Advanced Chartwork for Coastal Skippers - Three Bearing Fixes

Prerequisites

This lesson assumes you have completed the RYA Day Skipper shorebased theory (or equivalent) and can already:

• Convert between True, Magnetic and Compass directions using variation and a deviation card.
• Plot a two- or three-bearing fix and lay off a simple course to steer for one hour of tidal stream.
• Read a tidal diamond and a tidal stream atlas, and find times and heights of high and low water for a standard port in the Admiralty Tide Tables (ATT) or Reeds Nautical Almanac.
• Recognise IALA Region A buoyage and the common symbols of Admiralty chart 5011 (INT 1).

The RYA Coastal Skipper / Yachtmaster Offshore shorebased course is the theory foundation for this lesson. Its entry standard is Day Skipper shorebased knowledge, there is no minimum age for the theory course, and the written papers are passed at 60 per cent. For the Yachtmaster Coastal practical exam you also need the sea time and qualifying passages set out in the exam requirements (including 800 miles, 30 days at sea, 2 days as skipper and 12 night hours, with the practical exam taken at 17 or over). The exam is chartwork-heavy and is done with a paper chart, tables and almanac extracts, so the skills here must be fluent rather than merely familiar.

Learning Objectives

By the end of this lesson you will be able to do the following. Each objective is mapped to the RYA Coastal Skipper / Yachtmaster shorebased syllabus areas (G158) that the written papers and the practical exam test: position fixing, course shaping and plotting, tidal knowledge, and use of almanacs and Admiralty publications.

• Explain chart datum, charted depths, drying heights and heights above MHWS, and state the limits of chart accuracy (syllabus: use of Admiralty publications, chart information).
• Correct a compass error using a deviation card, a transit or a leading line, and update variation for the year (syllabus: course shaping, compass).
• Distinguish Dead Reckoning (DR) from Estimated Position (EP) and work an EP that includes tidal stream and leeway (syllabus: position fixing, course shaping and plotting).
• Choose, take and assess a three-bearing fix and diagnose a poor cocked hat (syllabus: position fixing by visual bearings).
• Use transits, clearing bearings, horizontal and vertical sextant angles, danger angles and doubling the angle on the bow (syllabus: position fixing, safe pilotage).
• Construct a running fix that transfers a position line correctly for tidal stream (syllabus: position fixing).
• Calculate times and heights of tide at secondary ports by interpolation, then find height at a given time and time for a given height (syllabus: tidal knowledge, almanacs).
• Calculate depth over a bar, clearance under the keel and depth of water for anchoring (syllabus: tidal knowledge, safe pilotage).
• Interpolate tidal stream rates for the actual range of the day and use them in a multi-hour course to steer (syllabus: tidal streams, course shaping).
• Verify position with soundings corrected for height of tide, and cross-validate GNSS against traditional methods (syllabus: electronic position finding equipment, position fixing).
• Present chartwork to examiner standard.

Why Advanced Chartwork Still Matters

A chartplotter tells you where the GNSS receiver thinks it is. It does not tell you whether that is right, whether the chart beneath it is on the same datum, or what the tide will do to you in the next two hours. At Coastal Skipper level the examiner expects you to navigate a yacht by night and day in tidal waters with no electronic aids at all, and to treat GNSS as one input among several. Electronics fail through flat batteries, water ingress, lightning and software faults; GNSS is also degraded by jamming, spoofing and multipath.

The difference between Day Skipper and Coastal Skipper chartwork is less about new techniques and more about rigour: multi-hour tidal vectors, interpolation rather than "nearest table", error budgets, and a habit of asking "how sure am I?" every time a mark goes on the chart. The RYA examiner will ask you at random moments where you are, where you will be in an hour, and what you would do if the plotter died now. This lesson gives you the tools to answer all three from a paper chart.

Chart Information You Must Understand

Before any plotting, you must read the chart itself correctly.

Datums and heights

• Chart datum (CD) is the level from which charted depths and tidal heights are measured. On British Admiralty charts it is Lowest Astronomical Tide (LAT), the lowest level predicted under average meteorological conditions. The sea can fall below chart datum with high pressure and an offshore wind, but rarely by much.
• Charted depths are in metres below chart datum. The depth of water at any moment is the charted depth plus the height of tide.
• Drying heights are underlined figures on the chart: metres above chart datum. The depth of water over a drying height is the height of tide minus the drying height.
• Heights of lights, towers and land are above Mean High Water Springs (MHWS), not above chart datum. At low tide a lighthouse stands higher above the sea than the charted figure.
• Clearance under bridges and cables is also measured from MHWS (check the chart note), so at high water springs you have the least clearance.
• Horizontal datum. Modern charts use WGS 84, the datum GNSS uses. Older charts may carry a note such as "Satellite-derived positions in this area cannot be plotted directly on this chart: move positions 0.05 minutes North and 0.03 minutes East". Read the note and never ignore it. On an unconverted chart a GNSS position can be tens or even hundreds of metres out.

