BOAT WITH TWO CAMBERED PLANING SURFACES

Abstract

Method and apparatus of various embodiments of a hydrodynamic design of planing boat or vehicle employing two substantially dihedral planing surfaces featuring cambered hydrodynamic profiles with their base lines, positioned successively along length of the boat and comprising a forward planing surface of swept back plan form and an aft planing surface, which, in order to match conformally the disturbance of water surface generated by the forward planing surface, specifically configured and arranged spatially and angularly relatively the forward planing surface, so that within each vertical longitudinal plane a section of aft planing surface is displaced vertically and its base line is turned relatively the base line of corresponding section of the forward planing surface within the same vertical longitudinal plane by the height and angle of the wave trough generated by the forward planing surface at the location of said section of aft planing surface.

Claims

1. A planing boat or any other vehicle employing similar mode of motion, which boat or vehicle is provided at its bottom part with at least one pair of substantially dihedral planing surfaces featuring cambered hydrodynamic profiles, which planing surfaces are successively arranged lengthwise of the boat or vehicle, have their leading and trailing edges coinciding with leading and trailing edges of their cambered profiles, a common vertical longitudinal center plane coinciding with keel lines of their dihedrals, and coinciding or being parallel to the center plane of the boat or vehicle, and half-planes protruding transversely both sides from said keel lines and common center plane, while vertical longitudinal sections of said planing surfaces have base lines coinciding with the base lines of the cambered profiles of these sections, said base lines define the angular positions of cambered profiles of said sections at some non-negative angles of incidence relatively the water surface, and the vertical and longitudinal positions of cambered planing surfaces of said sections are defined by the leading edge points of said cambered profiles, whereas said cambered planing surfaces skim in operational high-speed mode of motion along the surface of water and generate hydrodynamic lift to support at least partially said boat or vehicle by means of only positive hydrodynamic pressure on their facing downward profiled wetted surfaces, which said pair of cambered planing surfaces comprises: a forward planing surface having in the plan view half-planes being swept back relatively the keel line of its dihedral and the common vertical longitudinal center plane, and base lines of vertical longitudinal sections positioned at some non-negative angles of incidence relatively the undisturbed level of water surface, while operation of the forward planing surface causes the water surface to deflect downward and form a wave trough downstream of the trailing edges of said forward planing surface, and an aft planing surface located at some distance downstream, in the wake of the forward planing surface and within said wave trough, while the base lines of vertical longitudinal sections of said aft planing surface are positioned at some non-negative angles of incidence relatively the local level of water surface corresponding to the surface of said wave trough, wherein: each section by vertical longitudinal plane of said aft cambered planing surface is displaced vertically relatively the base line of section of the forward cambered planing surface in the same vertical longitudinal plane by the distance being equal to the vertical distance from said base line of the section of the forward planing surface to the surface of the wave trough at the location of the section of the aft planing surface, and the base line of each of said vertical longitudinal sections of aft cambered planing surface is inclined relatively the base line of vertical longitudinal section of the forward cambered planing surface in the same vertical longitudinal plane by the angle being equal to the sum of the angle of the slope of the surface of the wave trough in said vertical longitudinal section at the location of said section of aft planing surface and the difference between the non-negative angle of incidence of the base line of said section of the aft planing surface relatively the local surface of water corresponding to the surface of the wave trough and the non-negative angle of incidence of the base line of the section of the forward planing surfaces relatively the level of the undisturbed water surface.

2. A boat or vehicle according to claim 1, wherein each section by vertical longitudinal plane of said aft cambered planing surface is displaced in the vertical direction below relatively the base line of section of the forward planing surface in the same vertical longitudinal plane, and the base line of each of said vertical longitudinal sections of aft planing surface is turned clockwise relatively the base line of vertical longitudinal section of the forward planing surface in the same vertical longitudinal plane when viewed from the left side of the boat or vehicle, while the angle of deadrise of the aft planing surface is higher than the angle of deadrise of the forward planing surface and the width of said aft planing surface constitutes not more than 0.9 times of the width of the forward planing surface.

3. A boat or vehicle according to claim 1, wherein said forward planing surface generates not less than 80% of the total hydrodynamic lift generated by said pair of forward and aft cambered planing surfaces.

4. A boat or vehicle according to claim 1, wherein projections of half-planes of said aft planing surface onto the transverse plane have curved configurations with variable angles of deadrise of the half-planes gradually changing along the span of the aft planing surface from the keel line and the center plane outwards.

5. A boat or vehicle according to claim 1, wherein angles of incidence of half-planes of said aft planing surface gradually change along the span of the aft planing surface from the keel line and the center plane outwards.

6. A boat or vehicle according to claim 1, wherein relative cambers of sections by vertical longitudinal planes increase along the span of at least one of said planing surfaces from the keel line and the center plane outwards up to the outer tips of said planing surface.

7. A boat or vehicle according to claim 1, wherein the base line of each of said vertical longitudinal sections of said forward cambered planing surface is inclined nose-dive at some negative angle relatively the keel line of the boat or vehicle meaning that base lines of sections of said forward cambered planing surface are turned counterclockwise relatively the keel line of the boat or vehicle if viewed from the left side of said boat or vehicle.

8. A boat or vehicle according to claim 1, wherein the camber of at least some of said planing surfaces is a Virgil Johnson three-term camber.

9. A boat or vehicle according to claim 1, wherein outer tips of at least some of said planing surfaces are provided with end plates or deflectors protruding below the cambered profiles of tip sections of said planing surfaces.

10. A boat or vehicle according to claim 1, wherein the forward planing surface extends transversally beyond the chines of the boat by means of protrusions located at the intersections of the planing surface with the chines.

11. A boat or vehicle according to claim 10, wherein the upper surfaces of said protrusions extending transversally beyond the chines of the boat are provided with streamlined convex upper surfaces being similar to upper surfaces of hydrofoils.

12. A boat or vehicle according to claim 1, wherein at least some of said cambered planing surfaces are made in the form of panels or planes separated from the bottom of the boat or vehicle and connected to the bottom by means of structural members.

13. A boat or a vehicle according to claim 12, wherein said structural members comprise struts and/or flanges.

14. A boat or vehicle according to claim 12, wherein said planes of separated from the bottom planing surfaces provided with streamlined convex upper surfaces being similar to upper surfaces of hydrofoils.

15. A boat or a vehicle according to claim 12, wherein said forward cambered planing surface is made separated from the bottom of the boat or vehicle and the aft cambered planing surface is made integrated into the aft part of bottom of said boat or vehicle.

16. A boat or a vehicle according to claim 12, wherein said separated panels or planes are provided with flat plate portions connecting the leading edges of said panels or planes and the leading edges of the cambered profiled portions of bottom part of said separated panels or planes.

17. A boat or a vehicle according to claim 12, wherein at least some of said separated from the bottom of the boat or vehicle cambered planing surfaces in the form of panels or planes are made foldable or retractable.

18. A catamaran or other multihull boat according to claim 12, wherein said forward and aft cambered planing surfaces in the form of separated panels or planes are located under the bottoms of the forward and aft parts of two or larger number of hulls respectively.

19. A pontoon boat according to claim 12. provided with at least one pair of said forward and aft cambered planing surfaces in the form of separated panels or planes mounted at the bottoms of pontoon logs.

20. A seaplane or a wing-in-ground effect marine vehicle with take-off and landing gear employing the hydrodynamic configuration of the boat or vehicle according to claim 1.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0219] The accompanying drawings, which are incorporated herein and constitute part of this specification, illustrate exemplary embodiments, and together with the general description given above and the detailed description given below, serve to explain the features of the various embodiments.

[0220] FIG. 1 is a schematic diagram illustrating the side elevation view of a boat moving at relatively high Froude numbers and provided with a hydrodynamic system comprising two dihedral cambered planing surfaces successively arranged at relatively short distance from each other according to some embodiments.

[0221] FIG. 2 is a schematic diagram illustrating the front elevation view of a boat provided with a hydrodynamic system comprising two successively arranged cambered planing surfaces according to some embodiments and corresponding basically to the embodiment shown in the FIG. 1.

[0222] FIG. 3 is a schematic diagram illustrating the bottom plan view of a boat provided with a hydrodynamic system comprising two successively arranged cambered planing surfaces according to some embodiments.

