Patent Publication Number: US-8979487-B2

Title: High pressure turbine vane airfoil profile

Description:
TECHNICAL FIELD 
     The application relates generally to a vane airfoil for a gas turbine engine and, more particularly, to an airfoil profile suited for use in the second stage vane assembly of a high pressure (HP) turbine. 
     BACKGROUND OF THE ART 
     Every stage of a gas turbine engine must meet a plurality of design criteria to assure the best possible overall engine efficiency. The design goals dictate specific thermal and mechanical requirements that must be met pertaining to heat loading, parts life and manufacturing, use of combustion gases, throat area, vectoring, the interaction between stages to name a few. The design criteria for each stage is constantly being re-evaluated and improved upon. Each airfoil is subject to flow regimes which lend themselves easily to flow separation, which tend to limit the amount of work transferred to the compressor, and hence the total thrust or power capability of the engine. The pressure turbine is also subject to harsh temperatures and pressures, which require a solid balance between aerodynamic and structural optimization. Therefore, improvements in airfoil design are sought. 
     SUMMARY 
     In one aspect, there is provided a turbine vane for a gas turbine engine comprising an airfoil having a portion defined by a nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of Sections 1 to 7 set forth in Table 2, wherein the point of origin of the orthogonally related axes X, Y and Z is located at an intersection of a centerline of the gas turbine engine and a stacking line of the turbine vane, the Z values are radial distances measured along the stacking line, the X and Y are coordinate values defining the profile at each distance Z. 
     In another aspect, there is provided a turbine vane for a gas turbine engine, the turbine vane having a cold coated intermediate airfoil portion defined by a nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of Sections 1 to 7 set forth in Table 2, wherein the point of origin of the orthogonally related axes X, Y and Z is located at an intersection of a centerline of the gas turbine engine and a stacking line of the turbine vane, the Z values are radial distances measured along the stacking line, the X and Y are coordinate values defining the profile at each distance Z. 
     In another aspect, there is provided a turbine stator assembly for a gas turbine engine comprising a plurality of vanes, each vanes including an airfoil having an intermediate portion defined by a nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z of Sections 1 to 7 set forth in Table 2, wherein the point of origin of the orthogonally related axes X, Y and Z is located at an intersection of a centerline of the gas turbine engine and a stacking line of the turbine vane, the Z values are radial distances measured along the stacking line, the X and Y are coordinate values defining the profile at each distance Z. 
     In a still further aspect, there is provided a high pressure turbine vane comprising at least one airfoil having a surface lying substantially on the points of Table 2, the airfoil extending between platforms defined generally by coordinates given in Table 1, wherein a fillet radius is applied around the airfoil between the airfoil and platforms. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
       Reference is now made to the accompanying figures depicting aspects of the present invention, in which: 
         FIG. 1  is a schematic view of a gas turbine engine; 
         FIG. 2  is a schematic view of a gaspath of the gas turbine engine of  FIG. 1 , including a two-stage high pressure turbine; 
         FIG. 3  is a schematic elevation view of a high pressure turbine (HPT) stage vane having a vane profile defined in accordance with an embodiment of the present invention; and 
         FIGS. 4   a  and  4   b  are simplified 2D HP turbine vane airfoil cross-sections illustrating the angular twist and restagger tolerances. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  illustrates a gas turbine engine  10  of a type preferably provided for use in subsonic flight, generally comprising in serial flow communication a fan  12  through which ambient air is propelled, a multistage compressor  14  for pressurizing the air, a combustor  16  in which the compressed air is mixed with fuel and ignited for generating an annular stream of hot combustion gases, and a turbine section  18  for extracting energy from the combustion gases to drive the fan, the compressor, and produce thrust. 
     The gas turbine engine  10  further includes a turbine exhaust duct  20  which is exemplified as including an annular core portion  22  and an annular outer portion  24  and a plurality of struts  26  circumferentially spaced apart, and radially extending between the inner and outer portions  22 ,  24 . 
       FIG. 2  illustrates a portion of an annular hot gaspath, indicated by arrows  27  and defined by annular inner and outer walls  28  and  30  respectively, for directing the stream of hot combustion gases axially in an annular flow. The profile of the inner and outer walls  28  and  30  of the annular gaspath, “cold” (i.e. non-operating) coated conditions, is defined by the Cartesian coordinate values such as the ones given in Table 1 below. More particularly, the inner and outer gaspath walls  28  and  30  are defined with respect to mutually orthogonal x and z axes, as shown in  FIG. 2 . The x axis corresponds to the engine turbine rotor centerline  29 . The radial distance of the inner and outer walls  28  and  30  from the engine turbine rotor centerline and, thus, from the x-axis at specific axial locations is measured along the z axis. The z values provide the inner and outer radius of the gaspath at various axial locations therealong. The x and z coordinate values in Table 1 are distances given in inches from a selected point of origin O (see  FIG. 2 ). It is understood that other units of dimensions may be used. The x and z values have in average a manufacturing tolerance of about ±0.030″. The tolerance may account for such things as casting, coating, ceramic coating and/or other tolerances. It is also understood that the manufacturing tolerances of the gas path may vary along the length thereof. 
     The turbine section  18  has two high pressure turbine (HPT) stages located in the gaspath  27  downstream of the combustor  16 . Referring to  FIG. 2 , the HPT stages each comprises a stator assembly  32 ,  34  and a rotor assembly  36 ,  38  having a plurality of circumferentially arranged vane  40   a ,  40   b  and blades  42   a ,  42   b  respectively. The vanes  40   a,b  and blades  42   a,b  are mounted in position along respective stacking lines  44 - 50 , as identified in  FIG. 2 . The stacking lines  44 - 50  extend in the radial direction along the z axis at different axial locations. The stacking lines  44 - 50  define the axial location where the blades and vanes of each stage are mounted in the engine  10 . 
     Table 1 provides gaspath definition from upstream to downstream of the second stage HP vane airfoil  40   b  relative to its stacking line  48  (X=0 at stacking line  48 ). 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 COLD COATED GASPATH DEFINITION 
               
            
           
           
               
               
               
               
               
            
               
                   
                 INNER GASPATH 
                   
                 OUTER GASPATH 
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 X 
                 Z 
                 X 
                 Z 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 −3.908 
                 7.953 
                 −3.879 
                 9.686 
               
               
                   
                 −3.859 
                 7.960 
                 −3.829 
                 9.678 
               
               
                   
                 −3.809 
                 7.967 
                 −3.780 
                 9.671 
               
               
                   
                 −3.760 
                 7.974 
                 −3.730 
                 9.664 
               
               
                   
                 −3.710 
                 7.981 
                 −3.681 
                 9.657 
               
               
                   
                 −3.661 
                 7.988 
                 −3.631 
                 9.650 
               
               
                   
                 −3.611 
                 7.995 
                 −3.582 
                 9.643 
               
               
                   
                 −3.562 
                 8.002 
                 −3.532 
                 9.636 
               
               
                   
                 −3.512 
                 8.009 
                 −3.483 
                 9.629 
               
               
                   
                 −3.463 
                 8.016 
                 −3.433 
                 9.622 
               
               
                   
                 −3.413 
                 8.024 
                 −3.384 
                 9.615 
               
               
                   
                 −3.364 
                 8.031 
                 −3.334 
                 9.608 
               
               
                   
                 −3.314 
                 8.038 
                 −3.285 
                 9.600 
               
               
                   
                 −3.265 
                 8.045 
                 −3.235 
                 9.593 
               
               
                   
                 −3.215 
                 8.052 
                 −3.186 
                 9.586 
               
               
                   
                 −3.166 
                 8.059 
                 −3.136 
                 9.579 
               
               
                   
                 −3.116 
                 8.066 
                 −3.087 
                 9.572 
               
               
                   
                 −3.067 
                 8.073 
                 −3.037 
                 9.565 
               
               
                   
                 −3.017 
                 8.080 
                 −2.988 
                 9.558 
               
               
                   
                 −2.968 
                 8.087 
                 −2.938 
                 9.551 
               
               
                   
                 −2.918 
                 8.093 
                 −2.888 
                 9.549 
               
               
                   
                 −2.868 
                 8.093 
                 −2.838 
                 9.549 
               
               
                   
                 −2.818 
                 8.093 
                 −2.788 
                 9.549 
               
               
                   
                 −2.768 
                 8.093 
                 −2.738 
                 9.549 
               
               
                   
                 −2.718 
                 8.093 
                 −2.688 
                 9.549 
               
               
                   
                 −2.668 
                 8.093 
                 −2.638 
                 9.549 
               
               
                   
                 −2.618 
                 8.093 
                 −2.588 
                 9.549 
               
               
                   
                 −2.568 
                 8.093 
                 −2.538 
                 9.549 
               
               
                   
                 −2.518 
                 8.093 
                 −2.488 
                 9.549 
               
               
                   
                 −2.468 
                 8.093 
                 −2.438 
                 9.549 
               
               
                   
                 −2.418 
                 8.093 
                 −2.388 
                 9.549 
               
               
                   
                 −2.368 
                 8.093 
                 −2.338 
                 9.549 
               
               
                   
                 −2.318 
                 8.093 
                 −2.288 
                 9.549 
               
               
                   
                 −2.268 
                 8.093 
                 −2.238 
                 9.549 
               
               
                   
                 −2.218 
                 8.088 
                 −2.188 
                 9.549 
               
               
                   
