Thin Ship Research Articles

Third order contribution to the wave-making resistance of a ship at finite depth of water

This paper presents a potential based boundary element method for solving a nonlinear free surface flow problem for a ship moving with a uniform speed in finite depth of water. The free surface boundary condition is linearized by the systematic method of perturbation in terms of a small parameter up to third order. The surfaces are discretized into flat quadrilateral elements and the influence coefficients are calculated by Morino's analytical formula. Dawson's upstream finite difference operator is used in order to satisfy the radiation condition. The second order solution gives better result than the first or third order solution. So the present method with the second order solution can be adopted as a powerful tool for the hydrodynamic analysis of the thin ship in finite depth of water.

A flat ship theory on bow and stern flows

AbstractAn analytical solution of a two-dimensional bow and stern flow model based on a flat ship theory is presented for the first time. The flat ship theory is a counterpart to Michell's thin ship theory and leads to a mixed initial-boundary value problem, which is usually difficult to solve analytically. Starting from the transient problem, we shall first show that a steady state is attainable at the large time limit. Then the steady problem is solved in detail by means of the Wiener-Hopf technique and closed-form far-field results are obtained for an arbitrary hull shape. Apart from providing a better understanding of the underlying physics, the newly found analytical solution has shed some light on solving a longtime outstanding problem in the engineering practice of ship building, the optimisation of hull shape.

Prediction of Deformation to Thin Ship Panels for Different Heat Sources

The increasing use of thin steel plates in manufacturing and the shipbuilding industry has given rise to several issues: massive deformation problems, the need for many skilled workers, and the expense of costs for straightening in on-line processes. This study explains the results of experiments and predicts techniques for the control of deformation in thin panels. The objective of this paper is to explain the use of the G(1,1) Grey method to predict deformation. Bending and buckling are usually the dominant modes of deformation in heat working. It follows angular deformation. De- formation due to different heat sources is discussed. In this paper, laser and torch are used in different constraints, for example, free-free beam and cantilever beam. Many important factors include tiny adjustments during the heat forming process, such as changing the moment speed, intensity of input heating, plate thickness and heating path, to improve manufacture techniques and to predict deformation by data series. For the prediction of deformation, a method to estimate input heating of laser and torch is introduced. The proposed prediction method can be used during the forming process simply and efficiently.

Prediction of dimensional changes during fabrication of thin shell ship hull bottom units

The cumulative effect of distortion resulting from the welding of butts and stiffeners during the fabrication of ship hull units leads to an overall change in dimensions. This dimensional inaccuracy causes further erection difficulties owing to mismatch and misalignment. This problem has been addressed in the present work using the far field–near field concept. The near field has been assumed to extend from the weld line to a location where the peak temperature attained is 350°C, and the rest of the plate is far field. Plastic deformation is expected only in the near field, whereas the far field behaves elastically throughout the heating and cooling cycle. Measurements carried out on two units show a fairly good agreement with the calculated values.

Control of Distortion in Thin Ship Panels

The increased use of thin section (i.e., less than 10-mm (3/8-in.) thick) steel in ship panel construction has aggravated distortion problems, adding to the costs for fitting and flame straightening. This paper describes the results of a study to evaluate techniques for control of distortion in thin panels used in ship construction. The objective of this project is to identify cost effective techniques for controlling distortion. Buckling is usually the dominant mode of distortion in thin panels, followed by angular distortion. Means of reducing both forms of distortion are discussed. During the design phase relatively small adjustments to the design, such as changing plate thickness or stiffener spacing, can significantly reduce distortion. Improving manufacturing techniques, including reducing weld size, implementing intermittent welding, and restraining the panel during welding, can also make a major impact on reducing distortion. New techniques such as egg-crate construction, laser welding, thermal tensioning, back-side line heating, back-bending, and weld quenching also show promise.

On the longitudinal motion of a thin ship travelling with constant forward speed in deep sea

In this paper, the problem of the longitudinal motion of a thin ship with a constant forward speed and direction parallel to wave direction is solved by using Fourier transform and expanding the velocity potential in Fourier integral on Eigen functions. The influence of the forward speed on the velocity potential of fluid is considered. In the case of a thin ship with zero - forward speed the result shown good agreement with the one obtained by other authors.