[0223] FIG. 4 is a schematic diagram illustrating the side elevation view of a boat moving at relatively low Froude numbers and provided with a hydrodynamic system comprising two cambered planing surfaces successively arranged at relatively long distance from each other according to some embodiments.

[0224] FIG. 5 is a schematic diagram illustrating the transom elevation view of a boat provided with a hydrodynamic system comprising two successively arranged cambered planing surfaces according to some embodiments and corresponding basically to the embodiment shown in the FIG. 4.

[0225] FIG. 6 is a schematic diagram illustrating the front elevation view of a boat provided with a hydrodynamic system according to some embodiments comprising two successively arranged cambered planing surfaces where the forward planing surface extends beyond the width of the chines by means of the outside protrusions and features end deflectors on the outside tip extremities of both planing surfaces.

[0226] FIG. 7 is a schematic diagram illustrating the side elevation view of a boat provided with a hydrodynamic system according to some embodiments comprising two successively arranged cambered planing surfaces where the forward planing surface extends beyond the width of the chines by means of the outside protrusions and features end deflectors on the outside tip extremities of both planing surfaces.

[0227] FIG. 8 is a schematic diagram that illustrates the perspective aft bottom view of a boat provided with the hydrodynamic system of two successively positioned cambered planing surfaces arranged following stipulations of this invention, integrated into boat's bottom according to some embodiments and corresponding basically to the embodiments shown in the FIG. 6 and FIG. 7, featuring the forward planing surface extending beyond the width of the chines by means of the outside protrusions.

[0228] FIG. 9 is a schematic diagram illustrating the front elevation view of a boat provided with a hydrodynamic system comprising two successively arranged cambered planing surfaces with the forward planing surface being separated from the bottom and the aft planing surface being integrated into the aft part of boat's bottom according to some embodiments.

[0229] FIG. 10 is a schematic diagram illustrating the side elevation view of a boat provided with a hydrodynamic system according to some embodiments comprising two successively arranged cambered planing surfaces where the forward planing surface is separated from the bottom and the aft planing surface is integrated into the aft part of boat's bottom according to some embodiments.

[0230] FIG. 11 is a schematic diagram illustrating the aft elevation view of a boat provided with a hydrodynamic system comprising two successively arranged cambered planing surfaces where both the forward planing surface and the aft planing surface are separated from the bottom.

[0231] FIG. 12 is a schematic diagram that illustrates an along the flow section view of a separated planing surface provided with hydrofoil-like concave upper surface according to some embodiments.

[0232] FIG. 13 is a schematic diagram illustrating the front elevation view of a boat of catamaran configuration provided with a hydrodynamic system of separated cambered planing surfaces according to some embodiments.

[0233] FIG. 14 is a schematic diagram illustrating the front elevation view of a boat provided with a hydrodynamic system according to provisions of this invention and comprising a separated from the bottom foldable forward planing surface shown in the unfolded operational position.

[0234] FIG. 15 is a schematic diagram illustrating the front elevation view of a boat provided with a hydrodynamic system according to provisions of this invention, corresponding basically to the embodiment shown in the FIG. 14 and comprising the separated from the bottom foldable forward planing surface, shown in the folded position being retracted into the niche in the bottom of the boat.

[0235] FIG. 16 is a schematic diagram illustrating the side elevation view of a boat provided with a hydrodynamic system according to some embodiments comprising two integrated successively arranged cambered planing surfaces, whereas the forward planing surface is installed at some negative (nose-dive) angle relatively the keel line of the boat and the hydrodynamic base line of the center plane section of the aft planing surface coincides with the keel line of boat.

DETAILED DESCRIPTION OF THE INVENTION

[0236] Various embodiments will be described in detail with reference to the accompanying drawings. Wherever possible, the same reference will be used throughout the drawings to refer to the same or like parts. References made to particular examples and implementations are for illustrative purposes, and are not intended to limit the scope of the claims.

[0237] FIG. 1 depicts a schematic diagram illustrating the side elevation view of a boat according to some embodiments, where the boat 101 moves at operational speed at relatively high Froude numbers along the undisturbed water surface W in the direction F.

[0238] In this embodiment the boat 101 with its center plane keel line 102, chines 103 (only port side chine is visible on this elevation) and transom 104, is provided with a hydrodynamic system of two successively arranged dihedral cambered planing surfaces, while the interconnected operation of these two planing surfaces as components of the hydrodynamic system following this invention is shown and considered as applied to their center plane keel sections as a sample. Said hydrodynamic system comprises:

[0239] a forward planing surface 105 with its half-planes swept back relatively the keel line of its dihedral and the center plane of the hydrodynamic system coinciding with the boat's center plane keel line 102, and represented by swept back leading edges 106 and swept back trailing edges 107 (only port side edges are visible on this elevation), cambered profile of the center plane section 108 with its chord 109 and hydrodynamic base line 110 of the center plane section 108, determining the angle of incidence 111 of said center plane section 108 relatively the level of the undisturbed water surface W, and the tip profiled cambered section 112 coinciding in this embodiment with the chine 103;

[0240] and, located at relatively short distance downstream from the forward planing surface 105, an aft planing surface 113 with its half-planes determined by the center plane of the hydrodynamic system coinciding with the center plane and keel line of the boat 101, which half-planes are represented by leading edges 114 and trailing edges 115 coinciding in this embodiment with the transom 104, cambered profile of the center plane section 116 with its chord 117 and hydrodynamic base line 118, determining the angle of incidence 119 of the center plane section 116 relatively the local surface of water corresponding to the center plane flow line 120 of the wave trough generated by the forward planing surface 105, and the tip profiled cambered section 121.

[0241] The aft planing surface 113 supposed to maintain the required position in the vertical direction to ensure the correct trim position of the boat 101 and, accordingly, the required angle of incidence 111 of the forward surface 105, and also maintain the required angle of incidence 119 relative the local surface of water to generate the required lift, and in this sense, the spatial (i.e., vertical at the set longitudinal point) and angular position of the aft planing surface 113 should correspond to the local flow 120.

[0242] This embodiment corresponds to the boat 101 featuring a combination of relatively high Froude number and relatively short distance between the planing surfaces 105 and 113, which results in operation of the aft surface 113 on the descending section of the wave trough represented by the center plane flow line 120.

[0243] In order to reduce hydrodynamic resistance and improve efficiency of the hydrodynamic system comprising the two planing surfaces 105 and 113, as well as the efficiency of the boat 101 in general, the aft planing surface 113 configured relatively the forward surface 105 to conform to the relief of the wave trough generated by the forward surface 105 by the following means: [0244] 1. Positioning vertical longitudinal sections of the aft planing surface 113 below the base lines of the forward surface 105 by the vertical distances corresponding to the depressions of the surface of the wave trough under the base lines of the forward surface 105 at the location of the aft surface 113.

[0245] As applied to the exemplary keel and center plane section 116 of the aft planing surface 113, this means that the center plane section 116 is to be positioned below the hydrodynamic base line 110 by the distance 122 corresponding to the depth of the wave through represented by the center plane flow line 120, measured from the hydrodynamic base plane 110 at the location of the center plane point of the leading edge 114 of the aft planing surface 113.

[0246] Alternatively, the optimal vertical position 122 can be defined as the negative depth of the wave trough measured from the undisturbed water surface W (at the location of the aft surface) plus the distance between the leading edges of planing surfaces 105 and 113 times the tangent of the angle of incidence 111 (which product gives a positive value). [0247] 2. Turning the vertical longitudinal sections of the aft planing surface 113 (represented by their hydrodynamic base lines) by positive (turned clockwise in the port side view of this diagram) angles being equal to sums of the angles of slope of the wave trough at the position of sections of the aft surface 113 and the differences between the angles of incidence of the sections of the aft and forward surfaces relative their local surfaces of water.

[0248] As applied to the exemplary keel and center plane section 116 of the aft planing surface 113, this means that the hydrodynamic base plane 118 of the center plane section 116 is to be turned clockwise (in the port side view of this diagram) by a positive angle 123 relatively the hydrodynamic base plane 110, which angle 123 corresponds to the sum of a positive angle of inclination 124 of the flow of the wave trough represented by the center plane flow line 120 at the location the center plane point of leading edge 114 of the aft planing surface 113 to the undisturbed water surface W, and the difference between the positive angle of incidence 119 of the center plane section 116 of the aft surface 113 relative the surface of the wave trough and the positive angle of incidence 111 of the center plane section 108 of the forward surface 105 relative the undisturbed surface of water W.