Chart reliability

The source data diagram (or CATZOC zone of confidence on newer charts) shows how and when an area was surveyed. A chart based on a survey of the 1800s with widely spaced leadline soundings tells you the seabed might hide dangers between the soundings. Treat poorly surveyed areas with extra margin and do not run your 'safe' line close to a charted danger. Charts must be corrected from Notices to Mariners (and the temporary and preliminary notices) before use, and every skipper should know the date of the last correction.

Chart symbols

The symbols on chart 5011 (INT 1) are the dictionary you must be able to read without looking them up. Check in particular rock symbols (a cross for a rock awash, a dotted outline for a danger area, a plus sign for a submerged rock), wrecks (dangerous or non-dangerous), tidal diamond letters, overfalls, charted traffic separation schemes, restricted areas and cable and pipeline areas.

Compass Corrections and Checks

The compass is your primary directional reference. Chartwork is done in True; steering is done in Compass.

• Variation is the difference between True and Magnetic north, taken from the nearest compass rose on the chart and updated for the year using the annual change printed in its centre. For example, 2°30' W in 2015, decreasing by 8' a year, becomes 2°30' minus 80' = 1°10' W in 2025.
• Deviation is the error of your own compass caused by the boat's magnetic fields (engine, electronics, tools, speakers). It changes with heading and is found from the deviation card made when the compass is swung.

The order for converting a chart course to a helm course is True, Variation, Magnetic, Deviation, Compass ("True Virgins Make Dull Compasses"). Going from True to Compass, add West and subtract East. Going from Compass to True, do the reverse.

Checking the compass at sea

A compass check by transit or leading line takes seconds and proves the card is still valid.

1. Find a charted transit or leading line and read its true bearing from the chart.
2. Steer the boat exactly along it, or take a bearing across the transit with the steering compass, and note the compass reading.
3. Convert the true bearing to Magnetic using variation, then compare with the compass reading. The difference is the deviation on that heading.

Example: a pair of leading marks has a charted true bearing of 345°T. Variation is 1°W, so the magnetic bearing is 346°M. You steer along the line with the compass reading 350°C. Deviation = Magnetic minus Compass = 346 minus 350 = 4°W on this heading. If the card says 1°W for that heading the card is wrong by 3° and you should recheck it before relying on the compass at night or in poor visibility.

Remember that a hand-bearing compass held well away from the boat's steel, engine and electronics should show variation only, so a hand-bearing is usually converted with variation alone. If the hand-bearing compass disagrees with a known transit by more than 2 or 3 degrees, you are standing too near something magnetic.

Chartwork Standards

Your chart is a legal and practical record. Another competent navigator should be able to pick it up at any moment and understand where you are, where you were and what you intend. The diagram below shows the standard conventions.

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Rules the examiner looks for:

• Every fix, EP, DR and course alteration carries a four-figure time, with the log reading in the log book.
• Vectors are drawn to scale using dividers against the latitude scale (never the longitude scale), with direction and rate labelled.
• Use a soft 2B pencil, light lines for construction, and erase only when the information is genuinely obsolete.
• Work in True on the chart; convert to Compass only for the helmsman, and write both.
• Keep the chart clear. A ground track with a half-dozen overlaid constructions is a puzzle to anyone else, so rub out finished constructions once their result is marked.

Untidy work is not just cosmetic: missing times and stray lines are how navigators mistake an old EP for a current one.

Dead Reckoning and Estimated Position

Dead Reckoning (DR) is the position found by laying off only the course steered and the distance run through the water (from the log) since the last fix. It ignores tidal stream and leeway.

Estimated Position (EP) is the DR corrected for every external influence you can estimate: tidal stream (from diamonds or the atlas, interpolated for the day's range), leeway (from wind strength and point of sail) and any surface drift.

Why it matters

In the English Channel or the Solent, streams of 2 to 4 knots are routine. A boat logging 5 knots for one hour with a 2-knot cross stream ends up 2 nm from its DR. Over any leg longer than about 2 nm in tidal waters, an EP is mandatory: a DR alone is simply wrong.

Working an EP step by step

1. From the last fix, draw the heading steered corrected for leeway. Leeway is applied downwind: if you steer 090°T with the wind from the north (on your port side) and 5° leeway, the water track is 095°T.
2. Mark off the distance run through the water (log reading difference) along that water track.
3. From that point, lay off the tidal vector for the period: direction from the diamond or atlas, rate interpolated for the day's range, multiplied by the time.
4. The end of the tidal vector is the EP. Draw the triangle and write the time.
5. Join the fix to the EP with the ground track (double arrow). Measure its direction and length to give the course made good (CMG) and speed made good (SMG).

