Position Fixing and Position Lines

Position, position line and circle of position

In short: one observation gives a line you are somewhere on. Two or more lines that cross give a fix.

Read first: compass errors (every bearing must be true before you plot it) and chart projections and datums.

• Position: a single point on the chart, given by latitude and longitude, or by bearing and distance from a charted object.
• Position line (PL): a line on which the ship lies at the moment of the observation. A compass bearing or a transit gives a straight position line.
• Circle of position: a circle on which the ship lies. A range (radar range, vertical sextant angle, dipping distance) gives a circle centred on the object. A horizontal sextant angle between two objects also gives a circle, passing through both objects.
• Fix: the point where two or more position lines or circles, taken at the same time, cross. Mark it with a circle and the time.
• Angle of cut: with two lines aim for about 90°; with three, about 60° between them. Below about 30° a small bearing error moves the fix a long way.

Transferred position line

• If you have only one position line, you can carry it forward in time.
• Move the line, parallel to itself, by the ship’s course and distance made good over the ground in the interval (water track and distance run, plus tidal set and drift).
• Mark a transferred position line with a double arrowhead, so nobody mistakes it for a fresh observation.
• It is the basis of the running fix (see below). Its accuracy is only as good as your estimate of course, speed and tide.

DR, EP and fix — set, drift and leeway

In short: DR = course and speed through the water only. EP = DR corrected for tide/current and leeway. Fix = position from observations.

• Set: the direction towards which the current or tidal stream flows (a current setting 090° pushes you east).
• Drift: the distance the current carries you in a given time. Rate is the same thing per hour, in kn.
• Leeway: the angle between the heading and the water track, caused by wind pushing the ship sideways. Apply it downwind.
• Set and drift found from a fix: the vector from the EP (or DR, if no tide was allowed) to the fix at the same time is the actual set and drift you experienced. Use it for the next leg.
• Arrow convention: one arrowhead = water track, two = ground track, three = tidal stream.
• On the bridge: keep a DR/EP running even with GNSS. If the GPS fails, the EP is where you start.

Course to steer allowing for set, drift and leeway

1. Draw the intended ground track from your position.
2. From the start, lay off the tidal stream vector for one hour (set and rate).
3. From the end of that vector, swing an arc equal to your speed through the water until it cuts the intended track.
4. The line from the end of the tide vector to that point is the water track to make good. Its length along the track gives the speed over the ground.
5. Correct for leeway by steering into the wind by the leeway angle. Then convert true to compass.

Ground track, water track and heading

In short: heading is where the bow points; water track is where you move through the water; ground track is where you actually go over the seabed.

• Heading: the direction the ship’s head points at a given moment.
• Water track (course through the water): heading corrected for leeway.
• Ground track (course over the ground, COG): water track plus the effect of tidal stream/current. GNSS gives COG and SOG directly.
• Which mode for collision avoidance? Use sea-stabilised (water-referenced) true motion on radar for collision avoidance: true vectors then show the other ship’s heading through the water and its aspect, which is what the COLREG are based on. Use ground-stabilised for navigation, e.g. checking your progress past land and dangers.
• AIS and ECDIS show COG/SOG (ground-referenced). In a strong tide the AIS vector can point well away from the other ship’s real heading — do not judge aspect from it.

Visual fixes: compass bearings and transits

In short: three bearings of well-charted, fixed objects, corrected to true and plotted quickly, are the classic coastal fix.

Three-point (three-bearing) fix

• Choose three conspicuous, charted, fixed objects: lighthouses, headlands with a steep edge, church spires. Avoid buoys — they can drag or be off station.
• Prefer objects that are close and well spread: about 60° apart (or 120°) gives the best cut.
• Take the bearings ahead or astern first (they change slowly) and the one nearest the beam last (it changes fastest). Note the time.
• Convert each compass bearing to true (variation and deviation, or gyro error) before plotting.
• Two bearings give a fix; the third is the check. Without it, a wrong mark or wrong bearing goes unseen.

The cocked hat

• Three bearings rarely meet at one point. They form a small triangle: the cocked hat.
• Small cocked hat: take the position at the corner nearest the danger (or nearest your track to the danger) — assume the worst.
• Large cocked hat: something is wrong. Check: wrong object identified, compass error not applied or wrong, plotting error, too long between bearings. Take a new set.
• The same idea with radar ranges and bearings is covered in radar position fixing.

Transits

• A transit is two charted objects seen in line. It gives an exact position line with no compass error in it.
• Use leading lines and transits to stay on track in pilotage, and to check the compass error: compare the compass bearing of the transit with its charted true bearing.
• A transit crossed with a bearing or a range gives a good fix.

Running fix

In short: one object, two bearings at different times, the first one transferred by what you made good in between.

