Patent Publication Number: US-2011048306-A1

Title: Hydrofoil stabilizer of list, pitch and roll for sail vessels

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     Not Applicable. 
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not Applicable. 
     THE NAMES OF THE PARTIES TO A JOINT RESEARCH AGREEMENT 
     Not Applicable. 
     INCORPORATED-BY-REFERENCE OF MATERIAL SUBMITTED ON A COMPACT DISK 
     Not Applicable. 
     FIELD OF THE INVENTION 
     The present invention relates to sailboats, and more particularly to improved hydrofoil list, roll and pitch stabilizers for a sailboat. 
     DESCRIPTION OF THE RELATED ART 
     A type of conventional sailing boat is one, which comprises a hull, a sail assembly, and a keel structure, wherein the function of the keel is to operate as a vertical hydrofoil which resists lateral movement of the boat partially compensating wind and turn list so the boat can travel on an angled course in an upwind direction. For this, the keel has to be weighted so as to add ballast and lower the center of gravity of the boat to provide the stability of the boat. Despite of many modifications introduced in sailing boats, this basic design of sailing boats has for many centuries been the one most commonly used; but, the practice reveals that this solution is not enough to compensate wind and turn list, roll, pitch and yaw, which affect speeding yachts. Therefore, there were numerous attempts to solve this problem by means of underwater wings—hydrofoils—installed in different parts of yachts. Today it becomes even more important, because ship designer try to utilize “green energy”—the well-known power of wind—not only for small yachts, but also for large ships. 
     It is known in the prior art a number of applications of hydrofoils in boats. One of the oldest hydrofoils, which is known from beginning of XX century, is the bilge keel—the long underwater hydrofoil placed along a hull. Although not as effective at reducing roll, bilge keels are cheaper, easier to install, and do not require special internal space inside the hull. 
     One of the best known applications of hydrofoils is to lift the hull of the boat out of the water in such a way that the hull is being supported entirely by the lifting force provided by such hydrofoils—underwater wings—traveling through the water in high speed. This application is perfectly working in motor boat, but it can not be utilize in sail boat because of dangerous list that can turn the sailboat over keel. 
     There have been other proposed applications of hydrofoils—underwater fins—in boats to provide stability. One such application is shown in U.S. Pat. No. 1,499,900 issued to Zukucker, wherein a plurality of hydrofoils are mounted on two sides of a power boat. These fins may be adjusted both upwardly and downwardly to improve the stability of the boat. In two other patents, U.S. Pat. Nos. 3,377,975, Field, and 3,842,777 issued to Larsh, laterally extending fins are provided on opposite sides of a ship to alleviate any roll condition of the ship. 
     There have also been other various attempts in the prior art to stabilize sailing vessels by the use of hydrofoils. For example, in U.S. Pat. No. 1,356,300 issued to McIntire there are pair of bulky “stabilizing planes” mounted at the outer end of outrigger arms. Each stabilizing plane is slopped at a downward and inward inclination so, according to the author, compensating forces causing boat&#39;s list and yaw. 
     The similar solution dedicated to multi-hull boats is shown in U.S. Pat. No. 3,949,695 issued to Pless, which comprises pair of hydrofoil members mounted at the outer ends of outrigger arms on opposite sides of the hull. 
     As was noted above, hydrofoil members proposed in these patents are bulky, significantly increase width of the vessel and, because of this, useless. 
     U.S. Pat. No. 4,058,076 issued to Danahy shows hydrofoil members functioning in the similar way as those in the previous patents. In this patent the hydrofoil members look like triangle extending downwardly to end of the keel. 
     This solution has obvious disadvantages: the strange shape of hydrofoil members proposed in U.S. Pat. No. 4,058,076 makes the yacht ugly, and, because the hydrofoils is extended below the center of gravity of the yacht, the hydrodynamic forces applied to parts of such hydrofoils above and below the center of gravity produce momentums applied in opposite direction which can not effectively compensate the list. 
