Navigation Instruments · OUPV & Master Exam

Navigation Instruments Study Guide

Master the compass, GPS, radar, AIS, depth sounder, sextant, barometer, and chart plotting tools tested on the USCG OUPV and Master captain's license exam. Detailed explanations, reference tables, and solved practice problems.

13 instrument topicscovered with exam focus
70% requiredon navigation section

What This Guide Covers

Magnetic Compass — variation, deviation, compass adjustment
Gyrocompass — principles, errors, gyro vs magnetic
Hand Bearing Compass — taking bearings, correction
Depth Sounder — transducer, reading soundings, tides
GPS and Chartplotter — HDOP, datum, COG vs heading
Radar — controls, ARPA, relative vs true motion
AIS — Class A vs B, MMSI, limitations
Sextant — parts, index error, altitude corrections
Barometer — types, reading trends, 3-2-1 rule
VHF DF and other nav aids — RDF, LORAN, NAVTEX
Chart Tools — parallel rules, dividers, compass rose
USCG Exam Tips — common mistakes, what to memorize
Practice Problems with Full Solutions

1. Magnetic Compass

The magnetic compass is the oldest and most reliable navigation instrument. Every vessel is required to carry one as a backup to electronic systems. USCG exams test compass error calculation heavily.

Variation and Deviation

Variation

The angle between True North and Magnetic North at a given geographic location. Printed on the chart compass rose. Changes slowly over years (annual change noted on rose). Caused by the Earth's magnetic field; nothing on the vessel causes it.

Example: "Var 14W (2022) annual decrease 8'" means variation was 14 degrees West in 2022, decreasing 8 minutes per year.
Deviation

The error caused by the vessel's own magnetic field — engines, wiring, metal structure, electronics — acting on the compass needle. It changes with the vessel's heading and is unique to each vessel. Recorded in a deviation table after swinging the compass.

Example: On heading 090, deviation may be 3E. On heading 270, deviation may be 3W. Deviation is zero when heading magnetic north or south.

Compass Correction — CDMVT Method

Remember: Can Dead Men Vote Twice (Compass, Deviation, Magnetic, Variation, True). East errors are added; West errors are subtracted when converting Compass to True. Reverse the process (and reverse the sign) when converting True to Compass.

LetterTermWhat It Represents
CCompassWhat the compass reads
DDeviationAdd East (+) or subtract West (-) deviation
MMagneticResult after applying deviation
VVariationAdd East (+) or subtract West (-) variation
TTrueFinal true course or bearing
Worked Example

Compass reads 135. Deviation 4E. Variation 12W. Find true course.

Compass (C)135°
Deviation +4E139° Magnetic
Variation -12W127° True

To convert True back to Compass: reverse the signs. True 127 + 12W variation = 139 Magnetic; 139 - 4E deviation = 135 Compass.

Compass Card and Swinging the Compass

Compass Card

The graduated disc inside the compass bowl that rotates with the magnetic field. On most marine compasses it is graduated in degrees 0-360 or in points (32-point system: N, NNE, NE, ENE, etc.). The card is fixed to the magnetic needle assembly and floats in damping fluid.

Swinging the Compass

The process of comparing compass readings to known magnetic bearings on multiple headings (typically every 15 or 30 degrees around the full circle) to build a deviation table. Done at sea in calm conditions, or at a compass adjustment buoy. A compass adjuster uses compensating magnets to minimize deviation; residual errors go in the deviation table.

Deviation Table

A card posted near the compass listing deviation for each 15 or 30 degree compass heading. Used to find the deviation to apply before correcting for variation. Interpolate between tabulated headings. USCG exams frequently give you a deviation table and ask you to solve a compass correction problem.

Exam Tip:The most common exam mistake is reversing East/West signs when converting True to Compass (the reverse direction). Remember: True to Compass reverses everything — West errors ADD when going True to Compass, East errors SUBTRACT.

2. Gyrocompass

Required on SOLAS vessels. Not required on most recreational or small commercial vessels. Appears on USCG Master exams more than OUPV but basic principles can appear on any exam.

