{'fraction_non_alphanumeric': 0.02336696760488582, 'fraction_numerical': 0.003186404673393521, 'mean_word_length': 4.814814814814815, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
STUDY ON THE EFFECTS OF SIDE-WALL INTERFERENCE ON ADDED-MASS AND DAMPING COEFFICIENTS BY MEANS OF SLENDER-SHIP THEORY

Slender-ship theory is applied to develop a new method of calculating with quantitatively good accuracy the effects of side-wall interference on the added-mass and damping coefficients of a ship in a waterway. The present paper is restricted to the radiation problem of heave and pitch motions with zero forward speed, but it may be easily possible to extend to the forward-speed case and the diffraction problem.In the outer region, 3-D Green function satisfying the boundary condition on the side walls is placed along the ship's centerline on the free surface to describe the outer solution. The side-wall boundary condition is satisfied by considering an infinite number of image ships, and then the summation of the resultant infinite series is analytically obtained in a closed form.In the inner region, the radiation condition and side walls are absent, and thus the inner solution is identical to that of Newman's unified theory : the strip-theory solution plus a homogeneous solution multiplied by a three-dimensional interaction coefficient. This interaction coefficient is determined by the compatibility requirement of the inner and outer solutions in an overlap region. Therefore through this coefficient, the side-wall effects are incorporated in the inner solution.Computations of the added-mass and damping coefficients are performed for a floating spheroid of length-beam ratio L/B=8 in a channel of breadth ratio B T/B=16, and of L/B in a channel of B T/B = 5. Numerical results are in virtually perfect agreement with the results by a newly-developed 3-D panel method. This suggests that the theory proposed can be quite effectively used also in estimating the tank-wall effects on the results of experiments in a towing tank with limited width.