5.2 Plotting Courses, Bearings & Measuring Distance

Laying Off a Course Between Two Points

To find the course from your position to a destination — say from buoy R"2" to a harbor entrance — set one edge of the parallel rules through both points, then walk the rules to the nearest compass rose center and read the direction. The number pointing toward the destination is your course; the number 180° away is its reciprocal. Read the outer ring for a true course, which is what you draw and label on the chart (C 085°T).

Measuring Distance — Latitude Scale Only

Set your dividers with one point on each end of the leg, carry that spread to the latitude scale on the left or right side of the chart, and read the nautical miles — because 1 minute of latitude equals 1 nautical mile. Read the scale at roughly the same latitude as your track, since a Mercator chart's scale stretches toward the poles. For a long leg, open the dividers to a round number (5 or 10 nm), step along the course line, and add up the steps plus the remainder.

Never measure distance on the longitude scale across the top or bottom — on a Mercator chart a minute of longitude is not a nautical mile.

Worked example — stepping a long leg. A leg measures longer than your dividers can span. Open the dividers to 10 nm on the latitude scale, step along the course line three full steps (30 nm), then close them onto the leftover and read 7 nm on the scale. The leg is 30 + 7 = 37 nautical miles. Stepping keeps a long measurement accurate where a single wide, sagging divider span would not.

True vs. Magnetic Plots

The chart is a true world: courses and bearings you draw are true. To actually steer a course you must convert true → compass with the TVMDC ladder from Chapter 2 (going down: add West, subtract East). A shortcut is to read directions off the rose's inner (magnetic) ring, which already includes variation, and then apply only deviation to reach the compass course.

Worked example A — reading magnetic directly. You lay off a course and read 120°T on the outer ring. On the inner ring of a rose whose variation is 15°W, the same line reads 135°M. Check with TVMDC: True → Magnetic adds westerly variation, 120° + 15° = 135°M. The inner ring did the arithmetic for you.

Capstone Worked Problem — Compass Course and ETA

This is the classic combined question the module loves:

You depart buoy R"2" at 0910. From the chart you measure the course to buoy G"5" as 085°T and the distance as 18 nautical miles. Variation at the nearest rose is 8°W, your vessel's deviation on this heading is 2°E, and you make 12 knots. What compass course do you steer, and what is your ETA at G"5"?

Step 1 — compass course (TVMDC, going down, add West / subtract East):

Steer 091° by compass.

Step 2 — ETA (60 × D = S × T):

T = (60 × D) / S = (60 × 18) / 12 = 90 minutes = 1 h 30 m.

Depart 0910 + 1:30 = ETA 1040.

So the single answer is: steer 091°, arrive 1040. Notice the westerly variation pushed the number up 8°, and the easterly deviation pulled it back down 2°.

Plotting a Bearing as a Line of Position

To plot a bearing you observe to a charted object: take the bearing with a hand-bearing compass (it reads magnetic/compass), convert it to true, set the parallel rules to that true bearing at the rose, walk to the object, and draw the line from the object toward your side of it. You lie somewhere on that line of position (LOP) — specifically on the near side, in the reciprocal direction, since the bearing points toward the object. Two such lines crossing give a fix (Section 5.4).

Ranges — the Most Precise LOP

When two charted objects line up visually — a front and rear beacon, or a light behind a buoy — you are exactly on the straight range line through both, with no compass reading required. A range is the most accurate line of position available and is worth watching for whenever the problem places two objects in transit. The reciprocal discipline matters everywhere: the course to your destination is 180° from the course measured from it, and a bearing to an object is the reciprocal of the LOP direction you draw from it. Fixing which end of the line you mean before you read the rose prevents a 180° blunder.

Traps in Course and Distance Work

• Measuring on the longitude scale — the number-one distance error.
• Plotting a magnetic bearing as if it were true — always convert first.
• Confusing the course with its reciprocal — the direction to the destination, not from it.
• Reading the scale at the wrong latitude on a long north–south chart, where the scale visibly changes.