Position Fixing, Compass Errors and Tides

Prerequisites

You should already be able to plot a position, a bearing and a course on a paper chart, convert between True, Magnetic and Compass, and work a standard-port tide calculation, as taught in the RYA Day Skipper and Coastal Skipper/Yachtmaster courses. You should know the bridge equipment introduced in the bridge watchkeeping lesson (gyro, radar, ECDIS, GNSS, echo sounder) and the OOW's duty under MGN 315 to fix the position frequently, by more than one method.

For the Officer of the Watch (Unlimited) certificate (STCW Regulation II/1) you will normally be following an approved cadetship or have built up the required seagoing service, and you will be assessed on these topics in the MCA navigation examinations and the oral (MSN 1856 sets out the route; check the current version for exact service and course requirements). This lesson brings yacht-scale navigation up to merchant-ship standard: bigger draughts, tighter margins and a formal duty to know your compass error every watch.

Learning Objectives

Fix the ship's position by visual bearings, radar ranges and bearings, and a running fix, and judge how good each fix is.
Interpret a cocked hat and decide which point to plot.
Explain how a gyro compass and a magnetic compass work, and the errors each is subject to.
Find gyro error by transit, by amplitude and by azimuth, and work an amplitude from first principles.
Apply variation and deviation, and find deviation from an observed compass error.
Work a secondary-port tide using Admiralty Tide Tables (NP201).
Calculate under-keel clearance (UKC) allowing for tide, squat and survey accuracy.

Why Position Fixing Still Matters

GNSS gives a position every second, and ECDIS plots it on the chart. So why does STCW still demand that an OOW can fix by bearings and ranges? Because GNSS can fail, be jammed, be spoofed, or be fed to ECDIS with the wrong datum or a frozen antenna. MAIB and other investigators have recorded groundings where the OOW watched a perfectly plotted, perfectly wrong position. The OOW's duty is to cross-check the primary position source with an independent method, at intervals that suit the waters: every few minutes in pilotage, perhaps every 15 to 30 minutes on the coast, and as the master's standing orders require in the open ocean.

A fix is only as good as the information behind it. Every fix should be checked against the DR or EP, the echo sounder, and common sense.

Visual Fixes

Compass bearings

The classic coastal fix uses bearings of three charted, positively identified objects, taken with the gyro repeater's azimuth ring or a bearing circle and corrected for compass error before plotting.

Good practice:

Choose objects that are well charted and unmistakable: lighthouses, church spires, radio masts, the extremity of a steep headland. Avoid low points of land whose edge moves with the tide.
Choose nearby objects over distant ones: a 1° error puts the position line about 1 cable off at 6 miles, but only about 1.7 m off per 100 m of range.
For three objects, aim for a spread of about 60° (or 120°) between bearings. For two objects, aim for about 90°.
Take the bearings quickly. Take objects ahead or astern first (their bearings change slowly) and objects near the beam last (they change fastest). The time of the fix is the time of the last bearing.
Apply the gyro error (or compass error) before plotting. A bearing plotted without correction is a systematic error that no amount of care in plotting removes.

The cocked hat

Three position lines rarely meet at a point. They form a small triangle called a cocked hat. The diagram below shows a three-bearing fix with its cocked hat and a charted danger nearby.

Three bearings forming a cocked hat, with the fix taken at the corner nearest the charted rock

How to read it:

Small hat: normal small errors in reading and plotting. Plot the centre, or the corner nearest danger if the hat is close to a hazard.
Large hat: something is wrong. Check the identity of each object, the compass error you applied, the arithmetic, and how long you took between bearings. A large unknown compass error produces a hat even when everything else is perfect, because all three lines rotate the same way.
Always assume the worst: when in doubt, plot the position nearest the danger and navigate from there.

Transits and clearing lines

A transit (two charted objects in line) gives a position line with no compass error at all. It is the most accurate visual position line available, and the best way to check compass error (see below). Clearing bearings and clearing transits, drawn during passage planning, let the OOW see at a glance whether the ship is on the safe side of a danger without plotting a fix.

