WO1997024255A1

WO1997024255A1 - Oblique plane angle and froude number for hull with sinusoidal waterlines

Info

Publication number: WO1997024255A1
Application number: PCT/NO1996/000306
Authority: WO
Inventors: Roar R. Ramde
Original assignee: Petroleum Geo-Services A.S
Priority date: 1995-12-27
Filing date: 1996-12-23
Publication date: 1997-07-10
Also published as: AU1401797A

Abstract

A ship of a displacement type with a pointed bow, a transom stern, a longitudinal length of L, a beam of B and defining a base plane and a design waterline plane, the ship comprising: approximately sinusoidal waterlines; and a surface extending from the transom stern at the design waterline plane to the base plane at about L/2 and defining an angle between the base plane and an oblique plane, the oblique plane being defined by a line at the intersection of the transom stern and the design waterline plane and a point located on the surface at about 0.2L from the transom stern, and a L/B ratio of less than about 2.0. A ship of a displacement type with a pointed bow and a transom stern, a longitudinal length of L, and defining a base plane and a design waterline plane, the ship comprising: approximately sinusoidal waterlines; a surface extending from the transom stern at the design waterline plane to the base plane at about L/2 and defining an angle between: the base plane and an oblique plane, the oblique plane being defined by a line at the intersection of the transom stern and the design waterline plane and a point located on the surface at about 0.2L from the transom stern; and a froude number for the ship of greater than about 0.1. A ship of a displacement type with a pointed bow, a transom stern, a longitudinal length of L, a beam of B and defining a base plane and a design waterline plane, the ship comprising: approximately sinusoidal waterlines; a surface extending from the transom stern at the design waterline plane to the base plane at about L/2 and defining an angle between the base plane and an oblique plane, the oblique plane being defined by a line at the intersection of the transom stern and the design waterline plane and a point located on the surface at about 0.2L from the transom stern; a L/B ratio of less than about 2.0; a froude number for the ship of greater than about 0.1; and wherein the angle is less than about 14.0°.

Description

OBLIQUE PLANE ANGLE AND FROUDE NUMBER FOR HULL WITH SINUSOIDAL WATER LINES

Sinusoidal water-line hulls, in comparison to conven¬ tional hull designs, make it possible to improve a vessel's deadweight tonnage transverse stability, navigational and sailing properties and to reduce stresses on the hull beam whether the vessel is sailing in quiet water or into the waves. As explained in the Ramde patent, at given main dimensions of length, beam and draught, conventional hull configurations can obtain greater deadweight tonnage by increasing the fullness of the underwater portion of the hull, thereby increasing the total displacement. To improve the transverse stability of a conventionally formed hull, expressed as a higher initial metacenter, the breadth of the hull can be increased to obtain a greater moment of inertia at the waterline, optionally also raising the volumetric center of gravity of the underwater hull.

However, changes of this nature (increasing displacement and beam) , as demanded for transverse stability, result in unacceptable increases in a conventional vessel's resistance to propulsion in quiet waters as well as in heavy waves. To improve the seagoing properties of a conventional hull configuration, expressed as the vessel's angular movements about a transverse axis (pitching) , vertical movements (heave) , and angular movements about a longitudinal axis (roll) accelerations in these directions must be dampened. To decrease propulsion resistance compared to the resistance in quiet seas, one seeks to alter the vessel's natural frequency of pitching and heaving so that this frequency, insofar as possible, does not coincide with the frequency of the wave lengths which the vessel encounters. In the case of conventional hull designs, structural alterations result in only slight improvements in the seagoing properties of the vessel, and extreme pitching, rolling and heaving movements and a great increase in the resistance to propulsion will occur when the ship is sailing into the waves when the prevailing wave length is approximately equal in the ship's length at the waterline.

Hulls with sinusoidal waterlines exhibit superior seagoing properties, but like conventional hulls, they tend to have an increased resistance to propulsion with a decrease in the L/B ratio. Thus, they were originally designed with a ratio between the length and beam of about 2.0 or greater and an angle of 14.2 degrees between the oblique plane and the base plane. However, it is now observed that a lower L/B ratio yields increased transverse stability, particularly for roll motion but also for heave motion. Also, it is observed that vortices shed from the oblique plane angled at 14.2° which increases the ship's resistivity. This effect is believed to be caused by the steep angle of 14.2 degrees between the two planes, causing the flow in the boundary layer to separate and reverse direction of flow near the oblique plane of the bottom of the ship.

