The computer model of maneuvering characteristics was developed for the TITANIC on the basis of the design configurations. Using this computer model, turning and stopping trajectories were computed for the TITANIC at a cruising speed of 23.3 knots as shown in Figure 5. Turning trajectory shows that advance is 3.4 L, and stopping advance 6 L. This exceeds the distance to iceberg of 3 L when the iceberg was observed in front of the ship that night. In response to the report of iceberg ahead from the crow nest, the first officer gave the full port rudder and full astern commands. The ship response was determined in a computer simulation run with an initial speed of 23.3 knots (see Figure 5). The trajectory obtained in simulation runs have advance of 3.6 L that is exceeding the distance to the iceberg of 3 L, and could not avoid the iceberg. The collision time was 11:40 pm. As a result, the starboard-side bow-portion of the hull was damaged.

　

 Captain Edward Smith and Mr. Thomas Andrew, who was a naval architect of the shipbuilder Harland & Wolf, quickly went to the bow. By that time, five compartments among total of 16 compartments of the ship (see Figure 1) were having rapid ingress of water. If the extent of damage had been limited to the four compartments at the bow, the ship could have kept floating with the trim by the bow. However, the length of damage at the bow exceeded the so-called floodable length, i.e., five-compartment-lengths at the bow for this ship. Mr. Andrew told Captain Smith that the ship would be sinking due to successive flooding, compartment by compartment, from the bow.

　

 When we are driving on a highway with limited visibility due to dense fog or heavy rain, it is prudent to proceed at a lower speed. In a similar manner, a simulation run was made having an initial speed of 11.6 knots (a half of the cruising speed the TITANIC was proceeding) that gave an advance of 2.1 L that is less than the distance to the iceberg 3 L. It is clearly indicated in these simulation runs that if the TITANIC had been proceeding at a half of the cruising speed, the ship could have avoided contact with the iceberg using the full rudder and full astern maneuver which the first officer used. The first officer's command, a combination of full rudder and full astern, appears to be adequate. Unfortunately, this full-rudder and full-astern maneuver was used at full cruising speed. It should be stated that it was not the custom of passenger ships at that time to reduce speed even in the presence of ice and this ice floe was one the worst in the 20^th century in this area of the Atlantic Ocean.

　

 There have been some discussions whether the full-rudder and full-astern command given by the first officer was adequate or not as an iceberg-collision-avoidance maneuver. The basis for this discussion is that the full astern command makes the rudder ineffective because the rudder does not receive a propeller stream to be effective. In the case of TITANIC, the triple-propeller and single-rudder arrangement had an inherently small propeller stream towards the rudder. The ship trajectory responding to the full port rudder without the full astern shown in Figure 5 shows the advance of 3.4 L exceeding the distance to the iceberg of 3 L, eventually hitting the iceberg.

　

 If the first officer's command, a combination of the full port rudder and full astern had been given at 11 knots rather than at 23 knots, the collision could have been avoided. The officer's choice of command at the very critical time was appropriate except for the cruising speed of 23 knots the ship was making.

　

 The ship hit the iceberg at 11:40 pm. Two hours and 40 minutes later, the stern portion of the ship was high in the air with the trim by the bow angle of approximately 45 degrees, because of the flooding at the bow portion of the hull. This was a very unusual attitude relative to the water surface for the ship. Under this unusual condition, the gravitational force acting on the ship's stern portion generated a tremendous magnitude of bending moment on the midship section. As a result, large tensile stress was generated on the bridge-deck plating, and large compressive stress on the keel plating. Thus, the ship ruptured approximately at the midship location immediately prior to sinking to the ocean bottom.

　

 In recent years, there have been noticeable improvements in propeller-rudder systems particularly in luxurious cruise ship design. Flap-rudders and pod-propellers with much better shiphandling characteristics have been actively employed in many recently built large cruise ships. Flap-rudders are similar to flap-wings used in the airplane during take-off and landing which generate greater lift force (see Figure 6).

　

　

 For training purposes, a computer model was developed for the 880 ft cruise ship that was built in 1992 for a cruise ship line. This ship has twin flap-rudders located behind twin controllable-pitch -propellers, and runs at a cruising speed of 23 knots. The rudder rate of 6 deg/sec on this ship is effective for this high-speed ship, making the magnitude of advance distance smaller magnitude.

　

 Turning trajectory of this cruise ship was obtained in a simulation run for a rudder angle of 45 degrees. This simulation run trajectory is in good agreement with that obtained in ship trials by the shipbuilder. In comparison, the 883 ft long TITANIC had triple propellers. A single rudder was located behind the center propeller that was the smallest among three propellers, and ran at a cruising speed of 23 knots. This rudder-propeller arrangement made the rudder less effective.

　

 Figure 7 shows trajectories of this cruise ship together with that of the TITANIC. The figure shows how the 880 ft cruise ship with twin-flap-rudders behind twin propellers could have avoided the collision with the iceberg.

　

 On the early morning in summer of 1994, a 700 ft long cruise ship was proceeding toward north bound en route from Vancouver, B.C, to Ketchikan. When the fog cleared, Gravina Point was dead ahead. By the time the officer on the navigation bridge did an emergency maneuver including hard rudder and full astern, it was too late. This maneuver was similar to that of iceberg-collision-avoidance done on the TITANIC in 1912. The ship had twin controllable propellers and one rudder at the centerline (see Figure 8) that made the rudder ineffective. The ship ran aground on rocky shore as shown in the ship trajectory in Figure 9.