Abstract:
In a preferred embodiment, pairs of oscillating wind paddles are mounted in the lee of a wind turbine of the lift type. An oscillating wind paddle assembly has an upper pair of paddles moving between a first position at substantially right angles to the direction of wind and a second position substantially parallel to the direction of the wind and mounted on arms extending to either side of a shaft to which they are connected through a one-way clutch, and a lower pair of paddles moving between a position at substantially right angles to the direction of the wind and a second position substantially parallel to the direction of the wind and mounted on arms extending to either side of the same shaft to which they are connected through a one-way clutch, one of the paddles being a drive paddle and the other a recovery paddle, the two pairs of paddles being out of phase with respect to one another.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Application No. 60/947,049 filed Jun. 29, 2007 and No. 60/866,127 filed Nov. 16, 2006, the disclosures of which patent applications are incorporated herein by reference. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     Not Applicable. 
     BACKGROUND OF THE INVENTION 
     Wind mills or wind motors on a vertical axis have been known for a long time, see GRACEY U.S. Pat. No. 1,352,952, and MOORE U.S. Pat. No. 1,915,689. Means moving vanes or paddles from a position substantially at right angles to the direction of the wind, to a position at which they are substantially parallel to the wind are well known; see MOORE, supra, and BAIR U.S. Pat. No. 4,303,835. The object in the various prior art references has been to provide continuous rotation of a shaft, see LINDHORN U.S. Pat. No. 6,619,921, even when the windmill itself is capable of being driven in a reverse direction, see OUELLET U.S. Pat. No. 5,126,584. 
     An excellent discussion of the prior art is set out in WO 2006/093790, published 8 Sep. 2006, incorporated by reference herein. “The windfin articulated wind-powered generator” of that applications uses as its driving force a lift force to produce a flapping motion. The present invention utilizes a drag force. 
     In the windmill of the present invention, the vanes, panels or paddles are designed to oscillate, going through on the order of 120° for a hinged type to 80° for a non-hinged type with flaps, and reversing, occupying a great deal less space than the conventional windmill. The windmill of this invention can be used in combination with the usual windmill of the lift type, which rotates on a horizontal axis, the sort of windmill now used extensively in windmill farms, for the generation of electricity. The latter windmills occupy a large amount of space. The panels or rotors of these windmills commonly describe a circle hundreds of feet in diameter, and the closest placement of adjacent windmills or turbines is recommended to be the length of at least five times the diameter of the wind turbine&#39;s rotor, so that the adjacent wind turbines in the array are often placed at a distance of a quarter of a mile to half a mile, so that the air stream has time to “recover”. 
     BRIEF SUMMARY OF THE INVENTION 
     In accordance with this invention generally stated, an oscillating windmill is provided that, in its most elementary form, consists of vanes or paddles positioned at opposite ends of a horizontal rod connected at its center to a vertical shaft driven by the paddles alternately clockwise and counterclockwise, or, utilizing a one-way clutch and incremental segments, rotating in one direction. The paddle on one end of the rod is oriented to catch wind while the paddle in the other end is oriented to present the least surface to the wind, and means are provided for reversing the orientation of the paddles so that the rod is driven in the other direction when it has rotated through an arc sufficient to rotate the vertical shaft enough to accomplish useful work, but not through a full 180° if the windmill is to operate efficiently. Preferably, the vanes move the rod through no more than 120°, that is, 60° from a centerline. 
     For generating electricity, at least two pairs of paddles are preferably employed, one above the other but connected by one-way clutches to the vertical shaft. Preferably upper and lower pairs of paddles are oriented 180° apart, and oppositely disposed so that when a driving paddle of the upper assembly is engaging the shaft, the recovery paddle of the other paddle assembly is restoring the driving paddle with which it is associated to a beginning position. 
     In a preferred embodiment, the oscillating windmill just described, can be combined with a windmill of the lift type rotating on a horizontal axis, the shaft of the oscillating windmill being mechanically connected with a generator connected electrically to the generator of the lift type windmill. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       In the accompanying drawings which form part of the specification: 
         FIG. 1  is a view in perspective of a single partially rotated wind paddle; 
         FIG. 2A-J  illustrated the sequence of partial wind paddle rotations with alternating directions; 
         FIG. 3  is a second embodiment of oscillating windmill of this invention; 
         FIG. 4  is a third embodiment; 
         FIG. 5  is a fourth embodiment; 
         FIGS. 6A and 6B  illustrate two conditions of a fifth embodiment; 
         FIGS. 7A-O  illustrate the sequence of partial wind panel rotations with alternating directions of a sixth embodiment; 
       FIGS.  8 A 1 - 8 C 3  are a somewhat diagramatic illustrations of the amplitude range comparisons and drag force leverages of three (3) types of paddle; 
         FIG. 9  is a view in perspective of a second form of generator arrangement from that illustrated in  FIG. 3 ; 
         FIG. 10  is a fragmentary view in perspective of yet another system of generators to be operated by an oscillating windmill of this invention; and 
         FIGS. 11A-11K  are somewhat diagrammatic views in top plan, illustrating the sequence of partial wind panel rotations with alternating directions of yet another embodiment; and 
         FIG. 12  ia a graph showing Power P in Watts as a function increasing load force in F in Newtons. 
         FIGS. 12A-12K  are somewhat diagrammatic views in top plan of the sequence of wind panel rotations with alternating directions of the embodiment shown in  FIGS. 11A-11K   
     
    
    
