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Q6. A spade-type rudder has an area of 6.33 m². At its maximum designed rudder angle of 35^o, the centre of effort is 0.12 m aft of the axis of rotation and 1.6 m below the lower edge of the rudder stock bearing.

The force on the rudder normal to the plane of the rudder is given by the expression:

F_n=18.32 A v²  α newtons

where:    A=rudder area (m²)

v=ship speed (m⁄s)

α=rudder angle ( degrees)

The equivalent twisting moment (T_E )  is given by :

T_E=M+ √(M²+ T² )

where :          M=bending moment

T=torque

The maximum stress in the rudder material is to be limited to 77 MN/m².

Calculate EACH of the following:

(a) the diameter of the rudder stock required for a ship speed of 16 knots (10)

(b) the speed to which the ship must be restricted, given that the effective diameter of the stock is reduced by wear and corrosion to 375 mm. (6)