Therefore, there is a need for a sinusoidal waterline ship hull having a lower L/B ratio so that the roll and heave motions are dampened, while at the same time, having a reduced or maintained resistivity to propulsion.

The seagoing properties of the hull configuration of the present embodiments of the invention are improved, such that the hull's pitching and heaving movements are reduced, compared to the movements of conventional hulls travelling at the same rate of speed, as well as the previous sinusoidal waterline hulls. These movements are retarded such that the improved hull does not exhibit correspondingly large movements until the wave length/hull length ratio is more than twice as large, while at the same time the improved hull's resistance to propulsion is reduced. Also, the present invention provides smooth, substantially homogeneous, two-dimensional flow of water under the hull and past the stern, resulting in very low turbulence, and very quiet running.

According to one embodiment of the invention, there is provided a ship of a displacement type with a pointed bow

SUBSTITUTESHEET(RULE28) and a transom stern, a longitudinal length of L, and defining a base plane and a design waterline plane, the ship comprising: approximately sinusoidal waterlines; and a surface extending from the transom stern at the design waterline plane to the base plane at about L/2 and defining an angle between: the base plane and an oblique plane, the oblique plane being defined by: a line at the intersection of the transom stern and the design waterline plane and a point located on the surface at about 0.2L from the transom stern; wherein the angle is less than about 14.0°.

According to another embodiment of the invention, there is provided a ship of a displacement type with a pointed bow, a transom stern, a longitudinal length of L, a beam of B and defining a base plane and a design waterline plane, the ship comprising: approximately sinusoidal waterlines; and a surface extending from the transom stern at the design waterline plane to the base plane at about L/2 and defining an angle between: the base plane and an oblique plane, the oblique plane being defined by: a line at the intersection of the transom stern and the design waterline plane and a point located on the surface at about 0.2L from the transom stern, and a L/B ratio of less than about 2.0.

According to a further embodiment of the invention, there is provided a ship of a displacement type with a pointed bow and a transom stern, a longitudinal length of L, and defining a base plane and a design waterline plane, the ship comprising: approximately sinusoidal waterlines; a surface extending from the transom stern at the design waterline plane to the base plane at about L/2 and defining an angle between: the base plane and an oblique plane, the oblique plane being defined by: a line at the intersection of the transom stern and the design waterline plane and a point located on the surface at about 0.2L from the transom stern; and a froude number for the ship of greater than about 0.1.

According to a still further embodiment of the present invention, there is provided a ship of a displacement type with a pointed bow, a transom stern, a longitudinal length of L, a beam of B and defining a base plane and a design waterline plane, the ship comprising: approximately sinusoidal waterlines; a surface extending from the transom stern at the design waterline plane to the base plane at about L/2 and defining an angle between: the base plane and an oblique plane, the oblique plane being defined by: a line at the intersection of the transom stern and the design waterline plane and a point located on the surface at about 0.2L from the transom stern; a L/B ratio of less than about 2.0; a froude number for the ship of greater than about 0.1; and wherein the angle is less than about 14.0°.

The preceding embodiments are given by way of example, only. No limitation of the invention is intended by the inclusion of any particular feature or combination in the preceding examples, as it will be clear to a person of ordinary skill that the invention lends itself to other embodiments.

The present invention will be better understood by reading the following description of nonlimitative embodiments, with reference to the attached drawings which are briefly described as follows:

Figure 1 is a top plan view of a hull made according to an embodiment of the present invention.

Figure 2 is a side elevation of the hull of Fig. 1. Figure 3 is bottom plan view of the hull of Fig. 1.

Figure 4 is a side view of a hull made according to an embodiment of the present invention.

Figure 5 is a schematic diagram of a transverse cross- section of a bulge at the edge of the oblique surface. Figure 6 is a schematic diagram of a cross section of a bulge which extends both in horizontal and vertical directions.

Figure 7 represents a bottom plane view of half a hull according to Figure 5 made with a bulge running from the bow of the ship to the transom stern.

Figure 8 represents a sideview of the hull made according to an embodiment of the present invention. Figure 9 describes one embodiment of the invention shown from the starboard side.

Figure 10 shows an aft view of an embodiment of the invention. Figure 11 depicts a top view of an embodiment of the invention.

Figure 12a shows test results for the Taylor Wake for angular positions at a radius of 40mm relative to the scaled model. Figure 12b shows test results for the Taylor Wake for angular positions at a radius of 60mm relative to the scaled model.

Figure 12c shows test results for the Taylor Wake for angular positions at a radius of 80mm relative to the scaled model.

Figure 12d shows test results for the Taylor Wake for angular positions at a radius of 100mm relative to the scaled model.