[0249] The above described spatial and angular arrangement of the aft planing surface 113 relatively the forward planing surface 105 (represented by the relative angular positions of their hydrodynamic base lines and the spatial positions of the leading edges 114 of the aft planing surface 113 relatively the hydrodynamic base lines of the forward planing surface 105) makes it possible to optimally spatially arrange the aft planing surface 113 in the descending section of the substantially V-shaped channel of the wave trough and ensure the optimal angular position relative to surface flow lines of this channel, which allows to maximize the efficiency of the aft planing surface 113 and this way to maximize the efficiency of this hydrodynamic system and the boat 101 in general for the case of relatively high Froude numbers and relatively short distance between the planing surfaces 105 and 113, which combination of the above parameters should be characteristic of most planing boats when using the hydrodynamic planing system of this invention.

[0250] FIG. 2 depicts a schematic diagram illustrating the front elevation view of a boat according to some embodiments and corresponding basically to the embodiment shown in the FIG. 1, where a boat 101 with its center, plane keel line 102 and chines 103 is provided with two successively arranged at relatively short lengthwise distance cambered planing surfaces 105 and 113 including: the forward planing surface 105 with its width 201, leading edges 106, trailing edges 107 and the angle of deadrise 202, and the aft planing surface 113 with its leading edges 114, trailing edges 115, the width 203 and the angle of deadrise 204.

[0251] Providing the required lift and high hydrodynamic efficiency (the ratio of lift to hydrodynamic drag) over a wide range of speeds using the example of the forward cambered planing surface 105 of this embodiment involves endowing this surface with a large relative camber when operating a full area at low speeds, and a shallow relative camber with reduced (contracted to the keel line 102) wetted surface at high speeds. For this purpose, the relative camber (which in this case for each section is characterized by the chord of the chambered profile and the protrusion of the trailing edge 107 down from the base plane coinciding with the leading edge 106) should increase from the keel line 102 to the chines 103.

[0252] In the embodiment shown in FIG. 2, the downward protrusion of the trailing edge 107 decreases somewhat linearly from the keel line 102 to the chines 103, but not to the same and much lesser extent than the chords of the forward surface 105 decrease to the tips along the span, which results in a gradual increase in the relative camber from the keel line 102 to the chines 103 and, accordingly, the ability for the forward surface 105 to operate effectively over a wide range of speeds.

[0253] During motion at operational speed at relatively high Froude numbers the forward planing surface 105 of the boat 101 generates a deformation of the water surface in the form of a substantially V-shaped wave trough, which under the circumstances (high Froude number and short distance between the forward and aft planing surfaces) determines the operation of the aft surface in the descending part of the wave trough.

[0254] In order to reduce hydrodynamic resistance and improve efficiency of the hydrodynamic system comprising the two successive planing surfaces 105 and 113, as well as the efficiency of the boat 101 in general, the aft planing surface 113 configured to conform to the relief of the wave trough by means of lowering (in each vertical longitudinal plane) the leading edges 114 below the hydrodynamic base lines of the forward surface 105 by the distance between the base lines of the forward surface 105 and the surface of the wave trough at the location of the leading edges 114 (along with the corresponding the flow changes in the installation angles of the vertical longitudinal sections of the aft surface 113 relative the base lines of the forward surface 105, not shown in this front elevation view diagram).

[0255] As applied to the exemplary keel and center plane section of the aft planing surface 113, this means that, following the configuration of FIG. 1, the keel section is to be lowered by the distance 122 corresponding to the depth of the wave through relatively the base line of the keel section of the forward surface 105 at the location of the center plane point of the leading edges 114.

[0256] Fulfillment of the conditions of the present invention for the optimal vertical locations of sections of the aft surface 113 along its entire span in the embodiment under consideration results in a design when the deadrise angle 204 of the aft surface 113 is to be greater than the deadrise angle 202 of the forward surface 105.

[0257] Another additional condition for ensuring high efficiency of the hydrodynamic system according to this invention is the need for the aft surface 113 to avoid getting into the area of disturbances generated by the tip vortices of the forward surface 105 and to fit into the central part of the wave trough, which condition determines the width 203 of the aft surface 113 is to be smaller than the width 201 of the forward surface 105, so that the width 203 was no more than 0.9 of the width 201.

[0258] The above described configuration and spatial position make it possible to optimally arrange the aft planing surface 113 conformably the surface of the wave trough generated by the forward planing surface 105, which arrangement maximizes the efficiency of the aft planing surface 113 and this way ensures the ultimate efficiency of the hydrodynamic system according this invention and the boat 101 in general.

[0259] FIG. 3 depicts a schematic diagram illustrating the bottom plan view of a boat according to some embodiments, where the boat 101 with its center plane keel line 102, chines 103 and inclined transom 104, is provided with a hydrodynamic system according to this invention including two successively arranged dihedral cambered planing surfaces 105 and 113 being hatched in this diagram to indicate the ultimate operational wetted area corresponding the maximum hydrodynamic efficiency, and comprising: the swept back forward planing surface 105 with its width 201, leading edges 106 and trailing edges 107, and the aft planing surface 113 with its leading edges 114, trailing edges 115 coinciding with low edges of the transom 104 and the width 203. During motion at operational speed the forward planing surface 105, as a dynamic lift surface, generates a deformation of the water surface in the form of a substantially V-shaped wave trough extending downstream and determining the operational conditions for the aft surface 113.

[0260] In order to reduce hydrodynamic resistance and improve efficiency of the hydrodynamic system comprising the two successive planing surfaces 105 and 113, as well as the efficiency of the boat 101 in general, the aft planing surface 113 configured to conform to the relief of the wave trough, which special configuration presupposes specific spatial and angular position relatively the forward planing surface 105 (represented by hydrodynamic base lines of sections by vertical longitudinal planes), higher angle of deadrise in comparison with the forward planing surfaces 105, and, in particular, that the width 203 of the aft planing surface 113 is smaller than the width 201 of the forward planing surfaces 105, so that the width 203 constitutes not more than 0.9 of the width 201.

[0261] The above described configuration makes it possible to optimally arrange the aft planing surface 113 in the V-shaped channel of the wave trough, which allows to maximize the efficiency of the aft planing surface 113 and this way to maximize the efficiency of this hydrodynamic system comprising the two successively arranged cambered planing surfaces 105 and 113 and the boat 101 in general.

[0262] FIG. 4 depicts a schematic diagram illustrating the side elevation view of a boat according to some embodiments, where the boat 101 moves at operational speed at relatively low Froude numbers along the undisturbed water surface W in the direction F.

[0263] In this embodiment the boat 101 with its center plane keel line 102, chines 103 (only port side chine is visible on this elevation) and transom 104, is provided with a hydrodynamic system of two successively arranged dihedral cambered planing surfaces, while the interconnected operation of these two planing surfaces as components of the hydrodynamic system is shown and considered as applied to their center plane keel sections as a sample.

[0264] Said hydrodynamic system comprises:

[0265] a forward planing surface 105 with its half-planes swept back relatively the keel line of its dihedral and the center plane of the hydrodynamic system coinciding with the boat's center plane keel line 102 and represented by swept back leading edges 106 and swept back trailing edges 107 (only port side edges are visible on this elevation), cambered profile of the center plane section 108 with its chord 109 and hydrodynamic base line 110 of the center plane section 108, determining the angle of incidence 111 of said center plane section 108 relatively the level of the undisturbed water surface W, and the tip profiled cambered section 112 coinciding in this embodiment with the chine 103,

[0266] and, located at relatively long distance downstream from the forward planing surface 105, an aft planing surface 113 with its half-planes determined by the center plane of the hydrodynamic system coinciding with the center plane and keel line of the boat 101, which half-planes are represented by leading edges 114 and trailing edges 115 coinciding in this embodiment with the transom 104, cambered profile of the center plane section 116 with its chord 117 and hydrodynamic base line 118, determining the angle of incidence 119 of the center plane section 116 relatively the local surface of water corresponding to the center plane flow line 120 of the wave trough generated by the forward planing surface 105, and the tip profiled cambered section 121.

[0267] The aft planing surface 113 supposed to maintain the required position in the vertical direction to ensure the correct trim position of the boat 101 and, accordingly, the required angle of incidence 111 of the forward surface 105, and also maintain the required angle of incidence 119 relative the local surface of water to generate the required lift, and in this sense, the spatial (i.e., vertical at the set longitudinal point) and angular position of the aft planing surface 113 should correspond to the local flow 120.