Worked example

At 1400 you fix your position. Log 23.4. You steer 220°M; variation is 2°W so the heading is 218°T (Magnetic minus West gives True). The wind is north-west force 4, on your starboard beam, and you estimate leeway at 5°. A wind from the starboard side pushes the boat to port, so the water track is 213°T.

At 1500 the log reads 29.0, so you have run 5.6 nm through the water. The diamond for this hour gives 090°T at 1.6 knots at springs and 0.8 knots at neaps. Today's range is midway between springs and neaps, so you use 1.2 knots.

Plot 213°T for 5.6 nm, then 090°T for 1.2 nm. Working it out: 5.6 nm on 213°T moves you 4.7 nm south and 3.05 nm west; the stream then moves you 1.2 nm east, so the net movement is 4.7 nm south and 1.85 nm west. The EP at 1500 lies on a ground track of about 201°T, 5.1 nm from the 1400 fix, so CMG is 201°T and SMG is 5.1 knots. Write "1500 EP" against the triangle.

Notice what the DR alone would have told you: 5.6 nm on 218°T, a position about 1.6 nm west of the EP. Ignoring leeway and tide, you would be wrong by about 1.6 nm in one hour.

Assessing the EP

An EP carries uncertainty that grows with time since the last fix. A sensible working allowance is about 10 per cent of the distance run through the water plus any doubt in the tidal rate. Ask: how good was the last fix? Has the wind shifted, changing leeway? Was the helmsman holding the course? Fix again before closing any danger.

Estimating leeway

Leeway depends on wind strength, point of sail, hull shape and sea state. Typical values for a cruising yacht are 0° running, 2° to 5° reaching and 5° to 10° close-hauled (more when heavily reefed and pitching). Measure it: take a hand-bearing along the wake and compare it with the reciprocal of the heading. If you steer 090° and the wake bears 262° rather than 270°, leeway is 8°. A power vessel with high windage and little draft in a beam wind at low speed can make more leeway than a sailing yacht.

Three-Point Fixes

A visual fix from three compass bearings remains the most reliable traditional fix. The third bearing is what turns a "position" into a checked position.

Choosing objects

• Use charted, positively identified, permanent objects: lighthouses, church spires, conspicuous towers, headland extremities (with care: a sloping headland's apparent edge moves with your angle of view).
• Aim for angles between position lines of at least 30°, ideally around 60° between two lines or about 120° spread between three.
• Prefer near objects to far ones: a 2° compass error at 1 nm is about 65 m; at 10 nm it is about 650 m.
• Avoid using objects that are all in the same half of the horizon if you can: a fix from three objects within a 60° arc is poorly conditioned.

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

Taking the bearings

1. Identify all three objects on the chart and work out the expected bearings from your EP first.
2. Take the bearing that changes fastest last (objects on the beam change fastest; those near ahead or astern change slowest).
3. Complete all three within about 60 seconds and note the time and log.
4. Apply deviation (if you used the steering compass) and variation to get True bearings.
5. Plot, and label the fix with the time.

When sailing at 6 knots, the boat moves 0.1 nm in a minute, so a slow set of bearings spread over three minutes creates a large false cocked hat by itself.

Reading the cocked hat

Three lines rarely meet at a point; they form a triangle, the cocked hat.

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• Small and roughly equilateral: random errors only. Take the centre, or the corner nearest danger if close to hazards.
• Large: suspect a systematic error such as wrong deviation, a misidentified object, or the boat moving significantly between bearings.
• Long and thin: one bearing is likely wrong, often the middle object, or the objects are poorly spread.

If the expected bearing of an object (from your EP) differs from the observed bearing by more than a few degrees, re-check its identification before believing the fix. A consistent offset in all three bearings indicates compass error: rotating all three lines by the same amount until they meet will tell you the size of the error.

The rule for the cocked hat near dangers. If you are in confined water, always assume you are at the corner of the triangle nearest the danger. If any corner of the triangle puts you on the wrong side of a clearing line, you are not safe.

Transits and Clearing Bearings

A transit is formed when two charted objects line up. It gives a position line that is independent of compass error and extremely sensitive: a small lateral movement visibly opens the marks.

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Clearing bearings define the edge of safe water. Draw a line from a conspicuous object that just clears a danger with a margin, read its bearing, and note "NMT" (not more than) or "NLT" (not less than). Always state the bearing as you will measure it, that is, the bearing of the object from the boat.

