Position Fixing Methods in Coastal Navigation - Visual Fixes

Prerequisites

• Competent Crew level experience (or equivalent): you can steer a compass course, keep a lookout and handle basic deck work.
• Familiarity with a nautical chart: latitude and longitude, the compass rose, measuring distance on the latitude scale (1 minute of latitude = 1 nautical mile).
• Basic chart instruments: parallel rules or a Portland/Breton-type plotter, dividers, a soft 2B pencil and eraser.
• Compass conversions: True, Magnetic and Compass, using variation (from the compass rose) and deviation (from the boat's deviation card).
• For the Day Skipper Practical course the RYA expects theory to Day Skipper Shorebased level, at least 5 days and 100 nautical miles at sea, and a minimum age of 16.

Learning Objectives

By the end of this lesson you will be able to:

• Recognise the chart symbols and abbreviations used to identify fixing marks.
• Explain what a line of position (LOP) is and list the ways of obtaining one.
• Take and plot a three-bearing fix, and judge the quality of the resulting cocked hat.
• Use transits, depth contours and ranges as position lines.
• Plot a running fix when only one mark is available.
• Distinguish a Dead Reckoning (DR) position from an Estimated Position (EP) and plot both.
• Allow for leeway and tidal stream when working up an EP.
• Use GPS and chartplotters correctly as a cross-checked aid, not a sole source.
• Keep a navigational log that would let someone else reconstruct your position.
• Use and check a hand-bearing compass, and judge the accuracy of a bearing using the 1 in 60 rule.
• Choose, combine and plot fixing methods using standard RYA chart symbols, and decide how often to fix.

RYA Day Skipper Shorebased syllabus items covered (Chartwork and Navigation): chart symbols and abbreviations; lines of position, including bearings, transits and soundings; the three-bearing fix and the cocked hat; the running fix; dead reckoning and estimated position, including leeway and tidal stream; use of electronic position-fixing aids with checks against the chart; keeping a navigational log. Also touches the Day Skipper Practical items on position fixing by visual and electronic means and on log keeping.

Why Position Fixing Still Matters

Every navigational decision a skipper makes starts with one question: where are we now? Course to steer, ETA, whether you will clear a headland, when to turn into a channel — all depend on an accurate, recent position. GPS gives a position to a few metres almost all of the time, but the RYA syllabus insists that a Day Skipper can fix the boat without it, because:

• GPS signals can be jammed, spoofed or lost (aerial failure, power failure, a lightning strike, a flooded chart table).
• The chart and the receiver may use different horizontal datums. Older charts (for example on OSGB36 or ED50) can differ from WGS84 by 100 metres or more.
• A chartplotter shows you where the receiver thinks you are; it does not tell you whether the chart under it is accurate, up to date or zoomed to the right scale.
• Traditional fixes keep your eyes outside the boat and force you to identify the marks around you — which is what keeps you off the rocks.

The professional habit is simple: use GPS as one input, and regularly confirm it with an independent visual or depth-based fix.

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Chart Symbols for Fixing

Before you can take a bearing you must be certain what you are looking at, and that it is printed on the chart. Good fixing marks are conspicuous, charted precisely and unambiguous: lighthouses, church spires and towers, prominent headlands with a steep edge, beacons and charted daymarks. Buoys are poor fixing marks — they swing on their moorings and can be out of position — so use them for confirmation, not as primary fixing marks.

The reference below shows common symbols and abbreviations you will meet. The full set is in Admiralty publication 5011 (Symbols and Abbreviations used on Admiralty Charts), which every Day Skipper should own or have access to.

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Note especially:

• PA (Position Approximate) and ED (Existence Doubtful): never use such a feature as a fixing mark.
• Conspic marks a conspicuous object — ideal for bearings.
• Underlined figures are drying heights above Chart Datum; plain figures are depths below it.
• Light characteristics (Fl, Oc, Iso, Q) let you identify lights at night — covered fully in the pilotage lesson.