[0268] This embodiment corresponds to the boat 101 featuring a combination of relatively low Froude number and relatively long distance between the planing surfaces 105 and 113, which results in operation of the aft surface 113 on the ascending section of the wave disturbance generated by the forward surface 105 in the form of the wave trough and represented by the center plane flow line 120.

[0269] In order to reduce hydrodynamic resistance and improve efficiency of the hydrodynamic system comprising the two planing surfaces 105 and 113, as well as the efficiency of the boat 101 in general, the aft planing surface 113 configured relatively the forward surface 105 to conform to the relief of the wave trough generated by the forward surface 105 by the following means: [0270] 1. Positioning vertical longitudinal sections of the aft planing surface 113 above the base lines of the forward surface 105 by the vertical distances corresponding to the rise of the surface of the wave trough above the base lines of the forward surface at the location of the aft surface.

[0271] As applied to the exemplary keel and center plane section 116 of the aft planing surface 113, this means that the center plane section 116 is to be positioned above the hydrodynamic base line 110 by the distance 122 corresponding to the rise of the wave through represented by the center plane flow line 120, measured from the hydrodynamic base plane 110 at the location of the center plane point of the leading edge 114 of the aft planing surface 113.

[0272] Alternatively, the optimal vertical position 122 can be defined as the distance between the leading edges of planing surfaces 105 and 113 times the tangent of the angle of incidence 111 (which product gives a positive value) plus the offset of the wave trough (with its sign) at the location of the aft surface measured from the undisturbed water surface W. [0273] 2. Turning the vertical longitudinal sections of the aft planing surface 113 (represented by their hydrodynamic base lines) by negative (turned counterclockwise in the port side view of this diagram) nose-dive angles being equal to sums of the angles of slope of the wave trough at the position of sections of the aft surface and the differences between the angles of incidence of the sections of the aft and forward surfaces relative their local surfaces of water.

[0274] As applied to the exemplary keel and center plane section 116 of the aft planing surface 113, this means that the hydrodynamic base plane 118 of the center plane section 116 is to be turned counterclockwise (in the port side view of this diagram) by a negative (nose-dive) angle 123 relatively the hydrodynamic base plane 110 of the keel section 108 of the forward planing surface 105, which angle 123 corresponds to the sum of a negative angle of inclination 124 of the flow of the wave trough represented by the center plane flow line 120 at the location the center plane point of leading edge 114 of the aft planing surface 113 to the undisturbed water surface W, and the difference between the positive angle of incidence 119 of the center plane section 116 of the aft surface 113 relative the surface of the wave trough and the positive angle of incidence 111 of the center plane section 108 of the forward surface 105 relative the undisturbed surface of water W.

[0275] The above described spatial and angular arrangement of the aft planing surface 113 relatively the forward planing surface 105 (represented by the relative angular positions of their hydrodynamic base lines and the spatial positions of the leading edges of the aft planing surface 113 relatively the hydrodynamic base lines of the forward planing surface 105) makes it possible for the aft planing surface 113 to fit optimally the ascending continuation of the wave disturbance generated by the forward surface 105 in the form of the wave trough, in order to maximize the efficiency of the aft planing surface 113 through providing the optimal positions of sections of the aft planing surface 113 relative to the surface flow lines of the wave slope, which arrangement ensures the ultimate efficiency of this hydrodynamic system and the boat 101 in general in comparison with any other ways of arrangement of two successive planing surfaces. FIG. 5 depicts a schematic diagram illustrating the transom elevation view of a boat according to some embodiments and corresponding basically to the embodiment shown in the FIG. 4, where a boat 101 with its center plane keel line 102 and chines 103 is provided with two successively arranged cambered planing surfaces comprising: the forward planing surface with its width 201, leading edges 106 (invisible in this projection and conditionally shown in dotted lines) and trailing edges 107, and, located substantially further downstream relatively the forward surface, the aft planing surface with its leading edges 114, trailing edges 115 and the width 203.

[0276] During motion at operational speed the forward planing surface of the boat 101 generates a wave disturbance and deformation of the water surface in the form of a wave trough generated by the forward planing surface, while, taking into account relatively low Froude numbers of the boat 101 and relatively long distance between the forward and aft planing surfaces, the aft planing surface locates at the ascending part of the wave disturbance, which position determines its configuration and spatial-angular arrangement relatively the forward planing surface.

[0277] In order to reduce hydrodynamic resistance and improve efficiency of the hydrodynamic system comprising the two successive planing surfaces, as well as the efficiency of the boat 101 in general, the aft planing surface is configured to conform to the relief of the wave trough within the range of ascending flow by means of certain spatial and angular arrangement of the two planing surfaces comprising: shifting the sections of the aft planing surface up and above the base lines of the sections of the forward surface by the rise of wave disturbance above said base lines of the sections of the forward surface, and turning the base lines of the sections of the aft surface relatively the base lines of the sections of the forward surface by angles being equal to sums of the angles of slope of the wave trough at the position of sections of the aft surface and the differences between the angles of incidence of the sections of the aft and forward surfaces relative their local surfaces of water.

[0278] As applied to the exemplary keel and center plane section of the aft planing surface, this means that the central plane point of the leading edges 114 raised above the base line of the keel section of the forward surface by the distance 122 corresponding to the rise of the surface of the wave through measured from the hydrodynamic base plane of the forward surface at the location of leading edges 114, and the base line of said keel and center plane section of the aft planing surface is turned nose-dive relatively the base line of the keel section of the forward surface by an additional angle being equal to the angle of the slope of the ascending part of the wave disturbance generated by the forward surface in the form of the wave trough, while to fit only the central portion of the wave disturbance the width 203 of the aft planing surface is made smaller than the width 201 of the forward planing surface.

[0279] The above described spatial and angular arrangement of the aft planing surface relatively the forward planing surface makes it possible for the aft planing surface to fit optimally the ascending continuation of the wave disturbance generated by the forward surface in the form of the wave trough, in order to maximize the efficiency of the aft planing surface and this way to maximize the efficiency of this hydrodynamic system comprising the two successively arranged cambered planing surfaces and the boat 101 in general.

[0280] FIG. 6 depicts a schematic diagram illustrating the front elevation view of a boat according to some embodiments, where a boat 101 with its center plane keel line 102 and chines 103 is provided with a hydrodynamic system of two successively arranged cambered planing surfaces following provisions of this invention and comprising: the forward planing surface 105 with its leading edges 106 and trailing edges 107, and the aft planing surface 113 with its leading edges 114, trailing edges 115 and a width being smaller than the width of the forward planing surface 105 in order to fit the central channel of the wave trough generated by the forward planing surfaces 105, while the assumed relatively high Froude numbers of the boat 101 and relatively short distance between the two planing surfaces 105 and 113 presuppose operation of the aft surface 113 at the descending section of the wave trough generated by the forward surface 105, which results in the shown lower position of the aft surface 113 and higher angle of deadrise of the aft surface 113 in comparison with the angle of deadrise of the forward planing surface 105.

[0281] In this embodiment the forward planing surface 105 extends beyond the width of the chines 103 by means of the outside protrusions 601 located at the intersections of the planing surface 105 with the chines 103, and the outside extremities of both planing surfaces 105 and 113 provided with end deflectors 602 and 603 protruding below the profiled camber of the tip sections of said planing surfaces 105 and 113.

[0282] Protrusions 601, which bottom surfaces represent profiled continuations of the planing surface 105 outside the chines 103, enable to provide the planing surface 105 with additional width keeping the width of chines and the basic overall configuration and dimensions of the hull of the boat 101 unchanged that ensures higher aspect ratio and higher efficiency of the planing surface 105 as well as the boat 101 in general.

[0283] Arrangement of the deflectors 602 and 603 on outside tips of the planing surfaces 105 and 113 results in higher dynamic pressures at the peripheral sections of the planing surfaces 105 and 113, and a decrease in the intensity of the tip vortices, which in turn results in an increase in lift, a decrease in inductive resistance and an increase in the efficiency of the planing surfaces 105 and 113 that is equivalent to increasing the aspect ratio of the planing surfaces 105 and 113, but without any further increasing of their widths.