Figure 13 depicts a curve of constant wake fractions for the propeller disc.

Figure 14 is a starboard view of an embodiment of the invention having a skeg.

Figure 15 is a top view of an embodiment of the invention having a skeg. Figure 16 is an aft view of an embodiment of the invention having a skeg.

It is to be noted, however, that the appended drawings illustrate only typical embodiments of the invention and are therefore not to be considered a limitation of the scope of the invention which includes other equally effective embodi¬ ments.

Referring now to Fig. 1, according to one embodiment of the present invention, there is provided a hull 10 with more rounded lines than conventional hull configurations, expressed by the term for slenderness of line L/V¹³, where L is the length of the hull at the design waterline (dwl) corresponding to the depth T to the summer freeboard (see Fig. 2) , and V is the displacement volume of the hull at the design waterline. Further according to this embodiment, L/V¹'¹ is about 3 or greater, but the specific resistance to propulsion compared to conventional hull configurations is not increased. At the same time, the present embodiment provides that the hull beam B is such that the L/B ratio is between about 1 and about 2.2. The preferred ratio has been found to be about 1.7. B is the maximum beam of the hull at the design waterline (dwl) . According to this embodiment, the height of the metacenter of the hull 10 is more than doubled in relation to conventional hull configurations of the same length.

According to a further embodiment of the invention, the displacement distribution in the longitudinal direction approximates a Rayleigh wave. Such a wave is accomplished in the present embodiment with substantially squarely cut off, approximately harmonic sinusoidal waterlines (Figure 2: dwl, 1, 2, 3) with extremity or stationary points 12 and 14 at the ends of the hull fore and aft, while at the same time the base lines of the waterlines (0^, 0₁ , 0₂, 0₃) from the design waterline (dwl) and at increasing depths from this gradually are displaced in the direction of forward propulsion, shortened so far that an approximately oblique surface (s) , which may be straight, is defined. Further in accordance with this embodiment, surface (s) which comprises the stern half of the hull 10 and permits utilization of various propulsion systems.

Referring now to Figs. 2 and 3, according to a further embodiment of present invention, a ratio Bl/tl is defined at a transverse section through the hull 10 below the design waterline (dwl) at a distance of about 0.15 L from the stern, wherein (Bl) is the beam at the design waterline (dwl) and (tl) is the draught of the hull (measured from the same waterline) . According to this embodiment, the ratio Bl/tl is about 15. According to an alternative embodiment, the ratio Bl/tl is greater than the corresponding ratio for a section at L/2 where the beam (B₂) and draught (t₂) are measured in the same way.

According to a further embodiment of the invention a further hull ratio e=C_P/C,_Jw; is defined, wherein C,. is the hull's block coefficient and C._lwl is the hull's longitudinal prismatic coefficient expressed from the following equations: C_p= V/(A_L/ x L) and C_dwl= A_wl/LB, wherein L is the length at the design waterline, A is the area of a transverse section up to the waterline at L/2, V is the displacement volume to the design waterline, A_dwl is the waterline area, and B is the maximum beam at the waterline. According to this embodiment, the hull parameter e is about 1 or greater.

Referring again to Fig. 1 according to a further embodiment of the invention, the design waterline's areal center of gravity (LCF) is located around 0.2 L aft of midship, and the improved hull's volumetric center of gravity (buoyancy) (LCB) at the depth of about .3T below the design waterline (dwl) around 0.075 L forward of areal center of gravity, which may be expressed as LCF - LCB - 0.075 L. Referring again to Fig. 1, the hull 10 is shown with the approximately harmonic sinusoidal waterlines around the design waterline (dwl) with extremity points around the hull's bow and stern ends with, wherein the areal center of gravity (LCF) is about 0.2 L aft of L/2. Figure 2 shows the an embodiment of the invention's hull below the design waterline (dwl) in vertical section, where it is seen that the base lines are substantially squarely cut off. Further in accordance with this embodiment, there are approximately harmonic sinusoidal waterlines (0^, 0_ι, 0₂, 0₃) along a sloped generally planar surface (s) , which are displaced in the direction of forward propulsion of the vessel, and which coincide with the base plane (g) at about L/2. Further, the distance between the areal center of gravity (LCF) and the buoyancy center of gravity (LCB) of the hull 10 at the depth of the design waterline (dwl) is about 0.075L. The generally planar surface (s) in some embodiments takes the form of a curved surface with a very large radius, (for example between about 3 and about 5 times the maximum beam, and in a specific embodiment, about 4)

In Figure 3, the hull configuration of Figure 2 is shown in horizontal projection with the waterlines dwl, 1, 2, 3 and g in the examples with a U-frame at the bow end of the hull. According to alternative embodiments of the invention, other known frame forms are used. The embodiment of Figure 3 also has a ratio between beam and depth for a section around 0.15L from the stern and at L/2, where the respective beams and depths are designated B_: and B₂ and tj and t₂.