     U.S. Pat. No. 4,193,366 issued to Salminen proposes a single hydrofoil—underwater wing—profiled in such a way that provides vertical downward forces that, according to the author, have to compensate lateral aerodynamic force component exerted by wind against the sail assembly, thus diminishing the list and yaw angle in the travel of the boat. Analysis of forces and momentums (see  FIG. 1 ) applied to hydrofoil proposed in U.S. Pat. No. 4,193,366 shows that the hydrofoil does not produce any total momentum that compensates the list, because symmetric hydrofoil positioning (on the yacht) about center of gravity (C.G.) produces two equal momentums (in vertical plane passing the transversal axis) that compensate each other. Moreover, it causes yacht yaw. When such yacht travels without list (or roll), no rotational momentum is applied to the yacht. But when it starts listing, the center of hydrodynamic drag forces applied to the hydrofoil stills in the middle of the foil, but, because of the list, it is shifted at the distance of δ about vertical line passing through C.G. of the yacht. Therefore, hydrodynamic drag F drag  applied to the hydrofoil causes momentum M drag  turning the yacht in horizontal plane—the yaw. Moreover, wind forces F W  applied to the center of pressure of yacht&#39;s sail try to turn the yacht in the same direction; so the hydrofoil proposed in U.S. Pat. No. 4,193,366 can not compensate the list and yaw, but, just the reverse, cause significant yaw directly depending on angle of list of the yacht. 
     There have been other attempts in the prior art to utilize hydrofoils in combination with a set of “ailerons” lifting the hull of the sailing vessel totally out of the water. One of such devices is shown in U.S. Pat. No. 3,373,710 issued to Steinberg, in which a hydrofoil is positioned beneath the boat, wherein the “ailerons” are works as ailerons on an aircraft to maintain the sailboat in an upright position. 
     The similar, but more complex arrangement is proposed in U.S. Pat. No. 3,800,724 issued to Tracy. It shows a “winged sailing craft” which has a vertical airfoil to provide a force for forward travel, and a horizontal airfoil to provide stability. In addition, there are provided upper and lower hydrofoils. The upper hydrofoil lifts the vessel out of the water at lower speeds, and the lower hydrofoil provides either positive or negative lifting forces as required. 
     As was noted above, solution proposed in these two patents can not be applied to sail vessels, unlike to motor boats. All sail vessels are affected by wind forces applied high above the center of gravity of the vessel. These forces power the vessel, but also generate high momentum that is heeling over the vessel and tries to turn it upside down. To make sail vessel stable, a heavy ballast is placed below its center of gravity. Because of this, hydrofoils lifting a sail vessel from water make it very unstable. Analysis shows that it is necessary to install large hydrofoils or airfoils (having size of a sail) to stabilize such vessel. Obviously, such solution can not be utilized in yacht design. 
     Another solution is represented in U.S. Pat. No. 3,505,968 issued to Gorman and U.S. Pat. No. 3,968,765 issued to Menegus. They show a hydrofoil mounted below a hull of a sailboat and working as a conventional keel, but rotating about a horizontal longitudinal axis so that its lifting force can be exerted laterally to one side or another one. In one of embodiments, the hydrofoil is turned in such a way that provides an upward dynamic lifting force. 
     The task of vessel stability is a complex one, where all forces, —static and dynamic ones—affecting the vessel, particularly, sailing vessel, have to be taken in account. Moreover, because vectors of these forces do not pass through the center of gravity of the vessel, they produce momentums that try to turn the vessel in all three planes that in many cases decrease the vessel stability. As analysis of the prior art shows that the authors of the prior art miss some forces and momentums; in the result, the task of eliminating of adverse factors affecting sailing vessels has not been solved yet. Also, the hydrofoils proposed in the previous art affect yacht stability causing unnecessary vertical lifting and yaw. 
     SUMMARY OF THE INVENTION 
     In the present invention, there is a sailing vessel comprising a hull and a sail assembly that is mounted to the hull and arranged to be positioned relative to wind which is blowing at an angle to the longitudinal axis of the hull so that the sail develops an aerodynamic force having a lateral aerodynamic force component and a forward aerodynamic force component. The lateral aerodynamic force component causes list and yaw—the adverse factors affecting sailing vessels. The solution proposed in the present invention is based on analyses of all momentums affecting a sailing vessel; therefore it overcomes the unsolved problems of the prior art by means of utilization of specially positioned above and below the center of gravity of the vessel stationary and pivoted hydrofoils—the object of the present invention—which compensate forces causing wind list and yaw also minimizing roll and pitch. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
