Question

The time series of rudder angle (\(\delta\)) and heading angle (\(\psi\)) during a ship's maneuver are shown in the following figure. Identify the maneuver and the associated parameters (p, q, r and s) 

 

• A. turning maneuver, p: heading angle, q: rudder angle, r: 1st overshoot angle, s: 2nd overshoot angle
• B. spiral maneuver, p: heading angle, q: rudder angle, r: 1st overshoot angle, s: 2nd overshoot angle
• C. zig-zag maneuver, p: rudder angle, q: heading angle, r: 1st overshoot angle, s: 2nd overshoot angle
• D. zig-zag maneuver, p: heading angle, q: rudder angle, r: 1st overshoot angle, s: 2nd overshoot angle

Hint:

In control systems plots, the sharp, blocky signal is almost always the input/command (here, the rudder angle), and the smoother, lagging signal is the system's output/response (here, the ship's heading).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The question shows a standard ship maneuverability test plot and asks to identify the maneuver and the labeled parameters. The plot shows the ship's response (change in heading) to a prescribed sequence of rudder movements.
Step 2: Identifying the Maneuver:
The plot shows the rudder being put to one side (e.g., 20\(^{\circ}\)), held there until the ship's heading changes by a certain amount (e.g., 20\(^{\circ}\)), then reversed to the opposite side (\(-20^{\circ}\)), held there until the heading changes back past the original course, and so on. This repeated, alternating rudder command and the resulting oscillatory heading response is characteristic of a Zig-Zag Maneuver (also known as a Kempf maneuver).
- A turning maneuver would involve holding the rudder at a constant angle and observing the ship turn in a circle.
- A spiral maneuver involves a series of steady-state turning tests at different rudder angles to check for directional stability.
Therefore, the maneuver is a zig-zag maneuver. This eliminates options (A) and (B).
Step 3: Identifying the Parameters:
Now we need to identify the curves and angles for the zig-zag test.
- The input to the system is the rudder angle. The curve that shows sharp, step-like changes from +20\(^{\circ}\) to -20\(^{\circ}\) is the command input. This corresponds to the rudder angle (\(\delta\)). This curve is labeled 'p'.
- The output or response of the system is the ship's heading. The smoother, lagging, S-shaped curve that shows the ship's heading changing over time is the heading angle (\(\psi\)). This curve is labeled 'q'.
- The maneuver is typically described by the overshoot angles. After the rudder is reversed (e.g., from +20 to -20), the ship continues to turn in the original direction for some time due to its inertia before it starts turning back. The amount it overshoots the rudder reversal heading is the first overshoot angle.
- In the diagram, the rudder is reversed when the heading 'q' reaches 20\(^{\circ}\). The heading continues to increase to a maximum value before turning back. The difference between this maximum heading and the 20\(^{\circ}\) mark is the 1st overshoot angle. This is labeled 'r'.
- Similarly, after the rudder is brought back to the original side, the ship overshoots the original heading in the opposite direction. This is the 2nd overshoot angle, labeled 's'.
So, we have:
- p: rudder angle
- q: heading angle
- r: 1st overshoot angle
- s: 2nd overshoot angle
This matches the description in option (C). Option (D) incorrectly swaps the labels for heading and rudder angle.
Step 4: Why This is Correct:
The maneuver is clearly identifiable as a zig-zag test from the alternating rudder inputs. The labels correctly identify the rudder angle as the step-wise input (p), the heading as the smooth response (q), and the overshoot angles (r and s) as the key performance metrics of the maneuver.