Advanced Navigation Without Electronics - Dead Reckoning & EP

Prerequisites

You should already be confident with Day Skipper and Coastal Skipper chartwork:

• Plotting positions by latitude and longitude, measuring courses and distances.
• Applying variation and deviation, and using a deviation card.
• Constructing a course to steer to counteract tidal stream, and plotting an EP from a DR.
• Taking a three-bearing fix with a hand-bearing compass, and using transits and clearing lines.
• Reading tidal diamonds and tidal stream atlases, including interpolating between springs and neaps.

This lesson builds on those skills to navigate for 24 hours or more without satellite positioning, which the RYA expects a Yachtmaster Offshore to do. The Yachtmaster Offshore exam candidate must be 18 or over, and needs 2,500 nm, 50 days at sea (5 as skipper), 5 passages over 60 nm (including 2 overnight and 2 as skipper), and a valid SRC and first aid certificate; these qualifying passage requirements are covered in the passage planning lesson. The shorebased theory course (Coastal Skipper / Yachtmaster Offshore) is the usual route to the knowledge examined here, and its written papers are passed at 60 per cent.

Learning Objectives

By the end of this lesson you will be able to do the following. The RYA Yachtmaster Offshore syllabus (G158) items covered are named in brackets.

• Explain why non-electronic navigation remains a safety requirement offshore (syllabus: navigation, loss of electronic aids).
• Convert between True, Magnetic and Compass headings without error, update variation for the year and use a deviation card (syllabus: compass, course shaping).
• Calibrate the log and maintain an accurate DR plot and deck log for 24 hours or more (syllabus: dead reckoning, log and instruments).
• Estimate leeway and apply it, with tidal stream, to produce an EP (syllabus: course shaping, tidal streams).
• Express the accuracy of an EP as a circle of uncertainty and explain how it grows (syllabus: position fixing, assessment of accuracy).
• Plot a running fix, advancing the first position line along the ground track (syllabus: position fixing).
• Calculate the range of a light, use dipping distance for a position circle and plan a landfall (syllabus: lights, pilotage and landfall).
• Use a line of soundings to fix or confirm position against depth contours (syllabus: position fixing by depth).
• Explain how an altitude of Polaris gives a latitude check and how the noon sight gives latitude (syllabus: awareness of astro navigation).
• Follow a structured protocol when GNSS fails and use radar and other aids as a cross-check (syllabus: electronic position fixing equipment, failures).

Why Navigate Without Electronics?

GNSS (GPS, Galileo, GLONASS) is extraordinarily reliable, but the receiver on a yacht is one antenna, one power supply and one software stack. It can fail through:

• Loss of power (flat batteries, blown fuse, water in a connector).
• Antenna damage (a dismasting, a lightning strike, a broken cable).
• Jamming and spoofing, increasingly common near some coasts and during military exercises.
• Software faults and datum errors.

At 100 nm offshore, losing your position is not an inconvenience; it is a hazard that can put you on a lee shore at night. The Yachtmaster Offshore examiner may switch off the plotter at any point in the exam and will expect you to switch to traditional methods calmly and immediately, and to tell them at any moment how confident you are in your position.

Compass Conversions: True to Compass and Back

Every course and bearing that moves between the chart and the compass passes through two corrections:

• Variation: the difference between True north and Magnetic north at your location, printed on the chart's compass rose with its annual change.
• Deviation: the error in your particular compass caused by the boat's own magnetic fields, which changes with heading and is read from the deviation card.

The mnemonic True Virgins Make Dull Companions gives the order. Going from True to Compass (chart to helm), add West, subtract East ("West is best, East is least"). Going from Compass to True (hand-bearing to chart), do the opposite: subtract West, add East.

Worked example

Chart course 045°T. Variation 7°W. Deviation on this heading 3°E.

1. True 045°, add 7°W: Magnetic 052°M.
2. Magnetic 052°, subtract 3°E: Compass 049°C. Steer 049°C.

Reverse check: compass 049°C, add 3°E = 052°M, subtract 7°W = 045°T.