                 −2.169 
                 8.084 
                 −2.138 
                 9.549 
               
               
                   
                 −2.119 
                 8.079 
                 −2.088 
                 9.549 
               
               
                   
                 −2.069 
                 8.074 
                 −2.038 
                 9.549 
               
               
                   
                 −2.019 
                 8.069 
                 −1.988 
                 9.549 
               
               
                   
                 −1.970 
                 8.065 
                 −1.938 
                 9.549 
               
               
                   
                 −1.920 
                 8.060 
                 −1.888 
                 9.549 
               
               
                   
                 −1.870 
                 8.055 
                 −1.838 
                 9.549 
               
               
                   
                 −1.820 
                 8.050 
                 −1.788 
                 9.549 
               
               
                   
                 −1.770 
                 8.046 
                 −1.738 
                 9.549 
               
               
                   
                 −1.721 
                 8.041 
                 −1.688 
                 9.549 
               
               
                   
                 −1.671 
                 8.036 
                 −1.638 
                 9.549 
               
               
                   
                 −1.621 
                 8.031 
                 −1.588 
                 9.549 
               
               
                   
                 −1.571 
                 8.026 
                 −1.538 
                 9.550 
               
               
                   
                 −1.522 
                 8.020 
                 −1.489 
                 9.554 
               
               
                   
                 −1.472 
                 8.012 
                 −1.439 
                 9.558 
               
               
                   
                 −1.423 
                 8.004 
                 −1.389 
                 9.562 
               
               
                   
                 −1.374 
                 7.996 
                 −1.339 
                 9.566 
               
               
                   
                 −1.324 
                 7.988 
                 −1.289 
                 9.571 
               
               
                   
                 −1.275 
                 7.980 
                 −1.240 
                 9.575 
               
               
                   
                 −1.226 
                 7.971 
                 −1.190 
                 9.579 
               
               
                   
                 −1.176 
                 7.963 
                 −1.140 
                 9.583 
               
               
                   
                 −1.127 
                 7.955 
                 −1.090 
                 9.588 
               
               
                   
                 −1.078 
                 7.947 
                 −1.040 
                 9.592 
               
               
                   
                 −1.028 
                 7.939 
                 −0.990 
                 9.596 
               
               
                   
                 −0.979 
                 7.931 
                 −0.941 
                 9.600 
               
               
                   
                 −0.930 
                 7.923 
                 −0.891 
                 9.605 
               
               
                   
                 −0.880 
                 7.915 
                 −0.841 
                 9.609 
               
               
                   
                 −0.831 
                 7.907 
                 −0.791 
                 9.613 
               
               
                   
                 −0.782 
                 7.899 
                 −0.741 
                 9.617 
               
               
                   
                 −0.732 
                 7.890 
                 −0.692 
                 9.621 
               
               
                   
                 −0.683 
                 7.882 
                 −0.642 
                 9.626 
               
               
                   
                 −0.634 
                 7.874 
                 −0.592 
                 9.629 
               
               
                   
                 −0.584 
                 7.867 
                 −0.542 
                 9.633 
               
               
                   
                 −0.535 
                 7.861 
                 −0.492 
                 9.636 
               
               
                   
                 −0.485 
                 7.854 
                 −0.442 
                 9.640 
               
               
                   
                 −0.436 
                 7.847 
                 −0.392 
                 9.643 
               
               
                   
                 −0.386 
                 7.840 
                 −0.342 
                 9.647 
               
               
                   
                 −0.337 
                 7.833 
                 −0.293 
                 9.651 
               
               
                   
                 −0.287 
                 7.827 
                 −0.243 
                 9.654 
               
               
                   
                 −0.237 
                 7.820 
                 −0.193 
                 9.658 
               
               
                   
                 −0.188 
                 7.813 
                 −0.143 
                 9.661 
               
               
                   
                 −0.138 
                 7.806 
                 −0.093 
                 9.665 
               
               
                   
                 −0.089 
                 7.799 
                 −0.043 
                 9.668 
               
               
                   
                 −0.039 
                 7.793 
                 0.007 
                 9.672 
               
               
                   
                 0.010 
                 7.786 
                 0.057 
                 9.675 
               
               
                   
                 0.060 
                 7.779 
                 0.106 
                 9.679 
               
               
                   
                 0.109 
                 7.772 
                 0.156 
                 9.682 
               
               
                   
                 0.159 
                 7.765 
                 0.206 
                 9.686 
               
               
                   
                 0.208 
                 7.758 
                 0.256 
                 9.689 
               
               
                   
                 0.258 
                 7.752 
                 0.306 
                 9.693 
               
               
                   
                 0.307 
                 7.745 
                 0.356 
                 9.697 
               
               
                   
                 0.357 
                 7.738 
                 0.406 
                 9.700 
               
               
                   
                 0.407 
                 7.731 
                 0.456 
                 9.704 
               
               
                   
                 0.456 
                 7.724 
                 0.505 
                 9.707 
               
               
                   
                 0.506 
                 7.718 
                 0.555 
                 9.711 
               
               
                   
                 0.555 
                 7.711 
                 0.605 
                 9.714 
               
               
                   
                 0.605 
                 7.704 
                 0.655 
                 9.717 
               
               
                   
                 0.654 
                 7.699 
                 0.705 
                 9.718 
               
               
                   
                 0.704 
                 7.696 
                 0.755 
                 9.720 
               
               
                   
                 0.754 
                 7.693 
                 0.805 
                 9.721 
               
               
                   
                 0.804 
                 7.690 
                 0.855 
                 9.723 
               
               
                   
                 0.854 
                 7.687 
                 0.905 
                 9.724 
               
               
                   
                 0.904 
                 7.684 
                 0.955 
                 9.726 
               
               
                   
                 0.954 
                 7.681 
                 1.005 
                 9.727 
               
               
                   
                 1.004 
                 7.679 
                 1.055 
                 9.729 
               
               
                   
                 1.054 
                 7.676 
                 1.105 
                 9.730 
               
               
                   
                 1.104 
                 7.673 
                 1.155 
                 9.732 
               
               
                   
                 1.154 
                 7.670 
                 1.205 
                 9.733 
               
               
                   
                 1.203 
                 7.667 
                 1.255 
                 9.735 
               
               
                   
                 1.253 
                 7.664 
                 1.305 
                 9.736 
               
               
                   
                 1.303 
                 7.661 
                 1.355 
                 9.738 
               
               
                   
                 1.353 
                 7.659 
                 1.405 
                 9.739 
               
               
                   
                 1.403 
                 7.656 
                 1.455 
                 9.739 
               
               
                   
                 1.453 
                 7.656 
                 1.505 
                 9.739 
               
               
                   
                 1.503 
                 7.656 
                 1.555 
                 9.739 
               
               
                   
                 1.553 
                 7.656 
                 1.605 
                 9.739 
               
               
                   
                 1.603 
                 7.656 
                 1.655 
                 9.739 
               
               
                   
                 1.653 
                 7.656 
                 1.705 
                 9.739 
               
               
                   
                 1.703 
                 7.656 
                 1.755 
                 9.739 
               
               
                   
                 1.753 
                 7.656 
                 1.805 
                 9.739 
               
               
                   
                 1.803 
                 7.656 
                 1.855 
                 9.739 
               
               
                   
                 1.853 
                 7.656 
                 1.905 
                 9.739 
               
               
                   
                 1.903 
                 7.656 
                 1.955 
                 9.739 
               
               
                   
                 1.953 
                 7.656 
                 2.005 
                 9.739 
               
               
                   
                 2.003 
                 7.656 
                 2.055 
                 9.739 
               
               
                   
                 2.053 
                 7.656 
                 2.105 
                 9.739 
               
               
                   
                 2.103 
                 7.656 
                 2.155 
                 9.739 
               
               
                   
                 2.153 
                 7.656 
                 2.205 
                 9.739 
               
               
                   
                 2.203 
                 7.656 
                 2.255 
                 9.739 
               
               
                   
                 2.253 
                 7.656 
               
               
                   
                   
               
            
           
         
       
