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

F_n = 15.5 A v² α newtons

Where:      A = rudder area ( m²)

v = ship speed (m⁄s)

α = rudder helm angle ( degrees)

A ship travelling at a speed of 20 knots, has a rudder configuration as shown in Fig Q6.

The centre of effort for areas A₁ and A₂ are 32 % of width from their respective leading edges. The rudder angle is limited to 35^o from the ship’s centreline

Calculate EACH of the following:

(a) The diameter of the rudder stock required for a maximum allowable stress of 77 MN/m²  (12)

(b) The drag component of the rudder force when the rudder is put hard over at full speed. (4)