Updating variation

Check the year on the chart rose. If variation was 2°10' W in 2015, decreasing 9' annually, by 2025 it is about 2°10' minus 90' = 0°40' W. In much of the English Channel variation is now close to zero, so on older charts this error can be a couple of degrees. The map below shows how variation (declination) is distributed worldwide; the green zero line is the agonic line, where True and Magnetic north coincide.

Click to zoom

Image: NOAA/NCEI and CIRES (World Magnetic Model), public domain, via Wikimedia Commons (downscaled)

Offshore, variation changes quickly with position on a long passage: crossing the Bay of Biscay the variation changes by a few degrees. Use the variation from the nearest compass rose to your DR position and check the annual change, rather than the rose at the start of the passage.

Note that a hand-bearing compass held well away from the boat's magnetic influences has negligible deviation, so hand-bearings usually need only variation applied.

Deviation card and compass checks

Deviation is found by swinging the compass: head the boat on a series of headings, say every 30 or 45 degrees, and compare the steering compass with a known magnetic bearing, such as a transit. The results are written in a deviation card. Re-swing the compass after any change near it (new electronics, new engine, a heavy tool box) and check it against a transit or the sun at least once a season. At sea, a compass check against a transit or an astro bearing confirms the card.

Log Calibration and Distance Run

Distance run through the water is read from the log. A paddle-wheel log can over- or under-read by 5 to 10 per cent through fouling, speed, heel and wheel position, so it must be calibrated.

Measured distance run

1. Choose a straight run of known length (a measured mile or a distance between two charted marks) in slack water, or run it both ways in a tidal stream.
2. Run the course at normal passage speed and record the log reading at the start and the finish.
3. Repeat in the opposite direction and average the two log distances to cancel any stream.

Example: over a measured mile you read 1.10 nm in one direction and 1.06 nm in the other. The mean log distance is 1.08 nm for a true 1.00 nm. The log over-reads by 8 per cent. The true distance run is the log distance divided by 1.08, or log x 0.926. If the log shows 100 nm, the true distance is 92.6 nm. On a 24-hour passage covering 130 nm this would put the DR 10 nm ahead of the true position, if you did not apply the correction.

Calibrate before an offshore passage and check against GNSS or a fix during a period without tidal stream. Many offshore logs in a heavy sea read differently from the flat-water calibration.

Dead Reckoning Over 24 Hours

Dead reckoning (DR) projects a position forward from the last known position using only course steered and distance run through the water. Distance is best taken from the log reading rather than calculated from estimated speed.

The deck log is the foundation

You cannot reconstruct a DR you did not record. Log at least hourly and at every change of course, sail plan or event:

Ask the helm for the average course actually steered over the last hour, not the course they were told to steer. Under autopilot this is easy; when hand-steering in a seaway a helmsman may be consistently 5 degrees high or low, and only an honest answer gives a good DR.

Also log the engine hours, the sails set, the barometer and any hand-bearings, since these show you the weather and the fuel burn as well as the position.

How errors accumulate

Small, steady errors add up. A 2° steering error over 120 nm of run is a cross-track error of about 4 nm (1 in 60 rule: 1 degree gives 1 nm per 60 nm run, so 2 degrees gives 2 nm per 60 nm, or 4 nm per 120 nm). A log that over-reads by 4 per cent puts you nearly 5 nm ahead of your true position after 120 nm. Calibrate the log, as above.

Worked example: hourly DR

At 0600 your fix is 50°00' N 005°00' W; log 100.0. You steer 245°T with the wind from the north-west. At 0700 the log reads 106.0; at 0800 112.1. Distance run through the water: 6.0 nm in the first hour and 6.1 in the second, 12.1 nm on a water track of 245°T (less leeway if any). Along 245°T, 12.1 nm gives 5.1 nm south and 11.0 nm west. The DR latitude is 50°00' minus 5.1' = 49°54.9' N; the change in longitude is 11.0 / cos(49.9°) = 17.1' W, so the DR longitude is 005°17.1' W. Plot the DR with a short line and the time, and add the tide to move to the EP.