     
     More specifically, the stator assemblies  32 ,  34  each include the plurality of circumferentially distributed vanes  40   a  and  40   b  respectively which extend radially across the hot gaspath  27 .  FIG. 3  shows an example of a vane  40   b  of the second HPT stage. It can be seen that each vane  40   b  has an airfoil  54  having a leading edge  56  and a trailing edge  58 , extending between inner vane platform  60  and outer vane platform  62 . 
     The novel airfoil shape of each second stage HPT vane  40   b  is defined by a set of X-Y-Z points in space. This set of points represents a novel and unique solution to the target design criteria discussed above, and are well-adapted for use in a two-stage high pressure turbine design. The set of points are defined in a Cartesian coordinate system which has mutually orthogonal X, Y and Z axes. The X axis extends axially along the turbine rotor centerline  29 , i.e., the rotary axis. The positive X direction is axially towards the aft of the turbine engine  10 . The Z axis extends along the HPT vane stacking line  48  of each respective vane  40   b  in a generally radial direction and intersects the X axis. The positive Z direction is radially outwardly toward the outer vane platform  62 . The Y axis extends tangentially with the positive Y direction being in the direction of rotation of the rotor assembly  36 . Therefore, the origin of the X, Y and Z axes is defined at the point of intersection of all three orthogonally-related axes: that is the point (0,0,0) at the intersection of the center of rotation of the turbine engine  10  and the stacking line  48 . 
     In a particular embodiment of the second stage HPT vane, the set of points which define the vane airfoil profile relative to the axis of rotation of the turbine engine  10  and stacking line  48  thereof are set out in Table 2 below as X, Y and Z Cartesian coordinate values. Particularly, the vane airfoil profile is defined by profile sections  66  at various locations along its height, the locations represented by Z values. It should be understood that the Z values do not represent an actual radial height along the airfoil  54  but are defined with respect to the engine center line. For example, if the vanes  40   b  are mounted about the stator assembly  34  at an angle with respect to the radial direction, then the Z values are not a true representation of the height of the airfoils of the vanes  40   b . Furthermore, it is to be appreciated that, with respect to Table 2, Z values are not actually radial heights, per se, from the centerline but rather a height from a plane through the centerline—i.e. the sections in Table 2 are planar. The coordinate values are set forth in inches in Table 2 although other units of dimensions may be used when the values are appropriately converted. 
     Thus, at each Z distance, the X and Y coordinate values of the desired profile section  66  are defined at selected locations in a Z direction normal to the X, Y plane. The X and Y coordinates are given in distance dimensions, e.g., units of inches, and are joined smoothly, using appropriate curve-fitting techniques, at each Z location to form a smooth continuous airfoil cross-section. The vane airfoil profiles of the various surface locations between the distances Z are determined by smoothly connecting the adjacent profile sections  66  to one another to form the airfoil profile. 
     The coordinate values listed in Table 2 below represent the desired airfoil profiles in a “cold” non-operating coated condition (and at nominal restagger). However, the manufactured airfoil surface profile will be slightly different, as a result of manufacturing and applied coating tolerances. According to an embodiment, the coated condition includes a thermal barrier coating (TBC). 
     The Table 2 values are generated and shown to three decimal places for determining the profile of the HPT stage vane airfoil. However, as mentioned above, there are manufacturing tolerance issues to be addressed and, accordingly, the values for the profile given in Table 2 are for a theoretical airfoil. A profile tolerance of ±0.030 inches, measured perpendicularly to the airfoil surface is additive to the nominal values given in Table 2 below. The profile tolerance accounts for airfoil profile casting, coating and TBC tolerances. The second stage HPT vane airfoil design functions well within these ranges of variation. The cold or room temperature profile (including coating) is given by the X, Y and Z coordinates for manufacturing purposes. It is understood that the airfoil may deform, within acceptable limits, once entering service. 
     The coordinate values given in Table 2 below provide the preferred nominal second stage HPT vane airfoil profile. 
     
       
         
           
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 X 
                 Y 
                 Z 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
            
               
                 Section 1 
               
            
           
           
               
               
               
            
               
                 −0.767 
                 −0.552 
                 8.132 
               
               
                 0.588 
                 1.185 
                 8.132 
               
               
                 −0.767 
                 −0.552 
                 8.132 
               
               
                 −0.766 
                 −0.550 
                 8.132 
               
               
                 −0.765 
                 −0.547 
                 8.132 
               
               
                 −0.763 
                 −0.542 
                 8.132 
               
               
                 −0.760 
                 −0.538 
                 8.132 
               
               
                 −0.755 
                 −0.531 
                 8.132 
               
               
                 −0.748 
                 −0.522 
                 8.132 
               
               
                 −0.738 
                 −0.513 
                 8.132 
               
               
                 −0.723 
                 −0.504 
                 8.132 
               
               
                 −0.703 
                 −0.494 
                 8.132 
               
               
                 −0.678 
                 −0.486 
                 8.132 
               
               
                 −0.647 
                 −0.481 
                 8.132 
               
               
                 −0.614 
                 −0.477 
                 8.132 
               
               
                 −0.581 
                 −0.467 
                 8.132 
               
               
                 −0.546 
                 −0.449 
                 8.132 
               
               
                 −0.512 
                 −0.420 
                 8.132 
               
               
                 −0.478 
                 −0.383 
                 8.132 
               
               
                 −0.442 
                 −0.341 
                 8.132 
               
               
                 −0.405 
                 −0.295 
                 8.132 
               
               
                 −0.367 
                 −0.246 
                 8.132 
               
               
                 −0.327 
                 −0.194 
                 8.132 
               
               
                 −0.288 
                 −0.142 
                 8.132 
               
               
                 −0.248 
                 −0.089 
                 8.132 
               
               
                 −0.210 
                 −0.034 
                 8.132 
               
               
                 −0.171 
                 0.022 
                 8.132 
               
               
                 −0.134 
                 0.078 
                 8.132 
               
               
                 −0.096 
                 0.133 
                 8.132 
               
               
                 −0.059 
                 0.189 
                 8.132 
               
               
                 −0.022 
                 0.246 
                 8.132 
               
               
                 0.015 
                 0.302 
                 8.132 
               
               
                 0.052 
                 0.358 
                 8.132 
               
               
                 0.089 
                 0.415 
                 8.132 
               
               
                 0.125 
                 0.471 
                 8.132 
               
               
                 0.161 
                 0.528 
                 8.132 
               
               
                 0.198 
                 0.585 
                 8.132 
               
               
                 0.234 
                 0.642 
                 8.132 
               
               
                 0.269 
                 0.696 
                 8.132 
               
               
                 0.304 
                 0.751 
                 8.132 
               
               
                 0.337 
                 0.805 
                 8.132 
               
               
                 0.368 
                 0.854 
                 8.132 
               
               
                 0.398 
                 0.901 
                 8.132 
               
               
                 0.425 
                 0.945 
                 8.132 
               
               
                 0.450 
                 0.985 
                 8.132 
               
               
                 0.472 
                 1.021 
                 8.132 
               
               
                 0.492 
                 1.054 
                 8.132 
               
               
                 0.509 
                 1.083 
                 8.132 
               
               
                 0.524 
                 1.108 
                 8.132 
               
               
                 0.537 
                 1.129 
                 8.132 
               
               
                 0.547 
                 1.147 
                 8.132 
               
               
                 0.555 
                 1.160 
                 8.132 
               
               
                 0.560 
                 1.170 
                 8.132 
               
               
                 0.566 
                 1.178 
                 8.132 
               
               
                 0.572 
                 1.184 
                 8.132 
               
               
                 0.577 
                 1.186 
                 8.132 
               
               
                 0.583 
                 1.186 
                 8.132 
               
               
                 0.585 
                 1.186 
                 8.132 
               
               
                 0.588 
                 1.185 
                 8.132 
               
               
                 0.591 
                 1.184 
                 8.132 
               
               
                 0.594 
                 1.182 
                 8.132 
               
               
                 0.599 
                 1.177 
                 8.132 
               
               
                 0.602 
                 1.171 
                 8.132 
               
               
                 0.602 
                 1.161 
                 8.132 
               
               
                 0.599 
                 1.150 
                 8.132 
               
               
                 0.595 
                 1.137 
                 8.132 
               
               
                 0.590 
                 1.118 
                 8.132 
               
               
                 0.583 
                 1.095 
                 8.132 
               
               
                 0.575 
                 1.066 
                 8.132 
               
               
                 0.565 
                 1.032 
                 8.132 
               
               
                 0.553 
                 0.993 
                 8.132 
               
               
                 0.540 
                 0.949 
                 8.132 
               
               
                 0.524 
                 0.900 
                 8.132 
               
               
                 0.507 
                 0.846 
                 8.132 
               
               
                 0.487 
                 0.786 
                 8.132 
               
               
                 0.465 
                 0.722 
                 8.132 
               
               
                 0.443 
                 0.655 
                 8.132 
               
               
                 0.418 
                 0.583 
                 8.132 
               
               
                 0.391 
                 0.509 
                 8.132 
               
               
                 0.365 
                 0.435 
                 8.132 
               
               
                 0.337 
                 0.358 
                 8.132 
               
               
                 0.309 
                 0.282 
                 8.132 
               
               
                 0.280 
                 0.205 
                 8.132 
               
               
                 0.251 
                 0.129 
                 8.132 
               
               
                 0.221 
                 0.054 
                 8.132 
               
               
                 0.189 
                 −0.022 
                 8.132 
               
               
                 0.157 
                 −0.097 
                 8.132 
               
               
                 0.122 
                 −0.171 
                 8.132 
               
               
                 0.086 
                 −0.244 
                 8.132 
               
               
                 0.049 
                 −0.317 
                 8.132 
               
               
                 0.008 
                 −0.388 
                 8.132 
               
               
                 −0.037 
                 −0.457 
                 8.132 
               
               
                 −0.085 
                 −0.524 
                 8.132 
               
               
                 −0.137 
                 −0.587 
                 8.132 
               
               
                 −0.192 
                 −0.644 
                 8.132 
               
               
                 −0.254 
                 −0.695 
                 8.132 
               
               
                 −0.319 
                 −0.737 
                 8.132 
               
               
                 −0.386 
                 −0.765 
                 8.132 
               
               
                 −0.454 
                 −0.781 
                 8.132 
               
               
                 −0.518 
                 −0.784 
                 8.132 
               
               
                 −0.577 
                 −0.774 
                 8.132 
               
               
                 −0.628 
                 −0.757 
                 8.132 
               
               
                 −0.670 
                 −0.732 
                 8.132 
               
               
                 −0.703 
                 −0.706 
                 8.132 
               
               
                 −0.729 
                 −0.678 
                 8.132 
               
               
                 −0.748 
                 −0.653 
                 8.132 
               
               
                 −0.760 
                 −0.629 
                 8.132 
               
               
                 −0.768 
                 −0.609 
                 8.132 
               
               
                 −0.771 
                 −0.594 
                 8.132 
               
               
                 −0.772 
                 −0.582 
                 8.132 
               
               
                 −0.771 
                 −0.572 
                 8.132 
               
               
                 −0.770 
                 −0.565 
                 8.132 
               
               
                 −0.769 
                 −0.559 
                 8.132 
               
               
                 −0.768 
                 −0.555 
                 8.132 
               
            
           
