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Q6. A single screw ship with a service speed of 15 knots is fitted with a rectangular rudder, 5.5 m deep and 3.5 m wide with the axis of rotation 0.4 m aft of the leading edge. At a rudder angle of 35^o, the centre of effort is 32 % 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=577 A v²  sin⁡ α newtons

Where;

A=rudder area ( m² )

v=ship speed ( m⁄s)

α=rudder angle ( degrees)

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

Determine EACH of the following:

(a) The minimum diameter of the rudder stock required for ahead running;     (9)

(b) The speed of the ship, when running astern, at which the maximum stress level would be reached.(7)