Abstract:
An electric generator capable of generating electric power using kinetic energy of wind includes a first plurality of rotor plates, a second plurality of rotor plates, and a first plurality of blades capable of driving the first plurality of rotor plates, a second plurality of blades being formed to enable counter-rotation with respect to the first plurality of blades, wherein rotation of the first plurality of rotor plates relative to the second plurality of rotor plates induces electricity in a plurality of coils disposed on the second plurality of rotor plates, and wherein at least one of the first and second plurality of rotor plates are arranged co-axially with the shaft such that respective radii of the at least one of the first and second plurality of rotor plates are varied along the axial direction.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The present invention relates to power generators, and more particularly, to stackable wind power generators. 
         [0003]    2. Discussion of the Related Art 
         [0004]    Wind generators create electricity by converting kinetic energies of wind into electric energy. Wind powered generators have great advantages over other generators. Wind generators are not only environmentally safe but also economically sound and sustainable. Unlike fuel generators, there is no need to purchase fuel. The source of energy is wind, which can be obtained in nature. Because wind has kinetic energy to produce electricity, there is no byproduct produced. Accordingly, there is almost zero pollution. 
         [0005]    A wind generator converts mechanical energy from the wind into electrical energy using electromagnetic induction. Small wind generators that create 700-1,000 Watts can be easily made. However, there are limitations on how much energy a wind generator can produce. For example, building wind generators of bigger than 2,000 Watts is a major project requiring very large construction. Conventional wind generators that are large are unstable and inefficient. 
       SUMMARY OF THE INVENTION 
       [0006]    Accordingly, the present invention is directed to stackable hyper-surface wind generators that substantially obviates one or more problems due to limitations and disadvantages of the related art. 
         [0007]    An object of the present invention is to provide a compact wind generator capable of generating a large amount of electrical energy. 
         [0008]    Another object of the present invention is to provide a high efficiency wind generator in which a plurality of rotors are stacked in parallel. 
         [0009]    Another object of the present invention is to provide a high efficiency wind generator capable of implementing the counter-rotation mechanism. 
         [0010]    Another object of the present invention is to provide a reliable wind generator in which vibration in undesired directions is suppressed. 
         [0011]    Additional features and advantages of the invention will be set forth in the description which follows, and in part will be apparent from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings. 
         [0012]    To achieve these and other advantages and in accordance with the purpose of the present invention, as embodied and broadly described, the stackable hyper-surface wind generator includes a plurality of stator plates, a plurality of rotor plates and a plurality of blades capable of driving the plurality of rotor plates, wherein rotation of the plurality of rotor plates relative to the plurality of stator plates induces electricity in a plurality of coils disposed on each stator plate, and wherein at least one of the stator plates and the rotor plates are arranged co-axially with a shaft such that respective radii of the at least one of the stator plates and rotor plates are varied along the axial direction. 
         [0013]    In another aspect, an electric generator capable of generating electric power using kinetic energy of wind includes a first plurality of rotor plates, a second plurality of rotor plates, and a first plurality of blades capable of driving the first plurality of rotor plates, a second plurality of blades being formed to enable counter-rotation with respect to the first plurality of blades, wherein rotation of the first plurality of rotor plates relative to the second plurality of rotor plates induces electricity in a plurality of coils disposed on the second plurality of rotor plates, and wherein at least one of the first and second plurality of rotor plates are arranged co-axially with the shaft such that respective radii of the at least one of the first and second plurality of rotor plates are varied along the axial direction. 
