Ship Wave Resistance Research Articles

The Effect of a Surface Layer of Viscous Fluid on the Wave Resistance of a Thin Ship

A Modification to the gravity-wave free-surface condition is suggested, to account for dissipative properties of thin surface layers of material such as broken-up ice, slush, or oil spills. A corresponding correction to michell's wave-resistance integral is established, and computations are carried out for a parabolic strut.

The added resistance of a moving ship in waves

On the base of the method outlined in [1] more detailed analysis of the added resistance of ships in waves is shown. The practical estimation of the components of the added resistance is given. The comparison of the calculated and experimental result

Two-dimensional free-surface gravity flow past blunt bodies

Most of the wave resistance of blunt bow displacement ships is caused by the bow-breaking wave. A theoretical study of the phenomenon for the two-dimensional steady flow past a blunt body of semi-infinite length is presented. The exact equations of free-surface gravity flow are solved approximately by two perturbation expansions. The small Froude number solution, representing the flow beneath an unbroken free surface before the body, is carried out to second order. The breaking of the free surface is assumed to be related to a local Taylor instability, and the application of the stability criterion determines the value of the critical Froude number which characterizes breaking. The high Froude number solution is based on the model of a jet detaching from the bow and not returning to the flow field. The outer expansion of the equations yields the linearized gravity flow equations, which are solved by the Wiener-Hopf technique. The inner expansion gives a nonlinear gravity-free flow in the vicinity of the bow a t zero order. The matching of the inner and outer expansions provides the jet thickness as well as the associated drag.

The Wave Resistance of a Thin Ship with a Rotational Wake

An inviscid model for a ship with a viscous wake is developed. The wake is considered as a region of vorticity trailing behind the ship. The problem is systematically linearized by the use of a perturbation parameter representing the beam-to-length ratio. To first order it is found that the complete velocity potential is composed of two parts. The first is identical to the well-known solution for a thin ship without a wake. The second is the result of the specified vorticity distribution in the wake acting in the absence of the ship. The wake potential is determined for a semi-infinite, U-shaped vortex sheet. The wave resistance for a thin ship with a vortex sheet wake is analytically determined. The results clearly indicate the influence of the wake and its interactions with the ship. Numerical computations are presented for a mathematical form. They show that the wake-wave resistance is about 1 0 percent of the ship-wave resistance. The interaction term may be positive or negative depending on the wake attachment point. A comparison with experimental data is made. It is found that the present type of rotational wake model can account for the differences between Michell's integral and experiments for the mathematical form.

On The Wave Resistance of Surface Effect Ships

In an attempt to identify ways to reduce the peak wave resistance of surface effect ships, calculations of wave resistance are made for combinations of several singularity distributions with various parameters. Analyses are performed especially for the following components and parameters: various pressure planforms, the effect of sidewalls, the influence of sidewall camber, and the wave interference between the rectangular pressure planform with thin sidewalls and the front and rear skis. The result shows that, in general, the rectangular pressure planform is better than planforms of V-shaped bows and sterns. A gradual decrement of the sidewall displacement with the increasing Froude number is favorable, since not only the large buoyancy of sidewalls but also the low resistance helps the power reduction of SES for low-speed operations. Front and rear skis are helpful to reduce wave resistance for certain Froude numbers, although they may increase the drag for other Froude numbers. The camber of sidewall is not a good means for reducing the wave resistance of a rectangular pressure planform.

High-performance Computers In Advanced Boundary Elements Applications: Non-linear Modelling Of Ship Wave Resistance

The paper presents an algorithm for a non-linear computation of irrotational flow fields with free surface effects. Vectorized and parallelized algorithms and corresponding computer programs are developed for shared and distributed memory computers. Within this context a boundary element solver main tasks are discussed and benchmarked on different platforms. The above formalism is applied to the simulation of a non-linear 3-D numerical towing tank to compute ship wave resistance, wave patterns and fluid flow induced by a steadily advancing ship in calm water.

Analyses of Waves and the Wave Resistance due to Transom-Stern Ships

Waves and the wave resistance due to a ship with a transom stern are analyzed starting with an exact formulation of the general ship wave problem. Green's theorem is utilized together with the well-known Green's function which satisfies the linear free-surface boundary condition on the free surface. Here it is required to take at least the second-order terms in the formal development. It is found that the immersed transom stern acts to cancel stern waves. Using a limited form of Michell's wave-resistance formula, the wave resistance of the transom-stern ship is analyzed

The Asymptotic Approximation of Michell’s Integral for High Speed

An asymptotic approximation to Michell's integral is obtained for large values of the Froude number, providing an analytic estimate for the wave resistance of a thin ship at high speeds. The limiting value for a surface ship of arbitrary hull form is quite similar to that of an infinitely deep vertical strut, and in both cases the dominant term depends only on the waterplane area, while the displacement and details of the hull shape enter in the next term of the asymptotic expansion.

