OUPV & Master Exam — Navigation & Plotting

Navigation and Plotting: USCG Captain's License Exam Guide

Dead reckoning, the TVMDC compass correction formula, course plotting, position fixing, speed-time-distance, and chart tools — everything tested on the USCG OUPV and Master navigation exam.

Compass Types: Magnetic, Gyro, and GPS

The USCG exam tests your knowledge of each compass type — what north it reads, what errors it has, and when you use it.

Magnetic Compass

Exam Primary

Points To

Magnetic North

Errors

Variation + Deviation

Power

No power required

  • Subject to variation (geographic) and deviation (vessel-caused)
  • Must apply TVMDC formula to get true course
  • Deviation card specific to each vessel and heading
  • Works globally without power

Gyrocompass

Points To

True North

Errors

Gyro error (small, noted in log)

Power

Requires electricity

  • Reads true north — no variation or deviation to apply
  • Must be running for hours before it stabilizes
  • Fails if power is lost
  • Very accurate for commercial navigation

GPS Heading Sensor

Points To

True North

Errors

Satellite error (minimal)

Power

Requires electricity + satellite signal

  • Computes true heading from satellite positions
  • Requires movement to determine heading on some units
  • Dual-antenna systems provide accurate heading at rest
  • Integrated with chartplotters

The TVMDC Formula — Compass Correction

TVMDC is the spine of all USCG navigation problems. It converts between True, Magnetic, and Compass headings by applying Variation and Deviation in the correct sequence.

T  ·  V  ·  M  ·  D  ·  C

True  ·  Virgins  ·  Make  ·  Dull  ·  Companions

True → Compass (chart to helm)

Going right (T→C): subtract East, add West

“Cadets Are East” — C to T, Add East

Compass → True (bearing to chart)

Going left (C→T): add East, subtract West

Remember: apply each correction in reverse as you move left

Worked Examples

T → C

True → Compass (steering from a chart course)

Given: True Course: 090°T, Variation: 15°W, Deviation: 5°E

  1. 1Start with True course: 090°
  2. 2Apply Variation (15°W): West = Add → 090° + 15° = 105°M
  3. 3Apply Deviation (5°E): East = Subtract → 105° − 5° = 100°C

Answer: Steer 100° by compass

C → T

Compass → True (plotting a bearing from compass reading)

Given: Compass Bearing: 245°C, Deviation: 3°W, Variation: 10°E

  1. 1Start with Compass: 245°
  2. 2Apply Deviation (3°W): West = Subtract → 245° − 3° = 242°M
  3. 3Apply Variation (10°E): East = Add → 242° + 10° = 252°T

Answer: Plot 252° True on the chart

Variation

  • Difference between true north and magnetic north
  • Caused by Earth's magnetic field — varies by location
  • Found on the chart compass rose (inner and outer rings)
  • Changes slowly — annual change printed on the chart
  • Same for all vessels at the same location

Deviation

  • Error from the vessel's own magnetic field (metal, engines, electronics)
  • Different for each vessel — recorded on a deviation card
  • Changes with the vessel's heading
  • Determined by swinging the compass (comparing to a known bearing)
  • Can be reduced by a compass adjuster, but never fully eliminated

Dead Reckoning (DR)

Dead reckoning is the backbone of basic navigation — calculating where you are based on where you started, how fast you went, and in what direction. USCG exam problems test the formula directly.

Speed — Time — Distance

D = S × T

Distance (NM) = Speed (kts) × Time (hrs)

S = D ÷ T

Speed (kts) = Distance (NM) ÷ Time (hrs)

T = D ÷ S

Time (hrs) = Distance (NM) ÷ Speed (kts)

Critical: Time must be in decimal hours. Convert minutes by dividing by 60. Example: 45 min = 0.75 hrs. 30 min = 0.5 hrs.

How to Plot a DR Position

1

Start from a known position (fix, departure point, or buoy)

Label with time and a circle: ① 0800

2

Draw the course line in the direction of travel (true course)

Use parallel rulers aligned with the compass rose to lay down the correct bearing

3

Calculate distance: D = Speed × Time elapsed

Convert time to decimal hours. Use dividers to measure distance on the latitude scale (1 min lat = 1 NM)

4

Mark the DR position along the course line at that distance

Label with a triangle and time: △ 1030

5

Note: DR does not account for current, leeway, or steering error

A DR is your best estimate — update with a fix whenever a landmark or GPS allows

Worked Exam Problems

A vessel leaves a buoy at 0800 steering 135°T at 8 knots. What is the DR position at 1030?

Time elapsed: 2 hrs 30 min = 2.5 hrs. Distance = 8 × 2.5 = 20 NM. Plot 20 NM along 135°T from the buoy.