Operating Principle

A gyrocompass uses a rapidly spinning gyroscope (rotor) whose axis aligns with True North by exploiting the Earth's rotation. Unlike a magnetic compass, it points to True North, not Magnetic North — no variation correction is needed. It requires continuous electrical power and takes 1 to 4 hours to settle after startup.

Precession

Gyroscopic precession is the tendency of a spinning gyroscope to respond to an applied force 90 degrees later in the direction of rotation. In a gyrocompass, controlled precession is used to align the spin axis with True North. Uncontrolled precession from mechanical wear causes gyro error that must be monitored and corrected.

Gyrocompass Errors

Speed Error

Caused by the vessel's own motion over the Earth's surface. A vessel traveling east or west introduces a component that causes the gyro to deviate slightly from True North. Error is easterly when heading east and increases with speed. Significant on fast vessels at low latitudes.

Speed Error (minutes) ≈ 0.17 × Speed × sin(latitude) — consult correction tables
Latitude Error

The gyrocompass becomes unreliable at high latitudes (above approximately 75°) because the horizontal component of Earth's rotation — which the gyro uses to align — becomes very small near the poles. Accuracy degrades significantly.

Error increases as latitude increases toward 90°
Ballistic Deflection

A sudden acceleration (course change, speed change) imparts a force on the gyro's pendulous vane system, causing a temporary deflection. The compass will oscillate and then settle. This can cause momentary large errors during sharp turns.

Temporary; settles within minutes under normal conditions

Gyrocompass vs Magnetic Compass

FeatureGyrocompassMagnetic Compass
ReferenceTrue North (geographic)Magnetic North
Error typesSpeed error, latitude error, precessionVariation + deviation
Effect of ship's metalNoneSignificant (deviation)
Accuracy in polar regionsDegrades near polesVery unreliable near poles
Power requirementRequires continuous power; ~1-4 hours to settleNone
BackupMagnetic compass is backupPrimary backup when gyro fails
Typical error0.1 to 0.5 degrees when settledUp to several degrees without compensation
CostExpensive; large ship equipmentLow cost; small vessels standard

3. Hand Bearing Compass

A small, handheld compass used to take bearings of objects on shore or other vessels. Essential for visual fixes. Uses the same variation and deviation corrections as the ship's compass, though deviation is usually smaller when held away from the vessel's metalwork.

Taking Bearings

  1. Stand as far from metal and electronics as possible
  2. Hold compass level; sight through prism or lens at the object
  3. Read the bearing when the object is aligned with the lubber's line
  4. Record as compass bearing; apply deviation (small on handheld) and variation to get true bearing
  5. Plot on chart as a line of position (LOP) from the charted object
  6. Take at least two bearings simultaneously (or rapid succession) for a fix

Compass Rose Usage

The outer ring of a compass rose shows True bearings. The inner ring shows Magnetic bearings (already incorporating local variation). When plotting a magnetic bearing from a hand bearing compass, use the inner ring to lay off the bearing — no variation correction needed.

Shortcut: Use the magnetic (inner) ring of the compass rose to plot magnetic bearings directly. No math required if you read the bearing as magnetic and use the magnetic ring for plotting.
Three-Bearing Fix:For a reliable fix, take bearings on three objects roughly 120 degrees apart. Plot all three LOPs. If they form a triangle (cocked hat), your position is within it — place it on the most dangerous side. A tight triangle or single point = good fix.

4. Depth Sounder (Echo Sounder)

The depth sounder measures water depth by timing the return of a sound pulse from the seabed. Critical for safe navigation in shoal water and for confirming chart soundings.

Transducer

The transducer is mounted through the hull or on the transom. It converts electrical energy into sound pulses (usually 200 kHz for shallow water) and converts returning echoes back into electrical signals. Mounting position affects accuracy — air bubbles under the hull at speed can cause false readings.

Principle of Operation

A pulse of sound travels to the bottom at approximately 4,800 feet per second (1,500 m/s) in seawater. The instrument times the round trip and divides by two to get depth. The display shows depth below the transducer — add the transducer depth below the waterline to get depth below the surface (keel clearance matters).