[0284] FIG. 7 depicts a schematic diagram illustrating the side elevation view of a boat according to some embodiments, where a boat 101 with its center plane keel line 102, chines 103 (only port side chine is visible on this elevation) and transom 104, is provided with two successively arranged cambered planing surfaces following provisions of this invention and comprising: the swept back relatively the keel line 102 forward planing surface 105 with its swept back leading edges 106 and swept back trailing edges 107 (only port side edges are visible on this elevation), and the aft planing surface 113 with its leading edges 114 and trailing edges 115 coinciding in this embodiment with the transom 104.

[0285] The assumed relatively high Froude numbers of the boat 101 and relatively short distance between the two planing surfaces 105 and 113 presuppose operation of the aft surface 113 at the descending section of the wave trough generated by the forward surface 105, which results in the shown lower position of the aft surface 113.

[0286] The forward planing surface 105 extends beyond the width of the chines 103 by means of the outside protrusions 601 located at the intersections of the planing surface 105 with the chines 103, where the conditional line of contact of the chine 103 with protrusion 601 is indicated by the dotted line 701, while of the outside protrusions 601 are provided with streamlined convex upper surfaces 702, and the outside extremities of both planing surfaces 105 and 113 are provided with end deflectors 602 and 603 protruding below the profiled camber of the tip sections of said planing surfaces 105 and 113.

[0287] The use of protrusions 601 and deflectors 602 and 603 makes it possible to increase efficiency of the hydrodynamic system and the boat 101 in general, keeping at the same time the width of chines 103, the basic overall configuration and general dimensions of the hull of the boat 101 unchanged.

[0288] The streamlined hydrofoil-like upper surfaces 702 provide protrusions 601 with a structural strength and can be beneficial for the boat 101 in terms of better stability during sharp turns and facilitating the transition to planing mode, while in the principal high-speed planing mode of operation the upper surfaces 702 supposed to stay out of water not interfering operation of the forward surface 105 and not being exposed to the risk of cavitation.

[0289] FIG. 8 is a schematic diagram that illustrates the perspective aft bottom view of a boat provided with the hydrodynamic system of two successively positioned cambered planing surfaces being integrated into boat's bottom according to some embodiments following the provisions of this invention and basically corresponding to the embodiments of the FIG. 6 and FIG. 7.

[0290] In this embodiment the boat 101 with its center plane keel line 102, chines 103 and transom 104, is provided with two successively arranged cambered planing surfaces comprising:

[0291] the swept back relatively the keel line 102 forward planing surface 105 with its swept back leading edges 106, swept back trailing edges 107 and cambered profile of the center plane section 108,

[0292] and, located at the adjacent to transom 104 aft part of the boat's bottom, the aft planing surface 113 with its leading edges 114 and trailing edges 115 coinciding in this embodiment with the lower edges of the transom 104 and cambered profile of the center plane section 116, while the width of the aft planing surface 113 is smaller than the width of the forward planing surface 105 allowing the surface 113 to fit the central channel of the wave trough generated by the forward planing surfaces 105.

[0293] The forward planing surface 105 extends beyond the width of the chines 103 by means of the outside protrusions 601 located at the intersections of the planing surface 105 with the chines 103, while the outside extremities of both planing surfaces 105 and 113 provided with end deflectors 602 and 603 protruding below (upwards in this upside-down position) the profiled camber of the tip sections of said planing surfaces 105 and 113.

[0294] Protrusions 601 representing the profiled continuations of the planing surface 105 outside the chines 103 enable to provide the planing surface 105 with additional width keeping the width of chines and the basic overall configuration and dimensions of the hull of the boat 101 unchanged that ensures higher aspect ratio and higher efficiency of the planing surface 105 as well as the boat 101 in general.

[0295] Arrangement of the deflectors 602 and 603 on outside tips of the planing surfaces 105 and 113 results in higher dynamic pressures at the peripheral sections of the planing surfaces 105 and 113, and a decrease in the intensity of the tip vortices, which in turn results in an increase in lift, a decrease in inductive resistance and an increase in the efficiency of the planing surfaces 105 and 113 that is equivalent to increasing the aspect ratio of the planing surfaces 105 and 113, but without any further increasing of their width.

[0296] The forward planing surface 105 generates a deformation of the water surface and forms the wave trough downstream its trailing edges 107.

[0297] The aft planing surface 113 supposed to keep the required position in vertical direction in order to provide proper position of the boat 101 and accordingly the required angle of incidence of the forward surfaces 105 relatively the undisturbed water surface, and to keep the required angle of incidence relatively the local surface of water in order to generate the required lift, and in these terms the vertical and angular position of the aft planing surface 113 should correspond the local flow.

[0298] This embodiment assumes that the boat 101 features a combination of relatively high Froude number and relatively short distance between the planing surfaces 105 and 113 that result in operation of the aft surface 113 on the descending section of the wave trough.

[0299] In order to reduce hydrodynamic resistance and improve efficiency of the hydrodynamic system comprising the two planing surfaces 105 and 113, as well as the efficiency of the boat 101 in general, the aft planing surface 113 configured relatively the forward surface 105 to conform to the relief of the wave trough generated by the forward surface 105 by the following means: [0300] 1. Positioning vertical longitudinal sections of the aft planing surface 113 below the base lines of the forward surface 105 by the vertical distances corresponding to the depressions of the surface of the wave trough under the base lines of the forward surface 105 at the location of the aft surface 113.

[0301] As applied to the exemplary keel and center plane section 116 of the aft planing surface 113, this means that the center plane section 116 is to be positioned below the hydrodynamic base line of the center plane section 108 of the forward planing surface 105 by the distance corresponding to the depth of the wave through, measured from the hydrodynamic base line of the section 108 at the location of the center plane point of the leading edge 114 of the aft planing surface 113. [0302] 2. Turning the vertical longitudinal sections of the aft planing surface 113 (represented by their hydrodynamic base lines) by positive angles being equal to sums of the angles of slope of the wave trough at the position of sections of the aft surface 113 and the differences between the angles of incidence of the sections of the aft and forward surfaces relative their local surfaces of water.

[0303] As applied to the exemplary keel and center plane section 116 of the aft planing surface 113, this means that the hydrodynamic base line of the center plane section 116 is to be turned by a positive angle relatively the hydrodynamic base line of the center plane section 108 of the forward planing surface 105, which angle corresponds to the sum of a positive angle of inclination of the flow of the wave trough at the location the center plane point of leading edge 114 of the aft planing surface 113 to the undisturbed water surface, and the difference between the positive angle of incidence of the center plane section 116 of the aft surface 113 relative the surface of the wave trough and the positive angle of incidence of the center plane section 108 of the forward surface 105 relative the undisturbed surface of water.

[0304] The above described spatial and angular arrangement of the aft planing surface 113 relatively the forward planing surface 105 (represented by the relative angular positions of their hydrodynamic base lines and the spatial positions of the leading edges 114 of the aft planing surface 113 relatively the hydrodynamic base lines of the forward planing surface 105) makes it possible to optimally spatially arrange the aft planing surface 113 in the descending section of the substantially V-shaped channel of the wave trough and ensure the optimal angular position relative to surface flow lines of this channel, which allows to maximize the efficiency of the aft planing surface 113 and this way to maximize the efficiency of this hydrodynamic system and the boat 101 in general for the case of relatively high Froude numbers and relatively short distance between the planing surfaces 105 and 113, which combination of the above parameters should be characteristic of most planing boats when using the hydrodynamic planing system of this invention.

[0305] The boat's bottom of this embodiment provided also with ventilation opening 801 supplying atmospheric air (from intakes arranged above water level) to the area behind the swept back step formed by the trailing edges 107 of the forward planing surface 105.

[0306] Supply of atmospheric air to this area could be favorable to prevent formation of negative pressure zone that could be developed behind the swept back step when under motion this part of the boat's bottom happens to be completely submerged in water and supply of atmospheric air from chines is blocked:during motion at below planing speeds, acceleration in transitional to planing mode of motion, as a result of wave impact, etc.that leads to increased hydrodynamic resistance and deterioration of acceleration, seaworthiness and efficiency characteristics of the boat 101.

[0307] So, equalization of the pressure and preventing the formation of negative pressure zones by the natural supply of atmospheric air through ventilation opening 801 favorably affects operational properties of the boat 101.

