Abstract:
This wind turbine is enclosed in a housing structure with a bell shaped opening and a stack effect created on the roof. One side of the housing, facing the wind, opens up to receive air. The air that enters the housing is divided into multiple chambers. The chambers and turning vanes guide the air directly to the blades and help in minimizing air turbulence. The blades are angled to receive the maximum amount of the air. The air rotates the blades turning the rotor, converting mechanical rotation into electrical power. There is a horizontal rotor attached to vertical shaft which is used to generate electrical energy. The stack effect on the roof creates a negative air flow aiding in turning the rotor.

Description:
INCORPORATION BY REFERENCE TO ANY PRIORITY APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 13/945,827 filed on Jul. 18, 2013, entitled “WIND TURBINE WITH CHANNELS AND ROOF AIR EXHAUST” which claims the benefit of U.S. Provisional Application No. 61/673,675 filed Jul. 19, 2012, entitled WIND TURBINE both of the entire contents of which are hereby incorporated by reference herein and should be considered a part of this specification. 
    
    
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to wind turbines and, in particular, to wind turbines that have reduced profiles and enclosed rotors that are environmentally more friendly. 
     Description of the Related Art 
     There is a long history of harnessing the power of wind to create energy and electricity. For example, in 1887 a windmill was constructed to generate power and charge batteries. The windmill and many like it have been made in the same tradition with a tall upright standing cylindrical structure with several large blades attached, designed to catch non-turbulent wind from a high vantage point. There are generally multiple sets of gears inside a mechanism connected to a generator for the production of power. 
     It is a commonly known fact that horizontal and vertical axis turbines share a common attribute; that winds must have a high velocity of wind speed with sufficient power (torque) to produce useful generator output. In addition, they have a relatively low maximum wind velocity that they can operate in before they must be shut down to ensure they are not damaged. 
     Current designs are 197 to 262 feet in the air, have exposed rotors that are subject to some of the harshest environments, such as wind shears, sunlight, heat, sand, and various other damaging elements, requiring constant maintenance to ensure proper function. The height of the currently designed wind turbines limits their use in some areas, not only for aesthetics, but also because the exposed rotating blades are becoming a major concern for wildlife (such as birds). There is a growing controversy about the number of birds being killed or maimed each and every year by these open blade wind turbines. 
     Due to new safety regulations pertaining to the placement of some new and old style wind turbines, they are becoming limited and not an option for key locations of constant wind. There are zoning issues and the problem of hydraulic oil seeping into the ground. 
     Thus, there is a need for an improved wind turbine design that is more compact and can be formed in a more aesthetic manner. Further, there is a need for an improved wind turbine design that does not have as significant of an effect on wildlife as existing designs. 
     SUMMARY OF THE INVENTION 
     The aforementioned needs are satisfied by the wind turbine of the present invention which in, one implementation, includes a housing having an inlet opening and an exhaust opening. A rotor is rotatably mounted within the housing wherein the rotor has a plurality of blades and is coupled to a generator. The inlet opening is, in one implementation, formed adjacent a side wall of the housing and the exhaust opening is formed adjacent an upper surface of the housing. In one implementation, both the inlet opening and outlet opening are covered with netting or similar structures to inhibit the entry of wildlife into the housing that contains the rotor. 
     Preferably, a plurality of channels is formed from the inlet opening to the peripheral edges of the rotor so as to direct air from the inlet opening to the bladed surfaces of the rotor. In one implementation, the channels are formed so as to more equally distributed about the circumference of the rotor. In one implementation, there are two rows of channels formed at the inlet opening with a first row of channels being formed so as to direct air to the front side of the rotor and a second row of channels being formed so as to direct air to the back side of the rotor. 
     In one implementation, an air scoop structure is formed in front of the inlet opening so as to gather and direct air from a surface area that is greater than the inlet opening into the inlet opening. In this implementation, the air scoop structure is preferably formed so as to channel the air towards the inlet opening which increases the pressure of the air as a result of the decrease in the area of the inlet opening. 
     In one implementation, the exhaust opening is formed so as to have a stack effect that reduces the drag against the rotor and allows the rotor to turn more freely. In one implementation, the rotor is mounted in recess below the exhaust opening. 
     The rotor, in one implementation, is preferably a ring shaped structure having a plurality of vanes or blades that extend between two races. The blades preferably extend substantially radially outward between the two races and are angled such that air impacting on the blades from the channels in a substantially perpendicular direction to the blades results in a horizontal force against the rotor causing the rotor to rotate. 
     The enclosed turbine is very versatile in creating energy at unmatched low speeds of 2 mph vs. 8-14 mph with the traditional style turbines, as well as high wind speeds with little or no noise pollution. The enclosed turbine produces little to no air pressure at the top of the unit where the air exit location is, because the wind entering into the unit is being more completely used to create power. This turbine utilizes the housing structure to collect air through a large opening and funneling it to a smaller exit area, which increases the velocity of the air at the exit. The air exits substantially at the blades only. 