Radar Fixes

Radar gives ranges and bearings. They are not equally good:

Ranges are accurate. IMO radar performance standards (MSC.192(79)) require range accuracy within 30 m or 1% of the range scale in use, whichever is greater.
Bearings are less accurate. The horizontal beamwidth (typically 1° to 2° on X band) spreads a target's echo sideways, so the edge of a headland is measured too wide. Bearing accuracy is also only as good as the gyro input and heading line alignment.

So the best radar fix is three ranges of well-defined, steep-to objects (a small rock, a lighthouse island, a steep cliff). A range and a bearing of the same object is acceptable as a quick check. A visual bearing combined with a radar range of the same object is a very good fix: the best of both.

Watch for these errors:

Low coastlines: the radar paints the first high ground inland, not the waterline, so ranges are too long.
Misidentification: a radar picture of a coast looks different from the chart. Identify features before using them.
Racons and ramarks help identify a mark, but measure range from the start of the racon flash, which begins at the mark itself.

Parallel indexing is the radar equivalent of a clearing line. Draw a line on the display parallel to the planned track at the planned passing distance from a fixed target. If the target's echo stays on the line, the ship is on track. It gives continuous, real-time monitoring without plotting, and it works the same on ECDIS radar overlay.

Running Fix

When only one object is in sight, take a bearing, wait for its bearing to change by at least 30° (ideally nearer 90°), then take a second bearing. Transfer the first position line along the ship's movement over the ground in the interval, and the second position line crosses it at the running fix.

The diagram below shows the method with a tidal stream.

Running fix: the 0900 position line is transferred by the water track and tide, then crossed with the 1000 bearing

Step by step:

Plot the first bearing (the 0900 position line in the diagram).
From any point on it, lay off the course steered and the distance run through the water in the interval.
From the end of that, lay off the tidal stream for the same interval.
Through the end of the tide vector, draw a line parallel to the first position line. Mark it with double arrowheads to show it is a transferred line.
Plot the second bearing. Where it crosses the transferred line is the running fix.

The running fix depends entirely on the accuracy of the course, speed and tide used. An error of 0.5 knots in an assumed tidal stream over an hour shifts the fix by half a mile. Treat it as an estimate that is better than a DR, not as a true fix.

Two useful special cases need no plotting:

Doubling the angle on the bow: when the relative bearing doubles (for example from 30° to 60°), the distance off at the second bearing equals the distance run between them (no tide).
Four-point bearing: the special case 45° to 90° on the bow. Distance off when abeam equals the distance run.

The Gyro Compass

How it works

A gyro compass is a fast-spinning rotor made to seek the meridian by gravity control and damping. Because it responds to the earth's rotation, not magnetism, it points to true north, and it can drive repeaters, the autopilot, radar, ARPA, ECDIS and the VDR.

Practical points:

It needs time to settle after switching on. Start it several hours before sailing, following the maker's instructions.
Its directive force weakens towards the poles, and it becomes unreliable in very high latitudes.
It needs ship's power. Repeaters must be checked against the master gyro after any power interruption.

Gyro errors

Course, speed and latitude error (steaming error): when the ship moves north or south, the gyro settles on a direction slightly off the meridian. The error is roughly V cos(course) ÷ (5π cos latitude) degrees, where V is the speed in knots. At 15 knots heading north in 50° N it is about 1.5°. Most gyros correct this through speed and latitude inputs, so check the settings whenever speed or latitude changes significantly.
Ballistic deflection: a temporary error after a large change of course or speed, which dies away over some minutes. Damped designs reduce it.
Residual and mechanical error: what is left after all corrections. This is the error you measure by observation.

Gyro error is named High if the gyro reads more than the true bearing, and Low if it reads less. The rule: gyro high, subtract; gyro low, add. Record it in the compass error book and the deck log, and enter it on the gyro error board on the bridge.