         FIG. 1  depicts diagram of forces and momentums applied to sailing vessel having hydrofoils of the prior art. 
         FIG. 2  depicts the preferred embodiment of the present invention—the scheme of sailing yacht having completely submerged biplane hydrofoils. 
         FIG. 3  depicts diagram of forces and momentums applied to sailing vessel having biplane hydrofoils of the preferred embodiment. 
         FIG. 4  depicts variant of hydrofoil having shape of “seagull wing”, 
         FIG. 5  depicts variant of the preferred embodiment of the present invention—the scheme of double-hull sailing yacht employing biplane hydrofoil assembly, 
         FIG. 6  depicts variant of the preferred embodiment of the present invention—the scheme of sailing yacht having partially submerged upper foils—and diagram of forces and momentums applied to sailing vessel having hydrofoils of this embodiment. 
         FIG. 7  shows example of positioning of the hydrofoils on Alberg  30  yacht. 
         FIG. 8  depicts the scheme of another embodiment of sailing yacht that comprises assembly of pivoted hydrofoils, where  FIG. 8   b  shows possible design of the foil-mounted actuator. 
         FIG. 9  depicts the scheme of another embodiment of sailing yacht that comprises partially submerged hydrofoils assembled in a triplane manner. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION 
     Biplane Hydrofoils 
     The scheme of sailboat of the preferred embodiment of the present invention is shown in  FIG. 2 . This boat comprises a hull  1 , a sail assembly  21  and  22 , a keel  3 , a rudder  4 , a mast and hydrofoil members  6 ,  7 ,  8 ,  9 ,  10 ,  11 ,  12  and  13 . The arrangement of the hydrofoil members  6 ,  7 ,  8 ,  9   10 ,  11 ,  12  and  13  is of particular significance in the present invention and will be discussed in detail below. It also can comprise a small engine that is used when wind speed is not enough to power said boat. 
     The sail assembly is or may be of conventional design, and as shown on  FIG. 2  comprises a mast  5  to which a head sail  22  and a mainsail  21  are mounted. The hull  1  has a conventional design of a sailing yacht—a rounded, elongate configuration symmetrical about its longitudinal center axis. 
     Description of the First Variant of the Preferred Embodiments of the Present Invention 
     A Biplane Assembly of Submerged Hydrofoils Counteracting Vessel&#39;s Roll and Pitch 
     As shown on  FIG. 2 , the assembly of static (non-pivoted) hydrofoil members  6 ,  7 ,  8 ,  9 ,  10 ,  11 ,  12  and  13  is rigidly mounted on the hull  1  from both sides as four rows above and below the center of gravity (C.G.) of the yacht in such a manner that the vertical distance between plain of upper rows containing hydrofoils  6 ,  8 ,  10  and  12  to C.G. is equal to the vertical distance between plane of lower rows containing hydrofoils  7 ,  9 ,  11  and  13  and C.G.; so planes of the upper and lower hydrofoils are symmetrical about horizontal plane passing through C.G., wherein effective surfaces of the hydrofoils are equal. Also, distance between the pair of hydrofoils  6  and  7  ( 10  and  11 ) and C.G. is equal to distanced from the hydrofoils  8  and  9  ( 12  and  13 ) and C.G.; therefore these pairs of hydrofoils are symmetric about transverse axis passing through C.G. 
     The hydrofoils  6 ,  7 ,  8 ,  9 ,  10 ,  11 ,  12  and  13  are placed below vessel&#39;s waterline and hydrodynamically profiled to provide a carrying power, wherein the hydrofoils  6 ,  10  and  8 ,  12  provide upward lifting forces and the hydrofoils  7 ,  11  and  9 ,  13  provide downward forces. This arrangement of the hydrofoils of the preferred embodiment together with the hydrofoil shape provides compensation of adverse momentums affecting a sailing vessel equipped with the hydrofoils of the previous art; also, the assembly proposed in the preferred embodiment of the present invention develops momentum compensating roll and pitch (working as a shock absorber). 
     Diagram of forces and momentums applied to sailing vessel having biplane hydrofoils of the preferred embodiment is depicted in  FIG. 3 . 
     The diagram shows that all momentums and lifting forces developed by the hydrofoils compensate each other. Therefore, the arrangement of the symmetrically-positioned biplane hydrofoils proposed in the present invention utilizes hydrodynamic drag forces; it works as a shock absorber to compensate roll and pitch without other dynamic momentums and forces affecting a sailing vessel. 
     The shock absorption force (hydrodynamic drag) of a hydrofoil depends on surface of the hydrofoils and relative water-hydrofoil velocity. 
     This force is determined by formula: 
         F=C   x   ×s×ρ×V   2 /2  [1],
 