On the Numerical Radiation Condition in the Steady-State Ship Wave Problem

The waves created by a thin ship sailing in calm water are examined. The velocity potential of the ship in the zero Froude number case is known and the additional potential due to the waves is calculated by the Green function technique. The simple Green function corresponding to the Rankine source potential is used here. Two major problems exist with this method. In the Neumann-Poisson boundary-value problem- probably the first iteration toward a full nonlinear solution to the ship wave problem _it is necessary to impose a radiation condition in order to get uniqueness. This problem is related to the second one, which arises due to the existence of eigensolutions. The two-dimensional situation is here analyzed first, thereby easing the three-dimensional analysis. A numerical scheme is constructed and results for the twodimensional waves generated by a submerged vortex and for the three-dimensional waves due to the Wigley hull are presented.

On a Non-linear Effect on the Propagation of Free Wave around Ships

A non-linear effect due to self-interaction like in the Stokes' wave is discussed on propagation of the Kelvin's ship wave from the view point of the perturbation method under the assumption of thin ship. The main purpose of this paper is to improve the expression of the phase function of the Kelvin's ship wave by considering the varying magnitude of the first order solution in the thin ship theory, whose decreasing rate is R-1/2 inside the cusp line of the Kelvin's wave or R1/3 on it, where R is the distance from the source of the wave. It is shown that the difference of the phase function from the first order solution increases in correspondence with log R inside the cusp line and with R-1/3 on it. Calculated bow wave pattern of Wigley model is compared with an experimental result and the result of the thin ship theory.

Fundamental Studies on Hull Form Design by Means of Nonlinear Programming (3rd Report)

The minimum wave resistance problem based on Michell's thin ship theory has been investigated by means of variational approach so far. In this paper, a kind of the fairing constraint to hull form is introduced into the minimum wave resistance problem, and the optimization technique is applied instead of the variational approach.Two formulations are shown for the present problem and optimized by means of SUMT (Sequential Unconstrained Minimization Technique) as in the 1st & 2 nd reports. Numerical examples are given under several kinds of design conditions. As the fairing constraint is considered, the minimum wave resistance hull forms without swan necks are obtained.

The ray theory of ship waves and the class of streamlined ships

A new theory is given for calculating the wave pattern and wave resistance of a ship moving at low Froude number F. It applies to ships of any width, either full-bodied or slender. In this theory, the waves travel along rays which start at source points, such as the bow and stern, on the water-line. They propagate with the speed of waves in deep water, but are also advected by the double body flow. This is the flow about the ship and its image in the undisturbed free surface. The phase of a wave at any point on a ray is the optical length of the ray from the source to that point. The amplitude is determined by an excitation coefficient, which determines its initial value, and by an integral along the ray. The total wave height at any point is the sum of the heights on all the rays through the point. The theory is incomplete because the excitation coefficients are known only for thin ships. As an illustration, the theory is applied to the thin ship case, and the results then agree with Michell's thin ship solution evaluated for F small.A new class of ships, which we call streamlined ships, is introduced next. The usual linear free surface condition applies to the waves they produce. The ray theory is developed for these waves at low F, and it involves straight rays produced at all points on the rear half of the water-line. In addition, as an alternative to the ray theory, another method is presented for obtaining the waves at low F. It involves a Schrödinger-like equation in which distance along the ship's centre-line is the time-like co-ordinate.

Viscous Effect on Waves of Thin Ship

It is confirmed that a wave pattern and a wave making resistance at large Reynold's number are determined by the potential component of the flow field, and that the effect of the rotational component is negligible, by means of a linearized theory for ship waves in a viscous fluid under assumptions of Oseen's equation and equivalent laminar wake. In order to know a modified potential flow, boundary layer and viscous wake, as well as wave pattern, are measured. It is discovered that turbulence occurs beside and behind a ship near the free surface, and that it originates another sort of viscous wake. Making use of measured displacement thickness, the wave pattern and the wave making resistance are calculated and compared with measured values. A qualitative but plausible agreement is obtained.