[0308] FIG. 9 depicts a schematic diagram illustrating the front elevation view of a boat according to some embodiments, where a boat 101 with its keel line 102 and chines 103 provided with two successively arranged cambered planing surfaces following the provisions of this invention and comprising: a dihedral forward cambered planing surface 105 with its trailing edges 107 and tip deflectors 602, and a dihedral aft planing surface 113 with its trailing edges 115 and tip deflectors 603.

[0309] The forward planing surface 105 is made in a form of a plane being separated from the bottom of the boat 101, is provided with the streamlined convex upper surface 901 and is mounted on the bottom by means of the keel strut/flange 902, while the aft planing surface 113 is not separated, but integrated into the aft part of the bottom of the boat 101.

[0310] Through separating the forward planing surface 105 from the bottom of the boat 101 the bottom surfaces of the boat 101 at its bow part can be made with much higher angle of deadrise indicated by dotted lines 903 and this way ensure much sharper entry to pierce waves that considerably upgrades seaworthiness of the boat 101 not sacrificing lift and hydrodynamic efficiency (which guaranteed by the optimum configuration and the optimum spatial-angular relative arrangement of the cambered planing surfaces 105 and 113 according to the hydrodynamic design of this invention).

[0311] The streamlined convex upper surface 901 being similar to the upper surfaces of hydrofoils provide the separated design of planing surface 105 with additional strength and additional lift during acceleration in transitional mode of motion (from floating displacement mode to purely planing mode as far as the upper surface 901 of the plane 105 is still submerged), while during motion at operational speed in the purely planing mode said streamlined convex upper surface 901 will be excluded from generation of lift:it will be positioned above the level of water, will not contact the water (washed only by air and without any risk of cavitation) and will not affect operation of the planing surfaces 105 and 113.

[0312] The aft planing surface 113 in this embodiment does not require manufacturing as a separate unit and in the case of use of composite structural material (fiber reinforced plastics, e.g.) can be laminated altogether as one piece with the hull of the boat 101.

[0313] FIG. 10 depicts a schematic diagram illustrating the side elevation view of a boat according to some embodiments, where a boat 101 with its center plane continuous and unbroken keel line 102, chines 103 (only port side chine is visible on this elevation) and transom 104, is provided with two successively arranged cambered planing surfaces following the provisions of this invention and comprising: the swept back relatively the keel line 102 forward planing surface 105 with its swept back leading edges 106 and swept back trailing edges 107 (only port side edges are visible on this elevation), tip deflectors 602 and cambered profile of the center plane section 108 with hydrodynamic base line 110, and the aft planing surface 113 with its leading edges 114 and trailing edges 115 coinciding in this embodiment with the transom 104, tip deflectors 603 and cambered profile of the center plane section 116 with its hydrodynamic base line 118.

[0314] The assumed relatively high Froude numbers of the boat 101 and relatively short distance between the two planing surfaces 105 and 113 presuppose operation of the aft surface 113 at the descending part of the wave trough generated by the forward surface 105, which results in the required position of sections of the aft surface 113 below the base lines of the forward surface 105, while the base lines of these sections should be inclined at some positive angle relatively the base lines of the forward surface 105.

[0315] In this embodiment the forward planing surfaces 105 is made in a form of a plane being separated from the bottom of the boat 101, mounted on the bottom by means of the strut/flange 902 at some negative (nose-dive) angle of incidence relatively the keel line 102 and provided with the streamlined convex upper surfaces 901, while the aft planing surface 113 is not separated, but integrated into the aft part of the bottom of the boat 101, so that, as applied to the exemplary keel and center plane section 116, the hydrodynamic base line 118 of the center plane section 116 of the aft planing surface 113 coincides with the keel line 102.

[0316] Thus, following the provisions of the present invention for the case of the shown embodiment, in order to reduce hydrodynamic resistance and improve efficiency of the hydrodynamic system comprising the two planing surfaces 105 and 113, as well as the efficiency of the boat 101 in general, the hydrodynamic system comprising the forward planing surface 105 and the aft planing surface 113 configured the following way: [0317] 1. Vertical longitudinal sections (represented by their base lines) of the separated forward planing surfaces 105 should be turned nose-dive (counterclockwise in the port side view of this diagram) relatively the keel line 102 by positive angles being equal to sums of the positive angles of slope of the wave trough at the position of corresponding sections (lying within the same longitudinal vertical plane) of the integrated aft surface 113 and the differences between the non-negative angles of incidence of the sections of the aft 113 and forward 105 surfaces relative their local surfaces of water, which arrangement ensures the angular position of base lines (and, so, sections) of the integrated aft surface 113 relatively the base lines (and, so, sections) of the separated forward surface 105 required by provisions of this invention.

[0318] The above requirement in this case, as applied to the exemplary keel and center plane sections 108 and 116 of the planing surfaces 105 and 113 correspondingly, means that the hydrodynamic base line 110 of the center plane section 108 of the separated forward surface 105 should be inclined relatively the keel line 102 (and so, correspondingly, to the base line 118) by the negative angle 123, which absolute value is equal to the sum of the positive angle of inclination of the surface of the wave trough at the location the center plane point of the leading edges 114 of the aft planing surface 113 to the undisturbed water surface, and the difference between the non-negative angle of incidence of the center plane section 116 (represented by the base line 118) of the aft surface 113 relative the surface of the wave trough and the non-negative angle of incidence of the center plane section 108 (represented by the base line 110) of the forward surface 105 relative the undisturbed surface of water. [0319] 2. Vertical longitudinal sections of the aft planing surface 113 should be positioned vertically below the base lines of sections of the forward surface 105 by the distances corresponding to depths of depression of the surface of the wave trough under the base lines of sections of the forward surface 105 at the location of the aft surface 113.

[0320] The above requirement in this case, as applied to the exemplary keel and center plane section 116 of the aft planing surface 113, means that the inclination of the hydrodynamic base line 110 of the center plane section 108 of the separated forward surface 105 by the angle 123 relatively the keel line 102 should ensure positioning of the center plane section 116 (determined by the center plane point of the leading edges 114) below the hydrodynamic base line 110 by the distance 122 (i.e., the depth of depression of the surface of the wave trough under the base line 110 at the location of the aft surface 113), which arrangement meets the provisions of the present invention.

[0321] Through separation of the forward planing surfaces 105 from the bottom of the boat 101 the bottom surfaces of the boat 101 at its bow part can be made with much higher angle of deadrise and this way ensure much sharper entry to pierce waves that considerably upgrades seaworthiness of the boat not sacrificing lift and hydrodynamic efficiency (which guaranteed by the optimum configuration and the optimum spatial-angular relative arrangement of the cambered planing surfaces 105 and 113 according to the hydrodynamic design of this invention).

[0322] The streamlined convex upper surfaces 901 being similar to upper surfaces of hydrofoils provide the separated design of planing surface 105 with additional strength and additional lift during acceleration in transitional mode of motion (from floating displacement mode to purely planing mode, as far as the planes are still submerged), while during motion at operational speed in the purely planing mode said streamlined convex upper surfaces will be excluded from generation of lift:they will be positioned above the level of water, will not contact the water (washed only by air and without any risk of cavitation) and will not affect operation of the planing surfaces 105 and 113.

[0323] The aft planing surface 113 in this embodiment does not require manufacturing as a separate unit and in the case of use of composite structural material (fiber reinforced plastics, e.g.) can be laminated altogether as one piece with the hull of the boat 101.

[0324] The above described configuration and spatial-angular relative positioning of the separated forward planing surface 105 and the integrated aft planing surface 113 ensure optimal arrangement of the aft planing surface 113 being conformable to the relief of the wave trough generated by the forward planing surface 105, and this way maximize the efficiency of the aft planing surface 113, the efficiency of the hydrodynamic system according this invention and the boat 101 in general.

[0325] FIG. 11 depicts a schematic diagram illustrating the aft elevation view of a boat according to some embodiments, where a boat 101 with its keel line 102 and chines 103 provided with a hydrodynamic system of two successively arranged cambered planing surfaces following the provisions of this invention and comprising: the forward planing surfaces 105 with its trailing edges 107 and tip deflectors 602, and the aft planing surface 113 with its trailing edges 115, tip deflectors 603 and a width being smaller than the width of the forward planing surface 105 in order to fit the central channel of the wave trough generated by the forward planing surfaces 105, while the assumed relatively high Froude numbers of the boat 101 and relatively short distance between the two planing surfaces 105 and 113 presuppose operation of the aft surface 113 at the descending part of the wave trough generated by the forward surface 105, which results in the higher angle of deadrise of the aft surface 113 in comparison with the angle of deadrise of the forward planing surface 105.

