How does a rudder use water flow to turn a ship?

In naval architecture, a rudder functions as a hydrodynamic control surface, utilizing principles similar to an airfoil to steer a ship. When the rudder is turned to a nonzero angle of attack relative to the water flow, it develops lift.1

This lift generates a lateral force that creates a turning moment around the ship’s center of gravity, causing the vessel to change its heading. Because the magnitude of this lift is proportional to the square of the water velocity, rudders are most effective when positioned within the high-velocity wash generated by a propeller.123

When the rudder is at a zero-degree angle, it acts as a vertical stabilizing fin; however, when angled, its surface area provides the necessary swinging moment to initiate a turn. During a turn, the ship also experiences a drift angle, where the hull generates its own inward-acting hydrodynamic force that balances the centrifugal force and the rudder's force, allowing the ship to maintain a steady circular path.2