Leeway

Leeway is the sideways drift caused by the wind, measured as the angle between the boat's heading and her track through the water. It depends on point of sail, wind strength, sea state, hull form, keel area and boat speed.

Click to zoom

Typical values for a cruising yacht:

Motor-boats with high windage and shallow draft can have large leeway in a beam wind when slow.

Measuring it

Take a hand-bearing compass bearing along the wake and compare it with the reciprocal of the heading. If the heading is 090° and the wake bears 260° rather than 270°, the boat is making 10° of leeway. Repeat in different conditions and build a leeway table for your boat.

Applying it

Leeway is always applied downwind of the heading. On starboard tack (wind from starboard), the boat slips to port, so the water track is heading minus leeway. On port tack, add leeway. Example: heading 040°T on starboard tack, wind from the east, leeway 8°: water track 032°T. To make good a given water track you steer the other way: to achieve a water track of 040°T on that tack you must steer 048°T.

Tidal Streams Offshore

Offshore, tidal streams are weaker than in the narrows but they still affect your DR: 0.5 to 1.5 knots is typical over open water, rotating clockwise in the Northern Hemisphere (rotary streams) rather than flowing back and forth. Use the tidal stream atlas for the area (often with the rate shown as two figures for neaps and springs) and the diamonds for the nearest position, interpolating for the range. Add to this the effects of persistent currents (such as the North Atlantic Drift, the Portugal current, or the outflow from rivers), and the effect of strong or prolonged winds, which can set up drift of 2 to 3 per cent of the wind speed.

An easy mistake is to forget the tidal vector for hours when you are far from land because "the tide averages out". It does average out over a full tidal cycle of 12 hours 25 minutes, but not within the hours that matter if you are heading for a landfall or a danger.

Estimated Position and the Circle of Uncertainty

The EP improves on the DR by adding the effect of tidal stream (and current) for the time interval:

1. From the last fix, plot the water track (heading corrected for leeway) and the distance run by log.
2. From the end of that line, plot the tidal stream vector for the same period: direction from the tidal diamond or atlas, rate times hours.
3. The end of the tidal vector is the EP. The line from the fix to the EP is the ground track.

The circle of uncertainty

No EP is exact. Leeway might be 3° wrong, the tidal diamond is a prediction, the helmsman wandered, and the log may be imperfect. Show this on the chart by drawing a circle of uncertainty around each EP. A sensible starting rule is to grow the radius by about 10 per cent of the distance run since the last fix, plus an allowance for tidal stream uncertainty (perhaps 20 to 30 per cent of the total tidal set). After 40 nm from the last fix, a circle of about 4 to 5 nm is realistic.

Plan around the edge of the circle, not its centre. If any part of the circle overlaps a hazard, you are not clear of it. When the examiner asks where you are, answer: "Our EP is here; I'd put us within about 3 miles of it, because ..." That shows professional judgement.

Running Fixes

When only one charted object is visible, take two bearings of it at different times and use the boat's movement between them.

Procedure

1. Take a bearing of the object; note time and log reading. Plot it as position line LOP1.
2. Hold a steady course. Wait until the bearing has changed by at least 30° (ideally 45° to 90°) for a good angle of cut.
3. Take the second bearing; note time and log. Plot it as LOP2.
4. From any point on LOP1, plot the ground track for the interval: water track (heading plus leeway) for the distance run, then the tidal vector for the time interval.
5. Transfer LOP1 parallel to itself so it passes through the end of that ground track. This is the transferred position line (marked with double arrowheads).
6. Where the transferred LOP1 crosses LOP2 is the running fix.

Worked numbers

At 2100 a lighthouse bears 030°T, log 46.2. You steer 090°T, no leeway, speed 5 knots. Tide is setting 180°T at 1.2 knots. At 2230 the light bears 330°T, log 53.7.

• Distance run: 53.7 minus 46.2 = 7.5 nm along 090°T.
• Tidal vector: 1.5 hours times 1.2 = 1.8 nm along 180°T.
• Transfer LOP1 by 7.5 nm east and then 1.8 nm south. Where it cuts the 330°T bearing is the 2230 running fix.

