Abstract:
For reducing the number of anchors required for mooring a plurality of WECs in a body of water, the WECs are arrayed in two patterns enabling the sharing of anchors among the WECs. One pattern comprises pluralities of WECs disposed in polygonal shaped cells with an anchor disposed beneath each cell connected to all the WECs in the cell. A second pattern comprises a tessellated pattern of contiguous cells with WECs at the interface between contiguous pairs of cells being common to both cells of the pairs.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    This invention relates to wave energy converters (WECS) for converting energy in the waves on the surface of bodies of water to useful energy, and particularly to the mooring or anchoring of multiple groups or arrays of WECs of the floating buoy type. One known type of WEC, with which the present invention is primarily concerned, comprises a buoy including parts which are driven into movements in response to passing surface waves. Such movements are used for driving an energy transducer for generating useful energy. For retaining the buoy in place, one practice is to connect the buoy to three anchors spaced around the buoy. A problem with this, however, is that if a plurality of WECs is used for increasing the amount of generated power, the need for three anchors for each WEC (providing a buoy to anchor ratio of 1:3) is both expensive and space consuming. 
         [0002]    An object of this invention is the provision of mooring arrangements where the ratio of WEC buoys to anchors is significantly increased. 
       SUMMARY OF THE INVENTION 
       [0003]    A plurality of WECs is disposed within a body of water in two patterns. The first pattern comprises a grouping of the WECs in polygonal cells, preferably hexagonal or octagonal, with a WEC at each of the cell corners. The second pattern comprises a grouping of the polygonal cells in a tessellated pattern of contiguous cells with the WECs at the interface between contiguous pairs of cells being common to both cells. A plurality of anchors is disposed on the floor of the water body with a respective anchor underlying each cell and connected to all the WECs forming the cell. With some patterns, e.g. hexagonal-shaped cells, the anchor disposed beneath each cell is connected only to WECs included in the overlying cell. With other patterns, e.g. octagonal-shaped cells, the anchor disposed beneath each cell is connected to WECs both within and outside the overlying cell. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0004]    In the accompanying schematic drawings, which are not drawn to scale, like reference characters denote like components; and 
           [0005]      FIG. 1  shows an example of a WEC with which the present invention can be used; 
           [0006]      FIG. 2  shows an anchoring (mooring) layout for a plurality of WECs disposed in four contiguous hexagonal cells within a body of water; 
           [0007]      FIG. 2A  shows the anchoring connections for a buoy shown in  FIG. 2 ; 
           [0008]      FIG. 3  shows a hexagonal buoy field layout similar to that shown in  FIG. 2  but including a greater number of components and showing field edge anchors; 
           [0009]      FIG. 4  shows a general hexagonal field layout; 
           [0010]      FIG. 5  is similar to  FIG. 3  but shows WECs disposed in a basic square/octagon field layout; 
           [0011]      FIG. 5A  shows the mooring connections for one buoy shown in  FIG. 5 ; and 
       
    
    