         [0014]    It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]    The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention. In the drawings: 
           [0016]      FIG. 1  is a perspective view of a vertical-axis wind turbine (VAWT) generator according to an exemplary embodiment of the present invention; 
           [0017]      FIG. 2  is a perspective view of a stackable rotors and stators within the VAWT generator according to the exemplary embodiment of  FIG. 1 ; 
           [0018]      FIG. 3  is a perspective view of a single stator including a plurality of coils within the VAWT generator according to the exemplary embodiment of  FIG. 1 ; 
           [0019]      FIG. 4  is a cross-sectional view of a stackable rotors and stators within the VAWT generator according to the exemplary embodiment of  FIG. 1 ; 
           [0020]      FIG. 5  is a side view of the stackable stators within the VAWT generator according to the exemplary embodiment of  FIG. 1 ; 
           [0021]      FIG. 6A  is a perspective view of a catenoid; 
           [0022]      FIG. 6B  is a perspective view of an inverse-catenoid; 
           [0023]      FIG. 7  is a perspective view of a counter-rotating vertical-axis wind turbine (VAWT) generator according to another exemplary embodiment of the present invention; 
           [0024]      FIG. 8  is a perspective view of a stackable rotors and stators within the counter-rotating VAWT generator according to the exemplary embodiment of  FIG. 7 ; 
           [0025]      FIG. 9  is a perspective view of a single stator including a plurality of coils within the counter-rotating VAWT generator according to the exemplary embodiment of  FIG. 7 ; 
           [0026]      FIG. 10  is a cross-sectional view of a stackable rotors and stators within the counter-rotating VAWT generator according to the exemplary embodiment of  FIG. 7 ; 
           [0027]      FIG. 11A  is a perspective view of the counter-rotatable inner pipe within the VAWT generator according to the exemplary embodiment of  FIG. 7 ; 
           [0028]      FIG. 11B  is a perspective view of the counter-rotatable outer pipe within the VAWT generator according to the exemplary embodiment of  FIG. 7 ; 
           [0029]      FIG. 11C  is a perspective view of the counter-rotating pipes within the VAWT generator according to the exemplary embodiment of  FIG. 7 ; 
           [0030]      FIG. 12A-12C  are perspective views showing the method of making the counter-rotating VAWT generator according to the exemplary embodiment of  FIG. 7 ; 
           [0031]      FIG. 13  is a side view of the stackable stators within the counter-rotating VAWT generator according to the exemplary embodiment of  FIG. 7 ; 
           [0032]      FIG. 14  is a perspective view of a catenoid within a catenoid; 
           [0033]      FIGS. 15A-C  are front view, perspective view, and side view of a horizontal-axis wind turbine (HAWT) generator according to another exemplary embodiment of the present invention; 
           [0034]      FIG. 16  is a perspective view of a stackable rotors within the HAWT generator according to the exemplary embodiment of  FIGS. 15A-C ; 
           [0035]      FIG. 17  is a perspective view of a stackable rotors and stators within the HAWT generator according to the exemplary embodiment of  FIGS. 15A-C ; and 
           [0036]      FIG. 18  is a side view of a stackable rotors and stators within the HAWT generator according to the exemplary embodiment of  FIGS. 15A-C . 
       
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
       [0037]    Reference will now be made in detail to the embodiments of the present invention, examples of which are illustrated in the accompanying drawings. 
         [0038]    When an inductive element, i.e., a wire or a coil, is placed within a magnetic field and when the inductive element rotates within the magnetic field, current is induced within the inductive element. The magnitude of the induced current depends on the strength of the magnetic field, the length of the inductive element, and the speed with which the inductive element moves within the magnetic field. The strength of the magnetic field can be enhanced by using magnets with higher magnetization. However, there are limitations on the strength of the magnets due to intrinsic material properties. Accordingly, in accordance with aspects of the present invention, efficiency of the wind generator is enhanced by changing the structure and design of the wind generator. In an exemplary embodiment of the present invention, a plurality of rotors and a plurality of stators are stacked to enhance efficiency, thereby increasing the magnitude of the induced current. 
