Simulating the rudder

The rudder is quite an interesting thing, force-wise. When the ship stands still, no force is generated at all. When the ship moves, the force depends on the amount of deflected water which depends on the speed and the position of the rudder. It actually depends on the direction of speed, too, since it makes quite a difference if the ship moved "normally" or sideways (in example, when the bow and stern thrusters are used).

Then the force depends on the force produced by the engine as well. When the ship stands still and the engine goes full ahead, the water accelerated by the propeller will produce some force when it hits the rudder though the ship is not moving yet. This effect is often used when a ship tries to dock or undock: the captain revs the engine for a short time to make the ship turn without moving it (much). Or, another option: one end of the ship is moored while the engine is run to turn the ship.

I assume, too, that when the engine is run backwards the stream of water passing the rudder will be much more diffuse, producing less force compared to running the engine forward.

Summary: The forces produced by the rudder depend on the angle of the rudder, the speed and direction of the surrounding water, and the speed of the water jet produced by the propeller.