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.

Description

References CitedU.S. Patent Documents1,618,995March 1927Plum2,634,698April 1953Becker3,274,966September 1966Rethorst3,547,064December 1970Glass4,058,077November 1977Johansson5,191,853March 1993Adler5,588,389December 1996Carter.8,291,850October 2012Peters8,800,464August 2014Peters8,915,206December 2014Herrington et al.8,950,351February 2015Scism et al.9,242,699January 2016Keller10,189,544January 2019Brizzolara et al.OTHER PUBLICATIONS1. Sighard F. Hoerner, “Fluid-Dynamic Drag”, (1965).2. I. T. Egorov and V. T. Sokolov, “Hydrodynamics of High Speed Vessels”, Sudostroenie, 384 pages, (1965).

[0003] 3. Eugene P. Clement, “The Planing Characteristics of a 15-degree Deadrise Surface with Circular-Arc Camber”, R&D Report 2298, Hydrodynamics Lab., David Taylor Model Basin, Washington D.C., 30 pages, (1966).

[0004] 4. Eugene P. Clement, “How to Design an Efficient Stepped Planing Boat (Dynaplane Boat)”, 65 pages, (2006).FIELD OF THE INVENTION

[0005] The present invention relates to hydrodynamic designs of planing boats or other vehicles employing planing mode of motion with Froude numbers based on displacement (FrD) predominantly about or in excess of 3, and, more specifically, the invention is intended for reduction of hydrodynamic resistance and improvement in efficiency of planing boats by means of special configuration and spatial-angular relative arrangement of two successive planing surfaces with cambered hydrodynamic profile.PRIOR ART

[0006] As the Prior Art of the present invention there should be considered relevant previously developed designs of planing boats, i.e. the boats being supported in motion at operational speed by planing surfaces skimming along the surface of water (in contrast to submerged hydrofoils, e.g.) and generating dynamic lift by means of only positive hydrodynamic pressure on their facing downward wetted surfaces, and featuring positive angles of incidence, when the trailing edges of said wetted surfaces arranged lower than the leading edges of said wetted surfaces relatively the local level of water surface.

[0007] Thus, the field of the Prior Art determines planing boats, in contrast to boats supported by submerged hydrofoils, characterized by two-side lifting surfaces generating dynamic lift predominantly due to low hydrodynamic pressure on the upper surface, which determines their drawbacks such as a limited range of operational speeds caused by cavitation, bulky design, deep draft, limited seaworthiness due to air breakthroughs to the upper low-pressure surface resulting in loss of lift and downfalls with loss of speed in rough seas, which is especially applicable to relatively shallow-draft hydrofoils, or even bulkier design, much deeper draft, lower speed limits due to cavitation and high drag of struts in the case of deeply submerged hydrofoils.

[0008] That is, all those disadvantages that the subject of the present invention—as a planing design—is devoid of.

[0009] Further, the field of this invention relates to hydrodynamic designs of planing boats with dihedral planing surfaces provided with cambered hydrodynamic profiles, which ceteris paribus could ensure much higher hydrodynamic efficiency (characterizing by weight to drag ratio for boats and by lift to drag ratio for planing surfaces, e.g.) than flat non-cambered bottom surfaces of almost all known planing boats, while this superiority can be even greater when using swept back cambered planing surfaces of high aspect ratio.

[0010] Unfortunately, any information about hydrodynamic systems using cambered planing surfaces in the Prior Art is very scarce and, moreover, it could be found, in fact, nothing about the most efficient and also practical hydrodynamic configurations comprising two successively arranged cambered planing surfaces with the forward dihedral swept back planing surface (providing high aspect ratio and maximum efficiency), not to mention the requirements for their optimal relative position, ensuring the greatest hydrodynamic efficiency.

[0011] Successive or sequential arrangement in this case implies that the aft planing surface located in the wake of the forward planing surface and the center planes of these two dihedral planing surfaces coincide.

[0012] At the same time with regard to the use of cambered planing surfaces in the designs of the Prior Art, it should be noted that although their hydrodynamic characteristics can significantly exceed those of flat planing surfaces, it is problematic for a single cambered planing surface on the bottom of the boat to keep the optimal trim angle that can lead to dynamic instability such as porpoising, which questions their direct practical use in this configuration.

[0013] That is, one can hardly expect the full realization of potential efficiency from hydrodynamic designs based on a single cambered planing surface, until such surface alone can adjust and maintain itself in the most favorable in terms of efficiency position relative to the water surface.

[0014] In this regard, it is natural that the cambered planing surfaces of the Prior Art are used in stepped hull designs featuring additional stabilizing aft lifting surface, which fixes the trim angular position of the front cambered planing surfaces relative to the surface of water.

[0015] However, this configuration has an inherent disadvantage resulting in a decrease in hydrodynamic efficiency:

[0016] When skimming along the surface of the water, the forward dihedral planing surface generates a deformation of the water surface featuring, in particular, a depression immediately after and some distance downstream of trailing edges in the form of a shallow substantially V-shaped wave trough characterized by a vertically skewed flow relatively the undisturbed water surface (which later turns into a wave process damping relative to the undisturbed level of the water surface).

[0017] Therefore, in order to develop the necessary lifting force, any lift-generating surface placed aft of the forward surface in the wave trough is be installed at a trim angle, which should take into consideration said skewed flow.

[0018] For the most of known stepped hull boat designs (corresponding to typical boat dimensions and speeds) the skewed flow of the wave trough at the location of the aft lifting surface corresponds to a descending flow and necessitates to install the aft surface at steeper angular position that leads to an increase in the hydrodynamic resistance of the aft surface and a decrease in the hydrodynamic efficiency of this hydrodynamic design and the boat as a whole.

[0019] Consequently, to minimize hydrodynamic resistance and maximize efficiency of the stepped hull designs and, in particular, the designs provided with cambered planing surfaces, it is indispensable to search for ways to enhance efficiency of the aft stabilizing planing surface by means of specific configuration and arrangement.

[0020] In this connection it is impossible to determine the optimal position and configuration of the aft surface, and therefore it is impossible to achieve maximum efficiency of this hydrodynamic system and the boat as a whole, without knowing the relief of the wave trough, which is completely determined by the forward surface (including such parameters as dimensions, relative speed, lift coefficient, aspect ratio) and depends also on the distance between the surfaces.

[0021] Thus, the determination of the optimal configuration of the hydrodynamic system under consideration (guaranteeing maximum efficiency) must necessarily imply the relationship between the forward and aft surfaces, shaping and positioning of the aft surface relative to the forward one (through the parameters of the wave trough) regarding both forward and aft surfaces as a united hydrodynamic complex.

[0022] Accordingly, the claims of many inventions of the Prior Art about the “optimal” position of only one (aft, e.g.) surface, “optimal” design and the achieving “maximum” efficiency” of the stepped hull designs regardless of the interrelation of the two planing surfaces (regardless of the forward surface, e.g.) are meaningless.

[0023] Not to mention the fact that to our best knowledge it is impossible to find patented designs of stepped hulls with two cambered planing surfaces hinting at conformity of the aft surface to the wave trough generated by the forward surface and being dependent on its parameters, which in turn indicates that the claimed designs cannot be optimal and provide the greatest efficiency.