     Corresponding reference numerals indicate corresponding parts throughout the several figures of the drawings. 
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The following detailed description illustrates the invention by way of example and not by way of limitation. The description clearly enables one skilled in the art to make and use the invention, describes several embodiments, adaptations, variations, alternatives, and uses of the invention, including what is presently believed to be the best mode of carrying out the invention. 
     As various changes could be made in the above constructions without departing from the scope of the invention, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense. 
     Referring to  FIG. 1 , reference number  1  indicates a single partially rotating wind paddle system of this invention. One paddle  2  is shown as being oriented perpendicularly to the direction of wind blowing toward the drawing. The paddle  2  is mounted at the end of an arm  3 , connected to a shaft  4 . The other end of the arm  3  is connected to a paddle  5 . In  FIG. 1 , the paddle  5  is shown as oriented parallel to the direction of the wind, so as to present the smallest possible wind profile. Accordingly, the paddle  2  is being driven in a direction away from the viewer, while the paddle  5  is being driven in a direction toward the viewer. When the paddle  2  has reached a certain position angularly with respect to the shaft  4 , it is flipped 90 degrees to a position that is parallel with the wind, while the paddle  5  is flipped to the position in which it is perpendicular to the wind direction, and the cycle is then repeated, all as illustrated in  FIGS. 2A-J . The shaft  4  passes through a generator housing  8  of a generator, as illustrated in  FIG. 3 , except that, unlike the device of  FIG. 3  in which the direction of the power stroke is always in one direction of rotation, in the embodiment of  FIG. 1 , an intermediate gear arrangement is required when the direction of rotation is reversed, to drive the generator in one direction. 
     Referring now to  FIG. 3  for a second embodiment, reference numeral  15  indicates a system in which two pairs of panels, an upper pair  18  and a lower pair  20 , are connected to a shaft  22  through simple one-way clutches  24 . In this embodiment, panels  25  and  28  are drive panels, and panels  26  and  27  are recovery panels, restoring the drive panels to driving position at the end of their travel in the drive position. This provides a relatively continuous rotation of a generator  40 . 
     In this embodiment, shaft  22  passes through and is connected to a yaw control  36 , and into a gear box  32  and mounted in a casing  38  by means of support  34 . The casing  38  is sunk into the earth  39 . The gear box  32  houses gears that multiply the rotational speed of the shaft  22  transmitted to a generator drive shaft  37  connected to the rotor of generator  40 . The generator is electrically connected to transmit energy to a cable  35 , which is part of an electrical grid. The generator acts as a brake, aiding the stopping of the panels. The energy transferred can be regulated electronically. The amount of rotation of the rods  29  and  30  is limited by stops not here shown, or a mechanical brake which can be a part of the gear box arrangement. 
     Referring now to  FIG. 4 , the panels of the second embodiment  111 , here indicated by reference numerals  102  and  103 , are mounted on a nacelle  113  which receives a shaft on which blades  112  are mounted. Blades  112  are aero-dynamically patterned to act as a lift type windmill. The entire assembly is supported by a tower  107 . A bridge  109  connects the tower  107  with the nacelle. As can be seen in  FIG. 4 , the panels of the oscillating system are clear of the blades  112  by virtue of their limited travel. The oscillating wind panels serve as weather vanes, aiding the yaw control to keep the wind turbine and windmill headed into the wind. The panels  103  and  102  are mounted on shafts  104  and  105  which drive the generator  110  in housing  108 , electrically connected to a generator  114  in the nacelle  113 , hence to a power grid. 
     Referring now to  FIG. 5 , a third embodiment is shown, in which a multiplicity of panels  205  and  202  are mounted on vertical rods  207  and  208  respectively, in turn mounted on horizontal arms  209  and  210  respectively, carried by arms  212  connected to a shaft  215 , connected to a generator. In this embodiment, the panels swivel about a vertical axis, but the net result is the same. Various arrangements of such paddles are shown in  FIGS. 9 through 17  of my provisional application 60/866,127, incorporated herein by reference. 
     Referring now to  FIGS. 6A and 6B , panels  302  and  305  are shown as being made up of slats  307 , otherwise all as shown in  FIG. 1 . Clearly, similar shutter type panels can be used in the embodiment shown in  FIG. 5 . 
     Referring now to  FIG. 7 , the action of a hinge panel  401  is illustrated through one full cycle. A hinge  403  permits the panel to present a full face to the wind through its effective arc of travel. 
     Referring now to  FIGS. 8A , B, and C, forces of the wind through a half cycle of the hinged version, the unhinged version, and an unhinged version of a panel with an outer edge wing or flap  504  are illustrated. 
     Referring now to  FIG. 9 , a system is shown in which a multiplicity, in this case four, generators are driven by gear wheels  601  and  602 , in turn driven by a gear  623  engaged by a cog segment  620 . The gears  623  are connected to drive the gear wheels  601  and  602 , which in turn drive generators  630  by way of gears  640 . The gear  623  is revolvably mounted on an arm  615  carried by a shaft  610  driven by the panels of any of the embodiments shown. As can readily be seen, the gearing arrangements of this embodiment multiply the motion of the shaft  610  to increase the speed of revolution of the rotor of the generator  630 . 
     Referring now to  FIG. 10 , another multiple generator arrangement is shown. In this case, the gearing through the gear  623  is the same as that of  FIG. 9 . In this embodiment, the gears  623  drive sheaves  701 , each of which carries two v-belts  702  and  703 , obtaining around sheaves  704  and  705  of generator  630  to achieve the increased rate of revolution of the rotors of the generators  630 . 
     Referring to  FIG. 11 , a hinge is shown between the rods  210  and  212  of the embodiment shown in  FIG. 5 , to avoid shielding of the panels during a part of their cycles. 
     Various other arrangements of conventional windmills and wind turbines of this invention are illustrated in provisional application 60/947,049, incorporated herein by reference, see  FIG. 12  of that application, for example. 
     Numerous variations in the construction and operating of the oscillating windmill of the invention in addition to those illustrated in and suggested by  FIGS. 1-10  will occur to those skilled in the art in light of the foregoing disclosure. For example, the drive paddles of  FIG. 3  can be made with larger areas than the recovery paddles or the rod can be made shorter on the recovery paddle side, or the rod can be made telescoping to accommodate different wind velocities. The stops to limit the amount of rotation of the paddle can be fixed to the support, to engage the rods as they rotate, or can take the form of a mechanical brake on the vertical shaft. The slatted types of paddles can be made with more or fewer slats than those shown in  FIGS. 6A and 6B , and can be used in the vertically arranged panels of  FIG. 5 . These are merely illustrative. 
     The following discussion is intended to clarify the operation of the windmill of this invention as applied to the generation of electricity. 
     Performance of Oscillating Windmills 
     Oscillating windmills are similar to the conventional windmills in the sequential steps in which they extract the energy from wind and than convert it sequentially to different forms of mechanical energy. The final energy conversion is always from the rotational energy carried by high RPM shaft into the electrical energy. 
     There are corresponding losses associated with each energy conversion. 
     Wind Power 
     Wind power is a measure of the energy available in the wind. It is a function of the cube (third power) of the wind speed. If the wind speed is doubled, power in the wind increases by a factor of eight. This relationship means that small differences in wind speed lead to large differences in power. 
     Wind Power “Available” 
     The amount of power available in the wind is determined by the equation P=½rAv 3    
     Where: P=power, r=air density, A=cross-section of the measured wind stream, v=wind speed. 
     This equation states that the power is equal to one-half, times the air density, times the rotor area, times the cube of the wind speed. Air density varies according to elevation and temperature. 
     For the purposes of calculating wind power, the formula for air density is: p=(1.325×P)/T where T is the temperature in Fahrenheit+459.69 and P is the pressure in inches of Mercury adjusted for elevation. 
     Note: For comparison purposes, A=working paddle area whenever calculating the max wind power “available” to us to determine the Oscillating wind mill efficiency. 
     Whenever we talk about any comparison with a conventional windmill, we assume A to be the area swept by its rotor blades. 
     Energy Extraction from Wind Stream—Theory and General Case Betz&#39; Law 
     Maximum wind energy extraction possible is limited by the Betz law which says that you can only convert less convert less than 16/27 (or 59%) of the kinetic energy in the wind to mechanical energy using a wind turbine. 
     The calculations below will show that Oscillating Windmills&#39; efficiency would typically be in the range of 20 to 24% but stay constant, regardless of wind speed (for a given Oscillating wind mill). 
     This is very different from the conventional wind mills where the efficiency is almost the same for any modern wind mill but is not constant for any given wind mill. 
     For example the efficiency of the GE 3.6 MegaWatt Wind Mill is about 18% at its rated wind speed of 16 meters/sec but fluctuates between 15% to 32% in the lower wind speeds. 
     The wind stream contains a linear kinetic energy well defined by physics equation above. The power harvested or extracted by Oscillating windmill by the square area of its working paddles determines its efficiency. The power harvested and converted into electricity (in Watts) is divided by the power available in wind (also in Watts). 
     Power extracted &amp; converted, divided by Power available=Energy extraction efficiency 
               e   .   g   .               ⁢   P     Pav       =     Efficiency   ⁢           ⁢   of   ⁢           ⁢   Wind   ⁢           ⁢   energy   ⁢           ⁢   extraction           
Case of Oscillating Windmills—Energy Extraction from Wind Stream
 