           
               
            
               
                 Section 2 
               
            
           
           
               
               
               
            
               
                 −0.769 
                 −0.577 
                 8.329 
               
               
                 0.588 
                 1.184 
                 8.329 
               
               
                 −0.769 
                 −0.577 
                 8.329 
               
               
                 −0.768 
                 −0.575 
                 8.329 
               
               
                 −0.767 
                 −0.572 
                 8.329 
               
               
                 −0.765 
                 −0.567 
                 8.329 
               
               
                 −0.762 
                 −0.561 
                 8.329 
               
               
                 −0.758 
                 −0.554 
                 8.329 
               
               
                 −0.751 
                 −0.545 
                 8.329 
               
               
                 −0.741 
                 −0.536 
                 8.329 
               
               
                 −0.725 
                 −0.525 
                 8.329 
               
               
                 −0.705 
                 −0.515 
                 8.329 
               
               
                 −0.678 
                 −0.506 
                 8.329 
               
               
                 −0.648 
                 −0.500 
                 8.329 
               
               
                 −0.615 
                 −0.493 
                 8.329 
               
               
                 −0.582 
                 −0.479 
                 8.329 
               
               
                 −0.547 
                 −0.458 
                 8.329 
               
               
                 −0.513 
                 −0.427 
                 8.329 
               
               
                 −0.478 
                 −0.390 
                 8.329 
               
               
                 −0.442 
                 −0.348 
                 8.329 
               
               
                 −0.405 
                 −0.303 
                 8.329 
               
               
                 −0.366 
                 −0.254 
                 8.329 
               
               
                 −0.327 
                 −0.202 
                 8.329 
               
               
                 −0.288 
                 −0.150 
                 8.329 
               
               
                 −0.248 
                 −0.095 
                 8.329 
               
               
                 −0.209 
                 −0.040 
                 8.329 
               
               
                 −0.170 
                 0.015 
                 8.329 
               
               
                 −0.132 
                 0.070 
                 8.329 
               
               
                 −0.094 
                 0.126 
                 8.329 
               
               
                 −0.056 
                 0.182 
                 8.329 
               
               
                 −0.018 
                 0.238 
                 8.329 
               
               
                 0.019 
                 0.294 
                 8.329 
               
               
                 0.056 
                 0.351 
                 8.329 
               
               
                 0.093 
                 0.407 
                 8.329 
               
               
                 0.130 
                 0.464 
                 8.329 
               
               
                 0.167 
                 0.520 
                 8.329 
               
               
                 0.203 
                 0.577 
                 8.329 
               
               
                 0.240 
                 0.634 
                 8.329 
               
               
                 0.274 
                 0.689 
                 8.329 
               
               
                 0.309 
                 0.745 
                 8.329 
               
               
                 0.343 
                 0.798 
                 8.329 
               
               
                 0.373 
                 0.848 
                 8.329 
               
               
                 0.403 
                 0.895 
                 8.329 
               
               
                 0.430 
                 0.939 
                 8.329 
               
               
                 0.454 
                 0.980 
                 8.329 
               
               
                 0.476 
                 1.016 
                 8.329 
               
               
                 0.496 
                 1.049 
                 8.329 
               
               
                 0.512 
                 1.079 
                 8.329 
               
               
                 0.527 
                 1.104 
                 8.329 
               
               
                 0.539 
                 1.126 
                 8.329 
               
               
                 0.549 
                 1.144 
                 8.329 
               
               
                 0.556 
                 1.157 
                 8.329 
               
               
                 0.561 
                 1.167 
                 8.329 
               
               
                 0.566 
                 1.176 
                 8.329 
               
               
                 0.572 
                 1.181 
                 8.329 
               
               
                 0.577 
                 1.184 
                 8.329 
               
               
                 0.583 
                 1.185 
                 8.329 
               
               
                 0.586 
                 1.184 
                 8.329 
               
               
                 0.588 
                 1.184 
                 8.329 
               
               
                 0.592 
                 1.183 
                 8.329 
               
               
                 0.595 
                 1.181 
                 8.329 
               
               
                 0.600 
                 1.176 
                 8.329 
               
               
                 0.603 
                 1.170 
                 8.329 
               
               
                 0.603 
                 1.159 
                 8.329 
               
               
                 0.600 
                 1.148 
                 8.329 
               
               
                 0.597 
                 1.135 
                 8.329 
               
               
                 0.592 
                 1.117 
                 8.329 
               
               
                 0.586 
                 1.093 
                 8.329 
               
               
                 0.579 
                 1.064 
                 8.329 
               
               
                 0.570 
                 1.030 
                 8.329 
               
               
                 0.559 
                 0.991 
                 8.329 
               
               
                 0.546 
                 0.946 
                 8.329 
               
               
                 0.532 
                 0.897 
                 8.329 
               
               
                 0.516 
                 0.843 
                 8.329 
               
               
                 0.498 
                 0.783 
                 8.329 
               
               
                 0.477 
                 0.718 
                 8.329 
               
               
                 0.455 
                 0.651 
                 8.329 
               
               
                 0.431 
                 0.579 
                 8.329 
               
               
                 0.406 
                 0.504 
                 8.329 
               
               
                 0.380 
                 0.430 
                 8.329 
               
               
                 0.352 
                 0.353 
                 8.329 
               
               
                 0.324 
                 0.277 
                 8.329 
               
               
                 0.295 
                 0.201 
                 8.329 
               
               
                 0.266 
                 0.125 
                 8.329 
               
               
                 0.236 
                 0.049 
                 8.329 
               
               
                 0.204 
                 −0.026 
                 8.329 
               
               
                 0.171 
                 −0.101 
                 8.329 
               
               
                 0.137 
                 −0.175 
                 8.329 
               
               
                 0.101 
                 −0.248 
                 8.329 
               
               
                 0.063 
                 −0.321 
                 8.329 
               
               
                 0.021 
                 −0.391 
                 8.329 
               
               
                 −0.023 
                 −0.460 
                 8.329 
               
               
                 −0.071 
                 −0.526 
                 8.329 
               
               
                 −0.123 
                 −0.588 
                 8.329 
               
               
                 −0.179 
                 −0.645 
                 8.329 
               
               
                 −0.241 
                 −0.695 
                 8.329 
               
               
                 −0.306 
                 −0.736 
                 8.329 
               
               
                 −0.371 
                 −0.765 
                 8.329 
               
               
                 −0.438 
                 −0.784 
                 8.329 
               
               
                 −0.502 
                 −0.789 
                 8.329 
               
               
                 −0.561 
                 −0.784 
                 8.329 
               
               
                 −0.613 
                 −0.770 
                 8.329 
               
               
                 −0.657 
                 −0.749 
                 8.329 
               
               
                 −0.692 
                 −0.725 
                 8.329 
               
               
                 −0.719 
                 −0.701 
                 8.329 
               
               
                 −0.740 
                 −0.677 
                 8.329 
               
               
                 −0.755 
                 −0.655 
                 8.329 
               
               
                 −0.764 
                 −0.635 
                 8.329 
               
               
                 −0.769 
                 −0.620 
                 8.329 
               
               
                 −0.771 
                 −0.607 
                 8.329 
               
               
                 −0.771 
                 −0.597 
                 8.329 
               
               
                 −0.771 
                 −0.591 
                 8.329 
               
               
                 −0.770 
                 −0.584 
                 8.329 
               
               
                 −0.769 
                 −0.581 
                 8.329 
               
            
           
           
               
            
               
                 Section 3 
               
            
           
           
               
               
               
            
               
