Chart Navigation & Plotting

Mercator projection:

The standard nautical chart projection. Meridians are parallel vertical lines and parallels of latitude are horizontal lines spaced increasingly far apart toward the poles. The key navigational advantage: a rhumb line (a course of constant compass direction) plots as a straight line. The cost: area and distance are distorted with latitude, so you must measure distance only on the latitude scale at the side of the chart, abreast of your position.

Why you measure distance on the latitude scale:

One minute of latitude equals one nautical mile, everywhere. Because Mercator stretches the latitude scale toward the poles, you read distance from the side (latitude) scale at the same latitude as your work — never from the top or bottom (longitude) scale, where one minute of longitude is less than a mile except at the equator.

Gnomonic projection:

Used for great-circle sailing charts. A great circle plots as a straight line on a gnomonic chart, so the navigator draws the shortest route as a straight line, then transfers points to a Mercator chart to steer by rhumb-line legs.

Chart scale:

Scale is the ratio of chart distance to real distance (e.g., 1:40,000). A LARGE-scale chart (small number, e.g., 1:20,000) shows a SMALL area in great detail — used for harbors. A SMALL-scale chart (large number, e.g., 1:1,200,000) shows a LARGE area with little detail — used for ocean passages. "Large scale, large detail" is the memory aid.

Soundings and datum:

Charted depths (soundings) are given relative to a sounding datum — in U.S. waters, Mean Lower Low Water (MLLW), an average of the lower of each day's two low tides. Charted heights (bridges, lights) are usually referenced to Mean High Water (MHW). The chart's title block states the units (feet, fathoms, or meters) and the datum — always check it.

The 60 D Street formula:

D = S × T, where Distance is in nautical miles, Speed in knots, and Time in HOURS. Rearranged: S = D ÷ T and T = D ÷ S. Because time is usually given in minutes, navigators use the "60" forms: - Distance (NM) = Speed × Minutes ÷ 60 - Speed (kt) = 60 × Distance ÷ Minutes - Time (min) = 60 × Distance ÷ Speed The mnemonic "60 D Street" arranges 60, D (distance), S (speed), T (time) so you can solve for any one.

Worked example:

You make good 12 knots and must cover 9 nautical miles. Time = 60 × 9 ÷ 12 = 45 minutes. Conversely, if you run 9 NM in 45 minutes, Speed = 60 × 9 ÷ 45 = 12 knots.

Speed made good vs. speed through the water:

Speed through the water is what the log/engines produce; speed made good (SMG) is the speed actually achieved over the ground after current and steering error. In current problems you solve for the speed and course made good, which differ from the ordered speed and heading.

Distance to the horizon:

Distance to the visible horizon in nautical miles ≈ 1.17 × √(height of eye in feet). A related exam item is computing the geographic range a light becomes visible by combining the observer's horizon distance and the light's horizon distance from its charted height.

The three norths:

- True north — the direction of the geographic pole; what you plot against on the chart. - Magnetic north — where a compass needle would point with no nearby iron; differs from true by VARIATION. - Compass north — where the actual ship's compass points, after the ship's own magnetic fields add DEVIATION.

Variation:

The angular difference between true and magnetic north at a location, caused by the earth's magnetic field. It is printed inside the compass rose on the chart, with its annual rate of change, and depends only on geographic location — not on the ship's heading.

Deviation:

The error the ship's own iron and electrical fields induce in the compass. Deviation changes with the ship's HEADING (not location) and is read from the vessel's deviation table/card.

TVMDC — the conversion ladder:

True → Variation → Magnetic → Deviation → Compass. Going DOWN the ladder (true to compass) you ADD westerly errors. Going UP (compass to true) you ADD easterly errors. The classic mnemonics: "True Virgins Make Dull Companions — Add Whiskey" (add West going down) and "Can Dead Men Vote Twice — At Elections" (correcting compass to true, add East).

Worked example (true to compass):

True course 090°, Variation 10°W, Deviation 4°W. Magnetic = 090 + 10 = 100°. Compass = 100 + 4 = 104°. (West errors added when going from true down to compass.)

Parallel rulers and the compass rose:

To plot a course, align the parallel rulers (or a course plotter) with the desired direction at the compass rose, then "walk" them across the chart to the point of origin and draw the line. The compass rose has an outer true ring and an inner magnetic ring — use the ring that matches the direction you are plotting.

Dividers:

Dividers measure distance. Set them to a span on the latitude (side) scale, then step off that distance along the course line — or set them to the distance between two points and read the span against the latitude scale.

Standard line labels:

- A course line is labeled with the course ABOVE the line (e.g., "C 090 T" for true) and speed BELOW the line (e.g., "S 12"). - A direction is always three digits (045°, not 45°) and tagged T (true), M (magnetic), or psc (per standard compass).

Standard position labels:

- A FIX (a position from two or more crossing LOPs or GPS) is marked with a circle and labeled with the time (e.g., "1200"). - A DEAD RECKONING position is marked with a half-circle/dot and labeled with the time in a slanted style. - An ESTIMATED POSITION (DR corrected by a single LOP) is marked with a square.

Time labeling:

Times are written in four-digit 24-hour format. Consistent labels are scored on license exams and let a relief navigator instantly understand the plot.

The DR plot:

From the last fix, draw the course line in the direction being steered and step off distance along it using speed and elapsed time. Each plotted DR position assumes no current, no leeway, and perfect steering.

When to plot a DR position (the six rules):

By traditional practice you advance the DR: at every course change, at every speed change, every hour on the hour, at the time of every fix, at the time of a single LOP, and when obtaining a running fix. Knowing these "rules of DR plotting" is a common exam item.

