Advanced Chart Plotting & Navigation

NOAA Paper Charts vs. Electronic Charts

NOAA produces two primary chart products used by licensed mariners. Paper charts (RNC — Raster Nautical Charts) are scanned images of the traditional printed chart. They carry all the information tested on the USCG exam: depth soundings, contours, aids to navigation, hazards, anchorages, magnetic variation, and chart symbols defined in NOAA Chart No. 1.

Electronic Navigational Charts (ENC) are vector-based digital charts used by Electronic Chart Display and Information Systems (ECDIS). ENCs allow layers of information to be turned on or off, support automatic depth alarms, and integrate GPS. However, the USCG exam is conducted on paper (or equivalent raster) charts — you must be able to extract all information manually.

For the exam, NOAA Training Chart 1210Tr (Narragansett Bay area) is the most commonly used chart. Know how to read its legend, identify depths in fathoms vs. feet, and locate variation from the compass roses.

Chart Scale: Large Scale vs. Small Scale

Chart scale is expressed as a ratio: 1:80,000 means one unit on the chart equals 80,000 units on the earth. A large-scale chart (small ratio denominator, e.g., 1:10,000) shows a small geographic area in great detail — used for harbors, anchorages, and approach channels. A small-scale chart (large ratio denominator, e.g., 1:1,200,000) covers vast ocean areas with less detail — used for offshore passage planning.

Mercator Projection

Most nautical charts use the Mercator projection, which maps the spherical earth onto a cylinder aligned with the equator. When unrolled, the result is a flat chart where:

• Lines of latitude (parallels) run perfectly horizontal
• Lines of longitude (meridians) run perfectly vertical and parallel to each other
• Rhumb lines (constant compass course) appear as straight lines — crucial for navigation
• Scale increases toward the poles (Greenland appears enormous)
• Great circle routes appear as curved lines (except along the equator or meridians)

The Lambert conformal conic projection is used for some aeronautical charts and for charts covering wide bands of latitude (e.g., NOAA charts of Alaska). On Lambert charts, great circle routes appear nearly as straight lines, which is useful for long-distance passage planning, but rhumb lines are curved. For the USCG captain's exam, Mercator is the primary projection tested.

Chart Symbols and NOAA Chart No. 1

NOAA Chart No. 1 is the official reference for all symbols, abbreviations, and terms used on U.S. nautical charts. It is organized into sections: general (A), topography (C), hydrography (I), depths (I-J), nature of the seabed (J), rocks, wrecks, and obstructions (K), offshore platforms (L), tracks and routes (M), areas, limits (N), hydrographic instruments (O), lights (P), buoys and beacons (Q-S), radio, radar, and electronic position fixing (T), services (U), small craft facilities (V), and tides/currents (H).

For the exam, memorize the most commonly tested symbols: the anchor (anchorage), the wreck symbol (sunken obstruction), rock awash (asterisk with dot), the various buoy shapes (can, nun, spherical), the lighthouse symbol (purple flash), depth figures in fathoms vs. feet, and the dotted vs. dashed depth contour lines.

Reading Latitude and Longitude

Latitude is measured north or south of the equator from 0 to 90 degrees. On a Mercator chart, latitude lines run horizontally across the chart. The latitude scale is on the left and right borders of the chart. Each degree is divided into 60 minutes (denoted by a prime: '), and minutes are divided into tenths or seconds.

Longitude is measured east or west of the Prime Meridian (Greenwich) from 0 to 180 degrees. On a Mercator chart, longitude lines run vertically. The longitude scale appears on the top and bottom borders. Because meridians converge toward the poles on the globe (but are parallel on a Mercator chart), the longitude scale cannot be used to measure distance — only the latitude scale can.

Measuring Distance on a Nautical Chart

One minute of latitude = one nautical mile (nm). This is the fundamental relationship that makes the latitude scale the chart's distance ruler.

1. Use a pair of dividers to span the distance to be measured on the chart.
2. Transfer the dividers to the latitude scale on the side margin, aligning with the latitude nearest to the area being measured (not the top or bottom of the chart, which may be at a different latitude).
3. Count the minutes spanned — each minute equals one nautical mile.
4. For long distances, step the dividers along the route in shorter segments and sum the results.

Never measure distance using the longitude scale — longitude minutes do not equal nautical miles except at the equator. This is one of the most common mistakes on the exam.

Compass Rose and Chart Variation

Every nautical chart contains at least one compass rose — two concentric graduated circles. The outer ring is referenced to True North (geographic North Pole). The inner ring is referenced to Magnetic North and is rotated by the local magnetic variation.

Variation is stated in the center of the compass rose (e.g., "Var 14° 30' W (2020) Annual decrease 8'"). This means in 2020, variation was 14° 30' West — magnetic north is 14° 30' west of true north. The annual change allows you to update variation to the current year.

The TVMDC Framework

The five bearing types, arranged left (chart) to right (helm):

• True (T) — referenced to geographic North Pole; used for plotting on charts
• Variation (V) — angular difference between true and magnetic north at a given location; read from chart compass rose; changes by location and slowly over time
• Magnetic (M) — referenced to magnetic north; after applying variation to True
• Deviation (D) — error caused by the vessel's own magnetic field (engine, electrical wiring, metal); varies by compass heading; found on the vessel's deviation card
• Compass (C) — the actual reading on the vessel's compass; what the helmsman steers

Correcting: True to Compass

Use this when you know the course to steer from the chart (True) and need to tell the helmsman what compass heading to steer (Compass).