Lines of Position

A line of position (LOP), or position line, is a line on the chart on which you know the boat lies at a given moment. One LOP tells you only that you are somewhere along it; two or more crossing LOPs give a fix.

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Sources of an LOP:

An error of 1 degree in a bearing displaces the LOP by about 1/60 of the distance to the object — roughly 30 metres per mile. So a 3 degree error on a lighthouse 5 miles away moves the line about a quarter of a mile. Prefer near objects to distant ones.

The Hand-Bearing Compass

Almost every visual fix depends on one instrument, the hand-bearing compass. A good one is light, floats or is rubber-armoured, has a lit card or a small battery light for night use, and lets you read the card at the same instant as you sight the object. Some models use a prism so that the bearing is read in the eyepiece; others use a sighting notch, with the card visible alongside.

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Image: Mcapdevila, CC BY-SA 4.0, via Wikimedia Commons

Using it well

• Find your own best position. Walk the deck with the compass pointing at a fixed distant object and watch for changes in the reading. Magnetic influences such as the engine, the windlass, steel stanchions, a winch handle in your pocket, a phone or a camera can shift it by several degrees. Mark the quiet spots (often the stern, well clear of the engine and the binnacle) and use them every time.
• Check it against the steering compass. Sight a charted transit and compare. Then compare the hand-bearing compass against the steering compass on several headings. Large differences point to deviation in one or the other.
• Steady the instrument. Brace both elbows against the shrouds or the backstay, breathe out and read as the card steadies. In a seaway take the mean of the highest and lowest readings you see on the card as it swings.
• Aim at the base of a vertical object. A lighthouse is charted at its centre, so sight the middle of the tower, not the top of the lantern gallery. For a headland, take the steepest tangent edge and remember the charted position is the point, not the middle of the cliff.
• Be quick. At 6 knots the boat moves a cable (185 m) in a little over a minute, so a fix that takes five minutes to gather is already spread over half a mile.
• Write each bearing down at once with the time and the name of the mark, before you move on to the next object. Never trust memory.

How accurate is a bearing?

A reasonable hand-bearing compass reading from a yacht at sea is good to about plus or minus 2 to 3 degrees. The 1 in 60 rule tells you what that does to the position line. One degree of error displaces the line by about 1 mile for every 60 miles of distance, or about 1/60 of the distance. So:

This is why near objects are better fixing marks than far ones, and why a fix on a lighthouse 15 miles away should be treated as a rough check, not a precise position.

The Three-Bearing Fix

The three-point (three-bearing) fix is the standard Day Skipper visual fix.

Choosing marks

• Choose three charted, positively identified objects.
• Spread them well: ideally about 60 degrees apart (with three marks) — never closer than about 30 degrees, never near 180 degrees, as the lines then cross at shallow angles and small errors produce large position errors.
• Prefer near objects to distant ones.

Procedure

1. Identify all three marks on the chart before you go on deck.
2. Stand clear of steel rigging, the engine, speakers and mobile phones, which deflect a hand-bearing compass.
3. Take the bearing that changes most slowly first (the one nearest the bow or stern), and the one changing fastest (nearest the beam) last. This minimises the error caused by the boat moving between bearings.
4. Note the time and the log reading as you take the last bearing.
5. Convert each bearing from Magnetic to True if you are plotting with a True rose. A hand-bearing compass held away from the boat's influences has no deviation, so only variation applies.
6. Plot each bearing as a line from the object, drawn towards the sea (the reciprocal direction is where you are — you are on the bearing line through the object).
7. Mark the fix with a dot in a circle, labelled with the time and log reading, for example 1030 / 24.6.

Plotting each bearing with a Portland plotter

1. Set the bearing on the dial. If it is still magnetic, set it against the variation scale at the chart's variation instead of the main index, and the plotter converts it to true for you.
2. Put the plotter on the chart and turn the whole plotter, not the dial, until the grid lines on the dial lie along the meridians with N towards the top.
3. Keeping it square, slide it until the edge runs through the charted mark.
4. Draw the line on the sea side of the mark, then repeat for the next mark.