[0024] Therefore, the objective of the present invention is to provide a method and apparatus that could ensure the full realization of the potential capabilities of the hydrodynamic system consisting of two successively arranged cambered planing surfaces, based on the actual mechanics of the operation of such a system, by establishing conditions that ensure the development of the optimal configuration and relative position (both spatial and angular) of the two planing surfaces, which, in turn, should really guarantee the ultimate efficiency of a boat with such a hydrodynamic system.

[0025] Regarding the available design solutions, to provide the necessary stabilization, known hydrodynamic designs of the Prior Art use non-cambered flat bottom surfaces of the after-body of boat's hull, special flat planes and hydrofoils mounted on the transom of boat's hulls.

[0026] As it was mentioned, any flat and non-cambered planing surfaces obviously lose in efficiency to cambered planing surfaces, while hydrofoils have their inherent disadvantages mentioned above including the limited range of operational speeds caused by cavitation.

[0027] The use of super-cavitating hydrofoils in this case does not represent a solution to the problem due to a significant (two to three times, e.g.) drop in efficiency compared to conventional non-cavitating hydrofoils operating at moderate speeds.

[0028] At the same time, the use of hydrofoils as the aft stabilizer does not guarantee the realization of the full efficiency potential of the hydrodynamic systems under consideration.

[0029] The fact is that hydrofoils rather loosely sense and are not rigidly connected to the water surface, and, so, allow substantial variations in immersion relative to the water surface, and, accordingly, as the aft stabilizing device, allow significant variations in the trim angle of the boat hull, which property does not guarantee maintaining the optimal angle of incidence of the main forward planing surface and, correspondingly, does not guarantee implementation of the potential maximum efficiency of the boat.

[0030] The efficiency of the aft planing surface, and consequently the efficiency of the hydrodynamic system as a whole, could be increased in the case when highly efficient aft planing surface of the dihedral cambered design would be configured in conformity to the relief of the substantially V-shaped wave trough downstream the forward dihedral swept back cambered planing surface.

[0031] However, the known embodiments of the Prior Art do not give any hint of purposeful designs aimed at using this way of increasing efficiency and, accordingly, do not provide clear criteria and conditions for ensuring the full effectiveness of such systems.

[0032] Among the examples of the Prior Art that might somehow be relevant to the subject of this invention, there could be mentioned the following inventions, using at least one cambered planing surface:

[0033] U.S. Pat. No. 1,618,995 in regard to the subject of the present invention describes a design with some non-dihedral and non-swept back cambered planing surface being stabilized by some adjustable in the vertical direction, not dihedral (no deadrise) and flat aft “hydroplane”.

[0034] As a positive point, the invention contemplates that the position of the aft stabilizing surface (though, supposedly only vertical) should correspond to the disturbed surface of the water at its location, assuming, however, that this disturbance (named “hollow” or “waterfall”) is caused by the propeller and mentioning just a wave generated by the forward cambered surface (that is not correct in terms of actual mechanics of such hydrodynamic system).

[0035] Needless to say that the invention U.S. Pat. No. 1,618,995 doesn't provide any well-grounded indications or hints regarding the optimal relative position of the cambered planing surface and the “hydroplane” stabilizer, and the appropriate configuration of the “hydroplane” (the shape matching the relief of the surface of the “hollow” or “waterfall”), and presupposes only manual vertical (but not angular) adjustment of the position of such flat stabilizer following the intuition of the operator.

[0036] Accordingly, with the configuration and angular position of the aft planing surface being irrelevant to the real relief of the wave trough (and, fundamentally, without establishing the correspondence in the parameters of the forward planing surface, the shape of the aft planing surface and relative spatial and angular positions of the forward and aft planing surfaces of this hydrodynamic system), such design could not ensure the maximum efficiency of the boat.

[0037] The subject of the invention U.S. Pat. No. 9,242,699 (in contrast to the system considered in the present invention) implies a hydrodynamic system consisting of three supposedly cambered planing surfaces:—a “front lift surface”, “main lift surface” and a “back planing surface”.

[0038] This invention doesn't take into consideration that each subsequent planing surface should operate along the disturbed and deformed surfaces of the wave troughs generated by the preceding planing surface (when optimum position of each posterior planing surface is determined by parameters of the preceding planing surface) and, consequently, cannot provide clear specific stipulations concerning the optimum relative angular position of planing surfaces and their relative position in the vertical direction (corresponding real hydromechanics of such system) that as a result cannot ensure the high efficiency of the hydrodynamic system and the boat as a whole in the purely planing mode of operation.

[0039] Moreover, the design of the invention U.S. Pat. No. 9,242,699 doesn't take into consideration that each subsequent planing surface deflects the flow downward even more and, in order to generate the necessary lift, subsequent surfaces must have a larger angle of incidence and greater resistance, so that in addition to the second downstream surface worsening the overall efficiency, the third one worsens the efficiency even in the greater extent.

[0040] This conclusion is confirmed by the test results cited in the materials of the very invention:

[0041] The results obtained from trials of this hydrodynamic system do not reveal any unusually high efficiency:—the obtained average values of the relative resistance (drag to lift ratio) are about 0.15 (and vary from 0.13 to 0.2), which represents quite ordinary data and corresponds to the efficiency of a conventional properly-designed boat hull even of non-stepped design.

[0042] For comparison, even step hull boats in the 30s of the last century demonstrated relative resistance about 0.11, not to mention that the “Dynaplane boat” provided with cambered planing surface and mentioned in the materials of the invention has the drag to lift ratio as low as 0.08 (i.e., its efficiency is about two times higher).

[0043] The same “Dynaplane boat”, featuring the single swept back planing surface with cambered profile and aft stabilizing hydrofoil, can be considered as a forerunner of the design of the invention U.S. Pat. No. 10,189,544.

[0044] As it was said, the “Dynaplane boat” has proven itself as a design of high hydrodynamic efficiency.

[0045] However, the angles of deadrise of the cambered planing surface used in this design could hardly exceed 14 degrees (not to create some hydrodynamic problems) that in many cases could be found insufficient to provide required seaworthiness of boats. As it can be understood from the materials of the invention U.S. Pat. No. 10,189,544, it is aimed mainly at expanding the working range of the angles of deadrise of the cambered planing surface to more than 15 degrees by providing the surface with a non-linear distribution of camber, leaving, at the same time, the previous concept of the design with the single swept back cambered planing surface stabilized by the aft W-shaped non-cambered planing surface (which is not conformable to the wave trough) or a hydrofoil (as in the original design of “Dynaplane”) with all its mentioned above limitations in the case of conventional cavitating hydrofoil profile or with the considerable drop in efficiency in the case of supercavitating hydrofoil.

[0046] As it was mentioned before, another problem of employing hydrofoil as the aft stabilizing device relates to the fact that hydrofoils rather loosely sense and are not rigidly connected to the water surface, and, so, allow substantial variations in immersion relative to the water surface, and, accordingly, as the aft stabilizing element, allow significant variations in the trim angle of the boat hull, which property does not guarantee maintaining the optimal angle of incidence of the main forward planing surface and, correspondingly, does not guarantee implementation of the potential maximum efficiency of the boat.

[0047] That is, the idea of the invention U.S. Pat. No. 10,189,544 is mainly aimed at increasing the seaworthiness of the hydrodynamic configuration represented by the design of “Dynaplane”.

