Action of Rudder in turning a ship and its three phases

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We all know every ship has a rudder which helps in turning the ship and is always at the stern of the vessel after propeller. To understand the turning of the ship and how rudder turns the ship, lets assume that the helmsman has given rudder some angle to the starboard side.As soon as the helmsman gives rudder some angle to the stbd side, then at very moment a lift force acts on the rudder which is directed along the traverse direction to the ship in port side.
Other than this, the rudder force has another effect on the ship. It creates a moment about the CG of the ship. This direction of the moment will be towards stbd side because of the rudder force is acting about the CG of the ship.


When the rudder moment acts about the ship's CG, it slightly changes the ship's orientation by giving it a drift angle. See above figure. The ship with that drift angle is moving along the initial direction.From above fig it can be seen that the ship's velocity has two components. One is Surge velocity in longitudinal direction and other is Sway velocity in traverse direction.
With a sway velocity towards port side, the hull sways towards port. When it does so, it exerts a force on the water particles that are in its port side.The water particles in return, exert an opposite force on the ship's hull, due to inherent inertia of the water particles.The magnitude of this inertia force is equal to the displacement of the vessel to gain the equilibrium.This inertia force acts on the ship's hull in stbd direction.
This inertia force can be categorized into two. One half acting at the bow (Fwd of the CG) and other half at the stern (Aft of the CG). See the below figure. 


The inertia force at the stern will create a moment towards port side about the CG and forces at bow will create a moment towards stbd side about the CG. The hull is designed in such a way that the inertia forces at the bow is more than that at the stern. And thus the resultant moment is towards the stbd side. And this resultant moment turns the ship in the desired direction.

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