Chart navigation: from dead reckoning to GPS

Coordinates and the Mercator projection

Nautical charts use the Mercator projection: a cylindrical projection that preserves angles (conformal). The key property for the navigator — a straight line on a Mercator chart is a rhumb line, i.e. a line of constant course. This lets you plot a course as one straight line and steer keeping a constant compass heading.

Coordinates are given as a pair: latitude (φ) from 0° at the equator to 90° at the poles, north positive; longitude (λ) from 0° (Greenwich) to 180° east and west. In yachting we use degrees and decimal minutes: e.g. 59° 55.5′ N, 30° 15.2′ E. One minute of latitude equals one nautical mile (1852 m) — the main yardstick for distance.

Important: distances on a Mercator chart are measured only on the vertical latitude scale within the same horizontal band the route runs through. At high latitudes a minute of longitude is shorter than a minute of latitude.

Reading a nautical chart

A nautical chart is a dense document with dozens of types of information. The main elements:

• Chart heading: scale (1:50,000 — large, for approach; 1:500,000 — small, for passage), datum (WGS-84 — GPS standard), depth units (metres), depth datum (LAT — lowest astronomical tide).
• Depth contours: lines of equal depth. Usually 2, 5, 10, 20 m — critical for yachts.
• Depth colours: white — safe, blue — shallow, green — drying area (under water at high tide, dry at low).
• Hazard symbols: rocks (cross), wrecks, cables and pipelines.
• IALA aids to navigation: lateral (red/green on the sides of the channel), cardinal (N/E/S/W) for hazard avoidance, safe water (red-and-white stripes), special-purpose (yellow).
• Tidal data: reference-port tables, tidal diamonds with current direction and speed by hour.

Dead reckoning (DR)

Dead reckoning — finding the vessel’s position from a known course, speed and time. The formula is simple: distance = speed × time. At one knot (1 kt = 1 nautical mile per hour) the vessel covers one minute of latitude per hour.

Process: from a known point (fix) lay off the course in degrees, then the distance run, getting a DR position. Symbols: fix — circle with a dot and time, DR — half-circle with the time, EP (with set/drift) — triangle.

When there is wind or current, DR is corrected with a vector triangle:

• Vector of true course through the water (HDG + STW).
• Current vector (set and drift — direction and speed).
• Resultant vector — track over the ground (COG + SOG).

When planning a passage you often solve the inverse problem: what course to steer so that with a known current you arrive at the intended point. You draw the triangle: current vector + the unknown course-through-water side + the desired track side.

True, magnetic and compass course

Three courses to distinguish:

• True course (T): relative to the true meridian (toward the geographic north pole).
• Magnetic course (M): relative to the magnetic pole. Differs from true by the magnetic variation marked on the chart’s rose.
• Compass course (C): what the magnetic compass shows on board. Differs from magnetic by deviation — distortion from metal and electrical objects on the boat.

Conversion: T = C + deviation + variation (east corrections positive, west negative).

A typical exam task: a true course of 120° is plotted on the chart, variation 5°W, deviation on this course 2°E. What compass course do you steer? C = T − deviation − variation = 120 − 2 − (−5) = 120 − 2 + 5 = 123°.

The deviation table is taken during deviation work: the vessel is swung every 30° and the compass is compared against a known true heading.

GPS and its limits

GPS (Global Positioning System) gives a position with 3–10 m accuracy under normal conditions, but it does not replace traditional navigation. A good skipper always keeps a parallel DR and can fix position without GPS.

GPS limits:

• The receiver can fail or lose signal (clouds don’t matter, but the hull, tunnels and tall obstructions do).
• The chart datum may differ from WGS-84 (on older charts); if it does, the GPS point will be off by hundreds of metres.
• Spoofing and deliberate jamming in some regions — a real threat.
• GPS knows nothing about shoals, currents and weather — only coordinates.

Best practice: every 30–60 minutes mark a fix on a paper chart, run DR, compare with GPS. If the discrepancy exceeds 0.5 nm — check the datum and the variation. Never rely on electronics alone near the coast.