Abstract:
A turbomachine component includes a turbine stator nozzle member having an airfoil core shape. The airfoil core shape includes a nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in TABLE 1, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches, the profile sections at the Z distances being joined smoothly with one another to form a complete airfoil core shape.

Description:
BACKGROUND OF THE INVENTION 
     The subject matter disclosed herein relates to the art of turbomachines and, more particularly, to a turbomachine component having an airfoil core shape. 
     Many system requirements must be met for each stage of a turbomachine in order to meet design goals including an overall improvement in system efficiency. In particular, third stage nozzles must meet system requirements including airfoil loading and manufacturability. These third stage nozzles must operate within a particular set of boundary conditions based on operating conditions of the turbomachine while maintaining a shape that meets design specifications. 
     BRIEF DESCRIPTION OF THE INVENTION 
     According to one aspect of the exemplary embodiment, a turbomachine component includes a turbine stator nozzle member having an airfoil core shape. The airfoil core shape includes a nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in TABLE 1, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches, the profile sections at the Z distances being joined smoothly with one another to form a complete airfoil core shape. 
     According to another aspect of the exemplary embodiment, a turbomachine includes a turbine portion, and a turbine stator nozzle member provided in the turbine portion. The turbine stator nozzle member includes an airfoil core shape. The airfoil core shape includes a nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in TABLE 1, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches, the profile sections at the Z distances being joined smoothly with one another to form a complete airfoil core shape. 
     These and other advantages and features will become more apparent from the following description taken in conjunction with the drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
       The subject matter, which is regarded as the invention, is particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The foregoing and other features, and advantages of the invention are apparent from the following detailed description taken in conjunction with the accompanying drawings in which: 
         FIG. 1  is a partial cross-sectional view of a turbomachine including a nozzle assembly having an airfoil core shape in accordance with an exemplary embodiment 
         FIG. 2  is a perspective view of a nozzle assembly  FIG. 1 ; 
         FIG. 3  is a perspective view of a nozzle member of the nozzle assembly of  FIG. 2  illustrating the airfoil core shape defined at a plurality of sections; 
         FIG. 4  is another perspective view of the nozzle member of the nozzle assembly of  FIG. 3 ; 
         FIG. 5  is a cross-sectional view of the nozzle member of  FIG. 3  taken at one of the plurality of sections; and 
         FIG. 6  is a partial plan view of the one of the plurality of sections in  FIG. 4  indicating a design envelope of the airfoil core shape in accordance with an aspect of the exemplary embodiment. 
     
    
    
     The detailed description explains embodiments of the invention, together with advantages and features, by way of example with reference to the drawings. 
     DETAILED DESCRIPTION OF THE INVENTION 
     As shown in  FIG. 1 , a turbomachine  2 , constructed in accordance with an exemplary embodiment, includes a compressor portion (not shown) and a turbine portion  4 . Turbine portion  4  is enclosed by a turbine housing  6  and has an axial flow path  8 . Turbine portion  4  includes a plurality of nozzle assemblies  16 ,  18 , and  20 . Each nozzle assembly  16 ,  18 , and  20  is positioned upstream of a corresponding rotor blade assembly  22 ,  24 , and  26 . Nozzle assembly  16  and rotor assembly  22  combine to establish a first turbine stage  30 ; nozzle assembly  18  and rotor assembly  24  combine to form a second turbine stage  32 ; and nozzle assembly  20  and rotor assembly  26  combine to form a second turbine stage  34 . Of course it should be understood that each of the first, second and third turbine stages  30 ,  32 , and  34  include additional nozzle and rotor assemblies. It should be also understood that turbine portion  4  includes additional turbine stages that collectively establish, for example, a 9FB PP2 gas turbine frame. 
     As best shown in  FIG. 2 , third turbine stage nozzle assembly  20  includes a base portion  36  and a tip or shroud portion  38  between which extends a plurality of third stage nozzle members  40 - 42  each having an associated airfoil core shape  44 - 46 . As each nozzle member  40 - 42  is similarly formed, and includes substantially similar airfoil core shapes  44 - 46  a detailed description will follow with reference to  FIGS. 3 and 4  in describing third stage nozzle member  40  and airfoil core shape  44  with an understanding that nozzle members  41 - 42  and associated airfoil core shapes  45 - 46  include corresponding structure/design. Third stage nozzle member  40  includes a first end  50  that extends to a second end  52  through an airfoil portion  54  that is defined by airfoil core shape  44 . Third stage nozzle member  40  also includes a leading edge  58  and a trailing edge  60  between which extend a suction side  62  and a pressure side  64 . 
     Airfoil core shape  44  in accordance with an exemplary embodiment is configured for enhanced turbine performance. A list of X, Y, and Z coordinates or points for airfoil core shape  44  is presented in TABLE 1, and meets requirements for interaction between adjacent stages, aerodynamic efficiency and provides an improved aeromechanics margin over prior shapes. Moreover, the particular airfoil core shape  44  in accordance with the exemplary embodiment meets system requirements for flow dynamics, loading, and frequency response. The points are arrived at by iteration between aerodynamic and mechanical design improvements and are the only loci of points that allow turbomachine  2  to operate in an efficient, smooth manner. As will become more fully evident below, airfoil core shape  44  is represented as a set of 1920 points listed in TABLE 1. The 1920 points represent 15 airfoil sections. The X, Y, and Z coordinates, which represent a profile of airfoil core shape  44 , are created in a coordinate system which is defined relative to a cold engine part. The origin of the coordinate system on the cold centerline axis is X=0.0, Y=0.0 and Z=0.0. The Z coordinate axis is defined as a radial line from the Y coordinate axis; the X coordinate axis is defined as being normal to a plane defined by the Y-Z axis. The airfoil sections are cut normal to the Z coordinate axis. X and Y points, which make up the airfoil core profile shape  44  at each section, are in inches. The radial Z values in inches for the section planes have an origin of Z 0 . 
     The radial distance between each section varies however a total radial distance of airfoil core shape  44  is 15.0 inches. The bottom and top sections Z 0  and Z 1 , may be obscured by cast-in features that are not included in the X, Y, and Z points that define airfoil core shape  44 . All of the 1920 points are taken from a nominal cold or room temperature for each airfoil section of airfoil core shape  44 . Each airfoil section is joined smoothly with adjacent airfoil sections to form the airfoil core shape  44 . 
     It should be appreciated that as nozzle assembly  20  heats up during operation of turbine portion  4 , airfoil core shape  44  may change as a result of stress and temperature. Thus, the X, Y and Z points are provided at cold or room temperature for manufacturing purposes. Since the manufactured airfoil core shape may be different from a nominal airfoil core shape defined in Table 1, a tolerance of ±0.100 inches from the nominal profile is allowed and thus defines an overall design envelope for airfoil core shape  44 . The overall design is robust to this design envelope without impairment of mechanical or aerodynamic properties of third turbine stage  34 . 
     It should also be appreciated that the airfoil core shape  44  can be scaled up or scaled down geometrically for introductions into similar turbine designs, with smaller or larger frame sizes. Consequently, the X, Y, and Z coordinates in inches may be multiplied or divided by the same constant or number/factor to provide a scaled up or scaled down version of third stage nozzle  40  while retaining the airfoil core profile shape and unique properties. 
     As best shown in  FIG. 2 , a coordinate system for airfoil core shape  44  in accordance with exemplary embodiment is indicated generally at  100 . As discussed above, coordinate system  100  is defined relative to a cold nozzle. Coordinate system  100  includes an X-axis  105 , a Y-axis  110 , and a Z-axis  115 . The origin of coordinate system  100  is centered at first end  50  of nozzle member  40 . X-axis  105  is directed axially along a centerline axis (not separately labeled) of turbomachine  2  and Z-axis  115  is directed along a radial line normal to the centerline axis. The positive direction of X-axis  105 , Y-axis  110 , and Z-axis  115  is identified by label placement in  FIG. 2 . 
     As best shown in  FIGS. 3-5 , airfoil core shape  44  includes a plurality of sections  150 - 164 . Section  150  is located at Z 0  and the airfoil core shape  44  extends through sections  163  before terminating at section  164  located at Z 1 . As discussed above, sections  150 - 164  are cut normal to Z c -axis  115 . The X and Y coordinates which make up each section are presented in Table 1 are in inches. 
       FIG. 6  illustrates a design envelope for airfoil core shape  44 . The X, Y, and Z values listed in TABLE 1 illustrate ideal point location for each point of each section of airfoil core shape  44 . However, there exist variations from the ideal point location attributed to manufacturing tolerances and the like which must be taken into account. Thus, a design envelope is established which sets forth an acceptable outer boundary or distance from a nominal profile  250  for each section  150 - 165 . Therefore it should be understood that each X, Y, and Z point includes a tolerance or ±value. In consideration of process capability, a tolerance  260  of ±0.100 inches is allowed in the formation of airfoil core shape  30 . Tolerance  260  includes an upper limit  270  defined as a 0.100-inch deviation from nominal profile  250  and a lower limit  280 , defined as a −0.100-inch variation from nominal profile  250 . The design envelope or tolerance  260  is robust such that this variation does not impair mechanical and aerodynamic performance of third stage nozzle member  40 . 
     In no way limiting of the exemplary embodiment, airfoil core shape  44  provides an increased efficiency as compared to previous individual airfoil core shapes for third stage nozzle member  40 . Moreover, and in no way limiting of the exemplary embodiment, in conjunction with other airfoil core shapes, which are conventional or enhanced (similar to the enhancements herein), airfoil core shape  44 , as embodied by the invention, provides an increased efficiency as compared to previous individual sets of airfoil core shapes for third stage nozzle member  40 . This increased efficiency provides, in addition to the above-noted advantages, a power output with a decrease the required fuel, therefore inherently decreasing emissions to produce energy. Of course, other such advantages are within the scope of the exemplary embodiment. 
     
