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)**