Referring again to Figure 1, the length (L) and beam

(B) dimensions are shown. It has been determined that small

L/B values produce unexpected high viscous damping in roll, pitch and heave, indicated by higher natural periods. Tests were performed to determine the magnitude of this damping.

Two models were tested, B30 and B40, with L/B ratios 1.78 and 2.38 respectively. These models had the following characteristics: B30

Length Overall L_oa 78 . 50 m

Breadth "max 30 . 00 m

Displacement V 6070 m³

Draught T 7 . 06 m Wetted Surface s 2010 m²

Long. Center of Gravity From Stern LCG 32 . 00 m

Vert. Center of Gravity Above Base VCG 9 . 61 m

Metacenter Radius KM_T 14 . 14 m

Metacentric Height GM_T 4 . 02 m Transverse Radius of Gyration (Air) xx 8 . 51 m

Longitudinal Radius of Gyration (Air) k_w 20 . 45 m

ADDED MASS/MOMENTS Calculated Roll Period in Air T φ " 8 . 51 sec . Measured Roll Period in Water T φ 10 . 0 sec . Transverse Radius of Gyration in Water k_xx 1. 176 ^•

"xxair

Total Moment of Inertia I_xxTOT 1 . J O ^* lχχair Calculated Pitch Period in Air T'Θ 5.99 sec. Measured Pitch Period in Water T Θ 9.1 sec. Longitudinal Radius of Gyration in Water yy 1.51 yy.ιι t Total Moment of Inertia I_yyTOT 2.30 yyair

B40

Length Overall 78.50 m Breadth B_m 40.00 m Displacement v 6590 m³ Draught T 6.16 m Wetted Surface S 2445 m²

Long. Center of Gravity from Stern LCG 34.00 m Vert. Center of Gravity above Base VCG 7.03 m Metacenter Radius KM_T 22.87 m

Metacentric Height GM_T 15.84

Transverse Radius of Gyration (Air)k_xx 9.30 m Longitudinal Radius of Gyration (Air)k_yy 21.25 m

ADDED MASS/MOMENTS Calculated Roll Period in Air T φ' 4.7 sec. Measured Roll Period in Water T φ 7.2 sec.

Transverse Radius of Gyration in Water k_xx 1.537 ^•

^■"^xxair

Total Moment of Inertia I_xxTOT _i . J O ' lχχaj.r Calculated Pitch Period in Air T'Θ 5.43 sec. Measured Pitch Period in Water TΘ 9.0 sec. Longitudinal Radius of Gyration in Water _yy 1.66 k_yya - Total Moment of Inertia I_yyTOT * ^*?• • 7 ' ^■*"*> • T ^yyair

Before the testing in waves, pendulum tests in air were carried out with the models, to adjust the mass distribution according to the specified values. Inclining tests in water were carried out to control the metacentric height. Also motion decay tests in water were carried out for the three load conditions to obtain information on the natural periods, added mass and moments and the viscous damping. The tests in waves were carried out as follows: Heading 90 deg (beam seas)

Vessel speed 0 knot

Number of reg. waves 10 - Number of wave spectra 3 Number of load conditions,

B = 40 m 2(transport and operation)

Number of load conditions, B = 30 m 1 (operation) As shown in the table below, the increase in viscous dampening in roll, pitch and heave due to added displacement of oscillating water farther from the center of rotation is considerable compared to conventional vessels.

VISCUS DAMPENING

ROLL PITCH HEAVE

Ramform B30 0.38 X 1.3 X I_w

Ramform B40 1.36 X 1.75 X I_w 2.5 X Δ

Conventional 0.2-0.4 x iχ. 0.5-1.0 X Δ

Also, long trend probability analyses for roll in Northern North Atlantic showed that the roll amplitude over return periods up to 100 years are about 50% lower for the wider ship with the lowest L/B ratio of 1.78. An optimum L/B ratio is about 1.7. The main reason for this difference is the large ratio between the bottom plane area and the immersed volume. The practical consequences are that the angular roll motion and heave motion (vertical displacement) for the ship with the lowest L/B ratio will be lower than for the ship with a higher L/B ratio. This is, in particular, unexpected for roll motion. Increasing the beam relative to the length, however, tends to increase the resistivity of the ship, which normally yields a lower Froude Number. The Froude Number is defined as V/fgL)" where

V is the speed of the ship, g is the gravitational acceleration constant, and L is the length of the ship. The Froude Number, rather than the ship's absolute speed, defines whether a ship is fast or slow. Thus, two ships may have the same absolute speed and one of them could be a fast ship and the other a slow one, since the former may be short and the latter much longer. It is desirable to have a ship with a Froude Number between about 0.1 and about 0.35. Thus, even though the ship outlined above has a relatively low L/B ratio, which tends to increase the resistance, it should be between about 0.1 and about 0.35.