         [0039]      FIG. 1  is a perspective view of a vertical-axis wind turbine (VAWT) generator according to an exemplary embodiment of the present invention,  FIG. 2  is a perspective view of a stackable rotors and stators within the VAWT generator according to the exemplary embodiment of  FIG. 1 ,  FIG. 3  is a perspective view of a single stator including a plurality of coils within the VAWT generator according to the exemplary embodiment of  FIG. 1 , and  FIG. 4  is a cross-sectional view of a stackable rotors and stators within the VAWT generator according to the exemplary embodiment of  FIG. 1 . Key advantages of the VAWT arrangement are that the blades  130  do not have to be pointed into the wind to generate electricity. This is an advantage on sites where the wind direction is highly variable. In other words, VAWTs can utilize winds from varying directions. Vertical-axis turbine generators  100  can be installed on the ground. Alternatively, because the speed of wind is generally faster at a higher altitude, vertical-axis turbine generators  100  can be mounted on towers or building rooftops. 
         [0040]    As shown in  FIGS. 1-4 , an exemplary embodiment of a VAWT generator  100  according to the present invention includes a frame  110 , a shaft  120  that is rotatably connected to the frame  110 , a plurality of blades  130  that are connected to the shaft  120  through a base  140 , a plurality of rotors  150  including a plurality of permanent magnets  150 M, which are connected to the rotatable shaft  120 , and a plurality of stators  180  including a plurality of coils  180 C. The plurality of stators  180  and plurality of rotors  150  within the VAWTs are vertically arranged. The rotating blades  130  within the VAWT generator  100  convert the kinetic energy of wind into rotational momentum of a shaft  120  independent of the direction of the wind. When the plurality of rotors  150  rotate, the plurality of coils  180 C and the wires  180 W within the plurality of stators  180  experiences change in the magnetic field generated by the plurality of permanent magnets  150 M within the plurality of rotors  150 . Accordingly, electricity is generated in the plurality of coils  180 C and wires  180 W within the plurality of stators  180 . 
         [0041]    As shown in  FIGS. 2 and 4 , a plurality of rotors  150  includes a plurality of rotor plates  150 P and a plurality of alternating magnets  150 M. The plurality of rotor plates  150 P are fixed with one another by rods  160 . Each rotor  150  is interposed between each stator  180  and is stacked to enhance the efficiency of the generator  100 , thereby increasing the overall magnitude of the induced current. 
         [0042]    As shown in  FIG. 3 , there are three sets of wires  180 W on each stator  180  that electrically connect the plurality of coils  180 C to one another within a single stator plate  180 P. Of course, more or fewer sets of wires can be used. Although not completely shown, each coil  180 C has input and output wires. The input and output wires of each coil that form the three pairs of wires  180 W that electrically connect the plurality of coils  180 C to one another are shown in  FIG. 3 . However, the input and output wires of each coil that are connected to pass through the holes  170 H within the hub  170  are not shown. Stabilizing screws  170 S can be used to cast the wires together with the hub  170 . The holes  170 H within the hub  170  are used to pass the wires through to the next stack of stator  180 . The hub  170  may be made of metal, including aluminum, or other suitable material. 
         [0043]    In an exemplary embodiment of the present invention, the wind generator  100  is reliable and stable because vibration in undesired directions due to turbulence can be suppressed. Angular momentum of an object rotating around a reference point is a measure of the extent to which the object will continue to rotate around that point unless an external torque is applied. Mathematically, the angular momentum with respect to a point on the axis around which an object rotates is related to the mass of the object, the velocity of the object, and the distance of the mass to the axis. According to the theory of conservation of angular momentum, a system&#39;s angular momentum remains constant unless an external torque acts on it. In other words, torque is the rate at which angular momentum is transferred into or out of the system. 
         [0044]    Accordingly, in a closed system, wherein no external torque is applied to the objects within the system, the time derivative of angular momentum, i.e., the torque, is zero. An example of the conservation of angular momentum can be easily seen in an ice skater as he brings his arms and legs closer to the axis of rotation. Because angular momentum is the product of the velocity of the object and the distance of the object to the axis of rotation, the angular velocity of the skater necessarily increases by bringing his body closer to the axis of rotation, thereby decreasing the body&#39;s overall moment of inertia. 