Reading Chart Soundings

US chart soundings are in feet (on large-scale charts) or fathoms, referenced to MLLW (Mean Lower Low Water). A sounding of 12 on the chart means 12 feet at mean lower low water — the lowest the tide is likely to reach on average. Actual depth = chart sounding plus tide height above MLLW.

Correcting for Tide

Tide Correction Formula
Actual Depth = Chart Sounding + Tide Height Above MLLW
Chart Sounding = Depth Sounder Reading - Tide Height

Example: Sounder reads 15 feet. Tide is 3.0 feet above MLLW. Chart depth = 15 - 3 = 12 feet. This matches a 12-foot charted sounding, confirming your position over that shoal.

Safety note: At low tide, actual depth equals the chart sounding. Never assume more water than the chart shows unless you verify the current tide height.

5. GPS and Chartplotter

GPS (Global Positioning System) is the primary navigation system for virtually all mariners. Understanding its limitations and settings is critical for safe use — and for the USCG exam.

HDOP — Satellite Geometry

HDOP (Horizontal Dilution of Precision) measures the quality of satellite geometry affecting horizontal position accuracy. Lower is better.

1Ideal
1–2Excellent
2–5Good — adequate for navigation
5–10Moderate — use with caution
10+Poor — unreliable for precision

Datum — WGS-84 vs NAD-83

A chart datum defines the mathematical model of the Earth used to create the chart. GPS uses WGS-84. Most US coastal charts use NAD-83. The difference is very small (less than 2 meters) but in other parts of the world datum mismatches can be hundreds of meters.

WGS-84:GPS standard datum; used by all GPS receivers by default
NAD-83:Most US charts; very close to WGS-84 but not identical
Rule:Always set chartplotter datum to match the chart you are using

Key GPS Concepts for the Exam

COG — Course Over Ground

The actual direction the vessel is moving relative to the seabed, derived from changes in GPS position. Includes the effect of current and leeway. This is not the same as heading. COG is what matters for making good a course to a waypoint.

SOG — Speed Over Ground

The actual speed of the vessel relative to the seabed. Unlike knotmeter speed (speed through water), SOG accounts for current. In a following current SOG exceeds knotmeter speed; in a head current SOG is less.

XTE — Cross-Track Error

The distance the vessel is off the planned track (rhumb line or great circle route between waypoints). Displayed in nautical miles. A positive XTE means you are to the right of track; negative means left. Used to steer back on track.

Waypoints

Saved geographic positions (latitude and longitude) stored in the GPS. Used to define a route. The GPS shows bearing and distance to the next waypoint (BRG and DTW — distance to waypoint). Always verify waypoints against the chart before use.

BTW — Bearing to Waypoint

The true (or magnetic, depending on settings) bearing from current position to the next waypoint. Used to steer toward the waypoint. Differs from COG when current or leeway is present — must steer a slightly different heading than BTW to make good the direct route.

VMG — Velocity Made Good

Speed made good toward the destination or waypoint. Accounts for the vessel's COG angle relative to the desired track. In a crosswind or cross-current, VMG may be less than SOG. Useful for optimizing sailing angles.

COG vs Heading Exam Tip:A common exam question: "Your GPS shows COG 085 but your compass reads 090. Why?" Answer: current or leeway is pushing you to port (north), so you must head 090 to make good 085. The current is from the south or starboard side. COG is always the actual path; heading is where the bow points.

6. Radar

Radar (Radio Detection And Ranging) is essential for navigation in restricted visibility. Required on many commercial vessels; common on cruising yachts. USCG exams test radar operation, controls, and collision avoidance concepts heavily.

Radar Controls Reference

ControlPurpose
GainAmplifies the return signal
Sea Clutter (STC)Reduces echoes from wave tops near own vessel
Rain Clutter (FTC)Reduces precipitation echoes
RangeSets displayed area radius
VRM (Variable Range Marker)Measures range to a target
EBL (Electronic Bearing Line)Measures bearing to a target

ARPA — Automatic Radar Plotting Aid

ARPA tracks targets automatically and computes CPA, TCPA, true course, and true speed for each tracked target. Required on vessels 10,000 GT and above. Smaller vessels may have mini-ARPA. Must be monitored — ARPA data is only as good as the tracking quality; it can lose targets in sea clutter or swap tracks.