Try it with the digital Portland plotter. The exercises at the end of this lesson include a three-bearing fix plotted on its practice chart.

Worked example — converting bearings

Variation is 2 degrees W. You take: Lighthouse 035 degrees M, Church spire 340 degrees M, Headland 285 degrees M. Converting Magnetic to True: West is best, so subtract going from Magnetic to True (True = Magnetic minus westerly variation). True bearings: 033, 338 and 283 degrees T. Spacing 033 to 338 is 55 degrees, 338 to 283 is 55 degrees — a good spread.

The Cocked Hat

Three bearings rarely meet at a single point. They usually form a small triangle called a cocked hat. Its size tells you how good the fix is.

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• Small (under about a quarter of a mile): accept the fix; take the position at the centre of the triangle, or — prudently — at the corner nearest danger.
• Large (over about half a mile): something is wrong. Check for a misidentified mark, a mis-read or mis-plotted bearing, variation applied the wrong way, or a large time gap between bearings. Retake the fix.
• Consistent large triangle every time: suspect a systematic error, such as compass deviation from something in your pocket or the wrong variation.

Always assume you are at the point of the cocked hat that puts you closest to the nearest hazard until you can prove otherwise.

Transits

A transit is when two charted objects are seen exactly in line. It is the most accurate LOP available because no compass is involved — the line is defined purely by geometry.

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Uses of transits:

• Position line: a transit crossed with a bearing gives an excellent fix.
• Compass check: compare the charted bearing of a transit with what your steering compass reads when the boat's head lies along it. The difference (after variation) is deviation on that heading.
• Leading lines: harbour authorities often build leading marks so that a vessel on the transit is in the safe channel.
• Detecting tidal set: if you steer for a mark and the transit behind it opens, you are being set sideways.

Natural transits — a church in line with the edge of a headland, a beacon in line with a cottage — can be found in pilotage books or planned yourself from the chart.

Depth as a Position Line

An echo sounder gives a valuable check. Correct the reading to a charted depth by subtracting the height of tide (and allowing for the transducer or keel offset your instrument is set to). If the result is, for example, 10 metres, you must be close to the 10 metre contour. A single sounding is weak on its own, but:

• crossing a steep, distinct contour is a reliable LOP;
• a line of soundings taken at regular intervals along your track can be matched against the chart (a "line of soundings" fix);
• a sudden shallowing when you expected deep water is an immediate warning that your assumed position is wrong.

The Running Fix

When only one charted object is visible — a lone lighthouse on a featureless coast — you can still fix by using the boat's own movement. This is the running fix.

Procedure

1. Take a bearing of the object, note the time and log, and plot LOP 1.
2. Hold a steady course and speed. Wait until the bearing has changed by at least 30 degrees — ideally 45 to 90 degrees.
3. Take a second bearing, note time and log, and plot LOP 2.
4. From any point on LOP 1, lay off the course made good (water track corrected for tidal stream over the interval) and the distance run.
5. Through the end of that line draw a line parallel to LOP 1 — this is the transferred position line. Mark it with double arrowheads.
6. Where the transferred LOP crosses LOP 2 is your fix at the time of the second bearing.

Worked example

At 1000 a lighthouse bears 010 degrees T. You steer 045 degrees T at 5 knots. At 1030 it bears 320 degrees T. In 30 minutes you run 2.5 miles. Assume no tidal stream. From any point on the 1000 LOP draw 045 degrees T for 2.5 miles, transfer the 1000 LOP parallel through that point, and where it cuts the 1030 bearing is the 1030 running fix. If the tidal diamond shows a stream of 1 knot setting 090 degrees T, apply 0.5 miles along 090 degrees before transferring — otherwise your fix will be in error by that half mile.

The running fix is only as good as your course and distance between bearings, so it is less reliable than a simultaneous fix. Label it clearly as a running fix in the log.

Dead Reckoning and Estimated Position

Between fixes you keep track of the boat by calculation.