     The Oscillating windmills “insert” their paddle(s) into a windstream and move and operate essentially in the same direction, albeit much more slowly than the wind. 
     The Oscillating windmills are thus driven by the wind drag force. The kinetic energy of wind molecules hitting the leveraged paddle(s) or panel surface(s) is translated into the movement of the paddles in the downwind direction. 
     These paddles thus “semi-rotate” in the horizontal plane. This semi-rotation is reversed back and forth to form a steady oscillation with preset amplitude value. 
     Amplitude: 
     The amplitude never exceeds 180 degrees and is typically preset at approximately 90 degrees, depending on the size or scale of the windmill. 
     After starting the windmill operation the computer control can adjust this oscillating amplitude to values significantly larger or smaller to optimize the operation for the constantly changing wind speed conditions. 
     Oscillating Wind Mills with hinged paddle implementation also tend to have larger oscillation amplitude than the non-hinged ones. 
     Optimal Paddle Speed: 
     It is shown below that the ideal paddle speed is exactly one third of the wind speed. The maximum electricity is always generated at that speed. (The paddle speed is controlled by the increasing and decreasing the electricity generating load). 
     Energy Conversion Steps with Corresponding Energy Conversion Losses 
     Just as in the case of the conventional windmills, the oscillating windmills first extract the linear kinetic mechanical energy of the linear wind stream into the rotationally oscillating mechanical energy with small RPM and high torque. Another mechanical energy conversion process converts this oscillating energy into the fully rotating mechanical energy with high RPM and lower torque rotation, the last energy conversion step is from mechanical to electrical energy. This step is based on Faraday law of induction and is essentially identical to the electricity generation of the conventional windmills described elsewhere in this patent. 
                 Wind   ⁢           ⁢   Energy     -&gt;         Paddle   ⁢           ⁢   kinetic   ⁢           ⁢   Energy         100   ⁢   %     -     10   ⁢   %   ⁢           ⁢   loss         -&gt;         Oscillation   ⁢           ⁢   low   ⁢           ⁢   RPM   ⁢           ⁢   Energy         90   ⁢   %   ⁢           ⁢   left     -     3   ⁢   %         -&gt;       Hi   ⁢           ⁢   RPM   ⁢           ⁢   rotational   ⁢           ⁢   Energy       87   ⁢   %   ⁢           ⁢   left             ⁢     
           
Explanation of Energy Loss Estimates:
 
     The losses of the first energy conversion are not shown. This is really an efficiency of energy extraction from wind. This energy extraction efficiency is approximately 22% and the calculations are shown below. 
     For the subsequent loss approximations, the starting point is the kinetic energy of the paddles which we call 100%. The 10% loss due to the oscillation is caused by the loss of leverage as the paddles move away from their “zero” positions. 
     The last energy conversion step generating electricity will have additional energy loss of 2% (heat loss) consistent with the industry standards. 
     Performance Optimization 
     Oscillating Wind mill concept presents several areas which lend themselves to the optimization of the mechanical Power and Energy extracted from the Power of the wind stream available to it. 
     These areas area: 
     1) Various Shapes of the paddles in working and non-working positions and Cd=drag coefficients associated with it. The goal is to use a cost-effective paddle with maximum Cd when in “working position” and the minimum Cd when in the non-working position. For our calculation below we chose Cd=1.42 which is a drag coefficient for paddles in working positions made as: 
     a) Flat rigid rectangular paddles with aspect ratio of 4:1 (laminar flat in non-working position) 
     b) Parachute-like circular sail “paddle” (will fold flat in non-working position) 
     2) Optimal Speed of the Paddles Relative to the Current Wind Speed. 
     Paddle speed is controlled by increasing and decreasing the Electricity generating Load for different Wind velocities. Power extracted (in Watts)=Fd times Vp 
     Where: Fd=drag force (in Newtons) pushing the paddle and Vp=Velocity of the paddle (in meters/s) Fd in turn is defined by Drag equation as: Fd=½rAv 2    
     Where: P=power, r=air density, A=cross-section of the measured wind stream and v=velocity of the object relative to the fluid (wind). e.g. v=VT−Vp
 