     As discussed above, the roof of the housing structure is designed to create negative airflow, known as stack effect. This aids in turning the rotor. The housing enhances the wind turbine in many ways. It protects the rotor and all the components from the environment, creating less required maintenance as well as ease of maintenance. The housing structure is built to provide easy access to all parts of the wind turbine. The housing also protects this turbine from the typical categories of environmental impact, visual, noise, and wildlife, and protects the rotor, blades and all that makes up the turbine, creating less required maintenance. This wind turbine is quiet in operation and has a lower height of structure compared to typical wind turbines. Their small height enables them to have a variety of uses. One example would be used on the top of buildings. They can also be provided in a wide range of sizes and power generation capabilities. They are scalable and directional, meaning the housing and rotor size can be modified and the opening can be directed to the most optimal air flow direction. A netting, at all open surfaces, helps ensure the protection of wildlife. 
     The enclosed box turbine is less likely to harm wildlife, such as birds, differing from the turbines built with open blades high off the ground. Birds have been noted to land on the enclosed box turbine and fly away at will. The enclosed turbine can be made in various sizes with the inlet tunnels, blades, structure, and other parts scalable to any size to generate the amount of power desired. A scaled down version could be easily transported and assembled. This style of wind turbine can be built on the ground, on top of a building, or any desired location. 
     These and other objects and advantages of the present invention will become more apparent from the following description taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A and 1B  are schematic illustrations of one embodiment of an enclosed wind turbine; 
         FIGS. 2A-2G  are schematic illustrations of a rotor assembly of the enclosed wind turbine of  FIGS. 1A-1C ; 
         FIGS. 3A-3C  are schematic illustrations of the wind turbine of  FIGS. 1A and 1B  with side panels partially removed to show channels; 
         FIGS. 4A and 4B  are detailed schematics illustrating components of the channels of  FIGS. 3A-3C ; and 
         FIG. 5  is a schematic illustration of an optional air accelerator. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Reference will now be made to the drawings wherein like numerals refer to like parts throughout. As shown in  FIGS. 1A-1B , a wind turbine  100  is formed such that a rotor assembly  102  is positioned within a housing  104 . The housing  104  includes an air scoop opening assembly  106  that defines an opening  108  that directs air into a plurality of channels  110 . As will be described in greater detail below, the channels  110  direct the air to different circumferential locations of the rotor assembly  102  so that force is more equally distributed against the rotor assembly  102 . 
     In one implementation, the air scoop assembly  106  has an air scoop  112  that is comprised of four slanted walls that direct wind into the smaller dimensioned opening  108 . In one non-limiting example, the air scoop  112  has exterior dimensions of approximately 12 to 15 feet high by 12 to 15 feet wide and has interior panels  114  that are angled at an angle of approximately 30 to 45 degrees. The interior panels  114  border the opening  108  which has dimensions of approximately 12 feet wide by 8 feet high. It will be appreciated that various modifications to the dimensions described herein can be made by those skilled in the art without departing from the scope of the present invention. 
     In one implementation there are a total of 6 different channels  110  each having cross sectional dimensions of 4 feet by 4 feet that are arranged into two rows of three channels  110 . In this implementation, the top channels direct the air to the side of the rotor assembly  102  that is positioned proximate the opening  108  and the bottom row of channels directs the air to the side of the rotor assembly  102  that is located distal from the opening  108 . Lines  114  in  FIGS. 1A and 1B  detail the pathways defined by the channels  110  that direct the air towards the various different sections of the rotor assembly  102 . The channels  110  will be described in greater detail below with respect to  FIGS. 3A-3C . As is also schematically shown in  FIG. 1A , a screen  111  may also be placed in front of the channels  110  to inhibit animals or birds from entering the housing  104 . The channels  110  preferably are configured to alter shape with vanes so that the air is exhausted out of a round opening to match the rounded configuration of the housing  104  in the manner that is described below. 
     The housing  104  includes a cylindrical section  116  that is sized so as to receive the rotor assembly  102 . In one embodiment, the cylindrical section  116  of the housing  104  is sized so as to receive a rotor  120  of the rotor assembly  102  that is approximately 12 feet in diameter, however, the housing can be sized upwards and downwards to accommodate different sizes of rotors depending upon the implementation. The cylindrical section  116  of the housing  104  is, in one implementation, approximately 11 feet tall. 
     The housing  104  also includes the entry section  118  that is generally rectangular and provides a space through which the channels  110  can be routed from the opening  108  into an interior space  122  of the cylindrical portion  116  of the housing  104 . The channels  110  may also include vanes  124  that direct the air flow inward around corners and the like so that less energy of the air flow is lost due to the air travelling through the channels  110 . 
     As is shown in  FIGS. 1A and 1B , the rotor  120  of the rotor assembly  102  is mounted so as to be recessed beneath an upper opening  125  of the cylindrical section  116  of the housing  104 . The upper opening  125  acts as a stack that draws air out of the cylindrical housing  116  in a manner similar to a smoke stack which improves air flow and reduces back pressure against the rotation of the rotor  120 , thereby improving the efficiency of the turbine  100 . 