Example: a rock lies 0.3 nm off a headland light, on the north side of the approach. You approach from the west and want to pass at least 0.2 nm outside the rock, to the south. Draw the line from the light that clears the rock by 0.2 nm: it runs due west from the light (270°M), so seen from the boat on that line the light bears 090°M. If you are on the safe (south) side of the line, the light bears slightly less than 090°M. The clearing bearing is therefore "light NMT 090°M". Write it in plain words on the pilotage plan: "keep the light bearing not more than 090 magnetic". If the light bears more than 090°M, you have strayed towards the rock.

Combined verification:

1. A transit confirms where you are across the channel.
2. A clearing bearing confirms you are on the safe side of the hazard.
3. The echo sounder confirms the depth matches what you expect.

If the transit is on but the depth is wrong, stop and investigate: you may have the wrong pair of marks.

Horizontal and Vertical Sextant Angles

Sextant angles do not depend on the compass, so they give very accurate fixes close inshore. The examiner may ask for the principle even if you have no sextant aboard.

Horizontal sextant angles (HSA)

With the sextant held horizontally, you measure the angle between two charted objects, then between the middle and a third. Each angle defines a circle passing through the two objects and your position; the intersection of the two circles is the fix. Plot with a station pointer, or draw the rays on tracing paper and slide it over the chart until each ray passes through its object.

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A station pointer is a protractor with three arms. Set the two measured angles on it, then slide it over the chart until each arm touches its object; the centre is your position. The photograph below shows an older instrument of this kind.

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Image: Kognos, CC BY 4.0, via Wikimedia Commons (downscaled)

Its great virtue is that it uses no compass, so deviation and variation errors vanish; accuracy within about 50 m is achievable close inshore. Avoid the "danger circle" situation where all three objects and your position lie on the same circle: it gives no fix. Also avoid objects that subtend small angles (under about 30°) because small observation errors then move the position a long way.

Vertical sextant angles (VSA)

Measure the angle between the top of a lighthouse and the waterline at its base, so that the height you use is the height above the sea. Charted heights are above MHWS, so the true height above the water at the moment of observation is the charted height plus (MHWS minus the current height of tide).

Distance off (nm) = Height (m) x 1.856 / angle (minutes of arc)

Example: a light is charted at 55 m and the angle is 0°30' = 30'. Distance = 55 x 1.856 / 30 = 3.4 nm. Now correct for the tide: MHWS is 4.7 m and the height of tide is 2.0 m, so the true height above the water is 55 + 2.7 = 57.7 m. Distance = 57.7 x 1.856 / 30 = 3.57 nm. The uncorrected figure errs on the safe side (less distance than reality). Combine the VSA distance with a compass bearing of the same light to get a fix from one object. VSA is only valid if the base of the object is visible at the waterline; if land hides the base, you will measure too small an angle and over-estimate the distance.

Danger angles

A danger angle keeps you clear of a hazard without any need for a fix.

• Horizontal danger angle (HDA). Draw a circle that passes through two charted objects and just outside the danger. The angle subtended by the two objects at any point on that circle is constant. Points outside the circle see the objects at a smaller angle. Example: two beacons 1.0 nm apart, and a circle that clears the rock has an inscribed angle of 40°. The chord is 1.0 nm so the radius is 1.0 / (2 x sin 40°) = 0.78 nm. The note on the chart is "HDA NMT 40°". If you measure more than 40° with a sextant, you are inside the circle and in danger.
• Vertical danger angle (VDA). For an object of known height, calculate the angle that corresponds to the minimum safe distance and keep the measured angle less than that. Example: a 30 m tower and a minimum safe distance of 0.5 nm give an angle of 30 x 1.856 / 0.5 = 111' = 1°51'. The rule is "VDA NMT 1°51'". If the tower subtends more than that you are within 0.5 nm.

Doubling the angle on the bow

Note the time and log when a mark is, say, 30° on the bow. Hold course until it is 60° on the bow. The distance run between the two equals your distance off at the second bearing. The special case of 45° and 90° (the "four-point bearing") gives distance off abeam. It assumes no cross-tide; in a stream, use the distance over the ground, not the log distance.

Running Fixes with Tidal Stream

When only one charted object is available, a running fix transfers an earlier position line forward by the vessel's movement.

Procedure

1. At time 1 take a bearing of the object and plot it. Note the log reading.
2. Hold a steady course. When the bearing has changed by at least 30° (ideally 45° or more), take the second bearing at time 2.
3. From any point on the first position line, lay off the water track (with leeway) and the distance run.
4. From the end of that, lay off the tidal vector for the interval.
5. Through the end of the tidal vector, draw a line parallel to the first position line. Mark it with double arrows: this is the transferred position line.
6. Where the transferred line crosses the second bearing is the running fix.