Referring to Figure 4, a base plane (B) and an oblique plane (O) are shown. The base plane (B) is parallel to the design water line (dwl) and coincides with the keel line (K) of the ship. A surface (S) extends from the transom stern (700) at the design waterline plane (dwl) to the base plane (B) at about L/2. The oblique plane (O) intersects the transom stern (700) at the design waterline plane (dwl) and a point located on the surface (S) at about 0.2L from the transom stern (700) . The angle between the oblique plane (O) and the base plane (B) is defined as alpha (α) .

The angle ( ) dictates whether the water flowlines over the surface (S) remain attached to the surface (S) or whether the flowlines become separated. At smaller angles the flowlines do not separate from the surface (S) of the ship. If the flowlines do separate from the surface (S) , then vortices are formed at the region of separation which increases the ships resistance. Tests were performed to determine the angle which provides the lowest resistance.

A ship was tested in a model basin with respect to the effect of the variation in angle between the oblique plane and the base plane on model resistance. A resistance test was run with constant draught at F.P. and the dynamic suction in F.P. was measured at speeds 13 - 17 knots. The hull model M-1867 C was manufactured to the scale ratio 1:26.5. The model was equipped with a trip wire at station 9-1/2 in order to obtain turbulent flow. Stabilizing fins and thruster pods were not fitted to the model. All results refer to salt water with density 1025 kp/m³ and a sea temperature of 15°C.

The resistance tests were carried out as follows: Draught Trim Appendage Speed

(in) (knots)

4.95 0 - 13-18

4.95 1 deg f.wd - 13-17

4.95 l deg aft - 13-17

4.95 0 Fixed F.P. 13-17

4.95 0 Bow foil 13-17

Test Results:

Effective horse power for M-1867 C at draught T = 4.95 m, even keel = 100%.

v. Even Fixed

(knots) Keel 1° 1° aft P.P. f.wd.

13 100 99.1 105.8 105.2

14 100 114.8 108.3 107.4

15 100 106.6 93.8 91.4

16 100 103.2 88.7 84.1

17 100 108.6 93.9 86.4

The dynamic suction measured at F.P. for test with fixed forward draught:

V₃ Suction (knots) (tonnes)

13 104.6

15 141.4

17 188.3

From the test results, it was found that the resistance varies between 103.2 and 88.7% compared to the "even keel" angle, which was set to about 13.2 degrees or about l degree less than on model No. 1. The reduced resistance is due to the elimination of vortices because the flowlines remain attached to the oblique surface (S) . Reducing this angle further by about 1 degree, to about 12.2 degrees, the lowest resistance level in the design speed range was obtained. Thus, is was determined that a sinusoidal waterline hull having a L/B ratio of about 1.7 could still have a Froude Number of about 0.32 by adjusting the angle between the oblique plane and the base plane to be about 12.2°.

Figure 5 represents a schematic diagram of a transversal cross section of a sinusoidal waterline-type hull ship according to the present invention showing the principal transition curves shipside-bottom cross sections for a conventional ship which is represented by a dotted line and a sinusoidal waterline-type hull ship represented by the full line with a horizontally extending bulge. As the hull of the ship is substantially symmetrical, only one half of the transversal cross section of the ship is represented so that the center line plane 1 which is used as reference line to determine the beam of the ship at various heights of the transversal cross section. The hull of a conventional ship comprises a side board plane which is substantially parallel to the center line plane l and which runs into the bottom plane by a curved portion connecting the side board plane with the bottom plane of the ship. This curved portion is defined by a radius related to a imaginary point P constructed by the intersection of an elongated line lying in the side board plane and an elongated line lying in the bottom plane 2. This point P also corresponds to the maximum beam of a conventional ship characterized by B_max, _conv. The side board plane is parallel to the center line plane 1 in the area of the waterline 3 in the midship section of a conventional ship.