CPA: Closest Point of Approach — minimum distance if courses/speeds unchanged
TCPA: Time to CPA in minutes
True course: Actual course of the target over ground
True speed: Actual speed of the target over ground

Relative vs True Motion

Relative Motion Display (RM)

Own vessel is fixed at center. Target vectors show movement relative to own ship. Default mode; excellent for collision avoidance. A target moving toward the center is closing; a constant relative bearing with decreasing range = collision risk.

True Motion Display (TM)

Own vessel moves across the screen (periodically resets). Targets show actual courses and speeds. Better for situation awareness and chart overlay; own-vessel drift and current effects are visible. Less intuitive for CPA assessment.

Collision Avoidance with Radar (Rule 7 and 8)

A target at a constant bearing with decreasing range is on a collision course. This applies whether you use radar or visual observation. Take action early and boldly — Rules 16 and 8 require action that is apparent to the other vessel. Small course changes are dangerous because they may not register on the other vessel's radar.

Constant bearing + decreasing range
Collision risk — act immediately
CPA less than 0.5 nm
Set guard alarm; assess action needed
TCPA less than 6 minutes
Urgent — take action now if not already done

7. AIS — Automatic Identification System

AIS transponders broadcast and receive vessel identity, position, and navigation status on VHF frequencies. Required on SOLAS vessels; increasingly common on smaller commercial and recreational vessels.

Class A Transponder

  • Required on SOLAS vessels (300 GT+ international; 500 GT+ domestic; all passenger ships)
  • Transmits every 2–10 seconds underway, 3 min at anchor
  • 12.5 watts output
  • Transmits voyage data: destination, ETA, draught
  • SOTDMA (Self-Organized Time Division Multiple Access) protocol

Class B Transponder

  • Voluntary on smaller commercial and recreational vessels
  • Transmits every 30 seconds underway, 3 min at rest
  • 2 watts output — shorter range
  • Does not transmit destination, ETA, or draught
  • CSTDMA protocol — lower priority than Class A

AIS Data Fields

FieldDescription
MMSI9-digit Maritime Mobile Service Identity — unique vessel identifier
Vessel NameShip name as registered
Call SignRadio call sign
PositionLat/Lon from own GPS antenna
COGCourse Over Ground
SOGSpeed Over Ground
HeadingTrue heading from gyrocompass or GPS compass
ROTRate of Turn (Class A only)
Navigational StatusUnderway, at anchor, moored, not under command, etc.
Ship TypeCargo, tanker, passenger, fishing, sailing, etc.
DestinationNext port of call (Class A only, manually entered)
ETAEstimated time of arrival (Class A only, manually entered)
DraughtCurrent draught (Class A only, manually entered)

AIS Limitations

Not all vessels transmit

Fishing vessels, recreational boats, and many small craft do not carry AIS. Never assume a clear AIS display means clear water.

Data can be incorrect

AIS data is manually entered for some fields (destination, draught). Vessels may not update navigational status. Position relies on vessel's own GPS.

Range limitations

VHF range is typically 20–40 nm line of sight. AIS does not work over the horizon without satellite AIS (S-AIS).

AIS is not collision avoidance

AIS supplements radar and visual watch — it does not replace them. A vessel may be AIS-equipped but transmitting bad data.

MMSI required

To transmit on AIS, a vessel must have a programmed MMSI. MMSI is registered with the FCC or BoatUS for US recreational vessels.

AIS vs Radar

AIS provides identity; radar provides an independent position. Use both together. A radar target without AIS may be a small boat, rock, or debris.

8. Sextant

The sextant measures the angle between a celestial body and the horizon, allowing a line of position to be calculated. Required knowledge for Master Near Coastal and offshore endorsements. Appears on OUPV exams only at the conceptual level; full sight reduction appears on Master exams.