       FIGS. 2A-2G  provide exemplary illustrations of the components of one embodiment of a rotor assembly  102 . As shown in  FIGS. 2A and 2B , the rotor assembly  102  includes a mounting structure  127  that is comprised of a plurality of vertical legs  126  that contact the ground and a horizontal upper platform  128 . A rotatable shaft  130  is positioned within the upper platform  128  with bearing assemblies and the like so that the rotatable shaft  130  can rotate within the mounting structure  127 . A hub  132  ( FIG. 2C-E ) of the rotor  120  is then mounted to the rotatable shaft  128  so that the rotor can then rotate within the mounting structure  127 . As is also shown in  FIGS. 2A and 2B , various horizontal and vertical support structures can also be positioned within the housing  116  so as to stabilize the mounting structure  127  of the rotor assembly  102  when the rotor assembly  102  is rotating in response to wind being delivered to the rotor  120 . It will be appreciated that the exact configuration of the rotor assembly  102  can vary depending upon the dimensions of the structure and other design configurations and that the configuration of  FIGS. 2A and 2B  are simply exemplary. 
       FIG. 2C-2E  illustrates the rotor  120  of the rotor assembly  102 . The rotor  120  in this implementation includes a hub assembly  131  that defines the hub member  132  that is positioned over the rotatable shaft  130 . A plurality of radially extending support ribs  134  are positioned so as to extend outward from the hub member  132  and connect with an outer hub wall  136 . A plurality of angled blades  138  are then connected to the outer hub wall  136  so as to extend further outward to terminate in an outer vane wall  140 . The blades  138  are preferably angled such that air that is directed towards the blades  138  from a direction that is normal to the plane of the rotor  120  results in a horizontal force being exerted against the rotor  120  to induce the rotor  120  to rotate about the shaft  130 .  FIGS. 2D and 2E  provide exemplary dimensions of the rotor  120  and the placement, angle and twist of the ribs  138  that are suitable for the instant application. 
     In one specific implementation, the hub assembly  131  has a diameter of 4.5 feet and the outer vane wall  140  has a diameter of 12 feet and the hub assembly  131  and outer vane wall  140  are 18 inches wide. Further, in this specific implementation, there are 20 blades  138  that extend from the top surface of the outer vane wall  140  to the bottom edge of the outer vane wall  140  at an angle and are spaced apart. It will, however, be apparent that various changes to the dimensions and configurations can be made by those skilled in the art. 
       FIGS. 2F and 2G  are exemplary illustrations of one embodiment of a transmission assembly  142  and power generator  144  that are coupled to the shaft  130  such that when the rotor  102  is induced to rotate in response to wind travelling through the channels  110 , the rotational energy of the rotor  102  can be transferred into electrical power. The transmission assembly  142  converts the rotational energy from the rotating shaft  130  into linear energy via a system of belts  146  that are then connected to the generator motor  144  so that electrical energy can be produced by the generator motor  144 . In one implementation, the generator motor  144  comprises a known generator motor  144  that produces electrical energy. 
     As discussed above, the rotor  102  receives air via the channels  110 . The channels  110  are arranged within the housing  104  so that each radial portion of the rotor  120  is simultaneously receiving air from the channels  110 .  FIGS. 3A-3C  are schematic illustrations of the housing  104  with portions of the outer wall removed so as to illustrates the channels  110  and vanes  124  that are positioned within the channels  110  to direction the air from the opening  108  when it is flowing substantially parallel to the plane of the rotor  120  to a direction where it is flowing substantially perpendicular to the plane of the rotor  120 . 
     As shown and as discussed above, the three upper channels  110   a ,  110   b ,  110   c  are formed and have vanes  124  that are curved so as to direct the air flowing into those channels into the three 60 degree front segments  152  of the rotor  120 . The three bottom channels  110   d ,  110   e ,  110   f  are formed and have vanes  124  that are curved so as to direct the air flowing into those channels into three 60 degree rear segments  154  of the rotor  120 . In this way, the air that flows in through the opening  108  as a result of wind impacting upon the wind scoop opening assembly  106  is more evenly distributed about the rotor  120  so that substantially all surfaces of the rotor are simultaneously contributing to the conversion of wind energy into rotational energy of the rotor assembly  102 . The channels  110  are square at the opening  108 , however, at the exhaust, the openings are preferably sized and shaped to match the rounded contour of the section of the rotor  120  to which the channels  110  are exhausting air. 
       FIGS. 4A and 4B  provide further illustrations of the vanes  150  that are positioned within the channels  110 . Either the vanes  124  can extend through the entire channel, as shown in  FIGS. 3A-3C , or the vane  124  can be truncated and only occur at the location where the air is being turned from the horizontal direction at the opening  108  to the vertical direction towards the plane of the rotor  120 . 
       FIG. 5  illustrates a further optional feature of the assembly  100 . Air accelerators  160  can also be positioned in the air flow paths that channel the air from a larger space to a smaller space so as to increase the pressure of the air. The wind scoop opening assembly  106  performs this function and the higher pressure air can result in greater force being directed against the surfaces of the blades  138  of the rotor  102 . Additional or supplemental air accelerators  160  that similarly compress the air can also be included without departing from the scope of the present invention. 
     EXEMPLARY IMPLEMENTATIONS 
     The Applicant has performed calculations of the performance of the disclosed embodiments to determine the potential power generation for this embodiment. These calculations are summarized below. It should be appreciated that, while these calculations demonstrate the efficacy of this design, the specific dimensions and embodiments disclosed herein should not be limiting on the scope of the patent that is being sought. 
     The following wind turbine configuration is for 12 feet diameter×20 blades, and with up to 40 mph wind calculations. 
     12 ft Diameter and 20 Blade Configuration. 
     Blade width: Inner (approx.)=20.1735
         Outer (approx.)=29.0527       