The general shape of one embodiment of a sinusoidal waterline-type hull 10 significantly deviates from the general shape of a conventional hull form. On the one hand the hull 10 is curved at a certain radius in a concave way related to the center line plane 1 and running into a bulge 100 near the bottom plane 2, said bulge 100 going beyond the line through the side board plane and point P, which defines the maximum beam of a conventional ship B_max, _conv so that the maximum beam of a sinusoidal waterline-type hull ship is larger, by the difference between B_max, _conv and B_max, _sin than B_max, _conv. Such a bulge 100 which is arranged below the waterline 3 and which has smooth transition ranges from the side board of the ship into the bulge 100 and from the bulge into the bottom plane 2, increases the deadweight of the ship as well as the rolling, pitching and to a certain extent also heaving movements of the ship. However, the amount of improvement of the rolling behavior of a sinusoidal waterline-type hull ship without a bulge is rather limited because the water displaced by the hull form in the bottom plane range of the ship can easily flow transversely around the bulge 100 without giving a significant reduction of rolling behavior of the ship.

Figure 6 comprises a schematic diagram of a cross section of an improved sinusoidal waterline-type hull ship according to Figure 5. This sinusoidal waterline-type hull ship, however, comprises a horizontally and vertically extending bulge 200 according to the invention. The construction of point P corresponds to the one described with regard to Figure 5. As it can be seen from Figure 6, the bulge 200 encircles this point P both in horizontal and in vertical direction. Again, this point P represents the locus at which the local extension of the basically vertical ship side, the side board plane, and the basically horizontal bottom of the ship intersect. Furthermore, it can be seen from Figure 6 that the bulge 200 goes below the bottom plane 2 of the ship and comprises transition portions 5, i.e. the transition curves between the portion of the bulge 200 approaching the bottom plane 2 of the ship.

It very much depends on the properties to be achieved by the sinusoidal waterline-type hull ship whether the transition curves 5 comprise a steeper or a flatter transition region. The bulge 200 extending also in vertical direction beyond the bottom plane 2 increases the deadweight of the ship significantly and on the other hand significantly improves mainly the rolling capability of the ship. This rolling improvement, among others, results from the fact that, when the ship is rolling in seawaves, the water flowing around the hull in the bottom plane region 2 transversely from the center line of the ship towards the bulge 200 is forced downwards and hence, generating a lift component to the ship which related to the center line plane of the ship corresponds to a moment directed upwards.

In order to ensure that, nowhere on the hull of the ship, the bulge 200 goes below the keel line which is important from the point of view of docking the ship without giving rise to damage to the hull during the docking operation, the bulge 200 starts from a zero vertical extension at the area of about L/3 from the bow and gradually increases towards the transom stern 7 of the ship. Figure 7 represents a bottom plane view of half a hull according to Figure 5 made with a bulge 200 running from the bow of the ship up to the transom stern 7. This Figure indicates that the vertical extension of the bulge 200 can already start at the bow region of the ship and gradually increase therefrom to the transom stern. The line inside the bottom view represented in Figure 7 represents the point at the respective cross section where the bulge 200 runs into the bottom plane 2. That means the line shown represents a tangent line of the locus, where the bulge 200 runs into the bottom plane, that means that in the range L/3 from forward perpendicular FP of the ship, the only horizontally extending bulge runs into the bottom plane 2 of the ship at a point inside the distance between the center line plane of the ship and point P. According to a further embodiment of the invention, the vertical extension of the bulge 200 starts, for the reasons mentioned with regard to Figure 6, approximately at a point L/3 of the ship and gradually increases towards the transom stern. The width of the bulge 200, where the bulge comprises also a vertical extension with regard to the bottom plane 2 is preferably in a range defined by the ratio b/B approximately 0.5 to 0.8. The term b stands for the distance from the center line plane 1 to the tangent line, where the vertical extending bulge 200 runs into the bottom plane 2, whereas B represents the maximum width of the ship at this particular cross section, that means the distance between the center line plane l of the ship and the maximum beam including the horizontal extension of the bulge 200 with regard to point P .

Figure 8 represents a sideview of the hull made according to an embodiment of the present invention. The hull 10 of the sinusoidal waterline-type hull ship comprises a bulbous bow going in forward direction beyond forward perpendicular FP of the ship, a sloped surface 6 starting from about L/3 to the transom stern 7 of the ship. At a cross section forward perpendicular, the tangent line coincides with the center line of the bulbous bow 4. The bulge 200 is shown extending from and below surface 6.

