5.2 Plotting Courses, Bearings & Measuring Distance

Laying a Course Between Two Points

Most Q163 legs start the same way: you are at a fix or charted point A and must proceed to point B (buoy, light, waypoint, lat/long).

Procedure:

1. Mark A and B precisely (small, sharp dots).
2. Set one edge of the parallel rulers (or triangle edge) so it passes through both points.
3. Walk to the nearest compass-rose center.
4. Read the outer ring in the direction toward B—that is the true course.
5. Draw the track and label C xxx°T above the line.

The number 180° opposite on the same rose edge is the reciprocal—useful for return legs and for checking you did not read “from B to A” by accident.

Reciprocal rule: reciprocal = course ± 180°, then normalize to 000–360.

• Course 085°T → reciprocal 265°T
• Course 300°T → reciprocal 120°T

Worked course read

Parallel rulers through buoy R "2" and the harbor approach fix; rose outer ring toward the harbor reads 072°. Label C 072°T. Reciprocal for the outbound-to-inbound check: 072 + 180 = 252°T.

Measuring Distance — Latitude Scale Only

1 minute of latitude ≈ 1 nautical mile. On Mercator coastal training charts, that is why distance lives on the left/right latitude borders, not top/bottom longitude.

Steps:

1. Open dividers from A to B on the track (or step in chunks if long).
2. Without changing the spread, place them on the latitude scale near the track’s latitude.
3. Read the interval in minutes of latitude = NM (and tenths).

Long-leg stepping example. Leg longer than a comfortable divider span:

• Set dividers to 5.0 NM on the latitude scale.
• Step along the course: 4 full steps = 20.0 NM.
• Remainder measures 2.4 NM.
• Total distance = 22.4 NM.

Stepping beats one giant, sagging span that over-reads by several tenths—enough to miss an ETA option at 90%.

The fatal trap

Using the longitude scale for distance is the number-one arithmetic trap on training charts. One minute of longitude equals one NM only at the equator; at ~41°N (Block Island / Long Island training waters) a minute of longitude is only about 0.75 NM. A “12 NM” leg measured on longitude is wrong by miles.

True Plot → Compass to Steer

The chart is a true surface. When the question asks “What course do you steer by compass?” convert with TVMDC.

Uncorrecting (T → C): West best (add), East least (subtract).

Capstone worked problem — course, distance, TVMDC, ETA

Depart buoy R "2" at 0910. Charted true course to G "5" is 085°T; distance 18.0 NM. Variation 8°W, deviation on heading 2°E, speed 12 kn. Find compass course to steer and ETA (ignore current).

Compass course:

Steer 091° by compass.

ETA (60D = ST):

Time (minutes) = (60 × D) / S = (60 × 18) / 12 = 90 min = 1 h 30 m.
Depart 0910 + 1:30 → ETA 1040.

Answer package examiners love: 091°C, ETA 1040.

Second numeric set — wrap past 360°

True course 010°T, Var 6°E, Dev 4°E.

T→M: east least → 010 − 6 = 004°M
M→C: east least → 004 − 4 = 000°C (or 360°).

If subtraction goes negative: add 360. Example: T 005°, Var 10°E → M = 005 − 10 = −5 → 355°M.

Transferring Bearings as LOPs

An observed bearing to a charted object places you on a line of position (LOP).

Plotting sequence:

1. Convert the observation to true (TVMDC if taken by compass; relative bearing → true by adding true heading).
2. Set parallel rulers to that true direction at the rose center.
3. Walk to the charted object.
4. Draw the line through the object. You lie on the line on the side consistent with the bearing from ship to object (use the reciprocal carefully—see below).

Relative → true

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

Example. Heading 040°T, light at 030° relative starboard → true bearing 070°T.

Reciprocal bearings

If the bearing from ship to light is 070°T, the direction from light to ship is 070 + 180 = 250°T. When drawing from the light, you use the geometry so the vessel’s possible positions sit on the correct ray. Confusing “bearing of the light” with “bearing of the ship from the light” produces a 180° blunder—instant module fail if that LOP drives the fix.

Ranges

Two charted objects in line give a range LOP with no compass reading: you are on the straight line through both. Ranges are the most precise coastal LOPs; watch for them in harbor approaches and exam stems.

Labeled Plot Elements (C, S, T)

Professional and exam plots use consistent shorthand:

Also mark LOP times and object names when multiple bearings exist. When speed or course changes, start a new labeled leg from that position.

Speed–Time–Distance Without Current

Core formula (minutes form):

60 × D = S × T (D in NM, S in kn, T in minutes)

Drill 1. D = 7.5 NM, S = 10 kn → T = 60 × 7.5 / 10 = 45 min.
Drill 2. S = 8 kn, run 1 h 15 min (75 min) → D = 8 × 75 / 60 = 10.0 NM.
Drill 3. 15 NM in 1 h 12 min (72 min) → S = 60 × 15 / 72 = 12.5 kn.

Common Errors on Course & Distance Items

Practice package (work before looking)

1. Course 265°T to R "8", distance 9 NM, S 9 kn, depart 1400, Var 10°W, Dev 0° → compass course and ETA.
   • C = 265 + 10 = 275°C; T = 60 × 9 / 9 = 60 min → ETA 1500.
2. Heading 180°T, relative bearing 090° (starboard beam) to a tower → true bearing 270°T.
3. True course 000°T, Var 5°E, Dev 2°W → C = (000 − 5) + 2 = 357°C.

Course and distance work is pure technique. On a 90% module, neat true courses, latitude-scale miles, and careful TVMDC are how Masters clear Q163 before current triangles raise the difficulty.