                 −0.770 
                 −0.594 
                 8.526 
               
               
                 0.589 
                 1.183 
                 8.526 
               
               
                 −0.770 
                 −0.594 
                 8.526 
               
               
                 −0.769 
                 −0.592 
                 8.526 
               
               
                 −0.768 
                 −0.589 
                 8.526 
               
               
                 −0.766 
                 −0.583 
                 8.526 
               
               
                 −0.764 
                 −0.578 
                 8.526 
               
               
                 −0.760 
                 −0.571 
                 8.526 
               
               
                 −0.754 
                 −0.562 
                 8.526 
               
               
                 −0.744 
                 −0.552 
                 8.526 
               
               
                 −0.730 
                 −0.540 
                 8.526 
               
               
                 −0.710 
                 −0.529 
                 8.526 
               
               
                 −0.684 
                 −0.519 
                 8.526 
               
               
                 −0.655 
                 −0.511 
                 8.526 
               
               
                 −0.624 
                 −0.502 
                 8.526 
               
               
                 −0.592 
                 −0.486 
                 8.526 
               
               
                 −0.557 
                 −0.463 
                 8.526 
               
               
                 −0.522 
                 −0.433 
                 8.526 
               
               
                 −0.485 
                 −0.397 
                 8.526 
               
               
                 −0.447 
                 −0.356 
                 8.526 
               
               
                 −0.408 
                 −0.312 
                 8.526 
               
               
                 −0.368 
                 −0.264 
                 8.526 
               
               
                 −0.327 
                 −0.213 
                 8.526 
               
               
                 −0.287 
                 −0.161 
                 8.526 
               
               
                 −0.246 
                 −0.107 
                 8.526 
               
               
                 −0.206 
                 −0.053 
                 8.526 
               
               
                 −0.166 
                 0.002 
                 8.526 
               
               
                 −0.127 
                 0.058 
                 8.526 
               
               
                 −0.088 
                 0.113 
                 8.526 
               
               
                 −0.049 
                 0.169 
                 8.526 
               
               
                 −0.011 
                 0.225 
                 8.526 
               
               
                 0.027 
                 0.282 
                 8.526 
               
               
                 0.064 
                 0.338 
                 8.526 
               
               
                 0.102 
                 0.395 
                 8.526 
               
               
                 0.139 
                 0.452 
                 8.526 
               
               
                 0.175 
                 0.509 
                 8.526 
               
               
                 0.212 
                 0.566 
                 8.526 
               
               
                 0.248 
                 0.623 
                 8.526 
               
               
                 0.283 
                 0.679 
                 8.526 
               
               
                 0.317 
                 0.735 
                 8.526 
               
               
                 0.350 
                 0.789 
                 8.526 
               
               
                 0.380 
                 0.839 
                 8.526 
               
               
                 0.409 
                 0.887 
                 8.526 
               
               
                 0.436 
                 0.932 
                 8.526 
               
               
                 0.459 
                 0.973 
                 8.526 
               
               
                 0.481 
                 1.011 
                 8.526 
               
               
                 0.500 
                 1.044 
                 8.526 
               
               
                 0.516 
                 1.074 
                 8.526 
               
               
                 0.530 
                 1.100 
                 8.526 
               
               
                 0.541 
                 1.123 
                 8.526 
               
               
                 0.551 
                 1.141 
                 8.526 
               
               
                 0.558 
                 1.155 
                 8.526 
               
               
                 0.563 
                 1.165 
                 8.526 
               
               
                 0.567 
                 1.174 
                 8.526 
               
               
                 0.572 
                 1.180 
                 8.526 
               
               
                 0.577 
                 1.183 
                 8.526 
               
               
                 0.583 
                 1.184 
                 8.526 
               
               
                 0.586 
                 1.184 
                 8.526 
               
               
                 0.589 
                 1.183 
                 8.526 
               
               
                 0.592 
                 1.182 
                 8.526 
               
               
                 0.595 
                 1.181 
                 8.526 
               
               
                 0.600 
                 1.176 
                 8.526 
               
               
                 0.603 
                 1.170 
                 8.526 
               
               
                 0.604 
                 1.160 
                 8.526 
               
               
                 0.602 
                 1.149 
                 8.526 
               
               
                 0.599 
                 1.136 
                 8.526 
               
               
                 0.595 
                 1.117 
                 8.526 
               
               
                 0.590 
                 1.093 
                 8.526 
               
               
                 0.583 
                 1.064 
                 8.526 
               
               
                 0.576 
                 1.030 
                 8.526 
               
               
                 0.566 
                 0.990 
                 8.526 
               
               
                 0.556 
                 0.946 
                 8.526 
               
               
                 0.543 
                 0.897 
                 8.526 
               
               
                 0.529 
                 0.842 
                 8.526 
               
               
                 0.513 
                 0.782 
                 8.526 
               
               
                 0.494 
                 0.717 
                 8.526 
               
               
                 0.475 
                 0.649 
                 8.526 
               
               
                 0.452 
                 0.577 
                 8.526 
               
               
                 0.428 
                 0.503 
                 8.526 
               
               
                 0.403 
                 0.428 
                 8.526 
               
               
                 0.377 
                 0.352 
                 8.526 
               
               
                 0.349 
                 0.276 
                 8.526 
               
               
                 0.320 
                 0.200 
                 8.526 
               
               
                 0.291 
                 0.125 
                 8.526 
               
               
                 0.260 
                 0.050 
                 8.526 
               
               
                 0.228 
                 −0.025 
                 8.526 
               
               
                 0.195 
                 −0.099 
                 8.526 
               
               
                 0.160 
                 −0.172 
                 8.526 
               
               
                 0.123 
                 −0.244 
                 8.526 
               
               
                 0.084 
                 −0.315 
                 8.526 
               
               
                 0.042 
                 −0.384 
                 8.526 
               
               
                 −0.002 
                 −0.452 
                 8.526 
               
               
                 −0.051 
                 −0.517 
                 8.526 
               
               
                 −0.104 
                 −0.580 
                 8.526 
               
               
                 −0.161 
                 −0.636 
                 8.526 
               
               
                 −0.223 
                 −0.686 
                 8.526 
               
               
                 −0.289 
                 −0.727 
                 8.526 
               
               
                 −0.354 
                 −0.757 
                 8.526 
               
               
                 −0.421 
                 −0.777 
                 8.526 
               
               
                 −0.485 
                 −0.787 
                 8.526 
               
               
                 −0.545 
                 −0.786 
                 8.526 
               
               
                 −0.598 
                 −0.776 
                 8.526 
               
               
                 −0.643 
                 −0.758 
                 8.526 
               
               
                 −0.681 
                 −0.737 
                 8.526 
               
               
                 −0.710 
                 −0.714 
                 8.526 
               
               
                 −0.733 
                 −0.692 
                 8.526 
               
               
                 −0.750 
                 −0.671 
                 8.526 
               
               
                 −0.761 
                 −0.652 
                 8.526 
               
               
                 −0.767 
                 −0.638 
                 8.526 
               
               
                 −0.770 
                 −0.625 
                 8.526 
               
               
                 −0.771 
                 −0.615 
                 8.526 
               
               
                 −0.771 
                 −0.608 
                 8.526 
               
               
                 −0.771 
                 −0.601 
                 8.526 
               
               
                 −0.770 
                 −0.598 
                 8.526 
               
            
           
           
               
            
               
                 Section 4 
               
            
           
           
               
               
               
            
               