Velocity potential of the water when a thin ship pitches in shallow water

Velocity potential of the water when a thin ship pitches in shallow water

Roll Damping Moment of Numerical Models in Forward Motion

In this paper the forward velocity dependence of the roll damping moment on a ship is treated both experimentally and theoretically. Forced rolling tests using polynomial hull form models were conducted to measure the roll damping moment in forward motion. Influences of forward velocity, rolling frequency and principal dimensions are investigated. A theoretical prediction method, which is based upon the thin ship theory and modified to include effects of the ship width approximately, is presented. Calculated values agree well with the experiments through the velocity range in lower frequencies in spite of poor agreements in higher frequency range.

The refraction of head seas by a long ship. Part 2. Waves of long wavelength

It is known that head seas cannot travel without deformation along a cylinder of full constant cross-section, and recent calculations have indicated that the wave amplitude near the cylinder ultimately decreases as the waves travel along the cylinder, i.e. that the waves are refracted away from the axis of the cylinder. It was assumed in these calculations that the cross-section was a half-immersed circle of radius a of the same order as the wavelength 2π/K, but the method can probably be adapted to arbitrary full constant cross-sections. (There is however another calculation which indicates that for a thin ship the wave amplitude ultimately increases.) In the present paper these calculations are extended. The circular section is again studied but it is now supposed that the wavenumber Ka may be small. Uniformly valid expressions for the wave potential are obtained which show that for small Ka the refraction becomes significant only when Kx (the dimensionless distance along the cylinder) is so large that the product (Kx)½ v0(Ka) is also large; here the function v0(Ka) ∼ 2Ka arises in the solution of a certain eigenvalue problem. (The uniformly valid expressions also suggest an interpretation of the thin-ship calculation which resolves the apparent inconsistency.) The same method is applied to the waves generated by a pulsating source on an infinite cylinder, and similar results are obtained.

Wave Resistance and Wave Patterns of Thin Ships

The wave resistance R and wave height h(x, z) are evaluated asymptotically for small Froude number F = U(gL)−½ for a slender hull of any shape. Michell's theory for a thin ship of length L moving with constant speed U along a straight line is the starting point. It is found that asymptotically R and h depend only upon four properties of the ship—the slope of the hull and the slope of the profile curve of the hull at the waterline at bow and stern. Simple formulas are obtained for R and h in terms of these slopes. The wave pattern consists of four waves—a longitudinal and a transverse wave from the bow and a similar pair from the stern. Their phases are the same as those of Kelvin waves due to pressure points at the bow and stern, and they also decay with distance like cylindrical waves. However, their amplitudes have different angular variations from those of Kelvin waves.

A Method of Computing Nonlinear Wave Resistance of Thin Ships by Coordinate Straining

A systematical procedure is derived for determining the distribution of sources along the centerplane of a thin ship which generate a flow (and the associated wave resistance) satisfying the free-surface and body boundary conditions at second order. The method relies on a mapping of the flow domain onto a new domain by slightly straining the coordinates. The horizontal straining is selected such that the nonlinear solution should be easily derived from the first-order (Michell) solution in the strained domain. The results are shown to be similar to those obtained by Guilloton's method, but new features, such as the forward displacement of the bow singularities, are present.

Introductory Note to Companion Papers on Wave Resistance

The following two papers were submitted independently by the authors in April 1974 to the JOURNAL OF SHIP RESEARCH. Both studies were motivated by the desire to establish a sound theoretical foundation for Guilloton's method, which has been found by Gadd (1978) to be particularly successful in predicting the wave resistance of ship models. Noblesse, F., " A Perturbation Analysis of the Wavemaking of a Ship, with an Interpretation of Guilloton's Method"; see page 140. Dagan, G., " A Method of Computing Nonlinear Wave Resistance of Thin Ships by Coordinate Straining"; see page 149.