Effect of the Initial Acceleration Upon the Wave Resistance of Ship Models

In order to estimate the effect of the initial acceleration of a ship model upon its wave resistance after a steady velocity has been reached, an asymptotic expansion for large t is found for the wave resistance of a thin ship. Numerical computations are provided for a hull form of simplified type.

“Ships of Minimum Wave Resistance”

Detailed discussions are given to the problem of minimizing the theoretical wave resistance with special reference to the existence of the solution of the calculus of variation. Rigorous solutions are given to the integral equations which express the condition of the minimum wave resistance of strut-like ship forms with infinite draft under various side conditions. The solution determines the optimum shape of the water line. Optimum curves of sectional area of slender ships are calculated in a similar way. Resistance experiments are carried out with respect to the optimum forms, showing a good agreement with the theoretical result.

Calculation of the Wave Resistance of Ships, the Draught of Which is as Small as the Beam

A linearized theory on the wave resistance of ships, the draught of which is as small as the beam is presented. Some numerical results are obtained from the theory and the comparison of the computed and measured values shows a satisfactory agreement. The problem of the least resistance is discussed with respect to a special class of ship forms.

Calculation of the Wave Resistance of Ships, the Draught of Which is as Small as the Beam

Calculation of the Wave Resistance of Ships, the Draught of Which is as Small as the Beam

The Damping and Wave Resistance of a Pitching and Heaving Ship

This paper considers the damping and wave resistance of a thin ship which is moving in calm water with constant velocity and oscillating in pitch and heave. The velocity potential is obtained from Green's theorem after a process of systematic linearization in terms of perturbation parameters representing the beam-length ratio and the oscillation amplitude. An asymptotic expansion of the Green's function is derived from which the energy radiation is obtained. The coefficients of damping and increased wave resistance are then found by separation of the energy components. No separation of the two cross-coupling damping coefficients is obtained, however. Calculations are presented for a polynomial hull and compared with experimental data.

On the Theory of the Wave Resistance

The author introduces the velocity potential of the displacement ship by making use of Green's function or the fundamental singularity. This method is more rational than the one we have had. and deduces the result that singularities which are on the water line of the ship surface are of negligible order especially when the surface of the ship near this water line is vertical.Nextly, he obtains the integral eqations of solving the problems by the aid of Green's function in the potential theory in cases of submerged bodies and floating ships.Two applications of these eqations are developed in the paragraph 4 and 5.The one is of the problem of deeply submerged and high speed body. This is not very interesting, , but gives a mathematical foresight to the solution.The other is of the wave resistance of ships at very low speed. In the case of a hemisphere, the solution of the integral eqation tells us the wave making character at very low speed is confined itself in the neighbourhood of the bow. Thus obtained resistance formula is very simple and seems to be applied to the ordinary ship at very low speed so that may be useful.

Side-Wall Effects on ship Wave Resistance

With special interests to small experimental tank works, we have investigated the tankside wall effects on wave resistance of models.Applying the wave-making theory, we have carried out some numerical works for the series of mathematical models in the following cases.T/L=0.05, 0.10, 0.15, 0.20, ∞;b/L=1/4, 3/8, 1/2, 3/4, 1, 1.5, 2, ∞;F=V/√<Lg>=0.218-0.707, where L=ship length, T=ship draft, b=water width, V=ship speed. Finally, making use of the image method, we have made towing experiments with single, double and triple models of T/L=0.10. The model length L and tank water width b being 2.333m and 3.500m, the corresponding ratio b/L is 3/2, 3/4, and 1/2 respectively.Comparing the experimental results with theory, we find, unexpectedly large discrepancies that the side-wall effects are more remarkable with the experiments, even in consideration of skin friction augmentations, which may be roughly estimated as 4 and 10 percentages in case of b/L=3/4 and 1/2.

Fundamental Formula for Wave Motion caused by Moving Bodies

In this paper, considering the fact that accompanying with fundamental studies on the motion of ships, for instance on their steering faculty or manoeuvability, the theory of wave resistance of ships moving non-uniformly claims its significance, the author gives a fundamental formula for the surface disturbance of water in some general forms. Then some problems are studied as its applications. One of them is a calculation of additional virtual mass of spheres and spheroids floating on the surface of water. Another application is a calculation of wave resistance of a submerged circular cylinder moving along a straight line.