The Magnetic Compass

SOLAS Chapter V requires a magnetic compass, independent of any power supply, on all ships. It is the backup when the gyro fails. Its errors are:

Variation: the angle between true and magnetic north at that place. Taken from the chart compass rose, updated for annual change.
Deviation: the angle between magnetic north and the compass needle, caused by the ship's own magnetism. It changes with heading, so it is listed on the deviation card against the ship's head. Steel ships have permanent (hard iron) and induced (soft iron) magnetism. The compass adjuster corrects most of it with magnets, the soft iron spheres and the Flinders bar, leaving small residual deviations.
Heeling error: extra deviation when the ship rolls or lists, corrected with a vertical heeling magnet.

Deviation changes with cargo (especially steel), after dry-docking, after long periods on one heading, and with latitude. That is why it must be checked regularly, not just copied from an old card.

Converting

Compass error is the combined effect of variation and deviation. From compass to true: add easterly errors, subtract westerly. The old rhymes still work: error east, compass least; error west, compass best.

Deviation = compass error − variation (treating east as positive and west as negative).

Finding Compass Error

ICS Bridge Procedures Guide practice is to check gyro and magnetic compass error at least once a watch where possible, and after any large alteration of course. Compare both compasses on every check: the comparison of headings is entered in the log at regular intervals, so a failing gyro is spotted early.

By transit

When two charted objects come in line, read the gyro bearing of the transit and compare it with the true bearing measured from the chart. The difference is the gyro error. Leading lights and transits marked on the chart are ideal. This is the simplest and, in coastal waters, the most accurate method.

By azimuth

At sea, use a celestial body at low altitude (the sun below about 30° is best, because the azimuth circle is easier to use and the bearing changes less with small timing errors). Record the gyro bearing and the exact UTC, then compute the true azimuth using nautical almanac data and the ship's DR position, by ABC tables, azimuth tables, a calculator or approved software. The difference between true azimuth and observed bearing is the error. An azimuth can be taken at any time the body is visible and low, so it is the everyday ocean method.

By amplitude

An amplitude is a special azimuth taken when the body is on the rational (celestial) horizon, that is, at true altitude zero. It is the angle between the body's bearing and due east (when rising) or due west (when setting). Because altitude is zero, the calculation is simple and needs no exact time:

sin Amplitude = sin Declination ÷ cos Latitude

Naming: prefix E for a rising body, W for a setting one; suffix N or S, the same name as the declination.

When to observe: refraction lifts the sun by about half a degree near the horizon, and dip lowers the visible horizon, so the sun's centre is on the rational horizon when its lower limb is roughly half a diameter above the visible horizon. Take the bearing then.

The diagram below works the example that follows.

Amplitude of the rising sun at 50° N, declination 20° N, giving a true bearing of 057.9° and a gyro error of 1.1° high

Worked amplitude example

Ship in latitude 50° 00' N. Sun's declination from the almanac 20° 00' N. The rising sun's centre, on the rational horizon, bears 059.0° by gyro and 060.5° by standard magnetic compass. Variation from the chart is 3.0° W.

sin Amp = sin 20° ÷ cos 50° = 0.3420 ÷ 0.6428 = 0.5321.
Amp = 32.1°. Named E (rising) and N (declination north): E 32.1° N.
True bearing = 090° − 32.1° = 057.9° T.
Gyro bearing 059.0°, true 057.9°. The gyro reads more than true: gyro error 1.1° High. Subtract 1.1° from every gyro bearing and heading.
Magnetic compass 060.5°, true 057.9°. Compass reads more than true: compass error 2.6° W (error west, compass best).
Deviation = compass error − variation = 2.6° W − 3.0° W = 0.4° E on the present heading.

Check the result is sensible: a gyro error over about 2° or a sudden change from yesterday's value deserves investigation (speed and latitude settings, repeater alignment, gyro fault), and should be reported to the master.

Amplitudes of the sun are useful when it rises or sets clear of cloud. For bodies at higher latitudes or large declinations the amplitude grows quickly, and in very high latitudes the method becomes poor. Use an azimuth instead.

