Dead Reckoning

DR is vector addition. One vector represents the movement of the boat: distance given by the difference in the log readings, direction from the compass heading converted into True including allowance for leeway. The second vector represents the tide; identify the tidal hour, look up the set and rate and interpolate or extrapolate to get the correct rate. Draw the vectors onto the chart to obtain the Estimated Position.

The tides (UT) for the Port of Trumpton in June and tidal stream information for Trumpton roads:

1. It is  Friday 13th of June and you are feel compelled to withdraw from the rat race in order to participate in a jolly sail.
    You set off at 1145 DST steering a course 090(C) having first fixed you position by taking bearings on Trumpton  Church Spire, the South Trumpton cardinal buoy and Trumpstone lighthouse. At the end of the first hour your log records 5.6 miles sailed through the water. Wind is from the NW F4 and leeway is 5 degrees.

(i) Evaluate the water track vector
(ii) Evaluate the tidal vector

2. It is Sunday 15th of June.You depart Trumpton harbour at 0800DST on a heading of 270(C). This heading is maintained for two hours and the log records 12.6 miles through the water at the end of this period. Wind is from the North, F5 and leeway is 6 degrees.

(i) Evaluate the water track vector
(ii) Evaluate the tidal vectors.

Solutions

Magnetic variation is 4W and the deviation table is shown above.


1.    Compass     090(C)
      +deviation       4E
                         094(M)
       - variation      4W
                          090(T)
        leeway        +5
                          095(T)
The water track vector is 5.6 miles at 095(T) from the start

Time before HW is (1615 - 1045 = 0530); select HW-5 diamond
Tidal range is 11.1 - 2.8 = 8.3m; spreadsheet gives 1.3 kn.

The tidal stream vector is 1.3 Nm at 045(T)

2.           Compass 270(C)
             -deviation    4W
                             266(M)
            -variation     4W
                             262(T)
                leeway    -6
                             256(T)
The water track vector is 12.6 Nm at 256(T) from the start

First hour: time since HW (0700 - 0533 = 0127); select HW +2 diamond;  then HW + 3 diamond for subsequent hour.
Tidal range is 12.7 - 1.4 = 11.3m ; spreadsheet gives 3.1kn,  3.4kn tidal streams respectively.  

The tidal stream vectors are 3.1 Nm at 230(T) then 3.4 Nm at 230(T)

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