 Fd= ½ rA ( VT−Vp ) 2  
 
3) Optimal Load of Electricity Generation
 
     The electricity generation produces a proportional “mechanical breaking” action which in turn determines to produce the optimal Paddle velocity. 
     This is essentially a mechanical breaking load on the paddles. This mechanical load is derived from the electrical load of generating a particular amount of electricity at any given time. 
     This is essentially the same as braking a hybrid car (extracting electrical energy from car&#39;s kinetic energy) 
     Our calculation below show how the Load determines the paddle speed for various wind speeds. 
     Optimum Paddle speed relative to the wind speed is crucial for the optimal electricity generation. 
     The maximum speed of the paddle is when there is no electricity generating load present. The only “load” on the paddle would be the frictional forces of its pivot and the paddle would move with the speed close to the current speed of wind. But such paddle movement would not be very useful, since no electricity could be generated without a mechanical load “felt” by the paddle. 
     The minimal speed of the paddle would be with very large loads. Such loads would bring the paddle to a complete stop and again no electricity could be generated without a movement. 
     The optimal speed of the paddle is somewhere between the max and min speeds described above. This speed can be determined by increasing or decreasing the load or counter-torque on the paddles by increasing or decreasing the electricity production. For example, such “Load increase” will effectively apply a braking action on the paddle movement thus slowing it down. 
     All this is related to the electricity generating load as shown in the calculations tabled below: 
     The highlighted column in Tables below shows the Power P (in Watts) generated by Paddle&#39;s Drag force Fd=Load (in Newtons) multiplied by Paddle velocity Vp (in meters/sec). Power=Energy per second 
     The highlighted row in the Tables below show the optimal (ideal) values of Load Fd (drag force) and Paddle velocity Vp resulting in the maximum Power P. 
     P=*Vp (1 Watt=1 Newton*1 Meter/sec) Calculation of Load values to show the ideal loading e.g. optimal electricity generation 
     First the Fd values will be calculated for fixed (constant) VT wind speeds; while varying the paddle Vp speed.
 
Using the Drag equation:  Fd= ½ rACd ( VT−Vp ) 2  
 
     where c d =1.42; r=the density of air=1.225 kg/m 3 ; A=1 m 2   
                                                   FD = 0.5 Cd r A (vT − vP)2            Cd   0.5   Ro   A               1.42   0.5   1.225   1   0.86975                    
For constant Wind Velocity=10 meters/second
 
                                                                                   Vt   Vp   Vt − Vp   squared   Cd * r * A   Fd   P = FD * Vp                                10   1   9   81   0.86975     70.45     70.450       10   2   8   64   0.86975     55.66     111.328       10   3   7   49   0.86975     42.62     127.853       10   4   6   36   0.86975     31.31     125.244       10   5   5   25   0.86975     21.74     108.719       10   6   4   16   0.86975     13.92     83.496       10   7   3   9   0.86975     7.83     54.794       10   8   2   4   0.86975     3.48     27.832       10   9   1   1   0.86975     0.87     7.828       10   10   0   0   0.86975     0.00     0.000                    
For constant Wind Velocity=15 meters/second
 
                                                                                   Vt   Vp   Vt − Vp   squared   Cd * r * A   Fd   P = FD * Vp                                15   1   14   196   0.86975     170.47     170.471       15   2   13   169   0.86975     146.99     293.976       15   3   12   144   0.86975     125.24     375.732       15   4   11   121   0.86975     105.24     420.959       15   5   10   100   0.86975     86.98     434.875       15   6   9   81   0.86975     70.45     422.699       15   7   8   64   0.86975     55.66     389.648       15   8   7   49   0.86975     42.62     340.942       15   9   6   36   0.86975     31.31     281.799       15   10   5   25   0.86975     21.74     217.438       15   11   4   16   0.86975     13.92     153.076       15   12   3   9   0.86975     7.83     93.933       15   13   2   4   0.86975     3.48     45.227       15   14   1   1   0.86975     0.87     12.177       15   15   0   0   0.86975     0.00     0.000                    
For constant Wind Velocity=17 meters/second
 
                                                                                   Vt   Vp   Vt − Vp   squared   Cd * r * A   Fd   P = FD * Vp                                17   1   16   256   0.86975     222.66     222.656       17   2   15   225   0.86975     195.69     391.388       17   3   14   196   0.86975     170.47     511.413       17   4   13   169   0.86975     146.99     587.951       17   5   12   144   0.86975     125.24     626.220       17   6   11   121   0.86975     105.24     631.439       17   7   10   100   0.86975     86.98     608.825       17   8   9   81   0.86975     70.45     563.598       17   9   8   64   0.86975     55.66     500.976       17   10   7   49   0.86975     42.62     426.178       17   11   6   36   0.86975     31.31     344.421       17   12   5   25   0.86975     21.74     260.925       17   13   4   16   0.86975     13.92     180.908       17   14   3   9   0.86975     7.83     109.589       17   15   2   4   0.86975     3.48     52.185       17   16   1   1   0.86975     0.87     13.916       17   17   0   0   0.86975     0.00     0.000                    
For constant Wind Velocity=19 meters/second
 
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 Vt 
                 Vp 
                 Vt − Vp 
                 squared 
                 Cd * r * A 
                 Fd 
                 P = FD * Vp 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 19 
                 1 
                 18 
                 324 
                 0.86975 
                 
