Worked Example A

Worked Example A

At 1400 NP DST in the new year of 2012, we are at the safe water buoy in the Hiscock Sound. The GPS gives the position as 46°10’.60N 005°53’.4W. The speed log reads 548.8 miles.

In the log book we noted that the vessel steered 243°M and at 1530hrs when the speed log read 557.0 miles altered course to starboard onto a new bearing of 319°M. The boat then motored until the speed log read 565.8 miles.

  • What is the closest we get to the rocks during the first leg of the passage?
  • What is the charted depth if water at the end of the 2nd leg?

In this example we are working up a DR to determine our rough position. This does not take into account the tidal stream, leeway and effects of wind etc. Before we proceed with the DR we have to calculate the value of variation for the year 2012 and have supplementary questions that make us examine the chart around our new DR positions.

Determine Variation for year 2012

We can see form the question that we need to plot DR position lines on the chart. All bearings plotted on charts must be in relation to the True geographical north pole.

The direction bearings are given as magnetic bearings and know from our T-v-M-d-C mnemonic that when converting from a magnetic to true bearing we must correct for variation.

We therefore have to calculate the variation for year 2012 to convert bearing from Magnetic° to True°. To do this we have to do is have a look at the compass rose in the area that we are sailing.

Variation on the compass rose
Fig 7.1 – When converting a bearing from magnetic° to true° we must correct for variation. To calculate the variation for 2012 we must refer to the nearest compass rose to our position. The value for variation the year the chart was printed can be found ‘arrow A’.

The compass rose just to the west of Cape Woodward tells us that variation was 7°25’W in 2005 and is decreasing at a rate of 8° every year. We can calculate how much variation has changed from 2005 to 2012 as 7 x 8° = 56°. The variation in 2012 as 7°25’W – 56° = 6°29’W. We always round marine bearings up or down to the nearest degree and would therefore conclude that variation in 2012 is 6°W.

Leg 1 – DR Position 

It is easier for us to split our passage into two legs.

Using the CadET mnemonic we know that when converting from a magentic° to true° bearing we subtract westerly variation errors. So for the first leg of our passage:

243°M – 6°W = 237°T

For this leg of passage we can also calculate the distance we have travelled through the water by subtracting the log reading at the end of 1st leg from the log reading at the beginning of our passage.

557.0 miles – 548.8 miles = 8.2 miles distance travelled in leg 1

We can now plot this position on the chart:

1st dead reakoning position line.
Fig 7.2 – The DR position of leg 1. ‘A’, confirmed position fix is a small circle with dot. ‘B’, water track/heading indicated by line with single arrow. ‘C’, DR position indicated at end of water track by small line. The original fix and DR position has time and log readings added.

The coordinates for the end of the 1st leg are 46°06’.00N 006°03’.20E.

We can see form our plotted position line that the dangerous Robinson Rock may have been ¼ mile from our water track or heading line (Fig 7.2).

Leg 2 – DR Position

We can now proceed with plotting the second leg of our passage.

Again using the CADET mnemonic “Compass Add East True” we can see that when converting a bearing from a Compass° bearing towards a True° bearing we must subtract westerly variation.

319°M – 6°W variation = 313°T

For this leg we can calculate the distance travelled is

363 miles – 557.0 miles = 6 miles travelled through the water

We can plot this 2nd leg of passage on the chart starting at the end of the 1st leg dead reckon position (Fig 7.3).

2nd dead reakoning plot
Fig 7.3 – The DR position of leg 1 & 2. ‘A’, confirmed position fix is a small circle with dot. ‘B’, water track/heading indicated by line with single arrow. ‘C’, DR position indicated at end of water track by small line. The original fix and DR positions have time and log readings.

The coordinates for the end of the 2nd leg are 46°11’.40N 006°09’.40W. From our plot we can see that the charted depth at our dead reckon position is between the 20 and 30 metres depth contours.