PATENT DOCUMENT

Abstract:
An article of manufacture having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in a table. Wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z in inches, the profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.

Full Description:
BACKGROUND OF THE INVENTION 
       [0001]    The present invention relates to a turbine nozzle for a gas turbine. In particular, the invention relates to a third stage turbine nozzle airfoil profile. 
         [0002]    In a gas turbine, many system requirements should be met at each stage of a gas turbine&#39;s flow path section to meet design goals. These design goals include, but are not limited to, overall improved efficiency and airfoil loading capability. For example, and in no way limiting of the invention, a blade of a compressor stator should achieve thermal and mechanical operating requirements for that particular stage. Further, for example, and in no way limiting of the invention, a turbine nozzle airfoil profile should achieve thermal and mechanical operating requirements for that particular stage. Airfoil points have been patented as demonstrated by Bielek et al. in U.S. Pat. No. 6,503,054 B1 on Jan. 7, 2003. The patent identified from 100-150 points per section with each section having a uniform spacing, a stagger angle vs. radius, a throat angle vs. radius and a camber vs. radius. The number of points defined is dependent upon the rate of change of curvature of the section. In other words, for areas with higher curvature more points are used to define that region. 
       BRIEF DESCRIPTION OF THE INVENTION 
       [0003]    In accordance with a preferred embodiment of the present invention, there is provided a unique airfoil profile for the nozzles of a turbine stage, for example the third stage of a gas turbine. The nozzle airfoil profile is defined by unique loci of points to achieve the necessary efficiency whereby improved turbine performance is obtained. These unique loci of points define the nominal airfoil profile and are identified by the X, Y and Z Cartesian coordinates of Table 1, which follows. The points for the coordinate values shown in Table 1 are for a cold, in other words, room temperature, profile at various planar cross-sections of the nozzle airfoil along its length. The X and Y coordinates are given in distance dimensions, e.g., units of inches, and are joined smoothly at each Z location to form a smooth continuous airfoil cross-section. The Z coordinates are given in length dimension of inches along a nozzle-stacking axis coincident with a radius from the axis of turbine rotation. Each defined cross-section is then joined smoothly with adjacent cross-sections to form the complete airfoil shape. 
         [0004]    It will be appreciated that as each nozzle airfoil heats up in use, the profile will change as a result of stress and temperature. Thus, the cold or room temperature profile is given by the X, Y and Z coordinates for manufacturing purposes. Since the manufactured nozzle airfoil profile may be different from the nominal airfoil profile given by the following table, a distance of plus or minus 0.100 inches from the nominal profile in a direction normal to any surface location along the nominal defines the profile envelope for this nozzle airfoil. The envelope includes any possible airfoil surface coating process. The design is robust to this variation without impairment of the mechanical and aerodynamic functions. 
         [0005]    It will also be appreciated that the airfoil can be scaled up or scaled down geometrically for introduction into similar turbine designs. Consequently, the X, Y, and Z coordinates in inches of the nominal airfoil profile given below are a function of the same constant or number. That is, the X and Y and optionally the Z coordinate values in inches may be multiplied or divided by the same constant or number to provide a scaled up or scaled down version of the nozzle airfoil profile while retaining the airfoil section shape. 
         [0006]    In one aspect of the present invention, there is provided a turbine nozzle having an airfoil shape in an envelope within ±0.100 inches in a direction normal to any airfoil surface location wherein the airfoil has a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table 1. X and Y are distances in inches defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form a complete airfoil shape. 
         [0007]    In another aspect of the present invention, there is provided a turbine nozzle having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table 1. Wherein X and Y are distances in inches defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form a complete airfoil shape, the X and Y distances being scalable as a function of the same constant or number to provide a scaled-up or scaled-down nozzle airfoil. 
         [0008]    In a further aspect of the present invention, there is provided a turbine comprising a turbine nozzle arrangement having a plurality of nozzles, each of said nozzles having an airfoil shape in an envelope within ±0.100 inches in a direction normal to any airfoil surface location wherein the airfoil has a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table 1. wherein X and Y are distances in inches defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form a complete airfoil shape. 