[0326] In this embodiment both the forward planing surface 105 and the aft planing surface 113 are made in a form of planes being separated from the bottom of the boat 101, mounted on the bottom by means of the keel strut/flanges 902, supported by struts 1101 and 1102, and provided with the streamlined convex upper surfaces 901 and 1103 correspondingly.

[0327] Through separating the planing surfaces 105 and 113 from the bottom of the boat 101 the bottom surfaces of the boat 101 can be provided with much higher angle of deadrise all through the whole length of the bottom and this way ensure much sharper shape of the bottom in order to facilitate piercing the waves that considerably upgrades seaworthiness of the boat not sacrificing lift and hydrodynamic efficiency (which guaranteed by the optimum configuration and the optimum spatial-angular relative arrangement of the cambered planing surfaces 105 and 113 according to the hydrodynamic design of this invention).

[0328] The streamlined convex upper surfaces 901 and 1103 being similar to upper surfaces of hydrofoils provide the separated designs of planing surfaces 105 and 113 with additional strength and additional lift during acceleration in transitional mode of motion (from floating displacement mode to purely planing mode as far as the planes are still submerged), while during motion at operational speed in the purely planing mode said streamlined convex upper surfaces will be excluded from generation of lift:they will be positioned above the level of water, will not contact the water (washed only by air and without any risk of cavitation) and will not affect operation of the planing surfaces 105 and 113.

[0329] The designation 1-1 indicates the position of the along the flow section of the separated plane of the planing surface 105.

[0330] FIG. 12 depicts a schematic diagram illustrating one of possible embodiments of the along the flow section of the separated from the bottom plane comprising the forward planing surface 105 and corresponding to the designation 1-1 of the embodiment of the FIG. 11.

[0331] In this drawing, the bottom surface of the plane, which extends from the leading edge of the plane 1201 up to the trailing edge 1202, is provided in its aft part with concaved portion representing the cambered-profiled planing surface 105, so that the trailing edge of the planing surface 105 coincides with the trailing edge of the plane 1202.

[0332] As one of embodiments, the profiled planing surface 105 can reproduce a camber based on the Virgil Johnson three-term curve that was successfully applied in the past to planing surfaces of real boats.

[0333] In operational mode of motion the cambered planing surface 105 skims along the surface of water and generates dynamic lift that supports the boat, while the planing surface 105 is the only surface of this section that supposed to contact the water at the operational speed of motion. Thus, basically, to fulfill its duty of dynamic support of the boat at the operational speed the lifting surface of this section should be limited by the bottom surface 105.

[0334] In this embodiment the plane in its bottom part is provided also with a flat plate (a straight line in this sectional view) 1203 located between the leading edge of the plane 1201 and the leading edge 106 of the profiled part of bottom corresponding to the cambered planing surface 105, which supplementing plate 1203 can be useful to facilitate transitional modes of boat's operation and expand the range of speeds of pure planing, while in some embodiments like shown in the FIG. 12 said flat plate 1203 may coincide with hydrodynamic base line of the cambered profiled portion 105.

[0335] The embodiment shown in the FIG. 12 features also the streamlined convex upper surface 901 being similar to upper surfaces of hydrofoils.

[0336] Providing the shown embodiment with the streamlined convex upper surface 901 produces a double positive effect: [0337] 1. At moderate speed of the boat corresponding transitional mode of motion (from floating displacement mode to purely planing mode) when the separated planing surfaces supposed to be completely submerged in water, the upper streamlined convex surface 901 stays in contact with water and generates negative pressure resulting in additional hydrodynamic lift the same way as upper convex surfaces of hydrofoils that facilitates acceleration and take off of the boat up to the transition to the purely planing mode. During motion at the operational speed in the purely planing mode said streamlined convex upper surface 901 will be excluded from generation of lift:It will be positioned above the level of water, will not contact the water (washed only by air and without any risk of cavitation) and will not affect operation of the planing surfaces. [0338] 2. Providing the separated planing surfaces with the streamlined convex upper surfaces 901 makes them structurally stronger: The streamlined convex upper surface 901 increases the structural height of the section (in fact without increase in the drag) and, correspondingly, the moment of inertia and the moment of structural resistance of the section of planing surface that reduces bending stresses in the material of the separated planing surfaces.

[0339] FIG. 13 depicts a schematic diagram illustrating the front elevation view of a boat of catamaran configuration according to some embodiments following provisions of this invention, where the boat 101 comprises two hulls 1301 and separated from the hulls 1301 cambered planing surfaces 105 and 113 provided with convex upper surfaces 901 and 1103, and end deflectors 602 and 603.

[0340] Said separated forward 105 and aft 113 planing surfaces are arranged under and fastened to bottoms of the forward and aft portions of catamaran hulls 1301 correspondingly and additionally supported by struts 1302 at the center plane.

[0341] The assumed relatively high Froude numbers of the catamaran boat 101 and relatively short distance between the two planing surfaces 105 and 113 presuppose operation of the aft surface 113 at the descending part of the wave trough generated by the forward surface 105, which results in the higher angle of deadrise of the aft surface 113 in comparison with the angle of deadrise of the forward planing surface 105 and a smaller width of the aft surface 113 in comparison with the width of the forward planing surface 105 in order to ensure that the aft surface 113 fits the central undisturbed channel of the wave trough generated by the forward planing surfaces 105.

[0342] In the displacement mode and at low speed of motion the boat 101 is supported predominantly by Archimedean forces of hulls 1301, which keep the boat 101 floating at the water line W.

[0343] At higher speed of motion corresponding to the transitional mode, the separated cambered planing surfaces 105 and 113 generate some dynamic lift assisted by the lift produced by their convex upper surfaces 901 and 1103.

[0344] At the principal high-speed operational mode of motion the hulls 1301 as well as the convex upper surfaces 901 and 1103 are positioned above the water level and the boat 101 is supported exclusively by the dynamic lift generated by the cambered planing surfaces 105 and 113 arranged spatially and angularly relatively each other following the provisions of hydrodynamic design of the present invention, so that sections of the aft surface 113 are positioned below the hydrodynamic base lines of corresponding sections of the forward planing surface 105, and the hydrodynamic base lines of sections of the aft surface 113 are turned relatively the hydrodynamic base lines of corresponding sections of the forward planing surface 105 by some positive angle, which parameters of spatial and angular arrangements are determined by the parameters of depression of water surface generated by the forward surface 105.

[0345] This way the considered hydrodynamic system exploits the effect of the aft planing surface 113 being conformably arranged within the substantially V-shaped wave trough generated by the forward planing surface 105 that ensures high hydrodynamic efficiency of this system as well as the boat 101 in general.

[0346] Separation of the dynamic support function and endowing it with only planing surfaces 105 and 113 makes it possible to provide the hulls 1301 with very sharp formations that mitigate wave impacts and favorably affect the seaworthiness of the catamaran boat 101.

[0347] FIG. 14 depicts a schematic diagram illustrating the front elevation view of a boat according to some embodiments, where a boat 101 with its chines 103 provided with a hydrodynamic system following provisions of this invention and comprising two successively arranged cambered planing surfaces, of which only one separated from the bottom forward planing surface 105 provided with the streamlined convex upper surface 901 is shown.

[0348] In this embodiment the separated forward planing surface 105 is made foldable and shown in the unfolded position, while the bottom part of the boat 101 is provided with the recess niches 1401 (shown in a conditional break in the diagram), into which the forward planing surface 105 can be retracted.

[0349] The forward planing surface 105 is divided into two half-planes attached at their inner ends to the central hinge 1402 mounted at the keel of the boat's hull, so that the half-planes are independently pivotable upward around the longitudinal axis of this hinge 1402.

[0350] The outer ends of said half-planes are supported by rockable struts 1403 rotatably connected at their lower ends to said half-planes by the hinges 1404 with longitudinal axes of rotation.

[0351] The upper ends of said rockable struts 1403 are provided with the hinges 1405 similarly rotatable around the longitudinal axes of rotation, which hinges 1405 can be driven by, e.g., electro-hydraulic actuators or electric linear screw actuators (not shown in this diagram) and can slide along guides 1406 upward.