Answer: 20 nautical miles along 135°T

You need to travel 15 nautical miles. Your speed is 10 knots. How long will the passage take?

Time = Distance ÷ Speed = 15 ÷ 10 = 1.5 hours = 1 hour 30 minutes.

Answer: 1 hour 30 minutes

A vessel travels for 45 minutes and covers 6 nautical miles. What is the vessel's speed?

Convert time: 45 min = 0.75 hrs. Speed = Distance ÷ Time = 6 ÷ 0.75 = 8 knots.

Answer: 8 knots

A vessel steers 270°C. Deviation is 4°W. Variation is 12°W. What is the true course?

C → M: apply Deviation (4°W, subtract West) → 270° − 4° = 266°M. M → T: apply Variation (12°W, subtract West) → 266° − 12° = 254°T.

Answer: 254° True

Position Fixing Methods

A fix is a confirmed position from two or more independent sources. A running fix uses time and motion between bearings. Know when to use each method and how to label each on the chart.

Cross Bearing Fix

Most Common

Two or more simultaneous bearings of different charted objects

Accuracy

Excellent

Requires

Two or more visible landmarks or aids

  1. 1Take bearings of two different charted objects as simultaneously as possible
  2. 2Convert each bearing to true (apply deviation, then variation)
  3. 3Plot each LOP on the chart — a line from the object at the bearing angle
  4. 4The intersection is your fix — label with time and a circle
  5. 5Ideal crossing angle: 90° (minimum: 30°)

Running Fix

Two bearings of the same object taken at different times

Accuracy

Moderate (depends on DR accuracy between bearings)

Requires

One visible landmark, known course and speed

  1. 1Take first bearing, plot first LOP, note time
  2. 2Continue on course at known speed
  3. 3Take second bearing of same object, note time
  4. 4Calculate distance traveled between bearings (D = S × T)
  5. 5Advance (move) first LOP along course line by distance traveled
  6. 6Intersection of advanced LOP and second LOP = running fix

GPS Fix

Latitude and longitude directly from GPS receiver

Accuracy

Excellent (within ~3–5 meters for civilian GPS)

Requires

GPS receiver with satellite signal

  1. 1Read latitude and longitude from GPS display
  2. 2Find position on chart using latitude scale (left/right margin) and longitude scale (top/bottom margin)
  3. 3Plot the intersection of the lat/lon lines
  4. 4Label with time and a circle
  5. 5Cross-check against visual landmarks periodically

Four-Point Bearing (Bow-and-Beam)

Special running fix using 45° and 90° bearings of one object

Accuracy

Good — simple mental calculation

Requires

One visible landmark, constant course

  1. 1Note when a landmark bears 45° off the bow (4 points); record time
  2. 2When same landmark bears 90° off the bow (beam); record time
  3. 3Distance run between the two bearings = distance off when abeam
  4. 4No plotting required — pure arithmetic from speed × time

Course Made Good vs. Course to Steer

Course Made Good (CMG)

The actual path the vessel travels over the ground, accounting for the combined effect of steering, current, and leeway. CMG is what you see on the GPS track — the ground track. This is what appears on the chart as the intended track line from departure to destination.

  • The track you need to make good to reach your destination
  • Plotted on the chart as a straight line between waypoints
  • Affected by set (current direction) and drift (current speed)

Course to Steer (CTS)

The compass heading the helmsman steers through the waterto achieve the desired CMG, after correcting for compass errors (TVMDC), current, and leeway. CTS differs from CMG whenever a current or wind pushes the vessel off course.

  • Corrected for variation and deviation (TVMDC formula)
  • Offset from CMG to counteract current
  • Solved using the vector (current) triangle on the chart

The Current (Vector) Triangle

Vector A — Water Track

The vessel's speed and direction through the water (course to steer and speed through water). This is what the vessel is actually doing through the water.

Vector B — Current

The current's set (direction it flows toward) and drift (speed in knots). This vector is added to the water track vector.

Vector C — Ground Track

The resultant vector — the vessel's actual course and speed made good over the ground. This is the CMG and speed made good (SMG).

Chart Plotting Tools

The USCG exam chart plotting section requires you to use these tools correctly and quickly. Know each tool's purpose and technique before exam day.

Parallel Rulers

Transfer course lines to and from the compass rose

Walk the rulers across the chart by alternating each ruler in small steps. Align one edge with your course line, then walk to the nearest compass rose. Read the inner (magnetic) or outer (true) ring.

Exam Tip: Most common plotting tool on the USCG exam. Practice walking without slipping.

Course Plotter (Weems & Plath / Portland)

Measure and plot courses directly against chart meridians

Align the plotter's grid lines with a vertical meridian on the chart, then read the course on the protractor scale. More stable than parallel rulers on small or moving vessels.

