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Q6. A spade type rudder, supported only at the rudder head, has a depth of 4.8 m, with the following widths at equal intervals commencing from the top of the rudder.

2.80, 2.75, 2.40, 1.95 and 1.50 m

The top of the rudder is 0.4 m from the bearing at the rudder head.

The centre of effort of the rudder can be taken to act at the vertical centroid of the rudder and at a distance of 0.2 m from the axis of rotation.

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

F_n = 18 A V² α newtons

where: A = rudder area (m²)

V = ship speed (m/s)

α = rudder angle (degrees)

The equivalent twisting moment (TE) is given by:

T_E = M + √(M² + T² )

where: M = bending moment

T = twisting moment

Calculate the required diameter of the rudder stock, assuming a maximum allowable stress of 75 MN/m², for a ship speed of 20 knots and rudder angle 35°.