     Force from 2 mph Wind: 
     
       
         
           
             
               
                 
                   P 
                   , 
                   
                     Wind 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     pressure 
                     ⁢ 
                     
                       ( 
                       
                         P 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         f 
                       
                       ) 
                     
                   
                   , 
                   
                     = 
                       
                     ⁢ 
                     
                       .00256 
                       × 
                       
                         V 
                         ⋀ 
                       
                       ⁢ 
                       2 
                     
                   
                 
               
             
             
               
                 
                     
                   ⁢ 
                   
                     ( 
                     
                       V 
                       = 
                       
                         wind 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         speed 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         in 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Mph 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       0.0102 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       psf 
                     
                     = 
                     
                       0.0000708 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       psi 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   A 
                   = 
                     
                   ⁢ 
                   
                     The 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     projected 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     area 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                       
                           
                       
                       ⁢ 
                       
                           
                       
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     item 
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       1078.42 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         in 
                         2 
                       
                     
                     = 
                     
                       7.489 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ft 
                         2 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             Cd 
             , 
             
                 
             
             ⁢ 
             
               Drag 
               ⁢ 
               
                   
               
               ⁢ 
               coefficient 
             
             , 
             
               = 
               
                 2.0 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 for 
                 ⁢ 
                 
                   
                       
                   
                   ⁢ 
                   
                       
                   
                 
                 ⁢ 
                 flat 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   plates 
                   . 
                   
                      
                   
                   ⁢ 
                   For 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 a 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 long 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   cylinder 
                   ⁢ 
                   
                     
                         
                     
                     ⁢ 
                     
                         
                     
                   
                   ( 
                   
                     like 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     most 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     antenna 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     tubes 
                   
                   ) 
                 
               
             
             , 
             
               Cd 
               = 
               
                 1.2 
                 . 
               
