Why is it worth understanding this before the chart?
Navigation theory is the basis of the calculations: it explains why the course you measure on the chart is not the same as the one you steer with the compass, and how to go from one to the other. It is not an eliminating block, but it is the column that supports the chart block (which is): if you master courses and correction, the chart questions stop being scary.
The three norths
It all starts from the fact that there are three norths that do not coincide:
- True north (Nv): geographic north, that of the Earth's axis. It is the one used on the chart.
- Magnetic north (Nm): where the Earth's magnetic field points.
- Compass north (Na): the one your boat's compass actually shows.
The course is always the same angle of your bow; what changes is which north you measure it from. Hence the three courses: true (Rv), magnetic (Rm) and compass (Ra).
Magnetic declination (dm)
It is the angle between true north and magnetic north. It depends on the place and changes slowly over time; on the chart, the compass rose shows its value, its date and its annual change.
Compass deviation (Δ)
It is the angle between magnetic north and compass north. It is caused by the magnetism of the boat itself (iron, electronics), so it changes with the course you are on; it is recorded in the deviation table. In short: declination depends on the place, deviation depends on the boat and the course.
The total correction (Ct) and the sign rule
The total correction is the algebraic sum of declination and deviation:
To add with a sign there is a simple rule: East, positive (+); West, negative (−) —for both declination and deviation. A declination of 3° W is written as −3°; a deviation of 2° E, as +2°.
Going from one course to another
With the total correction you can now convert between the course you steer (compass) and the one you draw on the chart (true):
And along the way: Rm = Ra + Δ (deviation only) and Rv = Rm + dm (declination only).
Worked examples
- From compass to true. You steer Ra 075°, with dm 3° W and deviation 2° E. Ct = (−3) + (+2) = −1°. Rv = 075 + (−1) = 074°.
- From true to compass. You want to make good Rv 200°, with variation 2° W and zero deviation. Ct = −2°. Ra = Rv − Ct = 200 − (−2) = 202°. (With variation to the W, the compass course is greater.)
- Watch out for 0°/360°. You steer Ra 003°, with dm 2° W and deviation 3° W. Ct = (−2) + (−3) = −5°. Rv = 003 − 5 = −2°, which on the 360° rose equals 358°.
Bearings and relative bearings
- The bearing (D) is the direction to an object (a lighthouse) relative to north. It is corrected like the course: Dv = Da + Ct. The true bearing (Dv) is the one plotted on the chart. Important: the line is drawn with its origin at the object, so on the chart it is plotted from the lighthouse.
- The relative bearing is the direction to an object relative to your bow (the centreline); to starboard it is counted positive and to port negative. In practice it is barely used except for the wind angle.
When the wind or the current set you off
- Surface course (Rs): the one you actually follow due to the wind (leeway).
- Course made good: the actual track over the ground due to the current.
In both cases, to make good a track you must correct the course in the opposite direction to the agent.
How to study it without stress
- Fix two things and the rest follows: the sign rule (East +, West −) and the formula Rv = Ra + Ct.
- Always check whether your result «wraps around» when passing through 000°/360°.