INCLINOMETER DEVICE FOR SHIP STABILITY EVALUATION

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2 Figure 1. A ship subject to forces that causes an inclination A recent work (Vasconcellos, 2006) shows that, when in the upright position in calm waters, the line of action of the weight force (Wf) and the buoyancy force (Bf) are acting in the same vertical as shown in Fig. 2. If the vessel is now tilted by an external force, the relative position of the center of gravity and the center of buoyancy changes, causing a separation of the line of action of weight and buoyancy forces, which will be separated horizontally. Figure 2. Position of center of gravity and the center of buoyancy If the external force is removed it is clear that the vessel will return to its original position (vertical) as a result of the forces acting. The horizontal distance between the center of gravity and the line of action of the buoyancy force, acting in the center of buoyancy, when the boat is inclined is defined as righting arm (GZ), shown in Fig. 3. When we multiply the results of the buoyancy force by the arm straightening we obtain the righting moment. Figure 3. Righting arm (GZ)

4 For the tests of inclination, the geometric similarity and mass (weight and center of mass) ensures the quality of the prototype response given by the model response. Once submitted to the righting moment, the vessel can either return to its position of balance or, in certain cases, capsize. To know if it is possible to maintain the balance of a ship it is necessary to know the moment that is causing the inclination and to obtain the maximum angle of tilt that can be restored. The knowledge of the maximum angle of inclination is extremely important since this allows us to do a better risk analysis and, if necessary, make changes in the design or even the load distribution inside the ship in order to modify its righting moment and to ensure its stability in adverse sea conditions. In order to discover the relation between moment and inclination in each vessel, we designed an inclinometer, as the one showed in Fig. 4, which, when subjected to a force, create a moment and, consequently, inclines the boat model. Figure 4. Design of the inclinometer The equipment consists of a structure that is able to rotate. It is supported by the ship and sustained by a base, located outside the tank in which the experiment will occur. Weights of equal mass are placed on the top bar of the apparatus, equidistant from the center. After loading, is necessary to find the position of initial stability to be used for comparison. When a weight is away from its initial position, the difference between the distances creates a lever arm and consequently a moment in the structure. This moment is given by Eq. (2), where m is the mass of the displaced weight, g is the gravity, θ is the angle of inclination of the structure end d is the distance between the initial and the final position of the weight. M = [( m * g )cos θ ] * d (2) Then, this moment is equivalent transmitted to the model that will suffer an unknown inclination, as seen in Fig. 5. The tilt will be calculated by the apparatus by means of sensors. Knowing the angle of inclination and the moment create, we can plot a graph of stability of the vessel, and, by the graph, we know its maximum strength until the moment of its heel.

5 Figure 5. Handling of inclinometer With the help of sensors and other electronic equipment we can move the weights by the computer and get the exactly distance of their displacement, beyond the exact angle of tilt. The data generated are sent directly to the computer that will evaluate and plot the graphs. Besides the faster analysis of data also have more real results with fewer errors. 5. CONCLUSION Although the project is in its start phase, the primary prototype seems simple and very cost effective. The next phase results will be compared with software for stability curve evaluation and damage simulation performed. As part of scientific student research this project is following the chronogram. 6. REFERENCES Ferraz C., Souza V., Vasconcellos J.M., Experimento como Auxilio na Avaliação da Estabilidade Estática de Embarcações, SOBENA Laboceano, Inertia Calculation Procedure for Model Test Lech K. Kobylinski and S. Kastner, Stability and Safety of Ships, Ocean Engineering Series Editors, Elsevier, Vasconcellos, J. M. A., 2006, Studies of Stability, studies in floating off-shore engineering systems, Class Notes. Vasconcellos, J. M. A.,Cid M. 2006, SOBENA, calculation of weights and centers. 7. RESPONSIBILITY NOTICE The authors are the only responsible for the printed material included in this paper.

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