What is a helmsman's primary instrument for steering the ship?

The primary instrument for steering a ship is the rudder. The helmsman uses the rudder to control the direction of the vessel by altering its angle relative to the water flow. When the rudder is turned, it creates a difference in pressure on either side, which helps to pivot the ship in the desired direction. This mechanism is fundamental to navigation and maneuverability in maritime operations.

The other options play important roles in the operation and movement of a ship but do not serve the primary purpose of steering. The throttle regulates the engine power and speed of the ship but does not change its direction. The steering wheel, also known as the ship's wheel, is used to communicate the helmsman's intentions to the rudder but is not the actual mechanism that steers the ship. The gyrocompass is vital for navigation purposes, providing accurate heading information but does not directly steer the vessel. Thus, the rudder is the correct answer as it directly influences the ship's steering capability.