[0048] In this regard, the provisions of the invention U.S. Pat. No. 10,189,544 are not aimed at establishing the optimal relationship between the two cambered planing surfaces and endowing the boat of this design with maximum efficiency:

[0049] Although it declares that in some embodiments the external bottom surfaces of the after-body may be adapted “to accommodate distinctive profile of the free surface wake produced by the swept back cambered planing surface”, the idea of this configuration is not to position the aft surface to generate lift the most efficient way, but to avoid any contact (“wetting”) of the after-body with the surface of wave trough (that would be quite reasonable in the case of stabilizing hydrofoil, but not a planing surface like in the case of the subject of present invention).

[0050] Anyway, the invention U.S. Pat. No. 10,189,544 (as well as other relevant inventions) doesn't provide any specific requirements that determine how the forward swept back cambered surface and the aft lifting surface (a planing surface or aft hydrofoil) should be positioned relative each other (both in angular manner and regarding the vertical displacement) in order to arrange the aft surface the most optimal way to fit the flow of the wave trough generated by the forward lifting surface (i.e.: to correspond exactly the depth of depression and the angle of decent of the wave through at the location of the aft lifting surface) and this way to ensure the minimum drag and highest efficiency that is exactly the essence of this invention.

[0051] In this regard, the design of the invention U.S. Pat. No. 10,189,544 does not guarantee the maximum efficiency of this hydrodynamic system and the boat as a whole.

[0052] Summing up, taking into account that two planing surfaces arranged successively along the flow represent an interconnected hydrodynamic system in which the operating conditions and lift generating parameters of both planes are interdependent and, accordingly, only consideration of this hydrodynamic system as a united complex with its optimal configuration and mutual spatial and angular arrangement of these two surfaces can ensure the maximum possible efficiency, it can be concluded that to our knowledge not one of the found cases of the Prior Art establishes any clear patterns regarding the optimal configuration and arrangement of the two dihedral cambered planing surfaces in accordance with the hydromechanics of operation of such interrelated systems.

[0053] Consequently, the analysis of the Prior Art revealed no signs of boat designs that use hydrodynamic configuration of this invention featuring successively and properly spatially and angularly arranged cambered planing surfaces comprising the forward dihedral swept back cambered planing surface and the aft dihedral cambered planing surface, which conformally matches the flow depression generated by the forward planing surface and this way reduces hydrodynamic resistance and improves the efficiency of the boat, and establish clear criteria and conditions for ensuring the maximum efficiency of such hydrodynamic systems.

[0054] Thus, the subject of the present invention has no analogues and compares favorably with the Prior Art. It involves the use of highly efficient cambered planing surfaces while maintaining dynamic stability and ensuring the efficiency being superior to the known hydrodynamic designs of the Prior Art, and provides with the criteria and conditions to achieve the utmost efficiency of this hydrodynamic design.BACKGROUND OF THE INVENTION

[0055] One of the main tasks of developing planing boats—like other vehicles—is to increase their efficiency (that could be reduced to such simple criterion like weight to drag ratio) resulting in a higher speed and / or a reduction in power requirements and, anyway, reduction in specific fuel consumption (mpg, e.g.), longer range, higher payload, etc. Accordingly, the main way to increase efficiency is to reduce hydrodynamic resistance, which includes two principal components:—resistance of form and frictional resistance.

[0056] The former—resistance of form—depends on the angular position of planing surface supporting the boat in motion. Therefore, the change in the angular position of the planing surface in the direction of reduction—without rise of frictional resistance and without reducing the lift—is the way to increase the efficiency of the boat.

[0057] As it was mentioned, the maximum hydrodynamic efficiency of a planing surface (characterized by lift to drag ratio) can be achieved by means of use of high aspect ratio cambered planing surface that in application to a single-keel dihedral bottom surface featuring some angle of deadrise presupposes swept back configuration with both leading and trailing edges of both half-planes of the planing surface being inclined backwards relatively the keel line in the plan view, and with cords of the cambered profiles preferably tapering from the center plane keel sections to the outside chine ends (that reduces tip losses).

[0058] Taking into account the problems of stabilizing the trim of a single planing surface of this type, all these advantages in efficiency of the dihedral swept back cambered planing surface could be realized in the stepped hydrodynamic design comprising additional aft stabilizing planing surface successively arranged in the wake of the forward planing surface.

[0059] Consequently, it could be suggested that the aft planing surface should have similar dihedral configuration as the forward planing surface.

[0060] However, in this regard it should be taken into consideration that the aft planing surface successively positioned behind the abovementioned optimum forward planing surface skims not along the flat water surface corresponding undisturbed water level, but along some shallow substantially V-shaped channel of water depression created by the forward dihedral planing surface and corresponding the wave trough behind the generating dynamic lift forward surface that disturbs the ambient water surface and deflects water masses downwards (that later turns into a damping wave motion relatively the level of undisturbed water surface).

[0061] Moreover, the sweep of the forward planing surface back (giving greater aspect ratio and increasing efficiency) and tapering lead to the formation of a complex three-dimensional relief of the surface of the wave trough.

[0062] Thus, the task of reduction of hydrodynamic resistance and improvement in efficiency of such hydrodynamic configuration as well as the boat in general should presuppose proper shaping and positioning of the aft planing surface in order to conform the relief of the wave trough generated by the forward planing surface, which relief could be obtained, e.g., through CFD analysis or model tests.

[0063] Since the aft planing surface should conformably correspond to the wave trough created by the forward planing surface, its optimal spatial-angular position (relative to the forward planing surface) and shape should be determined by the parameters of the forward planing surface (generating this specific relief of the wave trough) and the distance between the forward and aft planing surfaces.

[0064] One of the most important parameters that directly determine the configuration of the wave trough is the lift coefficient, which depends on the angle of incidence, or, more specifically, on the position of the hydrodynamic base plane formed by hydrodynamic base lines of cambered profiles of the forward planing surface relative the surface water.

[0065] Thus, it would be reasonable to use this plane as a basis for determining the relative position of the forward and aft surfaces as components corresponding to the optimal configuration of such a hydrodynamic system.

[0066] In the vertical sectional along the flow view the hydrodynamic base plane of cambered profile represents a line, i.e. a base line or axis that serves as a basis for offsets along the chord, which determine the contour of the profile.

[0067] As an example, in the case of the well-known Virgil Johnson profile the hydrodynamic base plane is the reference line for the offsets provided by the equation determining the Johnson three-term camber curve:h=b·CL,d·(-20⁢X3 / 2+80⁢X2-64⁢X5 / 2) / 7.5π,

[0068] where:

[0069] b—chord length of the camber curve;

[0070] CL,d—two-dimensional design lift coefficient for a cambered planing surface;

[0071] X=x / b; where: x—abscissa along the chord of the profile.