     where C x —coefficient depending on shape of hydrofoil (for rectangular flat plate C x ≈1.1), s—projection of the surface of hydrofoil on the plane that is in perpendicular to vector of velocity, V—relative water-hydrofoil velocity, ρ—density of water. 
     When a yacht rolling, vector of water-foil velocity is lying on tangent to circumference having the center in C.G; so projection of the surface of hydrofoil on the plane that is in perpendicular to vector of velocity can be calculated by the formula: 
         s=S ×cos β  [2],
 
     Where: 
     β—angle between radius connecting C.G to geometrical center of the foil and horizontal plane of the yacht (see  FIG. 3 ),
 
S—hydrofoil surface.
 
     For periodical roll with amplitude of A (maximal movement of the foil about horizontal plane) and period T, the force will be approximately determined by the following formula: 
         F= 4π 2   ×s×ρ×A   2   /T   2  cos 2 (2 πt/T ).
 
     According to this formula, this drag force is a periodical function. Amplitude and mean value of the force—F a  and F m  respectively—applied to the hydrofoil will be determined by the formulas: 
         F   a =4π 2   ×s×ρ×A   2   /T   2  and  F   m =1/2 F   a =2π 2   ×s×ρ×A   2   /T   2 .
 
     Thus, mean value of momentum developed by the single foil can be determined by approximate formula: 
         M   m =2π 2 ×( a−L )× s×ρ×A   2   /T   2   [3],
 
     where a—½ of wing (foil) span, L—width of the foil. 
     Therefore, all 8 foils of this assembly will produce the compensating momentum of 8 M m . 
     As an example, if amplitude of pitch is 1 m and period of the pitch is 10 sec, the single hydrofoil having surface of 0.5 m 2  produces the amplitude of the resistance force F a  of 2200 N or 440 lbs; the mean value of this force producing by all hydrofoils will be about 1,760 lbs (800 kg), and mean value of the momentum determined by formula [3] (for large racing yacht with B=28 ft) will be about 24,600 lbs-ft (3,300 kg-m). 
     The hydrofoils of the present embodiment can be additionally profiled in such a way that plane of each foil is bent and have shape of “seagull wing” as depicted in  FIG. 4 , wherein plane of internal part of said foil passes yacht&#39;s C.G and plane of external part of said foil is in parallel to horizontal plane of the yacht. Therefore, internal part of said foil efficiently compensate yacht&#39;s roll (cos β=1 in formula [2]); and external part of said foil, which is in parallel to horizontal plane of the yacht, efficiently compensate yacht&#39;s pitch. 
     The hydrofoils of the present embodiment can be utilized in “combined yachts”—yachts jointed together in the process of utilization of old-model yachts. The scheme of such yachts and position of the hydrofoils on the hull of such yachts are shown on  FIG. 5 . The yacht shown on  FIG. 5  is a combination of two separate medium-size yachts, which hulls  41  and  42  were cut in such a way that allows said hulls to be jointed together. Such solution allows not only utilizing such yachts, but also enlarging its size so transforming it into higher-category yachts. For example, using this way of utilization for two medium-size yachts, such as Alberg  30  and similar, allows transforming them into single double-size yacht. Because such combined yachts has doubled average length (LOA), but keeps original beam (B), its roll an pitch stabilization is even more important than stabilization of a conventional yacht. 
     The hydrofoil assembly of this embodiment comprises two pairs of rows of hydrofoils—upper and lower ones—positioned in biplane manner, wherein upper rows (left and right) are positioned on both sides of the yacht above and below yacht&#39;s C.G on equal distances from said C.G. Each row contains three hydrofoils—front  43 , middle  44  and rear  45 , wherein the middle foil  44  is positioned in the place where the two hulls  41  and  42  are jointed. This position of hydrofoils allows compensating momentum bending yacht&#39;s hull that is important in the case of high pitch. The solution of this embodiment becomes even more efficient when the hydrofoils are pivoted and computer-controlled ones as described below in the following embodiment. 
     Description of the Second Variant of the Preferred Embodiments of the Present Invention 
     Biplane Assembly of Partially Submerged Hydrofoils Counteracting Vessel&#39;s List 
     The static hydrofoil assembly of the first variant of the previous embodiment can stabilize a sail boat in the cases of roll and pitch, but does not compensate wind and turn lists and yaw. This problem can be solved by means of a static hydrofoil assembly arranged in such a way that one of upper foils can be partially submerged (or completely out of water) when a sailing vessel is heeling over. In this case momentums generated by upper foils do not compensate each other and the resulting momentum is applied in opposite direction to the momentum generated by lateral wind so compensating wind list. 
     Scheme of hydrofoil assembly and diagram of forces and momentums applied to sailing vessel having biplane hydrofoils of this embodiment is depicted in  FIG. 6 . Here, the hydrofoil assembly is a submerged biplane one that is similar to the hydrofoil assembly of the first variant of the preferred embodiment so comprising two upper rows of profiled hydrofoil that produce upward lifting force, and two lower rows of profiled hydrofoils that produce equal downward lifting forces, wherein planes of upper hydrofoils and lower hydrofoils positioned on equal distances from C.G. of the yacht, and, unlike the hydrofoil assembly of the first variant, depth of the upper hydrofoils allow one row of said upper hydrofoils rising above water when vessel&#39;s list exceeds some predetermined value. 
     As was noted above, the conventional way of yacht stabilization is the hydrostatic one utilizing heavy keel, when C.G. of the yacht is positioned maximally below waterline. In the case, when a yacht is heeling over, the center of buoyancy (C.B.) of the yacht is shifted horizontally about its center of gravity (C.G.) on the distance named Righting Arm (G.Z.), so hydrostatic forces provide momentum compensating yacht&#39;s list and pitch. Even though exact calculation of G.Z is difficult, for small angle of list the hydrostatic compensating momentum can be defined by the approximate formula: 
         M   h   =Disp×G.Z=Disp ×sin φ×( b +δ)  [4],
 
     where:
 
(b+δ)—distance from waterline to C.G.,
 
Disp—displacement (weight of the yacht),
 
φ—angle of roll (list).
 
     Maximal angle of roll (list) for racing yachts is known as LPS (Limit of Positive Stability). It is the roll angle at which a boat will no longer right itself and become inverted (capsized). All racing yachts is designed for LPS of about 100-120 arc degrees. LPS roll angle is the extreme limit and the practical value of maximal roll (list) can be determined by the condition when yacht&#39;s deck touches water. It is approximately described by the formula: 
       φ m =arctan(2 h/B )  [5],
 
     where:
 
h—elevation of yacht deck above waterline,
 
B—yacht&#39;s overall beam.
 