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• Dead Reckoning (DR): from the last fix, lay off the course steered (converted to True) and the distance run by log. Ignores tide and leeway. Symbol: a short line across the track, labelled with the time.
• Estimated Position (EP): the DR position, then corrected for leeway and for tidal stream over the same period. Symbol: a triangle with a dot. This is the best estimate you have without a new fix.

Plotting an EP — step by step

1. From the last fix, draw the water track: the heading corrected for leeway, in True, with the distance from the log. Mark with one arrowhead.
2. From the end of the water track, draw the tidal stream vector: direction and rate from the tidal diamond or tidal stream atlas, multiplied by the time elapsed. Mark with three arrowheads.
3. The end of the tidal vector is the EP. The line from the fix to the EP is the ground track (course over ground), marked with two arrowheads.

Worked example

Fix at 1400, log 12.0. Compass heading 095 degrees C, deviation 2 degrees E, variation 2 degrees W, so the True heading is 095 (C) plus 2 E = 097 M, minus 2 W = 095 degrees T. Wind from the north giving 5 degrees of leeway, pushing you south: water track 100 degrees T. At 1500 the log reads 17.5, so 5.5 miles through the water. The diamond gives 1.5 knots setting 045 degrees T for this hour. Plot 100 degrees T for 5.5 miles, then 045 degrees T for 1.5 miles. The EP lies about 1.1 miles north and 1.1 miles east of the end of the water track.

Leeway

Leeway is the sideways drift of the boat caused by wind pressure on the sails, hull and rig. The boat points one way but moves through the water slightly downwind of that heading.

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• Typical values: 0 to 3 degrees on a reach in moderate wind, 5 to 10 degrees close-hauled in a fresh breeze, more in a shallow-draught boat or when motoring slowly into wind.
• Estimate it by looking at the angle between the wake and the fore-and-aft line, using a hand-bearing compass on the wake.
• Apply it downwind: if the wind is on the port side, you slip to starboard, so add leeway to the heading; wind on starboard, subtract.
• When working out a course to steer, apply leeway the other way — steer up into the wind to compensate.

Course to Steer (summary)

The course to steer (CTS) is the reverse of the EP: you know where you want to go and must find the heading which, combined with tidal stream, keeps you on the ground track. In outline:

1. Draw the ground track from the start to the destination and extend it.
2. From the start, lay off the tidal vector for one hour (or for the expected passage time).
3. From the end of the tidal vector, swing an arc of radius equal to your boat speed (for the same time) to cut the ground track.
4. The line from the end of the tidal vector to that point is the water track; measure its direction.
5. Adjust for leeway (into the wind), then convert True to Magnetic to Compass.

With a 2 knot stream setting 180 degrees T across a 270 degrees T ground track at a boat speed of 5 knots, the geometry gives a heading of about 294 degrees T (the stream needs a correction angle whose sine is 2 divided by 5, about 24 degrees). Speed made good along the track is about 4.6 knots. The diagrams below show the vector triangle and a worked calculation. This calculation is covered in depth, with full worked examples, in the Course Plotting and Tidal Navigation lesson.

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Reference Tables in the Almanac

Three small tables in the reference section of any almanac (and of the RYA Training Almanac used in the shorebased course) save time at the chart table:

• Distance for a given speed and time. Enter with speed in knots and time in minutes to read the distance run; it is the fastest way to turn a log interval into a DR distance when you have no calculator. Check one line of it by mental arithmetic (6 knots for 20 minutes is 2 miles) so that you can see at once if you have read the wrong row.
• Compass deviation table. Each boat should carry a deviation card prepared by swinging the compass; the almanac prints a blank table and the method. Deviation varies with the boat's heading, so always enter the table with the ship's head, not the bearing you are taking. A hand-bearing compass used well clear of magnetic influences has no usable deviation card, which is why it is checked against transits instead.
• Lights: distance off when rising and dipping. Enter with the height of the light (from the chart) across the top and your height of eye down the side to read the distance at which the light appears over or dips below the horizon. It is the geographic range formula tabulated, and it gives a circle of position to combine with a bearing at night.