[0072] As a first approximation, the parameters of the disturbed flow of the wave trough behind the forward planing surface can be roughly estimated using formulae derived from the theory of hydrofoils:y=-Cy·[1+(Frb2⁢ξ-2) / 2·λ]·b·sin⁡(X / Frb2⁢ξ);β=(Cy / Frb2⁢ξ)·[1+(Frb2⁢ξ-2) / 2·λ]·cos⁡(X / Frb2⁢ξ),

[0073] where

[0074] y—is the ordinate of the wave trough relatively the horizontal line corresponding the vertical position of the trailing edge;

[0075] β—is the angle of the wave slope relatively the undisturbed surface of water;

[0076] b—chord length of the camber curve of the forward planing surface;

[0077] Cy=2 L / ρ·V2·A—lift coefficient of the forward planing surface;

[0078] L—lifting force of the forward planing surface;

[0079] ρ—mass density of water;

[0080] V—speed of motion;

[0081] A—wetted area of the forward planing surface;

[0082] Frb=V / (g·b)1 / 2—Froude Number based on the chord of the forward planing surface;

[0083] g—acceleration of gravity;

[0084] λ—aspect ratio of the forward planing surface;

[0085] ξ=ek; where: e—base of the natural logarithm; k=−0.73 / λ0.2

[0086] X=x / b; where: x—distance from the forward planing surface along the flow.

[0087] The above formulae make it possible to estimate both qualitatively and quantitatively the parameters of the flow in a wave trough, represented by the configuration of its surface.

[0088] Providing that to generate required lift the forward and aft planing surfaces should be installed at some proper angles of incidence to their local flows, the formula for the angle of the wave slope (β), in particular, shows that to correspond the flow of the wave trough (in order to ensure the maximum efficiency) the aft planing surface (its base lines) should be inclined at some angle relatively the forward planing surface (its base lines) being equal not only to the difference in angles of incidence of the forward and aft planing surfaces relatively their local water surfaces, but also some additional angle of inclination corresponding to the angle of the slope (β) of the wave trough.

[0089] At the same time the formula for β indicates that close longitudinal arrangement of the forward and aft planing surfaces corresponds to operation of the aft surface at a descending part of the wave trough and positive angles of the wave slope (turned clockwise relatively the undisturbed surface of water when viewed from the left / port side of the boat) that produces a harmful effect and reduces efficiency of the aft surface and this hydrodynamic system in general. This harmful positive slope angle decreases with increasing distance from the forward planing surface and, so, to minimize the additional (positive and harmful) angle of inclination and this way to maximize efficiency, the aft planing surface should be positioned as far aft of the forward one as possible (within certain limitations discussed below).

[0090] The formula for the ordinate of the wave trough (y) establishes that to fit the flow of the wave trough and this way ensure the maximum efficiency, each section of the aft planing surface should be displaced vertically from the undisturbed water level by the height of the wave trough determined by the formula.

[0091] This means that with regard to the relative arrangement of the forward and aft planing surfaces, sections of the aft planing surface should be displaced vertically from the base lines of profiles of sections of the forward planing surface (within the same vertical longitudinal plane) by a distance corresponding to the ordinate of the wave trough (at the position of the aft surface) relative to the base line of this profile of the forward surface.

[0092] As a particular conclusion from the analysis of the formula for “y”, up to certain limits, a pattern can be traced that the further the aft surface is located from the forward surface, the deeper its optimal position relative to both the undisturbed water level and the base lines of sections of the forward surface, which pattern applies to most boats of typical dimensions and speeds.

[0093] For the same limited conditions, said ordinates of the wave trough at the location of sectional profiles of the aft planing surface relative to the base lines of corresponding profiles of the forward surface, meaning the vertical position of sectional profiles of the aft planing surface relative to the base lines of corresponding profiles of the forward surface (yAFTFWD) could be found from the following equation:YAFTFWD=y⁡(x=d)+d·tg⁢αFWD,

[0094] where

[0095] d—distance between leading edges of the forward and aft planing surfaces;

[0096] αFWD—angle of incidence of the base plane of the forward planing surface relatively the undisturbed surface of water.

[0097] The angles of the slope of the wave trough relatively the base lines of corresponding profiles of the forward surface at the location of sectional profiles of the aft planing surface:βBLFWD=β⁡(x=d)-αFWD,

[0098] and, correspondingly, the optimum angle of base line of sectional profile of the aft planing surface relative to the base line of sectional profile of the forward surface within the same vertical longitudinal planes should be equal to:ζAFTFWD=βBLFWD+αAFT=β⁡(x=d)+αAFT-αFWD,

[0099] where:

[0100] αAFT—angle of incidence of the base line of the section of the aft planing surface relatively the local surface of water corresponding to the ascending flow.

[0101] Thus the optimum angle between sections of the forward and aft planing surfaces, which angular positions are represented by base lines in sectional views in the same vertical longitudinal planes, should be equal to the sum of the angle of the slope of the wave trough “β” (with its sign) and the difference in angles of incidences of the aft and forward planing surfaces.

[0102] Taking into account the above it should be concluded that the optimal spatial and angular position of sectional profiles of the aft planing surface relative to the base lines of sectional profiles of the forward surface should be determined (through angle “β” and displacement “y”) by parameters of the forward planing surface such as angle of incidence, lift coefficient, aspect ratio, relative speed (Froude number) and the distance between the forward and aft surfaces.

[0103] As a practical example corresponding to a forward cambered planing surface featuring aspect ratio λ=3 and lift coefficient Cy=0.2, skimming along the surface of water at the speed of V=12 m / s (23.3 kt), for some specific section of this forward surface with the chord b=1.0 m, which determines the Froude number based on the chord Frb=V / (g·b)1 / 2=3.83, for the distance between the forward and aft surfaces d=4.0 m and equal angles of incidence of the forward and aft surfaces αAFT=αFWD=10, the above formulae determine the following values:YAFTFWD=-0.15⁢ m;ζAFTFWD=+2.260.

[0104] That is, to ensure maximum efficiency of the hydrodynamic system of two successively arranged cambered planing surfaces in the case under consideration, these planing surfaces must be brought to the optimal spatial-angular position, for which the sections of the aft planing surface must be shifted down from the base lines of the forward surface (by 0.15 m for the above specific section), and the base lines of the aft surface should be turned (clockwise if viewed from the port side) relative to the base lines of the forward surface (by the angle equal to 2.26 degrees for the above specific section).

[0105] Taking into account the swept-back in the plan view configuration and variable spanwise chords of the forward surface, the fulfillment of the conditions for compliance with the parameters of the wave trough determined by the formulae for each of the longitudinal vertical sections should, actually, lead to a configuration of the aft surface with variable spanwise angles of incidence and variable spanwise deadrise angles being larger than the deadrise angle of the forward surface.

[0106] As it was noted, the formulae used provide mainly qualitative and approximate quantitative estimates of the parameters of the wave trough, and therefore it is expedient to define more accurately the data on the subsidence and inclination angles of the wave slope (which determine the optimal relative position of the planing surfaces) using CFD analysis and towing tank tests (where only one optimal forward surface can be tested in order to scan the 3-dimensional downstream surface of the wave trough).

[0107] Following the above equations, various combinations of parameters can lead not only to variations in values of y and β, but also to a change in the sign of the functions y and β determining the optimal position of the aft planing surface.

[0108] In this regard, there could be established two distinctive cases that define two different ways of operation of the aft planing surface corresponding to descending flow of the first quarter-period and ascending flow of the second and the third quarter-periods of the quasi-sinusoidal wave motion of the surface of water in the wave trough.