       
         
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
             
             
               
                 Section 1 
                 Section 2 
                 Section 3 
                 Section 4 
               
             
          
           
               
                 X 
                 Y 
                 Z 
                 X 
                 Y 
                 Z 
                 X 
                 Y 
                 Z 
                 X 
                 Y 
                 Z 
               
               
                   
               
               
                 0.624 
                 −0.3966 
                 60.864 
                 0.493 
                 −0.2812 
                 59.864 
                 0.3094 
                 −0.0617 
                 58.864 
                 0.3745 
                 −0.1484 
                 57.864 
               
               
                 0.2077 
                 −0.0357 
                 60.864 
                 0.7264 
                 −0.4304 
                 59.864 
                 0.6313 
                 −0.3378 
                 58.864 
                 0.6855 
                 −0.3418 
                 57.864 
               
               
                 1.903 
                 −1.3094 
                 60.864 
                 2.5861 
                 −1.2323 
                 59.864 
                 0.6939 
                 −0.2092 
                 58.864 
                 0.42 
                 −0.0559 
                 57.864 
               
               
                 2.0022 
                 −0.9341 
                 60.864 
                 0.258 
                 −0.1345 
                 59.864 
                 0.398 
                 −0.0649 
                 58.864 
                 1.3701 
                 −0.7919 
                 57.864 
               
               
                 0.2649 
                 −0.0423 
                 60.864 
                 0.3581 
                 −0.0666 
                 59.864 
                 2.6118 
                 −1.2222 
                 58.864 
                 0.3584 
                 −0.129 
                 57.864 
               
               
                 1.0422 
                 −0.674 
                 60.864 
                 1.9419 
                 −1.2921 
                 59.864 
                 0.3438 
                 −0.0463 
                 58.864 
                 1.0772 
                 −0.5947 
                 57.864 
               
               
                 0.1807 
                 −0.0637 
                 60.864 
                 0.2665 
                 −0.0431 
                 59.864 
                 0.3251 
                 −0.0507 
                 58.864 
                 0.4773 
                 −0.2118 
                 57.864 
               
               
                 2.3312 
                 −1.6755 
                 60.864 
                 0.2456 
                 −0.1223 
                 59.864 
                 1.6169 
                 −1.0039 
                 58.864 
                 0.4011 
                 −0.0541 
                 57.864 
               
               
                 0.8719 
                 −0.3432 
                 60.864 
                 1.7222 
                 −1.1221 
                 59.864 
                 0.5055 
                 −0.2586 
                 58.864 
                 0.4376 
                 −0.0631 
                 57.864 
               
               
                 0.4126 
                 −0.2613 
                 60.864 
                 1.481 
                 −0.6325 
                 59.864 
                 2.0694 
                 −0.9224 
                 58.864 
                 1.6591 
                 −0.9949 
                 57.864 
               
               
                 0.227 
                 −0.0312 
                 60.864 
                 0.3229 
                 −0.0493 
                 59.864 
                 0.4155 
                 −0.0733 
                 58.864 
                 0.3828 
                 −0.0589 
                 57.864 
               
               
                 1.6816 
                 −1.1352 
                 60.864 
                 0.2397 
                 −0.0707 
                 59.864 
                 2.6081 
                 −1.8048 
                 58.864 
                 2.2157 
                 −1.4149 
                 57.864 
               
               
                 0.1764 
                 −0.0829 
                 60.864 
                 2.5737 
                 −1.8349 
                 59.864 
                 0.2987 
                 −0.0778 
                 58.864 
                 0.4433 
                 −0.1904 
                 57.864 
               
               
                 0.1791 
                 −0.1002 
                 60.864 
                 0.6404 
                 −0.2049 
                 59.864 
                 1.9041 
                 −1.2185 
                 58.864 
                 0.3531 
                 −0.1044 
                 57.864 
               
               
                 2.5603 
                 −1.2428 
                 60.864 
                 0.2855 
                 −0.0387 
                 59.864 
                 1.0281 
                 −0.5953 
                 58.864 
                 0.5116 
                 −0.2331 
                 57.864 
               
               
                 0.2827 
                 −0.0512 
                 60.864 
                 1.0896 
                 −0.6706 
                 59.864 
                 0.3794 
                 −0.1798 
                 58.864 
                 0.3573 
                 −0.0859 
                 57.864 
               
               
                 0.834 
                 −0.534 
                 60.864 
                 0.2378 
                 −0.1067 
                 59.864 
                 1.5225 
                 −0.6308 
                 58.864 
                 2.637 
                 −1.2112 
                 57.864 
               
               
                 2.1197 
                 −1.4893 
                 60.864 
                 0.3756 
                 −0.2076 
                 59.864 
                 2.1441 
                 −1.4075 
                 58.864 
                 1.0199 
                 −0.3496 
                 57.864 
               
               
                 0.1873 
                 −0.1159 
                 60.864 
                 2.3682 
                 −1.6481 
                 59.864 
                 0.3807 
                 −0.0563 
                 58.864 
                 0.3676 
                 −0.07 
                 57.864 
               
               
                 1.4392 
                 −0.6346 
                 60.864 
                 2.0359 
                 −0.9281 
                 59.864 
                 0.3159 
                 −0.1411 
                 58.864 
                 2.1021 
                 −0.9163 
                 57.864 
               
               
                 0.2001 
                 −0.128 
                 60.864 
                 0.3404 
                 −0.0581 
                 59.864 
                 0.5685 
                 −0.298 
                 58.864 
                 0.472 
                 −0.0798 
                 57.864 
               
               
                 0.2466 
                 −0.0343 
                 60.864 
                 0.2505 
                 −0.0544 
                 59.864 
                 0.2965 
                 −0.1134 
                 58.864 
                 0.7465 
                 −0.2135 
                 57.864 
               
               
                 1.3651 
                 −0.9001 
                 60.864 
                 0.6099 
                 −0.3555 
                 59.864 
                 0.304 
                 −0.1288 
                 58.864 
                 2.4818 
                 −1.633 
                 57.864 
               
               
                 0.1916 
                 −0.0471 
                 60.864 
                 0.9217 
                 −0.3452 
                 59.864 
                 0.2943 
                 −0.0965 
                 58.864 
                 0.4547 
                 −0.0715 
                 57.864 
               
               
                 2.5367 
                 −1.868 
                 60.864 
                 0.3048 
                 −0.0415 
                 59.864 
                 0.9713 
                 −0.3474 
                 58.864 
                 0.4087 
                 −0.1697 
                 57.864 
               