             
           
         
       
     
     Note the relationship between them is 1.2/2=0.6, not quite ⅔. 
     
       
         
           
             
               
                 
                   Force 
                   , 
                   
                     F 
                     = 
                       
                     ⁢ 
                     
                       A 
                       × 
                       P 
                       × 
                       Cd 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       0.153 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       lbs 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         =&gt; 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       0.153 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       lbs 
                       × 
                       20 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       blades 
                     
                     = 
                       
                     ⁢ 
                     
                       3.06 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       lbs 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Total 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         Force 
                         . 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 Total 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 Force 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 at 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   45 
                   
                     ∘ 
                     
                         
                     
                   
                 
                 ⁢ 
                 
                   ( 
                   
                     use 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     normal 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     to 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     blade 
                   
                   ) 
                 
               
               = 
               
                 
                   3.06 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   lbs 
                   × 
                   0.7071 
                 
                 = 
                 
                   2.164 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   lbs 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         apply 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         normal 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         to 
                         ⁢ 
                         
                           
                               
                           
                           ⁢ 
                           
                               
                           
                         
                         ⁢ 
                         blade 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         surface 
                       
                       ) 
                     
                     . 
                   
                 
               
             
             ⁢ 
             
                 
             
           
         
       
     
     Force from 12 mph Wind: 
     
       
         
           
             
               
                 
                   P 
                   , 
                   
                     Wind 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     pressure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       
                         P 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         f 
                       
                       ) 
                     
                   
                   , 
                   
                     = 
                       
                     ⁢ 
                     
                       .00256 
                       × 
                       
                         V 
                         ⋀ 
                       
                       ⁢ 
                       2 
                     
                   
                 
               
             
             
               
                 
                     
                   ⁢ 
                   
                     ( 
                     
                       V 
                       = 
                       
                         wind 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         speed 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         in 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Mph 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       0.3686 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       psf 
                     
                     = 
                     
                       0.00256 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       psi 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   A 
                   = 
                     
                   ⁢ 
                   
                     The 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     projected 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     area 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                       
                           
                       
                       ⁢ 
                       
                           
                       
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     item 
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       1078.42 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         in 
                         2 
                       
                     
                     = 
                     
                       7.489 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ft 
                         2 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             Cd 
             , 
             
                 
             
             ⁢ 
             
               Drag 
               ⁢ 
               
                   
               
               ⁢ 
               coefficient 
             
             , 
             
               = 
               
                 2.0 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 for 
                 ⁢ 
                 
                   
                       
                   
                   ⁢ 
                   
                       
                   
                 
                 ⁢ 
                 flat 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   plates 
                   . 
                   
                      
                   
                   ⁢ 
                   For 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 a 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 long 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 cylinder 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   
                     like 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     most 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     antenna 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     tubes 
                   
                   ) 
                 
               
             
             , 
             
               Cd 
               = 
               
                 1.2 
                 . 
               
             
           
         
       
     
     Note the relationship between them is 1.2/2=0.6, not quite ⅔. 
     
       
         
           
             
               
                 
                   Force 
                   , 
                   
                     F 
                     = 
                       
                     ⁢ 
                     
                       A 
                       × 
                       P 
                       × 
                       Cd 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       5.521 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       lbs 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         =&gt; 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5.521 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       lbs 
                       × 
                       20 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       blades 
                     
                     = 
                       
                     ⁢ 
                     
                       110.42 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       lbs 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Total 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         Force 
                         . 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 Total 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 Force 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 at 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   45 
                   ∘ 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   
                     use 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     normal 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     to 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     blade 
                   
                   ) 
                 
               
               = 
               
                 
                   110.42 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   lbs 
                   × 
                   0.7071 
                 
                 = 
                 
                   78.078 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   lbs 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         apply 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         normal 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         to 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         blade 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         surface 
                       
                       ) 
                     
                     . 
                   