                   281.80 
                 
                 281.799 
               
               
                 19 
                 2 
                 17 
                 289 
                 0.86975 
                 
                   251.36 
                 
                 502.716 
               
               
                 19 
                 3 
                 16 
                 256 
                 0.86975 
                 
                   222.66 
                 
                 667.968 
               
               
                 19 
                 4 
                 15 
                 225 
                 0.86975 
                 
                   195.69 
                 
                 782.775 
               
               
                 19 
                 5 
                 14 
                 196 
                 0.86975 
                 
                   170.47 
                 
                 852.355 
               
               
                 19 
                 6 
                 13 
                 169 
                 0.86975 
                 
                   146.99 
                 
                 881.927 
               
               
                 19 
                 7 
                 12 
                 144 
                 0.86975 
                 
                   125.24 
                 
                 876.708 
               
               
                 19 
                 8 
                 11 
                 121 
                 0.86975 
                 
                   105.24 
                 
                 841.918 
               
               
                 19 
                 9 
                 10 
                 100 
                 0.86975 
                 
                   86.98 
                 
                 782.775 
               
               
                 19 
                 10 
                 9 
                 81 
                 0.86975 
                 
                   70.45 
                 
                 704.498 
               
               
                 19 
                 11 
                 8 
                 64 
                 0.86975 
                 
                   55.66 
                 
                 612.304 
               
               
                 19 
                 12 
                 7 
                 49 
                 0.86975 
                 
                   42.62 
                 
                 511.413 
               
               
                 19 
                 13 
                 6 
                 36 
                 0.86975 
                 
                   31.31 
                 
                 407.043 
               
               
                 19 
                 14 
                 5 
                 25 
                 0.86975 
                 
                   21.74 
                 
                 304.413 
               
               
                 19 
                 15 
                 4 
                 16 
                 0.86975 
                 
                   13.92 
                 
                 208.740 
               
               
                 19 
                 16 
                 3 
                 9 
                 0.86975 
                 
                   7.83 
                 
                 125.244 
               
               
                 19 
                 17 
                 2 
                 4 
                 0.86975 
                 
                   3.48 
                 
                 59.143 
               
               
                 19 
                 18 
                 1 
                 1 
                 0.86975 
                 
                   0.87 
                 
                 15.656 
               
               
                 19 
                 19 
                 0 
                 0 
                 0.86975 
                 
                   0.00 
                 
                 0.000 
               
               
                   
               
             
          
         
       
     
     The Tables above clearly show that the optimal load is when the paddle speed stabilizes at exactly one third of the current wind speed. 
     The Maximum Power is generated at that ratio Paddle vs Wind speed as calculated separately below: 
     
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
               
               
                   
                 Vp = 
                   
                   
                   
                 Fd 
                 P = FD * Vp 
               
               
                 Vt 
                 ⅓ Vt 
                 Vt − Vp 
                 squared 
                 Cd * r * A 
                 Newton 
                 Watts 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 10 
                 3.333 
                 6.66667 
                 44.444 
                 0.86975 
                 
                   38.66 
                 
                 
                   128.852 
                 
               
               
                 15 
                 5 
                 10 
                 100 
                 0.86975 
                 
                   86.98 
                 
                 
                   434.875 
                 
               
               
                 17 
                 5.667 
                 11.3333 
                 128.44 
                 0.86975 
                 
                   111.71 
                 
                 
                   633.049 
                 
               
               
                 19 
                 6.333 
                 12.6667 
                 160.44 
                 0.86975 
                 
                   139.55 
                 
                 
                   883.795 
                 
               
               
                   
               
             
          
         
       
     
     These calculations are independently confirmed by several tables of calculations on the following pages. 
     These extensive calculations in the tables below were done by using the Drag Machine calculator publicly available on the Danish government site www.windpower.org; Specifically: http://www.windpower.orq/en/tour/wtrb/dragrace.htm 
     The Drag machine analogy is valid only up to the first energy conversion e.g. wind energy into the mechanical energy “harvested” by the Oscillating wind mill paddles. 
     The further energy conversion will be essentially losses and will be calculated below by different methods. 
     Ideal Loading 
     It is also useful to plot the Power as a function of loading which is shown in  FIG. 12 . The Wind speed of 17 meters/sec was chosen but the graph would look similar for all other speeds. 
     Power P in Watts as a Function of Increasing Load Force F in Newtons. 
     
         
         
           
             For constant Wind Speed=19 meters/sec; drag coeff.=1.42
           Paddle or Sail area=1 meter square (1 meter×1 meter);   
         
           
         
       
    
     Optimal Load=140 Newtons resulting in maximum power P=883.79 Watts 
     Optimal electricity generating load results in Optimal Paddle speed of 6.31 meter/sec 
     !! Operational paddle speed for optimal load is always ⅓ of wind speed=λ=0.333 !! 
     
       
         
               
               
               
               
               
               
               
             
           
               
                   
               
               
                   
                   
                   
                   
                   
                   
                 C P  = Power 
               
               
                 F = Load Force 
                 C D  = constant 
                 V T  = constant 
                 V P  = Paddle 
                   
                 P = Power 
                 efficiency 
               
               
                 in Newtons 
                 drag coef. 
                 Wind speed 
                 (or Sail) speed 
                 λ = Vp/Vt 
                 In Watts 
                 coef. 
               
