The force acting normal to the centreline plane of the rudder is given by:

Fn = 15.5 x A x V^2 x sin(alpha) newtons,

where A is the rudder area (m2), V is the speed (m/s) and alpha is the rudder angle.

The question refers to a drawing that is not reproduced here, but the standard method is as follows.

• The rudder stock is subjected to a bending moment and a torque due to the rudder force.
• The normal force Fn acts at the centre of pressure of the rudder, at a distance from the stock, producing a bending moment M = Fn x (distance from stock to centre of pressure).
• The torque on the stock is produced by the component of the force and the tiller arrangement; the maximum torque occurs when the rudder is hard over.
• The equivalent bending moment (or the combined stress) is calculated, and the stock diameter is found from the bending/torsion formula.
• For a solid circular shaft, the section modulus Z = (pi x d^3)/32, and the bending stress = M/Z.
• Combining bending and torsion, the equivalent bending moment Me = (M + sqrt(M^2 + T^2))/2, and the diameter is found from:

d^3 = (32 x Me)/(pi x sigma_allowable), where sigma_allowable = 77 MN/m2 = 77 x 10^6 N/m2.

• The diameter is then d = (32 x Me/(pi x 77 x 10^6))^(1/3) metres.
• The calculated diameter is rounded up to the next standard size and checked against classification society rules.

• The drag component is the component of the rudder force acting in the direction of the ship's motion (i.e. along the centreline, opposing the motion).
• The normal force Fn acts normal to the rudder plane. When the rudder is at an angle alpha to the centreline, the drag component (the component along the ship's centreline) is:

Drag = Fn x sin(alpha).

• At hard over, alpha is typically 35 degrees, so Drag = Fn x sin(35) = Fn x 0.574.
• The drag component increases the resistance of the ship and is a maximum at hard over and full speed.
• The value is obtained by substituting the rudder area, the full speed and the hard-over angle into the expression.

(Note: the specific numerical values of rudder area, speed and angle are given in the drawing referred to in the question; the candidate should substitute them into the expressions above to obtain the numerical answers.)