                 
               
             
             ⁢ 
             
                 
             
           
         
       
     
     Force from 25 mph Wind: 
     
       
         
           
             
               
                 
                   P 
                   , 
                   
                     Wind 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     pressure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       
                         P 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         f 
                       
                       ) 
                     
                   
                   , 
                   
                     = 
                       
                     ⁢ 
                     
                       .00256 
                       × 
                       
                         V 
                         ⋀ 
                       
                       ⁢ 
                       2 
                     
                   
                 
               
             
             
               
                 
                     
                   ⁢ 
                   
                     ( 
                     
                       V 
                       = 
                       
                         wind 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         speed 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         in 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Mph 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       1.600 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       psf 
                     
                     = 
                     
                       0.0111 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       psi 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   A 
                   = 
                     
                   ⁢ 
                   
                     The 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     projected 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     area 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                       
                           
                       
                       ⁢ 
                       
                           
                       
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     item 
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       1078.42 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         in 
                         2 
                       
                     
                     = 
                     
                       7.489 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ft 
                         2 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             Cd 
             , 
             
                 
             
             ⁢ 
             
               Drag 
               ⁢ 
               
                   
               
               ⁢ 
               coefficient 
             
             , 
             
               = 
               
                 2.0 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 for 
                 ⁢ 
                 
                   
                       
                   
                   ⁢ 
                   
                       
                   
                 
                 ⁢ 
                 flat 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   plates 
                   . 
                   
                      
                   
                   ⁢ 
                   For 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 a 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 long 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   cylinder 
                   ⁢ 
                   
                     
                         
                     
                     ⁢ 
                     
                         
                     
                   
                   ( 
                   
                     like 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     most 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     antenna 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     tubes 
                   
                   ) 
                 
               
             
             , 
             
               Cd 
               = 
               1.2 
             
           
         
       
     
     Note the relationship between them is 1.2/2=0.6, not quite ⅔. 
     
       
         
           
             
               
                 
                   Force 
                   , 
                   
                     F 
                     = 
                       
                     ⁢ 
                     
                       A 
                       × 
                       P 
                       × 
                       Cd 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       23.965 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       lbs 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         =&gt; 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       23.965 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       lbs 
                       × 
                       20 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       blades 
                     
                     = 
                       
                     ⁢ 
                     
                       479.3 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       lbs 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Total 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         Force 
                         . 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 Total 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 Force 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 at 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   45 
                   ∘ 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   
                     use 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     normal 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     to 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     blade 
                   
                   ) 
                 
               
               = 
               
                 
                   479.3 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   lbs 
                   × 
                   0.7071 
                 
                 = 
                 
                   338.913 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   lbs 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         apply 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         normal 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         to 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         blade 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         surface 
                       
                       ) 
                     
                     . 
                   
                 
               
             
             ⁢ 
             
                 
             
           
         
       
     
     Force from 28 mph Wind: 
     
       
         
           
             
               
                 
                   P 
                   , 
                   
                     Wind 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     pressure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       
                         P 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         f 
                       
                       ) 
                     
                   
                   , 
                   
                     = 
                       
                     ⁢ 
                     
                       .00256 
                       × 
                       
                         V 
                         ⋀ 
                       
                       ⁢ 
                       2 
                     
                   
                 
               
             
             
               
                 
                     
                   ⁢ 
                   
                     ( 
                     
                       V 
                       = 
                       
                         wind 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         speed 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         in 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Mph 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       2.007 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       psf 
                     
                     = 
                     
                       0.014 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       psi 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   A 
                   = 
                     
                   ⁢ 
                   
                     The 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     projected 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     area 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                       
                           
                       
                       ⁢ 
                       
                           
                       
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     item 
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       1078.42 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         in 
                         2 
                       
                     
                     = 
                     
                       7.489 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ft 
                         2 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             Cd 
             , 
             
                 
             
             ⁢ 
             
               Drag 
               ⁢ 
               
                   
               
               ⁢ 
               coefficient 
             
             , 
             
               = 
               
                 2.0 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 for 
                 ⁢ 
                 
                   
                       
                   
                   ⁢ 
                   
                       
                   
                 
                 ⁢ 
                 flat 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   plates 
                   . 
                   
                      
                   
                   ⁢ 
                   For 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 a 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 long 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 cylinder 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   
                     like 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     most 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     antenna 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     tubes 
                   
                   ) 
                 
               
             
             , 
             
               Cd 
               = 
               1.2 
             
           
         
       
     
     Note the relationship between them is 1.2/2=0.6, not quite ⅔. 
     
       
         
           
             
               
                 
                   Force 
                   , 
                   
                     F 
                     = 
                       
                     ⁢ 
                     
                       A 
                       × 
                       P 
                       × 
                       Cd 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     30.196 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     lbs 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       =&gt; 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     30.196 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     lbs 
                     × 
                     20 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     blades 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 Total 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 Force 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 at 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   45 
                   ∘ 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   
                     use 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     normal 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     to 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     blade 
                   
                   ) 
                 
               
               = 
               
                 
                   603.92 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   lbs 
                   × 
                   0.7071 
                 
                 = 
                 
                   427.032 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   lbs 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       ( 
                       
                         apply 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         normal 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         to 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         blade 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         surface 
                       
                       ) 
                     
                     . 
                   
