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Q4. For a box shaped barge 100 m in length, 15 m breadth, floating at an even keel draught of 8 m in sea water Of density 1025 kg/m³, the KG is 5 m.

A full breadth midship compartment 10 m long is divided by a centretine watertight longitudinal bulkhead to form two equal compartments. One of the compartments is bilged. The permeability of the flooded compartment is 85% . Calculate the angle of heel for the barge. (16)

Q6. A ship of 8000 tonne displacement has a rudder area of 22 m². The ship has a KM of 6.7 m, KG of 6.1 m and the centre of lateral resistance is 3.8m above the keel.

The maximum rudder angle is 35^oand the centroid of the rudder is 2.3 m above the keel.

The force generated normal to the plane of the rudder is given by

F = 580 Av² sin α

Where: A = rudder area

V = ship speed in m/s

α = rudder helm angle

Calculate EACH of the following, when the vessel is travelling at 20 knots:

(a) the angle and direction of heel due to the rudder force only, if it is put hard over to port;  (8)

(b) the angle and direction of heel due to the combination of centrifugal force and rudder force when the rudder is hard over to port and the vessel tums in a circle of 800 m diameter.  (8)

Q5. A ship has a length of 130 m and floats in the sea water of density 1025 kg/m³.  A model of this ship has a length of 5 m and a wetted surface area of 6 m².  The model has a total resistance of 45 N when towed at 1.85 m/s in fresh water of density 1000 kg/ m³.

(a) Using the data below, calculate EACH of the following:

(i) the ratio of residuary resistance to total resistance for the model; (5)

(ii) the ratio of residuary resistance to total resistance for the ship at the corresponding speed. (8)

(b) State why the two ratios should be different. (3)

The frictional coefficient for the model in fresh water is 1. 694

The frictional coefficient for the ship in sea water is 1. 418

Speed in m/s with the speed index (n) for ship and model 1.825