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Q5. A single screw vessel with a service speed of 15 knots is fitted with an unbalanced rectangular rudder 6 m deep and 4 m wide with an axis of rotation 0.2 m forward of the leading edge. At the maximum designed rudder angle of 35° the centre of effort is 30% of the rudder width from the leading edge. The force on the rudder normal to the plane of the rudder is given by the expression: Fn = 20.2 A v2α newtons

Where: A = rudder area (m2) v = ship speed (m/s)   α = rudder helm angle (degrees)

The maximum stress on the rudder stock is to be limited to 70 MN/m².

Calculate EACH of the following: (a) the minimum diameter of rudder stock required; (b) the percentage reduction in rudder stock diameter that would be achieved if the rudder was designed as a balanced rudder, with the axis of rotation 1.0 m aft of the leading edge.