               
                 3.1125 
                 −1.5619 
                 60.864 
                 0.2354 
                 −0.0896 
                 59.864 
                 1.3247 
                 −0.7964 
                 58.864 
                 1.5631 
                 −0.629 
                 57.864 
               
               
                 0.3005 
                 −0.0599 
                 60.864 
                 1.4088 
                 −0.8922 
                 59.864 
                 0.4423 
                 −0.2193 
                 58.864 
                 1.9437 
                 −1.2043 
                 57.864 
               
               
                 2.9284 
                 −2.2726 
                 60.864 
                 2.1574 
                 −1.4673 
                 59.864 
                 0.3629 
                 −0.0487 
                 58.864 
                 4.5333 
                 −4.0976 
                 57.864 
               
               
                 5.1631 
                 −2.9798 
                 60.864 
                 5.5353 
                 −3.257 
                 59.864 
                 2.379 
                 −1.6028 
                 58.864 
                 4.148 
                 −2.1138 
                 57.864 
               
               
                 3.7788 
                 −3.3862 
                 60.864 
                 4.3769 
                 −2.336 
                 59.864 
                 4.0043 
                 −3.4168 
                 58.864 
                 3.4973 
                 −1.7093 
                 57.864 
               
               
                 3.9304 
                 −2.0686 
                 60.864 
                 3.7661 
                 −3.2141 
                 59.864 
                 3.0463 
                 −2.2301 
                 58.864 
                 4.0546 
                 −3.3325 
                 57.864 
               
               
                 3.2916 
                 −2.7027 
                 60.864 
                 3.3948 
                 −2.7182 
                 59.864 
                 4.9583 
                 −2.7193 
                 58.864 
                 4.2235 
                 −3.5816 
                 57.864 
               
               
                 4.7175 
                 −2.6212 
                 60.864 
                 4.3987 
                 −4.2782 
                 59.864 
                 4.4728 
                 −4.2035 
                 58.864 
                 5.612 
                 −3.2054 
                 57.864 
               
               
                 4.0631 
                 −3.8603 
                 60.864 
                 5.1633 
                 −2.9295 
                 59.864 
                 3.6462 
                 −2.9221 
                 58.864 
                 3.2343 
                 −2.3383 
                 57.864 
               
               
                 3.3876 
                 −1.7268 
                 60.864 
                 3.1961 
                 −2.4806 
                 59.864 
                 5.6137 
                 −3.2681 
                 58.864 
                 4.7145 
                 −2.497 
                 57.864 
               
               
                 2.736 
                 −2.067 
                 60.864 
                 3.7614 
                 −1.9297 
                 59.864 
                 3.1493 
                 −1.5309 
                 58.864 
                 2.9919 
                 −2.0941 
                 57.864 
               
               
                 5.3516 
                 −3.1461 
                 60.864 
                 4.2545 
                 −4.0041 
                 59.864 
                 5.1981 
                 −2.9083 
                 58.864 
                 4.4672 
                 −2.3254 
                 57.864 
               
               
                 3.6256 
                 −3.1559 
                 60.864 
                 3.9383 
                 −3.4717 
                 59.864 
                 4.1697 
                 −3.6734 
                 58.864 
                 3.1673 
                 −1.5144 
                 57.864 
               
               
                 4.197 
                 −2.2468 
                 60.864 
                 3.5849 
                 −2.9629 
                 59.864 
                 3.2542 
                 −2.4537 
                 58.864 
                 4.3831 
                 −3.8368 
                 57.864 
               
               
                 4.3544 
                 −4.425 
                 60.864 
                 4.677 
                 −2.5504 
                 59.864 
                 4.1417 
                 −2.1434 
                 58.864 
                 3.4673 
                 −2.5914 
                 57.864 
               
               
                 3.1136 
                 −2.4846 
                 60.864 
                 3.131 
                 −1.5463 
                 59.864 
                 5.4319 
                 −3.1049 
                 58.864 
                 4.958 
                 −2.674 
                 57.864 
               
               
                 4.9699 
                 −2.819 
                 60.864 
                 5.3517 
                 −3.0905 
                 59.864 
                 3.8145 
                 −1.9335 
                 58.864 
                 3.8767 
                 −3.0897 
                 57.864 
               
               
                 3.9246 
                 −3.6211 
                 60.864 
                 2.9889 
                 −2.2503 
                 59.864 
                 3.8297 
                 −3.1663 
                 58.864 
                 2.7408 
                 −1.8592 
                 57.864 
               
               
                 3.6605 
                 −1.8955 
                 60.864 
                 4.0714 
                 −2.1295 
                 59.864 
                 2.8307 
                 −2.0137 
                 58.864 
                 5.4302 
                 −3.0475 
                 57.864 
               
               
                 5.5348 
                 −3.3182 
                 60.864 
                 4.9705 
                 −2.7737 
                 59.864 
                 3.4834 
                 −1.7297 
                 58.864 
                 3.8244 
                 −1.9087 
                 57.864 
               
               
                 3.4623 
                 −2.9266 
                 60.864 
                 4.101 
                 −3.7351 
                 59.864 
                 4.3259 
                 −3.9358 
                 58.864 
                 3.6903 
                 −2.8534 
                 57.864 
               
               
                 4.4596 
                 −2.4307 
                 60.864 
                 2.7734 
                 −2.0277 
                 59.864 
                 4.7132 
                 −2.5369 
                 58.864 
                 5.1969 
                 −2.8572 
                 57.864 
               
               
                 4.1945 
                 −4.1036 
                 60.864 
                 3.4476 
                 −1.7356 
                 59.864 
                 3.4543 
                 −2.6845 
                 58.864 
                 6.5692 
                 −4.272 
                 57.864 
               
               
                 6.7854 
                 −4.9958 
                 60.864 
                 7.2502 
                 −6.0195 
                 59.864 
                 4.464 
                 −2.3605 
                 58.864 
                 6.1251 
                 −3.7137 
                 57.864 
               
               
                 6.0561 
                 −3.8834 
                 60.864 
                 5.2305 
                 −6.622 
                 59.864 
                 6.8133 
                 −4.7778 
                 58.864 
                 6.8203 
                 −4.6726 
                 57.864 
               
               
                 4.5027 
                 −4.7521 
                 60.864 
                 5.0734 
                 −6.0075 
                 59.864 
                 5.2698 
                 −6.3382 
                 58.864 
                 7.1139 
                 −5.2898 
                 57.864 
               
               
                 5.0779 
                 −6.4512 
                 60.864 
                 4.6596 
                 −4.8401 
                 59.864 
                 6.6936 
                 −4.5699 
                 58.864 
                 5.5261 
                 −7.321 
                 57.864 
               
               
                 7.0808 
                 −5.6746 
                 60.864 
                 6.7999 
                 −4.8864 
                 59.864 
                 4.7383 
                 −4.7535 
                 58.864 
                 7.3221 
                 −5.9411 
                 57.864 
               
               
                 6.5228 
                 −4.532 
                 60.864 
                 6.0604 
                 −3.8036 
                 59.864 
                 6.5646 
                 −4.3676 
                 58.864 
                 6.9276 
                 −4.8738 
                 57.864 
               
               
                 5.7121 
                 −3.4964 
                 60.864 
                 5.2968 
                 −6.9397 
                 59.864 
                 7.184 
                 −5.6245 
                 58.864 
                 5.3364 
                 −6.1937 
                 57.864 
               
               
                 4.7655 
                 −5.4205 
                 60.864 
                 5.1547 
                 −6.3065 
                 59.864 
                 5.9606 
                 −3.612 
                 58.864 
                 7.2623 
                 −5.721 
                 57.864 
               
               
                 5.2466 
                 −7.223 
                 60.864 
                 7.0983 
                 −5.5523 
                 59.864 
                 5.4596 
                 −7.3652 
                 58.864 
                 6.2829 
                 −3.8956 
                 57.864 
               
               
                 6.893 
                 −5.218 
                 60.864 
                 6.5335 
                 −4.4335 
                 59.864 
                 7.017 
                 −5.193 
                 58.864 
                 5.2531 
                 −5.8671 
                 57.864 
               
