From compass course to course over ground

In this lesson we will learn how to calculate from the compass course to the course over ground.

The compass course

There are different north directions. Compass north is where the compass points. Magnetic north is where the compass would point if it were not affected by ship magnetism. True north is towards the North Pole. So the compass does not always point exactly to the North Pole. This is due to misalignment, which consists of variation and deviation. Anticlockwise misalignment, or from north to west, is negative. Clockwise misalignment, or from north to east, is positive.

Variation

Variation is that part of the misalignment that arises because the magnetic fields running from the south pole to the north pole across the earth do not run straight to the north pole, but “oscillate”. As a result, the compass points slightly too much to the West in one location and slightly too much to the East in another location. We get the variation from the chart.

The magnetic fields shift and so the variation also changes over time. If the chart says 10° W 2002 (8’E), it means that the variation was 10 degrees West in 2002 and shifts eastward 8 minutes every year. This is written in the sea charts.

If we wanted to calculate what the variation is in 2013, we calculate it as follows:

2013 relative to 2002 is 11 years later.
11 years x +8 minutes = +88 minutes, or +1° 28′.
-10°
+ 1° 28′
-8° 32 ‘.
So the variation in 2013 is 8° 32’W.
To make this sum easier, remember that -10° = -9° 60′.
-9° 60′ –
+ 1° 28′
-8° 32′ –

Note that 8° 32’W is rounded to whole degrees 9°W, because 32′ is more than half of 60′ so we round up (if rounding were necessary).

Deviation

Deviation is that part of the misalignment, which is caused by ship magnetism. For example, the engine affects the steering compass. Because the compass needle always points north and the boat rotates around that compass needle, the deviation depends on the course. In the deviation table one can find the deviation associated with a particular compass course. Below is a deviation table:

A handheld compass also suffers from deviation. So use it as far away from magnetic ship parts as possible. When we take a bearing with a handheld compass, we assume deviation 0 because, of course, we don’t have a deviation table from a handheld bearing compass, because it has no fixed place on board.

Heeling error

Heeling of a ship affects the compass needle because the vertical positioned ship’s magnetism is positioned differently from the compass (which remains horizontal even under inclination). When the ship is heeling, a force towards that ship’s magnetism is created that can be decomposed into a horizontal force (which creates another deviation) and a vertical force (which does not affect the compass needle). If the heeling angle doubles, the horizontal force is also doubled and hence the error doubles. The heeling error on east – west courses is minimal, but on north – south courses the biggest. This is because if the horizontal force points north or south, the deviation does not change. To calculate the error, first convert the true course to compass course at which the error should be calculated. Then you determine the error on the compass heading 0 degrees. Then determine the heading factor by reading the heading factor from the cosine graph or by typing the heading into your calculator and pressing COS. Then you determine the heeling angle factor, which is directly proportional to the heeling up to 20 degrees of inclination. So twice as much heel means twice as much heeling error and a heel error of e.g. 4 degrees at 10 degrees heel on starboard tack means a heel error of -4 degrees at 10 degrees heel on port tack. Finally, the heeling error is calculated by multiplying the heeling error on a compass course of 0 degrees by the course factor by the heeling angle factor.

Leeway

Under the influence of a crosswind, the boat not only goes straight ahead through the water, but is also moved sideways, which is called leewaying or drifting. An angle is created between the keel line (this is the true course) and the path the boat takes through the water (this is the retained true course also called upstream course). The angle between the keel line and the path through the water is called the drift angle. We can measure this angle in practice by casting out a long line and probing it with a compass and comparing that bearing with the compass course. To windward, the drift angle is maximum and to windward there is no drift angle because the boat is drifting in the same direction as it is heading. High waves amplify the drift angle. Relatively high upwind (or unloaded) boats drift a lot.

Current angle

When there is a current, it means that the water containing our yacht slides across the earth. This creates an angle between the way a yacht travels through the water (the retained true course = BWK = Upstream Course) and the way a yacht travels over the ground, the ground course (= GRK). We call this angle the current angle. The current angle cannot be observed from the boat by looking at the water. You can calculate it by comparing the BWK with the GRK. You can read the ground heading on the GPS, which shows the COG (Course Over Ground). You can also calculate it using a construction in the chart, which we will come back to later.

Course to steer / Estimated position

I f you need to calculating the course to steer / course steered, always use this formula:

Compass CTS = Compass Course to Steer / steered
Dev = Deviation
________+
Magnetic CTS = Magnetic Course to steer / steered
Leeway
________+
Magnetic WT = Magnetic Water Track = Magnetic Course Through Water
VAR = Variation
________+
True WT = True Water track = True Course through water –>–
Tidal set = –>>>–
________+
COG = Course Over Ground –>>–

For the current angle and leeway angle, if we are set aside clockwise (i.e. to starboard) then the angle is positive (+) and if anticlockwise (i.e. to port) then the angle is negative (-). Always make a sketch of the situation to determine whether you are dealing with a positive or negative angle.