Exam Tip: Faster to use than parallel rulers for many people. Know your preferred tool before the exam.

Dividers

Measure distance on the chart

Set the dividers to span the distance along your course line. Transfer to the latitude scale on the left or right margin — each minute of latitude = 1 nautical mile. Never use the longitude scale.

Exam Tip: The latitude scale is the only correct scale for distance measurement.

Pencil (Sharp)

Plot lines, mark positions, label fixes

Use light, thin lines — heavy lines obscure chart detail. Label each fix with the time (e.g., '1430') and a circle. Label DR positions with a triangle and time.

Exam Tip: Keep lines thin and label everything. Exam graders check your work step by step.

Latitude and Longitude on Charts

Reading Latitude

  • Measured North or South of the equator
  • Read on the left and right (vertical) margins of the chart
  • 1 degree = 60 nautical miles (always true)
  • 1 minute of latitude = 1 nautical mile
  • Use the latitude scale — not the longitude scale — for measuring distance
  • Use dividers set against the latitude scale at the same latitude as your course

Reading Longitude

  • Measured East or West of the Prime Meridian (Greenwich)
  • Read on the top and bottom (horizontal) margins of the chart
  • Longitude minutes get shorter as latitude increases — never use for distance
  • Used only for identifying E-W position — not for measurement

Plotting a Position from Lat/Lon

  1. 1Find the latitude value on the left or right margin. Draw or trace a faint horizontal line across the chart at that latitude.
  2. 2Find the longitude value on the top or bottom margin. Draw or trace a faint vertical line down the chart at that longitude.
  3. 3The intersection of the two lines is your position. Mark with a dot and a circle, labeled with the time.
  4. 4Cross-check: does the position make visual sense relative to nearby landmarks, depth contours, and your last known position?
Chart notation: Fixes are labeled with a circle and time (e.g., ⊙ 1430). DR positions are labeled with a triangle and time (e.g., △ 1500). Running fixes use a half-circle with an advance arrow.

Quick Reference — Exam Formulas and Rules

TopicRule / FormulaNotes
DistanceD = S × TTime in decimal hours. D in NM, S in knots.
SpeedS = D ÷ TKnow two values to find the third.
TimeT = D ÷ SConvert answer from decimal to hrs/min (×60).
True → MagneticApply Variation: East = subtract, West = addVariation from chart compass rose.
Magnetic → CompassApply Deviation: East = subtract, West = addDeviation from vessel deviation card.
Compass → TrueReverse: add East, subtract West (both errors)CDMVT — start at C, add East errors.
Distance measurementUse latitude scale only (left/right margin)1 minute latitude = 1 NM everywhere on Earth.
Fix labelCircle + time (⊙ 1430)Two or more simultaneous LOPs.
DR labelTriangle + time (△ 1500)Calculated from speed, course, time only.
Ideal crossing angle90° between LOPs (minimum 30°)Small angles produce large position error.
Running fixAdvance first LOP by distance runAccuracy depends on DR accuracy between sights.

Navigation Exam Tips

Convert minutes to decimal hours first

Every time problem on the exam requires decimal hours. Before doing any math, convert minutes by dividing by 60. Write it down — don't try to carry it in your head.

East is least, West is best (for True to Compass)

When converting True to Compass (going right in TVMDC): East errors are subtracted, West errors are added. Flip it going from Compass to True. The phrase 'East is least, West is best' means East = subtract going T→C.

Always use the latitude scale for distance

One minute of latitude equals one nautical mile everywhere on the chart. The longitude scale is shorter at higher latitudes and must never be used to measure distance.

Label everything as you plot

On the chart plotting exam, label each fix with a circle and time, each DR position with a triangle and time, and each course line with the course over the line. Unlabeled plots lose points.

Cross LOPs at 90° for the best fix

When choosing which objects to use for a cross bearing fix, pick objects that give LOPs crossing near 90°. Small crossing angles (less than 30°) produce large position errors — a small bearing error creates a large position error when lines are nearly parallel.

DR does not account for current or leeway

Exam questions frequently ask what a DR position is, then separately ask where the vessel actually is (the estimated position, accounting for current). Know the difference: DR = course and speed only; EP = DR corrected for current and leeway.

Frequently Asked Questions

What is the TVMDC rule and how is it used on the USCG exam?

TVMDC stands for True — Variation — Magnetic — Deviation — Compass. It is the sequence used to convert between true and compass headings. The mnemonic 'True Virgins Make Dull Companions' (or 'Timid Virgins Make Dull Companions') helps remember the order. To convert True to Compass: subtract East errors, add West errors (TVMDC going right = subtract East, add West). To convert Compass to True: add East errors, subtract West errors (CDMVT going left = add East, subtract West). Variation is the angular difference between true north and magnetic north (from the chart). Deviation is the error caused by the vessel's own magnetic field (from the deviation card).