On the Components of Ship Wave Resistance

Applying Prof. Havelock's method of analysis the author studies the relative importance of the transverse- and diverging-wave systems which are produced by a ship of Michell's type. Special reference is given to the effects of the depth or the width of a water upon the wave resistance, and the numerical calculations are made for the three cases:(a) deep water (h=∞, b=∞), (b) shallow water (h=finite, b=∞), (c) restricted water (h=finite, b=finite), where h denotes the depth of water, b the width.The main results obtained are as follows:1°. In (a), the contribution from the diverging wave system to the total wave resistance is lound as given by a steppedly increasing function of Froude number, with each step taking place at the hollows on the curve of the transverse wave resistance.2°. In (b), the resistance component due to the transverse waves attains its maximum at the speed just lower than the critical speed or the solitary wave velocity V=√gh, while the diverging wave resistance has its peak just at the critical speed.3°. In the case (c), the side-walls are found as affecting inverse effects upon the two contributions of the wave resistance : the transverse wave resistance being augmented, while the diverging wave resistance being reduced, in comparison with the case (b).

A New Theory of Wave Resistancc, based on the exact ship Surface Conditions

The former theory of ship wave resistance does not satisfy exactly the boundary condition on ship surface. The author examines the degree of this approximation with some models by finding the actual forms which are represented by the approximate source distribution. Even in the case of ordinary fine ship, the difference between the given and actual lines gets so large unexpectedly, that the author goes to obtain the exact source distribution by solving the integral equation, and then calculates the exact wave resistance.As the first application of the new theory, the effect of breadth is studied, and it is found that the effect depends remarkably on ship speed.As the second application, the effect of water-lines forms is studied and Prof T.H. Havelock's calculations, which are refered to by D.W. Taylor in his“Speed & Power of Ships”, p.47, Fig. 59 (1933 edit.), are corrected.By the numerical comparisons in these applications, we see that the former theory does fail in almost all cases which have been investigated by the former authors, Wigley, Weinblum and etc, etc, …….

Some Definite Integrals Occurring in Havelock's Work on the Wave Resistance of Ships

Some Definite Integrals Occurring in Havelock's Work on the Wave Resistance of Ships

Effect of Longitudinal Position of the Centre of Buoyancy of Ship

The effects of deviation of ship form-in brief, the effects of C.B. of ship upon the resistance are calculated theoretically, as an attempt to discover the least resistance ship form.Since Michell published his mathematical formula for ship wave resistance, the discrepancies between actual and theoretical cases have been researched by means of the model experiments by tank authorities in the world. Wigley, especially, made careful considerations for the effects of viscosity on the wave-making and be introduced an empirical allowance to the ship aft of amidships and calculated the wave-making resistance of the bow and stern separately from Michell's solution.In these cases, the ships were too slender compared with the sea-going vessels. In the broad ship, however, it is obvious that the aft ship is affected by viscosity and also by eddy-making probably. It may be very difficult to study theoretically these effects on the wave-making.The author has prepared this paper tentatively without investigating the mechanisms of wave-making in the first place.It is reasoned mathematically from Michell's formula that the least resistance ship form is symmetrical fore and aft in the perfect fluid, though this is transformed according with its speed. In general, therefore, the best ship form must be asymmetry lengthwise in actual case, this form is shown as follows, adopting two-dimensional flow for brevity, and taking axis of Ox lengthwise, Oy broadwise, and the origin O amidships, y=F1 (x2) +F2 (x), where F1 and F2 are even and odd functions respectively.A form which deviate from and has same area as the best form is written asy=F1 (x2) +F2 (x) +F3 (x).F3 is odd function and may be small compared with F1 +F2, supposing our present ships.It may be that the wave-making resistance of this form in actual fluid is correspondent with that of a next formula in perfect fluid, y=Fs+F3where Fs is an even function (the best form) and F3 as before.In this stage, Michell's formula can be applied. The effect of F3, the deviation from the least resistance form, can be separately calculated without considering the interferences with the main body Fs, although there are interference-phenomena in the wave syst m.A following formula was applied, F3=y=n {x-k/l- (x-k) 3/l3}where k and l are parameters to change the deviation.The additional wave-making resistance due to F3 is reduced toR=16ρc2n2/π1/r2 [5/3-2P3 (2p) -1/2P3 (2q) -2P3 (p+q) +2P3 (p-q)+6/r {2P4 (2p) +P4 (p+q) -P4 (p-q)}+6/r2 {16/15-5P5 (2p) +P5 (2q) +P5 (p+q) -P5 (p-q)}+36/r3 {P6 (2p) -P6 (p+q) +P6 (p-q)}+18/r4 {96/105-P7 (2p) -P7 (2q) +2P7 (p+q) -2P7 (p-q)}]