On The Wave Resistance of Surface Effect Ships

1971 ◽  
Vol 15 (01) ◽  
pp. 22-32
Author(s):  
Bohyun Yim
Keyword(s):  
Froude Number ◽  
Surface Effect ◽  
Power Reduction ◽  
Wave Resistance ◽  
Low Speed ◽  
Low Resistance ◽  
Wave Interference ◽  
Better Than

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.

scholarly journals The wave pattern of a doublet in a stream

1928 ◽  
Vol 121 (788) ◽  
pp. 515-523 ◽  
Keyword(s):  
Surface Effect ◽  
Ideal Point ◽  
Finite Size ◽  
Wave Pattern ◽  
Wave Resistance ◽  
Point Of View ◽  
The Body ◽  
Surface Elevation ◽  
More Care ◽  
Forced Waves

The following paper is a study of the surface waves caused by a doublet in a uniform stream, and in particular the variation in the pattern with the velocity of the stream or the depth of the doublet. In most recent work on this subject attention has been directed more to the wave resistance, which can be evaluated with less difficulty than is involved in a detailed study of the waves; in fact, it would seem that it is not necessary for that purpose to know the surface elevation completely, but only certain significant terms at large distances from the disturbance. Recent experimental work has shown con­siderable agreement between theoretical expressions for wave resistance and results for ship models of simple form, and attempts have been made at a similar comparison for the surface elevation in the neighbourhood of the ship. In the latter respect it may be necessary to examine expressions for the surface elevation with more care, as they are not quite determinate; any suitable free disturbance may be superposed upon the forced waves. For instance, it is well known that in a frictionless liquid a possible solution is one which gives waves in advance as well as in the rear of the ship, and the practical solution is obtained by superposing free waves which annul those in advance, or by some equivalent artifice. This process is simple and definite for an ideal point disturbance, but for a body of finite size or a distributed disturbance the complete surface elevation in the neighbourhood of the body requires more careful specification as regards the local part due to each element. It had been intended to consider some expressions specially from this point of view, but as the matter stands at present it would entail a very great amount of numerical calculation, and the present paper is limited to a much simpler problem although also involving considerable computation. A horizontal doublet of given moment is at a depth f below the surface of a stream of velocity c ; the surface effect may be described as a local disturbance symmetrical fore and aft of the doublet together with waves to the rear. Two points are made in the following work.

scholarly journals The Low Speed Wave Resistance Theory Imposing Accurate Hull Surface Condition

1979 ◽  
Vol 1979 (146) ◽  
pp. 27-34
Author(s):  
Yoshihiro Shimomura ◽  
Takamune Kitazawa ◽  
Takao Inui ◽  
Hisashi Kajitani
Keyword(s):  
Surface Condition ◽  
Wave Resistance ◽  
Low Speed ◽  
Resistance Theory

A Slender-Ship Theory of Wave Resistance

1983 ◽  
Vol 27 (01) ◽  
pp. 13-33
Author(s):  
Francis Noblesse
Keyword(s):  
Froude Number ◽  
Wave Resistance ◽  
Successive Approximations ◽  
Zeroth Order ◽  
Remarkable Effect ◽  
Ship Wave ◽  
First Order ◽  
Wigley Hull ◽  
Low Froude Number ◽  
The Waves

A new slender-ship theory of wave resistance is presented. Specifically, a sequence of explicit slender-ship wave-resistance approximations is obtained. These approximations are associated with successive approximations in a slender-ship iterative procedure for solving a new (nonlinear integro-differential) equation for the velocity potential of the flow caused by the ship. The zeroth, first, and second-order slender-ship approximations are given explicitly and examined in some detail. The zeroth-order slender-ship wave-resistance approximation, r(0) is obtained by simply taking the (disturbance) potential, ϕ, as the trivial zeroth-order slender-ship approximation ϕ(0) = 0 in the expression for the Kochin free-wave amplitude function; the classical wave-resistance formulas of Michell [1]2 and Hogner [2] correspond to particular cases of this simple approximation. The low-speed wave-resistance formulas proposed by Guevel [3], Baba [4], Maruo [5], and Kayo [6] are essentially equivalent (for most practical purposes) to the first-order slender-ship low-Froude-number approximation, rlF(1), which is a particular case of the first-order slender-ship approximation r(1): specifically, the first-order slender-ship wave-resistance approximation r(1) is obtained by approximating the potential ϕ in the expression for the Kochin function by the first-order slender-ship potential ϕ1 whereas the low-Froude-number approximation rlF(1) is associated with the zero-Froude-number limit ϕ0(1) of the potentialϕ(1). A major difference between the first-order slender-ship potential ϕ(1) and its zero-Froude-number limit ϕ0(1) resides in the waves that are included in the potential ϕ(1) but are ignored in the zero-Froude-number potential ϕ0(1). Results of calculations by C. Y. Chen for the Wigley hull show that the waves in the potential ϕ(1) have a remarkable effect upon the wave resistance, in particular causing a large phase shift of the wave-resistance curve toward higher values of the Froude number. As a result, the first-order slender-ship wave-resistance approximation in significantly better agreement with experimental data than the low-Froude-number approximation rlF(1) and the approximations r(0) and rM.

