1. On the Three-Dimensional Correction Factor for the Virtual Inertia Coefficient in the Vertical Vibration of Ships (J-value of an elliptical cylinder)

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In the present paper an attempt is made for a theoretical investigation into the three-dimensional virtual inertia coefficient of a circular and an elliptical cylinders of finite length which vertically vibrating in water with half immersed draught. As a result of the investigation, the J-values in the higher mode of the vibration was obtained. In addition, the effect of sectional form upon the J-value of the cylinder and the hydrodynamical pressure distribution along the keel of the cylinder were obtained. The present results of three-dimensional coefficient agreed fairly well with the experimental results. It is to be noted that there is noticeable discrepancy between the J-values in the vibration of the infinite long cylinder and finite one. The cause of the discrepancy was made distinct that it is the satisfaction or nonsatisfaction of the end condition of the cylinder in the potential function by the present study. Since the J-values of the ellipsoid and the elliptical cylinder are two extreme cases in the form under water line of a ship, the further investigation into the J-value for moderate ship forms between the ellipsoid and cylinder is to be required.
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