in confined waters. Bowditch Ch. 1 §103 Piloting by visual bearings remains the primary method and must be maintained as a cross-check regardless of electronic system availability. Bowditch Ch. 1 §101

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Quick Check

Q1 — You take compass bearings to three charted objects at the same moment and plot them on the chart. They form a small triangle. What is this called, and where do you place your position if a shoal lies just north of the triangle?

The triangle is called a triangle of error (cocked hat). Because the shoal lies north of the triangle, you place the vessel's assumed position at the northernmost vertex of the triangle — the corner closest to the hazard. This is the conservative approach consistent with checking cumulative errors against fixes whenever possible. Bowditch Ch. 7 §701 Bowditch Ch. 23 §2301

Q2 — At 0800 you take a bearing to a lighthouse and plot the LOP. At 0815 you take a bearing to the same lighthouse and plot a second LOP. You advance the 0800 LOP along your DR track to 0815 and cross it with the 0815 LOP. What type of position have you obtained, and how does its accuracy compare to a simultaneous fix?

You have obtained a running fix. It is less accurate than a fix derived from simultaneous LOPs because any error in the vessel's speed, course, or set and drift during the 15-minute interval is carried forward into the advanced LOP. Bowditch Ch. 7 §702

Q3 — A vessel is on course 090°T at 12 knots. At 1000, the relative bearing to a water tower is 030°. At 1020, the relative bearing to the same water tower is 060° — exactly double the first. How far off is the vessel from the water tower at 1020?

The vessel has run 4 nautical miles in 20 minutes at 12 knots. By the doubling-the-angle rule, the distance run between the two bearings equals the distance off the object at the second bearing. Therefore, the vessel is 4 nautical miles from the water tower at 1020. Bowditch Ch. 7 §703

Q4 — Which navigation method is primary in confined waters, and why?

Piloting is the primary method in confined waters. Dead reckoning alone is insufficient in confined waters, and electronic positioning may be obstructed by terrain or interference. Piloting — navigation by reference to landmarks, aids to navigation, and soundings — provides the direct positional reference required. Bowditch Ch. 1 §103

Q5 — You observe that the compass bearing to a vessel approaching from your starboard bow has not changed over the past five minutes, but the vessel appears larger. What does this indicate?

Constant compass bearing with decreasing range (CBDR) indicates risk of collision. Bowditch Ch. 7 §704 The increasing apparent size of the vessel confirms the range is decreasing. Risk of collision exists and action is required.