         [0045]    The plurality of blades  130  of the wind generator  100  are designed to convert linear motions of wind into rotational motions of the plurality of rotors  150 . In an ideal condition, the plurality of rotors  150  would only have spin angular momentum wherein the plurality of rotor  150  rotates around the shaft  120 . However, because the blades  130  are not ideal and also because the direction of wind is not homogeneous in space, the plurality of rotors  150  not only have spin angular momentum when external torque is applied to the blades  130 , but also have non-zero orbital angular momentum. Orbital angular momentum is an orbital motion of the shaft  120  itself, which would cause vibration of the wind generator  100  and further generate friction between the plurality of rotors  150  and the plurality of stators  180 . Accordingly, having a non-zero orbital angular momentum would decrease the spin angular momentum thereby degrading the efficiency of the wind generator  100 . In the exemplary embodiment of the present invention, the geometric dimensions of the stacked rotors  150  and stators  180  are designed to suppress the orbital angular momentum thereby enhancing the reliability and stability of the wind generator. 
         [0046]      FIG. 5  is a side view of the stackable stators within the VAWT generator according to the exemplary embodiment of  FIG. 1 . In  FIG. 5 , the rotors are not shown to simplify the structure.  FIG. 6A  shows a perspective view of a catenoid and  FIG. 6B  shows a perspective view of an inverse-catenoid. In particular, a catenoid is a surface of revolution that can be expressed in the following form (Equation 1): 
         [0000]        x ( u,v )= a ·cos( u )·cos  h ( v/a ) 
         [0000]        y ( u,v )= a ·cos  h ( v/a )·sin( u ) 
         [0000]        z ( u,v )= v   [Equation 1] 
         [0047]    In addition, an inverse-catenoid is a surface of revolution that can be expressed in the following form (Equation 2): 
         [0000]        x ( u,v )= sech ( u )·cos( v ) 
         [0000]        y ( u,v )= sech ( u )·sin( v ) 
         [0000]        z ( u,v )= u −tan  h ( u )  [Equation 2] 
         [0048]    A catenoid and inverse-catenoid hyper-surfaces are pseudo-spheres that have the same surface area as a sphere. Accordingly, an obvious advantage of having either a catenoid or inverse-catenoid configuration is to have a larger radial center of mass, while maintaining the surface area of the entire generator  100 . 
         [0049]    As shown in  FIG. 5 , the plurality of coils  180 C within each layer of stator  180  are structured to form a sphere  190 S. In addition, as shown in  FIG. 2 , the plurality of rotor plates  150 P are structured to form an inverse-catenoid hyper-surface  190 C. These geometric dimensions of the plurality of rotors  150  and stators  180  suppress the orbital angular momentum of the plurality of rotors  150  and stators  180  thereby enhancing the reliability and stability of the wind generator. U.S. Pat. No. 5,192,212 illustrates a hyper-surface orbital model, which represents planetary systems. Although it is merely a model representing the orbiting path of a hyper-surface, it can be used as a balancing tool because our planetary system is fundamentally balanced through the hyper-surface geometry. 
         [0050]    Although not shown, in another exemplary embodiment, the length of the plurality of coils  180 C can be varied along the axial direction. More particularly, the length of the plurality of coils  180 C can be increased and subsequently decreased along the axial direction. 