Parts of the Sextant

PartFunction
FrameRigid arc-shaped structure; graduated in degrees
Index arm (alidade)Pivoting arm that moves along the arc
Micrometer drumFine adjustment; reads minutes and tenths
Index mirrorAttached to index arm; reflects the body being measured
Horizon mirrorFixed; shows both horizon (clear half) and reflected body (silvered half)
TelescopeMagnifies view; reduces parallax
Shade glassesFilters for sun observation without eye damage
Vernier scaleOn older sextants; provides arc-second precision

Altitude Corrections — Order of Application

IC1. Index Error (IE)Hs ± IE = Hs corrected

Caused by misalignment of the index mirror. Check by setting arc to zero and looking at the horizon — if not a straight line, read the error. If the error is 'on the arc' (arc reads a positive number), subtract IE from Hs. If 'off the arc' (reads negative), add IE. Mnemonic: on is off; off is on.

D2. Dip (Height of Eye Correction)Hs - Dip = Apparent Altitude (Ha)

The observer's height above sea level causes the visible horizon to be depressed below the true horizontal plane. The higher the eye, the greater the dip. Dip is always subtracted. Found in the dip table using height of eye in feet or meters.

R3. RefractionAlways subtracted; largest near horizon

The atmosphere bends light, making celestial bodies appear slightly higher than they actually are. Refraction is always subtracted. It is greatest near the horizon (can be 34' of arc at the horizon) and zero at the zenith. Standard refraction tables assume standard atmosphere.

SD4. Semi-Diameter (Sun / Moon only)Lower limb: add SD. Upper limb: subtract SD.

When shooting the lower or upper limb of the sun or moon, a semi-diameter correction is applied to get the altitude of the center. For lower limb (most common), SD is added. For upper limb, SD is subtracted. Not needed for stars or planets.

PA5. Parallax (Moon / planets only)Mostly relevant for moon sights

For nearby bodies (moon, Venus), parallax in altitude (PA) is applied. The moon's horizontal parallax is significant — up to 61' of arc. For stars, parallax is negligible (less than 0.001'). HP (horizontal parallax) is found in the Nautical Almanac daily pages.

Index Error Memory Aid:"If it's on the arc, it's off (subtract). If it's off the arc, it's on (add)." Alternatively: IOWA — Index error On the arc = subtract (West = subtract in compass corrections; same mnemonic pattern). Or simply memorize: on = minus, off = plus.

9. Barometer

The barometer measures atmospheric pressure and is one of the most valuable weather prediction tools available to the mariner. Pressure trends over time are more important than the absolute value.

Aneroid Barometer

Contains a sealed metal capsule (aneroid cell) that expands and contracts with pressure changes. Movement is mechanically linked to a needle on a graduated dial. No liquid — safe at sea, not affected by motion. Most common type on boats. Must be calibrated against a known standard (weather service reading corrected to sea level).

Mercury Barometer

The original and most accurate barometer. Uses the weight of a mercury column to measure atmospheric pressure. Standard pressure = 760 mm Hg = 29.92 inches Hg = 1013.25 mb (hPa). Fragile, hazardous if broken, and sensitive to motion — not practical at sea. Used as the calibration standard ashore. Still referenced in USCG exam questions on units.

Pressure Units Reference

MeasurementStandard Sea Level Pressure
Millibars (mb)1013.25 mb
Hectopascals (hPa)1013.25 hPa
Inches of Mercury (inHg)29.92 "Hg
Millimeters of Mercury (mmHg)760 mmHg

Reading Pressure Trends

Steady fall (slow)

Approaching low — rain likely in 12–24 hours

Rapid fall (3 mb/hr)

Strong storm approaching — rough seas, strong winds

Very rapid fall (6+ mb/hr)

Severe storm or gale — seek shelter immediately

Steady rise (slow)

Clearing weather, high pressure building — improving

Rapid rise after low

Strong gradient — winds may increase temporarily behind the front

Steady high pressure (1020+)

Fair weather typical; sustained high = drought risk ashore

The 3-2-1 Rule

A practical rule of thumb for storm intensity based on pressure drop over 3-hour intervals:

3 mb in 3 hours
Moderate storm
6 mb in 3 hours
Strong storm
9+ mb in 3 hours
Violent storm / Gale

11. Chart Plotting Tools

Chart plotting skills — using parallel rules, dividers, and the compass rose — are tested directly on the USCG exam with actual chart problems. Practice with a real nautical chart.