scholarly journals Steady hydrodynamic interaction between human swimmers

2019 ◽  
Vol 16 (150) ◽  
pp. 20180768 ◽  
Author(s):  
Zhi-Ming Yuan ◽  
Mingxin Li ◽  
Chun-Yan Ji ◽  
Liang Li ◽  
Laibing Jia ◽  
...  
Keyword(s):  
Drag Reduction ◽  
Hydrodynamic Interaction ◽  
Surface Effect ◽  
Swimming Performance ◽  
Interactive Effect ◽  
Free Water ◽  
Wave Drag ◽  
Competitive Swimming ◽  
Flow Solver ◽  
Wave Interference

This study focuses on the hydrodynamic interaction between two or three human swimmers in competitive swimming. Although the swimming performance of a single swimmer has been widely examined, studies on the interaction between multiple competitive swimmers are very rare. Experiments showed evidence that the drag of a swimmer could be modified by the existence of the other adjacent competitors (Chatard & Wilson. 2003 Med. Sci. Sports Exerc . 35 , 1176–1181. ( doi:10.1249/01.MSS.0000074564.06106.1F )). The following questions arise: (1) what mechanism determines the interaction; (2) which position experiences drag reduction or drag increase; (3) how much can drag be reduced or increased in a formation? According to the authors' knowledge, such questions have not been addressed by any published literature. Therefore, the main purpose of this study is to find the mechanism of the hydrodynamic interaction between human swimmers and to quantify this interactive effect by using a steady potential flow solver. The free-surface effect was fully taken into account in our calculations. We firstly calculated the wave drag of a swimmer swimming solely in an open swimming pool. Then we calculated the wave drag of the same swimmer when he/she swam in the wake region of one or two leading swimmers. The results showed that the hydrodynamic interaction made a significant contribution to the drafter's wave drag. By following a leading swimmer, a drafter at wave-riding positions could save up to 63% of their wave drag at speed of 2.0 m s −1 and lateral separation of 2.0 m. Particularly, when a drafter is following two side-by-side leaders, the drag reduction could even be doubled. To the authors' knowledge, this study is the first to demonstrate that the hydrodynamic interaction between human swimmers can best be described and explained in terms of wave interference effect on the free water surface. When the wave cancellation effect is observed, the wave drag of a drafter could be minimized, and this wave cancellation effect can be achieved only when the drafter is in a wave-riding position.

Waves and wave resistance of thin bodies moving at low speed: the free-surface nonlinear effect

1975 ◽  
Vol 69 (2) ◽  
pp. 405-416 ◽  
Author(s):  
G. Dagan
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Surface Condition ◽  
Perturbation Expansion ◽  
Wave Resistance ◽  
The Body ◽  
Thin Body ◽  
Two Dimensional ◽  
First Order ◽  
Flow Past

The linearized theory of free-surface gravity flow past submerged or floating bodies is based on a perturbation expansion of the velocity potential in the slenderness parameter e with the Froude number F kept fixed. It is shown that, although the free-wave amplitude and the associated wave resistance tend to zero as F → 0, the linearized solution is not uniform in this limit: the ratio between the second- and first-order terms becomes unbounded as F → 0 with ε fixed. This non-uniformity (called ‘the second Froude number paradox’ in previous work) is related to the nonlinearity of the free-surface condition. Criteria for uniformity of the thin-body expansion, combining ε and F, are derived for two-dimensional flows. These criteria depend on the shape of the leading (and trailing) edge: as the shape becomes finer the linearized solution becomes valid for smaller F.Uniform first-order approximations for two-dimensional flow past submerged bodies are derived with the aid of the method of co-ordinate straining. The straining leads to an apparent displacement of the most singular points of the body contour (the leading and trailing edges for a smooth shape) and, therefore, to an apparent change in the effective Froude number.

scholarly journals Getting the ducks in a row

2021 ◽  
Vol 932 ◽  
Author(s):  
Simen Å. Ellingsen
Keyword(s):  
Design Research ◽  
Unmanned Vehicles ◽  
Wave Resistance ◽  
Resistance Force ◽  
Total Drag ◽  
Wave Interference ◽  
Us Military ◽  
Individual Wave ◽  
Concomitant Resistance ◽  
Shaped Pattern