[0109] In the first quarter-period, when X / Frb2ξ varies from 0 to π / 2 that corresponds to the descending flow, to ensure the maximum efficiency sections of the aft planing surface should be positioned below the base lines of the forward surface by the distances (yAFTFWD) corresponding to the depths of the wave trough below the base lines of the forward surface at the position of the aft surface, and the base lines of sections of the aft surface should be inclined to the base lines of the forward surface by additional positive angles being equal to the angle βBLFWD at the position of the aft surface, so that the optimum angles of base lines of the aft planing surface relative to the base lines of the forward surface within the same vertical longitudinal planes should be equal to ζAFTFWD.

[0110] Such requirements for the position of the aft surface arise, e.g., in the case of relatively short distance between the forward and aft surfaces, and relatively high Froude numbers, which conditions apply to most boats of typical dimensions and speeds.

[0111] In the case of relatively large distance between the forward and aft surfaces, and relatively low Froude numbers, the aft planing surface may find itself in the second and the third quarter-period range (when X / Frb2ξ varies from π / 2 to 3π / 2) corresponding to the ascending flow.

[0112] The goal of achieving maximum efficiency in this case might require placement of sections of the aft planing surface above the base lines of the forward surface by the distance corresponding to the rise of the surface of the wave trough above the base plane of the forward surface at the position of the aft surface, and inclination of the base lines of the aft surface to the base lines of the forward surface by an additional negative angle being equal to the angle βBLFWD at the position of the aft surface, presupposing turning the sections of the aft surface counterclockwise by this additional angle when viewed from the left (port) side of the boat.

[0113] Placing the aft surface within these quarter-periods of the wave process (when X / Frb2ξ varies from π / 2 to 3π / 2) eliminates the negative influence of the aft surface and leads not to a decrease, but to an increase in hydrodynamic efficiency.

[0114] In general, referring to the above formulae for evaluation of the parameters of the flow of the wave trough behind the forward planing surface, which determine the optimum position of the aft planing surface, there could be established limits for some distinctive ranges of operation of the aft surface.

[0115] The first quarter-period range corresponding to the descending flow of the wave trough could be roughly evaluated as the distance (x=d) within πFrb2ξ / 2 times the length of the chord of the forward planing surface. At longer distances the angle of the inclination of the flow of the wave trough relatively the undisturbed surface of water, as well as the additional angle of inclination of the aft planing surface, changes the sign from positive to negative.

[0116] The negative additional angle reaches its extreme value at the boundary of the second and third quarter-period ranges (when the distance between the forward and aft surfaces (x=d) is equal πFrb2ξ times the length of the chord of the forward planing surface), which corresponds to the ultimate efficiency of the hydrodynamic system consisting of two successive planing surfaces.

[0117] The maximum rise of the optimum vertical position of the aft planing surface above the base plane of the forward surface corresponds to the distance close to 3πFrb2ξ / 2 times the length of the chord of the forward planing surface.

[0118] At approximately the same distance the surface of the wave trough rises to its maximum height above the undisturbed water level and the angle β is zeroed, i.e., the tangent to the contour of the surface of the wave trough becomes parallel to the undisturbed water level, while the optimum angle between base lines of sections of the aft and forward surfaces becomes equal to the difference in their angles of incidence.

[0119] Consequently, at the distances beyond 3πFrb2ξ / 2 times the length of the chord of the forward planing surface the angle of the inclination of the flow of the wave trough relatively the undisturbed surface of water, as well as the additional angle of inclination of the aft planing surface change the sign again from negative to positive.

[0120] As a practical example, at the Froude number based on the chord of the forward planing surface: Frb=V / (g·b)1 / 2 being equal 3.83 (e.g.: b=1.0 m; V=12 m / s, i.e. 23.3 kt) and λ=3:

[0121] the aft planing surface will reach its lowest optimum vertical position and the additional angle of the aft planing surface will change its sign from positive to negative when the distance between the two planing surfaces will be about 7 lengths of the chord (7 m, e.g.);

[0122] the ultimate negative angle of wave slope and, so, the maximum hydrodynamic efficiency of the system comprising two successively arranged planing surfaces will correspond to the distance between the two planing surfaces about 14 lengths of the chord (14 m, e.g.), and the aft planing surface will reach its highest optimum vertical position when the distance between the two planing surfaces will be about 21 lengths of the chord (21 m, e.g.) that should also correspond to the next change of the sign of the optimum additional angle of inclination of the aft planing surface from negative to positive.

[0123] In this regard, it should be noted that the hydrodynamic system comprising the two successively arranged cambered planing surfaces, in the case of placing the aft planing surface in accordance with the present invention (providing the spatial-angular position according the provisions of the present invention) within the first quarter-period range of the flow of the wave trough, corresponding to the descending flow (which is typical for many real boat designs), ensures the highest possible hydrodynamic efficiency for any design with the aft surface located within the range of descending flow.

[0124] However, the positive additional angle of inclination of the aft surface (corresponding to the angle of the descending flow within the first quarter-period range of the wave trough) tilts the directed upward vector of the dynamic lift force of the aft planing surface backwards, so that the projection of said directed upward lift vector onto the horizontal plane produces an additional back-looking component (being similar to some additional resistance) that increases drag and decreases the hydrodynamic efficiency of the boat.

[0125] So, the hydrodynamic efficiency in the case when the aft surface located within the range of descending flow should always be lower than the combination of efficiencies of the forward and aft surfaces as single isolated planing surfaces.

[0126] In the case of placing the aft planing surface within the second and third quarter-period ranges (and ultimately at the boundary of these ranges) of the flow of the wave trough corresponding to the ascending flow, the directed upward vector of the dynamic lift force of the aft planing surface is tilted forward in the direction of movement of the boat by the angle corresponding to the angle of slope of the ascending flow at the location of the aft planing surface, and the projection of said directed upward lift vector onto the horizontal plane produces an additional forward-looking component (being similar to some additional thrust) that reduces drag and increases the hydrodynamic efficiency of the boat.

[0127] That is, in this way the aft planing surface will actually recover a part of the energy spent by the forward planing surface to disturb the incoming water flow and to deflect the masses of water down relatively the level of undisturbed water surface in the form of generation of the flow of the wave trough.

[0128] Thus, in the case of placement of the aft planing surface in accordance with the provisions of the present invention within the second and third quarter-period ranges of the flow of the wave trough corresponding to the ascending flow, the hydrodynamic system ensures the efficiency that always exceeds the combination of efficiencies of the forward and aft surfaces as single isolated planing surfaces, while placement of the aft planing surface at the boundary of the second and third quarter-period ranges ensures the highest possible efficiency of the system comprising two successively arranged planing surfaces.

[0129] As a practical example illustrating the improvement in efficiency, there can be considered a boat based on the above mentioned embodiment of the present invention with the aft planing surface supporting 50% of the boat's weight located at the boundary of the second and third quarter-period ranges (corresponding to the utmost negative inclination of the slope of the wave trough).

[0130] If the aft planing surface will use the ascending flow following the stipulations of this invention and as a result will be inclined to additional 2 degrees nose-dive to fit the flow, and the lift to drag ratio of planing surfaces (as single isolated planing surfaces) is 5 (corresponding, e.g., to flat not cambered planing surfaces) the hydrodynamic efficiency of the boat will increase by about 10%.

[0131] For the lift to drag ratio 10 the hydrodynamic efficiency of the boat will rise by about 20%.