                 −0.770 
                 −0.602 
                 8.723 
               
               
                 0.589 
                 1.182 
                 8.723 
               
               
                 −0.770 
                 −0.602 
                 8.723 
               
               
                 −0.770 
                 −0.599 
                 8.723 
               
               
                 −0.769 
                 −0.596 
                 8.723 
               
               
                 −0.767 
                 −0.591 
                 8.723 
               
               
                 −0.765 
                 −0.586 
                 8.723 
               
               
                 −0.762 
                 −0.578 
                 8.723 
               
               
                 −0.756 
                 −0.569 
                 8.723 
               
               
                 −0.747 
                 −0.559 
                 8.723 
               
               
                 −0.733 
                 −0.547 
                 8.723 
               
               
                 −0.714 
                 −0.535 
                 8.723 
               
               
                 −0.689 
                 −0.524 
                 8.723 
               
               
                 −0.660 
                 −0.515 
                 8.723 
               
               
                 −0.630 
                 −0.504 
                 8.723 
               
               
                 −0.598 
                 −0.486 
                 8.723 
               
               
                 −0.563 
                 −0.462 
                 8.723 
               
               
                 −0.526 
                 −0.434 
                 8.723 
               
               
                 −0.488 
                 −0.399 
                 8.723 
               
               
                 −0.447 
                 −0.360 
                 8.723 
               
               
                 −0.407 
                 −0.318 
                 8.723 
               
               
                 −0.365 
                 −0.271 
                 8.723 
               
               
                 −0.323 
                 −0.221 
                 8.723 
               
               
                 −0.281 
                 −0.170 
                 8.723 
               
               
                 −0.239 
                 −0.116 
                 8.723 
               
               
                 −0.198 
                 −0.062 
                 8.723 
               
               
                 −0.158 
                 −0.008 
                 8.723 
               
               
                 −0.118 
                 0.048 
                 8.723 
               
               
                 −0.079 
                 0.103 
                 8.723 
               
               
                 −0.040 
                 0.159 
                 8.723 
               
               
                 −0.001 
                 0.215 
                 8.723 
               
               
                 0.037 
                 0.272 
                 8.723 
               
               
                 0.074 
                 0.329 
                 8.723 
               
               
                 0.111 
                 0.386 
                 8.723 
               
               
                 0.148 
                 0.443 
                 8.723 
               
               
                 0.185 
                 0.500 
                 8.723 
               
               
                 0.221 
                 0.558 
                 8.723 
               
               
                 0.256 
                 0.616 
                 8.723 
               
               
                 0.291 
                 0.672 
                 8.723 
               
               
                 0.325 
                 0.729 
                 8.723 
               
               
                 0.357 
                 0.783 
                 8.723 
               
               
                 0.387 
                 0.834 
                 8.723 
               
               
                 0.415 
                 0.883 
                 8.723 
               
               
                 0.441 
                 0.928 
                 8.723 
               
               
                 0.464 
                 0.970 
                 8.723 
               
               
                 0.485 
                 1.007 
                 8.723 
               
               
                 0.503 
                 1.041 
                 8.723 
               
               
                 0.519 
                 1.072 
                 8.723 
               
               
                 0.532 
                 1.098 
                 8.723 
               
               
                 0.543 
                 1.121 
                 8.723 
               
               
                 0.552 
                 1.139 
                 8.723 
               
               
                 0.559 
                 1.153 
                 8.723 
               
               
                 0.564 
                 1.163 
                 8.723 
               
               
                 0.568 
                 1.172 
                 8.723 
               
               
                 0.573 
                 1.178 
                 8.723 
               
               
                 0.578 
                 1.181 
                 8.723 
               
               
                 0.583 
                 1.183 
                 8.723 
               
               
                 0.586 
                 1.183 
                 8.723 
               
               
                 0.589 
                 1.182 
                 8.723 
               
               
                 0.592 
                 1.181 
                 8.723 
               
               
                 0.596 
                 1.180 
                 8.723 
               
               
                 0.601 
                 1.175 
                 8.723 
               
               
                 0.604 
                 1.169 
                 8.723 
               
               
                 0.605 
                 1.159 
                 8.723 
               
               
                 0.603 
                 1.148 
                 8.723 
               
               
                 0.600 
                 1.135 
                 8.723 
               
               
                 0.597 
                 1.116 
                 8.723 
               
               
                 0.592 
                 1.092 
                 8.723 
               
               
                 0.586 
                 1.063 
                 8.723 
               
               
                 0.579 
                 1.029 
                 8.723 
               
               
                 0.571 
                 0.989 
                 8.723 
               
               
                 0.562 
                 0.944 
                 8.723 
               
               
                 0.551 
                 0.894 
                 8.723 
               
               
                 0.538 
                 0.839 
                 8.723 
               
               
                 0.523 
                 0.778 
                 8.723 
               
               
                 0.507 
                 0.712 
                 8.723 
               
               
                 0.489 
                 0.644 
                 8.723 
               
               
                 0.468 
                 0.571 
                 8.723 
               
               
                 0.446 
                 0.496 
                 8.723 
               
               
                 0.422 
                 0.421 
                 8.723 
               
               
                 0.396 
                 0.344 
                 8.723 
               
               
                 0.369 
                 0.267 
                 8.723 
               
               
                 0.340 
                 0.191 
                 8.723 
               
               
                 0.310 
                 0.116 
                 8.723 
               
               
                 0.279 
                 0.040 
                 8.723 
               
               
                 0.246 
                 −0.034 
                 8.723 
               
               
                 0.212 
                 −0.108 
                 8.723 
               
               
                 0.176 
                 −0.181 
                 8.723 
               
               
                 0.138 
                 −0.253 
                 8.723 
               
               
                 0.097 
                 −0.323 
                 8.723 
               
               
                 0.052 
                 −0.391 
                 8.723 
               
               
                 0.006 
                 −0.459 
                 8.723 
               
               
                 −0.044 
                 −0.523 
                 8.723 
               
               
                 −0.100 
                 −0.584 
                 8.723 
               
               
                 −0.158 
                 −0.637 
                 8.723 
               
               
                 −0.221 
                 −0.685 
                 8.723 
               
               
                 −0.288 
                 −0.724 
                 8.723 
               
               
                 −0.353 
                 −0.753 
                 8.723 
               
               
                 −0.419 
                 −0.772 
                 8.723 
               
               
                 −0.482 
                 −0.782 
                 8.723 
               
               
                 −0.541 
                 −0.783 
                 8.723 
               
               
                 −0.594 
                 −0.774 
                 8.723 
               
               
                 −0.639 
                 −0.758 
                 8.723 
               
               
                 −0.677 
                 −0.738 
                 8.723 
               
               
                 −0.707 
                 −0.717 
                 8.723 
               
               
                 −0.731 
                 −0.696 
                 8.723 
               
               
                 −0.748 
                 −0.676 
                 8.723 
               
               
                 −0.760 
                 −0.658 
                 8.723 
               
               
                 −0.766 
                 −0.644 
                 8.723 
               
               
                 −0.769 
                 −0.632 
                 8.723 
               
               
                 −0.771 
                 −0.622 
                 8.723 
               
               
                 −0.771 
                 −0.616 
                 8.723 
               
               
                 −0.771 
                 −0.609 
                 8.723 
               
               
                 −0.771 
                 −0.605 
                 8.723 
               
            
           
           
               
            
               
                 Section 5 
               
            
           
           
               
               
               
            
               
