A primary concern in the development of sailing vessels has been the persistent quest and desire to improve speed. More sail area, more efficient sails, low friction paint, lighter materials and a plethora of hull designs have been created in furtherance of this venture. In the arena of hull designs, the principle approach is concentrated on reducing the hull drag thus increasing the speed for a given driving force derived from the sails.
FIGS. 1A-1B show the different forces acting on a sailing yacht 100. These figures are described in detail in Larson, L., Eliasson, R E., xe2x80x9cPrinciples of Yacht Designxe2x80x9d, International Marine/Ragged Mountain Press, 2nd edition (Jun. 2, 2000), the entirety of which is herein incorporated by reference. (In the plan view the horizontal components of the forces are displayed, while the lateral and vertical forces are shown in the rear view.) When the hull is driven through the water a resistance is developed. Under equilibrium conditions, when the yacht is sailing at constant speed in a given direction, the resistance is balanced by a driving force from the sails. Unfortunately, this equilibrium condition cannot be created without at the same time obtaining a side force, which in turn is balanced by a hydrodynamic lateral force or side force. The latter is developed by the underwater body when sliding slightly sideward. This deviation from the steered course is the leeway angle xcex, resulting in a leeway of V sin xcex. Since the turning moment Mk, under equilibrium conditions must be zero, the resulting hydrodynamic and aerodynamic forces in the horizontal plane must act essentially along the same line. The drag force and lateral force are force vectors parallel to the vectors ĵS and îS respectively, of the course sailed reference frame {overscore (S)}, as are the driving and heeling forces created by the wind. The axis ĵS of reference frame {overscore (S)} is oriented parallel to the velocity vector of the sailboat and defines a plane with îS that is parallel to the surface of the body of water in which the sailboat rests, {overscore (S)} is not a inertial reference. In contrast the boat reference frame {overscore (B)} includes vectors î, ĵ and {circumflex over (k)} representing the longitudinal, lateral and vertical axis of the boat, reference frame {overscore (B)} respectively, which is fixed in the sailboat.
The view at the bottom of FIG. 1 is along the direction of motion ĵS. It is seen that the resulting hydrodynamic and aerodynamic forces are at right angles to the mast. This is not exactly true but is an approximation made in sailing yacht theory. The heeling moment from the aerodynamic force is balanced by the righting moment from the buoyancy force and weight. The angle from perpendicular {circumflex over (k)}S of the sailboat caused by heeling is defined as the heeling angle xcfx86.
In FIG. 1A the apparent wind direction is shown. This is not the true wind direction, since the wind felt onboard the yacht is influenced by its speed through the air. FIG. 2 illustrates the relations between the true and apparent wind speeds and direction, the velocity triangle.
FIG. 3 shows a resistance curve for a typical sailboat being towed upright in smooth water. At low speeds the dominating component is the viscous resistance due to frictional forces between the hull and the water. The friction gives rise to eddies of different sizes, which containing energy left behind the hull in the wake. This component increases relatively slowly with speed, as opposed to the second component, the wave resistance, which occurs because the hull generates waves, transferring energy away from the vessel. The sum of the viscous and wave resistance components is referred to as the upright resistance.
FIG. 4 shows a breakdown of the total resistance of a typical sailboat beating to windward at 6.8 knots in a fresh breeze. The viscous resistance has been subdivided into components. In addition to the viscous and wave components, there are three new forces: heel, induced resistance and added resistance. The heel resistance is the sum of the changes in viscous and wave resistance due to heel. This component is introduced in sailing theory for convenience. Since the method for obtaining the two resistance components for upright hulls are well established in ship hydrodynamics it is an advantage to consider the effects of heel separately.
The induced resistance is cause by the leeway. When the yacht is moving slightly sideways, water flows from the higher pressure on the leeward side, below the tip of the keel and rudder, and also below the bottom of the hull, to the lower pressure on the windward side, thus creating longitudinal vortices.
There are four major resistance components: the viscous resistance, the wave resistance, the induced resistance and the added resistance in wave. All of which are functions of the shape of the hull.
FIG. 5 shows a typical pressure distribution on the hull at a given depth. It is seen that the bow and stem pressures are higher than in the undisturbed water at this depth, while the pressure in the middle part of the hull is lower. A slightly lower pressure is found at the stern than at the bow, giving rise to the resistance component, which is indirectly cased by friction through the boundary layer.