               
                 6.2209 
                 −4.0928 
                 60.864 
                 5.7134 
                 −3.4292 
                 59.864 
                 5.0872 
                 −5.679 
                 58.864 
                 5.7889 
                 −3.3688 
                 57.864 
               
               
                 4.9845 
                 −6.1045 
                 60.864 
                 4.9832 
                 −5.7111 
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                 7.2323 
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                 57.864 
               
               
                   
               
             
          
           
               
                 Section 5 
                 Section 6 
                 Section 7 
                 Section 8 
               
             
          
           
               
                 X 
                 X 
                 Y 
                 Z 
                 X 
                 X 
                 X 
                 Y 
                 Z 
                 X 
                 Y 
                 Z 
               
               
                   
               
               
                 2.1341 
                 −0.9097 
                 56.864 
                 1.9143 
                 −1.0939 
                 55.864 
                 0.5679 
                 −0.0795 
                 54.864 
                 0.596 
                 −0.1669 
                 53.864 
               
               
                 0.5049 
                 −0.0752 
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                 0.6653 
                 −0.2718 
                 55.864 
                 0.5859 
                 −0.0778 
                 54.864 
                 2.734 
                 −1.153 
                 53.864 
               
               
                 0.8354 
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                 −0.2223 
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                 0.5366 
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                 54.864 
                 1.7177 
                 −0.6183 
                 53.864 
               
               
                 0.4336 
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                 −1.6799 
                 55.864 
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                 0.5889 
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                 53.864 
               
               
                 2.176 
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                 53.864 
               
               
                 1.0674 
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                 53.864 
               
               
                 0.5465 
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                 53.864 
               
               
                 0.4575 
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                 1.4242 
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                 53.864 
               
               
                 0.4155 
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                 2.6391 
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                 53.864 
               
               
                 2.6617 
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                 53.864 
               
               
                 0.5275 
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                 53.864 
               
               
                 0.6592 
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                 53.864 
               
               
                 0.4251 
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                 53.864 
               
               
                 1.9383 
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                 53.864 
               
               
                 0.4176 
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                 53.864 
               
               
                 1.6027 
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                 53.864 
               
               
                 0.4903 
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                 54.864 
                 0.6076 
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                 53.864 
               
               
                 0.4821 
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                 0.4732 
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                 55.864 
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                 53.864 
               
               
                 1.1479 
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                 53.864 
               
               
                 2.4098 
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                 53.864 
               
               
                 0.798 
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                 53.864 
               
               
                 0.6029 
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                 53.864 
               
               
                 0.4397 
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                 53.864 
               
               
                 1.6974 
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                 53.864 
               
               
                 0.4119 
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                 53.864 
               
               
                 3.9124 
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                 53.864 
               
               
                 4.0923 
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                 53.864 
               
               
                 3.3073 
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                 53.864 
               
               
                 4.9696 
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                 54.864 
                 4.9524 
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                 53.864 
               
               
                 4.2732 
                 −3.4788 
                 56.864 
                 4.3086 
                 −3.352 
                 55.864 
                 3.5037 
                 −1.6176 
                 54.864 
                 4.3773 
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                 7.4672 
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                 6.5587 
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                 5.6053 
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                 6.8841 
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                 5.6415 
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                 7.2477 
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                 54.864 
                 7.3762 
                 −7.0019 
                 53.864 
               
               
                   
               
             
          
           
               
                 Section 9 
                 Section 10 
                 Section 11 
                 Section 12 
               
             
          
           
               
                 X 
                 Y 
                 Z 
                 X 
                 Y 
                 Z 
                 X 
                 Y 
                 Z 
                 X 
                 Y 
                 Z 
               
               
                   
               
               
                 0.6467 
                 −0.1544 
                 52.864 
                 1.3916 
                 −0.615 
                 51.864 
                 1.1303 
                 −0.2547 
                 50.864 
                 0.9121 
                 −0.1279 
                 49.864 
               
               
                 0.7022 
                 −0.0936 
                 52.864 
                 2.6185 
                 −1.023 
                 51.864 
                 2.4035 
                 −1.2353 
                 50.864 
                 0.8321 
                 −0.2013 
                 49.864 
               
               
                 1.7562 
                 −0.6127 
                 52.864 
                 0.7213 
                 −0.1163 
                 51.864 
                 0.7921 
                 −0.1155 
                 50.864 
                 2.4343 
                 −1.2155 
                 49.864 
               
               
                 1.3449 
                 −0.6145 
                 52.864 
                 0.7056 
                 −0.1636 
                 51.864 
                 1.5999 
                 −0.7166 
                 50.864 
                 2.6696 
                 −0.9793 
                 49.864 
               
               
                 0.6532 
                 −0.1204 
                 52.864 
                 1.7203 
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                 5.6474 
                 −6.4534 
                 51.864 
                 5.5222 
                 −8.0184 
                 50.864 
                 5.5807 
                 −8.059 
                 49.864 
               
               
                 7.352 
                 −6.6639 
                 52.864 
                 7.2002 
                 −5.1823 
                 51.864 
                 6.7861 
                 −7.9428 
                 50.864 
                 6.9896 
                 −7.265 
                 49.864 
               
               
                 5.7519 
                 −8.8159 
                 52.864 
                 6.0911 
                 −8.7098 
                 51.864 
                 5.5359 
                 −7.4721 
                 50.864 
                 5.5085 
                 −7.7565 
                 49.864 
               
               
                 7.1941 
                 −7.551 
                 52.864 
                 7.3137 
                 −6.1489 
                 51.864 
                 6.4255 
                 −8.345 
                 50.864 
                 6.6822 
                 −7.8572 
                 49.864 
               
               
                 5.5763 
                 −8.5302 
                 52.864 
                 5.7849 
                 −8.6546 
                 51.864 
                 6.0789 
                 −8.5085 
                 50.864 
                 5.5607 
                 −7.0688 
                 49.864 
               
               
                 6.9159 
                 −8.2017 
                 52.864 
                 7.2383 
                 −7.0306 
                 51.864 
                 7.2633 
                 −5.9906 
                 50.864 
                 6.3455 
                 −8.1899 
                 49.864 
               
               
                 5.5329 
                 −8.0916 
                 52.864 
                 5.587 
                 −8.416 
                 51.864 
                 5.7771 
                 −8.459 
                 50.864 
                 6.0045 
                 −8.3147 
                 49.864 
               
               
                 6.5475 
                 −8.6726 
                 52.864 
                 7.0128 
                 −7.7676 
                 51.864 
                 7.1921 
                 −6.856 
                 50.864 
                 7.209 
                 −5.9988 
                 49.864 
               
               
                 5.6157 
                 −7.0722 
                 52.864 
                 5.5213 
                 −8.0516 
                 51.864 
                 5.5776 
                 −8.2297 
                 50.864 
                 5.6974 
                 −8.2096 
                 49.864 
               
               
                 6.1765 
                 −8.8956 
                 52.864 
                 6.6684 
                 −8.3292 
                 51.864 
                 6.9781 
                 −7.5811 
                 50.864 
                 7.1102 
                 −6.8441 
                 49.864 
               
               
                 7.3543 
                 −6.1045 
                 52.864 
                 5.596 
                 −7.1585 
                 51.864 
                 5.5121 
                 −7.8728 
                 50.864 
                 5.5367 
                 −7.942 
                 49.864 
               
               
                 5.8985 
                 −8.898 
                 52.864 
                 6.3087 
                 −8.6323 
                 51.864 
                 6.6444 
                 −8.1342 
                 50.864 
                 6.8866 
                 −7.512 
                 49.864 
               
               
                 7.3128 
                 −7.0228 
                 52.864 
                 7.2702 
                 −5.5659 
                 51.864 
                 5.595 
                 −6.9975 
                 50.864 
                 5.5086 
                 −7.5627 
                 49.864 
               
               
                 5.6746 
                 −8.734 
                 52.864 
                 5.9533 
                 −8.7135 
                 51.864 
                 6.292 
                 −8.4319 
                 50.864 
                 6.5553 
                 −8.0102 
                 49.864 
               
