The present work describes a prediction method for the bottom slamming pressure on the keel level. The new procedure consists in using the ship's Centre of Gravity Response Amplitude Operator results (CGRAO). This method analyzes the translational and rotational motion on a regular wave in order to find if there is an emergence of the ship forefoot. This method is based on a fine time steps and on a precise geometric calculation which yields to an exact calculation of the pressure at the impact of a point at the keel with the wave. Also the advantage of this method is to show a precise time evolution of the bottom impact with the wave and in consequence to enhance the physical understanding of the slamming phenomenon. The slamming pressure calculation, in the present work, is based on the empirical correlation (Chuang 1967) and Wagner theory according to Faltinsen (1990). The ship model chosen for this application is the famous S175 container ship in the ballast load condition and Froude number varies from 0.1to 0.278 in the head sea.


A complete description of slamming phenomenon is a complex task, which is beyond any existing theory. This phenomenon is due when the fore end of a ship emerges on the water surface. The impact pressure as consequences are affected by the local form of the hull's bottom section form, the vertical relative velocity between the ship and the wave, the relative angle between the keel and the water surface. Many authors have started more complex investigations in order to look deep into the slamming phenomenon and have deducted the appearance criteria of this later based on the velocity, deadrise angle, hull geometric parameters. They have concluded that the impact pressure magnitude is not a sufficient indicator in order to judge the occurrence of slamming. Ochi & Motter (1973) expressed the slamming phenomenon to the ship's vertical relative movement conditions. He defined the slamming by an appearance of the ship's fore end at 0.9Lpp and, at the impact instant, exceeding a certain threshold vertical relative velocity, between the wave surface and the bow. However, the more promising approach according to John &Victor (1995) conclusions for the slamming pressure evaluations may be based on the semi empirical method given by Stavovy & Chuang (1976). The slamming phenomenon nature and the maximum impact pressure calculation have been studied by Chuang (1967), who has taken in consideration the air entrapment. He noticed that the deadrise angle is also important, and if it is less than 3°, the air entrapment appears. In this work, the CGRAO responses are used in order to describe the ship relative movement to the wave. Only those resonances frequencies giving a keel emergence are taken into account.

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