Tides for Big Ships

Why it matters more

A yacht drawing 2 m can usually afford a generous margin. A loaded tanker or bulk carrier drawing 14 m or more in a channel with 15 m charted depth cannot. For deep-draught ships, the tide calculation decides when the ship sails, how fast it may go, and whether it can enter at all. Errors of a few tens of centimetres matter.

Admiralty Tide Tables (NP201)

NP201 (Admiralty Tide Tables Volume 1) covers the United Kingdom and Ireland, including the Channel ports of Europe. It has:

Part I: daily predictions of high and low water times and heights at standard ports, plus a tidal curve for each standard port showing how the height changes between HW and LW, with separate curves for springs and neaps where needed.
Part II: time and height differences for secondary ports, each referenced to a standard port.
Part III: harmonic constants for the simplified harmonic method.

Times are in the zone time stated on each page (for UK ports, UT; add an hour for BST). Heights are above chart datum, which on Admiralty charts is normally close to lowest astronomical tide (LAT). Digital equivalents (ADMIRALTY TotalTide and the ECDIS tide overlays) use the same data.

Secondary port method

Secondary-port differences are given against particular standard-port HW and LW times (for example 0000 and 1200, 0600 and 1800) and against the standard port's mean spring and neap heights (MHWS, MHWN, MLWN, MLWS). You interpolate between them for the day's actual times and heights.

Worked example (a hypothetical secondary port, for practice)

Standard port: HW 0612, 5.6 m. LW 1236, 0.9 m.

Secondary port data:

	HW at 0000 and 1200	HW at 0600 and 1800	MHWS	MHWN
Standard port			6.0 m	4.8 m
Differences	+0020	+0040	−0.4 m	−0.2 m

Time of HW: 0612 is 12 minutes after 0600. Between 0600 (+0040) and 1200 (+0020) the difference changes by 20 minutes over 6 hours, so at 0612 it is +0040 − (20 × 12 ÷ 360) = +0039. Secondary port HW = 0612 + 0039 = 0651.

Height of HW: 5.6 m is two-thirds of the way from MHWN (4.8) to MHWS (6.0). The difference changes from −0.2 to −0.4, so it is −0.2 − (0.2 × 2/3) = −0.33, call it −0.3 m. Secondary port HW = 5.6 − 0.3 = 5.3 m. Work LW the same way, then use the standard port's curve with the secondary port's times and heights to find the height at any time between.

Add any seasonal changes in mean level given in the tables, then consider the weather. High pressure lowers sea level (roughly 1 cm for each hPa above the average of about 1013 hPa), and strong onshore or offshore winds and storm surges can change levels by much more. UK storm-surge warnings and negative-surge warnings for the Thames, Dover Strait and southern North Sea are broadcast for deep-draught ships for exactly this reason.

Under-Keel Clearance

The terms

Charted depth: depth below chart datum.
Height of tide: height of the sea above chart datum at the time.
Static draught: the ship's draught when stopped, read from the marks and corrected for density, heel and trim.
Squat: the extra sinkage (and usually change of trim) when the ship moves through shallow water, caused by the water accelerating under and around the hull and its pressure dropping.
UKC: depth of water below the keel. Static UKC ignores squat; dynamic UKC includes it.

Every company's safety management system sets a minimum UKC policy, often expressed as a percentage of draught or a fixed figure that varies with the area (open sea, approaches, berth). Follow it, and treat it as a minimum, not a target.

Squat

Barrass's practical formulas give a good estimate of maximum squat in metres:

Open water: squat ≈ Cb × V² ÷ 100
Confined channel: squat ≈ Cb × V² ÷ 50 (about double)

where Cb is the block coefficient and V is the speed through the water in knots. Squat goes with the square of speed: halve the speed and squat falls to a quarter. That is why slowing down is the most powerful tool you have in shallow water. Full-form ships (large Cb, such as tankers and bulk carriers) squat more and tend to squat by the head, which also reduces steering control.