[0132] In the case of highly efficient planing surfaces (cambered, properly profiled and adjusted surfaces of high aspect ratio) with lift to drag ratio as single isolated planing surfaces equal to 15, the same configuration will result in hydrodynamic efficiency in excess of 20 (rise by more than 35%). That is completely unattainable for the known hydrodynamic designs of the Prior Art.

[0133] This example shows that the great maximum potential efficiency of the hydrodynamic design following the provisions of the present invention can be realized primarily in the case of using planing surfaces of high hydrodynamic efficiency corresponding to cambered surfaces of high aspect ratio.

[0134] The point that the aft planing surface must be located and efficiently operate within the shallow substantially V-shaped channel of the wave trough generated by the forward planing surface, implies specific optimal configuration of the aft planing surface.

[0135] Due to the fact that different along the span sections of the swept back and tapering towards the tips forward planing surface have different chords and are displaced along the flow, they generate different deviations of the flow that leads to a distortion of contours of water surface in the cross sections of the wave trough compared with the projections of the trailing edges of the forward planing surface onto the transverse plane.

[0136] As a result, the cross section of the wave trough by the transverse plane at the location of the aft planing surface at least within the first quarter-period range of the wave trough is somewhat deeper (i.e., stretched in the vertical direction) than the projections of the trailing edges of the forward planing surface. This leads to the fact that in order to fit conformally to the configuration of the wave trough, the aft planing surface must have a higher angle of deadrise than the forward planing surface.

[0137] Under certain combination of parameters of the forward surface, speed and position of the aft surface, these distortions of the wave trough can result in a significant curvature of contours of the water surface, which will require imparting a substantially curved configuration and variable angles of incidence of the half-planes of the aft surface.

[0138] At the same time, the peripheral (extending downstream from the tips of the forward surface) areas of the wave trough characterize by disturbances caused by tip vortices, while the walls of the wave trough tend to converge as they move away from the forward (generating flow deflection) planing surface, which factors adversely affect the operation of the aft planing surface located downstream and narrows the width of the wave trough available to accommodate the aft surface. This makes it expedient to limit the span of the aft planing surface to only the central portion of the wave trough and to exclude peripheral portions.

[0139] Thus, to avoid any losses in efficiency the width of the aft planing surface should be less than the width of the forward planing surface and constitute not more than 0.9 times of the width of the forward planing surface at any position of the aft surface.

[0140] Summing up it can be concluded that the task of reduction of hydrodynamic resistance and improvement in efficiency of the successively arranged two cambered planing surfaces as well as the boat of this hydrodynamic design in general should presuppose proper shaping and spatial-angular positioning of the aft planing surface relatively the forward planing surface in order to embody the optimum configuration conforming the shape of the wave trough generated by the forward planing surface by means of:

[0141] 1. Displacing each vertical longitudinal sectional profile of the aft planing surface in the vertical direction by some distance from the base line of profile of section of the forward planing surface within the same vertical longitudinal plane, which distance corresponds to the ordinate of the surface of the wave trough relatively the base line of profile of the forward planing surface at the location of the aft planing surface (that may result in different angles of deadrise of the aft planing surface in comparison with the forward planing surface);

[0142] 2. Installing the base line of each vertical longitudinal sectional profile of the aft planing surface at some additional angle relatively the base line of sectional profile of the forward planing surface in the same vertical longitudinal plane, while this additional angle should correspond to the angle of inclination of the slope of the wave trough, so that the resulting angle between the base lines of the forward and aft planing surfaces should be equal to the sum of the angle of inclination of the slope of the wave trough (with its sign) and the difference between the angles of incidence of the aft and forward surfaces;

[0143] The values of parameters determining the optimum position and shape of the aft planing surface conforming the shape of the wave trough generated by the forward planing surface should depend on a number of specific hydrodynamic characteristics, such as: relative speed, lift coefficient and aspect ratio of the forward planing surface, and distance between the two planing surfaces, while the exact relief of the surface of the wave trough behind the forward planing surface could be obtained through CFD analysis or towing tank tests.

[0144] However, for a number of real practical designs of boats moving at relatively high Froude numbers and featuring relatively short distance between the forward and aft planing surfaces (that corresponds location of the aft planing surface in the descending part of the wave trough) the optimal configuration should presuppose the following:

[0145] 1. Each section by vertical longitudinal plane of the aft cambered planing surface is displaced in the vertical direction below the base line of section of the forward planing surface in the same vertical longitudinal plane;

[0146] 2. The base line of each of 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 (port) side of the boat by the angle being equal to the sum of the positive 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 forward planing surfaces relatively the level of the undisturbed water surface;

[0147] 3. The angle of deadrise of the aft planing surface is higher than the angle of deadrise of the forward planing surface;

[0148] 4. The width of the aft planing surface is to be not more than 0.9 times of the width of the forward planing surface.

[0149] Although the effect of the gain in efficiency due to the conformal configuration of the aft planing surface is likely to manifest itself in practically acceptable values over a wider range of above parameters, it will be particularly noticeable in the case of boats with a combination of low Froude numbers and large distance between the forward and aft planing surfaces.

[0150] Thus, the above-mentioned regularities, corresponding to the provisions of the present invention, provide with the methods for developing the optimal hydrodynamic design of a boat or a vehicle with two successively arranged cambered planing surfaces, which ensures the highest hydrodynamic efficiency.

[0151] Such methods may include, for example, the following sequence:

[0152] 1. There should be determined the optimal parameters (profiles, chords, etc.) of the forward (upstream) planing surface, which provide the highest hydrodynamic efficiency (lift to drag ratio) corresponding to movement along undisturbed water surface at the operational speed of the boat, for the given maximum width (ensuring the maximum aspect ratio) and for the required lifting force corresponding to the given distribution between the forward and aft planing surfaces (90% and 10%, e.g.), which, with the known position of the center of gravity of the boat, also determines the distance of this planing surface (its center of pressure) forward from the boat's center of gravity, assuming the farthest downstream position of the aft planing surface (at the transom, e.g.).

[0153] 2. The found optimal parameters, including the distribution of the lift coefficients (i.e. circulation) and chords (i.e. Froude numbers based on chords) along the width of the forward planing surface, completely determine the relief of the wave trough and specifically the vertical displacements and angles of inclination of surface of the wave trough relatively the base lines of the sections of the forward planing surface in each vertical longitudinal plane at the location of the aft planing surface, which can be calculated analytically, obtained through CFD analysis or from measurements on a towing tank model (only one optimal forward surface can be tested in order to scan the 3-dimensional downstream surface of the wave trough).

[0154] 3. There should be determined the optimal parameters (profiles, chords, etc.) of the aft (downstream) planing surface, which provide the highest hydrodynamic efficiency (lift to drag ratio) assuming its skimming along undisturbed water surface at the operational speed of the boat, for the available maximum width of the wave trough, while not exceeding 0.9 of the width of the forward (upstream) planing surface, and for the required lifting force corresponding to the given distribution between the forward and aft planing surfaces (90% and 10%, e.g.).

[0155] 4. Each section by the vertical longitudinal plane of the found in 3. optimal aft planing surface should be properly arranged relatively the base line of the corresponding section of the forward planing surface, meaning that it should be brought in accordance with the parameters obtained in 2. for the location of the aft planing surface, i.e.: each aft section (referring to its leading edge) should be shifted vertically relative to the base line of the forward section by the distance from this line to the surface of the wave trough, and positioned properly angularly, so that the angle between the base lines of the forward and aft surfaces has to be equal to the sum of the angle of the wave slope (with its sign) and the difference in angles of incidence of these sections of the aft and forward surfaces relative to the local surfaces of water (which angles of incidence ensure generation of the required dynamic lift following 1. and 3.).

