Worked Example A

Worked example 7A

At 1230 NP DST on Wednesday 6th November 2012, a boat is returning from a fishing trip at Robinson Rock and making towards the safe water mark in the Hiscock Sound. The log reads 3456.2 and boat speed is 7 knots.

The tidal stream from 1230 to 1330hrs is 192°T and 1.8 knots. Use Variation 7°W

What is the magnetic Course To Steer to the safe water mark in Hiscock sound?
If the wind is from NW and creating 5° leeway, what is the magnetic course to steer (M°) to get to the Hiscock sound safe water mark.

The fix and ground track (COG)

Fig 8.6
Fig 8.6 – Draw a line between the two positions making sure to carry the line a little further last the destination mark. It does not matter if this line carries on over the land area on the chart. This line represents our ground track, the course over ground that the boat will actually travel in relation to the seabed. Always remember when plotting lines to mark them up with the right symbols, in this case two small arrows.

The first thing we need to do is locate our start point (Robinson Rock) and our destination (Hiscock Sound SWM).

We can draw a line between the two points remembering to carry it on a little past the safe water mark.

Measure the distance between the two positions.

The distance between the two positions is 7.25 miles and with a boat speed it should take us around an hour to travel between them (Fig 8.6). This means that we need to work up the plot using one hour of tide.

The tidal vector

Fig 8.7
Fig 8.7 – When we are working up a CTS the tidal vector is always placed at our origin.

Next we draw in the tidal stream vector, which we are given in the question from our start point at Robinson Rock.

192° 1.8 knots

Again remember to use proper plotting symbols, in this case three arrow to describe a tidal vector. At this stage you can already see that we will be stemming the tide on our passage.

The boat speed vector

Fig 8.8
Fig 8.8 – We have estimated the journey to take 1 hour (ground track), we have added 1 hour of tide (tidal vector) and arc’ed off 1 hour of boat speed (water track).

We can now set the dividers to our boat speed which was given in the question as 7 knots. Place one point of the dividers at the end of the tidal vector, and ‘arc’ the other point of the dividers until it meets our ground track (COG).

You will notice it crosses the ground track line a little before our destination at the safe water mark. As mentioned earlier it is good practice to always check the dividers against the nearest latitude part of scale to make sure they have not moved during the plotting process.

We can see that the tide is impeding our progress a little and will slow the boat down as we proceed into it. This is why the water track line does not reach our destination point. If on the other hand the tide was pushing us northwards our water track line would carry on further than our destination at the safe water mark.

Remember the symbols, one arrow for water track, two arrows for the ground track and three arrow for the tidal vector.

Determining the heading from water track

Fig 8.9
Fig 8.9 – We get our CTS from the bearing of the water track. We must steer 056° Magnetic from the rock along the ground track to our destination at the safe water mark to counteract the tide.

We can now measure the bearing of our water track which gives us the heading for our course to steer (Fig 8.9).

We are lifting a bearing directly from the chart so will be in °True. We can use the plotter to measure the bearing which is


This is the heading or direction we need to steer from our origin to counteract 1 hour of tide to reach our destination along the ground track.

We can use our T-v-M-d-C mnemonic that tells us when converting a True bearing to Magnetic bearing we must take variation into account. The CadET mnemonic reminds us that when converting a compass bearings towards a true bearing must add easterly variation. Conversely when converting true bearings towards compass bearings we subtract easterly errors and add westerly errors.

Magnetic heading is 049°T + 7°W variation = 056° Magnetic

Taking leeway into account.

Fig 8.10
Fig 8.10 – Its important to apply the leeway correctly if we added instead of subtracted, we would be 10° off course which could cause significant problems especially on a long passage.

The magnetic CTS is 056°M but does not take into account the leeway caused by the northwest wind. In a CTS plot we take account of the leeway in our calculation so we can counteract its affect and stay on a straight course.

We are told that will have 5° leeway produced by a northwesterly wind and always a good idea to write a wind arrow on the chart so we get a better visualisation whats going on and helps us decide if we need to add or subtract the 5° (Fig 8.10).

If we did not compensate for leeway we would be pushed off course in a southerly direction by 5° and the vessels heading would be 061°M. However if we compensate for the leeway and steer 051° we will stay on course, in effect the leeway producing wind will be blowing us back on course.

To establish that you have properly understood the concepts behind plotting a course to steer, make sure:

You draw water track (boat speed line) line from end of tidal vector
The water track line should equate to the boat speed of the vessel
Make sure the water track arcs the ground track on the plot and have not just joined the end of the water track to the destination position.

Time to go (TTG)

At Day Skipper level you will only ever be asked whether a passage will take less than and hour, an hour or more than an hour. When you take more advanced navigation course you will be asked precisely how long a passage will last or the time to go until you finish a passage.

Important Points

  • Both the proposed ground track AND the tidal vector are plotted from the starting position which could be a fix or an EP.
  • While drawing in the ground track it is worth extending it well beyond the destination.
  • Boat speed is always ARC’d across the proposed ground track from the end of the tide and NEVER just joined to the destination.
  • The course to steer is from the end of the tide to where the ARC intersects the proposed ground track.
  • Draw a wind arrow near your water track to make it clear which way leeway should be applied.
  • Be careful to use the correct plotting symbols otherwise you might be woken up to explain them to whoever is now on watch!
  • You need to develop plotting accuracy within: o 0’.1 of arc (0.1 mile = 1 cable = 200 yards) for distance and o 1° of arc for bearing.
  • It is critically important to remember that COG and SOG can ONLY be derived from measurements along the ground track and that the water track plays no part at all in these measurements – EVER!
  • Bearings can go up to 360° and are always written with 3 digits, where there are less then leading zeroes are used to make up the number, e.g. 000°T.
  • Marine bearings are always rounded to the nearest whole number of degrees, e.g. 045o29’T would be rounded down to 045oT and 045o30’T would be rounded up to 046oT.
  • Whenever you are asked to plot a position on a chart in an exercise or assessment, as well as showing us the plotting, you need to demonstrate your understanding and ability by typing the latitude and longitude coordinates in the text of your answer.