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(1) Ship Motions and Vectors (see Fig. 4)
 
 This screen displays a bird's eye view of the motions of the rudder and the hull. In addition, the normal force acting on the rudder and the longitudinal and the transverse component of the force acting on the centre of gravity of the hull in association with steering attempts and turning moments are shown with arrows. For ship's speed, the longitudinal velocity component (u), the transverse velocity component (v) and the composite velocity vector (Vs) are shown with arrows at the right-hand corner of the same screen.
 
 The lengths of arrows of these forces, moments and velocities change according to their magnitudes. As a consequence, ship motions and dynamic forces acting on the hull can be seen with continuous animation graphs. Viewing these screens, drifts of the ship due to steering operation, turning motion, speed reduction, and generation of kick and drift angle at their initial stage can be studied.
 
Fig.4 Ship motions and vectors
 
(2) Tracks of Ship's Motions (see Fig. 5)
 
 This screen displays tracks of the ship's motion. Together with the current position and posture of the ship, past ship's posture and tracks of the centre of gravity of the hull are displayed at specific time intervals. In addition, numerical information on the conditions set for simulation such as length, breadth, depth, draft of the ship and depth of water, time elapsed, position of the centre of gravity of the hull and heading direction is displayed.
 
Fig.5 Tracks of ship's motions
 
 Viewing sub-window (1) and sub-window (2) at the same time, it is possible to understand what force and moment would act on the hull when the ship assumes a certain position in the intended turning motion. Furthermore, concepts such as final diameter, maximum advance, maximum transfer, final turning radius and reach after a steady state of turning motion can be studied. Besides, the effects of differences in conditions such as ship size, rudder angle, draft, and depth of water, the magnitude of stern kick and the water area that the ship occupies can also be studied.
 
(3) Position of Pivoting Point (see Fig. 6)
 
 The current positions of the centre f gravity of the hull and the pivoting point are displayed. And, the tracks of the moving pivoting point with time are also displayed. This allows students to learn how the position of the pivoting point moves in association with the developing turning angular velocity after the rudder is taken.
 
Fig. 6 Position of pivoting point
 
(4) Time History Data (see Fig. 7)
 
 The changes of heading direction (φ), rudder angle (δ), turning angular velocity (r), ship's speed (Vs), drift angle (β), and heeling angle (θ) are time-historically displayed. With these displays, the students can learn the relationships among various factors involved in the ship motions during turning operations. For instance, relationships among changing phenomena such as developing turning angular velocities in association with the changing heading direction, generation of drift angles and decreasing ship's speed due to increasing turning angular velocities can be studied.
 
Fig. 7 Time history data
 
 Furthermore, by simultaneously viewing sub-window (4) and sub-window (1) or sub-window (2), relationships among various factors of ship motions throughout all phases of turning motion from the transient initial state to the steady state can be studied.
 
(5) Heeling of the Hull (see Fig. 8)
 
 Vectors of rudder forces, the lateral components of the water pressure and centrifugal forces are shown with arrows, and at the same time, the states of heeling of the hull are displayed with an animation. The students study the changing heeling motions of the hull from the transient initial state of turning motions to the steady state thereof.
 
Fig. 8 Heeling of the hull
 
 By simultaneously viewing sub-window (5) and sub-window (4), the students can study the relationship between the changing heading direction and the changing heeling angles of the hull in association with the developing turning angular velocities. On animated displays, heeling angles are multiplied by a factor of five for emphasized presentations, so that changes in heeling angles of the hull can be readily sensed. Actual heeling angles of the hull are displayed numerically.







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