[0156] Such a procedure (1. to 4.) gives both planing surfaces the optimal configuration and brings both planing surfaces to the optimal position relative to each other, providing the greatest hydrodynamic efficiency of such a system of planing surfaces and the boat as a whole.

[0157] When implementing the above steps it should be taken into account that with increasing speed, the wetted width of substantially dihedral planing surface may decrease, so that the lift is becoming generated by a progressively smaller wetted area around the keel line of this surface.

[0158] As a consequence, the selected optimal parameters of surface profiles for relatively low speeds with large relative camber (i.e., ratio of the depth of camber to the cord of profile) to ensure generation of the necessary lift at relatively low speeds, may not be optimal for high speeds requiring shallower relative cambers to achieve the maximum efficiency (lift to drag ratio).

[0159] To overcome this contradiction, the planing surface (meaning forward planing surface, aft surface or both of them) can be provided with profiles with variable along the span relative cambers, which decrease from the chines tips to the keel line, while maintaining the average relative camber required for low speeds.

[0160] Thus, the planing surface, using its full area, will provide the necessary lift and high efficiency at low speeds (due to large average relative camber) and will not lose high efficiency when moving at high speeds with a small wetted area (due to the shallower relative camber in the area around the keel line).

[0161] It should be noted that taking into consideration reliefs of real wave troughs behind planing surfaces and swept back surfaces in particular, the fulfillment of conditions 4. may result in a somewhat curved optimal configuration of the aft surface in projection onto the transverse plane and variable optimal angles of incidence along the span of half planes of the aft surface even with straight lines of the trailing edge of the forward planing surface.

[0162] The found optimal position and configuration of the planing surfaces also determines the shape of the boat's bottom or the proper configuration and arrangement of separated planing surfaces (planing hydrofoils, e.g.) on the boat's bottom.

[0163] In this connection, the forward planing surface can be installed at some negative angle relatively the keel line of the boat, i.e.: the base line of each section of the forward cambered planing surface can be inclined nose-dive at some negative angle relatively the keel line of the boat or vehicle meaning that the base lines should be turned counterclockwise relatively the keel line of the boat if viewed from the left (port) side of the boat.

[0164] This arrangement 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, which reduces the draft and makes the structure more compact.

[0165] In the case of 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.

[0166] 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.

[0167] To further improve efficiency of the planing surfaces of this invention, the outside tips of the planing surfaces could be provided with end plates or deflectors.

[0168] It is known from aero-hydrodynamics that such plates lead to an increase in dynamic pressures at the peripheral sections of the planing surfaces 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 increase in the efficiency of the planing surfaces.

[0169] That is, the use of such end plates is equivalent to increasing the aspect ratio of the planing surface, but without increasing of its width.

[0170] As it was mentioned, the maximum hydrodynamic efficiency (lift to drag ratio) can be achieved through use of cambered planing surface featuring high aspect ratio that means the need to make the planing surface as wide in transverse direction as possible.

[0171] However, for real practical boat designs the width of the planing surface is usually limited by the width of the chines of boat's hull.

[0172] In order to overcome this limitation and increase the width of the planing surface (and therefore its aspect ratio and effectiveness) without changing the basic configuration and dimensions of the boat, the hull in the area where the planing surface intersects with the chines can be provided with outside protrusions extending beyond the width of the chines (but preferably not exceeding the maximum width of the boat), while the bottom surfaces of these protrusions should represent the profiled continuation of the planing surface.

[0173] Otherwise not to exceed the width of the boat during mooring said protrusions can be made foldable.

[0174] At the same time said protrusions can provide some additional benefits like improvement in the transverse stability of the boat in the planing mode of motion and damping of rolling of the boat in the displacement mode (that should enhance the comfort of staying aboard).

[0175] Providing said protrusions extending beyond the hull on the sides of the boat with streamlined convex upper surfaces being similar to upper surfaces of hydrofoils having a certain volume and being able to generate dynamic lift could further improve stability of the boat and facilitate take off and acceleration of the boat in the transitional mode of motion from the displacement mode to the purely planing mode of motion as far as the upper surfaces of protrusions are submerged and stay below the water level.

[0176] In the course of practical development of a boat on the basis of the hydrodynamic design of this invention there might be found that optimum angles of deadrise of planing surfaces should be relatively low that could determine small angles of deadrise of bottom surfaces mating with the planing surfaces that in its turn could deteriorate seaworthiness of the boat. (Small angles of deadrise of bottom surfaces lead to slamming and high dynamic shock loads that limits the ability to operate such boats in rough seas.)

[0177] In this case at least some of the planing surfaces could be made in a form of flat-top panels or profiled planes being separated from the bottom of the boat. This way the bottom surfaces of the boat could be made with much higher angle of deadrise (much higher than the angle of deadrise of planing surfaces) and ensure much sharper entry that should considerably upgrade seaworthiness of the boat not sacrificing lift and hydrodynamic efficiency (guaranteed by the optimum configuration and high efficiency of planing surfaces).

[0178] Such separated panels or planes can be connected to the bottom by means of structural members comprising, e.g., short struts with flanges, or flanges alone (in the case of direct attachment of the panel or plane to the keel of the boat's hull, e.g.).

[0179] Moreover, in some embodiments it may be found rational to distance at least some of the planing surfaces in the form of panels or planes somewhat further away from the bottom of the boat by means of hydrofoil-style struts that could further enhance seaworthiness of the boat.

[0180] In this case, taking into account that the struts should support planing surfaces skimming along the surface of water, said hydrofoil-style struts could be made much shorter than the struts of hydrofoils, which should result in less bulky design and much shallow draft in comparison with conventional submerged hydrofoils in the displacement mode, not to mention the negligible draft of planing surfaces in comparison with hydrofoils in the operational high-speed mode of motion.

[0181] This circumstance is added to the absence of cavitation and corresponding absence of speed limitation as the main advantage of this hydrodynamic planing system over hydrofoils.

[0182] At the same time the separated from the bottom design of forward planing surfaces immediately solves such fundamental problem of the stepped hulls as ventilation of the step:

[0183] Without free access of atmospheric air, which often happens with stepped hulls at low speeds (when the step is submerged below the water surface) and during riding in rough seas, when high water level or passing waves block air access to the area behind the step, seal it and create a negative pressure zone, the bottom behind the step sticks to the water and generates a lot of resistance that slows down the boat and negates its effectiveness.

[0184] The forward planing surface of separated from the bottom design ensures direct, free and natural access of the flow and air over the upper surface to the trailing edges of the separated plane at any speed and mode of motion and this way prevents formation of any negative pressure zones, excludes any sticking to the water that eliminates any harmful increase in resistance and substantially improves efficiency of the boat in a wide range of speeds and under any sea-state conditions.

