# Worked Example A

##### Worked example 7B

At vessel is on the ‘2005 Passage Race’ in the Northern Territories from Whale Bay towards Port Fraser. The navigator has placed a waypoint at the centre of the compass rose immediately to the west of Whale Bay. The GPS displays the range and bearing to the waypoint as 284°T, 4.30 miles.

At 1200 NT DST (zone 0) the log reads 3456.2 miles.
The tidal stream that affects the boat while on passage is 035° 2.2m,

Plot this confirmed position on the chart
What is the latitude and longitude of this fix?

From this position, the helmsman has steered his best course to the wind on 272°M.

What is the dead reckoning (DR) position of the vessel?
What is the estimated position (EP) of the vessel 2 hours later at 1400 hours NT DST, when the log reads 3466.00 miles?

##### Step 1 – Fixing our Position by Range and Bearing to a Waypoint

Firstly we need to fix our position. One of the quickest and most accurate ways of doing this is by using the GPS. In this case the navigator has placed a waypoint at the centre of the compass rose and can plot range and bearings to this waypoint (Fig 7.9).

Fig 7.9 – 284°T is dialed up on plotter ‘A’ with large Blue course arrow and edge of plotter towards waypoint at centre of compass rose. 4.30 miles is transferred from latitude scale ‘B’ and transferred to line to give a confirmed position ‘C’.

We dial up 284°T on the plotter, with it pointed to the centre of compass rose where our imaginary waypoint is located.

Remember the bearing is towards the waypoint. Holding the plotter firmly we can draw a line from the centre of the waypoint towards where we think our vessel may be located.

It perfectly ok to go past where we actually are as we need to use the dividers to measure the distance from the latitude scale and transfer it to the line we have just drawn therefore measuring the range from the waypoint to the vessel. and measure distance from waypoint to our vessel.

Using the nearest part of latitude scale we can set the dividers to 4.30 miles and transfer this distance to our newly drawn position line. It always good practice to take the dividers back to the scale to check they have not moved during the measuring process.

Our confirmed position or fix of the vessel at 1200 NT DST (zone 0) on 25th June is:

46°20’.0N 005°38’.0W

We always use a dot and small circle for a confirmed position.

##### Step 2 – plotting the DR position

The heading of the vessel is given as 272°M which needs converting to a True bearing before we can plot it on the chart.

To convert this we need to know the variation in 2005, which from the information on the compass rose we know it is 7°W.

Using the nemonic CADAT ‘Compass Add East True’ we are reminded that to convert from a Compass bearing towards a True bearing we must add East variation errors which can therefore deduce in this example that we must subtract westerly variation errors.

272°M – 7°W variation = 265° True

We can place this true heading bearing on the chart (Fig 7.10).

Fig 7.10 – We can dial bearing 265°T up on our plotter ‘A’ place our pencil at our previously calculated fix (‘B’), align the north arrow on the plotter with the longitude parallels (‘D’). Holding the plotter firmly we can draw a line along the edge of the plotter in the direction of course steered (‘C’) and then mark the line with a arrow to indicate that it is a heading i.e. water track.

Now we can calculate the distance the boat has travelled from the log readings given in the question.

By subtracting the log reading at the beginning of the passage 3456.2 miles from the log reading at the end of the passage 3466.00 we can calculate the distance run is 9.8 miles.

We can use the nearest bit of Longitude scale and set out compass to 9.8 miles and transfer this distance to the line we have drawn (Fig 7.11),

7.11 – We measure 9.8 miles from the longitude scale with the dividers ‘A’ and transfer this distance to our water track ‘C’ by placing one of the divider points on the fix and where the other divider point touches the line ‘B’ we can mark with a pencil to provide a DR position.

This distance from the fix to the end of the DR run should be 9.8 miles. To ensure that the dividers did not move and to reduce error, you should recheck the gap in the dividers with the scale.

We can now write the relevant information, log , time, and make sure our plot is marked up with the correct symbols.

The dead reckoning position for the vessel at 1400hrs NP DST on the 25th June 2005 is:

43°23’.25N 005°51’.4W

##### Step 3 Estimated Position by adding the tidal stream vector

We now have to add the tidal vector to the end of the DR position line to obtain an estimated position. In this question we are given the tidal stream data but as we shall see below most of the time you have to calculate the tidal streams in the same way as we did in Module 6.

Form the question we know that the tidal stream data for the 2 hours we have been on passage is:

035° 2.2 knots

We can now plot the tidal stream from our DR position to give a more accurate Estimated Position (Fig 7.12).

Fig 7.12 – We dial up 035°T and plot the tidal vector on the chart from our DR position ‘A’. We can then measure 2.2 miles from longitude scale and mark this position along the tidal vector line to give our estimated position ‘B’.

The tidal vector line is finished off with three small arrows and Estimated Position are indicated by a small triangle with a pencil dot in the middle. As usual all position have the time and log reading written beside them.