Working it through, the fix lies 8.5 nm from the lighthouse on a bearing of 150°T from it (so the light bears 330°T from the boat). Had you ignored the tide, you would plot the fix 7.5 nm from the light, about 1 nm out. The tidal error in a running fix is the part of the tidal set that lies across the second bearing, not the full 1.8 nm, but it can be enough to put you on the wrong side of a clearing line.

A running fix is only as good as the run between bearings: any error in leeway, log or tide goes straight into the fix. Treat it as better than an EP but weaker than a simultaneous three-bearing fix.

Lights: Range, Visibility and Dipping Distance

On a night passage the lights are your main fixing aid, so you must understand how far you can see them.

• Nominal range is the charted range of the light in clear weather (meteorological visibility of 10 nm), as in the Admiralty List of Lights.
• Luminous range is the distance at which the light can be seen with the visibility of the day, found from a diagram in the List of Lights.
• Geographic range is the distance to the horizon from the light's height and your height of eye, set by the curvature of the Earth:

Geographic range (nm) = 2.03 x (square root of height of eye in metres + square root of height of light in metres)

A light is seen at the lesser of the luminous and geographic ranges. The chart heights are above MHWS, so for a more accurate figure use the actual height of the light above the sea at the time: charted height plus (MHWS minus the height of tide).

Example: a light is charted at 49 m. Your height of eye is 3 m. Geographic range = 2.03 x (1.73 + 7.00) = 17.7 nm. If the charted nominal range is 22 nm and the visibility is only 8 nm, the luminous range from the List of Lights diagram will be well below 22 nm (perhaps about 14 nm), and you will see the light at that lesser range. In a clear atmosphere at the geographic range it appears just on the horizon.

Dipping distance

Dipping distance is the distance at which a light appears or disappears over the horizon from a given height of eye. It uses the same formula as geographic range. It gives a position circle: if you note the time the light first appears from a known height of eye, you are at the dipping distance from it.

Example: a light is 36 m high (charted), MHWS is 4.8 m and the height of tide is 2.0 m, so the true height is 36 + 2.8 = 38.8 m. Height of eye is 2.5 m. Dipping distance = 2.03 x (1.58 + 6.23) = 15.9 nm. Without the tide correction you would get 15.4 nm, half a mile less, which is on the safe side. Plot a position circle of radius 15.9 nm around the light, and the bearing of the light gives a fix.

Remember that haze, a rolling sea and a temperature inversion can alter the apparent range. Dipping distance is a useful check but treat it as an approximate position line, not a precise fix.

Landfall Techniques

A landfall after a long offshore leg is when your uncertainty meets a hazard. Plan it carefully.

• Aim off. Aim deliberately to one side of the target, by more than your circle of uncertainty, so that when you reach the coast you know which way to turn. If you aim straight at a harbour and your error is 3 nm, you do not know whether to turn left or right.
• Arrive in daylight if possible, or time the landfall for dawn, so that you can identify marks visually.
• Use a distinctive feature, such as a light with a unique characteristic, a headland or a contour line, rather than a plain stretch of coast.
• Check light characteristics with a stopwatch: count the flash and period and compare with the chart and the List of Lights.
• Expect loom. A powerful light is visible as a glow in the sky beyond the horizon before the light itself appears.
• Use depth. Look for the 100 m, 50 m or 20 m contour to confirm distance from the coast.
• Know the stream near the coast. A landfall at slack water is easier than one in a 3-knot cross stream.

Fixing by Depth Contours

The echo sounder is a valuable position tool in fog or at night, especially where the seabed has a definite slope or features. It gives you a line of soundings that you match to the chart.

Click to zoom

Procedure

1. Correct each sounding to chart datum: subtract the height of tide at the time (and add the transducer depth if your sounder reads below the keel or the transducer).
2. Record soundings at regular intervals of time or log distance, for example every half mile.
3. Mark the soundings on a strip of tracing paper along a line drawn to the course, at the chart scale, spaced by distance run.
4. Slide the strip over the chart, keeping it parallel to your ground track, until the soundings match the charted depths.
5. Where they fit, you have a position, or at least confirmation of which side of a feature you are on.