What is dead reckoning and how do you calculate a DR position?

Dead reckoning (DR) is the process of calculating your current position based on a known past position, your course steered, speed, and elapsed time. The formula is: Distance = Speed × Time (D = S × T). If you know two of the three values, you can find the third. For example: traveling at 6 knots for 2 hours covers 12 nautical miles. Plot this distance along your course line from the last known position to get your DR position. A DR position does not account for current, leeway, or steering error — it is the position you would be at if all conditions were perfect.

What is the difference between variation and deviation?

Variation is the angular difference between true north (geographic North Pole) and magnetic north (where the compass needle actually points). Variation is caused by Earth's magnetic field and is shown on nautical charts in the compass rose — it changes with location and changes slowly over time (the annual change is printed on the chart). Deviation is the error in a magnetic compass caused by the vessel's own metal, engines, electrical systems, and equipment. Deviation changes with the vessel's heading and is recorded on a deviation card specific to that vessel. Both errors must be applied using TVMDC to convert between true and compass courses.

How do you use the speed-time-distance triangle on the USCG exam?

The speed-time-distance (STD) triangle is a memory aid for the three related formulas: Distance = Speed × Time; Speed = Distance ÷ Time; Time = Distance ÷ Speed. On the USCG exam, time is expressed in hours or in minutes converted to hours (divide minutes by 60). All distances are in nautical miles and speeds in knots. Example: a vessel traveling at 8 knots for 45 minutes covers 8 × (45/60) = 8 × 0.75 = 6 nautical miles. Practice converting minutes to decimal hours — it is the most common calculation error on the exam.

What is a running fix and when is it used?

A running fix is a position fix obtained by taking two bearings of the same object at different times, then advancing the first line of position (LOP) along the course and distance traveled to intersect with the second LOP. It is used when only one landmark or navigational aid is visible. The accuracy of a running fix depends on how accurately you know your course made good and speed made good during the interval — any current or leeway error will shift the advanced LOP and introduce error into the fix.

What is the difference between Course to Steer and Course Made Good?

Course to Steer (CTS) is the compass heading the helmsman actually steers, corrected for compass error (using TVMDC). Course Made Good (CMG) is the actual path the vessel travels over the ground, accounting for the effect of current and leeway. To reach a destination in a current, you must steer a course that is offset from the intended track — the CTS will be different from the CMG. The vector triangle (sometimes called the current triangle) is used to solve for CTS given a known current set and drift: draw the intended track, subtract the current vector, and the result is the course to steer through the water.

How do you read latitude and longitude on a nautical chart?

Latitude is measured in degrees North or South of the equator and is read on the left and right margins (vertical sides) of the chart. Longitude is measured in degrees East or West of the Prime Meridian and is read on the top and bottom margins (horizontal sides) of the chart. One degree of latitude always equals 60 nautical miles. One minute of latitude equals one nautical mile — use the latitude scale on the side of the chart (not the longitude scale) to measure distances with dividers. Longitude minutes are shorter near the poles and must not be used for distance measurement.

What chart plotting tools are required for the USCG exam?

The USCG captain's license exam (chart plotting section) requires: parallel rulers or a course plotter (such as a Weems & Plath plotter or Portland plotter) to transfer courses to and from the compass rose; a pair of dividers to measure distances against the latitude scale; a sharp pencil; and the relevant NOAA chart(s). Some exam versions use a plotting sheet instead of a full chart. Know how to walk parallel rulers from a course line to the compass rose and read true course, then apply variation and deviation to get compass course.

What is the difference between a magnetic compass and a gyrocompass?

A magnetic compass points toward magnetic north and is subject to variation (geographic difference between true and magnetic north) and deviation (vessel's own magnetic interference). It requires no power and works everywhere. A gyrocompass is an electrically powered spinning gyroscope that aligns itself with true north — it is not affected by the vessel's magnetic field or by geographic variation, so it reads true north directly. Gyrocompasses are used on larger commercial vessels and are more accurate for navigation. GPS-based heading sensors are a third type — they compute heading from satellite positions and also read true north.

How do you take a bearing and plot a line of position?

To take a visual bearing: use a hand bearing compass or the ship's compass bearing ring to measure the magnetic bearing of a charted landmark or navigational aid. Convert the magnetic bearing to a true bearing by applying variation (add East variation, subtract West variation). On the chart, place the parallel rulers through the center of the compass rose at the true bearing angle, then walk them to the identified landmark. Draw a line from the landmark in the direction back toward your vessel — this is your Line of Position (LOP). Where two or more LOPs cross is a fix. For accuracy, LOPs should cross at angles of 90° ideally, or at least 30° apart.

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