What DR ignores:

DR accounts only for course and speed through the water. It deliberately ignores current, wind leeway, and steering error — which is precisely why an actual fix usually falls off the DR track. The offset between the DR and the fix reveals the set and drift of the current.

Leeway:

The downwind sideways drift a vessel makes due to wind on the hull and rigging. It is applied as a correction to the course made good, separate from current set.

Estimated position (EP):

When you have only a single LOP (not enough for a full fix), you advance the DR and drop a perpendicular from the DR position to the LOP; the foot of that perpendicular is the estimated position, marked with a square. It is the best single-LOP estimate of where you actually are.

Line of position (LOP):

A line somewhere along which the vessel must be — for example a visual bearing to a charted object, a radar range arc, or a depth contour. A single LOP narrows your position to a line; it cannot give a point alone.

Fix from crossing LOPs:

Two LOPs that cross give a fix at their intersection. THREE LOPs are preferred: if they form a small triangle ("cocked hat"), the size of the triangle indicates the quality of the fix; a large triangle warns of a bad bearing or an error in identifying the object. Choose objects whose LOPs cross near 90° (or for three, spread ~60° apart) for the strongest fix.

Bearings — relative vs. true:

A relative bearing is measured from the ship's head (000° relative = dead ahead). To plot it you convert to true: True bearing = true heading + relative bearing (then reduce by 360 if over 360). Always plot LOPs as true bearings on the chart.

Running fix:

When only one object is available, take a bearing, run a known course and distance, then take a second bearing on the same object. Advance the FIRST LOP forward along the DR by the distance run between the two bearings; where the advanced first LOP crosses the second LOP is the running fix (labeled "R FIX"). It assumes the DR (course and distance) between bearings is accurate.

Special-angle running fixes:

The "bow and beam" bearings (45° relative then 90°/abeam) and "doubling the angle on the bow" give the distance off without trigonometry: when the relative bearing doubles, the distance run equals the distance off at the second bearing. These shortcuts are common exam questions.

Definitions:

- SET is the DIRECTION toward which the current flows, in degrees true. (Note: current is named for where it flows TO — opposite the convention for wind, which is named for where it comes FROM.) - DRIFT is the SPEED of the current, in knots.

Finding set and drift:

Plot the DR position and the fix for the same time. The vector FROM the DR position TO the fix is the current: its direction is the set, and its length divided by the elapsed time is the drift. The current pushed you from where you "should" be (DR) to where you actually are (fix).

The current triangle:

Three vectors: the vessel's course and speed through the water (heading/log speed), the current (set and drift), and the resulting course and speed made good (track over the ground). Given any two, you solve the third graphically by completing the triangle.

Steering to offset a current:

To make good a desired track through a known current, lay off the desired track, construct the current vector, and find the heading that — combined with the current — puts the resultant on the intended track. The angle you steer up-current of the track is the "drift angle" or current correction.

Course and speed made good:

The resultant vector's direction is the course made good (COG); its length over the elapsed time is the speed made good (SMG). These are what you actually achieve, and they differ from ordered course and speed whenever current acts.

Tide vs. tidal current:

Tide is the vertical movement of the water level; tidal current is the horizontal flow caused by that rise and fall. High water does not generally coincide with slack current — there is usually a lag.

Datums:

Charted depths are referenced to a sounding datum (U.S.: Mean Lower Low Water, MLLW). To get actual water depth, ADD the predicted height of tide to the charted sounding. Charted vertical clearances (bridges, overhead cables) are referenced to Mean High Water (MHW); at any tide below MHW you have MORE clearance than charted.

Height of tide and the rule of twelfths:

Between low and high water, the rule of twelfths estimates how much the tide has risen: in the six hours of a semidiurnal cycle, the tide rises 1/12 of the range in the first hour, 2/12 in the second, 3/12 in the third and fourth, then 2/12 and 1/12. It approximates the sinusoidal rise for quick mental estimates between table reference times.

Spring and neap tides:

Spring tides (largest range) occur near the new and full moon, when sun and moon align. Neap tides (smallest range) occur near the quarter moons, when sun and moon are at right angles. Spring/neap has nothing to do with the season.

Slack and current strength:

Tidal current tables give the times of slack water (zero current) and the times and velocities of maximum flood and ebb. Flood sets toward shore/upstream; ebb sets seaward/downstream. Plan transits of narrow passages for slack or fair (favorable) current.

Red, right, returning:

When returning from seaward (entering a harbor or going upstream), keep RED marks on your starboard (right) side and GREEN marks on your port side. Red marks are even-numbered nuns (cone-topped) and red lights; green marks are odd-numbered cans (flat-topped) and green lights. Region A (most of the rest of the world) is the reverse — red to port returning.

Lateral marks:

- Red nun buoys / red "TR" daybeacons — starboard side returning, even numbers. - Green can buoys / green square daybeacons — port side returning, odd numbers. - Numbers increase as you go upstream/inbound.

Preferred-channel (junction) marks:

Horizontally banded red-and-green buoys mark a channel junction. The color of the TOP band shows the preferred channel: top red = primary channel to starboard (treat as a red mark, keep to starboard returning); top green = preferred channel to port.

Safe-water and isolated-danger marks:

- Safe-water marks: red-and-white VERTICAL stripes, spherical or with a red topmark — marks a fairway/midchannel, safe water all around; pass on either side. - Isolated-danger marks: black with red band(s), two black ball topmarks — stationed over a danger with navigable water around it.

Special and information marks:

Yellow marks indicate special areas (anchorages, dredging, traffic separation, military). They carry no lateral meaning.

Light characteristics:

Lights are described by color, rhythm, and period (e.g., "Fl R 4s" = flashing red every 4 seconds). The Light List and the chart give the full characteristic, height, and nominal range. Quick-flashing lights often mark points of greatest navigational interest.