Chapter 27
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  Navigation can be defined as the science of determining a vessel's position at sea and calculating a safe course to another position.

  Coastal navigation is used when a vessel is within sight of or close to land, when it's position can be established by the observation of prominent objects or physical features.

  Astro navigation is used in long sea passages out of sight of land, where position is determined by taking sights of celestial bodies.

  Radio navigation can be used in all waters, when position is found by taking bearings of radio transmitters, or by the interpretation of special radio signals.


   The principle requirements of chartwork are:

    1. To calculate the compass course required to move a vessel in safety from one point to another on a chart.

    2. To keep up a continuous running plot of the progress of the vessel.

    3. To obtain fixes of the position of the vessel at regular intervals.

    4. To maintain the chart in good condition.

  Points to note:

    a. All chartwork must be done with a 2B pencil, anything harder makes grooves in the chart, which cannot be erased.

    b. Chartwork should not be erased when the chart is wet.

    c. Chartwork should not be erased until the end of a passage when it should be erased, unless required for record purposes.

Measurement of Distance

  The unit of measurement on the chart is the nautical mile, which in fact is one minute of arc measured along a meridian.  The actual length of the arc varies slightly between the equator and the poles, but a mean length of 6080 feet or 1852 metres is now universally adopted as the International Nautical Mile.

  Distances on the chart are measured on the degree and minute scale that forms the border margin of the vertical side of the chart. They must be taken at the latitude of the measurement required, because in Mercator's projection the distances between lines increase towards the poles, and so the scale will vary at different latitudes.

  One tenth of a nautical mile is called a cable, and for all practical purposes this is taken to measure 600 feet or 200 metres.

Measurement of Speed

  The speed of a vessel is measured in knots, one knot being the equivalent of one nautical mile in one hour.  A speed of ten knots is equal to about 11.5 statute miles per hour or 20 kilometres per hour.

Magnetic Variation

  Magnetic North does not coincide with True North, but varies on either side of it by reason of a slow continuous movement that takes place over the centuries.  The difference between true and magnetic north is called Magnetic Variation, and this varies over the surface of the earth and does not remain constant anywhere.

  In the Baltic magnetic variation is, at present, from about 003o W to almost nil, the actual variation for any area given on the compass rose or roses printed on the chart. For example, it may be given as "Var 2o 10' W (1991) decreasing abt 3' annually", and this will indicate the variation at the actual location of the compass rose on which it appears, not necessarily for the whole area of the chart.

  The conversion of Magnetic to True North or vice-versa can easily be understood by simply visualising the True North point of the compass rose. If Magnetic North is to the left of True North, that is westerly variation, then obviously the compass bearing of any given course will be more than the true bearing.  Similarly if Magnetic North is to the right of True North, that is an easterly variation, the compass bearing will be less than that of the true bearing.

Compass Deviation

  Compass deviation is created when the local magnetic field in a yacht deflects the compass needle away from Magnetic North, to which it would otherwise be pointing. Unlike variation, deviation alters according to the direction in which the yacht is heading. Temporary deviation can be caused by placing a ferrous or magnetic article near the steering compass, but this can be avoided with proper care, eg don't put the portable radio right underneath the bulkhead compass!

  Permanent deviation caused by engines and other fixed installations can be eliminated by the use of small corrector magnets, and this is normally done by a skilled compass adjuster.  Afterwards the vessel is "swung" through various headings, preferably on a proper compass swinging range, and any residual deviation recorded on a deviation card.  Ideally compasses should be swung at the start of every sailing season and a new deviation card compiled.

  Deviation is applied to a compass course in exactly the same manner as variation, westerly deviation being added and easterly deviation subtracted in order to ascertain the correct magnetic course.

  Apart from the deviation table, it is good practice to check the accuracy of the steering compass from time to time by comparing the heading shown with known bearings such as leading marks and transits.

The Basic Calculation

    a. From a start point, A, on the chart, plot the required course to B.  Find the true (T) bearing of this line by using the plotter, or transferring the line to the compass rose.

    b. Apply Variation to this bearing by adding Westerly Variation or subtracting Easterly - this is then the Magnetic (M) bearing.

    c. Apply Deviation in the same way to get the Compass Course (C).

Ch 27 01

    True bearing                          085o (T)

    Apply Variation, say, 2o W :  085o (T) +  2o =  087o (M)

    Apply Deviation, say, 4o E :  087o (M) -  4o =  083o (C)

    083o is the compass course.  Note that bearings and courses are always given in three figures. The calculation is always done in the same order, and in reverse when working from compass to chart.

To Compensate for Tide or Current

  If a boat was steered straight across a fast flowing river, it would be swept downstream before reaching the far bank, in order for it to get straight across, the boat would have to point partly upstream.  Tides and Currents have the same effect, and the solution is also the same, except that out at sea, there are few convenient banks from which to judge the amount of compensation required.

    a. Plot the desired course between A and B as before. The remainder of this calculation does not have to be done on this line, or even on the chart at all, although it is usually most convenient to do it there.

    b. From point A draw a line in the direction that the tidal stream or current is flowing, say one hours worth of flow, eg: for a one knot current, mark off one nautical mile to C.

    c. From C scribe an arc, of radius equivalent of the boat's speed through the water for one hour, to cut line AB at D. eg: for a boat speed of 4 knots, the radius of arc is four nautical miles at the same scale at which the current was measured.

    d. Join CD, this is the True Bearing of course required, now repeat the basic calculation to find the compass course.

