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The Compass

Course Conversions

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While navigating, two different courses or directions are in permanent use: the Compass Course read from the compass and the Course-over-Ground (CoG) read from the nautical chart. Both can differ considerably from the True Heading, which is roughly the course of the vessel through the water (keel line).

In a rough approximation, the Course-over-Ground can be used as Compass Course and vice-versa. This is feasible while sailing in regions with small magnetic variation on a fibreglass yacht, normally showing low deviation errors and if corrections for drift are neglectable.

However, if accurate and safe navigation is an issue, correct course conversions between Compass Course and Course-over-Ground will have to be applied.




Compass Course and True Heading

Compass Course and True Heading differ by the compass error. Compass error is the sum of the magnetic variation, which is location and time dependent and magnetic deviation, which depends on the magnetic characteristics of the ship and on the sailed course.

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Magnetic variation can be obtained from the compass rose on the nautical chart. It will show the variation of the charted region for a specific year. Since magnetic variation varies with time, also the rate of change per year is indicated on the compass rose.

In the example on the left, the variation for the year 2009 is -4°15' (West).

This means, that the compass needle north-pole will point to 355°45' instead of pointing to True North at 000° (the upper branch of the local meridian).
The annual change of the magnetic variation is +8' (East). So the variation in this region will slightly decrease in the next years.

Magnetic deviation is the magnetic influence of the immediate environment upon the compass. It is usually caused by the steel or iron aggregates installed on the ship. Especially on steel ships the deviation may be considerable. The deviation also depends on the orientation of the ship within the earth magnetic field. Practically, the compass deviation depends on the heading of the ship. Therefore, a "Deviation Table" should be elaborated for each permanently installed compass showing the compass deviation for different headings or courses (000° through 360°).

The conversion scheme for obtaining True Heading from the Compass Course is as follows:

  True-Heading     = Compass-Course + deviation + variation

Both deviation and variation have an algebraic sign: deviation/variation pointing to West are negative - deviation/variation pointing East are positive.

Magnetic Heading is the compass course corrected for deviation only:

  Magnetic-Heading = Compass-Course + deviation

Although "Magnetic Heading" has no real practical meaning it is used as intermediate result in the course conversion schemes and as input parameter for the (inverse) deviation table.

Compass
Course
 
Deviation
Magnetic
Heading
 
Variation
True
Heading
       
056° -3° 053° +1° 54°        
          ------------ add corrections --------->

Example: the compass reading is 056°, deviation is -3° (W) and variation is 1° (E). The True Heading is 054°.

In the above scheme, corrections are added proceeding from left to right and corrections are subtracted working from right to left.

Example: from the nautical chart we read a True Heading of 245° deviation is +4° (E) and variation is +1° (E). In this case,  the helmsman will have to steer a Compass Course of 240°.

Compass
Course
 
Deviation
Magnetic
Course
 
Variation
True
Heading
       
240° +4° 244° +1° 245°        
          <--------- subtract corrections -------
 
 


True Heading and Course-over-Ground

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To account for drift due to leeway and current, the True Heading will have to be corrected further to obtain the Course-over-Ground. The Course-over-Ground (CoG) should correspond to the planned Course Line in the nautical chart.

In the example on the left the CoG to safely cross the narrows between the two islands is 250°. To account for the drift due to the indicated wind and current, the course to steer (Compass Course) will have to be lower.

To obtain the necessary drift corrections, the influence of leeway and current on the course of the vessel will have to be determined expressed in degrees. As with deviation and variation, the corrections for drift will have to have assigned an algebraic sign: when a drift component sets the vessel to port (e.g. wind from starboard), it's sign will be negative; when drift sets to starboard (e.g. wind from port), the sign for the correction will be positive.



Leeway

Each sailing vessel will be set leeward by some amount. Accumulated over time this will result in a deviation from the expected position, which can be specified by a course correction for leeway expressed in degrees. Corrections for leeway must be estimated from observed deviations of accurately determined positions and by experience. Correcting the True Heading for leeway gives the direction of the vessel through the water (Course-through-the-Water).

Leeway depends on the sailed course compared to the direction of the wind ("Point of Sail") and also on the specific form of the hull as well as on the wind force. By observing leeway in current-free waters under different sailing conditions, a table similar to the following can be elaborated (e.g. by comparing True Heading course with the GPS-derived CoG):

 Point of Sail   Wind 3-5 Bft.  Wind 6-7 Bft.  Wind > 7 Bft.
 close hauled 2° - 4° 5° - 10° 12° - 20°
 beam reach 2° - 3° 4° - 5° 5° - 10°
 broad reach 2° - 3° 4° - 5°
 downwind

Changes in wind force will also imply a variation of the number and the type of sails set.



Current

When the sailed water is in motion compared to the fixed earth surface, an additional correction for current must be applied to the "Course-through-the-Water". Current is specified by set and drift. Set is the direction in which the water flows as a result of current. Drift specifies the speed with which the water flows. As such, current can be represented as a vector with magnitude (drift) and direction (set).

Current is caused by tides, wind or by the general circulatory of the oceans. Tidal currents are periodic in nature. Information on current can be partly obtained from the nautical charts reporting seasonal mean values for set and drift. For regions with particular tidal currents, special tide calendars may be required to obtain accurate information on current.

Knowing set and drift, the course correction to account for current on the Course-over-Ground (in degrees) is determined by vector addition of the True Speed of the vessel and the speed (drift) of the current. From this addition, the resulting course angle can be determined as well as the correction for current.


This vector addition is done by drawing the "speed triangle" in which the vectors represent the involved speed vectors. Alternatively, the vectors can be interpreted as the displacement of the vessel in one hour, resulting from the vessel´s speed through the water and the drift due to the current.

In the example on the right, the vessel has a Speed-through-the-Water of 5 kn, course 60°. Current sets with 2 kn to 315°. The vectors are drawn on a piece of grid paper with a speed scale of 1 kn per grid interval. The resulting Speed-over-Ground (SoG) is 4.9 kn, course 37°. The course correction for current is 23° and because the current sets the vessel to port side, this correction is negative (-23°). 

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Conversion Scheme

As with the compass corrections the corrections for leeway and current have an algebraic sign: deviations to the port (wind and/or current from starboard) are negative - deviations to the starboard side (wind and/or current from portside) are positive.

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example

The CoG to sail between the small islands is read from the chart: 250°. Wind SE 5 Bft causes some current setting our vessel to starboard. The drift due to current is determined to be +2°. Drift due to leeway is estimated to be +5°. Variation is read from the chart: +1° (E) and deviation is known from the deviation table: +4° (E) for a magnetic course of  240°.
The result of the course conversion yields a steering (compass) course of 238°, which differs significantly from the CoG read from the chart (250°).


Compass
Course
 
Deviation
Magnetic
Course
 
Variation
True
Heading
 
Leeway
Course thr.
Water
 
Current
Course o.
Ground
238° +4° 242° +1° 243°  +5° 248°  +2°  250°
<--------- subtract corrections -------



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