Worked example

Height of tide 2.4 m, transducer 0.5 m below the waterline and sounder set to read below the transducer. Sounder reads 21.1 m: depth below waterline = 21.6 m; reduced to chart datum: 21.6 minus 2.4 = 19.2 m. You are close to the 20 m contour.

A single depth tells you little on a flat seabed. A sequence across contours, or crossing a distinctive bank or channel, can be as good as a bearing. A single depth contour can also be a position line: "follow the 20 m contour north until the light is abeam" is classic landfall technique.

Radar and Electronic Cross-Checks

If the electronics are still working, use more than one source and compare them.

• Radar range of a clear headland or a lighthouse is the most accurate radar measurement, accurate to a fraction of a mile. A range from two or three objects gives a fix; a range and a visual bearing from the same object gives a fix from one mark.
• Radar bearing is less accurate than range, and depends on heading marker alignment and the beam width, so use range in preference.
• GNSS and the plotter should be compared with the DR or EP at least hourly; any difference larger than your circle of uncertainty needs a reason.
• AIS gives other traffic but not your own position independently of GNSS.

Remember that the radar and the plotter can both be fed from the same GNSS source. A visual fix and an echo sounder check are independent of electronics, which is why they matter.

Polaris: a Latitude Check

Celestial navigation is covered in depth in the Yachtmaster Ocean syllabus, but an Offshore candidate should understand the principle and know the simplest sight: Polaris.

Polaris lies within about 0.7° of the celestial North Pole. To an observer in the Northern Hemisphere, the altitude of the celestial pole above the horizon equals the observer's latitude. So the corrected altitude of Polaris is approximately your latitude.

Click to zoom

The corrections

1. Index error: the sextant's own error, checked against the horizon before each set of sights.
2. Dip: the horizon appears lower from a raised eye; at 2.5 m height of eye, dip is about 2.8 minutes, subtracted.
3. Refraction: light is bent as it passes through the atmosphere, making bodies appear higher; about 1 minute at 45°, subtracted.
4. Polaris tables from the Nautical Almanac: three small corrections (a0, a1, a2) accounting for Polaris not being exactly at the pole, minus 1 degree.

The sight must be taken during nautical twilight, when both the star and the horizon are visible. An Offshore-level navigator uses this as a sanity check on DR latitude, not as a precision fix. Even an error of 3 to 5 minutes of arc (3 to 5 nm) is useful after a day without a fix.

Worked example

You take a sight of Polaris at evening twilight. Sextant altitude (Hs) 50°41.0'. Index error 2.0' on the arc, so subtract 2.0': 50°39.0'. Dip at 2.5 m height of eye: minus 2.8': 50°36.2'. Refraction at this altitude is about 0.8': 50°35.4' = Ho. From the Pole Star tables, a0 = +0°42.4', a1 = +0.5', a2 = +0.9'.

Latitude = Ho minus 1° + a0 + a1 + a2 = 50°35.4' minus 60' + 42.4' + 0.5' + 0.9' = 50°19.2' N. If the DR latitude was 50°28' N, the difference of 9 nm tells you the DR is that far north and gives a line of latitude to use as a cross-check.

Meridian altitude of the sun

The sun at its highest altitude, at local noon, also gives latitude. Take the maximum altitude, correct it to Ho, and calculate zenith distance (ZD) = 90° minus Ho. If the sun bears south in the Northern Hemisphere and its declination is North, latitude = ZD + declination. Example: Ho 52°10.0', declination N 18°20.0'. ZD = 37°50.0'. Latitude = 37°50.0' + 18°20.0' = 56°10.0' N. Longitude from the same sight needs accurate time, which is the Ocean level technique.

GPS Blackout Protocol

The moment GNSS fails, follow a set routine so nothing is forgotten.