                 −0.771 
                 −0.600 
                 8.920 
               
               
                 0.590 
                 1.181 
                 8.920 
               
               
                 −0.771 
                 −0.600 
                 8.920 
               
               
                 −0.770 
                 −0.598 
                 8.920 
               
               
                 −0.769 
                 −0.595 
                 8.920 
               
               
                 −0.768 
                 −0.589 
                 8.920 
               
               
                 −0.766 
                 −0.584 
                 8.920 
               
               
                 −0.762 
                 −0.576 
                 8.920 
               
               
                 −0.757 
                 −0.567 
                 8.920 
               
               
                 −0.748 
                 −0.556 
                 8.920 
               
               
                 −0.734 
                 −0.543 
                 8.920 
               
               
                 −0.715 
                 −0.531 
                 8.920 
               
               
                 −0.690 
                 −0.519 
                 8.920 
               
               
                 −0.661 
                 −0.509 
                 8.920 
               
               
                 −0.630 
                 −0.498 
                 8.920 
               
               
                 −0.597 
                 −0.481 
                 8.920 
               
               
                 −0.562 
                 −0.459 
                 8.920 
               
               
                 −0.524 
                 −0.431 
                 8.920 
               
               
                 −0.484 
                 −0.399 
                 8.920 
               
               
                 −0.443 
                 −0.361 
                 8.920 
               
               
                 −0.401 
                 −0.320 
                 8.920 
               
               
                 −0.358 
                 −0.274 
                 8.920 
               
               
                 −0.315 
                 −0.224 
                 8.920 
               
               
                 −0.273 
                 −0.174 
                 8.920 
               
               
                 −0.231 
                 −0.121 
                 8.920 
               
               
                 −0.189 
                 −0.067 
                 8.920 
               
               
                 −0.149 
                 −0.013 
                 8.920 
               
               
                 −0.109 
                 0.042 
                 8.920 
               
               
                 −0.070 
                 0.097 
                 8.920 
               
               
                 −0.031 
                 0.153 
                 8.920 
               
               
                 0.007 
                 0.210 
                 8.920 
               
               
                 0.044 
                 0.266 
                 8.920 
               
               
                 0.081 
                 0.323 
                 8.920 
               
               
                 0.118 
                 0.381 
                 8.920 
               
               
                 0.154 
                 0.438 
                 8.920 
               
               
                 0.190 
                 0.496 
                 8.920 
               
               
                 0.225 
                 0.554 
                 8.920 
               
               
                 0.261 
                 0.612 
                 8.920 
               
               
                 0.294 
                 0.669 
                 8.920 
               
               
                 0.327 
                 0.725 
                 8.920 
               
               
                 0.359 
                 0.780 
                 8.920 
               
               
                 0.388 
                 0.832 
                 8.920 
               
               
                 0.416 
                 0.881 
                 8.920 
               
               
                 0.441 
                 0.926 
                 8.920 
               
               
                 0.464 
                 0.968 
                 8.920 
               
               
                 0.485 
                 1.006 
                 8.920 
               
               
                 0.503 
                 1.040 
                 8.920 
               
               
                 0.519 
                 1.070 
                 8.920 
               
               
                 0.532 
                 1.097 
                 8.920 
               
               
                 0.543 
                 1.119 
                 8.920 
               
               
                 0.552 
                 1.137 
                 8.920 
               
               
                 0.559 
                 1.152 
                 8.920 
               
               
                 0.564 
                 1.162 
                 8.920 
               
               
                 0.568 
                 1.171 
                 8.920 
               
               
                 0.573 
                 1.177 
                 8.920 
               
               
                 0.578 
                 1.180 
                 8.920 
               
               
                 0.584 
                 1.181 
                 8.920 
               
               
                 0.587 
                 1.181 
                 8.920 
               
               
                 0.590 
                 1.181 
                 8.920 
               
               
                 0.593 
                 1.180 
                 8.920 
               
               
                 0.596 
                 1.178 
                 8.920 
               
               
                 0.601 
                 1.174 
                 8.920 
               
               
                 0.605 
                 1.167 
                 8.920 
               
               
                 0.605 
                 1.157 
                 8.920 
               
               
                 0.603 
                 1.146 
                 8.920 
               
               
                 0.600 
                 1.133 
                 8.920 
               
               
                 0.597 
                 1.114 
                 8.920 
               
               
                 0.592 
                 1.091 
                 8.920 
               
               
                 0.586 
                 1.062 
                 8.920 
               
               
                 0.579 
                 1.027 
                 8.920 
               
               
                 0.571 
                 0.987 
                 8.920 
               
               
                 0.562 
                 0.943 
                 8.920 
               
               
                 0.551 
                 0.893 
                 8.920 
               
               
                 0.539 
                 0.837 
                 8.920 
               
               
                 0.526 
                 0.777 
                 8.920 
               
               
                 0.510 
                 0.711 
                 8.920 
               
               
                 0.493 
                 0.642 
                 8.920 
               
               
                 0.474 
                 0.569 
                 8.920 
               
               
                 0.453 
                 0.494 
                 8.920 
               
               
                 0.431 
                 0.418 
                 8.920 
               
               
                 0.407 
                 0.341 
                 8.920 
               
               
                 0.381 
                 0.264 
                 8.920 
               
               
                 0.353 
                 0.188 
                 8.920 
               
               
                 0.324 
                 0.112 
                 8.920 
               
               
                 0.293 
                 0.038 
                 8.920 
               
               
                 0.261 
                 −0.036 
                 8.920 
               
               
                 0.226 
                 −0.109 
                 8.920 
               
               
                 0.190 
                 −0.182 
                 8.920 
               
               
                 0.151 
                 −0.253 
                 8.920 
               
               
                 0.110 
                 −0.323 
                 8.920 
               
               
                 0.064 
                 −0.391 
                 8.920 
               
               
                 0.016 
                 −0.457 
                 8.920 
               
               
                 −0.034 
                 −0.521 
                 8.920 
               
               
                 −0.090 
                 −0.580 
                 8.920 
               
               
                 −0.149 
                 −0.634 
                 8.920 
               
               
                 −0.213 
                 −0.682 
                 8.920 
               
               
                 −0.280 
                 −0.721 
                 8.920 
               
               
                 −0.346 
                 −0.750 
                 8.920 
               
               
                 −0.412 
                 −0.770 
                 8.920 
               
               
                 −0.476 
                 −0.780 
                 8.920 
               
               
                 −0.536 
                 −0.781 
                 8.920 
               
               
                 −0.589 
                 −0.772 
                 8.920 
               
               
                 −0.635 
                 −0.757 
                 8.920 
               
               
                 −0.673 
                 −0.738 
                 8.920 
               
               
                 −0.704 
                 −0.717 
                 8.920 
               
               
                 −0.729 
                 −0.696 
                 8.920 
               
               
                 −0.746 
                 −0.676 
                 8.920 
               
               
                 −0.758 
                 −0.658 
                 8.920 
               
               
                 −0.765 
                 −0.643 
                 8.920 
               
               
                 −0.769 
                 −0.631 
                 8.920 
               
               
                 −0.771 
                 −0.621 
                 8.920 
               
               
                 −0.771 
                 −0.614 
                 8.920 
               
               
                 −0.771 
                 −0.607 
                 8.920 
               
               
                 −0.771 
                 −0.604 
                 8.920 
               
            
           
           
               
            
               
                 Section 6 
               
            
           
           
               
               
               
            
               
                 −0.770 
                 −0.592 
                 9.117 
               
               
                 0.591 
                 1.179 
                 9.117 
               
               
                 −0.770 
                 −0.592 
                 9.117 
               
               
                 −0.770 
                 −0.589 
                 9.117 
               
               
                 −0.769 
                 −0.586 
                 9.117 
               
               
                 −0.768 
                 −0.581 
                 9.117 
               
               
                 −0.766 
                 −0.575 
                 9.117 
               
               
                 −0.763 
                 −0.568 
                 9.117 
               
               
                 −0.757 
                 −0.558 
                 9.117 
               
               
                 −0.749 
                 −0.547 
                 9.117 
               
               
                 −0.736 
                 −0.535 
                 9.117 
               
               
                 −0.717 
                 −0.522 
                 9.117 
               
               
                 −0.693 
                 −0.510 
                 9.117 
               
               
                 −0.664 
                 −0.499 
                 9.117 
               
               
                 −0.632 
                 −0.489 
                 9.117 
               
               
                 −0.598 
                 −0.475 
                 9.117 
               
               
                 −0.561 
                 −0.455 
                 9.117 
               
               
                 −0.522 
                 −0.430 
                 9.117 
               
               
                 −0.481 
                 −0.399 
                 9.117 
               
               
                 −0.439 
                 −0.362 
                 9.117 
               
               
                 −0.397 
                 −0.322 
                 9.117 
               
               
                 −0.353 
                 −0.276 
                 9.117 
               
               
                 −0.310 
                 −0.228 
                 9.117 
               
               
                 −0.268 
                 −0.178 
                 9.117 
               
               
                 −0.225 
                 −0.125 
                 9.117 
               
               
                 −0.184 
                 −0.071 
                 9.117 
               
               
                 −0.144 
                 −0.017 
                 9.117 
               
               
                 −0.104 
                 0.039 
                 9.117 
               
               
                 −0.065 
                 0.094 
                 9.117 
               
               
                 −0.027 
                 0.150 
                 9.117 
               
               
                 0.011 
                 0.207 
                 9.117 
               
               
                 0.048 
                 0.264 
                 9.117 
               
               
                 0.084 
                 0.321 
                 9.117 
               
               
                 0.120 
                 0.379 
                 9.117 
               
               
                 0.156 
                 0.437 
                 9.117 
               
               
                 0.191 
                 0.495 
                 9.117 
               
               
                 0.226 
                 0.553 
                 9.117 
               
               
                 0.261 
                 0.612 
                 9.117 
               
               
                 0.294 
                 0.669 
                 9.117 
               
               
                 0.327 
                 0.726 
                 9.117 
               
               
                 0.358 
                 0.781 
                 9.117 
               
               
                 0.387 
                 0.832 
                 9.117 
               
               
                 0.415 
                 0.881 
                 9.117 
               
               
                 0.440 
                 0.927 
                 9.117 
               
               
                 0.462 
                 0.969 
                 9.117 
               
               
                 0.483 
                 1.007 
                 9.117 
               
               
                 0.501 
                 1.041 
                 9.117 
               
               
                 0.517 
                 1.071 
                 9.117 
               
               
                 0.531 
                 1.097 
                 9.117 
               
               
                 0.542 
                 1.119 
                 9.117 
               
               
                 0.552 
                 1.138 
                 9.117 
               
               
                 0.559 
                 1.152 
                 9.117 
               
               
                 0.564 
                 1.162 
                 9.117 
               
               
                 0.569 
                 1.170 
                 9.117 
               
               
                 0.574 
                 1.176 
                 9.117 
               
               
                 0.579 
                 1.179 
                 9.117 
               
               
                 0.585 
                 1.180 
                 9.117 
               
               
                 0.588 
                 1.180 
                 9.117 
               
               
                 0.591 
                 1.179 
                 9.117 
               
               
                 0.594 
                 1.178 
                 9.117 
               
               
                 0.597 
                 1.177 
                 9.117 
               
               
                 0.602 
                 1.172 
                 9.117 
               
               
                 0.605 
                 1.166 
                 9.117 
               
               
                 0.606 
                 1.155 
                 9.117 
               
               
                 0.603 
                 1.144 
                 9.117 
               
               
                 0.600 
                 1.131 
                 9.117 
               
               
                 0.596 
                 1.113 
                 9.117 
               
               
                 0.590 
                 1.089 
                 9.117 
               
               
                 0.584 
                 1.059 
                 9.117 
               
               
                 0.577 
                 1.025 
                 9.117 
               
               
                 0.568 
                 0.985 
                 9.117 
               
               
                 0.558 
                 0.940 
                 9.117 
               
               
                 0.547 
                 0.890 
                 9.117 
               
               
                 0.535 
                 0.834 
                 9.117 
               
               
                 0.522 
                 0.773 
                 9.117 
               
               
                 0.507 
                 0.707 
                 9.117 
               
               
                 0.491 
                 0.638 
                 9.117 
               
               
                 0.472 
                 0.564 
                 9.117 
               
               
                 0.452 
                 0.488 
                 9.117 
               
               
                 0.431 
                 0.412 
                 9.117 
               
               
                 0.408 
                 0.333 
                 9.117 
               
               
                 0.383 
                 0.255 
                 9.117 
               
               
                 0.356 
                 0.178 
                 9.117 
               
               
                 0.328 
                 0.102 
                 9.117 
               
               
                 0.297 
                 0.026 
                 9.117 
               
               
                 0.265 
                 −0.049 
                 9.117 
               
               
                 0.230 
                 −0.123 
                 9.117 
               
               
                 0.193 
                 −0.196 
                 9.117 
               
               
                 0.153 
                 −0.267 
                 9.117 
               
               
                 0.111 
                 −0.337 
                 9.117 
               
               
                 0.063 
                 −0.404 
                 9.117 
               
               
                 0.015 
                 −0.469 
                 9.117 
               
               
                 −0.037 
                 −0.533 
                 9.117 
               
               
                 −0.094 
                 −0.592 
                 9.117 
               
               
                 −0.154 
                 −0.644 
                 9.117 
               
               
                 −0.219 
                 −0.690 
                 9.117 
               
               
                 −0.286 
                 −0.727 
                 9.117 
               
               
                 −0.352 
                 −0.754 
                 9.117 
               
               
                 −0.419 
                 −0.772 
                 9.117 
               
               
                 −0.483 
                 −0.779 
                 9.117 
               
               
                 −0.541 
                 −0.778 
                 9.117 
               
               
                 −0.594 
                 −0.767 
                 9.117 
               
               
                 −0.639 
                 −0.751 
                 9.117 
               
               
                 −0.677 
                 −0.730 
                 9.117 
               
               
                 −0.707 
                 −0.709 
                 9.117 
               
               
                 −0.731 
                 −0.687 
                 9.117 
               
               
                 −0.748 
                 −0.667 
                 9.117 
               
               
                 −0.759 
                 −0.648 
                 9.117 
               
               
                 −0.766 
                 −0.634 
                 9.117 
               
               
                 −0.769 
                 −0.622 
                 9.117 
               
               
                 −0.771 
                 −0.612 
                 9.117 
               
               
                 −0.771 
                 −0.605 
                 9.117 
               
               
                 −0.771 
                 −0.598 
                 9.117 
               
               
                 −0.771 
                 −0.595 
                 9.117 
               
            
           
           
               
            
               
                 Section 7 
               
            
           
           
               