Parallel Rules
How It Is Used

Transfer a bearing from compass rose to chart position (or vice versa)

Exam Tip

Walk rules across chart by alternating; check each step or you will slip

Course Plotter (Portland Plotter)
How It Is Used

Lay directly on a meridian or parallel to read course without a compass rose

Exam Tip

Faster than parallel rules; less slippage error on small-scale charts

Dividers
How It Is Used

Measure distance by stepping off against the latitude scale (not longitude)

Exam Tip

Always measure distance on the latitude scale at the same latitude as the area of interest

Compass Rose
How It Is Used

Outer ring = true directions; inner ring = magnetic directions (with variation noted)

Exam Tip

Read variation from inner ring label; note year and annual change for corrections

Three-Arm Protractor
How It Is Used

Fix position from three charted objects by simultaneous bearings

Exam Tip

Extremely accurate; not affected by compass errors

Rolling Ruler
How It Is Used

Alternative to parallel rules; rolls along a straight edge

Exam Tip

Less common aboard; can slip if straight edge is not secured

Nautical Chart Symbols — Essential Exam Items

Symbol / AbbreviationMeaning
R (on buoy)Red buoy (even-numbered; return from sea on starboard)
G (on buoy)Green buoy (odd-numbered; return from sea on port)
RW (on buoy)Safe water mark (fairway / mid-channel); red and white vertical stripes
fl R 4sFlashing red light, 4-second period
fl (2+1) G 6sGroup flashing green — 2 flashes, then 1, every 6 seconds (preferred channel marker)
WkWreck — potentially hazardous
ObstnObstruction — shallow or submerged hazard
PAPosition Approximate — not precisely located
EDExistence Doubtful — charted feature may not exist
M, S, G, R, Sh, Co, CyBottom composition: Mud, Sand, Gravel, Rock, Shells, Coral, Clay
Anchoring symbolRecommended anchorage; circle with anchor symbol
DWDeep Water (route or lane)
Subm pilesSubmerged pilings — danger at low tide
1013mb (on chart)Not on nautical charts; barometric pressures appear on weather charts

12. USCG Exam Tips — Navigation Instruments

The navigation instruments section tests both conceptual knowledge and calculation skills. Here are the areas where students most often lose points.

Compass CorrectionsHIGH
  • Memorize CDMVT (Can Dead Men Vote Twice) and the East = add, West = subtract rule
  • When converting True to Compass, reverse all signs: East becomes subtract, West becomes add
  • Always check: is the answer reasonable? A big deviation or variation change should move the answer significantly
  • Deviation comes before variation — always apply D before V in the mnemonic
  • USCG exam problems often give a deviation table — interpolate between entries
GPS and ChartplotterHIGH
  • Know the difference between COG/SOG (over ground) and heading/knotmeter (through water)
  • Datum mismatch questions: GPS is WGS-84; charts may be NAD-83 or other datums
  • HDOP below 2 is good; above 5 is a warning
  • XTE tells you how far off track you are — positive = right of track, negative = left
  • Waypoints must be verified against the chart — GPS shows you the waypoint, not the hazard between you and it
RadarHIGH
  • Constant bearing + decreasing range = collision course (Rule 7)
  • Gain too high: noise and clutter obscure targets. Gain too low: weak targets disappear
  • Sea clutter suppresses close-range returns — small boats near you may disappear if FTC is over-applied
  • ARPA gives CPA and TCPA — know these abbreviations and what they mean
  • Relative motion: target moving toward center of screen is closing
Depth SounderMEDIUM
  • Sounder reads depth below transducer — add transducer depth below waterline for true depth
  • Chart soundings are at MLLW — add tide height to get actual depth at that moment
  • Speed can cause aeration under hull, giving false shallow readings
  • A double trace or second bottom reading indicates a thermocline or density layer
AISMEDIUM
  • Class A: required on SOLAS vessels, 12.5W, transmits every 2–10 seconds
  • Class B: voluntary, 2W, every 30 seconds — often misses fast-approaching contacts
  • MMSI is 9 digits — required to transmit on AIS
  • AIS does not replace radar — vessels without AIS (small boats, submarines) will not appear
  • AIS navigational status is manually set — it may be wrong (vessel may show 'at anchor' while underway)
Sextant and CelestialMASTER EXAM
  • Index error: on the arc = subtract, off the arc = add
  • Dip is always subtracted — height of eye table required
  • Refraction is always subtracted — atmospheric correction table required
  • Hs (sextant altitude) → apply IC → apply Dip → get Ha (apparent altitude) → apply altitude corrections → get Ho (observed altitude)
  • Ho (observed) is compared to Hc (computed) to plot an intercept (toward or away from the body's GP)