Also, the improved hull configuration provides zones of reduced hull wake. Hull wake describes a phenomenon wherein water particles flowing around the hull have vector components in the same direction as the forward motion of the ship. Regarding propeller placement, it is important to know the speed of the water through the space occupied by the propeller relative to the ship. The wake fraction is given as Taylor-wake W_τ = 1 - V_a/V, where V_a = Speed of water through the propeller disc, and V = Speed of the ship. Thus, where W_τ is nearly one (1) , the water particles moving through the propeller disc have forward components nearly as great as the ship. This is undesirable. However, if W_τ is nearly zero (0) , then the forward vector components of the water particles are almost non existent. Therefore, it is best to position the propellers where W_τ is nearly zero (0) . Referring to Figures 9, 10 and 11, one embodiment of the invention is shown from the starboard side, the aft, and the top, respectively. Here, a propeller is positioned below the oblique surface (10) near a corner of the stern of the ship. A second propeller (30) is also positioned below the oblique surface (10) near the opposite corner of the stern of the ship.

Tests were performed to determine the magnitude of the hull wake at the stern corners. The test parameters included:

Model: M-1867C

Scale: 1:26.50

Draught: T_AP = 5 .44m, T_FP = 4 . 18m Trim: 1 degree aft

Speed: 10.0 knots

Center of propeller disc: 6.25m from transom;

15m from centerplane; 1.46m from base plane

The pitot-tube, of course, measures the velocity of the water particles through the propeller disc. The pitot-tube wake survey was undertaken by moving the pitot-tube systematically over the propeller disc area. Referring the Figures 12a - 12d, test results for the Taylor Wake are provided for angular positions at radii ranging from 40mm to 100mm, respectively relative to the scale model. The data from the graphs in Figures 12a - 12d are incorporated into a curve of constant wake fractions for the propeller disc shown in Figure 13. As shown in Figure 13, there is no hull wake across most of the propeller disc. Only between 330° and 30° is there a slight hull wake and even here the wake fraction is less than 0.2. This means that a propeller which is attached to the hull of the ship at this location runs through water flowlines that are nearly undisturbed by the ship's hull.

Referring again to Figure 9, another aspect of the invention is depicted. The central axis (21) of the propeller (20) is parallel to the base plane (11) of the ship. This serves two purposes: first, the entire thrust vector of the propeller is in the forward direction of the ship; and second, the axis (21) of the propeller (20) can be swivelled 360° to direct the thrust vector in any direction parallel to the base plane (11) of the ship. With the entire thrust component oriented in the direction of the ship's forward motion more efficiently utilizes the power necessary to propel the ship.

Referring again to Figure 11, propellers (20) and (30) are shown, one in each of the stern corners below the oblique plane. This allows for improved maneuverability and control of the ship. Not only may the ship be steered by varying the thrust from the propellers (20) and (30) , but the axes of the propellers (20) and (30) may be swivelled from side to side so as to provide thrust vectors transverse to the forward motion of the ship. The propellers (20) and (30) may be efficiently swivelled because they are operated in zones of fluid flow where there is almost no hull wake. Also, a third propeller (40) is shown, which extends below the keel line near the bow. This propeller also has the ability to swivel from side to side for added maneuverability.

Another embodiment of the invention is shown in Figure 14. It represents a schematic side view of a hull comprising a skeg extending in the longitudinal direction from about L/3 measured from forward perpendicular FP of the ship with regard to the length L of the ship to the transom stern 7. The skeg 300 corresponds to the shaded area in Figures 14 - 16. The general shape of the hull form of the sinusoidal waterline-type hull ship comprises a bulbous bow 4 extending in forward direction beyond forward perpendicu- lar FP of the ship, a sloped or oblique surface 6 starting from about L/3 and running to the transom stern 7 of the ship and a base plane 2 which forms the borderline plane for the maximum vertical extension of the center skeg 300, so that the center skeg 300 has a maximum vertical extension or height which in each cross section of the ship corresponds to the center plane 2.