1. Take a bearing of the object. Note the time and log reading.
2. Hold your course. After the bearing has changed by a useful angle (at least about 30°), take a second bearing of the same (or another) object. Note the time and log.
3. From any point on the first position line, lay off the water track and distance run, then the set and drift of the tide (and leeway) for the interval.
4. Through the end of that construction, draw the first position line again, parallel to itself: this is the transferred position line (double arrowheads).
5. Where it crosses the second position line is the running fix. Mark it with the time of the second bearing.

• Weakness: any error in course, speed, tide or leeway goes straight into the fix. Treat it as less reliable than a simultaneous fix.
• Use it when: only one object is in sight, e.g. a single light on a dark coast.
• Quick special cases (no tide): doubling the angle on the bow — distance run between bow angles α and 2α equals the distance off at the second bearing. Four-point bearing — 45° on the bow then abeam: distance run equals the distance off when abeam.
• A range can be transferred the same way: move the centre of the circle by the run made good.

Fixes with the sextant: horizontal and vertical angles

In short: near the coast a sextant gives very accurate angles — and so a fix or a distance off — with no radar and no compass error.

Horizontal sextant angles (HSA)

• Measure the horizontal angles between three charted objects: the left and centre, then the centre and right. A compass can also be used for these angles, with less accuracy.
• Each angle puts you on a circle through two objects. Set both angles on a station pointer, place it on the chart so the three arms pass through the three objects: the centre is your fix.
• No compass error enters the fix.
• Trap: if the ship lies on, or near, the circle that passes through all three objects, the fix is indeterminate. Choose objects so the centre one is nearer to you than the other two, or in line with them.

Vertical sextant angle (VSA) — distance off

1. Take a compass bearing of the object (lighthouse, peak) and convert it to true.
2. Find the object’s charted height: for lights and features it is given above MHWS.
3. Measure the vertical angle from the top of the object down to the waterline at its foot; adjust for height of eye.
4. Enter the distance-by-vertical-angle table in Norie’s Nautical Tables (height and angle) and read the distance off. Close in, distance ≈ height ÷ tan(angle).
5. Lay off the distance along the true bearing: fix.

• Below MHWS the object stands higher than charted, so the table gives a distance a little shorter than the real one — the error is on the safe side.
• A VSA without a bearing still gives a circle of position, useful as a clearing range off a danger.

Sextant errors

• Adjustable errors — “PSI”:

1. Perpendicularity — the index mirror must be perpendicular to the frame.
2. Side error — the horizon mirror is not perpendicular to the plane of the instrument.
3. Index error — with the sextant set at 0°, index and horizon mirrors must be parallel. Check it, and apply it to every sight.

• Non-adjustable errors: collimation (telescope not parallel to the frame — only an expert can adjust it on most modern sextants), graduation (scale errors), centring (index arm pivot not at the centre of the arc) and shade errors (shade glasses not parallel-sided).
• Instrument error = the sum of the non-adjustable errors. It is given on the sextant’s certificate.

Other position lines: soundings, dipping lights, radar, GNSS and stars

In short: any measurement you can link to a charted feature gives a position line. Combine different kinds to check one against another.

• Bearing (or transit) + depth contour: where the bearing crosses the charted contour you measure. First make sure the echo sounder is checked (compare it with a lead line), then reduce the sounding to chart datum by working out the height of tide, and allow for the transducer depth/draught setting.
• Line of soundings: record soundings at known intervals along your track, mark them on tracing paper at chart scale, and slide it over the chart until it matches. Works best on a sloping or uneven seabed.
• Bearing + dipping distance: a powerful light rising or dipping on the horizon gives a range; see dipping distance.
• Radar: range and bearing of one object (VRM gives the range, EBL the bearing), or three radar ranges — ranges are more accurate than radar bearings.
• GNSS (GPS): fast and accurate, but a single source. MGN 379 (M+F) warns never to rely totally on one position-fixing device and to check GNSS against other means, including visual observations. Watch the chart datum of the GNSS position.
• Celestial: you need accurate time, a sextant, the Nautical Almanac and sight reduction tables (the “Air tables”). A noon sight (meridian passage) gives your latitude; a morning sun sight run up to noon (sun-run-sun or sun-run-merpass) gives a running fix. Azimuth = bearing of the body; altitude = angle above the horizon; zenith distance = 90° − altitude. The almanac also gives sunrise and sunset times.

How often to fix — and what parallel indexing is not

In short: fix often enough that you can never run into danger between two fixes.

• Rule of thumb: set the fix interval so that, between fixes, the ship cannot cover more than half the distance to the nearest navigational danger. Close to danger, fix more often.
• Use a primary and a secondary method (e.g. GNSS checked by visual bearings or radar). This is part of the OOW’s duties on watch.
• Link it to safe speed, COLREG Rule 6: the faster you go near danger, the less time between fixes. Mnemonic for the Rule 6(a) factors: “VD Makes Little Willies Drip” — Visibility, traffic Density, Manoeuvrability, background Lights at night, Wind/sea/current, Draught v. depth. Full detail in look-out and safe speed.
• Parallel indexing (PI): a way to monitor the track continuously by radar. It is not a way to fix a position, but it is a good back-up to a GNSS position.