     Therefore, for the yacht with LOA (Length Overall) of 141 ft, B (Overall Beam) of 28 ft, D (Draft) of 19 ft, when height of yacht&#39;s deck of fully loaded yacht is 5 ft, the maximal list will be about 20 arc degrees. 
     As depicted in  FIG. 6 , upper hydrofoils are positioned below waterline on depth of δ. Thus, when the yacht is listing, hydrofoils positioned on one side of the hull are going up, whereas the hydrofoils positioned on the opposite side of the hull are going down. When ascending foils start going out of water, the lifting force of the foils declines because just part of these foils contacts with water. 
     Height of end of the foil rising above water can be determined by the formula: 
         H=a−b ×(1−cos  h )/sin φ−δ/sin φ,
 
     where:
 
a—½ of wing span of the hydrofoil (wing),
 
b—distance from C.G to hydrofoil plane,
 
δ—depth of the hydrofoil plane,
 
φ—angle of the list.
 
     Dry width of the hydrofoil (width of part of the foil that is out of water), can be determined by the formula: 
         w   dry   =a −( b +δ)/sin φ+ b/tgφ   [6].
 
     The dry width w dry  may be larger than real width W of the hydrofoil. It means that all surface of the hydrofoil is above water. When it happens, only hydrofoils, which still in water produce the lifting force and compensating momentum. 
     For the large racing yacht (mentioned above) with LOA=141 ft, B=28 ft, D=19 ft, which is equipped with hydrofoil assembly of the present embodiment and having depth of the upper wing plane δ=2 ft, distance from C.G to wing plane b=6.7 ft, ½ of wing span of the hydrofoil a  32  14 ft, the possible dry length w dry  of the foil determined by formula [6] is shown on the Table 1: 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Angle of list φ 
                 Dry width w dry   
               
               
                   
                 (arc degrees) 
                 (ft) 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 20 
                 6.96 
               
               
                   
                 10 
                 1.89 
               
               
                   
                 8 
                 −0.84 
               
               
                   
                 5 
                 −9.2 
               
               
                   
                   
               
            
           
         
       
     
     The calculation shows that end of the foil starts going out of water at φ=9 arc degrees. 
     The lifting force F 1  of this foils declines because only part of the foil stills in water, so the lifting force can be determined by the formula: 
         F   1   =F   y ×(1 −w   dry   /W )  [7],
 
     where:
 
F y —total lifting force of the underwater foil,
 
w dry —dry width of the foil,
 
W—width (lateral dimension) of the foil.
 
     Total lifting force of a wing is determined by the formula: 
         F   y   =C   y   ×S×ρ×V   2 /2  [8],
 
     where:
 
C y —lifting coefficient,
 
P—density of media,
 
V—water-foil velocity,
 
S—surface of the foil.
 
     Coefficient C y  depends on many factors and can be determined by approximate formulas or by the graphs in textbooks. 
     For non-profiled foil (thin plate) C y  can be determined by the formula: 
         C   y =2π×sin α  [9],
 
     where:
 
α—angle of attack.
 
     For airplane-like wing coefficient C y  can be estimated as shown on the Table 2. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 α (arc degrees) 
                 C y   
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 −4.5 
                 0 
               
               
                   
                 −3 
                 0.3 
               
               
                   
                 0 
                 0.5 
               
               
                   
                 5 
                 0.8 
               
               
                   
                 6 
                 1.0 
               
               
                   
                 9 
                 1.15 
               
               
                   
                 12 
                 1.3 
               
               
                   
                   
               
            
           
         
       
     
     Below it is the example of operation of the hydrofoil assembly of the present embodiment dedicated to the large racing yacht mentioned above. 
     Thus, for single profiled foil having surface of 1.5 m 2  the upward lifting force will be about 6,360 N (918 kg of force or 1,890 lbs) at V=10 kt (18.5 km/hour) and α=0. 
     If two upper foils are dry (&gt;10 arc degree list) and two opposite foils still in water, the total lifting force compensating wind list will be about 1840 kg and produce the compensating momentum of 7730 kg-m. Hydrostatic momentum M h  (see formula [4]) will be around 18,000 kg-m. 
     Lateral wind of 20 kt (37 km/hour) produces listing momentum of 24,000 kg-m (at SA=400 sq.m. and height of center of wind pressure of 12 m). 
     Thus, the compensating momentum of the hydrofoils (7,730 kg-m) together with hydrostatic compensating momentum of the yacht (18,000 kg-m) provides total compensating momentum exceeding 25,000 kg-m that can successfully counteract wind listing momentum keeping the yacht at the list not exceeding 10 arc degrees (at mentioned above conditions). 
     Another example of calculation is dedicated to medium-size Alberg  30  yacht having Displacement=9,000 lbs, LOA=30.2 ft, D=4.2 ft, Beam=8.8 ft and SA=410 sq.ft. Maximal roll (list) will be φ m =40 arc degrees (see formula [5]). 
     For the upper hydrofoils positioned 1.5 ft below waterline, wing (hydrofoil) span of 8.8 ft and the distance from C.G. to wing (hydrofoil) plane of 1 ft (δ=1 ft, a=4.4 ft, b=1 ft, see formula [6]) the value of the dry width w dry  of hydrofoil for different angles of the list is shown on TABLE 3. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                 Angle of list φ 
                 Dry width w dry   
               