[0185] As another embodiment of the hydrodynamic design of the present invention, the boat can be provided with a separated forward planing surface installed at a certain distance and at some negative angle relatively the keel line of the boat, which angle corresponds to the optimum angle between the forward and aft planing surfaces following stipulations of the present invention. In this case the aft planing surface being integrated into the aft part of the boat's bottom (i.e., laminated as one piece altogether with the hull, e.g.) will have a proper spatial-angular position relative the forward surface keeping the straight and unbroken keel line of the boat.

[0186] It would be reasonable to provide said planes of such separated design of planing surfaces with streamlined convex upper surfaces being similar to upper surfaces of hydrofoils.

[0187] That would endow said separated planes with additional strength and additional lift during acceleration in transitional mode of motion (from displacement mode to purely planing mode as far as planes should still be submerged), while during motion at operational speed in the purely planing mode said streamlined convex upper surfaces will be excluded from generation of lift, i.e., 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.

[0188] To facilitate the transition from displacement to planing mode, which involves the generation of dynamic lift only by the bottom part of the separated planes with exclusively positive hydrodynamic pressures, and to expand the range of speeds of pure planing on these separated planes, the front part of the bottom surfaces of the separated planes can be equipped with additional flat surfaces extending from the leading edges of the cambered profiled part of planes' bottoms forward to the leading edges of the entire separated planes.

[0189] Such flat surfaces can be aligned with the base lines of the cambered profiles of the separated planes.

[0190] Either all the separated planing surfaces, or at least only the planes of the forward separated planing surfaces (in the case of the integrated aft planing surface) can be made foldable or retractable and, thus, when folded, not to protrude beyond the dimensions of the boat's hull, and, e.g., can snuggle against the hull of the boat, which could substantially facilitate operation in shallow water in the displacement mode, lading of the boat and make the boat trailerable.

[0191] To further improve the ease of lading and trailing the boat, the planing surfaces in the folded position can be retracted into special recess niches on the bottom of the boat to make them flush with the bottom surfaces.

[0192] The above hydrodynamic system following provisions of the present invention can also be applied to boats of catamaran and other multihull configurations.

[0193] In this case the forward and aft separated planing surfaces should be mounted under bottoms of the forward and aft portions of catamaran hulls correspondingly, completely support the hulls and keep them above the water surface during motion at operational speed, and, so, ensure low drag and high hydrodynamic efficiency of such catamaran or multihull boat, while removing of the dynamic support function from the hulls and generating dynamic lift only by separated planing surfaces makes it possible to provide the catamaran hulls with very sharp formations that mitigate wave impacts and favorably affect the seaworthiness of such double-hull or multihull boats.

[0194] In the same way a pontoon boat can be 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 bottom parts of pontoon logs. The use of two parallel hydrodynamic systems, each consisting of a forward and aft planing surface according to the present invention, could be more suitable for, e.g., a three-log pontoon boat design.

[0195] As another possible application, the hydrodynamic system of this invention can be used as a take-off and landing gear for seaplanes and wing-in-ground effect marine vehicles.

[0196] The minimized hydrodynamic drag during the take-off of such aerial vehicle guarantees the lowest possible power requirements, quick acceleration and the shortest take-off distance.

[0197] Accordingly, it is the object of this invention to provide a method and apparatus of various embodiments of a hydrodynamic design based on a system of successively arranged two dihedral planing surfaces of cambered hydrodynamic profiles, which system utilizes the effect of conformity of aft cambered planing surface to the wave trough downstream the forward planing surface in order to reduce hydrodynamic drag and improve efficiency of planing boats by means of special shape of the aft planing surface and spatial-angular relative arrangement of the two successive cambered planing surfaces.SUMMARY OF THE INVENTION

[0198] Various embodiments are disclosed herein for a method and apparatus of a hydrodynamic design of planing boat or vehicle provided with a hydrodynamic system comprising two successively arranged dihedral planing surfaces featuring cambered hydrodynamic profiles, which, in order to reduce the resistance and increase the efficiency of the boat or vehicle, are arranged in such a way so that the aft planing surface conformally corresponds the relief of the water surface disturbance generated by the forward swept back planing surface in the form of the wave trough, and for this purpose vertical longitudinal sections of the aft surface are displaced vertically relatively the base hydrodynamic lines of sections of the forward planing surface, which displacements are equal to the ordinates of the surface of the wave trough relatively the base hydrodynamic lines of sections of the forward planing surface at the position of the aft surface, and base hydrodynamic lines of sections of the aft surface are turned relatively the base hydrodynamic lines of sections of the forward surface by the angle being equal to sum of the angle of slope of the wave trough at the position of the aft surface and the difference between the angles of incidence of the sections of the aft and forward surfaces, which provisions establish clear conditions for optimum shape of the aft surface and optimum spatial-angular relative arrangement of the two successive cambered planing surfaces in order to ensure the maximum efficiency of this hydrodynamic system and the boat or vehicle in general.

[0199] In some embodiments the vertical longitudinal sections of the aft surface are positioned below the base hydrodynamic lines of sections of the forward planing surface and turned clockwise relatively the base hydrodynamic lines of sections of the forward planing surface when viewed from the left (port) side of the boat or vehicle, while the aft planing surface is provided with higher angle of deadrise than 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.

[0200] In some embodiments 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.

[0201] In some embodiments 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.

[0202] In some embodiments 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.

[0203] In some embodiments cambers of sections by vertical longitudinal planes linearly increase along the span of at least one of said planing surfaces from the keel line and the center plane outwards to the tip chines of said planing surface.

[0204] In some embodiments the base line of each of vertical longitudinal sections of forward cambered planing surface is inclined nose-dive at some negative angle relatively the keel line of the boat or vehicle.

[0205] In some embodiments the camber of the planing surfaces represents a Virgil Johnson three-term camber.

[0206] In some embodiments the outside tips of at least some of planing surfaces provided with end plates or deflectors protruding below the profiled camber of the tip sections of said planing surfaces.

[0207] In some embodiments the width of the forward planing surface extends beyond the width of boat's chines by means of side protrusions.

[0208] In some embodiments said protrusions provided with convex upper surfaces being similar to the upper surfaces of hydrofoils.

[0209] In some embodiments the cambered planing surfaces are made in the form of panels or planes separated from the boat's bottom and connected to the bottom by means of structural members.

[0210] In some embodiments said structural members comprise struts and / or flanges.

[0211] In some embodiments said separated planing surfaces provided with convex upper surfaces being similar to the upper surfaces of hydrofoils.

[0212] In some embodiments 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.

[0213] In some embodiments the forward cambered planing surfaces of the separated from the boat's bottom design inclined at some negative (nose-dive) angle relatively boat's keel line, while the aft cambered planing surface integrated into the bottom of the after-body of boat's hull.

[0214] In some embodiments the separated planing surfaces provided at their bottom part with flat portions arranged between the leading edge of said panels or planes and the leading edge of the cambered profiled portion of said bottom part.

[0215] In some embodiments 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.

[0216] In some embodiments the forward and aft separated planing surfaces of the hydrodynamic system following stipulations of this invention mounted under bottoms of the forward and aft portions of hulls of catamaran or multihull boats correspondingly.

[0217] In some embodiments at least one pair of said forward and aft cambered planing surfaces in the form of separated panels or planes is mounted at the bottoms of pontoon logs.

[0218] In some embodiments the hydrodynamic system following stipulations of this invention serves as a take-off and landing gear for seaplanes and wing-in-ground effect marine vehicles.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.

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.

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