               
                 7.1007 
                 −7.8187 
                 52.864 
                 7.3046 
                 −6.5032 
                 51.864 
                 7.2238 
                 −5.4185 
                 50.864 
                 5.6173 
                 −6.6036 
                 49.864 
               
               
                 5.546 
                 −8.3817 
                 52.864 
                 5.6984 
                 −8.5857 
                 51.864 
                 5.9436 
                 −8.5134 
                 50.864 
                 6.2087 
                 −8.2648 
                 49.864 
               
               
                 6.7592 
                 −8.4382 
                 52.864 
                 7.1556 
                 −7.3753 
                 51.864 
                 7.2544 
                 −6.3382 
                 50.864 
                 7.1941 
                 −5.4538 
                 49.864 
               
               
                 5.5481 
                 −7.814 
                 52.864 
                 5.5441 
                 −8.2736 
                 51.864 
                 5.6906 
                 −8.3936 
                 50.864 
                 5.8725 
                 −8.3018 
                 49.864 
               
               
                 6.3996 
                 −8.7887 
                 52.864 
                 6.887 
                 −8.0161 
                 51.864 
                 7.1141 
                 −7.1949 
                 50.864 
                 7.1884 
                 −6.3389 
                 49.864 
               
               
                 5.6386 
                 −6.6007 
                 52.864 
                 5.5298 
                 −7.7789 
                 51.864 
                 5.5342 
                 −8.0906 
                 50.864 
                 5.6122 
                 −8.1131 
                 49.864 
               
               
                 7.281 
                 −5.5136 
                 52.864 
                 6.5244 
                 −8.4777 
                 51.864 
                 6.8569 
                 −7.826 
                 50.864 
                 7.0324 
                 −7.1382 
                 49.864 
               
               
                 6.0656 
                 −8.9161 
                 52.864 
                 5.6378 
                 −6.6849 
                 51.864 
                 5.523 
                 −7.6053 
                 50.864 
                 5.514 
                 −7.8189 
                 49.864 
               
               
                   
               
             
          
           
               
                 Section 13 
                 Section 14 
                 Section 15 
                 Section 16 
               
             
          
           
               
                 X 
                 Y 
                 Z 
                 X 
                 Y 
                 Z 
                 X 
                 Y 
                 Z 
                 X 
                 Y 
                 Z 
               
               
                   
               
               
                 1.8435 
                 −0.8028 
                 48.864 
                 2.1023 
                 −0.6442 
                 47.864 
                 2.5262 
                 −1.144 
                 46.864 
                 2.4083 
                 −1.0297 
                 45.864 
               
               
                 1.5317 
                 −0.609 
                 48.864 
                 1.0043 
                 −0.1322 
                 47.864 
                 1.0215 
                 −0.1492 
                 46.864 
                 1.222 
                 −0.1896 
                 45.864 
               
               
                 1.2193 
                 −0.4161 
                 48.864 
                 0.9415 
                 −0.1969 
                 47.864 
                 1.3546 
                 −0.4362 
                 46.864 
                 1.5731 
                 −0.5343 
                 45.864 
               
               
                 2.4651 
                 −1.1937 
                 48.864 
                 1.1 
                 −0.313 
                 47.864 
                 1.2494 
                 −0.2233 
                 46.864 
                 1.0789 
                 −0.1576 
                 45.864 
               
               
                 0.8825 
                 −0.1892 
                 48.864 
                 0.9638 
                 −0.141 
                 47.864 
                 1.0233 
                 −0.238 
                 46.864 
                 1.3767 
                 −0.4185 
                 45.864 
               
               
                 0.9065 
                 −0.224 
                 48.864 
                 0.9649 
                 −0.2311 
                 47.864 
                 1.0006 
                 −0.2043 
                 46.864 
                 1.0822 
                 −0.2449 
                 45.864 
               
               
                 0.9264 
                 −0.1248 
                 48.864 
                 1.505 
                 −0.5595 
                 47.864 
                 1.6856 
                 −0.6349 
                 46.864 
                 2.4667 
                 −0.7524 
                 45.864 
               
               
                 0.891 
                 −0.209 
                 48.864 
                 1.0242 
                 −0.1395 
                 47.864 
                 1.0607 
                 −0.1391 
                 46.864 
                 1.6711 
                 −0.5923 
                 45.864 
               
               
                 0.948 
                 −0.1255 
                 48.864 
                 2.4957 
                 −1.1698 
                 47.864 
                 1.5332 
                 −0.354 
                 46.864 
                 1.1362 
                 −0.1507 
                 45.864 
               
               
                 2.067 
                 −0.6563 
                 48.864 
                 0.9413 
                 −0.1758 
                 47.864 
                 1.0075 
                 −0.1644 
                 46.864 
                 2.6821 
                 −1.1949 
                 45.864 
               
               
                 0.968 
                 −0.1337 
                 48.864 
                 1.3701 
                 −0.4772 
                 47.864 
                 1.465 
                 −0.5023 
                 46.864 
                 1.2784 
                 −0.3608 
                 45.864 
               
               
                 2.6941 
                 −0.9566 
                 48.864 
                 2.7179 
                 −0.9334 
                 47.864 
                 1.165 
                 −0.1842 
                 46.864 
                 1.3311 
                 −0.2394 
                 45.864 
               
               
                 0.8825 
                 −0.1676 
                 48.864 
                 0.9832 
                 −0.1325 
                 47.864 
                 1.1338 
                 −0.3039 
                 46.864 
                 1.1805 
                 −0.3026 
                 45.864 
               
               
                 2.1548 
                 −0.9975 
                 48.864 
                 1.4861 
                 −0.356 
                 47.864 
                 2.7411 
                 −0.9096 
                 46.864 
                 1.0966 
                 −0.1481 
                 45.864 
               
               
                 0.8908 
                 −0.1477 
                 48.864 
                 2.0683 
                 −0.9049 
                 47.864 
                 1.0087 
                 −0.2233 
                 46.864 
                 2.1335 
                 −0.8661 
                 45.864 
               
               
                 0.9062 
                 −0.1327 
                 48.864 
                 0.9499 
                 −0.2163 
                 47.864 
                 2.1064 
                 −0.8886 
                 46.864 
                 1.0592 
                 −0.192 
                 45.864 
               
               
                 1.439 
                 −0.3576 
                 48.864 
                 1.235 
                 −0.3951 
                 47.864 
                 1.0401 
                 −0.1402 
                 46.864 
                 1.0599 
                 −0.2122 
                 45.864 
               
               
                 4.6966 
                 −3.0824 
                 48.864 
                 1.2551 
                 −0.2479 
                 47.864 
                 1.2441 
                 −0.3702 
                 46.864 
                 1.1792 
                 −0.1701 
                 45.864 
               
               
                 4.9225 
                 −3.4215 
                 48.864 
                 0.949 
                 −0.1561 
                 47.864 
                 1.3339 
                 −0.2624 
                 46.864 
                 1.0657 
                 −0.173 
                 45.864 
               
               
                 5.3639 
                 −2.3884 
                 48.864 
                 1.6398 
                 −0.6419 
                 47.864 
                 1.0002 
                 −0.1837 
                 46.864 
                 1.4749 
                 −0.4764 
                 45.864 
               
               
                 4.446 
                 −2.7659 
                 48.864 
                 3.8455 
                 −1.4768 
                 47.864 
                 1.5753 
                 −0.5686 
                 46.864 
                 1.5794 
                 −0.3518 
                 45.864 
               
               
                 3.3195 
                 −1.7652 
                 48.864 
                 4.3134 
                 −2.5452 
                 47.864 
                 1.0805 
                 −0.1452 
                 46.864 
                 1.1165 
                 −0.146 
                 45.864 
               
               
                 4.3112 
                 −2.6155 
                 48.864 
                 5.1032 
                 −2.1533 
                 47.864 
                 2.1373 
                 −0.6315 
                 46.864 
                 1.068 
                 −0.2306 
                 45.864 
               
               
                 5.0256 
                 −3.5993 
                 48.864 
                 3.8459 
                 −2.1086 
                 47.864 
                 5.4902 
                 −2.3254 
                 46.864 
                 5.9539 
                 −2.5907 
                 45.864 
               
