5.4 Fixes, Running Fixes & Timed Plot Problems

What Counts as a Fix on the Plot

A fix is a position determined from observations at a known time—stronger than pure DR because it is tied to charted reality. On Q163 and on a Master’s near-coastal watch:

• Plot LOPs in true.
• Intersection = fix → mark with a circle and time.
• Restart DR from that fix for all subsequent legs.

One LOP alone is not a fix; it only constrains you to a line.

Two-Bearing Fix

1. Observe bearings to two well-separated charted objects (as nearly simultaneous as possible).
2. Convert each to true.
3. Plot both LOPs from the objects.
4. Intersection = fix; label FIX hhmm.

Worked example

At 0915:

• Lighthouse bears 040°T
• Water tower bears 110°T

Angle of cut = 110 − 40 = 70° (acceptable; nearer 90° is better). Intersection = 0915 fix.

Geometry quality

If cut is skinny, change objects or add a third LOP rather than trusting a smeared intersection near hazards.

Three-Bearing Fix

Three true LOPs ideally meet at a point. Real observations form a small triangle of error (cocked hat):

• Small triangle + good object spacing → use geometric center as fix.
• Large triangle → re-shoot bearings, recheck object ID, recheck TVMDC.

Three LOPs detect mistakes that two LOPs hide—worth the extra minute on a 90% module when objects are available.

Running Fix — Advance a LOP

When only one suitable object is available:

1. Bearing #1 at time t₁ → plot LOP₁.
2. Run known course and speed for interval Δt (DR).
3. Bearing #2 at t₂ → plot LOP₂.
4. Advance LOP₁ by the DR course and distance for Δt (every point on LOP₁ moves parallel to the track by the run distance).
5. Intersection of advanced LOP₁ with LOP₂ = running fix at t₂.

You may instead retire LOP₂ backward to t₁. Same geometry, opposite direction.

Numeric sketch

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

Worked running-fix story

• 1000: Light A bears 320°T → LOP₁.
• Steer 090°T at 8 kn.
• 1030: Light A bears 000°T → LOP₂.
• Advance LOP₁ 4.0 NM due east (8 kn × 0.5 h).
• Cross advanced LOP₁ with LOP₂ → running fix 1030.

Limitation: A running fix assumes the DR run (course, speed, no unknown current). Unaccounted set biases the advanced LOP. If the problem also gives current, advance using the ground track (CMG and SMG), not water-only DR—or solve set/drift first from a prior DR–fix pair.

Timed DR Then Fix

Many multi-part plot questions chain steps:

1. Start at a labeled fix.
2. Plot DR for a stated course/speed/time (semicircles at intermediate times if asked).
3. Take bearings → fix.
4. Compare fix to DR → set/drift.
5. From the new fix, compute CTS for the next leg and ETA.

Combined arithmetic example

0800 fix. Steer C 090°T, S 10 for 1 hour (ignore current first).
0900 DR is 10 NM east of the 0800 fix.
0900 two-bearing fix is 1.0 NM north of the 0900 DR.
Set = 000°T, drift = 1.0 kn.
Next: make good 090°T to a buoy 12 NM east of the 0900 fix, boat still 10 kn, same current.

Current sets north, so for easterly track head south of east.
sin θ = 1/10 = 0.1 → θ ≈ 5.7° ≈ 6°.
CTS ≈ 096°T.
SOA ≈ √(10² − 1²) ≈ 9.95 kn ≈ 10 kn for practical multiple choice (nearly full speed; small cross component).

Time to buoy ≈ 60 × 12 / 9.95 ≈ 72 min → ETA about 1012 if departing 0900.

(If options are coarse, SOA ≈ 10 kn → 72 min still; the CTS of ~096°T is the discriminative answer.)

ETA Problems Combining STD With Current

Always identify which speed the stem wants:

Formula recap: T_min = 60D / S; D = ST/60; S = 60D / T.

QC checklist after every ETA:

1. Distance from latitude scale, not longitude.
2. Speed is the correct one (STW vs SOA vs SMG).
3. Time unit consistency (hours vs minutes).
4. Departure time + interval with correct 60-minute hours (e.g., 0945 + 90 min = 1115, not 1035).
5. Course labels T/M/C match what the option states.

ETA wrap drill

Depart 2340, run 8.0 NM at SOA 6 kn.
T = 60 × 8 / 6 = 80 min.
2340 + 80 min = 0100 next day—not 2420.

Strategy: Finish 10 Questions Accurately

Scoring reality: 9/10 required. Two “almost right” plots fail the module. Time is usually generous (up to ~3.5 hours in many chart-plot administrations—confirm your notice); do not rush, but do not dawdle on one stuck item while nine others wait.

Recommended pace

Accuracy over heroics

• Prefer a second measurement of a critical distance over guessing between two close options.
• If two LOPs nearly parallel, distrust the fix—re-plot or use a third object if given.
• Keep the chart uncluttered: erase abandoned lines so you do not measure the wrong track.
• Write intermediate TVMDC and 60D=ST lines; mental math under stress is how 5° and 0.3 NM disappear.

High-frequency Q163 skill stack (checklist)

1. Tools / rose / true labels
2. Course & distance (latitude scale)
3. TVMDC to compass when asked
4. Two-/three-bearing fix
5. Running fix advance
6. Set/drift from DR vs fix
7. CTS + SOA current triangle
8. ETA with correct speed

If you can execute that stack without scale or reciprocal errors, the 90% bar is achievable. Treat Chart Plot like the passenger-carrying skill it is: one bad plot is one too many—on the exam and on the water.