Other signs of shallow-water effect: increased vibration, reduced speed for the same revolutions, sluggish steering, a larger turning circle, and a wave building up at the bow.

Survey accuracy (CATZOC)

The chart depth is not exact. ECDIS shows the category of zone of confidence (CATZOC). Depth accuracy for the main categories is:

CATZOC	Depth accuracy
A1	± (0.5 m + 1% of depth)
A2 and B	± (1.0 m + 2% of depth)
C	± (2.0 m + 5% of depth)
D	worse than C
U	unassessed

In zone B, a charted 14.2 m could really be about 12.9 m. Your passage plan should allow for it.

Worked UKC example

The diagram below shows the figures for this example.

Under-keel clearance: charted depth plus height of tide, minus draught and squat

A bulk carrier with Cb 0.82 and static draught 13.5 m must cross a bar charted at 14.2 m in open water. Predicted height of tide at the time is 2.3 m. Company policy for this area: minimum dynamic UKC of 10% of static draught, that is 1.35 m.

Depth of water = 14.2 + 2.3 = 16.5 m.
Static UKC = 16.5 − 13.5 = 3.0 m.
Squat at 10 knots = 0.82 × 10² ÷ 100 = 0.82 m.
Dynamic UKC = 3.0 − 0.82 = 2.18 m. More than 1.35 m: acceptable.

Now suppose a high-pressure system and offshore wind mean the tide is only 1.0 m:

Depth of water = 15.2 m, static UKC = 1.7 m.
At 10 knots, dynamic UKC = 1.7 − 0.82 = 0.88 m. Below the minimum.
At 6 knots, squat = 0.82 × 36 ÷ 100 = 0.30 m, dynamic UKC = 1.40 m. Just above the minimum.

The options are to slow down (keeping enough speed to steer), wait for more tide, or both. This decision belongs in the passage plan, with the master's approval, and not in the OOW's head at the last moment. Do not forget allowance for wave-induced motion (pitch, roll and heave all bring the keel closer to the bottom in a swell) and for CATZOC.

Worked Example: A Coastal Watch

You take over the 0400 to 0800 watch on a 180 m container ship, 15 knots, coasting past a headland in 50° N with GNSS feeding ECDIS.

On handover you check the gyro error board: 0.5° Low from yesterday's azimuth. The magnetic compass comparison is within its usual difference.
0430 you fix by radar ranges of a lighthouse island (4.2 miles), a steep headland (6.0 miles) and a small rock (3.1 miles). The three range arcs meet in a tight point 0.2 miles inshore of the GNSS position. You check: the GNSS antenna position offset is set correctly, and a visual bearing of the lighthouse, corrected for gyro error, agrees with the radar fix. You report the discrepancy to the master and switch the ECDIS to compare against the second GNSS receiver, which agrees with the radar fix. The first receiver's input had frozen.
0545 the sun rises clear. You observe its centre bearing when the lower limb is half a diameter above the horizon and work an amplitude: gyro error 0.6° Low, consistent with yesterday. You record it in the compass error book.
0630 a leading line comes on. Its charted true bearing is 312.0°; it reads 311.4° by gyro. Error 0.6° Low again. Good: two independent checks agree.
Before handover you check the arrival tide for the pilot station using NP201 data in the passage plan, and confirm the UKC at the planned speed through the approach channel still meets company policy with the latest weather.

Common Mistakes

Trusting a single position source. GNSS on ECDIS is not a fix you have checked. Cross-check by an independent method.
Forgetting to apply gyro error before plotting bearings, or applying it the wrong way. Gyro high, subtract; gyro low, add.
Using radar bearings of headland edges as if they were accurate. Use ranges.
Ignoring a large cocked hat. It is a warning, not an untidy plot.
Running fixes with a guessed tide treated as true fixes.
Taking an amplitude when the sun touches the horizon. The centre is on the rational horizon when the lower limb is about half a diameter above the visible horizon.
Copying old deviation figures after loading steel cargo or a refit.
Using standard-port heights at a secondary port, or forgetting the time zone (UT versus local summer time).
Ignoring squat, or forgetting it roughly doubles in a confined channel.
Treating the minimum UKC as a target rather than a floor.