         [0051]    Although not shown, in another exemplary embodiment, the plurality of coils  180 C within each layer of stator  180  and the plurality of rotor plates  150 P can be arranged in the axial direction such that respective radii are varied along the axial direction. More particularly, the plurality of coils  180 C within each layer of stator  180  can be arranged in the axial direction such that respective radii are linearly increased and subsequently decreased along the axial direction and at the same time, the plurality of rotor plates  150 P can be arranged in the axial direction such that respective radii are linearly increased and subsequently decreased along the axial direction. In another exemplary embodiment, the plurality of coils  180 C within each layer of stator  180  can be arranged in the axial direction such that respective radii are linearly decreased and subsequently increased along the axial direction and at the same time, the plurality of rotor plates  150 P can be arranged in the axial direction such that respective radii are linearly decreased and subsequently increased along the axial direction. In another exemplary embodiment, the plurality of coils  180 C within each layer of stator  180  can be structured to form a catenoid hyper-surface and at the same time, the plurality of rotor plates  150 P can be structured to form a catenoid hyper-surface. In another exemplary embodiment, the plurality of coils  180 C within each layer of stator  180  can be structured to form an inverse-catenoid hyper-surface and at the same time, the plurality of rotor plates  150 P can be structured to form an inverse-catenoid hyper-surface. In another exemplary embodiment, the plurality of coils  180 C within each layer of stator  180  can be structured to form an inverse-catenoid hyper-surface and at the same time, the plurality of rotor plates  150 P can be structured to form a sphere. In yet another exemplary embodiment, the plurality of coils  180 C within each layer of stator  180  can be structured to form a sphere and at the same time, the plurality of rotor plates  150 P can be structured to form a sphere. 
         [0052]      FIG. 7  is a perspective view of a counter-rotating vertical-axis wind turbine (VAWT) generator according to another exemplary embodiment of the present invention,  FIG. 8  is a perspective view of a stackable rotors and stators within the counter-rotating VAWT generator according to the exemplary embodiment of  FIG. 7 ,  FIG. 9  is a perspective view of a single stator including a plurality of magnets within the counter-rotating VAWT generator according to the exemplary embodiment of  FIG. 7 , and  FIG. 10  is a cross-sectional view of a stackable rotors and stators within the counter-rotating VAWT generator according to the exemplary embodiment of  FIG. 7 . 
         [0053]    In this exemplary embodiment of the present invention, a counter rotation scheme is implemented to enhance the efficiency. In related art generators, kinetic energy is transformed into rotational energy by rotating the rotors. In this embodiment, rather that having the stators fixed, the stators are connected to an additional independent set of blades that are oriented in the opposite direction with respect to the orientation of the set of blades that are connected to the rotors (which will be referred to as the “first plurality of rotors”). Accordingly, the stators will be referred to as the “second plurality of rotors.” In other words, there are first plurality of rotors  1050  and second plurality of rotors  1080  that rotate independently of each other wherein the blades  1030 B of the second plurality of rotors  1080  are oriented such that the first plurality of rotors  1050  and the second plurality of rotors  1080  counter-rotate. 
         [0054]    An exemplary embodiment of the counter-rotating VAWT generator  1000  according to the present invention includes a frame  1010 , a shaft  1020  that is rotatably connected to the frame  1010 , a first plurality of blades  1030 A that are connected to the shaft  1020  through a first base  1040 A, a second plurality of blades  1030 B that are connected to the shaft  1020  through a second base  1040 B, a first plurality of rotors  1050  that are connected to the inner pipe  1020 A of the shaft  1020 , and a second plurality of rotors  1080  that are connected to the outer pipe  1020 B of the shaft  1020 . As shown in  FIGS. 7-10 , the first plurality of rotors  1050  and the second plurality of rotors  1080  within the counter-rotating VAWTs are vertically arranged. 
         [0055]    The first plurality of rotating blades  1030 A within the counter-rotating VAWT generator  1000  convert the kinetic energy of the wind into rotational momentum of the inner pipe  1020 A. At the same time, the second plurality of rotating blades  1030 B converts the same kinetic energy of the wind into a rotational momentum of the outer pipe  1020 B, which rotates in the opposite direction of the inner pipe  1020 A. Because the first plurality of rotors  1050  rotate in the opposite direction of the second plurality of rotors  1080 , the plurality of coils  1080 C and the wires  1080 W within the second plurality of rotors  1080  experiences twice as fast of a change in the magnetic field generated by the plurality of permanent magnets  1050 M within the first plurality of rotors  1050 . Accordingly, electricity is generated in the plurality of coils  1080 C and wires  1080 W within the second plurality of rotors  1080  more efficiently. 
