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Q6. 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^o 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:

F_n = 20.2 A v²  α 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;(9)

(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. (7)