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Q6) A ship of 10000 tonne displacement has a rudder area of 25 m². The ship has a KM of 6.9 m, KG of 6.3 m and the centre of lateral resistance is 3.9 m above the keel.

The maximum rudder angle is 35 degrees, and 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=590 A v²  sin⁡α  (N)

where, A=rudder area ( m²)

v=ship speed (m⁄s)

α-rudder helm angle ( degrees)

Calculate EACH of the following, when the vessel is travelling at 22 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 turns in a circle of 800 m diameter. (8)