Ships – Watercraft with means used in providing sailpower – Having specifically defined hull shape
Reexamination Certificate
2003-03-14
2004-02-24
Avila, Stephen (Department: 3617)
Ships
Watercraft with means used in providing sailpower
Having specifically defined hull shape
C114S140000
Reexamination Certificate
active
06694907
ABSTRACT:
BACKGROUND
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., “Principles of Yacht Design”, 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 &lgr;, resulting in a leeway of V sin &lgr;. Since the turning moment M
k
, 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 ĵ
S
and î
S
respectively, of the course sailed reference frame {overscore (S)}, as are the driving and heeling forces created by the wind. The axis ĵ
S
of reference frame {overscore (S)} is oriented parallel to the velocity vector of the sailboat and defines a plane with î
S
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 ĵ
S
. 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 &phgr;.
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 w
cs
is increased to w
lw
, and the length is decreased generally as a function of L
lwl
sin &lgr; and L
lwl
cos &lgr; respectively, where L
lwl
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 &lgr; is analogous to the angle of attack &agr;.
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 |&lgr;|≠0 and reducing pressure recapture for all &lgr;. As with all hydrofoils of symmetric nature, the lift and drag are a function of the leeway angle &lgr;. The minimum drag coefficient C
Do
occurs at &lgr;=0 and while lift or lateral force increases generally linearly with &lgr;, the drag increases exponentially proportional to &lgr;
2
. 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 b
2
/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
π
where
∂
C
l
∂
λ
is the slope of the lift curve. Thus the hull for typical sailboats have a very low AR and accordan
Avila Stephen
Muldoon Patrick Craig
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