Worked example

At 1000, Lighthouse A bears 045°T. Log 10.0. You steer 090°T at 5 knots with no leeway; the stream sets 270°T at 2 knots. At 1100, log 15.0, the lighthouse bears 315°T.

Lay 090°T for 5 nm from a point on the 1000 line, then 270°T for 2 nm, so the net movement is 3 nm to the east. Draw the transferred 045° line through that point; it crosses the 315° bearing at the 1100 running fix. By geometry, the fix is 2.1 nm from the lighthouse, on a bearing of 135°T from it (so the light bears 315°T from the boat).

Had you ignored the tide, you would have moved the line 5 nm east and the fix would be placed 3.5 nm from the lighthouse, about 1.4 nm from the true position and wrongly on the safe side. Keep the interval between the bearings to an hour or less in tidal waters: each error in course, log and tide accumulates.

A running fix is a better position than an EP but weaker than a simultaneous three-bearing fix; label it "RF" and treat it with care near dangers.

Tidal Heights: Standard and Secondary Ports

Standard ports have full daily predictions. Secondary ports carry time and height differences referenced to a standard port. At Coastal Skipper level you interpolate both, rather than picking the nearest value.

Time zones

Tide tables are normally in UT (or the zone time stated at the head of the page). During British Summer Time, you must add one hour to read your watch. Failing to convert is one of the most common exam errors. Always write "UT" or "BST" beside every time in your working.

Time differences

The secondary port table lists differences against particular standard port HW and LW times (for example, standard port HW at 0000 and 1200, and at 0600 and 1800). You interpolate according to the time of the standard port HW, not the range.

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Example. Standard port HW today at 0830 UT. Secondary port HW differences: at 0600 and 1800 = +0005; at 0000 and 1200 = -0010. 0830 lies 2.5 hours into the 6-hour gap between 0600 and 1200, so the difference moves 2.5/6 of the way from +0005 to -0010, a change of 15 minutes x 2.5/6 = 6 minutes. Difference = +0005 - 0006 = -0001. Secondary HW is therefore about 0829 UT (0929 BST).

An accuracy of plus or minus 5 to 10 minutes is usually adequate. Label your workings "Time diff" so that you never mix minutes with metres.

Height differences

Height differences are interpolated against the height of the tide at the standard port (between MHWS and MHWN for HW, between MLWN and MLWS for LW). Time and height differences are independent; you cannot derive one from the other.

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HW worked figures. The standard port has MHWS 4.7 m and MHWN 3.4 m, and today's HW is 4.0 m. At the secondary port the differences are -0.3 m at springs and -0.2 m at neaps. The difference today is -0.2 + (-0.1 x (4.0 - 3.4) / (4.7 - 3.4)) = -0.2 - 0.046 = -0.25 m. Secondary HW height = 4.0 - 0.25 = 3.75 m.

LW worked figures. The standard port has MLWN 1.5 m and MLWS 0.5 m, and today's LW is 0.9 m. At the secondary port the differences are +0.1 m at neaps and +0.3 m at springs. The fraction from MLWS to MLWN is (0.9 - 0.5) / (1.5 - 0.5) = 0.4. The difference today is +0.3 + 0.4 x (0.1 - 0.3) = +0.22 m. Secondary LW height = 0.9 + 0.22 = 1.12 m, call it 1.1 m. The range at the secondary port is 3.75 - 1.1 = 2.65 m.

Many people find the graphical method quicker: draw a small graph with the standard port heights on one axis and the differences on the other, join the spring and neap values with a straight line and read off today's value. Either is acceptable; show your workings.

Height at a given time and time for a given height

Once you have the secondary port HW, LW and range, use the standard port tidal curve (choose the spring or neap curve, or interpolate between them if the range is in between). The rule of twelfths is an approximation only, assuming a six-hour tide with the fall or rise in twelfths of 1, 2, 3, 3, 2, 1 in successive hours. It is a good check but the examiner wants the curve. For ports between Swanage and Selsey the standard port curves are special, and Portsmouth and Southampton need their own curves.

Example (rule of twelfths as a check). HW height is 3.75 m at 0829 UT and the range is 2.65 m. Two hours after HW (1029 UT), the tide has fallen 1 + 2 = 3 twelfths of 2.65 = 0.66 m, so the height is about 3.1 m.

Depth of Water: Bars, Clearances and Anchoring

Depth over a bar or drying bank

The depth over a drying height is the height of the tide minus the drying height. Example: draught 1.8 m, required clearance under the keel 1.0 m, so you need 2.8 m of water. The bar is charted with a drying height of 0.3 m, so you need a height of tide of at least 2.8 + 0.3 = 3.1 m. With HW 3.75 m and a range of 2.65 m, the tide must not fall more than 0.65 m below HW, which is about 25 per cent of the range, reached roughly two hours either side of HW. The bar is safe from about 0629 UT to 1029 UT (0729 to 1129 BST), with the tide at its deepest at 0829 UT.

