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Q1. A spade type rudder, supported only at the rudder head, has a depth of 3.6 m, with the following widths at equal intervals commencing from the top of the rudder:

2.10 m, 2.05 m, 1.80 m, 1.45 m and 1.00 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 0.15 m from the axis of rotation.

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

Where:

F_n  = 18.32Av² α Newtons

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 = twisting moment

Calculate the required diameter of the rudder stock, assuming a maximum allowable stress of 70 MN/m², for a ship speed of 18 knots and rudder angle 35^o. (16)