Low-Aspect-Ratio Flat-Ship Theory

The integral equation, first obtained by H. Maruo, which determines the pressure distribution generating flow past a slender ip of vanishing is studied further. New results obtained include predictions of singular centerplane effects of gravity for pointed bodies, a solution for ships with cusped parabolic waterplanes, and some preliminary numerical solutions of the integral equation in the general case. I. Introduction T HIS paper is an extension of a study by MaruoJ on ''ships of small draft, ships/' or surfaces, all of which are equivalent descriptions. The small-draft assumption allows linearization of the free-surface boundary condition, as in the comparable case of thin ships, or ships of small beam.2 However the present linearized problem is much harder to solve, since the generating singularity distribution (effectively a distribution of pressure points on the limiting waterplane) is not explicitly given in terms of hull shape, but requires solution of an integral equation. This problem is analogous to the lifting-surface problem of aerodynamics, whereas the thin-ship problem corresponds to the simpler thickness problem of aerodynamics. Although this paper contains a brief reconsideration of the general flat-ship problem, to emphasize some aspects not discussed by Maruo, the paper is devoted mainly to the lowaspect-ratio limit. Thus the wetted length of the ship is supposed much greater than its beam, the latter having already been assumed much greater than the draft by the flat-ship requirement. The ship is therefore not only flat, but also slender. An alternative derivation is given here of an integral equation equivalent to one obtained by Maruo, having as its unknown function a pressure distribution representing the ship. This integral equation is also obtainable from the highFroude-number slender-body theory of Ogilvie, 3 by assuming that the ship is not only slender, but also flat. Maruo's low-aspect-ratio flat-ship integral equation is formally valid only at moderately-high Froude numbers, specifically such that U2B/gL2 is a quantity of order unity, where U is ship speed, B its beam and L its length, and g is gravity. The equation reduces to that of low-aspect-ratio wing theory in aerodynamics as g->0. One approach to practical solution of any planing problem, whether or not the aspect ratio is low, is to expand in an asymptotic series for very high Froude number, commencing with the aerodynamic g = 0 limit as the leading term.4 Maruol obtains the first two terms in this series for the lift on a flat delta wing, and an alternative treatment of this class of expansion, for general hull shapes, is presented here. In particular, very strong effects of gravity near the center plane of pointed bodies are demonstrated. At all Froude numbers, the low-aspect-ratio flat-ship integral equation possesses a similarity solution, such that the pressure distribution has the same shape at all stations. This linearized but gravity-dependent result should not be confused with the well-known conical solution for nonlinear planing or water entry in the absence of gravity (Gilbarg,5 p.360). In fact the present geometrical requirement is for a cusped parabolic waterplane shape but an arbitrary section shape, whereas the nonlinear zero-gravity solution requires a triangular plan form and section shape. The low-aspect-ratio flat-ship integral equation is amendable to direct computation, and we present here some preliminary examples of its numerical solution. Much more work needs to be done to derive efficient procedures, and the present computer program can only be considered as a crude first attempt. However, the results are of considerable interest, indicating rather dramatic gravity effects especially near the center plane, as predicted analytically, and confirming Maruo's1 estimate of the lift coefficient of a delta wing at sufficiently high Froude number.

On the Principal Particulars of Ship Hull Form and Wave Pattern Resistance (II)

Series tests were performed for eleven mathematical hull forms to investigate the relationship of the principal particulars and wave resistance, by wave pattern analysis. In the previous paper, the results of wave resistance, residual resistance, dipping and form factor on the frictional resistance were mainly presented for these models, and some consequences were compared with the results of linearized theory. In this paper, from the different angle than the previous one, directly measured wave resistance is firstly compared with calculated wave resistance by Michell's theory, and also the experimental results are shown for the amplitude functions and spectra of ship waves, which are compared with the results calculated by Michell's theory and by the method of source distribution on the hull surface.Some examinations are made how closely the principle of linear superposition of free waves is realized. Further, the comparisons in the amplitude functions and spectra are shown for two thin ships, one is added to the fore part and the other to the after part of an original hull form respectively.

Free surface effects on the side force and moment acting on a ship hull with a drift angle

The purpose of this research is to study the free surface effects on the side force and the yaw moment acting on a ship hull advancing with a steady drift angle.First, on the assumptions of thin ship, small drift angle and low wave height, the problem was divided into a symmetric and an antisymmetric ones. Since the symmetric term had no effects on this problem, for the antisymmetric problem, approximate formulas to estimate the free surface effects were obtained on the assumption of slenderness.Next, by means of model experiment, free surface effects were examined, and it was ascertained that the above approximate formulas could explain the experiment results on the whole.