               
                 4.0005 
                 −2.3096 
                 48.864 
                 3.3366 
                 −1.7213 
                 47.864 
                 3.6895 
                 −1.9214 
                 46.864 
                 5.1024 
                 −2.0224 
                 45.864 
               
               
                 4.0975 
                 −1.6551 
                 48.864 
                 4.9141 
                 −3.3314 
                 47.864 
                 3.3437 
                 −1.1904 
                 46.864 
                 3.6632 
                 −1.8434 
                 45.864 
               
               
                 3.4953 
                 −1.8943 
                 48.864 
                 4.6924 
                 −3.0002 
                 47.864 
                 4.8526 
                 −3.1645 
                 46.864 
                 3.6639 
                 −1.2991 
                 45.864 
               
               
                 5.5054 
                 −2.4851 
                 48.864 
                 4.1007 
                 −1.6052 
                 47.864 
                 4.7719 
                 −1.9009 
                 46.864 
                 3.1348 
                 −1.4781 
                 45.864 
               
               
                 4.159 
                 −2.4594 
                 48.864 
                 2.779 
                 −1.349 
                 47.864 
                 4.1647 
                 −2.3276 
                 46.864 
                 5.7114 
                 −2.4052 
                 45.864 
               
               
                 4.9286 
                 −2.1153 
                 48.864 
                 5.3458 
                 −2.304 
                 47.864 
                 5.8112 
                 −2.5522 
                 46.864 
                 2.9542 
                 −1.363 
                 45.864 
               
               
                 4.5745 
                 −2.9216 
                 48.864 
                 3.6798 
                 −1.9747 
                 47.864 
                 3.3523 
                 −1.6762 
                 46.864 
                 4.5888 
                 −1.7476 
                 45.864 
               
               
                 3.6679 
                 −2.0276 
                 48.864 
                 6.1408 
                 −2.9171 
                 47.864 
                 3.9195 
                 −1.4655 
                 46.864 
                 4.5755 
                 −2.7126 
                 45.864 
               
               
                 3.7096 
                 −1.4558 
                 48.864 
                 5.109 
                 −3.6832 
                 47.864 
                 4.5989 
                 −2.8067 
                 46.864 
                 3.4899 
                 −1.7176 
                 45.864 
               
               
                 5.7805 
                 −2.6892 
                 48.864 
                 5.6774 
                 −2.5314 
                 47.864 
                 5.3246 
                 −2.2195 
                 46.864 
                 6.0694 
                 −2.6904 
                 45.864 
               
               
                 4.7063 
                 −1.9863 
                 48.864 
                 4.8564 
                 −2.0094 
                 47.864 
                 3.8527 
                 −2.051 
                 46.864 
                 5.0207 
                 −3.3928 
                 45.864 
               
               
                 3.8366 
                 −2.1658 
                 48.864 
                 4.446 
                 −2.6915 
                 47.864 
                 6.1121 
                 −2.8048 
                 46.864 
                 3.9969 
                 −2.1119 
                 45.864 
               
               
                 5.6443 
                 −2.5852 
                 48.864 
                 5.5133 
                 −2.4153 
                 47.864 
                 2.8045 
                 −1.3168 
                 46.864 
                 5.3096 
                 −2.1432 
                 45.864 
               
               
                 2.7531 
                 −1.3794 
                 48.864 
                 4.3545 
                 −1.7364 
                 47.864 
                 4.9663 
                 −3.3521 
                 46.864 
                 3.9739 
                 −1.4451 
                 45.864 
               
               
                 5.9134 
                 −2.7974 
                 48.864 
                 3.5098 
                 −1.8459 
                 47.864 
                 4.4899 
                 −1.7517 
                 46.864 
                 3.8325 
                 −1.9746 
                 45.864 
               
               
                 4.4819 
                 −1.8611 
                 48.864 
                 5.8375 
                 −2.6533 
                 47.864 
                 4.3119 
                 −2.4752 
                 46.864 
                 4.4451 
                 −2.5564 
                 45.864 
               
               
                 5.148 
                 −2.249 
                 48.864 
                 3.5892 
                 −1.3505 
                 47.864 
                 5.6526 
                 −2.436 
                 46.864 
                 3.3135 
                 −1.5961 
                 45.864 
               
               
                 4.812 
                 −3.2481 
                 48.864 
                 4.1635 
                 −2.3934 
                 47.864 
                 3.5224 
                 −1.7967 
                 46.864 
                 4.9213 
                 −3.2152 
                 45.864 
               
               
                 3.0384 
                 −1.5692 
                 48.864 
                 3.0598 
                 −1.5321 
                 47.864 
                 3.6321 
                 −1.327 
                 46.864 
                 5.8343 
                 −2.4958 
                 45.864 
               
               
                 3.3193 
                 −1.2611 
                 48.864 
                 3.3321 
                 −1.2259 
                 47.864 
                 4.7301 
                 −2.9826 
                 46.864 
                 4.3075 
                 −2.4065 
                 45.864 
               
               
                 6.0423 
                 −2.9103 
                 48.864 
                 4.5724 
                 −2.8433 
                 47.864 
                 5.0506 
                 −2.0562 
                 46.864 
                 4.8924 
                 −1.9065 
                 45.864 
               
               
                 6.3853 
                 −3.2657 
                 48.864 
                 4.6066 
                 −1.8708 
                 47.864 
                 4.0114 
                 −2.1863 
                 46.864 
                 4.6986 
                 −2.8747 
                 45.864 
               
               
                 6.8863 
                 −4.1088 
                 48.864 
                 4.0074 
                 −2.248 
                 47.864 
                 5.9648 
                 −2.6749 
                 46.864 
                 3.3529 
                 −1.1552 
                 45.864 
               
               
                 5.6222 
                 −5.5762 
                 48.864 
                 5.9924 
                 −2.7815 
                 47.864 
                 3.0803 
                 −1.4935 
                 46.864 
                 6.1801 
                 −2.7953 
                 45.864 
               
               
                 6.1665 
                 −3.0282 
                 48.864 
                 4.8057 
                 −3.162 
                 47.864 
                 5.0709 
                 −3.5449 
                 46.864 
                 5.513 
                 −2.2703 
                 45.864 
               
               
                 6.8212 
                 −3.955 
                 48.864 
                 5.0152 
                 −3.5053 
                 47.864 
                 4.2056 
                 −1.6068 
                 46.864 
                 5.1069 
                 −3.5642 
                 45.864 
               
               
                 5.2094 
                 −3.967 
                 48.864 
                 5.2738 
                 −4.05 
                 47.864 
                 4.4594 
                 −2.6375 
                 46.864 
                 4.2824 
                 −1.5942 
                 45.864 
               
               
                 6.7481 
                 −3.8051 
                 48.864 
                 5.6019 
                 −5.4386 
                 47.864 
                 6.2225 
                 −2.9127 
                 46.864 
                 4.8139 
                 −3.0424 
                 45.864 
               
               
                 5.2897 
                 −4.1563 
                 48.864 
                 6.4575 
                 −3.2692 
                 47.864 
                 5.5817 
                 −6.1341 
                 46.864 
                 4.1555 
                 −2.2557 
                 45.864 
               
               
                 7.0698 
                 −4.7496 
                 48.864 
                 6.6356 
                 −3.53 
                 47.864 
                 6.6798 
                 −3.5375 
                 46.864 
                 5.5717 
                 −5.7624 
                 45.864 
               
               
                 5.1213 
                 −3.7813 
                 48.864 
                 7.0566 
                 −4.8205 
                 47.864 
                 5.5521 
                 −5.094 
                 46.864 
                 6.9788 
                 −5.1485 
                 45.864 
               
               
                 7.1247 
                 −5.1126 
                 48.864 
                 6.2521 
                 −3.0292 
                 47.864 
                 6.9423 
                 −4.2882 
                 46.864 
                 6.9078 
                 −4.2438 
                 45.864 
               
               
                 6.9434 
                 −4.2656 
                 48.864 
                 6.3579 
                 −3.1466 
                 47.864 
                 5.3213 
                 −4.1282 
                 46.864 
                 5.5702 
                 −5.5483 
                 45.864 
               