               
                   
               
             
             
               
                 130.00 
                 1.42 
                 19.00 
                 6.77 
                 0.36 
                 
                   880.66 
                 
                 0.21 
               
               
                 131.00 
                 1.42 
                 19.00 
                 6.73 
                 0.35 
                 
                   881.28 
                 
                 0.21 
               
               
                 132.00 
                 1.42 
                 19.00 
                 6.68 
                 0.35 
                 
                   881.84 
                 
                 0.21 
               
               
                 133.00 
                 1.42 
                 19.00 
                 6.63 
                 0.35 
                 
                   882.32 
                 
                 0.21 
               
               
                 134.00 
                 1.42 
                 19.00 
                 6.59 
                 0.35 
                 
                   882.74 
                 
                 0.21 
               
               
                 135.00 
                 1.42 
                 19.00 
                 6.54 
                 0.34 
                 
                   883.09 
                 
                 0.21 
               
               
                 136.00 
                 1.42 
                 19.00 
                 6.50 
                 0.34 
                 
                   883.36 
                 
                 0.21 
               
               
                 137.00 
                 1.42 
                 19.00 
                 6.45 
                 0.34 
                 
                   883.57 
                 
                 0.21 
               
               
                 138.00 
                 1.42 
                 19.00 
                 6.40 
                 0.34 
                 
                   883.71 
                 
                 0.21 
               
               
                 139.00 
                 1.42 
                 19.00 
                 6.36 
                 0.33 
                 
                   883.78 
                 
                 0.21 
               
               
                 
                   140.00 
                 
                 
                   1.42 
                 
                 
                   19.00 
                 
                 
                   6.31 
                 
                 
                   0.33 
                 
                 
                   883.79 
                 
                 
                   0.21 
                 
               
               
                 141.00 
                 1.42 
                 19.00 
                 6.27 
                 0.33 
                 
                   883.72 
                 
                 0.21 
               
               
                 142.00 
                 1.42 
                 19.00 
                 6.22 
                 0.33 
                 
                   883.59 
                 
                 0.21 
               
               
                 143.00 
                 1.42 
                 19.00 
                 6.18 
                 0.33 
                 
                   883.39 
                 
                 0.21 
               
               
                 144.00 
                 1.42 
                 19.00 
                 6.13 
                 0.32 
                 
                   883.12 
                 
                 0.21 
               
               
                 145.00 
                 1.42 
                 19.00 
                 6.09 
                 0.32 
                 
                   882.79 
                 
                 0.21 
               
               
                 146.00 
                 1.42 
                 19.00 
                 6.04 
                 0.32 
                 
                   882.39 
                 
                 0.21 
               
               
                 147.00 
                 1.42 
                 19.00 
                 6.00 
                 0.32 
                 
                   881.92 
                 
                 0.21 
               
               
                 148.00 
                 1.42 
                 19.00 
                 5.96 
                 0.31 
                 
                   881.39 
                 
                 0.21 
               
               
                 149.00 
                 1.42 
                 19.00 
                 5.91 
                 0.31 
                 
                   880.79 
                 
                 0.21 
               
               
                 150.00 
                 1.42 
                 19.00 
                 5.87 
                 0.31 
                 
                   880.12 
                 
                 0.21 
               
               
                   
               
               
                 c P  = share of the power of the wind, which the machine is able to convert into mechanical power. 
               
               
                 λ = Vp/Vt = ratio of variable paddle speed Vp over the constant wind speed Vt . . . Vt always &gt; Vp. 
               
             
          
         
       
     
     Power P in Watts as a Function of Increasing Load Force F in Newtons.
         For constant Wind Speed=10 meters/sec; drag coeff.=1.42
           Paddle or Sail area=1 meter square (1 meter×1 meter);   
               

     Optimal Load=39 Newtons resulting in maximum power P=128.84 Watts 
     Optimal electricity generating load results in Optimal Paddle speed of 3.30 meter/sec 
     !! Operational paddle speed for optimal load is always ⅓ of wind speed=λ=0.333 !! 
                                                     F = Load   c D  =   V T  =   V P  = Paddle           c P  = Power       Force in   constant   constant   (or Sail)   λ =   P = Power   efficiency       Newtons   drag coef.   Wind speed   speed   Vp/Vt   In Watts   coef.                   100.00   1.42   17.00   6.28   0.37     627.73     0.21       101.00   1.42   17.00   6.22   0.37     628.61     0.21       102.00   1.42   17.00   6.17   0.36     629.41     0.21       103.00   1.42   17.00   6.12   0.36     630.12     0.21       104.00   1.42   17.00   6.06   0.36     630.76     0.21       105.00   1.42   17.00   6.01   0.35     631.32     0.21       106.00   1.42   17.00   5.96   0.35     631.80     0.21       107.00   1.42   17.00   5.91   0.35     632.20     0.21       108.00   1.42   17.00   5.86   0.34     632.52     0.21       109.00   1.42   17.00   5.81   0.34     632.77     0.21       110.00   1.42   17.00   5.75   0.34     632.94     0.21       111.00   1.42   17.00   5.70   0.34     633.03     0.21         112.00       1.42       17.00       5.65       0.33       633.05       0.21         113.00   1.42   17.00   5.60   0.33     632.99     0.21       114.00   1.42   17.00   5.55   0.33     632.85     0.21       115.00   1.42   17.00   5.50   0.32     632.64     0.21       116.00   1.42   17.00   5.45   0.32     632.35     0.21       117.00   1.42   17.00   5.40   0.32     631.99     0.21       118.00   1.42   17.00   5.35   0.31     631.56     0.21       119.00   1.42   17.00   5.30   0.31     631.05     0.21       120.00   1.42   17.00   5.25   0.31     630.47     0.21       121.00   1.42   17.00   5.21   0.31     629.81     0.21       122.00   1.42   17.00   5.16   0.30     629.08     0.21       123.00   1.42   17.00   5.11   0.30     628.28     0.21       124.00   1.42   17.00   5.06   0.30     627.41     0.21       125.00   1.42   17.00   5.01   0.29     626.46     0.21               c P  = share of the power of the wind, which the machine is able to convert into mechanical power.       λ = Vp/Vt = ratio of variable paddle speed Vp over the constant wind speed Vt . . . Vt always &gt; Vp.            
Power P in Watts as a Function of Increasing Load Force F in Newtons.
         For constant Wind Speed=15 meters/sec; drag coeff.=1.42
           Paddle or Sail area=1 meter square (1 meter×1 meter);   
               

