(Extracts courtesy of A.N.T.A. publications, Ranger Hope © 2008



Vessel Positioning

Cross Bearings
Ranges of Two or More Points
Combined Range and Bearing
Bearing and Sounding
Line of Soundings
Running Fix
Doubling Angle on the Bow
Four Point Bearing
Transit Bearing
Danger or Clearing Bearings
Vertical Sextant Angle



Plotting allowing for current

Conventions, Symbols
Speed, Distance and Time
Tidal Streams and Current
Plotting Positions
Dead Reckoning or Estimated Position
Counteract Tide, Current or Wind

Running Fix with Tide







Vessel Positioning

Plotting a Position

When latitude and longitude are given, or read from a GPS receiver, the preferred method of plotting the position is to first identify the approximate area and use the parallel rules to lay off the given parallel of latitude from the closest side latitude scale. Longitude can then be measured along this parallel using dividers set against the appropriate longitude scale.

To plot a position given bearing and distance from a known point, parallel rules are used to mark off the true bearing by “walking” them from the nearest compass rose.

Dividers or compasses are then used to mark off the distance from the point. Remember that distance is measured from the adjacent latitude scale.


By Cross Bearings

Bearings taken may be:

a) Relative - as with pelorus or radar in ship’s head up display.
b) Compass - using the magnetic compass
c) Gyro - when a gyro repeater is used.

In any case the bearing must be converted to true before laying it off on the chart.

Each position line (LOP) should be identified by a single arrow at the end of the line away from the object observed.

When position lines intercept at (or nearly at) a point, that point should be encircled and the time of the fix noted alongside.

When position lines fail to intercept at a point and a “cocked hat” results, it may be due to any of the following:

a) Too long a delay between taking bearings
b) Wrong identification of an object
c) Error in plotting
d) Compass error wrongly applied
e) Unknown compass error
f) Poor survey of the area

If the cocked hat cannot be reduced or eliminated by any of the above checks then the position of the ship should be taken as that part of the cocked hat which will place the ship in most danger.

Figure 1: Fix by cross bearings showing a “cocked hat”

By Ranges of Two or More Points

This is the preferred method when fixing the position by radar observations. Ranges taken from the radar are generally more accurate than radar bearings. Avoiding the steps necessary to convert relative or compass bearings to true also reduces the chance of error.

Ranges must be taken off the adjacent latitude scale and the relevant arc plotted on the chart using compasses. Both ends of the arcs should be marked with a single arrow, the point of intersection circled, and the time of the fix written alongside.

Selection of objects for ranges is as important as it is with bearings, and any cocked hat should be treated in much the same way.

Figure 2: Fix Using Radar Ranges


By Combined Range and Bearing

When only one suitable object is available the position may be fixed with a single bearing of that object combined with its range. Although the range would usually be measured by radar it is still preferable to obtain the bearing visually. The bearing can usually be taken more accurately by visual means.

By a Bearing and Sounding

This method may be used providing :

· Allowance is made to reduce the sounding to chart datum.
· The depth contours are well defined.
· The contour in question only crosses the position line in one possible place.
· The depth contour crosses the position line at a wide angle.

Figure 3: Fixes Using Soundings

By a Line of Soundings

By taking soundings at a regular time intervals and converting that time to distance run, a line of soundings may be constructed along the edge of a piece of paper. If this is manoeuvred across the chart parallel to the vessel’s track a match may be found with charted soundings. This again required converting to chart datum and a chart with sufficient soundings. Even then there may be more than one track where a good match can be found. Any position obtained by this method should therefore be treated with a great deal of caution and checked by other means as soon as possible.


By Running Fix

Transferring a position line was mentioned earlier as a means of reducing a cocked hat when there is an unplanned delay between bearings. It is more commonly used when only one object is available for bearings and there is no means of measuring the range. In this case there is a planned delay between bearings so that the change in bearing will provide an acceptable angle of cut.

Figure 4: A Running Fix

The first position line is transferred forward by the distance and in the direction the vessel is thought to have travelled between bearings. The transferred position line is drawn parallel to the first position line. It is marked with double arrows at each end. The Fix is where it intersects the second position line.


A vessel is steering 312°(T) at 10 knots. At 1400 Lady Musgrave Island is observed bearing 280°(T). At 1442 it bears 252°(T). Assuming there is no set or drift between bearings, find the position at 1442.