Vessels – in the widest sense – travelling on a water surface continuously do work the water surrounding it, causing energy to be radiated in the form of surface waves. The concomitant resistance force, the wave resistance, can account for as much as half the total drag on the vessel, so reducing it to a minimum has been a major part of ship design research for many decades. Whether the ‘vessel’ is an ocean-going ship or a swimming duckling, the physics governing the V-shaped pattern of radiated waves behind it is in essence the same, and just as fuel economy is important for commercial vessels, it is reasonable to assume that also swimming waterfowl seek to minimise their energy expenditure. Using theory and methods from classic marine hydrodynamics, Yuan et al. (J. Fluid Mech., vol. 928, 2021, R2) consider whether, by organising themselves optimally, ducklings in a row behind a mother duck can reduce, eliminate or even reverse their individual wave resistance. They describe two mechanisms which they term ‘wave riding’ and ‘wave passing.’ The former is intuitive: the ducklings closest to the mother can receive a forward push by riding its mother's stern waves. The latter is perhaps a more striking phenomenon: when the interduckling distance is precisely right, every duckling in the row can, in principle, swim without wave resistance due to destructive wave interference. The phenomenon appears to be the same as motivates the recent US military research project Sea Train, a row of unmanned vehicles travelling in row formation.

Waves and Wave Resistance for Air-Cushion Vehicles with Time-Dependent Cushion Pressures

1978 ◽  
Vol 22 (03) ◽  
pp. 170-177
Author(s):  
H. J. Haussling ◽  
R. T. Van Eseltine
Keyword(s):  
Shallow Water ◽  
Froude Number ◽  
Water Depth ◽  
Critical Frequency ◽  
Wave Resistance ◽  
Time Dependent ◽  
Length Ratio ◽  
Wave Patterns ◽  
Air Cushion ◽  
Air Cushion Vehicles

Wave patterns and wave resistance are computed for air-cushion vehicles with time-dependent cushion pressures moving at uniform speed over deep and shallow water. The effect of beam-to-length ratio, Froude number, and water depth on the resistance is investigated. The resistance is found to exhibit a distinctive behavior at a critical frequency. This behavior corresponds to a singularity in the resistance at the critical frequency. The importance of this behavior is found to diminish with decreasing beam-to-length ratio and increasing Froude number.

Convergence of a Sequence of Slender-Ship Low-Froude-Number Wave-Resistance Approximations

1984 ◽  
Vol 28 (03) ◽  
pp. 155-162
Author(s):  
Francis Noblesse
Keyword(s):  
Froude Number ◽  
Wave Resistance ◽  
Beam Length ◽  
Remarkable Property ◽  
Ship Hulls ◽  
Low Froude Number ◽  
Vertical Cylinders ◽  
Elliptical Cylinders ◽  
Double Hull ◽  
Special Case

Convergence of the sequence of slender-ship low-Froude-number wave-resistance approximations /"/, n > 0, obtained as a particular case of the slender-ship theory of wave resistance recently proposed by the author, is proved for the special case of ship hulls in the form of vertical cylinders with elliptical waterlines. Specifically, it is shown that we have where b is the thickness (beam/length) ratio of the cubical cylinder, Fis the Froude number, and r lf(b,F) is the Guevel-Baba-Maruo-Kayo low-Froude-number wave-resistance approximation associated with the exact zero-Froude-number (double-hull) potential. Vertical elliptical cylinders thus have the remarkable property that the ratio iipj{b,F)/rpp(b,F) is independent of the Froude number, that is, depends only on the thickness ratio of the cylinder.

Low-Aspect-Ratio Flat Ship Theory for Moderate Froude Numbers

1991 ◽  
Vol 35 (04) ◽  
pp. 325-330
Author(s):  
S. L. Cole
Keyword(s):  
Aspect Ratio ◽  
Froude Number ◽  
Potential Flow ◽  
Order Term ◽  
Leading Edge ◽  
Wave Resistance ◽  
Intermediate Region ◽  
Leading Order ◽  
Cross Sectional ◽  
Low Aspect Ratio

Low-aspect-ratio flat ship theory models ships whose dimensions satisfy draft << beam <<length. This paper systematically derives the inner and outer linearized problems for moderate Froude number potential flow past such a ship and their solutions. These solutions are matched through an intermediate region. It is found that the leading-order term for the wave resistance for moderate speed low-aspectratio flat ship theory is the same as found in slender ship theory for ships with equivalent cross-sectional areas. Flat ship theory, however, predicts singularities in the flow along the outside of the ship's leading edge which are not present in slender ship theory. A simple example demonstrating these spurious singularities is worked out.

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