Aaron

[Analogy to a Car]
An object changes direction due to external forces acting upon it. A car for example changes direction because of the interactions at the contact patch of the tire and road surface. When a slip angle is introduced between the tire direction and facing a force is generated which changes the path of the car. This slip angle is initiated in the front tires via the steering wheel. As a secondary reaction the car yaws causing the rear tires to also generate a slip angle and generated forces in the rear. Both sets of the tires forces act to directly turn the vehicle.

For a ship, the helm/rudder would be analogous to the steering wheel/front tire slip angle and the turning of the ship would be due to the yawing of the car chassis which indirectly introduces a rear tire slip angle. The big difference is the forces generated by the rudder is not enough to turn the ship proper, it is only enough to generate the slip angle or drift. The drift angle then sets up hydrodynamic forces between the water and the hull which does the heavy lifting to rotate the ship.



[How does it work]
The magnitude of the force to change direction and to yaw the ship is directly related to the drift angle (B) and the rate of yaw (r). Lambda is the ratio of 2 times the draught divided by the ship length. A theoretical equation for the hydrodynamic coefficients is


, and an example plot for a long plate with zero yaw rate is:


These coefficients are used to calculate the lateral force and the yaw moment using these equations:

Y and N is calculated using the ocean water density, ship speed, length and draught.

The lateral force changes the ship’s velocity (lateral and rearward) and the yaw moment would turn the bow about the center of gravity.

[The Take Away]
The rudder doesn’t directly turn the ship, it only sets up the drift angle. It’s the resultant drift angle and water vortex pattern around the ship’s hull that creates the lateral and yaw forces and moments.