To Compensate for Leeway

  Leeway is created by the wind pushing the yacht sideways through the water. The amount of leeway depends on a number of factors, the principle of which are the design of the yacht, the point of sailing and the weather, and it may be estimated by observing the angle between the fore and aft line of the yacht and the "wake course" stretching out astern.  Compensation for leeway can be made by adding or subtracting this angle to or from the magnetic course.

  In conditions where the total amount of correction for variation, deviation, current and leeway adds up to a considerable difference between the true course and the course to steer, correction for deviation should be the last to be applied, otherwise the changes in deviation for various headings may create an unacceptably large error.

Plotting the Course

  A continuous running plot of the course is maintained by plotting Dead Reckoning positions (DR) and Estimated Positions (EP) at intervals during the passage.

  The yacht's DR position is assumed to be at the distance logged from the last fixed point on the magnetic bearing steered, with no allowance made for either current or leeway.  The DR position is marked with a cross.

  The yacht's EP is then calculated by allowing for current and leeway, and this is done by drawing a current vector diagram as already described.  The EP is marked with a triangle, and the time and log readings entered alongside.

  The DR and EP should be plotted during the course of a passage until each definite fix of the yacht's position is made, from where it is continued until the next fix is obtained.

Ch 27 02

Position Fixing

  Position fixing is a means of determining the position of a vessel at sea and is normally done by establishing the intersection of two or more position lines.  A fix is marked on the chart with a circle, and a dot where necessary.  The time, and log reading or estimated log reading should be entered alongside.

Position Lines

  If an observer on a boat takes an accurate compass bearing on a positively identified object, and transfers that bearing to the appropriate chart as a line from the object, the line is known as a position line, and for as long as it remains in the same place, the boat must be on the position line somewhere.  It follows two or more position lines, from bearings taken within a short space of time, will "fix" the boat's position on the chart. Bearings marked on the chart are always shown with an arrow pointing away from the object on which the bearing was taken. Position lines do not have to be bearings - as will be seen.

Simple Cross Bearings

  The bearings of two positively identified objects on shore are taken, converted to reverse and then plotted on the chart. The intersection of the two lines will give a reasonable fix, particularly if the two objects chosen are roughly at right angles to each other.

Ch 27 03

Three Cross Bearings

  The intersection of the position lines plotted from three objects on shore will usually result in a triangular€¯ area of doubt", known as a Cocked Hat. Traditionally the fix is taken as being in the centre of the Cocked Hat, but if there is any nearby hazard or danger the yacht's position is assumed to be at the point of the triangle nearest to the danger.

Ch 27 04

Transit and Compass Bearing

  The most accurate position line is a transit bearing, when two positively identified objects on shore are observed to be in line with each other. At the time of observation the yacht's position must be somewhere on a line drawn through the two positions and extended to seaward, and if at the same time a compass bearing of a third object is taken, the intersection of the two position lines will give an accurate fix.

Ch 27 05

Circle of Position and Compass Bearing

  A useful method of position finding at night in good visibility is to observe a lighthouse that is just seen to appear over the horizon. By reference to the appropriate Rising and Dipping Tables, or by calculation, distance off can be found and an arc of position plotted.  A compass bearing on the light will give a second position line, and thus a fix is obtained.

Ch 27 06

Doubling the Angle on the Bow

   The same procedure as in a four point bearing is used, except that the observer can take a bearing on the object at any time and at any angle less that 45o.  The second bearing is taken when the first included angle has doubled, when the distance run between the two bearings will be equal to the distance from the position of the second bearing to the observed object. It will be seen that in both these methods an isosceles triangle is constructed, where two sides and two included angles are equal.

Ch 27 07

Transferred Position Line

  This method may be used where a bearing can be taken on an object on shore, or where a bearing can be taken on one object that then goes out of sight and a second bearing taken on another object further along the coast.  Once again speed and course must be accurately determined, and maintained.

    In the first case, the yacht's course and speed is known, however the distance off the coast is not known and may be to one side or the other of the assumed course plotted on the chart.  A bearing is taken on an object ashore and log and time noted. After the vessel has continued on her course until the bearing of the object has changed by about 60o or more, a second bearing is taken on the object and the time and log recorded. The actual distance covered is then calculated, making adjustments for current or tidal stream.

    This distance is then plotted from any convenient point on the first position line on a line parallel to the course line, and the first bearing transferred to the new position. The point where the transferred line crosses the second bearing line is the position of the vessel at the time of taking the second bearing.  (The transferred position line is marked with an arrow at each end).

Ch 27 08

When taking bearings on two objects on shore at different times, speed and course must again be known. A bearing is obtained on the first object seen, which later passes out of sight. A bearing is then obtained on a second object that has appeared on shore, and the actual distance covered between the two bearings is calculated.

    As in this example, this distance is plotted on a line drawn from the first position line, parallel to the course line, the first bearing transferred to this position, and the point where it crosses the second bearing is the fix at the time the second bearing was taken.

Ch 27 09

Any method of obtaining a fix that requires the speed and course to be known is called a running fix. Owing to the inevitable errors that will occur in assessing distance run and steering a steady course a running fix is usually less accurate than cross bearings.

Line of Soundings

  As well as taking bearings from objects on shore, an estimate of position and distance off can sometimes be made with the help of soundings taken with the echo sounder. A line of soundings is taken at regular intervals, reduced to chart datum if necessary, and the resulting line plotted on tracing paper or the edge of ordinary paper.  From this trace, an approximate distance off shore can be deduced by laying it on the chart parallel to the course being steered and moving it about until the soundings coincide with those on the chart.  In poor visibility this method can be very useful, particularly where the seabed has a distinctive contour line.

Ch 27 10


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