Doubling the Angle on the Bow

This is a refinement of the running fix which takes advantage of the properties of isosceles triangles.
As illustrated the angle on the bow when the first bearing is taken is 35°. The time of this bearing is noted and the bearing then carefully watched until the angle on the bow doubles to 70°. The triangle formed by the two position lines and the course line is isosceles, therefore the range at the time of the second bearing is equal to the distance run between bearings.


Figure 5: Doubling the angle of the bow


In practice the distance run is simply calculated (speed x time) and this distance used as a range in conjunction with the second bearing.
A ship steering 058°(T) observes a single light at 0606 which bears 035° relative. At 0636 the light bears 070° relative. Ship’s speed 10 knots. What is the true bearing and distance of the light at 0636?

Time between bearings = 30 minutes (0.5 hrs)
So distance run = 10 x 0.5 miles
= 5.0 n. miles
True course = 058°(T)
Relative bearing = 070°(R)
So true bearing = 128°(T)

Answer: At 0636 the light bears 128°(T) at distance 5.0 n.miles.



The Four-Point Bearing

This is a further refinement of the running fix in which the first bearing is taken when the object is at four points (45°) on the bow. When the object is on the beam the range will be the same as the distance run since the first bearing was taken. The disadvantage of the four point bearing is that the range of the single object is not known until it is abeam. This is of little help in passing at a safe distance.

The four point bearing is illustrated below:


Figure 6: Four Point Bearing

With all types of running fix the accuracy of the final position depends on the accuracy of the prediction of the course and distance made good between bearings.



The Transit Bearing

When two charted objects come into line they are said to be in transit. It has already been shown how a transit can be used to check the compass error. A transit can also be used to obtain a fix in conjunction with another position line such as a range (or be used to obtain a fix in conjunction with another position line such as a range (or even a sounding) without use of the compass. Both possibilities are illustrated below.


Figure 7: Transit with Radar Range



Figure 8: Transit with Sounding



Danger or Clearing Bearings

Many ports have provided leading lights or shapes to guide mariners safely into harbour, avoiding shoals and other dangers.
In places where such aids are not provided, the navigator may still be able to select a leading line provided by the transit of natural features. Thus approaching an anchorage with a coastal hill in transit with a more distant peak may ensure that the vessel clears dangerous rocks.
The advantage of a transit is that the mariner is assured of a safe approach regardless of any compass error.

When a suitable transit is not available a single danger bearing may be taken from the chart. As shown below - so long as land’s end is bearing 244°(T) or less then the danger will be avoided.



Figure 9: Single Danger Line

A single position line may also be transferred ahead to give a course to steer to safely clear a charted danger. As illustrated below the vessel can safely turn on to a course of 312°(T) at 0430 hrs. and be assured of clearing the danger so long as the speed is accurately known and allowance is made for any set and drift.


Figure 10: Transferred Clearing Bearing


Vertical Sextant Angle

The distance off a light can be found by taking the vertical angle the light subtends at the vessel above sea level (See Figure 11).


Figure 11: Vertical Sextant Angle

The height LS can be found on the chart. The angle at V can be measured with a sextant. Using nautical tables, enter the section called ‘distance by vertical angle’ which gives the distance off using the sextant angle and height of the object in feet or metres.


Assuming the vertical angle at V to be 40° of arc and the height of the light SL to be 85 metre (280 ft.) the distance off (SV) would be 3.9 metre.

Set your compasses to 3.9 metre and scribe an arc with the lighthouse as centre. If a bearing is taken at the same time a fix can be obtained from only one object.

Figure 12


When using the sextant, set it at 0° and the view through the telescope would be as in Figure 13.


Figure 13: Sextant Image


The image of the lighthouse is brought down to sea level as in Figure 14.

The reading on the sextant, corrected for any index error is the Vertical Sextant Angle.


Figure 14: Sextant Image


Explanation of Instruments

If the error is “OFF” the Arc add to Sextant Reading.
If the error is “ON” the Arc subtract from Sextant Reading.

Selection of suitable points for bearings and radar ranges.
When selecting objects or features for observation of their bearing or range, the following should be taken into consideration

· The objects must be conspicuous
· They must be charted
· There must be no danger of ambiguity
· Ends of land should be steep to avoid errors due to tide level and possible lines of breakers
· When two objects are chosen the angle of cut should be as near 90° as possible.
· When three objects are selected the angle of cut should be as near 60° as possible.
· Close objects are preferred to distant objects because any error will be exaggerated by long position lines.





Plotting with Current
Conventions, Symbols
Speed, Distance and Time
Tidal Streams and Current
Plotting Positions
Dead Reckoning or Estimated Position Leeway
Counteract Tidal Stream or Current
and Wind
Running Fix with Tide

Plotting with Current


FIX + time (Fix) This is the position of a vessel as determined by the intersection of two or more position lines.
It is denoted by the symbol below with the time of observation.

