Simple analytical relations for the bow wave generated by a ship in steady motion are given. Specifically, simple expressions that define the height of a ship bow wave, the distance between the ship stem and the crest of the bow wave, the rise of water at the stem, and the bow wave profile, explicitly and without calculations, in terms of the ship speed, draught, and waterline entrance angle, are given. Another result is a simple criterion that predicts, also directly and without calculations, when a ship in steady motion cannot generate a steady bow wave. This unsteady-flow criterion predicts that a ship with a sufficiently fine waterline, specifically with waterline entrance angle 2αE smaller than approximately 25°, may generate a steady bow wave at any speed. However, a ship with a fuller waterline (25°<2αE) can only generate a steady bow wave if the ship speed is higher than a critical speed, defined in terms of αE by a simple relation. No alternative criterion for predicting when a ship in steady motion does not generate a steady bow wave appears to exist. A simple expression for the height of an unsteady ship bow wave is also given. In spite of their remarkable simplicity, the relations for ship bow waves obtained in the study (using only rudimentary physical and mathematical considerations) are consistent with experimental measurements for a number of hull forms having non-bulbous wedge-shaped bows with small flare angle, and with the authors' measurements and observations for a rectangular flat plate towed at a yaw angle.
Dimensional analysis and other fundamental theoretical considerations (thin-ship limit, shallow-draft and deep-draft limits) are used, with bow-wave measurements for six wedge-shaped hull forms, to obtain simple analytical expressions that explicitly define the height, location, and steepness of the bow wave generated by a ship in terms of the ship speed, draft, and waterline entrance angle. These simple analytical expressions are in excellent agreement with the available experimental measurements for six wedge-shaped hull forms. Good agreement is also obtained for other ship-bow forms, especially if a simple procedure—illustrated for the Wigley hull and the Series 60 model—is used to define an effective ship draft and an effective waterline entrance angle.
Shape optimization is a growing field of interest in many areas of academic research, marine design, and manufacturing. As part of the Computational Research and Engineering Acquisition Tools and Environments Ships Hydromechanics Product, an effort is underway to develop a computational tool set and process framework that can aid the ship designer in making informed decisions regarding the influence of the planned hull shape on its hydrodynamic characteristics, even at the earliest stages where decisions can have significant cost implications. The major goal of this effort is to utilize the increasing experience gained in using these methods to assess shape optimization techniques and how they might impact design for current and future naval ships. Additionally, this effort is aimed at establishing an optimization framework within the bounds of a collaborative design environment that will result in improved performance and better understanding of preliminary ship designs at an early stage. The initial effort demonstrated here is aimed at ship resistance, and examples are shown for full ship and localized bow dome shaping related to the Joint High Speed Sealift hull concept.
This study considers the three-dimensional potential flow due to a ship advancing with constant average speed in a train of regular waves. A modified integro-differential equation for determining the velocity potential on the mean position of the hull surface is obtained, and a solid theoretical basis for obtaining a numerical solution of the equation via a panel method is developed following the approach used by Kochin more than 50 years ago. In short, the approach is essentially based on a Fourier representation of the solution of a modified integro-differential equation. This approach circumvents the fundamental difficulties associated with the numerical evaluation of the Green function and its gradient, and their subsequent integration over the panels used to approximate the hull surface of a ship.
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