                 
               
             
             ⁢ 
             
                 
             
           
         
       
     
     Force from 40 mph Wind: 
     
       
         
           
             
               
                 
                   P 
                   , 
                   
                     Wind 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     pressure 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       
                         P 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         f 
                       
                       ) 
                     
                   
                   , 
                   
                     = 
                       
                     ⁢ 
                     
                       .00256 
                       × 
                       
                         V 
                         ⋀ 
                       
                       ⁢ 
                       2 
                     
                   
                 
               
             
             
               
                 
                     
                   ⁢ 
                   
                     ( 
                     
                       V 
                       = 
                       
                         wind 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         speed 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         in 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Mph 
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       4.096 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       psf 
                     
                     = 
                     
                       0.028 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       psi 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   A 
                   = 
                     
                   ⁢ 
                   
                     The 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     projected 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     area 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                       
                           
                       
                       ⁢ 
                       
                           
                       
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     item 
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       1078.42 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         in 
                         2 
                       
                     
                     = 
                     
                       7.489 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ft 
                         2 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             Cd 
             , 
             
                 
             
             ⁢ 
             
               Drag 
               ⁢ 
               
                   
               
               ⁢ 
               coefficient 
             
             , 
             
               = 
               
                 2.0 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 for 
                 ⁢ 
                 
                   
                       
                   
                   ⁢ 
                   
                       
                   
                 
                 ⁢ 
                 flat 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   plates 
                   . 
                   
                      
                   
                   ⁢ 
                   For 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 a 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 long 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 cylinder 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   
                     like 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     most 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     antenna 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     tubes 
                   
                   ) 
                 
               
             
             , 
             
               Cd 
               = 
               1.2 
             
           
         
       
     
     Note the relationship between them is 1.2/2=0.6, not quite ⅔. 
     
       
         
           
             
               
                 
                   Force 
                   , 
                   
                     F 
                     = 
                       
                     ⁢ 
                     
                       A 
                       × 
                       P 
                       × 
                       Cd 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     60.392 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     lbs 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       =&gt; 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     60.392 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     lbs 
                     × 
                     20 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     blades 
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     1 
                     , 
                     207.84 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     lbs 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Total 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       Force 
                       . 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               Total 
               ⁢ 
               
                   
               
               ⁢ 
               Force 
               ⁢ 
               
                   
               
               ⁢ 
               at 
               ⁢ 
               
                   
               
               ⁢ 
               
                 45 
                 ∘ 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 ( 
                 
                   use 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   normal 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   to 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   blade 
                 
                 ) 
               
             
             = 
             
               
                 1 
                 , 
                 207.84 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 lbs 
                 × 
                 0.7071 
               
               = 
               
                 854.064 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 lbs 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   
                     ( 
                     
                       apply 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       normal 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       to 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       blade 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       surface 
                     
                     ) 
                   
                   . 
                 
               
             
           
         
       
     
     Using the above-force calculations applied to the rotor assembly  102  described above and using the below formulas yields the following power generation: 
     Power Calculation Formulas: 
     
       
         
           
             
               Torque 
               inlb 
             
             = 
             
               
                 
                   
                     
                       Power 
                       hp 
                     
                     · 
                     63025 
                   
                   RPM 
                 
                 + 
                 
                   
 
                 
                 ⁢ 
                 
                   Power 
                   hp 
                 
               
               = 
               
                 
                   RPM 
                   · 
                   
                     Torque 
                     inlb 
                   
                 
                 63025 
               
             
           
         
       
       
         
           
             
               1 
               · 
               hp 
             
             = 
             
               745.7 
               ⁢ 
               
                   
               
               ⁢ 
               W 
             
           
         
       
       
         
           
             RPM 
             = 
             
               
                 63025 
                 · 
                 
                   Power 
                   hp 
                 
               
               
                 Torque 
                 inlb 
               
             
           
         
       
       
         
           
             centripetal 
             ⁢ 
             
                 
             
             ⁢ 
             acceleration 
           
         
       
       
         
           
             a 
             = 
             
               
                 
                   v 
                   2 
                 
                 r 
               
               ⁢ 
               
                   
               
               ⁢ 
               centripetal 
               ⁢ 
               
                   
               