               
               
            
               
                 −0.770 
                 −0.577 
                 9.314 
               
               
                 0.591 
                 1.180 
                 9.314 
               
               
                 −0.770 
                 −0.577 
                 9.314 
               
               
                 −0.769 
                 −0.574 
                 9.314 
               
               
                 −0.769 
                 −0.571 
                 9.314 
               
               
                 −0.767 
                 −0.566 
                 9.314 
               
               
                 −0.765 
                 −0.561 
                 9.314 
               
               
                 −0.762 
                 −0.553 
                 9.314 
               
               
                 −0.756 
                 −0.544 
                 9.314 
               
               
                 −0.748 
                 −0.534 
                 9.314 
               
               
                 −0.735 
                 −0.521 
                 9.314 
               
               
                 −0.716 
                 −0.508 
                 9.314 
               
               
                 −0.692 
                 −0.496 
                 9.314 
               
               
                 −0.663 
                 −0.486 
                 9.314 
               
               
                 −0.629 
                 −0.477 
                 9.314 
               
               
                 −0.594 
                 −0.466 
                 9.314 
               
               
                 −0.558 
                 −0.448 
                 9.314 
               
               
                 −0.518 
                 −0.424 
                 9.314 
               
               
                 −0.477 
                 −0.394 
                 9.314 
               
               
                 −0.435 
                 −0.358 
                 9.314 
               
               
                 −0.393 
                 −0.318 
                 9.314 
               
               
                 −0.349 
                 −0.272 
                 9.314 
               
               
                 −0.305 
                 −0.224 
                 9.314 
               
               
                 −0.263 
                 −0.174 
                 9.314 
               
               
                 −0.221 
                 −0.121 
                 9.314 
               
               
                 −0.180 
                 −0.068 
                 9.314 
               
               
                 −0.140 
                 −0.013 
                 9.314 
               
               
                 −0.101 
                 0.042 
                 9.314 
               
               
                 −0.062 
                 0.098 
                 9.314 
               
               
                 −0.024 
                 0.154 
                 9.314 
               
               
                 0.013 
                 0.210 
                 9.314 
               
               
                 0.050 
                 0.267 
                 9.314 
               
               
                 0.086 
                 0.325 
                 9.314 
               
               
                 0.122 
                 0.382 
                 9.314 
               
               
                 0.157 
                 0.440 
                 9.314 
               
               
                 0.192 
                 0.498 
                 9.314 
               
               
                 0.227 
                 0.557 
                 9.314 
               
               
                 0.261 
                 0.615 
                 9.314 
               
               
                 0.293 
                 0.672 
                 9.314 
               
               
                 0.326 
                 0.729 
                 9.314 
               
               
                 0.357 
                 0.784 
                 9.314 
               
               
                 0.386 
                 0.836 
                 9.314 
               
               
                 0.413 
                 0.885 
                 9.314 
               
               
                 0.438 
                 0.930 
                 9.314 
               
               
                 0.461 
                 0.972 
                 9.314 
               
               
                 0.482 
                 1.010 
                 9.314 
               
               
                 0.500 
                 1.044 
                 9.314 
               
               
                 0.516 
                 1.074 
                 9.314 
               
               
                 0.530 
                 1.100 
                 9.314 
               
               
                 0.542 
                 1.122 
                 9.314 
               
               
                 0.551 
                 1.140 
                 9.314 
               
               
                 0.559 
                 1.153 
                 9.314 
               
               
                 0.564 
                 1.163 
                 9.314 
               
               
                 0.569 
                 1.172 
                 9.314 
               
               
                 0.575 
                 1.178 
                 9.314 
               
               
                 0.580 
                 1.180 
                 9.314 
               
               
                 0.586 
                 1.181 
                 9.314 
               
               
                 0.588 
                 1.181 
                 9.314 
               
               
                 0.591 
                 1.180 
                 9.314 
               
               
                 0.595 
                 1.179 
                 9.314 
               
               
                 0.598 
                 1.177 
                 9.314 
               
               
                 0.602 
                 1.172 
                 9.314 
               
               
                 0.605 
                 1.165 
                 9.314 
               
               
                 0.605 
                 1.155 
                 9.314 
               
               
                 0.603 
                 1.144 
                 9.314 
               
               
                 0.599 
                 1.131 
                 9.314 
               
               
                 0.595 
                 1.113 
                 9.314 
               
               
                 0.589 
                 1.089 
                 9.314 
               
               
                 0.582 
                 1.060 
                 9.314 
               
               
                 0.574 
                 1.025 
                 9.314 
               
               
                 0.565 
                 0.985 
                 9.314 
               
               
                 0.555 
                 0.940 
                 9.314 
               
               
                 0.544 
                 0.890 
                 9.314 
               
               
                 0.532 
                 0.834 
                 9.314 
               
               
                 0.518 
                 0.773 
                 9.314 
               
               
                 0.504 
                 0.706 
                 9.314 
               
               
                 0.488 
                 0.637 
                 9.314 
               
               
                 0.470 
                 0.563 
                 9.314 
               
               
                 0.451 
                 0.486 
                 9.314 
               
               
                 0.431 
                 0.409 
                 9.314 
               
               
                 0.409 
                 0.330 
                 9.314 
               
               
                 0.385 
                 0.252 
                 9.314 
               
               
                 0.360 
                 0.174 
                 9.314 
               
               
                 0.332 
                 0.096 
                 9.314 
               
               
                 0.303 
                 0.020 
                 9.314 
               
               
                 0.271 
                 −0.056 
                 9.314 
               
               
                 0.236 
                 −0.131 
                 9.314 
               
               
                 0.199 
                 −0.204 
                 9.314 
               
               
                 0.159 
                 −0.276 
                 9.314 
               
               
                 0.116 
                 −0.346 
                 9.314 
               
               
                 0.067 
                 −0.413 
                 9.314 
               
               
                 0.017 
                 −0.478 
                 9.314 
               
               
                 −0.036 
                 −0.542 
                 9.314 
               
               
                 −0.094 
                 −0.600 
                 9.314 
               
               
                 −0.155 
                 −0.651 
                 9.314 
               
               
                 −0.221 
                 −0.697 
                 9.314 
               
               
                 −0.290 
                 −0.733 
                 9.314 
               
               
                 −0.358 
                 −0.758 
                 9.314 
               
               
                 −0.426 
                 −0.773 
                 9.314 
               
               
                 −0.490 
                 −0.777 
                 9.314 
               
               
                 −0.549 
                 −0.772 
                 9.314 
               
               
                 −0.601 
                 −0.759 
                 9.314 
               
               
                 −0.646 
                 −0.740 
                 9.314 
               
               
                 −0.683 
                 −0.718 
                 9.314 
               
               
                 −0.712 
                 −0.696 
                 9.314 
               
               
                 −0.735 
                 −0.673 
                 9.314 
               
               
                 −0.751 
                 −0.652 
                 9.314 
               
               
                 −0.761 
                 −0.634 
                 9.314 
               
               
                 −0.767 
                 −0.619 
                 9.314 
               
               
                 −0.770 
                 −0.606 
                 9.314 
               
               
                 −0.771 
                 −0.597 
                 9.314 
               
               
                 −0.771 
                 −0.590 
                 9.314 
               
               
                 −0.771 
                 −0.583 
                 9.314 
               
               
                 −0.770 
                 −0.580 
                 9.314 
               
               
                   
               
            
           
         
       
     
     It should be understood that the finished second stage HPT vane  40   b  does not necessarily include all the sections defined in Table 2. The portion of the airfoil  54  proximal to the platforms  60  and  62  may not be defined by a profile section  66 . It should be considered that the vane  40   b  airfoil profile proximal to the platforms  60  and  62  may vary due to several imposed constraints. However, the HPT vane  40   a  has an intermediate airfoil portion  64  defined between the inner and outer vane platforms  60  and  62  thereof and which has a profile defined on the basis of at least the intermediate sections of the various vane profile sections  66  defined in Table 2. 
     It should be appreciated that the intermediate airfoil portion  64  of the HPT stage vane  40   b  is defined between the inner and outer gaspath walls  28  and  30  which are partially defined by the inner and outer vane platforms  60  and  62 . More specifically, the Z values defining the gaspath  27  in the region of the stacking line  48  fall within the range of about 7.79 to about 9.67 which generally correspond to the z values around the stacking line  48  (X=0). The airfoil profile physically appearing on HPT vane  40   b  and fully contained in the gaspath may include Sections 1 to 7 of Table 2. The skilled reader will appreciate that a suitable fillet radius is to be applied between the platforms  60  and  62  and the airfoil portion of the vane. The vane inner diameter and outside diameter endwall fillets are in the range of about 0.0805″ to about 0.135″. 
       FIGS. 4   a  and  4   b  illustrate the tolerances on twist and restagger angles. The twist “N” is an angular variation at each vane section, whereas restagger is the angular reposition of the entire airfoil. Both the twist and the restagger angles are about the stacking line  48 . The section twist “N” (section restagger) tolerance with respect to the stacking line is +/−0.75 degrees. The global restagger capability for the airfoil with respect to the stacking line is +/−2.0 degrees. 
     The above description is meant to be exemplary only, and one skilled in the art will recognize that changes may be made to the embodiments described without department from the scope of the invention disclosed. Modifications which fall within the scope of the present invention will be apparent to those skilled in the art, in light of a review of this disclosure, and such modifications are intended to fall within the appended claims.