The almanac's list of abbreviations is the key to the port pages and passage notes (AB alongside berth, ca cable, Ldg leading, Lt Ho lighthouse, SWM safe water mark, and so on); keep it to hand until the abbreviations are second nature.

Keeping the Navigational Log

The log book is a legal record, a safety tool and the raw material for every DR and EP you plot. If the electronics fail, a good log lets you construct an EP from the last fix.

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Record at least hourly, and at every alteration of course, fix, change of sail plan or significant event:

In confined waters, poor visibility or near danger, log every 15–30 minutes. Write the GPS latitude and longitude down regularly — if the plotter dies, that is your last known position.

Choosing and Combining Fixing Methods

Not every method is equally good. As a rule of thumb, rank them by how little they depend on measurement error:

Combinations that work

• Transit plus bearing. Cross a transit with a hand-bearing on a third mark. The transit pins you to a line exactly; the bearing locates you on it.
• Bearing plus depth. If you are on a bearing line and the echo sounder shows a charted 10 m (after tide correction), the point where the line crosses the 10 m contour is a plausible position. Confirm with a second sounding a few minutes later.
• Bearing plus radar range. On a lone lighthouse, a radar range gives a circle of position that crosses the bearing line at a good angle. The radar range is usually more accurate than a visual bearing; use the radar for range, the hand-bearing compass for bearing.
• Two objects and a clearing line. Where you cannot get a third bearing, use a transit as a clearing line and treat the intersection as a fix.

Angle of cut

Whatever the method, the angle at which the two lines cross matters. Lines that cross at 90 degrees give the best fix; the error area is a small square. At 30 degrees it is a long thin diamond several times longer than it is wide, and at 150 degrees it is the same shape. Prefer marks whose bearings differ by 60 to 120 degrees for two marks, or about 60 degrees between marks for three.

Plot Conventions

Good plotting is part of the RYA assessment. Use the standard symbols and keep the chart clean.

Keep pencil lines light and short: rub out obsolete lines when you have no further use for them, and write bearings along the line they belong to. The skipper reading your chart in a seaway should be able to see the last fix, the DR or EP since then, and the intended track in a glance.

Fix Frequency and Judgement

The RYA syllabus expects the Day Skipper to work out how often to fix, based on risk. A useful rule:

• Open water, no dangers within 5 miles: every 30 to 60 minutes, and always at a change of course.
• Coastal passage with the shore in sight: every 15 to 30 minutes.
• Near dangers, in a tidal stream, or in poor visibility: every 10 to 15 minutes, or continuously by clearing lines.
• Immediately whenever something does not look as expected: a mark that does not appear, a sounding that does not match.

Each fix should also be tested against the last EP. If the new fix is more than the likely error (say a quarter of a mile after an hour) from the EP, find out why: a stronger stream than predicted, more leeway, a log reading too high, or a blunder in the fix.

Using GPS Correctly

Electronic position fixing is normal practice in the modern yacht, and the RYA expects you to use it properly. That means:

• Check the datum. Set the receiver to WGS84 unless the paper chart instructs otherwise. A chart printed on OSGB36 or ED50 can be 100 m or more out compared with WGS84. Most modern Admiralty charts carry a note about satellite-derived positions; read it.
• Know the limits. Standard GPS is good to about 5 to 10 metres in open sky; in a harbour entrance with high buildings or in poor satellite geometry it can be much worse. Chartplotters may also show an unreliable chart overlay at the zoom you are using.
• Plot a GPS position on the paper chart regularly, at least hourly, and note the latitude and longitude in the log. Compare it with the EP: the difference tells you the true tidal stream and leeway.
• Use the data fields sensibly. Course over ground (COG) and speed over ground (SOG) give the ground track and speed made good directly; the difference between COG and your steered heading is the combined effect of tide and leeway.
• Cross-check with the echo sounder and visual marks. If the plotter places you in 20 m of water but the sounder reads 4 m, believe the sounder.
• Have a backup. A handheld GPS in a waterproof bag, a second source of position on a phone, and the paper chart. Keep the paper chart up to date with Notices to Mariners corrections.