     Optimal Load=87 Newtons resulting in maximum power P=434.87 Watts 
     Optimal electricity generating load results in Optimal Paddle speed of 5.00 meter/sec 
     Operational paddle speed for optimal load is always ⅓ of wind speed=λ=0.333 
                                                         c D  =   V T  =   V P  =           c P  =       F = Load   constant   constant   Paddle           Power       Force in   drag   Wind   (or Sail)   λ =   P = Power   efficiency       Newtons   coef.   speed   speed   Vp/Vt   In Watts   coef.                   79.00   1.42   15.00   5.47   0.36     432.09     0.21       80.00   1.42   15.00   5.41   0.36     432.75     0.21       81.00   1.42   15.00   5.35   0.36     433.32     0.21       82.00   1.42   15.00   5.29   0.35     433.80     0.21       83.00   1.42   15.00   5.23   0.35     434.19     0.21       84.00   1.42   15.00   5.17   0.34     434.49     0.21       85.00   1.42   15.00   5.11   0.34     434.71     0.21       86.00   1.42   15.00   5.06   0.34     434.83     0.21         87.00       1.42       15.00       5.00       0.33       434.87       0.21         88.00   1.42   15.00   4.94   0.33     434.83     0.21       89.00   1.42   15.00   4.88   0.33     434.70     0.21       90.00   1.42   15.00   4.83   0.32     434.48     0.21       91.00   1.42   15.00   4.77   0.32     434.18     0.21       92.00   1.42   15.00   4.72   0.31     433.80     0.21       93.00   1.42   15.00   4.66   0.31     433.33     0.21       94.00   1.42   15.00   4.60   0.31     432.78     0.21       95.00   1.42   15.00   4.55   0.30     432.14     0.21               c P  = share of the power of the wind, which the machine is able to convert into mechanical power.       λ = Vp/Vt = ratio of variable paddle speed Vp over the constant wind speed Vt . . . Vt always &gt; Vp.            
Power P in Watts as a Function of Increasing Load Force F in Newtons.
         For constant Wind Speed=10 meters/sec; drag coeff.=1.42
           Paddle or Sail area=1 meter square (1 meter×1 meter);   
               

     Optimal Load=39 Newtons resulting in maximum power P=128.84 Watts 
     Optimal electricity generating load results in Optimal Paddle speed of 3.30 meter/sec 
     Operational paddle speed for optimal load is always ⅓ of wind speed=λ=0.333 
     
       
         
               
               
               
               
               
               
               
             
           
               
                   
               
               
                   
                 c D  = 
                 V T  = 
                 V P  = 
                   
                   
                 c P  = 
               
               
                 F = Load 
                 constant 
                 constant 
                 Paddle 
                   
                   
                 Power 
               
               
                 Force in 
                 drag 
                 Wind 
                 (or Sail) 
                 λ = 
                 P = Power 
                 efficiency 
               
               
                 Newtons 
                 coef. 
                 speed 
                 speed 
                 Vp/Vt 
                 In Watts 
                 coef. 
               
               
                   
               
             
             
               
                 32.00 
                 1.42 
                 10.00 
                 3.93 
                 0.39 
                 
                   125.90 
                 
                 0.21 
               
               
                 33.00 
                 1.42 
                 10.00 
                 3.84 
                 0.38 
                 
                   126.73 
                 
                 0.21 
               
               
                 34.00 
                 1.42 
                 10.00 
                 3.75 
                 0.37 
                 
                   127.42 
                 
                 0.21 
               
               
                 35.00 
                 1.42 
                 10.00 
                 3.66 
                 0.37 
                 
                   127.97 
                 
                 0.21 
               
               
                 36.00 
                 1.42 
                 10.00 
                 3.57 
                 0.36 
                 
                   128.39 
                 
                 0.21 
               
               
                 37.00 
                 1.42 
                 10.00 
                 3.48 
                 0.35 
                 
                   128.67 
                 
                 0.21 
               
               
                 38.00 
                 1.42 
                 10.00 
                 3.39 
                 0.34 
                 
                   128.82 
                 
                 0.21 
               
               
                 
                   39.00 
                 
                 
                   1.42 
                 
                 
                   10.00 
                 
                 
                   3.30 
                 
                 
                   0.33 
                 
                 
                   128.84 
                 
                 
                   0.21 
                 
               
               
                 40.00 
                 1.42 
                 10.00 
                 3.22 
                 0.32 
                 
                   128.74 
                 
                 0.21 
               
               
                 41.00 
                 1.42 
                 10.00 
                 3.13 
                 0.31 
                 
                   128.50 
                 
                 0.21 
               
               
                 42.00 
                 1.42 
                 10.00 
                 3.05 
                 0.31 
                 
                   128.14 
                 
                 0.21 
               
               
                 43.00 
                 1.42 
                 10.00 
                 2.97 
                 0.30 
                 
                   127.65 
                 
                 0.21 
               
               
                 44.00 
                 1.42 
                 10.00 
                 2.89 
                 0.29 
                 
                   127.05 
                 
                 0.21 
               
               
                 45.00 
                 1.42 
                 10.00 
                 2.81 
                 0.28 
                 
                   126.32 
                 
                 0.21 
               
               
                 46.00 
                 1.42 
                 10.00 
                 2.73 
                 0.27 
                 
                   125.47 
                 
                 0.20 
               
               
                 47.00 
                 1.42 
                 10.00 
                 2.65 
                 0.26 
                 
                   124.50 
                 
                 0.20 
               
               
                 48.00 
                 1.42 
                 10.00 
                 2.57 
                 0.26 
                 
                   123.41 
                 
                 0.20 
               
               
                   
               
               
                 c P  = share of the power of the wind, which the machine is able to convert into mechanical power. 
               
               
                 λ = Vp/Vt = ratio of variable paddle speed Vp over the constant wind speed Vt . . . Vt always &gt; Vp. 
               