D.R. + time (Dead Reckoning)
This is the position based on the true course and distance run through the water from the last known position. Denoted by the symbol below with time

E.P. + time (Estimated Position)
This is the position of best possible approximation based on course and distance since the last known position, with an estimation for Set, Drift and Leeway.
Denoted by the symbol, with time.

COURSE (Co) The Intended Heading

Course to Steer. The course related to the compass used by the helmsman.

Course made good. The (CMG) is the actual course over the ground between 2 observed positions.

Distance and Speed These are generally related to the vessels movement through the water. i.e. ascertained from the log or calculated from engine revs.

Distance made good These are related to the
Speed made good. measurement between 2 observed positions i.e. over the ground.

SET The direction towards which a current and/or tidal stream flows.

DRIFT The distance covered in a given time due to the movement of a current and/or tidal stream.

RATE OF DRIFT The speed of the current and/or tidal stream.

DRIFT ANGLE The angular difference between the track through the water and the track over the ground.

LEEWAY The effect of the wind blowing the vessel to leeward. It depends on the winds strength and direction, type of vessel and its draught. Generally estimated from experience.

LEEWAY ANGLE The angular difference between the ships heading and the track through the water.

POSITION LINE It is a line on the chart on which the vessel lies or has lain. It may be straight as in a bearing or curved as in ranges.



Conventions, Symbols, Abbreviations - On the chart we use the following conventions.


These symbols are used in the examples in this book.

Speed, Distance and Time

Many problems in navigation require an ability to manipulate these three associated values. Having measured a distance along an intended track it may be necessary to work out an estimated time of arrival at a given speed; or to calculate the speed required to arrive at a destination at a certain time (to catch the tide for example). It may also be necessary to calculate the distance travelled in a certain time so that the dead reckoning or estimated position can be plotted (see Outcome 6).

The three equations which may be needed are:






Tidal Streams and Current

Tides are the periodic rise and fall of the level on the sea due to various celestial bodies.

The ‘tidal stream’ is the horizontal movement of water that result from the tides.

In general the direction of flow will change once or twice a day depending on the type of tide.

A ‘current’ is the horizontal movement of water not caused by tides and generally follows some seasonal pattern.

Example: The East Coast current of Australia. Winds tend to influence the rate of currents.

Interpreting information on ‘currents’.

Consulting the symbol book 5011 you will find the symbol for current is:


Figure. 15: “Current” Symbol on a Chart

It may have an average rate above the line as shown.

Have a look at the smaller scale charts to see if you can observe the symbol and its direction. You may also find reference to currents under the title in the holes.



Figure. 16: “Current” Information on a Chart


If you consult the Australian Pilot Vol 111, surface currents are given on a quarterly basis, as in the diagram for January shown on the following page in figure 17.
The surface currents covered by this volume are described in some detail from pages 16-18 and also in the more specific area text.


Figure 18: January Surface Currents from Australian Pilot Vol 111



We will now consider the interpretation of information on ‘tidal streams’.
These are mentioned in Australian Pilots, covering the area for each volume. For example ‘tidal’ streams are found on pages 18 and 19 of Volume. III of this publication.

An example from the specific text is shown below for Stonehaven Anchorage in Figure19.


Figure. 19: Tidal Streams Stonehaven Anchorage
Extract from Australian Pilot Vol. 111


On the chart the symbols for tidal streams are shown below - in figure 20 make sure you know the difference between ebb and flood tidal stream. The rates are generally shown on the arrow.



Figure 20: “Tidal Stream” Chart Symbols See Appendix Chart 5011 – Symbols.



On certain charts you may notice tables as shown in Figure 21.

They contain position for which tabulated tidal stream data are given.


An example of a chart area is given in Figure 21, Shoal Water Bay.


The hours before and after high water relate to a standard port, which can be found from the Australian National Tide Tables etc.

The direction is given for each hour and the rate for Spring and Neap tides is given in knots.

Note how the tidal diamonds relate to the chart area. They are coloured Magenta on all charts.

The diamond with an ‘F’ in it is close east of the word ‘North’ in North Channel.

Figure 21: Extract from Chart AUS822 showing tabulated Tidal Stream Data for Positions in Shoalwater Bay



Another type of tidal stream information is produced in the Australian National Tide Tables, and is given in graphical form. They cover 3 port areas.

A. Darwin
B. Broome
C. Sydney Harbour

They are to some extent self explanatory. The diagram for Broome is shown in Figure 22.