Click to zoom

Phase 1: Immediate

1. Note the time and the last good position, course and speed. Plot it on the paper chart immediately. If the plotter is still showing a position, check it is not frozen.
2. Start the DR from that position and log the log reading.
3. Brief the crew calmly: helmsmen must now report average course steered.
4. Hoist or check the radar reflector. With no GNSS position, your AIS transponder may stop transmitting a valid position too.

Phase 2: Establish

1. Plot DR and EP hourly, applying variation, deviation, leeway and tide.
2. Take visual bearings of anything identifiable; use the echo sounder continuously.
3. Check whether a handheld GPS, phone or tablet can provide a backup position (keep a charged handheld in the grab bag for exactly this).

Phase 3: Sustain

1. Keep the deck log scrupulously.
2. Draw circles of uncertainty and widen safety margins accordingly.
3. Take running fixes and depth contour fixes whenever possible; take a Polaris check at twilight if a sextant is aboard.
4. Re-plan landfall around a well-lit, deep-water approach and aim off by at least your uncertainty.

Worked Example: Night Electronics Failure Offshore

You are 60 nm offshore at 0100. Total electrical failure has taken out the plotter, AIS and radar. You have been maintaining a paper DR for 8 hours. Visibility is 2 nm. You estimate your position within a circle of about 6 nm radius. A shipping lane lies 4 nm to starboard of your DR track.

Step 1: Recognise the risk. The edge of your circle of uncertainty (6 nm) already overlaps the shipping lane (4 nm away). You must assume you might be in or very near it.

Step 2: Immediate action. Alter course away from the lane to increase the margin, for example 30° to port, which opens the distance by about 1 nm for every 2 nm run. Check navigation lights (now probably on a backup battery or replaced by a masthead tricolour or handheld). Ensure the radar reflector is up.

Step 3: Lookout. Assign specific sectors to each crew member on deck. Brief them on what a ship's lights look like at 2 nm in poor visibility.

Step 4: Position. Use the echo sounder. If the chart shows the edge of a bank 10 nm ahead, the change in depth will confirm when you cross it. Take a Polaris altitude at morning twilight if a sextant is aboard.

Step 5: Consider stopping. If hazards ahead are close and the uncertainty is large, heaving-to until daylight is a legitimate decision: you can then identify land and marks visually.

Step 6: Communicate. Handheld VHF can be used to call a ship you see, giving your best position as a bearing and distance from a charted feature with your uncertainty stated. If you need help, DSC and Mayday call on the fixed VHF will include the last position, which you should update by voice.

Common Mistakes

• Applying variation or deviation the wrong way. Write out T-V-M-D-C on every conversion and check by reversing.
• Using the ordered course rather than the course actually steered. Ask helms for their average heading.
• Forgetting leeway, or applying it upwind. Leeway is always towards the leeward side.
• Treating an EP as a fix. Draw the circle of uncertainty and plan around its edge.
• Advancing a running fix line by heading and log only. Advance it along the ground track, including tidal set and drift.
• Taking running fix bearings too close together. Wait for at least 30° change for a good cut.
• Not reducing soundings to chart datum. Correct for height of tide and transducer offset before comparing with the chart.
• No log calibration. An uncalibrated log produces a steadily growing along-track error.
• Forgetting the height of tide in range of lights. Charted heights are above MHWS; at low tide the light is higher and visible further.
• Aiming straight at the landfall. Aim off by more than your uncertainty.
• No paper backup. Keep a paper chart of adequate scale with the route drawn and positions plotted hourly.

Exam Tips

• Expect the examiner to cover the plotter at some point and ask for your position. Give the time, the source, the circle of uncertainty and your plan.
• Know the T-V-M-D-C sequence without thinking, and state both True and Compass when you give a course.
• Keep a neat deck log: the examiner will read it and judge whether you could reconstruct the track from it.
• Show you can cross-check: a plotter position is not enough, so confirm with depth, a bearing or a light.
• At night, name the light characteristic you expect before you see it.