Rule: West errors ADD going T to C. East errors SUBTRACT going T to C.

Uncorrecting: Compass to True

Use this when you take a bearing with a handheld compass (Compass bearing) and need to plot it on the chart (True bearing).

Rule: West errors SUBTRACT going C to T. East errors ADD going C to T.

Course Over Ground vs. Course Through Water

Course Through Water (CTW), also called heading or course steered, is the direction the vessel's bow points relative to the water mass — what the helmsman steers. It is affected by leeway but not by current, because current moves the entire water mass.

Course Over Ground (COG) is the actual path the vessel traces across the chart, accounting for both its motion through the water and the movement of the water itself (current). COG is what GPS displays. The difference between COG and CTW is caused by current (set and drift) and leeway. On a vector triangle, CTW + current vector = COG.

Set and Drift Defined

Set is the direction the current flows toward, expressed as a true bearing (e.g., Set 270T means the current is pushing the vessel westward). This is counterintuitive compared to wind naming conventions — a northerly wind blows from the north, but a northerly current sets toward the north.

Drift is the speed of the current in knots. Together, set and drift define the current vector that must be vectored into the course triangle to find COG and SOG, or to determine the course through the water (CTW) needed to make good a desired track.

Constructing the Current Triangle

The current vector triangle has three sides, each representing a vector. The three vectors sum to zero (i.e., they form a closed triangle):

1. Water track (CTW and boat speed) — the vessel's motion through the water
2. Current vector (set and drift) — the water's motion over the ground
3. Ground track (COG and SOG) — the vessel's actual motion over the ground

Finding Course to Steer (CTW) to Make Good a Track

This is the reverse problem: you know the desired ground track (COG) and the current (set/drift), and must find the course through the water (CTW) to steer so that after the current acts, the vessel actually tracks along the desired line.

Dead Reckoning (DR)

Dead reckoning calculates position using only the last known fix, course steered, and speed through the water — no correction for current or leeway. Despite its name (likely derived from "deduced reckoning," abbreviated ded. reckoning), it is a reliable baseline for position tracking when carefully maintained.

DR rules:

• Plot a new DR every hour, at every course change, and at every speed change.
• DR is plotted on the course line as a half-circle labeled with time (e.g., 1430).
• The DR track runs from the last known fix along the heading at speed-through-water.
• Label the course line with C (course in degrees T) and S (speed in knots).
• DR error accumulates with time and distance — take fixes whenever possible to reset.

Estimated Position (EP)

An Estimated Position starts from the DR position and applies all known errors: current (set and drift) and leeway. It is a better approximation than DR and is plotted as a square on the chart.

Advancing a DR / Running Fix

A running fix uses two LOPs taken at different times. The first LOP is "advanced" along the ship's track to the time of the second LOP. Where the advanced LOP crosses the second LOP is the running fix.

1. Take bearing on object A at time T1 — plot LOP1.
2. Note course and speed. Run the vessel until the bearing on object A (or a second object B) changes significantly.
3. At time T2, take second bearing — plot LOP2.
4. Calculate distance run: D = S × (T2 - T1).
5. Move LOP1 parallel to itself in the direction of travel by the distance run — this is the "advanced LOP."
6. Where advanced LOP1 crosses LOP2 = running fix at T2. Mark with circle, label "R Fix T2."

Fix by Two Bearings (Cross Bearing Fix)

This is the most common fix method on the USCG exam. Two (or three) charted objects are observed simultaneously (or near-simultaneously) with a hand bearing compass.

1. Identify two charted objects (buoys, lighthouses, towers, headlands) that can be clearly seen.
2. Take a magnetic bearing to each object with a hand bearing compass.
3. Convert each bearing: Compass → Magnetic → True using TVMDC (deviation of the hand bearing compass is often zero or small).
4. On the chart, draw a line from each object in the direction of the reciprocal bearing (bearing + 180° or - 180°) — this is the line of position (LOP).
5. The intersection of the two LOPs is the fix. Mark it with a circle and dot, labeled with time.
6. If using three bearings, the small triangle formed (cocked hat) indicates accuracy — fix is at the center or, for safety, at the vertex closest to danger.

Fix by Bearing and Depth (Sounding)

When only one charted object is visible, a single LOP combined with a depth sounding can establish a fix — if the chart shows a distinctive depth contour in the area.

1. Take a bearing on the one visible charted object — draw the LOP on the chart.
2. Take a sounding with the depth sounder. Correct raw reading: subtract transducer depth (the instrument offset) to get actual depth.
3. Correct for tide: Actual depth at charted datum = (sounder reading + transducer offset) - tide height above MLLW.
4. Identify where the corrected depth contour line intersects the LOP — that is the fix.
5. This fix is less reliable than a two-bearing fix; use it only when no second object is available.

Leeway and Its Effect on Position

Leeway is the angular difference between the vessel's heading (course steered) and the vessel's actual direction of motion through the water. Wind from the port side pushes the vessel to starboard — leeway is measured as degrees to leeward (downwind side).

Tide Correction for Depth

Nautical chart depths are referenced to Mean Lower Low Water (MLLW) — the average of the lower of the two daily low tides. Tide heights from tide tables are heights above (or below, for minus tides) this datum.

Problem Type 1 — Complete TVMDC Conversion

Problem Type 2 — DR then EP with Current

Problem Type 3 — Course to Steer Through Current

Problem Type 4 — Tide-Corrected Depth for Safe Passage