What to Memorize (Short List)

CDMVT — Can Dead Men Vote Twice (compass correction order)
East = add, West = subtract (Compass to True direction)
Standard pressure: 1013.25 mb = 29.92 inHg
Sound speed in seawater: ~4,800 ft/sec (1,500 m/s)
HDOP below 2 = excellent GPS geometry
AIS Class A: 12.5W, 2–10 sec update; Class B: 2W, 30 sec
MMSI = 9-digit vessel identity number
Dip = always subtract from Hs to get Ha
IC: on = subtract, off = add
CPA = Closest Point of Approach; TCPA = Time to CPA
COG = over ground (GPS); Heading = through water (bow direction)
Chart soundings = MLLW; add tide for actual depth
3-2-1 rule: 3/6/9+ mb drop in 3 hours = moderate/strong/violent storm
Refraction = always subtract from apparent altitude

13. Practice Problems with Solutions

Work through these problems before your exam. Each mirrors actual USCG question formats. Try to solve before expanding the answer.

1Your compass reads 215. Deviation is 5W. Variation is 10E. What is the true course?Show Answer
Step-by-Step Solution
  1. 1.Start: Compass = 215
  2. 2.Apply deviation (5W = subtract): 215 - 5 = 210 Magnetic
  3. 3.Apply variation (10E = add): 210 + 10 = 220 True
Answer: True course = 220
2You observe the sun and get a sextant altitude (Hs) of 42 degrees 18.4 minutes. Index error is 2.4 minutes off the arc. Height of eye is 10 feet. What is the apparent altitude (Ha)?Show Answer
Step-by-Step Solution
  1. 1.IE off the arc = add: 42-18.4 + 2.4 = 42-20.8
  2. 2.Dip for 10 ft height of eye (from table) = -3.1 minutes: 42-20.8 - 3.1 = 42-17.7
  3. 3.Ha = 42 degrees 17.7 minutes
Answer: Ha = 42 degrees 17.7 minutes (then apply refraction and sun corrections for Ho)
3A depth sounder reads 18 feet. The chart datum is MLLW. The current tide height is 4.2 feet above MLLW. What is the actual depth of water?Show Answer
Step-by-Step Solution
  1. 1.Sounder reads actual water depth (not chart depth)
  2. 2.Chart depth = sounder reading - tide height = 18 - 4.2 = 13.8 feet (charted depth at MLLW)
  3. 3.Or: actual depth = charted depth + tide = 13.8 + 4.2 = 18 feet
  4. 4.The vessel has 18 feet of actual water beneath it right now
Answer: Actual depth = 18 feet. Chart depth at that spot = 13.8 feet.
4Your GPS shows COG 090, SOG 6 knots. Your heading is 095 and knotmeter shows 6.5 knots. What can you infer?Show Answer
Step-by-Step Solution
  1. 1.COG (090) differs from heading (095) by 5 degrees to port
  2. 2.SOG (6.0) is less than knotmeter (6.5)
  3. 3.A current is setting you slightly to port (north) and reducing your speed
  4. 4.You are experiencing a current from starboard that is pushing you left of heading
Answer: There is a current from the south-southeast, pushing vessel left and reducing SOG vs boatspeed.
5On radar you observe a target at bearing 040 relative. Over 6 minutes the bearing has not changed but range has decreased from 5.0 nm to 3.5 nm. What action should you take?Show Answer
Step-by-Step Solution
  1. 1.Constant bearing + decreasing range = collision risk (Rule 7)
  2. 2.CPA = 0 if nothing changes
  3. 3.You are the give-way vessel unless the other is overtaking or this is a crossing where you are stand-on
  4. 4.Take bold, early, and substantial action per Rule 8: alter course significantly to starboard or reduce speed
Answer: Collision risk exists. Take early and substantial action — likely alter significantly to starboard.

