4.7 Bearings, LOPs & Fixes

Position Without Guesswork

Piloting is the art of fixing a vessel’s position relative to charted objects in coastal and inland waters—the daily bread of a Master LT 100 on near-coastal routes. Electronics help, but Q162 Navigation General and Q163 Chart Plot still expect classical methods: bearings, lines of position (LOPs), fixes, running fixes, and distance off.

A fix is a position determined from observations at a known time, plotted and labeled on the chart. It is stronger than a pure dead reckoning (DR) position (Section 4.8) because it is tied to real objects, not only course and speed.

Relative Bearings vs True Bearings

Relative bearing

A relative bearing is measured from the ship’s head using a scale where:

• 000° relative = dead ahead
• 090° relative = broad on the starboard beam
• 180° relative = dead astern
• 270° relative = broad on the port beam

Relative bearings answer “Where is it from me right now relative to my bow?” They are useful for collision avoidance and lookout reports, but you do not plot relative bearings directly as true LOPs without converting.

Converting relative to true (or compass)

True bearing ≈ true heading + relative bearing (normalize to 0–360°).

Example. True heading 040°T, relative bearing to a lighthouse 030° starboard → true bearing = 040 + 030 = 070°T.

If heading is known only by compass, convert heading to true first (TVMDC), then add relative bearing—or convert the resulting compass bearing to true. Consistency beats clever shortcuts.

True bearing for the chart

A true bearing is the direction from the vessel to the object (or sometimes object to vessel—know which the problem states) measured from true north. When you plot an LOP from a visual bearing on a chart, you work in true.

Reciprocal: If the bearing from ship to light is 070°T, the bearing from light to ship is 070° + 180° = 250°T. Plotting practice: you draw the line through the light on the reciprocal so the vessel lies somewhere on that line.

Line of Position (LOP)

A single bearing to a charted object produces a line of position: the vessel is somewhere along that line (neglecting small distance effects). One LOP alone is not a fix. It only reduces possible positions to a line.

Sources of LOPs in Master-level coastal work:

• Visual bearings to lights, towers, tanks, points, daymarks
• Ranges (two objects in line) — an especially strong LOP
• Radar ranges/bearings (as taught in electronics sections)
• Depth curves (weak/supporting)
• Celestial LOPs (not the focus of Master 100 NC, but the LOP concept is the same)

Label every LOP with time and object. On Chart Plot, unlabeled lines lose points even when geometry is right.

Two-Bearing Fix

Observe bearings to two well-separated charted objects at essentially the same time (or note times if simultaneous is impossible). Convert both to true, plot both LOPs, and take the intersection as the fix.

Worked concept.

• Bearing to Light A: 050°T
• Bearing to Stack B: 120°T
• Angle of cut = 120 − 50 = 70° (acceptable; nearer 90° is better)

Intersection of LOP A and LOP B = fix, labeled with time, e.g. FIX 1012.

Ideal geometry

Aim for an angle of cut between LOPs of about 30° to 150°, with ~90° best. When two objects are almost in the same direction, the LOPs are nearly parallel and a 1° bearing error slides the intersection miles along the line.

Three-Bearing Fix

A three-bearing fix uses three objects. Perfectly observed, all three LOPs meet at one point. In real life they form a small triangle of error (cocked hat). Practical rules:

• Prefer the geometric center of a small triangle when errors are random and objects are well spaced.
• If the triangle is large, distrust the observations—re-shoot bearings, check identification of objects, check TVMDC conversions.
• Three LOPs detect mistakes that two LOPs hide.

For exam storytelling: three-bearing fixes are the quality standard when time and visibility allow; two-bearing fixes are minimum for a plotted fix.

Running Fix

When only one suitable object is available, you cannot get a simultaneous two-LOP fix. A running fix uses time and motion:

1. Take bearing #1 to the object at time t₁; plot LOP₁.
2. Run a known course and speed (DR) for interval Δt.
3. Take bearing #2 at time t₂; plot LOP₂.
4. Advance LOP₁ by the DR course and distance for Δt (move every point on LOP₁ parallel to the track by the DR distance).
5. Intersection of advanced LOP₁ with LOP₂ is the running fix at t₂.

You can also retire a later LOP backward to an earlier time. Same geometry, opposite direction.

Limitation: A running fix is only as good as the DR between observations. Unknown current (set/drift) biases the advanced LOP. Still, it is standard coastal technique and a Chart Plot staple.

Numeric sketch. Speed 10 kn, interval 30 minutes → distance run = 10 × 0.5 = 5.0 NM. Advance LOP₁ 5.0 NM along the DR track direction.

Distance Off: Horizontal and Vertical Angles

Sometimes you need distance to an object, not only a bearing.

Horizontal sextant angle (concept)

If two charted objects have a known baseline distance between them, a measured horizontal angle at the vessel places you on a circle of position (constant angle subtends the same chord). Combined with a bearing or a second angle, you fix position. Exam items test the idea: constant horizontal angle → arc/circle of position; intersection with another LOP → fix.

Vertical sextant angle (concept)

If an object’s height is known (e.g., lighthouse height from Light List) and you measure the vertical angle from sea level to the top, distance off follows from trigonometric tables or the rough rule used in many texts:

Distance (NM) ≈ (height in feet × 0.565) / vertical angle in minutes
(form depends on units; exams often provide the table or a simplified formula).

Conceptually: taller object + larger angle → closer distance. Vertical angle distance off combined with a bearing yields a fix (bearing LOP + range circle).

You do not need surveyor-level derivation for Master 100; you need to recognize when distance-off methods apply and that height must be correct (charted/list height above the proper datum).

Dangers of Poor LOPs

Master near-coastal habits

• Pre-select conspicuous objects along the route before departure (tanks, lights, points).
• Prefer ranges when entering harbors—two objects in line give a highway-grade LOP.
• Cross-check GPS with at least an occasional visual fix in pilot waters.
• When the angle of cut is poor, change objects or add a third LOP rather than trusting a skinny intersection.
• Record time, bearing, object, and conversion so another officer can reconstruct the fix.

Linking to compass work

Every visual compass bearing is a compass observation until you apply deviation for the ship’s head and variation to reach true for the chart. Sections 4.5–4.6 are not optional theory—they are the front end of every plotted LOP.

Piloting is professional skepticism: assume a single pretty intersection can still be wrong until geometry, identification, and conversions all agree.