The pressure distribution is related to the Fineness Ratio (FR) which is generally analogous to a first order aspect ratio. The larger the FR, the less significant the pressure differential and the component of drag associated with the pressure differential. The FR commonly applied in aeronautics to quantify the drag on a fuselage and is defined by the length of fuselage divided by its width, L/w.
The higher the FR the lower the pressure drag induced on a body. As in an aircraft the penalty of increasing FR is an increase in the friction component of the viscous drag; however, the reduction of pressure drag generally more than offsets this increase. A detrimental consequence of leeway is a reduction in the FR, as seen in FIG. 1. The width of the hull wcs is increased to wlw, and the length is decreased generally as a function of Llwl sin xcex and Llwl cos xcex respectively, where Llwl is the length of the hull at the water line, resulting in the FR being reduced and an increase in pressure drag.
The drag increase due to heel and leeway while related and generally described in relationship with FR described above, is more completely described by modeling the submerged hull and the keel as two distinct airfoils. In the case of the hull a very poor airfoil, in this case xcex is analogous to the angle of attack xcex1.
The submerged portion of the hull can be modeled as a short symmetric hydrofoil. The hull hydrofoil for a typical sailboat has a relatively sharp leading edge and a more blunt trailing edge, as seen from FIG. 1. The result of these characteristics further diminish the drag performance desired in hydrofoils and analogously airfoils by increasing the onset of flow separation for |xcex|xe2x89xa00 and reducing pressure recapture for all xcex. As with all hydrofoils of symmetric nature, the lift and drag are a function of the leeway angle xcex. The minimum drag coefficient CDo occurs at xcex=0 and while lift or lateral force increases generally linearly with xcex, the drag increases exponentially proportional to xcex2. An additional component of drag related to the induced drag is predominantly a function of the three dimensional characteristics of the hydrofoil, specifically the Aspect Ratio (AR) defined as b2/S where b is twice the depth of the hull and S is twice the lateral surface area of the submerged hull projected normal to the lateral axis. The resulting drag coefficient is generally given as:       C    D    =            C              D        0              +                            (                                                    ∂                                  C                  l                                                            ∂                λ                                      ⁢            λ                    )                2                    AR        ⁢                  xe2x80x83                ⁢        π            
where       ∂          C      l            ∂    λ  
is the slope of the lift curve. Thus the hull for typical sailboats have a very low AR and accordantly for xcexxe2x89xa00 a very undesirable L/D ratio.
The keel, on the other hand, is not subject to the same constraints and limitation as the hull, such as buoyancy, cabin space, heel stability, bending moments and other structural and functional requirements implicit to the hull. Therefore, the keel can be designed with more favorable hydrofoil characteristics to achieve an advantageous L/D ratio. However, regardless of how well designed the keel, the leeway angle of both the hull and the keel are identical. Therefore to obtain the necessary lateral side force to counteract the lateral component of drag and lift created by the sail, a drag penalty in addition to that associated with the lift or lateral force creation function of the keel is experienced due to the encumbrance of the hull, thus reducing the speed of the sailboat.
Several prior art approaches have been employed to reduce this drag penalty. Single tack racing sailboats have been created that include a cambered keel that has a fixed angle of incidence xcex1i so that no leeway angle is experience by the hull at the design speed. However, these specialized craft do hot operate effectively on the opposite tack or other off design environments, a characteristic that renders such craft unusable in cruising and a vast majority of racing formats.
Another common approach in the prior art has been to have a variable angle keel with respect to the hull. The angle of attack of the keel is varied by the crew in order to reduce or eliminate the leeway angle experienced by the hull. While these keels are effective, the mechanical requirements add some complexity to the sailboat and take additional mental effort by the crew to coordinate the keel angle and rudder deflection with the lateral force required to balance the sailboat while maintaining a proper course and proper sail trim. Furthermore, most racing formats discourage or restrict the use of variable angle keels.
The subject matter of the present disclosure seeks to reduce the hull component of heel resistance in its various forms, including but not limited to those discussed above, which essentially is the marginal increase of the resistance components due to the leeward motion of the sailboat with respect to the course steered.
