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Analytical bow waves for fine ship bows with rake and flare

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The bow wave generated by a steadily advancing ship is considered for a family of fine ruled ship bows with rake and flare. This family of ship bows is defined in terms of four parameters: the ship draft D, the entrance angles a and a at the top and bottom waterlines, and the rake angle d . The corresponding bow wave similarly depends on four parameters: the draft-based Froude number F and the three angles a , a′, and d . An extensive parametric study, based on thin-ship theory, is performed to explore the variations of the water height Z0 at the ship stem X = 0, the location X 0 (measured from the ship stem) of the intersection of the bow-wave profile with the mean freesurface plane Z = 0, and the bow-wave profile, with respect to the four parameters F, a, a′, and d. This parametric study extends the previously reported similar study of the height Z bof the bow wave and the location X bof the bow-wave crest. These two complementary parametric studies yield simple analytical relations, which extend relations given previously for wedge-shaped ship bows without rake or flare. In spite of their remarkable simplicity, the analytical relations given here yield bow waves that are comparable to computational fluid dynamics (CFD) waves given by Euler-flow calculations. The analytical relations, which explicitly account for the influence of the four primary parameters F, a, a′, and d, can be used immediately—without hydrodynamic calculations—for ship design, notably at early design stages when the precise hull geometry is not yet known. The study also provides insight for ship bow design. Specifically, it suggests that a bow with positive rake and negative flare may be beneficial, and that a bulb located aft of the stem and integrated with the hull may be an advantageous alternative to a traditional bulb protruding ahead of the bow, in agreement with the results of a hull-form optimization analysis.
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Document Type: Research Article

Publication date: 2011-03-01

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  • The Journal of Ship Research is a quarterly publication providing highly technical papers on applied research in hydrodynamics, propulsion, ship motions, structures, and vibrations. While the Journal requires that papers present the results of research that advances ship and ocean science and engineering, most contributions bear directly on other disciplines, such as civil and mechanical engineering, applied mathematics, and numerical analysis. High quality papers are contributed from the U.S., Canada and overseas, with representation from established authorities as well as new researchers.
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