               ⁢ 
               acceleration 
             
           
         
       
       
         
           
             v 
             = 
             
               
                 ar 
               
               ⁢ 
               
                   
               
               ⁢ 
               velocity 
             
           
         
       
       
         
           
             r 
             = 
             
               
                 
                   v 
                   2 
                 
                 a 
               
               ⁢ 
               
                   
               
               ⁢ 
               radius 
             
           
         
       
       
         
           
             circular 
             ⁢ 
             
                 
             
             ⁢ 
             velocity 
           
         
       
       
         
           
             v 
             = 
             
               
                 
                   2 
                   ⁢ 
                   π 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   r 
                 
                 T 
               
               ⁢ 
               
                   
               
               ⁢ 
               circular 
               ⁢ 
               
                   
               
               ⁢ 
               velocity 
             
           
         
       
       
         
           
             r 
             = 
             
               
                 vT 
                 
                   2 
                   ⁢ 
                   π 
                 
               
               ⁢ 
               
                   
               
               ⁢ 
               radius 
             
           
         
       
       
         
           
             T 
             = 
             
               
                 
                   2 
                   ⁢ 
                   π 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   r 
                 
                 v 
               
               ⁢ 
               
                   
               
               ⁢ 
               period 
             
           
         
       
     
     
       
         
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Wind Speed 
                 Turbine 
                 No. 
                 Torque 
                 Torque 
                   
                 Power 
                 Power 
               
               
                 (mph) 
                 Diameter 
                 Blades 
                 (in-lb) 
                 (ft-lb) 
                 RPM 
                 (hp) 
                 (watts) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 2 
                 12 
                 20 
                 79.453 
                 6.621 
                 6.928 
                 0.009 
                 6.513 
               
               
                 12 
                 12 
                 20 
                 2866.676 
                 238.890 
                 41.615 
                 1.893 
                 1411.496 
               
               
                 25 
                 12 
                 20 
                 12443.39 
                 1036.949 
                 86.701 
                 17.118 
                 12764.803 
               
               
                 28 
                 12 
                 20 
                 15678.75 
                 1306.563 
                 97.310 
                 24.208 
                 18051.787 
               
               
                 40 
                 12 
                 20 
                 31357.48 
                 2613.123 
                 112.378 
                 55.913 
                 41694.01721 
               
               
                   
               
             
          
         
       
     
     A. Summary Comparison 
     
       
         
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Wind Speed 
                 Turbine 
                 No. 
                 Torque 
                 Torque 
                   
                 Power 
                 Power 
               
               
                 (mph) 
                 Diameter 
                 Blades 
                 (in-lb) 
                 (ft-lb) 
                 RPM 
                 (hp) 
                 (watts) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 2 
                 12 
                 20 
                 79.453 
                 6.621 
                 6.928 
                 0.009 
                 6.513 
               
               
                 12 
                 12 
                 20 
                 2866.676 
                 238.890 
                 41.615 
                 1.893 
                 1411.496 
               
               
                 25 
                 12 
                 20 
                 12443.39 
                 1036.949 
                 86.701 
                 17.118 
                 12764.803 
               
               
                 28 
                 12 
                 20 
                 15678.75 
                 1306.563 
                 97.310 
                 24.208 
                 18051.787 
               
               
                 40 
                 12 
                 20 
                 31357.48 
                 2613.123 
                 112.378 
                 55.913 
                 41694.01721 
               
               
                   
               
             
          
         
       
     
     B. Efficiency Considerations 
     Total efficiency loss is 11% (from +20%-15%-16% calculated below). This takes into account chamber improvements, otherwise it would be a 31% efficiency loss. 
     i. Chamber
         Wind is collected and enters the chamber at the upper and lower inlets. The upper inlet feeds the forward-most turbines while the lower inlet feeds the aft-most turbines. The chamber is 360° adjustable to face the wind from any direction.   The wind exits the chamber vertically onto the turbine blades.       

     The above calculations demonstrate that there is a significant improvement in efficiency in the generation of power using the enclosed wind turbine with the stack effect and the air pressurization features of the wind scoop. Although the foregoing has shown, illustrated and described various embodiments and uses of the present invention, it will be apparent from the foregoing description that various changes, modifications and alterations to the systems described herein, and the uses thereof may be made by those skilled in the art without departing from the spirit of the present invention. Hence, the scope of the present invention should not be limited to the foregoing discussion but should be defined by the appended claims and all reasonable interpretations of scope thereof.