               
                   
                 (arc degrees) 
                 (ft) 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 10 
                 −1.4 
               
               
                   
                 15 
                 0.4 
               
               
                   
                 18 
                 1.0 
               
               
                   
                 20 
                 1.3 
               
               
                   
                 25 
                 1.8 
               
               
                   
                 28 
                 2.0 
               
               
                   
                   
               
            
           
         
       
     
     As Table 3 shows, the hydrofoil with width W=2 ft is completely above water at 28-degree list. 
     For single profiled foil having surface of 10.8 sq.ft (1 m 2 ) the lifting force will be about 1260 lbs (612 kg) at V=10 kt and α=0. 
     If the row of two upper foils is dry (&gt;28 arc degree list) and the opposite row stills in water, the total lifting force will be about 1220 kg that produces the compensating momentum of 1610 kg-m. Hydrostatic momentum M h  determined by the formula [4] will be about 1,150 kg-m at list of 28 arc degrees. 
     Lateral wind of 20 kt (37 km/hour) produces listing momentum of about 2,000 kg-m at SA=410 sq.ft (38.1 m 2 ) and height of the center of wind pressure of 14 ft (4.2 m). 
     Thus, the hydrodynamic compensating momentum of hydrofoils (1,614 kg-m) together with hydrostatic compensating momentum of the yacht (1,150 kg-m) provides total compensating momentum of 2,764 kg-m that can successfully counteract the wind listing momentum. 
     At the list angle of 20 arc degrees only part of hydrofoils is involved in wind list compensation. Here, the hydrostatic compensation momentum determined by formula [4] will be about 837 kg-m; and hydrodynamic compensation momentum will be about 1,047 kg-m (at yacht speed of 10 kt.). Totally they provide 1,900 kg-m compensating momentum counteracting wind listing momentum of 2,000 kg-m. Thus, complete compensation will be achieved at list angle of about 21 arc degrees. 
     Thus, at the list below 15 degrees, the hydrofoils do not works as list compensator, but still working as roll and pitch stabilizer; and list compensation is provided by conventional hydrostatic forces. The lifting force of the hydrofoils starts counteracting listing momentum at list angle of 15 degrees and produce full compensating momentum at list angle of 28 degrees. Therefore, such hydrofoil assembly protects the yacht from the list exceeding 21 degrees. The lower hydrofoils positioned below C.G produce downward lifting force, which stabilizes the yacht. 
     The hydrofoil assembly can be installed on a yacht when it is on service in a dry dock; the foils can be rigidly mounted on yacht&#39;s hull, or the foils can be clipped to a harness that is attached to yacht&#39;s hull. The possible position of hydrofoil assembly of the present embodiment on Alberg  30  yacht is shown on  FIG. 7 . 
     The symmetrical position of the hydrofoils is the preferable one, but for some sailing vessels having shallow C.G and complicated underwater shape it is difficult to keep upper and lower foils on the same distance from C.G. In this case these distances can be different, but lifting forces of upper foils and lower foils have to be equal. 
     Description of Another Embodiment of the Present Invention 
     Biplane Assembly of Pivoted Hydrofoils 
     Unlike the first embodiment of this invention—biplane assembly of static (non-pivoted) completely submerged (never out of water) hydrofoil members rigidly mounted on the hull above and below C.G.—that can partially compensate roll and pitch, but can not compensate wind list, an assembly of similar pivoted hydrofoils allows compensating all adverse momentums caused by roll, pinch and lateral wind. 
     The scheme of assembly of the pivoted hydrofoils is depicted in  FIG. 8 . 
     Here, the assembly of submerged hydrofoils is the similar to one shown on  FIG. 2 , but, in this embodiment, the hydrofoils can change its angle of attack by means of actuators. Variation of angle of attack alters coefficient C y ; therefore lifting force of the hydrofoil changes too (see formula [8]). According to Table 2, coefficient C y  varies from 0 at the angle of attack of −4.5 degrees and 0.5 at the angle of attack of 0 degrees up to 1.15 at the angle of attack of 9 degrees. 
     Thus, the lifting force of the single foil proposed above for Alberg  30  yacht (at yacht speed of 10 kt) will vary from 1260 lbs (612 kg) at α=0 up to 2,900 lbs (1,400 kg) at α=9 degrees. In this case, momentum (in vertical lateral plane) developed by the single foil will vary from 805 kg-m up to 1,850 kg-m respectively; and the lifting force is equal to 0 at the angle of attack of −4.5 degrees. 
     Also, the foil develops momentum in vertical longitude plane. If each foil is positioned on the horizontal longitude distance of 12 ft from C.G, the foil produces momentum that varies from 2,200 kg-m (α=0) up to 5,060 kg-m (α=9). 