               
                 5.601 
                 −5.3592 
                 48.864 
                 5.463 
                 −4.6226 
                 47.864 
                 6.4262 
                 −3.1447 
                 46.864 
                 6.6918 
                 −3.5247 
                 45.864 
               
               
                 5.6261 
                 −6.2298 
                 48.864 
                 5.58 
                 −5.2265 
                 47.864 
                 5.5942 
                 −5.7175 
                 46.864 
                 5.2573 
                 −3.9171 
                 45.864 
               
               
                 7.1009 
                 −4.9306 
                 48.864 
                 5.6114 
                 −6.0779 
                 47.864 
                 6.8094 
                 −3.8289 
                 46.864 
                 6.2853 
                 −2.9059 
                 45.864 
               
               
                 5.6334 
                 −5.794 
                 48.864 
                 6.8491 
                 −3.97 
                 47.864 
                 5.4825 
                 −4.6951 
                 46.864 
                 5.5421 
                 −5.121 
                 45.864 
               
               
                 5.6345 
                 −6.012 
                 48.864 
                 6.7864 
                 −3.8192 
                 47.864 
                 7.0035 
                 −4.6621 
                 46.864 
                 6.9696 
                 −4.7852 
                 45.864 
               
               
                 5.4266 
                 −4.5439 
                 48.864 
                 5.6143 
                 −5.6515 
                 47.864 
                 5.1662 
                 −3.7424 
                 46.864 
                 6.8365 
                 −3.9275 
                 45.864 
               
               
                 6.2786 
                 −3.1444 
                 48.864 
                 7.0221 
                 −4.5987 
                 47.864 
                 5.5647 
                 −6.3527 
                 46.864 
                 6.5589 
                 −3.2723 
                 45.864 
               
               
                 5.5696 
                 −5.1435 
                 48.864 
                 6.5502 
                 −3.3971 
                 47.864 
                 6.6018 
                 −3.3984 
                 46.864 
                 5.5657 
                 −5.9765 
                 45.864 
               
               
                 6.6666 
                 −3.6596 
                 48.864 
                 5.1952 
                 −3.8649 
                 47.864 
                 5.5748 
                 −5.3012 
                 46.864 
                 5.5148 
                 −4.9086 
                 45.864 
               
               
                 5.3621 
                 −4.3487 
                 48.864 
                 5.5975 
                 −6.2907 
                 47.864 
                 6.9056 
                 −4.133 
                 46.864 
                 5.1857 
                 −3.7391 
                 45.864 
               
               
                 6.4859 
                 −3.3921 
                 48.864 
                 5.3447 
                 −4.2382 
                 47.864 
                 5.3828 
                 −4.3149 
                 46.864 
                 6.9356 
                 −4.4235 
                 45.864 
               
               
                 5.5307 
                 −4.9416 
                 48.864 
                 6.9503 
                 −4.2803 
                 47.864 
                 7.0362 
                 −5.0995 
                 46.864 
                 5.5535 
                 −6.1806 
                 45.864 
               
               
                 6.5799 
                 −3.5234 
                 48.864 
                 7.0803 
                 −5.0437 
                 47.864 
                 6.3275 
                 −3.0259 
                 46.864 
                 6.747 
                 −3.6564 
                 45.864 
               
               
                 5.4829 
                 −4.7417 
                 48.864 
                 5.51 
                 −4.8181 
                 47.864 
                 5.5916 
                 −5.9259 
                 46.864 
                 6.384 
                 −3.0223 
                 45.864 
               
               
                 6.9927 
                 −4.425 
                 48.864 
                 5.4078 
                 −4.4292 
                 47.864 
                 6.7489 
                 −3.6812 
                 46.864 
                 6.9771 
                 −4.9668 
                 45.864 
               
               
                 7.0347 
                 −4.5865 
                 48.864 
                 6.9897 
                 −4.4387 
                 47.864 
                 5.5205 
                 −4.8879 
                 46.864 
                 6.8716 
                 −4.0658 
                 45.864 
               
               
                 7.1529 
                 −5.8568 
                 48.864 
                 6.7153 
                 −3.6724 
                 47.864 
                 6.9723 
                 −4.4449 
                 46.864 
                 5.3783 
                 −4.2812 
                 45.864 
               
               
                 7.1429 
                 −6.0513 
                 48.864 
                 5.6173 
                 −5.8648 
                 47.864 
                 5.2522 
                 −3.9442 
                 46.864 
                 6.6291 
                 −3.3965 
                 45.864 
               
               
                 7.1416 
                 −5.2954 
                 48.864 
                 6.9036 
                 −4.1239 
                 47.864 
                 6.5178 
                 −3.2689 
                 46.864 
                 5.3215 
                 −4.0979 
                 45.864 
               
               
                 7.1557 
                 −5.6622 
                 48.864 
                 5.5485 
                 −5.0155 
                 47.864 
                 5.5888 
                 −5.5091 
                 46.864 
                 5.5605 
                 −5.3344 
                 45.864 
               
               
                 6.9476 
                 −7.0709 
                 48.864 
                 6.9033 
                 −6.8722 
                 47.864 
                 6.8614 
                 −3.9797 
                 46.864 
                 6.9559 
                 −4.6041 
                 45.864 
               
               
                 5.5116 
                 −7.6373 
                 48.864 
                 5.5071 
                 −7.4046 
                 47.864 
                 5.4365 
                 −4.504 
                 46.864 
                 6.7951 
                 −3.7908 
                 45.864 
               
               
                 6.9878 
                 −6.9462 
                 48.864 
                 7.0134 
                 −6.4395 
                 47.864 
                 7.0246 
                 −4.8804 
                 46.864 
                 5.5369 
                 −6.3843 
                 45.864 
               
               
                 6.4677 
                 −7.8773 
                 48.864 
                 5.5043 
                 −7.2104 
                 47.864 
                 6.8441 
                 −6.7092 
                 46.864 
                 5.433 
                 −4.4883 
                 45.864 
               
               
                 6.066 
                 −8.1055 
                 48.864 
                 7.0854 
                 −5.8728 
                 47.864 
                 5.5053 
                 −7.0343 
                 46.864 
                 6.4754 
                 −3.1446 
                 45.864 
               
               
                 5.5058 
                 −7.5763 
                 48.864 
                 5.5032 
                 −7.3361 
                 47.864 
                 6.5551 
                 −7.3194 
                 46.864 
                 5.4785 
                 −4.6976 
                 45.864 
               
               
                 6.5985 
                 −7.7336 
                 48.864 
                 5.7573 
                 −7.8562 
                 47.864 
                 6.2584 
                 −7.62 
                 46.864 
                 6.6956 
                 −6.7886 
                 45.864 
               
               
                 6.3947 
                 −7.9415 
                 48.864 
                 6.6989 
                 −7.3414 
                 47.864 
                 5.9443 
                 −7.7118 
                 46.864 
                 6.0056 
                 −7.5103 
                 45.864 
               
               
                 7.1254 
                 −6.2452 
                 48.864 
                 6.4527 
                 −7.6721 
                 47.864 
                 7.0392 
                 −5.3188 
                 46.864 
                 6.8869 
                 −6.1359 
                 45.864 
               
               
                 5.5353 
                 −7.7576 
                 48.864 
                 7.0688 
                 −6.0625 
                 47.864 
                 5.666 
                 −7.5853 
                 46.864 
                 5.5136 
                 −7.0614 
                 45.864 
               
               
                 5.6128 
                 −7.9233 
                 48.864 
                 5.8757 
                 −7.9027 
                 47.864 
                 6.958 
                 −6.2449 
                 46.864 
                 6.2514 
                 −7.4136 
                 45.864 
               
               
                 5.6986 
                 −8.0156 
                 48.864 
                 5.7042 
                 −7.8208 
                 47.864 
                 5.5199 
                 −7.2903 
                 46.864 
                 5.5191 
                 −6.588 
                 45.864 
               
               
                 5.8721 
                 −8.1024 
                 48.864 
                 5.5153 
                 −7.4726 
                 47.864 
                 6.7412 
                 −6.9827 
                 46.864 
                 6.5258 
                 −7.1144 
                 45.864 
               
