yaw disturbance of, say, 1 degree is given from an initial straight course (Eda and Landsburg, 1983). The stable ship eventually comes to a new straight course, which is near the original heading. The heading of an unstable vessel, on the other hand, continues to change with time, until nonlinear hydrodynamic forces override the inherent instability of the hull form. Such a ship requires constant helm corrections to maintain a desired heading.

Many ships have been built with some degree of inherent instability. Typical examples are large tankers, which generally have inherent instability of course at loaded conditions because of relatively large values of the block coefficient and beam-to-length ratios. The degree of instability is substantially increased with an increase in beam-to-draft ratio, which is the case for shallow-draft, wide-beam ships.

The practical effects of dynamic instability can be understood by reviewing trajectory results from three ships with different levels of dynamic instability (Eda and Landsburg, 1983). The type and characteristics of the hulls are given in Table D-1. The solid-line curves in Figure D-2 show steady turning rates (predicted results from Figure D-3 spiral tests) for ships A, B, and C. Arrows along the curves show the sequence of results predicted for the spiral tests. Dotted lines indicate the jump in steady turning rates during spiral tests of dynamically unstable ships B and C. Predicted zig-zag maneuver (Z maneuvers) trajectories were computed for these ships at an approach speed of 14.5 knots.

Results of the simulations for ships A, B, and C (Figure D-4) indicate dynamic behavior during the Z maneuvers. The dynamically stable ship, A, has a small overshoot angle, and can quickly finish a Z maneuver. The unstable ship, B, has a larger overshoot angle, and it takes more time to complete the test than