     In the first embodiment all foils are submerged ones and have pre-installed angle of attack of 0 degree; and upper foils provide upward lifting, whereas the lower foils provide downward lifting force. Thus, such hydrofoil assembly works as a roll compensator, but does not produce any rotating momentum because the momentums developed by the hydrofoils compensate each other. 
     In the case of pivoted foils, they can produce rotating momentums that can be used to compensate roll, pitch and wind list. For roll and pitch compensation, the foils have to be turned synchronically with movements of yacht&#39;s hull, but counteracting them. So, the lifting forces have to be in opposite direction to vector of velocity of yacht&#39;s hull. 
     To compensate wind listing, the foils have to develop rotating momentums counteracting listing momentum caused by wind. This compensation can be estimated for the hydrofoil assembly proposed above for Alberg  30  yacht. 
     As was noted above, the lateral wind of 20 kt (37 km/hour) produces listing momentum of about 2,000 kg-m at SA=38.1 m 2  (410 sq.ft) and height of the center of wind pressure of 4.2 m (14 ft). Hydrostatic compensating momentum of the yacht calculated by the formula [4] is 690 kg-m at 10-degree list. So, the hydrofoil assembly has to develop additional 1,310 kg-m momentum. If the assembly is symmetrical about C.G and the yacht is heeling to left side, the left upper and right lower foils have to be turned on the same angle of attack of 5 arc degrees (see formula [8] and Table 2). It provides additional upward (for upper foils) and downward (for lower foils) forces developing momentum that, together with hydrostatic momentum, compensates the wind list. 
     Because the lifting forces produced by hydrofoils are dynamic ones that depend on yacht speed (F γ ˜V 2 ), angle of attack of the foils has to be regulated according to the vessel&#39;s speed. In the case of low speed when the lifting forces of the mentioned above foils are not enough to compensate the wind list, other hydrofoils can be involved. So (see example above), if the yacht is heeling to left side at low speed, the right upper and left lower foils have to be turned on the negative angle of attack of −4.5 arc degrees (see formula [8] and Table 2) where C y =0. Hydrostatic compensating momentum of the yacht calculated by the formula [4] is 690 kg-m at 10-degree list. The lateral wind of 20 kt produces listing momentum of 2,000 kg-m. So, the hydrofoil assembly has to develop 1,310 kg-m momentum. At the yacht speed of 5 kt the compensating momentum produced by these four foils (at the same angle of attack of 5 degrees) will be only 327 kg-m that is not enough. So, if the left upper and right lower foils is turned on the angle of attack of 9 arc degrees (see formula [8] and Table 2) and the right upper and left lower foils are turned on the angle of attack of −4.5 arc degrees, the hydrofoil assembly produce rotating momentum of 3,500 kg-m counteracting with the wind list. This momentum will be enough to compensate lateral wind of 28 kt at the vessel speed of 5 kt. Also these hydrofoils (at the angles of attack mentioned above) can compensate lateral wind of 20 kt at the yacht speed of 3 kt. 
     The pivoted foils of this embodiment can be controlled by electromechanical or hydraulic actuators placed inside of the hull ( FIG. 8   a ), or the actuators can be mounted inside of the foil as depicted in  FIG. 8   b . Example of such foil-mounted actuator is shown on  FIG. 8   b . Here, a reversible electromotor  33  is firmly mounted inside of foil  32 , wherein the shaft  34  of the electromotor  33  is a worm-gear. Another shaft  35  is firmly mounted on yacht&#39;s hull  1  and supported in the foil  32  by bearings  36  and  37  in such a way that the foil  32  can rotate about the shaft  35 . The part of the shaft  35  is a gear, which is engaged to said worm-gear. To feed the electromotor  33 , the shaft  35  has a channel  38  where an electrical cable  39  is placed. Seal  310  protects interior of the hydrofoil  32  from water. 
     Therefore, when the power is on, the electromotor  33  together with foil  32  starts rotating about the shaft  35  in the direction depending on polarity of voltage applied to the electromotor  33 . 
     This hydrofoil-mounted actuator can be also utilized in pivoted “seagull wing” hydrofoils (see  FIG. 4 ) turning whole hydrofoil or just its external part. 
     For the accurate compensation of wind list, the actuators have to be computer-controlled ones, wherein the controlling computer  311  has to have information about yacht&#39;s speed, wind speed and direction ( FIG. 8   c ). This information can be obtained by means of special sensors  312  and  313  connected to the computer  311 . Basing on this information, the controlling computer  311  according to special algorithm incorporating formula [8] and Table 2 develops commands to turn each foil on the specific angle of attack. 
     If the actuators are fast enough (time response is less than about 2 seconds), this hydrofoil assembly can be utilize to compensate not only the wind list, but also other adverse momentums affecting the yacht, such as roll, pitch and yaw. In this case, the controlling computer has to have additional real-time information about position of the vessel and its dynamic, which can be obtain from onboard gyroscope  314 . To achieve fast and reliable response, advanced fuzzy logic expert system and processors can be utilized. 
