5.4 Fixes: Two/Three-Bearing, Running Fix & Distance-Off

What a Fix Is

A fix is a position established by crossing two or more lines of position (LOPs) taken at essentially the same time. Mark it with a circle and the time, and restart your DR from it — the fix resets whatever error the DR had accumulated. The most common LOP is a bearing to a charted object, converted to true and drawn from the object.

Two-Bearing Fix

Observe two charted objects, convert both bearings to true, plot each LOP, and take the intersection as your fix. Accuracy is best when the LOPs cross near 90°; nearly parallel LOPs give a "smeared," uncertain crossing.

Worked example. At 0915 the lighthouse bears 040°T and a water tower bears 110°T. Draw the 040°T LOP from the lighthouse and the 110°T LOP from the tower; where they cross is your 0915 fix (circle, 0915). The two lines cross at about 70° — acceptable, though a pair nearer 90° would be sharper.

Three-Bearing Fix and the Cocked Hat

Three bearings almost never meet at one point; they form a small triangle called a "cocked hat." A small cocked hat means a good fix — take the position at its center (or, near danger, at the corner closest to the hazard). A large cocked hat warns of a bad bearing, an uncorrected compass error, or too much time between sights. Rule of technique: shoot the object nearest the beam last, because objects near the beam change bearing fastest, so taking them last minimizes the error from the seconds that pass between sights.

Running Fix — One Object Over Time

When only one object is available you can still fix your position over time with a running fix: take a bearing, run a known course and distance, take a second bearing on the same object, then advance the first LOP by that run and cross it with the second.

Worked example. At 1000 a lighthouse bears 030°T — draw LOP 1. You run C 090°T at 12 knots. At 1030 the same lighthouse bears 320°T — draw LOP 2. The run is D = (12 × 30)/60 = 6.0 nm. Advance LOP 1 by sliding it 6.0 nm in the direction 090°T (parallel to itself), then cross the advanced LOP 1 with LOP 2. Their intersection is your 1030 running fix (labeled R Fix). It is less certain than a two-object fix because it assumes the DR run was accurate.

Distance Off — Bow-and-Beam Bearings

You can find how far you will pass an object using two relative bearings and the distance run between them.

Bow-and-beam: note the time when the object is 45° on the bow (045° relative), and again when it is abeam (090° relative). The distance run between those two bearings equals the distance off when abeam, because the two bearings and the track form a 45°–45°–90° isosceles triangle.

Worked example. Making 10 knots, the object is 45° on the bow at one time and abeam 12 minutes later. Distance run = (10 × 12)/60 = 2.0 nm, so you pass the object 2.0 nm off when it comes abeam.

Distance Off — Doubling the Angle on the Bow

A more general trick: when the second relative bearing is twice the first, the distance run between them equals the distance from the object at the second bearing.

Worked example. The object is first 30° on the bow, and later 60° on the bow (the angle doubled). Running 12 knots for 15 minutes between the two, distance run = (12 × 15)/60 = 3.0 nm, so at the moment of the 60° bearing you are 3.0 nm from the object. A third method, the vertical sextant angle, converts the measured angle to a charted object's known height into a distance off — useful past a lighthouse of known elevation, though bow-and-beam and doubling are the two the plotting module leans on.

Danger Bearings — an LOP That Keeps You Safe

The same line-of-position geometry has a defensive use. A danger bearing is a single bearing drawn from a charted object that just clears an off-lying hazard — a shoal or rock. Label it NMT ("not more than") or NLT ("not less than"). As long as your observed bearing to that object stays on the safe side of the danger bearing, you are in clear water; the instant it crosses to the wrong side, you are standing into danger. It is a fast, powerful check at night or in fog, needing only one object and one bearing rather than a full fix.

Crossing Angle Matters

For any two-LOP fix, remember why the crossing angle is graded so heavily: near 90° a small bearing error moves the intersection only slightly, but as the lines approach parallel the same error slides the crossing far along both lines. When you can choose objects, pick a pair roughly abeam of each other so their bearings differ by close to a right angle.

Fix Traps

• Not restarting DR at the fix — the whole point of fixing is to reset the DR.
• Ignoring a large cocked hat instead of re-shooting a suspect bearing.
• Forgetting the running fix assumes an accurate run — a strong unaccounted current will throw it off.