Summary

• GNSS can fail; a Yachtmaster Offshore must navigate for 24 hours or more without it.
• True to Compass: add West, subtract East. Compass to True: the reverse. Update variation for the year and for the position.
• Calibrate the log over a measured distance in both directions; an 8 per cent error is about 10 nm in 130.
• DR uses course steered and log distance; it is only as good as the deck log.
• Leeway is measured by wake angle and applied downwind of the heading.
• EP = water track plus tidal vector; it always carries a circle of uncertainty that grows with distance since the last fix.
• Running fix: advance the first position line along the ground track by the run between bearings.
• Geographic range = 2.03 x (square root of eye height plus square root of light height); dipping distance gives a position circle.
• Landfall: aim off, arrive in daylight, confirm with depth and light characteristics.
• Lines of soundings, reduced to chart datum, can fix position where the seabed has character.
• Polaris altitude, corrected, approximately equals latitude: a useful sanity check; the noon sight gives latitude as ZD plus or minus declination.
• On GNSS failure: record the last position, start a DR, brief the crew, widen margins.

Check Your Understanding

1. Chart course 210°T, variation 3°W, deviation 4°E. What compass course do you steer?

Answer: 210 + 3 (West) = 213°M; 213 minus 4 (East) = 209°C.

2. A hand-bearing compass reads 156°C on an object. Variation is 1°E. What true bearing do you plot?

Answer: Hand-bearing compass deviation is taken as zero, so 156°M. Compass to True: add East, so 157°T.

3. You are heading 300°T on port tack, close-hauled, with an estimated leeway of 7°. What is your water track?

Answer: On port tack the wind comes from the port side and pushes the boat to starboard, increasing the heading. Water track = 307°T.

4. Twelve hours after your last fix you have run 60 nm and tides have set you 8 nm in total. Roughly how big should your circle of uncertainty be?

Answer: About 10 per cent of 60 nm = 6 nm, plus roughly 20 to 30 per cent of the 8 nm tidal set (2 nm), giving a radius of around 7 to 8 nm. Plan as though you could be anywhere within it.

5. In a running fix, why must the first position line be advanced along the ground track and not just the heading?

Answer: The boat's real movement over the seabed between bearings includes tidal set and leeway. Using heading and log alone ignores the tide and produces a fix that is out by the tidal drift across the bearing for the interval.

6. Why is a single echo sounder reading of little use for fixing, while a line of soundings can be valuable?

Answer: Many places on the chart share any single depth. A sequence of soundings at known intervals along a known track produces a profile that, if the seabed has slopes or features, fits the chart in only one place.

7. Your sounder reads 14.0 m below the transducer, which is 0.6 m below the waterline. Height of tide is 3.1 m. What is the depth at chart datum?

Answer: Depth below waterline 14.6 m; minus 3.1 m tide = 11.5 m charted depth.

8. What is the principle behind the Polaris latitude check, and why is it only a sanity check at Offshore level?

Answer: Polaris lies very close to the celestial pole, whose altitude equals the observer's latitude. Its corrected altitude therefore gives latitude. It is approximate because of small-boat sextant accuracy, twilight timing and correction errors, and it gives latitude only, not longitude.

9. What are your first three actions when the plotter freezes 50 nm offshore?

Answer: Record the time and last reliable position, course and speed and plot them on the paper chart; start a DR from that point with the log reading; brief the crew, including asking helms to report average course steered and increasing lookout.

10. Over a measured mile the log reads 1.04 nm and 1.00 nm in the two directions. By what percentage does it over-read, and what is the true distance if the log shows 80 nm?

Answer: The mean is 1.02 nm for a true 1.00 nm, so it over-reads by 2 per cent. The true distance is 80 / 1.02 = 78.4 nm.

11. A light is charted at 25 m above MHWS. Your height of eye is 4 m. What is the geographic range?

Answer: 2.03 x (2 + 5) = 14.2 nm. If the tide is below MHWS the light stands higher above the sea and the range is slightly more.

12. You are bound for a harbour 120 nm away with an EP uncertainty of 5 nm on arrival. How should you set your landfall course?

Answer: Aim off to one side of the harbour by more than 5 nm (say 7 to 8 nm), and arrive in daylight. When you reach the coast you know which way to turn, and you can confirm with the depth contour and the light characteristic.