     Description of Another Embodiment of the Present Invention 
     Passive Triplane Assembly of Hydrofoils 
     The scheme of the hydrofoil assembly of the present embodiment is depicted in  FIG. 9 . Here, the partially submerged biplane hydrofoil assembly of the embodiment depicted in  FIG. 6  is additionally equipped with two other upper rows of the foils  20 ,  23 ,  26  and  28  positioned above yacht waterline in such a manner that allow the foils placed on one side of a vessel entering water when the vessel is heeling over. These additional foils are hyrodynamically profiled to generate upward lifting force. Therefore, the assembly comprises said upper rows of the foils  20 ,  23 ,  26  and  28  providing upward force (when they in water), the middle rows of the foils  6 ,  8 ,  10  and  12  (see  FIG. 9 ) providing upward force and the lower rows of the foils  7 ,  9 ,  11  and  13  providing downward force, wherein, when a yacht is in vertical position, the upper row is above waterline, the middle row is below waterline and above C.G, the lower row is below waterline and below C.G; the distance between the middle row and C.G is equal to the distance between the lower row and C.G, and height of the upper row above waterline is equal to the depth of the middle row below waterline. 
     The assembly works as follows: 
     When a yacht is heeling over (for example to left side), the left upper row of foils  26  and  28  enters water providing upward lifting force. The right middle row of the foils  10  and  12  (see  FIGS. 9 and 6 ) is going out of water, so the left row foils  6  and  8  stills in water also generating upward lifting force. The lower rows of foils  7 ,  9 ,  11  and  13  still in water providing downward lifting force that counteracts total lifting forces and does not allow the yacht lifting up. 
     The assembly of the present embodiment is the passive one; it does not require any foil alignment and computer-controlled rotation. This solution allows significantly increasing momentum counteracting wind list that is especially important at the conditions of low yacht&#39;s speed. Below is an example of such assembly dedicated to Alberg  30  yacht. For single profiled foil having surface of 10.8 sq.ft the lifting force will be about 1260 lbs (612 kg) at V=10 kt and angle of attack of α=0. 
     If two upper foils enter in water, the total lifting force compensating wind list will be about 2,690 lbs (1 220 kg) and produce the compensating momentum of 11,820 lbs-ft (1610 kg-m). 
     If two middle foils are out of water and two opposite foils still in water, the total lifting force compensating wind list will be about 1220 kg and produce the compensating momentum of 1610 kg-m. 
     Hydrostatic momentum M h  determined by the formula [4] will be about 690 kg-m at list angle of 13 arc degrees, 427 kg-m at 8 degrees and 267 kg-m at 5 degrees. Lateral wind of 20 kt (37 km/hour) produces listing momentum of about 2,000 kg-m at SA=38.1 m 2  (410 sq.ft) and height of the center of wind pressure of 4.2 m (14 ft). 
     Thus, the maximally possible hydrodynamic compensating momentum of hydrofoils (3,200 kg-m) achieved at yacht&#39;s speed of 10 kt together with hydrostatic compensating momentum provides the rotating momentum that is well enough for wind list compensation. Because the list momentum and compensating momentum have to be in balance, the upper and middle foils can be partially submerged to provide together with hydrostatics the total value of rotating momentum of 2,000 kg-m. 
     If the yacht is traveling with lower speed, such as 6 kt, the hydrodynamic momentum of foil assembly will decline to 1,300 kg-m; so the complete compensation of the lateral wind will be achieved when the left foils of upper row are completely in water and the right foils of the middle row are completely out of water. 
     Optionally, the distance between the upper row and waterline can differ from the distance between the middle row and waterline; so, for example, the right middle foils can leave water at lower list and the left upper foils enters water at higher list. Such solution provides smoother regulation of yacht&#39;s position. 
     Thus, if yacht&#39;s list is less than some angle (depending on upper and middle hydrofoils position), the hydrofoil assembly does not work as a list compensator, but still working as roll and pitch stabilizer; here the list compensation is provided by conventional hydrostatic forces. The lifting force of the hydrofoils starts counteracting listing momentum at list angle when the upper foils touch water and middle foils leave water; and the assembly produces full compensating momentum at list angle when the left upper foils are completely in water and right middle foils leave water completely. The lower hydrofoils positioned below C.G produce downward lifting force, which counteracts upward lifting forces (not the momentums) generated by upper and middle hydrofoils so stabilizes the yacht in vertical direction.