GPS is a source of position; the skipper is responsible for judging whether the position makes sense.

Worked Example — A Morning on the South Coast

You leave a harbour at 0900 bound east along the coast, 4 miles offshore, motor-sailing at 5 knots.

1. 0900: Departure fix from the harbour entrance light and two headlands. Cocked hat is under 0.1 mile. Logged: 0900, log 0.0, fix.
2. 1000: Plot a DR: 090 degrees T for 5.0 miles. Then the EP: tide sets 070 degrees T at 1.2 knots, so add 1.2 miles on 070. The EP is about 0.4 miles north of the DR — closer to the shore than intended.
3. 1005: Take a three-bearing fix: lighthouse 350 degrees M, spire 040 degrees M, headland 290 degrees M (variation 2 W, so 348, 038, 288 T). The cocked hat is 0.15 miles across and lies 0.2 miles north-east of the EP. Accept, plot at the corner nearest the shore.
4. 1010: Cross-check with the plotter: GPS position agrees to within 0.1 miles. The echo sounder reads 14.2 m, tide height 2.4 m, so the charted depth is about 11.8 m — consistent with the chart.
5. Decision: you are being set inshore more than expected; alter 5 degrees to seaward and recalculate the course to steer for the next headland.

Worked Example: A Running Fix With Tide

This is the full running fix as the RYA expects you to plot it, including the tidal stream.

You are heading 090 degrees C along a coast, with deviation 2 degrees W and variation 3 degrees W. Heading: 090 C, deviation 2 W gives 088 M, variation 3 W gives 085 T. Speed 6 knots through the water, no leeway because you are on a broad reach in a light breeze. A lighthouse is on the starboard bow but there is no other mark.

1. 1100. Lighthouse bears 125 degrees M. Convert to True: 125 minus 3 = 122 T. Plot the LOP, through the lighthouse, labelled 1100 / 122 T. Log reads 30.0.
2. 1130. Lighthouse bears 175 degrees M, so 172 T. Plot LOP 2, labelled 1130 / 172 T. Log reads 33.0.
3. Water track. Water track is 085 T, 3.0 miles (the log difference).
4. Tidal stream. The tidal diamond gives 2.0 knots setting 060 T for the half hour, so the stream moves you 1.0 mile towards 060 T.
5. Transfer. From any convenient point on LOP 1, lay off 085 T for 3.0 miles and then 060 T for 1.0 mile. Through the end of the vector draw a line parallel to LOP 1 (122 T). Mark it with two arrowheads and label 1100 transferred to 1130.
6. Fix. The point where the transferred LOP crosses LOP 2 is the 1130 running fix. Label the fix 1130 / 33.0, and log it as a running fix.
7. Assess. The bearing changed by 50 degrees, so the angle of cut is good. The result relies on the predicted stream of 2 knots; if the true stream were 1 knot higher the fix would be 0.5 miles off. Treat the position as an approximate fix: stay a margin further offshore than the plot suggests until a second independent check.

Compare the same fix without tide: you would have transferred only 3.0 miles along 085 T and plotted the fix up to a mile away from the correct position. This is the most common examiner point: forgetting the tidal stream in the transfer.

Exam Tips

• Quote your plotting conventions aloud: "That is a fix, with time and log." Instructors are looking for you to name the method and the quality.
• When asked "how good is this fix?", discuss the angle of cut, distance to the marks, the cocked hat and how recently the bearings were taken.
• Always state your assumptions about the tidal stream (source, rate, direction, time).
• On a practical, expect to be asked to take a three-bearing fix under way, plot it without help and give your best estimate of the boat's position, including what you are doing to stay clear of the nearest danger.
• Show that you check GPS against the chart, and that you know the datum of the chart.

