Imagine the navigator has just fixed the vessels position on the chart and now has to determine what course the vessel has to steer to get to the next waypoint in the passage plan.
If they join the fix position and the next waypoint with a straight line then they will be able to determine what track the vessel will have to make across the ground to reach the next waypoint.
However there will inevitable be a tidal stream running and there may be the effect of leeway to deal with and the course that is steered must take this into account.
Consider the following:
A vessel at position A in the diagram below has to reach position B.
The vessel’s speed is 6 knots and a tidal stream is setting due south at two knots. A southerly wind is expected to cause 5 of leeway.
Find the course to steer to reach position B
To solve this type of problem we need to use our imagination.
Lets say that the vessel is initially at position A but is lying stopped. Leeway has no effect on a stopped vessel but it will still be affected by the tidal stream. The tidal stream will cause the vessel to drift to the south and after one hour it would have gone 2 nm and ended up at position C.
If the vessel had been steaming at 6 knots during that hour then if we drew a circle of radius 6 nm, centred on C, we would have found all possible positions the vessel could have reached in that time.
Our problem is that the vessel has to move down the ground track in order to get to the destination B.
The circle will only cut the ground track at one position, which is marked as D.
If we now join up positions C and D this will give us the water track that the vessel has to steer in order to end up somewhere on AB.
After one hour the vessel would have been set by the current to position C.
We can now lift off the water track direction from the compass rose on the chart.
Leeway will now have to be applied to obtain the true ships head and then this can be converted into either a compass or gyro course as necessary.
The navigator will also have to determine what time the vessel will arrive at B, in order to get an accurate idea of the estimated time of arrival (ETA) at his final destination.
The distance AB can easily be measured off the latitude scale on the chart.
However it would be wrong to divide this distance by the speed given in the question. (This would be considered an error in Principle in an examination) This is represented by CD on the diagram, however in the time it takes the vessel to move along CD through the water, it will have moved form A to D along the ground track and AD will represent its actual speed over the ground.
Therefore AD will give us the actual speed made good over the ground in one hour.
To find the total time required to go from A to B we simply divide the length of AB by the length of AD and this will give the time to reach B in hours.
Note:
There are assumptions made in this type of problem.
1) The tide must remain constant throughout the period
2) T he effect of the wind must also be considered constant.
To summarise:
1) Mark on the vessels initial position
2) Mark on the vessels final position
3) Join 1) and 2) above with a straight line, this will give the required ground track the vessel must make.
4) From 1) above lay off one hours worth of tidal stream.
5) Set a pair of compasses to represent the vessels speed through the water and from the end of the tide vector, scribe an arc which will cut the ground track.
6) Draw a straight line between the end of the tide vector and the position where the arc cuts the ground track. This will give the required water track of the vessel.
7) If applicable apply any leeway to the ground track to obtain the true ships head. (Note in this type of problem, leeway should always be applied against the direction the wind is blowing from)
8) Convert the true ships head to either a compass course or gyro course as required.
9) Measure the distance moved along the ground in one hour to obtain the speed made good across the ground.
10) Measure the total distance between the initial and final positions.
11) Divide the total distance by the distance covered in one hour to obtain the steaming time required to get from A to B.
On the chartlet below the vessel is initially at position A and is required to get to position B.
A current is setting 120 (T) at 3 knots and a Northerly wind is causing 5 of leeway. The vessels speed is 8 knots.
If the vessel is at position A at 1200 hrs find each of the following:
a) The true course to steer to reach position B.
b) The ETA at position B
From the chart:
Water track = 034.5 (T) (CD on chart)
Leeway = -5 (apply against the wind)
True Ships Head = 029.5 (T)
Ground Speed = 6.2 knots (AD on chart)
Total Distance = 8.9 nmls (AB on chart)
Steaming Time = AB / AD = 8.9 / 6.2
= 1.44 hrs
= 1 h 26m
Lesson 09.doc Course to Steer DGR 1999
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dariusz.lipinski