Do not use the whole window. The usual practice is to plan to cross the bar with a margin of at least an hour from either end, and never to use the minimum clearance on an ebb tide you cannot afford to be stuck on.

Clearance beneath a bridge or cable

Charted clearances are measured from MHWS. At a lower tide there is more air clearance. Air clearance = charted clearance + (MHWS - height of tide at the time) - air draught. Example: clearance 12.0 m, MHWS 4.7 m, tide at passing 2.7 m, air draught 10.5 m. Air clearance = 12.0 + 2.0 - 10.5 = 3.5 m.

Depth of water for anchoring

Calculate the depth you will have at high water (when you need the most chain) and the depth at low water (so you stay afloat).

Example: anchoring at 1500 in a charted depth of 3.2 m, with the height of tide at that time 1.8 m and HW of 4.4 m at 2100. Depth now = 3.2 + 1.8 = 5.0 m. Depth at HW = 3.2 + 4.4 = 7.6 m. Add bow height above the water of 1.0 m: 8.6 m. At a scope of 5:1, you need 8.6 x 5 = 43 m of cable out. At low water of 0.6 m the depth will be 3.2 + 0.6 = 3.8 m, so with a draught of 1.8 m you have 2.0 m under the keel. Allow a swinging circle of cable length plus boat length, and check the holding and shelter.

Interpolating Tidal Stream Rates

Diamonds and atlases give spring and neap rates. For anything other than a pure spring or neap day, interpolate using the day's range at the reference port.

Rate = neap rate + (spring rate - neap rate) x (today's range - neap range) / (spring range - neap range)

Example: spring 2.5 knots, neap 1.2 knots; spring range 4.5 m, neap range 2.0 m; today 3.5 m. Rate = 1.2 + 1.3 x 1.5 / 2.5 = 1.98, call it 2.0 knots.

Most almanacs include a "computation of rates" graph that does this visually. Do not extrapolate far beyond springs: at exceptional springs the rate may exceed the tabulated figure, so add a margin near races and overfalls. In tidal atlases the rates are printed as two figures such as 13,25 meaning 1.3 knots at neaps and 2.5 knots at springs.

Streams are not constant across a channel and the diamond is only valid in the position shown: near headlands the stream can be much stronger and in bays it can eddy in the opposite direction. Allow for this in your margins.

Course to Steer over Several Hours

For a passage of more than an hour, lay off all the tidal vectors end to end from the start point, then swing an arc of the total water distance from the end of the last vector to cut the ground track.

1. Draw the ground track from start to destination.
2. Estimate passage time from distance and boat speed (say 2 hours).
3. From the start, lay off hour 1 and hour 2 tidal vectors in sequence.
4. Set dividers to boat speed x passage time; from the end of the second vector, strike an arc on the ground track.
5. The line from the end of the vectors to the arc point gives the water track. Correct for leeway (steer up into the wind) and convert to Compass.
6. If the arc cuts the ground track short of or beyond the destination, adjust the passage time and repeat.

Because the hourly streams partly cancel, this gives one steady course rather than several alterations, keeps you close to the intended ground track on average and avoids the cumulative error of averaging the tide. If you arrive at the end of hour 2 short of the destination, add a part-hour vector in proportion.

Tidal gates and planning

A tidal gate is a place where the stream is strong enough that you can only pass profitably, or only safely, at a particular time (a headland race, a narrow entrance). Plan backwards from the gate: decide the time you want to pass it, calculate the time to get there at the speed you will really make, and set your departure time. The RYA expects a margin of at least an hour at a gate in case of delay, and a plan B if you miss it.

Depth as a Position Check

The echo sounder is the one instrument that tells you about the seabed directly. Use it constantly to confirm position.

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Expected depth = charted depth + height of tide, adjusted for where your transducer is. Most instruments are set to show depth below the transducer, below the keel or below the surface; know which, and note the offset.

Example: charted depth 5.0 m, height of tide 3.0 m, so you expect 8.0 m of water below the surface. A sounder showing 4.5 m tells you either that you are not where you think, or that your tide calculation is wrong. Low barometric pressure and an onshore gale can raise sea level by 0.3 m or more; high pressure and offshore winds can lower it, sometimes by a similar amount.

Techniques: crossing a distinctive contour (the 10 m line off a headland) gives a position line; a line of soundings plotted on tracing paper at the chart scale can be slid along your track to match the seabed.