Summary

Fix the position regularly by more than one method, and always cross-check GNSS independently.
Three visual bearings about 60° apart give a cocked hat. A large hat means a mistake; plot the corner nearest danger when in doubt.
Radar ranges are accurate; radar bearings are not. Combine a visual bearing and a radar range for a strong fix.
A running fix transfers a position line by course, distance and tide. It is only as good as those inputs.
The gyro points to true north but has steaming, ballistic and residual errors. Named High or Low.
The magnetic compass has variation and deviation. Deviation = compass error − variation.
Find compass error every watch where possible: by transit in coastal waters, by azimuth or amplitude at sea.
sin Amplitude = sin Dec ÷ cos Lat; observe when the sun's lower limb is half a diameter above the horizon.
Secondary-port tides from NP201 need interpolation of time and height differences, then the standard port's curve.
UKC = charted depth + height of tide − draught − squat, with allowances for CATZOC and ship motion. Squat varies with speed squared: slowing down is the main remedy.

Check Your Understanding

Why are three radar ranges usually a better fix than three radar bearings?

Answer: Range accuracy is high (IMO standard 30 m or 1% of the range scale), while bearings are smeared by the horizontal beamwidth and depend on gyro accuracy and heading line alignment. Edges of land in particular are measured too wide in bearing.

You plot three corrected bearings and get a large cocked hat. List four possible causes.

Answer: Misidentified object; wrong or unknown compass error applied; plotting or arithmetic error; too long an interval between bearings while the ship moved fast. Poorly charted objects or distant objects with small angular spread also make it worse.

In which order should you take bearings for a visual fix, and why?

Answer: Objects ahead or astern first, objects near the beam last, because bearings near the beam change fastest. The fix is timed at the last bearing.

Latitude 40° N, sun's declination 15° S, setting sun. Find the amplitude and the true bearing.

Answer: sin Amp = sin 15° ÷ cos 40° = 0.2588 ÷ 0.7660 = 0.3379, so Amp = 19.7°. Setting body, declination south: W 19.7° S. True bearing = 270° − 19.7° = 250.3° T.

In question 4 the gyro bearing was 249.5°. What is the gyro error, and how is it applied?

Answer: True 250.3°, gyro 249.5°: gyro reads less than true, so the error is 0.8° Low. Add 0.8° to every gyro reading.

True bearing 145°, magnetic compass bearing 148°, variation 4° W. Find the compass error and the deviation.

Answer: Compass reads 3° more than true, so compass error is 3° W. Deviation = 3° W − 4° W = 1° E.

Why should you not simply use the old deviation card after the ship has loaded a cargo of steel coils?

Answer: The cargo changes the ship's induced magnetism, so deviation on each heading may change. Compass error must be checked by observation and the deviation recorded afresh.

A ship with Cb 0.80 is making 12 knots in a confined channel. Estimate the squat, and the squat if she slows to 8 knots.

Answer: Confined: 0.80 × 144 ÷ 50 = 2.3 m. At 8 knots: 0.80 × 64 ÷ 50 = 1.0 m. Reducing speed by a third cuts squat by more than half.

Charted depth 11.0 m, height of tide 1.8 m, draught 10.6 m, squat 0.5 m, CATZOC B. What is the dynamic UKC, and is it really available?

Answer: 11.0 + 1.8 − 10.6 − 0.5 = 1.7 m. CATZOC B depth accuracy is ± (1.0 m + 2% of depth), about ± 1.2 m here, so the real clearance could be as little as about 0.5 m before allowing for ship motion. The passage plan should account for this.

Name two weather effects that can make the actual tide lower than predicted.

Answer: High atmospheric pressure (roughly 1 cm lower for each hPa above average) and offshore winds or a negative storm surge.