[0352] Thus, if the vertical push of the actuators moves the upper hinges 1405 up along the guides 1406 and raises the rockable struts 1403 (with some rotation relative to the longitudinal axes) and correspondingly moves up the lower hinges 1404, the half-planes of the surface 105 will rotate on the central hinge 1402 upward around the longitudinal axis of this hinge 1402 and will enter the recess niches 1401 so as not to protrude from the bottom and be flush with the bottom surfaces.

[0353] This way the shown in FIG. 14 embodiment with foldable/retractable separated planes can substantially facilitate operation in shallow water in displacement mode, lifting the boat with a crane, pulling the boat 101 ashore, and make the boat 101 trailerable, without exposing the risk of damage to the separated planes.

[0354] FIG. 15 depicts a schematic diagram illustrating the front elevation view of a boat according to some embodiments and corresponding basically to the embodiment shown in the FIG. 14, where a boat 101 with its chines 103 provided with a hydrodynamic system following provisions of this invention and comprising two successively arranged cambered planing surfaces, of which only one separated from the bottom forward planing surfaces 105 is shown.

[0355] In this embodiment the bottom part of the boat 101 is provided with the recess niches 1401 (shown in a conditional break in the diagram), while the separated forward planing surfaces 105 is made foldable and shown in the folded position being retracted into the recess niches 1401.

[0356] The forward planing surface 105 is divided into two half-planes attached at their inner ends to the central hinge 1402 mounted at the keel of the boat's hull, so that the half-planes are independently pivotable around the longitudinal axis of this hinge 1402.

[0357] The outer ends of said half-planes are supported by rockable struts 1403 rotatably connected at their lower ends to said half-planes by the hinges 1404 with the longitudinal axis of rotation.

[0358] The upper ends of said rockable struts 1403 are provided with the hinges 1405 similarly rotatable around the longitudinal axis of rotation, which hinges 1405 can be driven by, e.g., electro-hydraulic actuators or electric linear screw actuators (not shown in this diagram) and can slide along guides 1406.

[0359] Thus, in this configuration, the actuators have moved the upper hinges 1405 along the guides 1406 to their utmost upper position, which pulled and raised the rockable struts 1403 (with some rotation relative to the longitudinal axes) and moved up the lower hinges 1404. As a result the half-planes of the surface 105 rotated on the central hinge 1402 upward around the longitudinal axis of the hinge 1402 and have come to their uppermost position, entered and snuggled in the recess niches 1401 not protruding from the bottom and being flush with the bottom surfaces.

[0360] This way the shown in FIG. 15 embodiment with the retracted separated planes substantially facilitates operation in shallow water in displacement mode, lifting the boat with a crane, pulling the boat 101 ashore, and makes the boat 101 trailerable, without exposing the risk of damage to the separated planes.

[0361] FIG. 16 depicts a schematic diagram illustrating the side elevation view of a boat according to some embodiments, where a boat 101 with its center plane keel line 102, chines 103 (only port side chine is visible on this elevation) and transom 104, is provided with two successively arranged cambered planing surfaces following the provisions of this invention and comprising: the swept back relatively the keel line 102 forward planing surface 105 with its swept back leading edges 106 and swept back trailing edges 107 (only port side edges are visible on this elevation), cambered profile of the center plane section 108 with hydrodynamic base line 110, and the aft planing surface 113 with its leading edges 114 and trailing edges 115 coinciding in this embodiment with the transom 104, tip deflectors 603 and cambered profile of the center plane section 116 with its hydrodynamic base line 118.

[0362] The assumed relatively high Froude numbers of the boat 101 and relatively short distance between the two planing surfaces 105 and 113 presuppose operation of the aft surface 113 at the descending part of the wave trough generated by the forward surface 105, which results in the required position of sections of the aft surface 113 below the base lines of the forward surface 105, while the base lines of these sections should be inclined at some positive angle relatively the base lines of the forward surface 105.

[0363] In this embodiment the forward planing surfaces 105 is integrated into the forward part of the bottom of the boat 101 and arranged at some negative (nose-dive) angle of incidence relatively the keel line 102, while the aft planing surface 113 is integrated into the aft part of the bottom of the boat 101, so that, as applied to the exemplary keel and center plane section 116, the hydrodynamic base line 118 of the center plane section 116 of the aft planing surface 113 coincides with the keel line 102.

[0364] Thus, following the provisions of the present invention for the case of the shown embodiment, in order to reduce hydrodynamic resistance and improve efficiency of the hydrodynamic system comprising the two planing surfaces 105 and 113, as well as the efficiency of the boat 101 in general, the hydrodynamic system comprising the forward planing surface 105 and the aft planing surface 113 configured the following way: [0365] 1. Vertical longitudinal sections (represented by their base lines) of the forward planing surfaces 105 should be turned nose-dive (counterclockwise in the port side view of this diagram) relatively the keel line 102 by positive angles being equal to sums of the positive angles of slope of the wave trough at the position of corresponding sections (lying within the same longitudinal vertical plane) of the integrated aft surface 113 and the differences between the non-negative angles of incidence of the sections of the aft 113 and forward 105 surfaces relative their local surfaces of water, which arrangement ensures the angular position of base lines (and, so, sections) of the integrated aft surface 113 relatively the base lines (and, so, sections) of the forward surface 105 required by provisions of this invention.

[0366] The above requirement in this case, as applied to the exemplary keel and center plane sections 108 and 116 of the planing surfaces 105 and 113 correspondingly, means that the hydrodynamic base line 110 of the center plane section 108 of the forward surface 105 should be inclined relatively the keel line 102 (and so, correspondingly, to the base line 118) by the negative angle 123, which absolute value is equal to the sum of the positive angle of inclination of the surface of the wave trough at the location the center plane point of the leading edges 114 of the aft planing surface 113 to the undisturbed water surface, and the difference between the non-negative angle of incidence of the center plane section 116 (represented by the base line 118) of the aft surface 113 relative the surface of the wave trough and the non-negative angle of incidence of the center plane section 108 (represented by the base line 110) of the forward surface 105 relative the undisturbed surface of water. [0367] 2. Vertical longitudinal sections of the aft planing surface 113 should be positioned vertically below the base lines of sections of the forward surface 105 by the distances corresponding to depths of depression of the surface of the wave trough under the base lines of sections of the forward surface 105 at the location of the aft surface 113.

[0368] The above requirement in this case, as applied to the exemplary keel and center plane section 116 of the aft planing surface 113, means that the inclination of the hydrodynamic base line 110 of the center plane section 108 of the forward surface 105 by the angle 123 relatively the keel line 102 should ensure positioning of the center plane section 116 (determined by the center plane point of the leading edges 114) below the hydrodynamic base line 110 by the distance 122 (i.e., the depth of depression of the surface of the wave trough under the base line 110 at the location of the aft surface 113), which arrangement meets the provisions of the present invention.

[0369] The above described configuration and spatial-angular relative positioning of the integrated forward planing surface 105 and the aft planing surface 113 ensure optimal arrangement of the aft planing surface 113 being conformable to the relief of the wave trough generated by the forward planing surface 105, and this way maximize the efficiency of the aft planing surface 113, the efficiency of the hydrodynamic system according this invention and the boat 101 in general.

[0370] In this embodiment the forward cambered planing surface 105 in its upstream part is provided with a flat plate 1203 connecting the leading edges 106 of the forward surface 105 with the surfaces of the forward part of the bottom of the boat 101, which plate 1203 coincides with hydrodynamic base lines of the cambered profiles of sections of the forward planing surface 105.

[0371] In the case of use of composite structural material (fiber reinforced plastics, e.g.) both the forward cambered planing surface 105 and the aft cambered planing surface 113 in this embodiment can be laminated altogether as one piece with the hull of the boat 101. The arrangement of this embodiment makes it possible to significantly reduce, or even completely avoid, the protrusion of the cambered planing surfaces downwards from the base plane of the boat coinciding with the keel line 102, which reduces the draft and makes the structure more compact.

[0372] Regarding the manufacturing the hull of the boat by means of lamination in a mold, such configuration can facilitate forming of the bottom surfaces of the boat to reproduce the design of this invention through modification of the original conventional hull design using overlays and inserts on the bottom surfaces of the original mold of the conventional design.

[0373] In this case all the design following this invention can be arranged within the limits of the skin of the original conventional boat not protruding outside its original shape.