         [0056]    As shown in  FIGS. 8 and 10 , a first plurality of rotors  1050  includes a first plurality of rotor plates  1050 P and a plurality of alternating magnets  1050 M. The first plurality of rotor plates  1050 P are fixed with one another by rods  1060 . As shown in  FIG. 9 , there are three sets of wires  1080 W on each second plurality of rotors  1080  that electrically connect the plurality of coils  1080 C to one another within a single rotor plate  1080 P. Of course, more or fewer sets of wires can be used. Although not completely shown, each coil  1080 C has input and output wires. The input and output wires of each coil that form the three pairs of wires  1080 W that electrically connect the plurality of coils  1080 C to one another are shown in  FIG. 3 . However, the input and output wires of each coil that are connected to pass through the holes  1070 H within the hub  1070  are not shown. Stabilizing screws  1070 S can be used to cast the wires together with the hub  1070 . The holes  1070 H within the hub  1070  are used to pass the wires through to the next stack of rotors  1050  and  1080 . The hub  1070  may be made of a metal including aluminum or other suitable material. 
         [0057]      FIG. 11A  is a perspective view of the counter-rotatable inner pipe within the VAWT generator according to the exemplary embodiment of  FIG. 7 ,  FIG. 11B  is a perspective view of the counter-rotatable outer pipe within the VAWT generator according to the exemplary embodiment of  FIG. 7 , and  FIG. 11C  is a perspective view of the counter-rotating pipes within the VAWT generator according to the exemplary embodiment of  FIG. 7 . 
         [0058]    As shown in  FIG. 11A , a pair of inner bearings  1021 A, a pair of bearing caps  1022 B, and the inner pipe holder  1023  are formed to allow the inner pipe  1020 A to freely rotate against the inner bearing  1021 A. As shown in  FIG. 11B , the shaft  1020  comprises an inner pipe  1020 A and an outer pipe  1020 B that are spaced apart and do not touch each other. The outer bearing  1021 B and the outer bearing cap  1022 B are components attached on the top are bottom of the outer pipe  1020 B. The inner circumference of outer bearing  1021 B holds the inner pipe  1020 A. This allows the outer pipe  1020 B to rotate freely along the axis parallel to the inner pipe  1020 A.  FIG. 11C  shows a complete assembly of the counter-rotating pipes  1020 A and  1020 B, which comprises two sets of bearings that hold each pipe so that each can rotate freely in opposite directions. 
         [0059]      FIGS. 12A-12C  are perspective views showing the method of making the counter-rotating VAWT generator according to the exemplary embodiment of the present invention. As shown in  FIG. 12A , the first layer of a first plurality of rotor plates  1050 P is inserted into the shaft  1020  and rods  1060  and a first layer of the plurality of alternating magnets  1050 M are formed thereon. Subsequently, as shown in  FIG. 12B , the first layer of a second plurality of rotor plates  1080 P is inserted into the shaft  1020  and a first layer of the plurality of coils  1080 C are formed thereon. In addition, a hub  1070  and a counter-rotatable outer pipe (not shown) are formed to fix the second plurality of rotor plates  1080 P. Then, as shown in  FIG. 12C , the second layer of a first plurality of rotor plates  1050 P is inserted into the shaft  1020  and rods  1060  and a second layer of the plurality of alternating magnets  1050 M are formed thereon. One of ordinary skill in the art would recognize that this sequence can be repeated until a desired number of layers are formed. 
