The three-point fix

Two lines: a fix with no check

In Lesson 11 you took a bearing of a charted object with the hand-bearing compass, converted it to true and drew it on the chart as a position line: a line you know you are somewhere on. A bearing of a second object gives a second line, and where the two cross is a fix — a position worked out from what you can see, rather than estimated.

The trouble is that two lines always cross somewhere. Misread the compass, take a bearing of the wrong object, apply variation the wrong way or slip with the plotter, and the two lines still cross in a neat, convincing point. Nothing on the chart warns you that the fix is wrong.

Two lines give you a position. Three lines give you a position and a check.

The three-point fix and the cocked hat

So take a bearing of a third object. If all three bearings were perfect, the three lines would meet at a single point. In practice they almost never do. A hand-bearing compass in a moving boat is rarely better than a degree or two, the lines are drawn by hand, and the boat moves while you take them. The lines form a small triangle called a cocked hat.

The size of the hat tells you how far to trust the fix. A small hat means the three bearings agree. A large hat means at least one of them is wrong — and, unlike a two-line fix, you know about it. How small is small depends on how far away the objects are. A handy rule, the 1 in 60 rule, says that a 1° error moves a line sideways by about a sixtieth of the distance to the object:

With objects three to five miles away and errors of a degree or two, each line can be a cable or two out, so a hat a cable or two across is a normal, good result. Treat these figures as a rough guide, not a rule.

Choosing your three objects

The angle at which two position lines cross is called the angle of cut. When the cut is wide, an error in either line moves the crossing only a little. When it is shallow, the lines run almost alongside each other, and a tiny error slides the crossing a long way along them.

Spread is the first thing to look for, but not the only one. Good objects for a fix are:

• Fixed and precisely charted. Lighthouses, church spires, radio masts and beacons on rocks are ideal. A buoy can be used, especially a close one, but it swings round its mooring and can drag or be moved, so a fixed object is better.
• Sharp, not vague. A rounded hill top or the edge of a sloping headland is hard to pin down to a single point, so its bearing is less exact.
• Near rather than far. By the 1 in 60 rule, the same bearing error moves a line twice as far for an object twice as far away.
• Positively identified. Compare its shape, colour and any name or number with the chart, and check that it lies roughly where you would expect from your estimated position.

Taking the bearings

Use the hand-bearing compass where it is well away from the steering compass, the engine, loudspeakers and electronics. There, as Lesson 10 explained, it has no deviation to allow for, so a reading needs only variation to turn it into a true bearing. Brace yourself, hold the compass at eye level, and if the card swings, read the middle of the swing. Write each bearing down as soon as you have it.

On a moving boat every bearing changes as you go, but not at the same rate. Here is how far the bearing of an object 3 M away changes in 5 minutes at 6 knots:

Objects nearly ahead or astern change bearing slowly; the one on the beam changes fastest. So the common guidance is: take the bearings ahead and astern first, and the one nearest the beam last, then note the time at once. The slow ones hardly move while you take the others, and the fast one is taken closest to the time you write down. (This assumes the objects are at similar distances: a very close object changes bearing quickly wherever it is.)

Be quick — all three within a minute or two — and note the time and the log reading. A fix is where you were at that moment, and you will need both to work out where you are later.

Plotting the fix

1. Convert each bearing to true. On the practice chart in 2027, variation is 2°44'W, which rounds to 3°W. Remember the aid “Variation West, Magnetic Best”: with westerly variation the magnetic figure is the bigger one, so subtract 3° to get true.
2. Plot each line. Set the plotter to the true bearing, put its edge through the object and draw the line. You only need the part near where you expect to be, which keeps the chart clean.
3. Mark the fix in the middle of the cocked hat with the fix symbol, a circle with a dot (⊙), and write the time beside it in 24-hour form. Many navigators add the log reading. You will meet the other symbols, the dead reckoning cross and the estimated position triangle, in Lesson 14.

The builder offers only objects that could really be seen from the hidden position. The practice chart gives no heights for the land, so this course keeps it simple: the radio mast and Beacon Hill (87 m) stand above the rest of the island and can be seen over it, but lower objects — the church spire, the old tower and the lighthouses — show only over land close in front of them, within about 2 M.

Checking the fix

Before you trust a fix, test it against something independent:

• The depth. Compare the echo sounder with the charted depth at the fix. The height of tide normally adds water over chart datum, and Module 4 shows you how much; allowing for it, the two should roughly agree. A sounding far shallower than the charted depth is a warning.
• Where you expected to be. From your last fix, the course you steered and your speed, you have a rough idea of where you should be (Lesson 14 makes this precise). A fix miles from that needs explaining.
• The log. Write the time, the fix and the log reading in the logbook (Lesson 15), so the next fix can be checked against this one.

When the cocked hat is big

A large hat means at least one line is wrong. In the video, a poor choice of objects — the church spire and radio mast, only 7° apart — gave a long, thin hat 1.5 M long, with one corner 1.4 M from the real position. Taking West Ledge buoy for Mew Rock beacon gave a hat 1.5 M across. The usual causes:

So take the bearings again, and check each step. If the hat is still large and you cannot find out why, assume you are at the corner of the hat nearest danger, and navigate from there with a wide margin until you can get a better fix.

Other ways to fix

The three-point fix is the everyday fix within sight of land, but not the only one. Next lesson, a transit — two objects in line — gives an especially accurate position line with no compass at all. When only one object is in sight, a running fix uses two bearings of it taken some time apart, allowing for the boat’s run between them; you will meet it later in the course, once you can work out dead reckoning. And a GPS position is best treated the same way as any fix: checked against the depth and against what you can see.