The objects of the subject matter of the disclosure and embodiments herein provide a hull with a fixed angle keel with respect to the hull that when heeled, orients the keel to an angle of attack substantially related to the heel angle. The angle of attack being sufficient to create on the keel a lateral force substantially equal and opposite to the lateral force derived from the wind. The submerged portion of the hull however, remains symmetrical and oriented parallel to the course sail as does its associated drag contribution vector. Thereby reducing or substantially eliminating the lateral force generated by the hull and the associated drag contribution.
It is an object of the disclosure to overcome the problems in the prior art and present a novel sailboat hull. An embodiment of the sailboat hull having a bow, a stem, a starboard side, a port side and a keel, the hull defined with a longitudinal axis, a lateral axis, and a vertical axis, each of said axes is perpendicular to each of the other axes. An embodiment of the sailboat hull having a first plane defined by said longitudinal axis and said vertical axis and a bottom surface symmetric with respect to said first plane. The hull is further defined by at least one starboard straight line lying on the starboard side of said first plane and intersecting the first plane at a point at or aft of the stem. The hull contains a plurality of starboard cross sections located along the starboard straight line, each with a hull contour defined by the intersection of one of a plurality of cutting planes and the bottom surface on said starboard side and an orthogonal line perpendicular to a line tangent to the hull contour, and intersecting the starboard straight line. The orthogonal line of the hull embodiment is within the respective one of the plurality of cutting planes; and a portion of the hull contour proximate to the orthogonal line is symmetric with respect to the orthogonal line. The sailboat hull having at least one of said plurality of starboard cross sections located between ⅔rds of the hull length Llwl and the bow of the hull and, the keel is symmetric with respect to said first plane.
It is another object of the disclosed subject matter to present a sailboat hull with a bow, a stem, a starboard side, a port side and a keel. The hull defined by a longitudinal axis, a lateral axis, and a vertical,:axis, where each of said axes is perpendicular to each of the other axes. The hull contains a first plane defined by the longitudinal and vertical axis; a bottom surface symmetric with respect to the first plane; and at least one starboard straight line. The starboard straight line of the hull lies on said starboard side of the first plane and intersects it at a point at or aft of said stern. A plurality of stations are located along at least one starboard straight line, with a station positioned between ⅔ of the length Llwl of the hull and the bow. Each of the plurality of stations have an orthogonal line intersecting at least one starboard straight line, where the bottom surface forms the respective intersections, and a portion of the bottom surface proximate to the respective intersection is normal to the orthogonal line. In embodiments of the hull, each station""s orthogonal line is co-planar with each of the other stations orthogonal line and the keel is symmetric with respect to the first plane.
It is still another object of the disclosed subject matter to present a novel improvement to a method of reducing the drag on a sailboat traveling on a body of water under the power of the wind. The sailboat having a fixed centerline and being at a angle of heel to the leeward. A novel improvement being passively inducing a keel angle of attack proportional to the angle of heel. The improved method includes providing a hull wherein the hull is symmetric with respect to a first plane defined by the centerline and perpendicular to a surface of the body of water when the heel angle xcfx86 is zero, providing a rigid keel with a zero lift line parallel to said centerline, and, providing at least one starboard path line, The starboard path line being parallel to the direction of travel while on a port tack at an angle xcex from the centerline and intersecting the first plane aft of the stern. The improvement also includes shaping a starboard side of the hull such that a portion of the starboard side proximate to a starboard plane is substantially symmetric with respect to the starboard plane, wherein the starboard plane is perpendicular to the surface of a body of water and includes at least one starboard path line when the hull is heeled to starboard.
It is yet another object of the disclosed subject matter to present a novel sailboat hull with a bow, a stern, a starboard side, a port side, and a keel. The hull defined by a longitudinal axis, a lateral axis, and a vertical axis Each of the axes is perpendicular to each of the other axes. Embodiments of the hull include a first plane defined by the longitudinal axis and vertical axis, a bottom surface symmetric with respect to the first plane and a secondary plane oblique to the first plane and intersecting the longitudinal axis at or aft of the stern and intersecting the bottom surface on the starboard side. The secondary plane in embodiments of the hull intersects the first plane at an angle "PHgr" about the longitudinal axis and an angle xcex9 about the vertical axis, where "PHgr" and xcex9 do not equal zero. In an embodiment of the hull, a starboard portion of the bottom surface of the hull proximate to the secondary plane is substantially symmetric with respect to the second plane; the starboard portion is longitudinally located at least between the mid-ship and bow, having a length of at least 10% of the hull length at the water line LLWL.
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