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Q2. A single screw ship with a service speed of 16 knots is fitted with a rectangular rudder, 6.5 m deep and 4 m wide, with its axis of rotation 0.4 m from the leading edge. At a rudder helm angle of 35 degrees, the center of effort is 32% of the rudder width from the leading edge. The force (F) on the rudder normal to the plane of the rudder is given by the expression:

F = 577 A v² sin α (newtons)

Where:

A = area of the rudder (m²)

v = ship speed (m/s)

α = rudder angle (degrees)

The maximum stress on the rudder stock is to be limited to 70 MN/m².

Calculate EACH of the following, for a rudder angle of 35 degrees:

(a) The minimum diameter of the rudder stock for ahead running;

(b) The speed of the ship, when running astern, at which the maximum stress Level would be reached.