A ship with a standard right-handed coordinate system has positive \(x\), \(y\), and \(z\) axes respectively pointing towards bow, starboard, and down as shown in the figure. If the ship takes a starboard turn, then the drift angle, sway velocity, and the heel angle of the ship for a steady yaw rate respectively are:
A ship with a standard right-handed coordinate system has positive \(x\), \(y\), and \(z\) axes respectively pointing towards bow, starboard, and down as shown in the figure. If the ship takes a starboard turn, then the drift angle, sway velocity, and the heel angle of the ship for a steady yaw rate respectively are:
Show Hint
- Positive, negative, and positive
- Negative, positive, and positive
- Negative, positive, and negative
- Positive, negative, and negative
The Correct Option is D
Solution and Explanation
Step 1: Understanding the right-handed coordinate system.
In the standard right-handed coordinate system for a ship: - The \( x \)-axis points forward (towards the bow), - The \( y \)-axis points to the starboard side, - The \( z \)-axis points downward. A starboard turn involves a steady yaw motion (rotation about the \( z \)-axis), causing changes in drift angle, sway velocity, and heel angle.
Step 2: Analyze the drift angle.
The drift angle is the angle between the direction of motion of the ship and its heading. For a starboard turn, the drift angle is positive because the ship's actual motion shifts towards the port side.
Step 3: Analyze the sway velocity.
Sway velocity is the velocity along the \( y \)-axis (starboard direction). During a starboard turn, the sway velocity is negative as the ship moves slightly towards the port side.
Step 4: Analyze the heel angle.
The heel angle is the inclination of the ship about the \( x \)-axis. For a starboard turn, centrifugal forces cause the ship to heel towards the port side, resulting in a negative heel angle.
Conclusion: For a steady yaw rate during a starboard turn, the drift angle, sway velocity, and heel angle are positive, negative, and negative respectively.
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