There may be times when it is not possible to obtain a fix from two or more charted objects. In cases like this then we can utilise the method known as the running fix.
In this case let us assume that we have only one object that we can obtain a true bearing from, e.g. a rock lighthouse.
If we know the ships course and speed and also any external factors such as leeway and tidal stream then it will still be possible to fix the vessels position. (this is more commonly done on ocean passages where a morning sight is run up to noon so as to fix the ships noon position)
Consider the diagram below.
A vessel steaming at 10 knots on a course of 103 (T) observes a light bearing 045 (T) at 0900 hrs.
A second observation of the same light at 1000 hrs gave a bearing
of 299 (T)
During that time the vessel experienced a tidal stream setting 244 (T) at a rate of 3 knots and a Northerly wind was estimated to cause 10 of leeway.
Find the position of the vessel at 1000 hrs.
Solution
1) Lay off the true bearing of the light to obtain the 0900 hrs position line.
2) No distance is given so all we can say is that we are somewhere on the line. Pick a DR position anywhere on the position line and label this as the 0900 hrs DR.
3) From the information given calculate the water track that the vessel will make.
Course = 103 (T)
Leeway = +10
W.Track = 113 (T)
4) From the 0900 hrs DR lay off the water track for a distance corresponding to one hours worth of speed, i.e. 10 nmls.
5) Mark this as the 1000hrs DR.
6) From the 1000 hrs DR lay off one hours worth of tidal stream, to find the 1000hrs EP.
7) Draw a straight line between the 0900 hrs DR and the 1000 hrs EP to obtain the ground track.
8) Transfer the 0900 hrs position line through the EP to get a transferred position line for 1000hrs. If the vessel was somewhere on the 0900 hrs position line then it must now be somewhere on the transferred position line.
9) Lay off the true bearing of the light at 1000 hrs to obtain an actual position line for 1000 hrs.
10) If the vessel must be somewhere on the transferred line and the 1000 hrs line then the only position the vessel can be in is where the transferred line and the actual 1000 hrs line intersect. This is marked as the 1000 hrs position.
11) To determine the position of the vessel at 0900 hrs all we have to do is to transfer the ground track through the fix for 1000hrs and then run it backwards until it crosses the original 0900 hrs position line.
There are several ways in which the position lines may be obtained but no matter how the position lines are stated the method of construction is the same in each case.
The one exception to the above is the case where a range is given instead of a bearing.
Example
A vessel proceeding in the Southwest bound lane of the Tuskar Rock Traffic Separation Scheme obtains a range of 4 mls off Tuskar Rock at 0900 hrs.
The vessel is steering 235 (T) at 7 knots. A tidal stream is setting 270 (T) at 2 knots and a Northerly wind is causing 5 of leeway.
At 1000 hrs the vessel obtains a bearing of Black Rock of 015 (T)
Find the position of the vessel at 1000 hrs and 0900 hrs
1) Draw a circle of radius 4 mls centred on Tuskar Rock Light.
(The vessel must be somewhere on the circle and in the South West bound lane)
2) Instead of selecting a DR position on the circle we are going to take our DR position as the light itself.
(this will allow us to transfer the centre of the position circle after we have allowed for course steered, speed, tidal stream and leeway.)
3) From the information given calculate the water track.
Course = 235 (T)
Leeway = - 5
W.Track = 230 (T)
4) Lay off water track for one hour (7mls) from the light, to find a DR for 1000 hrs.
5) From the 1000 hrs DR lay off one hours worth of tide to find the 1000 hrs EP.
6) Join the initial DR to the 1000 hrs EP to get the ground track.
7) Draw a circle of radius 4 mls centred on the 1000 hrs EP. This now gives us a transferred position circle.
8) Lay off true bearing of Black Rock.
9) Where the transferred position circle and the 1000 hrs bearing intersect is where the vessel is.
10) To find the 0900 hrs position we simply run the ground track back from the 1000 hrs position until it cuts the original position circle. This gives the vessels position at 0900 hours.
Note: In some cases you may find that the transferred position circle will be cut twice by the second bearing line, giving an ambiguous second position.
However to resolve this you should apply the ground track to both these positions and find out where the ground track intersects the original position circle.
Read the question again very carefully as there will usually be something in the question, which will eliminate one of the positions on the original ground track. It may be depth of water given in the question, the colour of the light sectors or one position may put the vessel over the land.
Lesson14.doc Running Fix DGR1999
5
dariusz.lipinski