         [0060]    Similar to the VAWT generator according to the first exemplary embodiment, the first and second plurality of blades  1030 A and  1030 B of the wind generator  1000  are designed to convert linear motions of wind into rotational motions of the first and second plurality of rotors  1050  and  1080 . Because the first and second plurality of blades  1030 A and  1030 B are generally not ideal and also because the direction of wind is generally not homogeneous in space, the first and second plurality of rotors  1050  and  1080  not only have spin angular momentum when external torque is applied to the first and second plurality of blades  1030 A and  1030 B, but also have non-zero orbital angular momentum, which would cause vibration of the wind generator  1000  and further generate friction between the first and second plurality of rotors  1050  and  1080 . Accordingly, having a non-zero orbital angular momentum would decrease the spin angular momentum, thereby degrading the efficiency of the wind generator  1000 . 
         [0061]    In the exemplary embodiments of the present invention, the geometric dimensions of the first and second plurality of rotors  1050  and  1080  are designed to suppress the orbital angular momentum thereby enhancing the reliability and stability of the wind generator.  FIG. 13  is a side view of the stackable rotors within the counter-rotating VAWT generator according to the exemplary embodiment of  FIG. 7 . In  FIG. 13 , the first plurality of rotors  1050  are not shown to simplify the structure. As shown in  FIG. 13 , the plurality of coils  1080 C within the second plurality of rotors  1080  are structured to form a sphere  1090 S. On the other hand, as shown in  FIG. 8 , the first plurality of rotor plates  1050   p  are structured to form an inverse-catenoid hyper-surface  1090 C. A catenoid and inverse-catenoid hyper-surfaces are pseudo-spheres that have the same surface area as a sphere. Accordingly, an advantage of having either a catenoid or inverse-catenoid configuration is to have a larger radial center of mass, while maintaining the surface area of the entire generator  100 . 
         [0062]    Although not shown, in another exemplary embodiment, the length of the plurality of coils  1080 C can be varied along the axial direction. More particularly, the length of the plurality of coils  1080 C can be increased and subsequently decreased along the axial direction. 
         [0063]    Although not shown, in another exemplary embodiment, the first plurality of rotor plates  1050 P and the plurality of coils  1080 C can be arranged in the axial direction such that respective radii are varied. In another exemplary embodiment, the first plurality of rotor plates  1050 P can be arranged in the axial direction such that respective radii are linearly increased and subsequently decreased along the axial direction and at the same time, the plurality of coils  1080 C can be arranged in the axial direction such that respective radii are linearly increased and subsequently decreased along the axial direction. In another exemplary embodiment, the first plurality of rotor plates  1050 P can be arranged in the axial direction such that respective radii are linearly decreased and subsequently increased along the axial direction and at the same time, the plurality of coils  1080 C can be arranged in the axial direction such that respective radii are linearly decreased and subsequently increased along the axial direction. In another exemplary embodiment, the first plurality of rotor plates  1050 P can be structured to form a catenoid hyper-surface and at the same time, the plurality of coils  1080 C can be structured to form a catenoid hyper-surface. In another exemplary embodiment, the first plurality of rotor plates  1050 P can be structured to form an inverse catenoid hyper-surface and at the same time, the plurality of coils  1080 C can be structured to form an inverse catenoid hyper-surface. In another exemplary embodiment, the first plurality of rotor plates  1050 P can be structured to form a sphere and at the same time, the plurality of coils  1080 C can be structured to form an inverse catenoid hyper-surface. In yet another exemplary embodiment, the first plurality of rotor plates  1050 P can be structured to form a sphere and at the same time, the plurality of coils  1080 C can be structured to form a sphere. 