             
          
         
       
     
     Power is energy transfer per unit of time. Power may be measured at any point in time, whereas energy has to be measured during a certain period, e.g. a second, an hour, or a year. 
     If a wind turbine has a rated power or nameplate power of 1000 kW, that tells you that the wind turbine will produce 1000 kilowatt hours (kWh) of energy per hour of operation, when running at its maximum performance (i.e. at high winds above, say, 15 metres per second (m/s)). 
     Summary for All Wind Speeds 
     For Cd=1.42 which is a drag coeff of hollow semi-sphere or 
     A flat plate rectangle=1 meter square with approx 4:1 aspect ratio 
     Power is in Watts/1 Meter sq of Working Area 
     Wind speed=3 meters per second 
     Max Power=3.48 Watts/1 meter sq of working area 
     Wind speed=4 meters per second 
     Max Power=8.24 Watts//1 meter sq of working area 
     Wind speed=5 meters per second 
     Max Power=16.09 Watts/1 meter sq of working area 
     Wind speed=6 meters per second 
     Max Power=27.83 Watts/1 meter sq 
     Wind speed=7 meters per second 
     Max Power=44.20 Watts/1 meter sq of working area 
     Wind speed=8 meters per second 
     Max Power=65.97 Watts/1 meter sq of working area 
     Wind speed=9 meters per second 
     Max Power=93.93 Watts/1 meter sq of working area 
     Wind speed=10 meters per second 
     Max Power=128.84 Watts/1 meter sq 
     Wind speed=11 meters per second 
     Max Power=171.50 Watts/1 meter sq 
     Wind speed=12 meters per second 
     Max Power=222.65 Watts/1 meter sq 
     Wind speed=13 meters per second 
     Max Power=283.08 Watts/1 meter sq 
     Wind speed=14 meters per second 
     Max Power=353.57 Wafts/1 meter sq 
     Wind speed=15 meters per second 
     Max Power=434.87 Watts/1 meter sq 
     Wind speed=16 meters per second 
     Max Power=527.78 Watts/1 meter sq 
     Wind speed=17 meters per second 
     Max Power=633.05 Watts/1 meter sq 
     Wind speed=18 meters per second 
     Max Power=751.46 Watts/1 meter sq 
     Wind speed=19 meters per second 
     Max Power=883.79 Watts/1 meter sq 
     Wind speed=20 meters per second 
     Max Power=1,030.81 Watts/1 meter sq 
     Wind speed=21 meters per second 
     Max Power=1193.29 Wafts/1 meter sq 
     Wind speed=22 meters per second 
     Max Power=1,372.01 Watts/1 meter sq 
     Wind speed=23 meters per second 
     Max Power=1567.73 Watts/1 meter sq 
     Wind speed=24 meters per second 
     Max Power=1,781.24 Watts/1 meter sq 
     Wind speed=25 meters per second 
     Max Power=2013.31 Watts/1 meter sq 
     Wind speed=26 meters per second 
     Max Power=2264.70 Watts/1 meter sq 
     Wind speed=27 meters per second 
     Max Power=2536.19 Watts/1 meter sq 
     The Power Curve of Oscillating Wind Mill 
     The summary of maximum numbers for various speeds shown on the preceding page above could be plotted to form a power curve for the Oscillating Wind Mill with the working surface of only 1 meter square. 
     Multiplying these Watt numbers by 1,000 would result in numbers in Kilowatts. 
     These would correspond to the Oscillating wind mill with thousand times greater paddle work surface. 
     Instead of 1 meter square, it would be 1,000 meter square corresponding for example to the wind mill with 10 working paddles on each side stacked in the “horizontal architecture”. 
     Each paddle would be a rectangle with horizontal side=5 meters and vertical side of 20 meters. 
     The surface of each paddle would be 100 meters square. 10 paddles=1,000 meter sq. working total. 
     Such Oscillating Wind mill would be rated at 633 KiloWatt at wind speed of 17 meters/sec 
     The power curve of such Oscillating wind mill would not include the losses from the subsequent energy conversions described below and estimated at about 13%. 
     Neither it would include the small counter-torque losses caused by paddles in non-working positions. 
     Since such non-working positions are highly aerodynamic with additional small profile, these counter-torque losses should not approach 2%. 
     So the total losses are estimated not to exceed 15% from the calculations above. 
     But these calculations would automatically increase by 15% if we increase the paddle drag coefficient used in these calculations by 15%. Such increase from Cd=1.41 to lets say Cd=1.6 would enable us to make the fair comparison of numbers above with the industry power curves for the conventional wind mills. 
     Energy Conversion Losses Associated with Each Conversion Step. 
     Just as in the case of the conventional windmills, the oscillating windmills first extract the linear kinetic mechanical energy of the linear wind stream into the rotationally oscillating mechanical energy with small RPM and high torque. 
     1) Oscillating Loss: 
     The loss here is due to physics e.g. loss of leverage as the paddle rotates away from the plane perpendicular to the wind stream. Such loss is a function of the pre-set Amplitude. 
     Our calculations show it to be around 9% for the Oscillations of −45 to +45 degrees from the mid-position where the paddle is also perpendicular to the wind stream regardless of whether it is or it is not “hinged”. 
     For non-hinged paddles there is an additional loss during the oscillation due to the sinusoidal loss of the drag force, as paddles become more and more angled to the wind direction. 
     2) Loss from Low RPM Oscillation to High RPM Rotations 
     Another mechanical energy conversion process converts this oscillating energy into the fully rotating mechanical energy with high RPM and lower torque rotation. 
     Loss here is estimated to be approximately 3% depending on the actual conversion mechanism used. 
     3) Loss from Mechanical to Electrical Energy Generation 
     The last energy conversion step is from mechanical to electrical energy. This step is based on Faraday law of induction and is essentially identical to the electricity generation of the conventional windmills described elsewhere in this patent. We estimate 2% loss consistent with the industry generators. 
     
       
         
           
             
               Wind 
               ⁢ 
               
                   
               
               ⁢ 
               Energy 
             
             -&gt; 
             
               
                 
                   Paddle 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   kinetic 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   Energy 
                 
                 
                   
                     100 
                     ⁢ 
                     % 
                   
                   - 
                   
                     10 
                     ⁢ 
                     % 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     loss 
                   
                 
               
               -&gt; 
               
                 
                   
                     Oscillation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     low 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     RPM 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Energy 
                   
                   
                     
                       90 
                       ⁢ 
                       % 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       left 
                     
                     - 
                     
                       3 
                       ⁢ 
                       % 
                     
                   
                 
                 -&gt; 
                 
                   
                     Hi 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     RPM 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     rotational 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Energy 
                   
                   
                     87 
                     ⁢ 
                     % 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     left