       [0012]    Table 1 lists buoy (B) to anchor (A) ratios (B/A) for selected hexagonal layouts. 
       DETAILED DESCRIPTION 
       [0013]    The present invention concerns the disposition of a plurality of wave energy converters (WECs) in a body of water. An example of a WEC suitable for use with the present invention is shown, schematically, in  FIG. 1 . The WEC includes a generally flat float  2  having a central opening  4  there through and an elongated float  6 , referred to as a “spar”, slidably extending through the flat float central opening  4 . The two floats bob up-and-down in response to passing surface waves but in different phase relationships with the waves, hence in out-of-phase relationship with each other. Such out-of-phase, relative movements between the two floats are used for generating useful energy by driving a power take off (PTO) device, e.g. a hydraulic cylinder for pressurizing a fluid used to drive a turbine for driving an electric generator. 
         [0014]    For increasing the amount of generated power, groups of WECs are interconnected in “farms” of WECs disposed within a body of water. In accordance with this invention, groups of WECs are interconnected in patterns for tiling the surface area where they are located. A tiling of a surface consists of an arrangement of polygons which together covers the entire area of a two-dimensional surface. Many such tilings are possible using one or more types of regular and/or irregular polygons. However, for greater simplicity, only periodic tilings (tessellations), using regular polygons, are herein disclosed. In the accompanying drawings and in the description below a WEC is also referred to as a buoy and identified by the letter “B”. 
         [0015]    Given a two dimensional water body floor, a set of rules governing the placement of buoys and anchors is as follows: 
         [0016]    1. Buoys are arranged on the water body surface in a plurality of contiguous polygonal-shaped cells, with each buoy being at a respective cell vertex. 
         [0017]    2. A plurality of anchors is disposed on the seabed one each beneath the centroid of each cell. 
         [0018]    3. Each anchor beneath a cell of buoys is connected to all the buoys within the cell and, in some instances, to buoys within adjacent cells. 
         [0019]    Disposition of buoys and anchors in accordance with these rules is efficient in the sense that it results in relatively high values for the aggregate “buoy to anchor ratio” of the buoy field, and also provides a stable mooring for each buoy. The buoy to anchor ratio is the quotient B/A, where B is the total number of buoys and A is the total number of anchors in the buoy field. 
         [0020]    Example Using Hexagonal Tiling 
         [0021]    Periodic tiling of a plane using a plurality of identical polygons can be achieved using an equilateral triangle, square or hexagon. Of these, hexagonal placement produces the highest value for B/A, i.e., it requires the fewest anchors per buoy.  FIG. 2  shows part of a buoy field layout generated by applying the above placement rules to a hexagonal tiling. In the layout, WEC buoys (B) are disposed in a body of water in hexagonal “cells” and the cells are grouped together in a tessellated pattern of contiguous cells. Dash lines are used to show the hexagonal shape of the cells. Four cells C 1 , C 2 , C 3  and C 4  are shown. Adjoining cells share common sides, e.g. the side extending between points marked  16  and  18  is common to both cells Cl and C 2 . 
         [0022]    A buoy, indicated ( FIG. 2 ) by a circle labeled B, is placed at each hexagon vertex, e.g. at vertices  12 ,  14 ,  16 ,  18 ,  20  and  22  of the cell C 1 . An anchor, indicated by a dot labeled A, is placed on the floor of the water body beneath each hexagon centroid. Each anchor A is connected to six buoys B at the vertices of the corresponding hexagon by means of mooring connections  30 . Each buoy within the interior of the buoy field (e.g. the buoys located at the vertices  18  and  20 ) is on three hexagons. For example, the buoy at the vertex  18  is located on the three hexagons C 1 , C 2  and C 3 . The result is that each such interior buoy has, as shown in  FIG. 2A  for the buoy at the vertex  20 , a stable symmetrical three-point mooring formed by connections to the anchors in the three hexagons (C 1 , C 3  and C 4  in  FIG. 2 ) that contain the corresponding vertex. 
         [0023]    The buoys on the outside edges of the buoy field shown in  FIG. 2 , for example, the buoys at the vertices  12 ,  14 ,  16 , etc. are also provided with three- point moorings. How this is accomplished will become evident in connection with the below description of  FIG. 3 . 
         [0024]    A measure of the efficiency of a buoy layout is given by the asymptotic value of B/A, i.e. the value for a buoy field of infinite extent. For the field layout shown in  FIG. 2 , the asymptotic value of B/A is 2. For any specific practical (finite) realization of this layout the value of B/A will be less than the asymptotic value. In general, the larger the field, the closer B/A is to the asymptotic value. 
         [0025]      FIG. 3  shows a buoy field layout with 32 buoys (B) and 24 anchors (A). As in  FIG. 2 , actual mooring lines are shown by solid lines and dash lines outline the hexagonal polygons. Note that at the boundary of the field additional anchors are present to provide a stable mooring for buoys at the edges of the field. For this layout the value of B/A is 1.33. (Although not shown, similar additional anchors are preferably present at the edges of the field shown in  FIG. 2 .) 
         [0026]      FIG. 4  shows the generic layout of a buoy field based on a regular hexagonal tiling. This layout has a row of M hexagons at the upper boundary, (M+1) hexagons in the next row, and so on, increasing up to N hexagons at the center of the field and decreasing back to M at the lower boundary. For this arrangement the total number of buoys and anchors in the field is given by: 
         [0000]        B=N  exp 2+4 N+ 4− M exp 2− M    
         [0000]        A= 2 N  exp 2+4 N+ 2−2 M  exp 2 
         [0027]    Table 1 (included in the Drawing) shows values of A, B and B/A for selected values of M and N. 
         [0028]    The value of B/A approaches the theoretical maximum asymptotic value as the size of the buoy field increases. 
         [0029]    Example Using Square/Octagon Tiling 
         [0030]    Other more efficient layouts can be based on more complex tilings. As an example,  FIG. 5  shows a layout based on a tiling of a plane using two types of regular polygons—the square and the octagon. As in  FIGS. 2 and 3 , dash lines are used to outline the polygons; namely, four contiguous octagons  01 - 04  in an annular array around a central square S 1 . In this example, one buoy B is located at each vertex, and one anchor A is located on the water body floor at the centroid of each octagon. Each anchor is connected to twelve buoys; eight in the surrounding octagon, and four more, one in each of the adjacent squares. Each buoy has, as shown in  FIG. 5A , an asymmetrical, but still stable, three-point mooring. 
         [0031]    This configuration achieves an asymptotic B/A value of 4. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 B/A ratio for selected hexagonal layouts 
               
             
          
           
               
                 M 
                 N 
                 A 
                 B 
                 B/A 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 7 
                 8 
                 0.857 
               
               
                 1 
                 2 
                 14 
                 16 
                 1.143 
               
               
                 1 
                 3 
                 23 
                 30 
                 1.304 
               
               
                 1 
                 4 
                 34 
                 48 
                 1.412 
               
               
                 1 
                 5 
                 47 
                 70 
                 1.459 
               
               
                 1 
                 6 
                 52 
                 96 
                 1.548 
               
               
                 1 
                 7 
                 79 
                 126 
                 1.595 
               
               
                 1 
                 8 
                 98 
                 160 
                 1.633 
               
               
                 1 
                 9 
                 119 
                 198 
                 1.664 
               
               
                 1 
                 10 
                 142 
                 240 
                 1.690 
               
               
                 2 
                 11 
                 163 
                 280 
                 1.718 
               
               
                 3 
                 12 
                 184 
                 320 
                 1.739 
               
               
                 4 
                 13 
                 205 
                 360 
                 1.758 
               
               
                 5 
                 15 
                 259 
                 462 
                 1.784 
               
               
                 10 
                 20 
                 374 
                 682 
                 1.824 
               
               
                 20 
                 50 
                 2284 
                 4402 
                 1.927