         [0064]    An exemplary embodiment wherein the plurality of stators and the plurality of rotors form catenoid hyper-surfaces, thereby forming a catenoid within a catenoid, will be shown in a horizontal-axis wind turbine (HAWT) generator configuration.  FIG. 14  is a perspective view of a catenoid within a catenoid.  FIGS. 15A-C  are front view, perspective view, and side view of a horizontal-axis wind turbine (HAWT) generator according to another exemplary embodiment of the present invention,  FIG. 16  is a perspective view of a stackable rotors within the HAWT generator according to an exemplary embodiment of  FIGS. 15A-C ,  FIG. 17  is a perspective view of a stackable rotors and stators within the HAWT generator according to the exemplary embodiment of  FIGS. 15A-C , and  FIG. 18  is a side view of a stackable rotors and stators within the HAWT generator according to the exemplary embodiment of  FIGS. 15A-C . 
         [0065]    An exemplary embodiment of the HAWT generator  2000  according to the present invention includes a frame  2010 , a plurality of blades  2020  that are connected to the shaft  2060 , which is rotationably connected to the frame  2010 , a tail  2030 , a cover  2040 , a plurality of rods  2050 , a plurality of stators  2100  including a plurality of stator plates  21  OOP and a plurality of coils  2100 C, and a plurality of rotors  2200  including a plurality of rotor plates  2200 P and a plurality of permanent magnets  2200 M. 
         [0066]    As shown in  FIGS. 15A-18 , the rotating blades  2020  within the HAWT generator  2000  convert the kinetic energy of the wind into rotational momentum of a shaft  2060 . The blades  2020  use engineered airfoils that capture the energy of the wind. However, unlike VAWT generators, the cover  2040  must face the wind for the conversion of kinetic energy of wind into rotational momentum of the shaft  2060 . The tail  2030  allows the wind generator  2000  to track the direction of the wind as the wind shifts direction, thereby enabling the cover  2040  and the blades  2020  to turn accordingly to face the wind. 
         [0067]    When the plurality of rotors  2200  rotate, the plurality of coils  2100 C within the plurality of stators  2100  experience change in the magnetic field generated by the plurality of permanent magnets  2200 M within the plurality of rotors  2200 . Accordingly, electricity is generated in the plurality of coils  2100 C within the plurality of stator  2100 . 
         [0068]    The plurality of blades  2020  of the wind generator  2000  are designed to convert linear motions of wind into rotational motions of the plurality of rotors  2200 . In an ideal condition, the plurality of rotors  2200  would only have spin angular momentum wherein the plurality of rotors  2200  rotates around the shaft  2060 . However, because the blades  2020  are not ideal and also because the direction of wind is not homogeneous in space, the plurality of rotors  2200  not only have spin angular momentum when external torque is applied to the blades  2020 , but also have non-zero orbital angular momentum, which contributes to decreasing the spin angular momentum thereby degrading the efficiency of the wind generator  2000 . 
         [0069]    In the exemplary embodiment of the present invention, the geometric dimensions of the plurality of rotors  2200  and the plurality of stators  2100  are designed to suppress the orbital angular momentum thereby enhancing the reliability and stability of the wind generator. As shown in  FIG. 15C , the plurality of stators  2100  and the plurality of rotors  2200  can form catenoid hyper-surfaces, thereby forming a catenoid within a catenoid. In addition, as shown in  FIG. 18 , the plurality of stator plates  2100 P can be structured to form a catenoid hyper-surface while the plurality of rotor plates  2200 P are structured to form a cylinder. 
         [0070]    Although not shown, in another exemplary embodiment, the plurality of stator plates  2100 P can be structured to form an inverse catenoid hyper-surface while the plurality of rotor plates  2200 P are structured to form a cylinder. In another exemplary embodiment, the plurality of stator plates  2100 P can be structured to form an inverse catenoid hyper-surface while the plurality of rotor plates  2200 P are structured to form a sphere. In yet another exemplary embodiment, both the plurality of stator plates  2100 P and the plurality of rotor plates  2200 P can be structured to form either an inverse-catenoid hyper-surface or a sphere. 
         [0071]    It will be apparent to those skilled in the art that various modifications and variations can be made in the stackable hyper-surface wind generator of the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.