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Q6. A spade-type rudder has an area of 6.89 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 1.75 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 Av² 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 17 knots; (8)

(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 410 mm.  (8)