               
                 5.5271 
                 −7.1305 
                 48.864 
                 7.0941 
                 −5.2678 
                 47.864 
                 5.5212 
                 −6.7892 
                 46.864 
                 6.7883 
                 −6.5324 
                 45.864 
               
               
                 5.5039 
                 −7.4186 
                 48.864 
                 5.5498 
                 −6.7369 
                 47.864 
                 6.4391 
                 −7.4646 
                 46.864 
                 6.9402 
                 −5.7895 
                 45.864 
               
               
                 6.2008 
                 −8.0626 
                 48.864 
                 5.549 
                 −7.6053 
                 47.864 
                 6.1278 
                 −7.6851 
                 46.864 
                 5.5313 
                 −7.1496 
                 45.864 
               
               
                 6.793 
                 −7.432 
                 48.864 
                 6.9731 
                 −6.6256 
                 47.864 
                 5.823 
                 −7.6846 
                 46.864 
                 5.7189 
                 −7.4284 
                 45.864 
               
               
                 5.6094 
                 −6.4472 
                 48.864 
                 6.0653 
                 −7.904 
                 47.864 
                 7.0257 
                 −5.6907 
                 46.864 
                 6.362 
                 −7.3196 
                 45.864 
               
               
                 5.5557 
                 −6.9029 
                 48.864 
                 7.0985 
                 −5.4922 
                 47.864 
                 5.5848 
                 −7.4794 
                 46.864 
                 5.8267 
                 −7.4847 
                 45.864 
               
               
                 5.5549 
                 −7.8156 
                 48.864 
                 5.9386 
                 −7.9124 
                 47.864 
                 6.8854 
                 −6.569 
                 46.864 
                 6.6394 
                 −6.9127 
                 45.864 
               
               
                 7.0662 
                 −6.6301 
                 48.864 
                 6.5171 
                 −7.6023 
                 47.864 
                 5.5058 
                 −7.1571 
                 46.864 
                 5.9451 
                 −7.5109 
                 45.864 
               
               
                 5.8101 
                 −8.0824 
                 48.864 
                 6.7592 
                 −7.2284 
                 47.864 
                 6.6061 
                 −7.2416 
                 46.864 
                 6.8588 
                 −6.2692 
                 45.864 
               
               
                 6.1293 
                 −8.0896 
                 48.864 
                 5.6567 
                 −7.7785 
                 47.864 
                 6.3178 
                 −7.5776 
                 46.864 
                 6.9738 
                 −5.3626 
                 45.864 
               
               
                 5.9364 
                 −8.1129 
                 48.864 
                 6.6315 
                 −7.4504 
                 47.864 
                 6.0063 
                 −7.7116 
                 46.864 
                 5.5052 
                 −6.9718 
                 45.864 
               
               
                 7.1518 
                 −5.4787 
                 48.864 
                 5.5122 
                 −7.085 
                 47.864 
                 5.7136 
                 −7.6254 
                 46.864 
                 6.1897 
                 −7.4521 
                 45.864 
               
               
                 5.5092 
                 −7.3224 
                 48.864 
                 6.813 
                 −7.1121 
                 47.864 
                 6.9874 
                 −6.061 
                 46.864 
                 5.584 
                 −7.2802 
                 45.864 
               
               
                 5.6512 
                 −7.971 
                 48.864 
                 6.5766 
                 −7.5281 
                 47.864 
                 5.5347 
                 −7.3557 
                 46.864 
                 6.4713 
                 −7.1925 
                 45.864 
               
               
                 6.9021 
                 −7.1938 
                 48.864 
                 6.3245 
                 −7.7831 
                 47.864 
                 6.7963 
                 −6.8474 
                 46.864 
                 6.745 
                 −6.6616 
                 45.864 
               
               
                 6.3335 
                 −7.9872 
                 48.864 
                 7.0953 
                 −5.6826 
                 47.864 
                 5.5115 
                 −6.9116 
                 46.864 
                 6.0656 
                 −7.5004 
                 45.864 
               
               
                 6.0014 
                 −8.1137 
                 48.864 
                 6.3831 
                 −7.7368 
                 47.864 
                 6.4996 
                 −7.394 
                 46.864 
                 6.9107 
                 −6.0017 
                 45.864 
               
               
                 6.2689 
                 −8.028 
                 48.864 
                 6.9405 
                 −6.7496 
                 47.864 
                 6.195 
                 −7.6564 
                 46.864 
                 5.8851 
                 −7.5021 
                 45.864 
               
               
                 5.5031 
                 −7.515 
                 48.864 
                 6.127 
                 −7.8875 
                 47.864 
                 5.8828 
                 −7.7026 
                 46.864 
                 5.5056 
                 −6.792 
                 45.864 
               
               
                 5.5806 
                 −7.8712 
                 48.864 
                 6.1964 
                 −7.8598 
                 47.864 
                 7.0354 
                 −5.5049 
                 46.864 
                 5.5534 
                 −7.2167 
                 45.864 
               
               
                 6.7286 
                 −7.5461 
                 48.864 
                 5.8148 
                 −7.8838 
                 47.864 
                 5.6216 
                 −7.5353 
                 46.864 
                 6.3088 
                 −7.369 
                 45.864 
               
               
                 7.1 
                 −6.4383 
                 48.864 
                 5.6128 
                 −7.726 
                 47.864 
                 6.9208 
                 −6.4272 
                 46.864 
                 5.6236 
                 −7.3386 
                 45.864 
               
               
                 5.5849 
                 −6.6753 
                 48.864 
                 5.576 
                 −6.5141 
                 47.864 
                 5.5107 
                 −7.224 
                 46.864 
                 6.5755 
                 −7.0331 
                 45.864 
               
               
                 5.5171 
                 −7.2264 
                 48.864 
                 6.8609 
                 −6.9932 
                 47.864 
                 6.6781 
                 −7.1145 
                 46.864 
                 6.826 
                 −6.4014 
                 45.864 
               
               
                 7.0228 
                 −6.8199 
                 48.864 
                 5.5289 
                 −7.5398 
                 47.864 
                 5.543 
                 −6.571 
                 46.864 
                 6.9611 
                 −5.5763 
                 45.864 
               
               
                 6.8507 
                 −7.3143 
                 48.864 
                 7.0449 
                 −6.2516 
                 47.864 
                 6.3734 
                 −7.5303 
                 46.864 
                 5.5032 
                 −6.8819 
                 45.864 
               
               
                 6.6568 
                 −7.6557 
                 48.864 
                 6.0022 
                 −7.9126 
                 47.864 
                 6.0679 
                 −7.7023 
                 46.864 
                 5.6716 
                 −7.3903 
                 45.864 
               
               
                 5.7519 
                 −8.0531 
                 48.864 
                 6.2623 
                 −7.8245 
                 47.864 
                 5.7663 
                 −7.6587 
                 46.864 
                 6.1238 
                 −7.4825 
                 45.864 
               
               
                 6.5356 
                 −7.8078 
                 48.864 
                 5.5238 
                 −6.9598 
                 47.864 
                 7.0097 
                 −5.8762 
                 46.864 
                 6.4116 
                 −7.2665 
                 45.864 
               
               
                 5.5212 
                 −7.6979 
                 48.864 
                 5.5768 
                 −7.6678 
                 47.864 
                 5.556 
                 −7.4191 
                 46.864 
                 5.7709 
                 −7.46 
                 45.864 
               
               
                   
               
             
          
         
       
     
     At this point it should be understood that the points disclosed in Table 1 are exemplary, variations/deviations from the points in Table 1 at one or more sections that do not substantially affect the desired properties obtained by the airfoil core shape of the exemplary embodiments fall within the scope of the exemplary embodiments of the invention. 
     While the invention has been described in detail in connection with only a limited number of embodiments, it should be readily understood that the invention is not limited to such disclosed embodiments. Rather, the invention can be modified to incorporate any number of variations, alterations, substitutions or equivalent arrangements not heretofore described, but which are commensurate with the spirit and scope of the invention. Additionally, while various embodiments of the invention have been described, it is to be understood that aspects of the invention may include only some of the described embodiments. Accordingly, the invention is not to be seen as limited by the foregoing description, but is only limited by the scope of the appended claims.