Frequently Asked Questions

What is the difference between variation and deviation on a compass?

Variation is the angle between true north and magnetic north at a given location — it is caused by the Earth's magnetic field and is printed on nautical charts. It changes with geographic location and slowly over time. Deviation is the error caused by the vessel's own magnetic influences (engines, electronics, metal) acting on the compass needle. It differs by heading. To convert compass to true: apply deviation first (Compass + East Dev = Magnetic), then variation (Magnetic + East Var = True). Use the phrase 'Can Dead Men Vote Twice' or 'CDMVT' to remember the order.

What does HDOP mean on a GPS and why does it matter?

HDOP stands for Horizontal Dilution of Precision. It is a measure of GPS satellite geometry quality. A low HDOP (ideally less than 2) means satellites are well-spread across the sky and the position fix is more accurate. A high HDOP (above 5) means satellites are clustered together, degrading accuracy. On coastal passages, always check HDOP before relying on a GPS position for a close approach. WGS-84 is the standard datum used by GPS — always verify your chartplotter datum matches your paper chart datum (NAD-83 on many US charts is very close but not identical to WGS-84).

What is the difference between COG and heading on a GPS chartplotter?

Heading is the direction the bow of the vessel is pointed, measured from north. COG (Course Over Ground) is the actual direction the vessel is traveling over the seabed, accounting for leeway and current. In a strong beam current, a vessel might be headed 090 degrees but making good a COG of 080 degrees — the current is setting it north. COG is what the GPS measures from actual position changes. For navigation, COG is what matters for arrival at a waypoint; heading matters for collision avoidance and radar bearings.

What is CPA and TCPA on radar?

CPA is Closest Point of Approach — the minimum distance that will exist between your vessel and a target if both vessels maintain their current courses and speeds. TCPA is Time to Closest Point of Approach — how many minutes until CPA is reached. ARPA (Automatic Radar Plotting Aid) calculates CPA and TCPA automatically for tracked targets. A CPA of zero means a collision. Mariners set a CPA alarm (commonly 0.5 to 1 nautical mile) so they are alerted when a target's projected path comes within the guard zone.

What is the difference between Class A and Class B AIS transponders?

Class A AIS transponders are required on SOLAS vessels (commercial ships 300 GT and above on international voyages, cargo ships 500 GT and above domestically, and all passenger ships). They transmit position every 2 to 10 seconds underway, with a 12.5-watt output. Class B transponders are used on smaller commercial and recreational vessels. They transmit less frequently (every 30 seconds underway), use 2 watts, and do not transmit voyage data or destination. MMSI (Maritime Mobile Service Identity) is the 9-digit vessel identifier broadcast by AIS — it links to vessel name, call sign, and flag state in databases.

How do you correct a sextant altitude for index error, dip, and refraction?

Sextant altitude corrections are applied in order: (1) Index Error (IE) — if the arc is on the arc, subtract; if off the arc, add. Mnemonic: 'If it's on, it's off; if it's off, it's on.' (2) Dip — always subtracted from sextant altitude (Hs) to get apparent altitude (Ha). Dip accounts for the observer's height of eye above sea level; higher eye = greater dip correction. (3) Refraction — always subtracted (atmosphere bends light upward, making objects appear higher than they are). Additional corrections apply for the sun (semi-diameter, parallax). The result after all corrections is the true altitude (Ho — Observed altitude).

What is the 3-2-1 barometric pressure rule?

The 3-2-1 rule helps mariners gauge storm intensity from barometric pressure drops. A drop of 3 millibars per 3 hours indicates a moderate storm approaching. A drop of 6 millibars per 3 hours indicates a strong storm. A drop of 9 or more millibars per 3 hours indicates a violent storm (hurricane or severe gale). Some sources state it as: 3 mb drop = caution; 6 mb drop = severe; 9+ mb drop = extreme danger. Standard sea-level pressure is 1013.25 mb (29.92 inches of mercury). A rising barometer after a low indicates improving weather; a rapid rise can itself herald unsettled conditions.

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