Fig. 15 shows a bottom plan view according to Fig. 14 showing the longitudinal and transversal extension and shape in a principal representation of the center skeg. In longitudinal direction of the ship, the center skeg starts with a zero vertical extension, that means at a level coinciding with the base plane 2 and gradually increasing in height, that means in vertical extension towards the transom stern 7 so that the lowermost portion of the skeg coincides with the base plane 2 at each and every cross section of the ship. For reducing turbulence, the thickness of the skeg gradually decreases to zero value at the transom stern 7 of the ship. In order to further increase the rolling stability of the ship and to increase the deadweight of the ship without altering the overall dimensions of the ship, the skeg comprises skeg bulges 310 which are arranged in the lower portions of the skeg, that means in the area of the skeg adjacent to the base plane 2 without going beyond the base plane 2. The skeg bulges 310 tangentially run out of the substantially parallel side walls of the skeg 300 at a location of about L/3 of the ship, and gradually increase towards a maximum horizontal extension at the aft portion of the ship, from which the horizontal extension of the skeg bulges 310 gradually decrease to zero extension and therefore coinciding with the aftmost portion of the skeg 300. With a skeg of thickness (b) , it is advantageous to have a maximum horizontal extension from the starboard extension to the port extension of said skeg bulges which correspond to 2b, that means double the width or thickness of the skeg. If the beam of the ship is designated with B, the thickness of the skeg related to the beam of the ship, that means b/B is approximately 1 over 10.

Fig. 16 represents a schematic view from the transom stern according to Fig. 14 for a sinusoidal waterline-type hull ship with a skeg including skeg bulges as well as horizontally and vertically extending hull bulges. This view according to Fig. 16 represents a combination of hull bulges 200 with the inventive center skeg 300 including skeg bulges 310 on either side of the skeg 300. The skeg 300 as well as the skeg bulges 310 result in an increased deadweight of about 20 to 30 percent of the ship without altering the overall dimensions of the ship. As it can be seen from Fig. 16, the skeg bulges 310 tangentially run into the substantially parallel sidewalls of the center skeg 300 at the transition periods from the skeg bulges into the center skeg wall. Both the center skeg 300 and the hull bulges 200 alone and in combination result in a significantly improved rolling behavior of the ship.

While the particular embodiments for the device of the present invention as herein disclosed in detail are fully

SUBSTfTUTESHEET(RULE26) capable of obtaining the objects and advantages herein stated, it is to be understood that they are merely illustrative of the presently preferred embodiments of the invention and that no limitations are intended by the details of construction or design herein shown other than as described in the appended claims.

Claims

C l i m s

1. A ship of a displacement type with a pointed bow and a transom stern, a longitudinal length of L, and defining a base plane and a design waterline plane, the ship comprising:

approximately sinusoidal waterlines; and

a surface extending from the transom stern at the design waterline plane to the base plane at about L/2 and defining an angle between: the base plane and an oblique plane, said oblique plane being defined by: a line at the intersection of the transom stern and the design waterline plane and

a point located on said surface at about 0.2L from the transom stern,

wherein said angle is less than about 14.0°.

2. A ship as in claim 1, wherein said angle is between about 12.5° and about 14.0°.

3. A ship as in claim 1, further comprising a L/B ratio of less than about 2.0.

4. A ship as in claim 1, further comprising a froude number for the ship of greater than about 0.1.

5. A ship of a displacement type with a pointed bow, a transom stern, a longitudinal length of L, a beam of B and defining a base plane and a design waterline plane, the ship comprising:

approximately sinusoidal waterlines; and

a point located on said surface at about 0.2L from the transom stern, and

a L/B ratio of less than about 2.0.

6. A ship as in claim 5, wherein said L/B ratio is between about 1.4 and about 2.0.

7. A ship as in claim 5, wherein said L/B ratio is about 1.7.

8. A ship as in claim 5, further comprising a froude number for the ship of greater than about 0.1.

9. A ship as in claim 5, wherein said angle is less than about 14.0°.

10. A ship of a displacement type with a pointed bow and a transom stern, a longitudinal length of L, and defining a base plane and a design waterline plane, the ship comprising:

approximately sinusoidal waterlines;

a point located on said surface at about 0.2L from the transom stern; and

a froude number for the ship of greater than about 0.1.

11. A ship as in claim 10, wherein said froude number is between about 0.1 and about 0.35.

12. A ship as in claim 10, wherein said angle is less than about 14.0°.

13. A ship as in claim 10, further comprising a L/B ratio of less than about 2.0.

14. A ship of a displacement type with a pointed bow, a transom stern, a longitudinal length of L, a beam of B and defining a base plane and a design waterline plane, the ship comprising:

approximately sinusoidal waterlines;

a point located on said surface at about 0.2L from the transom stern;

a L/B ratio of less than about 2.0;

a froude number for the ship of greater than about 0.1; and

wherein said angle is less than about 14.0°.

15. A ship as in claim 14, wherein said froude number is between about 0.1 and about 0.35.

16. A ship as in claim 14, wherein said L/B ratio is between about 1.4 and about 2.0.

17. A ship as in claim 14, wherein said angle is between about 12.5° and about 14.0°.