Common Mistakes

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• Navigating by GPS alone. Cross-check with a visual or depth fix at least every hour on passage, more often near danger.
• Ignoring leeway. Five to ten degrees uncorrected over a few hours puts you a mile or more off track, often towards a lee shore.
• Accepting a big cocked hat. Retake the fix and find the error.
• Applying variation or deviation the wrong way. Use a memory aid: "Error West, Compass Best; Error East, Compass Least" (when going from True to Compass, add West, subtract East).
• Plotting bearings from the wrong end. The LOP passes through the object; you are on it.
• Using buoys or features marked PA/ED as fixing marks.
• Forgetting to note time and log at the moment of the fix, making it useless for later EPs.
• Taking bearings near metal or with a phone in your pocket.
• Incomplete log. If the electronics fail, an empty log means you have no last known position.

Summary

• An LOP is a line you know you are on; two or more crossing LOPs make a fix.
• The three-bearing fix is the standard visual fix: well-spread, near, positively identified marks; slowest-changing bearing first.
• A small cocked hat is acceptable; assume you are at the corner closest to danger. A large one means an error — find it.
• Transits are the most accurate LOP and also check your compass.
• Depth soundings, corrected for tide, are a valuable independent check.
• A running fix transfers an earlier LOP by course and distance made good.
• DR uses course and distance only; EP adds leeway and tidal stream.
• GPS is an aid to be cross-checked, not a replacement for seamanship.
• Keep an hourly log, more often in confined waters.

Check Your Understanding

1. What is a line of position, and how many do you need to fix the boat?

Answer: A line on the chart on which the boat is known to lie at a given time. Two crossing LOPs give a fix; three are preferred so the cocked hat reveals any error.

1. Why should you take the bearing nearest the beam last when taking a three-bearing fix?

Answer: Bearings near the beam change fastest as the boat moves. Taking them last, closest to the time logged, minimises the error caused by movement between bearings.

1. Your cocked hat is 0.7 miles across. What do you do?

Answer: Treat the fix as unreliable. Check mark identification, the readings, variation and plotting, then retake the fix. Meanwhile assume you are at the position closest to danger.

1. Why is a transit more accurate than a compass bearing?

Answer: It depends only on two objects being in line, so there is no compass error, deviation or reading error involved.

1. A lighthouse is 6 miles away and your bearing is 3 degrees in error. Roughly how far is the LOP displaced?

Answer: About 1/60 of the distance per degree: 6 multiplied by 3 divided by 60 = 0.3 miles.

1. What is the difference between a DR and an EP?

Answer: A DR uses only course steered and distance run through the water. An EP also corrects for leeway and tidal stream, so it is the better estimate of the true position.

1. You are close-hauled on port tack (wind on the port side) and estimate 6 degrees of leeway. Heading is 200 degrees T. What is your water track?

Answer: With the wind on the port side you slip to starboard, so add: 206 degrees T.

1. Only one lighthouse is visible. How can you fix the boat?

Answer: With a running fix: take a bearing, run a known course and distance until the bearing has changed by at least 30 degrees, take a second bearing, then transfer the first LOP by the course and distance made good and cross it with the second.

1. Your echo sounder reads 9.0 m and the height of tide is 3.5 m. What charted depth should you look for (assume the sounder reads depth below the surface)?

Answer: 9.0 minus 3.5 = 5.5 m; you should be near the 5 m contour, in about 5.5 m charted depth.

1. Give two reasons not to rely on GPS alone.

Answer: Any two of: signal loss or jamming; power or equipment failure; datum mismatch between receiver and chart; inaccurate or out-of-date charts; it encourages heads-down navigation instead of keeping a lookout.

1. A hand-bearing compass reading may be 3 degrees in error. You are using a lighthouse 12 miles away. How far could your position line be displaced, and what does it tell you about choosing marks?

Answer: About 12 multiplied by 3 divided by 60 = 0.6 miles. Distant marks give poor position lines; prefer near, well-spread marks.

1. In a running fix a 2 knot stream sets 060 degrees T. The bearings were 30 minutes apart. What must you add when transferring the first position line, and what happens if you forget?

Answer: One mile along 060 degrees T, in addition to the water track (course and log distance). If you forget, the fix is displaced by about one mile.