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Q6. The force acting normal to the plane of a rudder is given by the expression:

Fn = 20.2 A V² a newtons

Where :         A = rudder area (m²)

V = ship speed (m/s)

a = rudder angle (degrees)

A manoeuvrability specification for a ship that requires a transverse rudder force of 92 kN is generated when the angle of helm is 35^o with the ship travelling at 5 knots.

(a) Determine suitable dimensions for a rectangular rudder having an aspect ratio (depth to width ratio) of 1.5.  (6)

(b) The rudder stock is designed to have a diameter of 360 mm with the allowable shear stress in the material limited to 70 MN/m² at its service speed of 16 knots. At the maximum helm angle of 35^o, the centre of effort is 35% of the rudder width from the leading edge of the rudder.

Calculate the maximum distance of the axis of rotation from the leading edge of the rudder so that the stock is not overstressed at the service speed. (10)