Cross-Validating GNSS

GNSS should be compared regularly with a visual fix or EP and the comparison logged.

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A practical rule: if GNSS and a good visual fix agree within about 0.25 nm in open coastal waters (much less in pilotage), carry on and log it. If they disagree by more, do not simply believe either: take an independent fix, check the GNSS datum setting and satellite status, and consider jamming. Examiners specifically look for candidates who notice and explain differences; silently accepting one source is a fail point.

Common causes of an apparent difference are a different datum (WGS 84 versus an old chart), a chartplotter offset between antenna and the helm, a stale or frozen position, and an uncorrected chart. Write the check in the log: time, GNSS position, visual fix, difference and action.

Worked Example: A Morning Passage

You leave a harbour mouth at 0800 BST (0700 UT) bound for a headland 11.5 nm away on a bearing of 245°T, with a harbour entrance and a bar 2 nm beyond it. You motor-sail at 6 knots. Variation is 2°W and deviation on the likely heading is 3°E. Draught is 1.8 m.

1. Tide heights. The destination is a secondary port. Standard port HW is 0830 UT (4.0 m), so from the height and time examples above, the secondary HW is 3.75 m at about 0829 UT and LW is 1.1 m, a range of 2.65 m. The bar dries 0.3 m and you want 1.0 m clearance under the keel, so you need a height of tide of 3.1 m, which is available from about 0629 to 1029 UT (0729 to 1129 BST). Your arrival at the bar at about 0930 UT (1030 BST) is within the window with an hour to spare.
2. Stream rates. The range today is 3.5 m, giving interpolated rates of 2.0 knots at 160°T for the first hour and 1.4 knots at 150°T for the second.
3. Course to steer. Plot the two tidal vectors from the start: the first moves you 0.7 nm east and 1.9 nm south, the second 0.7 nm east and 1.2 nm south, so the end of the second vector is 1.4 nm east and 3.1 nm south of the start. Swing an arc of 12.0 nm (6 knots for 2 hours) from that point to cut the 245°T ground track: it cuts at 11.6 nm, so the headland at 11.5 nm is reached in just under 2 hours. The water track is 261°T. The wind is north-west, on the starboard bow, and leeway is 5°, which pushes the boat to port, so steer 5° to windward: 266°T. Magnetic (add 2°W): 268°M. Compass (subtract 3°E): 265°C.
4. Monitoring. At 0900 BST (0800 UT) your EP is about 6 nm along the ground track. A three-point fix puts you 0.5 nm north of the EP, which is 0.2 nm north of the intended ground track. GNSS agrees with the fix within 0.1 nm. This is within tolerance, so you hold the course, log the difference and note that the stream is slightly weaker than predicted.
5. Approach. The headland light has a clearing bearing "light NMT 090°M" to keep you outside a reef. At 0930 UT the sounder reads 6.2 m; you expected the charted depth of 3.0 m plus a height of tide of about 3.5 m, 6.5 m, which is consistent with your intended track. A fresh fix confirms your position before the bar, which you cross with 1.0 m under the keel at a height of tide of about 3.5 m.
6. Compass check. As you line up the entrance leading marks (charted 087°T, 089°M with 2°W variation) you read 086°C on the steering compass, which gives a deviation of 3°E, matching the card.

Common Mistakes

The diagram below summarises the faults examiners see most often.

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• Trusting GNSS blindly. Always compare against an independent fix or EP.
• Running fixes without tide. In a 2-knot stream, one hour without the tidal vector is a 2 nm error.
• Mixing time and height differences. Time differences interpolate against standard port HW time; height differences against standard port height. Label each.
• Using the nearest diamond's spring rate on a neap day. Interpolate for the range.
• Applying leeway the wrong way. Leeway moves you downwind; to compensate, steer up into the wind.
• Using the longitude scale for distance. Always the latitude scale, level with your work.
• Forgetting UT and BST. Tide tables are usually in UT; your watch is in BST in summer.
• Long running-fix intervals. Keep to an hour or less in tidal waters.
• Undated marks. Every mark gets a four-figure time.
• Confusing the direction of a clearing bearing. State it as the bearing of the object from the boat, with NMT or NLT.
• Forgetting that charted heights are above MHWS. At low water a lighthouse is taller than charted, and a bridge has more clearance.
• Forgetting the tide when judging a bar. Check both that there is enough water and that you have a margin if you are delayed.

Practise "blind" chartwork: cover the plotter, navigate a 3 nm leg by chart, compass, log and tide only, then compare. Aim for errors under 0.25 nm.