Notice how the stream changes well before high water, and for practical purposes around the time of low water.


Figure 22: Tidal Stream Diagram - Broome



In the Torres Strait specific stream data is given for each day at Hammond Rock. Read the notes in Appendix B from the tide tables about this area.

Figure 23: Hammond Rock - Tidal Stream Data (From Australian National Tide Tables)



Plotting Positions

Plotting a Dead Reckoning (DR) and Estimated Position’s (EP’s)

It is now time to consider plotting DR’s and EP’s - finding Set and Drift and making allowance for tides, currents and wind. As you will remember, a D.R. position uses true course steered and vessels speed only. If we start at position P (fix) and steer 090°T for one hour, we arrive at position Q (D.R.) as shown on the chart extract drawing Figure 24.

If the navigator is aware of the existence of a current or tidal stream he can make an allowance for it and plot an Estimated Position (E.P.)

As illustrated etc. (see below)


Fig 24 Plotting a D.R. and E.P.

As illustrated the vessel has been steering 090°(T) for one hour at 7.0 knots. The navigator estimates that the tide has been running to the north at 2 knots during that time. Given the starting position at “P” the D.R. is plotted at “Q” - then one hour’s set and drift is applied to give the estimated position at “R”




We will now consider Leeway.

If a vessel is steering 090°(T) with a southerly wind, which is expected to cause 10° leeway (this is ascertained through vessel experience) then the vessel’s track will be 100°(T).

In practice it would be far more sensible to adjust the vessel’s course, counteracting expected leeway so that the desired track is achieved. See example Fig 26.

Figure 25: Estimating Track after allowing for Set, Drift and Leeway



A vessel is required to make good a course of 060°(T) in a strong South Easterly wind which is expected to cause 5 degrees leeway.

Figure 26: Allowance for Leeway


Course to make good 060°(T)
To counter leeway + 5
Course to steer 065°(T)



Finding Set and Drift

If a reliable fix places a vessel in a position which is different from the D.R. position, that difference will be the result of current and/or tide (and possibly wind).

In the illustration below a vessel obtained a good fix at 0600 (position “A”) and set course 285°(T) at a speed of 10 knots. At 0630 the D.R. was at position “B”, but a reliable fix showed the true position to be at “C”. In this case the set is 050°(T) and the drift is 1.0 mile. Since the time period was thirty minutes the rate of the current was 2 knots.


Figure 27: Finding Set and Drift



To Counteract a Known Tidal Stream or Current

If the navigator knows the direction and speed of a tidal stream, the course to steer to counteract that tidal stream can be found.

From the starting point “A”, a vessel needs to make good a track of 080 (T) to arrive at position “B”. The tide is known to set 200 (T) at 2 knots. The vessel’s speed is 10 knots.

To find the course to steer:

1. Lay of the required course to make good, “AB”.
2. Plot one hour’s set and drift from “A” to “C”.
3. With centre “C” lay off ship’s speed - the distance she will travel through the water in one hour - to point “D”
4. The direction “CD” is the true course to steer from “A”
5. The distance “AD” is the speed that will be made good
6. To find the E.T.A. at “B” the distance “AB” is divided by the speed made good “AD”.


Figure 28: Counteracting a known tidal stream or current



To Counteract Tidal Stream and Wind

The tidal stream must be counteracted first. The correction for leeway is applied to the result.


Figure 29: Constructing a Triangle from Tidal Stream and Wind


The Triangle A.C.D. is for construction only and can be of any size depending on chart scale.

For ease of calculation it is usually made to 1 hr. or intervals thereof.

It is required to make good a course of 090°(T) with a tide setting 220°(T) at 4 knots and a northerly wind causing an estimated leeway of 6 degrees. Ship’s speed is 13 knots. What is the true course to steer?


Figure 30: Counteracting Tidal Stream and Wind



From the vector plot - course to steer to counteract tide 076°T
to counteract wind -6°
Therefore: course to steer to counteract wind and tide 070°T


Running Fix with Tide

As was previously discussed, the accuracy of a running fix depends on the accuracy of the course and speed made good between bearings.

If the navigator is aware of the existence of a tidal stream or current, allowance must be made for set and drift experienced in the time interval between bearings.

If the vessel is steering 040°(T) at 10 knots, the tide is setting 090° at 3 knots and the run is 30 minutes between bearings then the first bearing must be transferred ahead 5 miles in a direction of 040° and 1.5 miles in a direction of 090°. This is illustrated below.


Figure 31: Running Fix and Tide