. "Appendix D: Hydrodynamics, Physical Models, and Mathematical Modeling." Simulated Voyages: Using Simulation Technology to Train and License Mariners. Washington, DC: The National Academies Press, 1996.
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FIGURE D-2 Steady turning rate versus rudder angle.
Source: Eda and Landsburg (1983)
ship A which is stable. While ship B finished the 15-15 degrees Z test in a stable fashion, it could not finish Z maneuver tests of 7.5-7.5 and 5-5 degrees in a stable manner (i.e., heading angle is oscillatory divergent in unstable patterns).
In the case of the very unstable ship, C, where the heading angle is divergent after the first execution of the rudder angle, recovery cannot be achieved by the use of the opposing rudder angle at the second execution. The ship did finish the 15-15 degree Z maneuver test in stable fashion because of the significant contribution of the nonlinear terms.