Exam Tips

• Show every step of working: the examiner awards marks for method, so a correct answer with no working may lose marks.
• Write the units and the time zone on every figure.
• Check the answer for sense. A secondary port HW 50 minutes away from the standard port is plausible; 5 hours is a sign that you used the wrong column.
• Ask yourself after every plot whether the position is sensible: does it match the depth, the lights you can see and the time elapsed?
• In the practical exam, tell the examiner what you are doing and why, and state your confidence in your position without being asked.

Summary

• Charted depths are above chart datum (LAT) and heights of lights and land are above MHWS; read the chart notes on datum and the source diagram.
• DR uses only course and distance through the water; EP adds tide and leeway. In tidal waters, always work an EP and record CMG and SMG.
• Choose well-spaced, positively identified, near objects for fixes; take bearings quickly and read the cocked hat diagnostically.
• Transits, horizontal sextant angles and danger angles are free of compass error; clearing bearings mark safe water and must be stated as NMT or NLT.
• Use VSA to find distance off from a light: d = 1.856 x h / angle in minutes, adding the correction for height of tide.
• Running fixes must include the tidal vector and should span an hour or less.
• Interpolate secondary port time differences by standard port HW time and height differences by standard port height; use the curve for heights at a given time.
• Compute depth over bars, clearance under bridges and scope for anchoring from charted depth plus height of tide.
• Interpolate stream rates by the day's range and use the end-to-end vector method for a multi-hour course to steer.
• Expected depth equals charted depth plus height of tide; use soundings as a constant check.
• Cross-check GNSS regularly; investigate any unexplained difference.
• Present clean, timed, labelled chartwork that someone else could take over.

Check Your Understanding

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

Answer: A DR uses only the course steered and the distance run through the water. An EP adds tidal stream, leeway and other influences. In tidal waters any leg longer than about 2 nm needs an EP, because a 2-knot stream alone can move you 2 nm in an hour.

1. Your three-bearing fix produces a large triangle. What should you check?

Answer: Check the identification of each object against the chart, the deviation applied for your heading, and whether the bearings were taken quickly (within about 60 seconds). Compare each observed bearing with the expected bearing from your EP to find the rogue line.

1. Steering 090°T with the wind from the north and 5° leeway, what is your water track?

Answer: 095°T. Leeway pushes you downwind, which is to the south. To make good 090°T through the water you would steer 085°T.

1. Standard port HW is 0900 UT. Secondary port HW differences are +0020 at 0600 and 1800 and +0050 at 0000 and 1200. What is the secondary port time difference and the HW time in BST?

Answer: 0900 is halfway from 0600 to 1200, so the difference is halfway from +0020 to +0050: +0035. Secondary HW is 0935 UT, which is 1035 BST.

1. Diamond rates are 3.0 knots at springs and 1.4 knots at neaps. Spring range 4.0 m, neap range 2.0 m, today's range 3.0 m. What rate do you use?

Answer: 1.4 + (1.6 x 1.0 / 2.0) = 2.2 knots.

1. In a running fix, from where do you lay off the vessel's movement, and what must be included?

Answer: From any point on the first position line, lay off the water track and distance run, then the tidal vector for the interval. Draw the transferred position line through the end of the tidal vector, parallel to the original.

1. A light 40 m high above the sea subtends a vertical angle of 20 minutes of arc. Roughly how far off is it?

Answer: 40 x 1.856 / 20 = 3.7 nm.

1. Charted depth 2.4 m, height of tide 3.1 m, echo sounder (set to read below the surface) shows 9.5 m. What do you conclude?

Answer: You expected about 5.5 m. A reading 4 m deeper means you are probably not where you think (likely in deeper water off your intended track), or your tide calculation is wrong. Take an independent fix before going on.

1. GNSS and a good visual fix are 0.6 nm apart. What do you do?

Answer: Do not proceed on either alone. Take another independent fix, check the GNSS datum and satellite status, consider jamming or spoofing, and log the discrepancy and how you resolved it. Increase your margins until it is resolved.

1. A bar dries 0.5 m. Your draught is 1.6 m and you want 0.8 m under the keel. What height of tide do you need to cross it?

Answer: You need 1.6 + 0.8 = 2.4 m of water over the bar. The height of tide must be the water depth plus the drying height: 2.4 + 0.5 = 2.9 m or more.

1. A beacon pair has a horizontal danger angle of NMT 35°. You measure 42° with the sextant. Are you safe?

Answer: No. A larger angle means you are inside the danger circle, closer to the hazard than the safe boundary. Alter away from the danger immediately and take a fix.

1. A transit has a charted true bearing of 120°T and variation is 3°W. You steer along it with the steering compass reading 125°C. What is the deviation?

Answer: Magnetic bearing = 120 + 3 = 123°M. Deviation = Magnetic minus Compass = 123 - 125 = 2°W on this heading.