         [0009]    In a further aspect of the present invention, there is provided a turbine comprising a turbine nozzle arrangement having a plurality of nozzles, each of said nozzles having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table 1 wherein X and Y are distances in inches defining the airfoil profile at each distance Z, the profiles at the Z distances being joined smoothly with one another to form a complete airfoil shape, the X and Y distances being scalable as a function of the same constant or number to provide a scaled-up or scaled-down nozzle airfoil. These and other aspects, advantages and salient features of the invention will become apparent from the following detailed description, which, when taken in conjunction with the annexed drawings, where like parts are designated by like reference characters throughout the drawings, disclose embodiments of the invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]      FIG. 1  is a schematic illustration of a turbine having a turbine nozzle arrangement employing the nozzles and nozzle airfoil, as embodied by the invention; 
           [0011]      FIG. 2  is a frontal view of a turbine nozzle including an airfoil and sidewalls, as embodied by the invention; 
           [0012]      FIG. 3  is a suction side view of a turbine nozzle including an airfoil and sidewalls, as embodied by the invention; 
           [0013]      FIG. 4  is a pressure side isometric view of a turbine nozzle including an airfoil and sidewalls, as embodied by the invention; and 
           [0014]      FIG. 5  is a sectional illustration through the airfoil with points illustrated thereon, where the point coordinates are with respect to the coordinate system orientation illustrated therein, as embodied by the invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0015]    Referring now to  FIG. 1 , there is illustrated a portion of a turbine  10  in which a, such as but not limited to, a third stage turbine nozzle, having an airfoil profile, as defined herein, may be utilized. The turbine  10  includes first, second, and third stage nozzle arrangements  1 ,  2 , and  3  having nozzles in conjunction with the respective buckets of the various stages of the rotor. It will be appreciated that a three-stage turbine is illustrated, as an exemplary turbine, which in no means is intended to limit the invention. For ease of discussion, a third stage will be discussed herein, but as a non-limiting configuration. Any stage for the turbine nozzle is within the scope of the invention. 
         [0016]    The exemplary third stage comprises a triplet airfoil nozzle arrangement and a rotor assembly whereby the nozzles are upstream of the buckets. It will be appreciated that a plurality of nozzles are spaced circumferentially, one from the other, about the third stage nozzle arrangement and in this instance there are twenty (20) nozzles mounted on the third stage nozzle arrangement. 
         [0017]    Referring now to  FIGS. 2 ,  3 , and  4 , there is illustrated a turbine nozzle constructed in accordance with the present invention including three airfoils  11 ,  12 ,  13  mounted between an inner  15  and outer  16  sidewall. The nozzles  11 ,  12 ,  13  are suitably mounted on the surrounding hardware by suitable means (not illustrated). The airfoils  11 ,  12 ,  13  and sidewalls  15 ,  16  are collectively referred to as a nozzle. The airfoils have a profile including a 2-dimensional shape with suction  26  and pressure  25  sides, respectively, as well as a leading edge  20  and trailing edge  21 . 
         [0018]    Referring now to  FIG. 5 , a section through an airfoil is shown with respective callouts for pressure side  25 , suction side  26 , leading edge  20 , and trailing edge  21  is illustrated.  FIG. 5  also illustrates a typical distribution of points for a section shown in Table 1. The points are defined such that more points represent the areas in which the rate of change of the curvature is greater as seen at the leading and trailing edge. 
         [0019]    A Cartesian coordinate system of X, Y and Z values given in Table 1 define profiles of nozzle airfoils. The coordinate values for the X, Y, and Z coordinates are set forth in inches in Table 1, although other units of dimensions may be used. The Cartesian coordinate system has orthogonally-related X, Y and Z-axes with the Z axis extending perpendicular to a plane normal to a plane containing the X and Y values. The Z distance commences at 0 at the turbine centerline. The Y-axis lies parallel to the turbine rotor centerline, i.e., the rotary axis. 
         [0020]    By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, and the profile of the airfoil can be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section at each distance Z is fixed. The surface profiles of the various surface locations between the distances Z are determined by smoothly connecting the adjacent cross-sections to one another to form the airfoil surface. These values represent the airfoil profiles at ambient, non-operating or non-hot conditions and are for an uncoated airfoil. The sign convention assigns a positive value to Z values and positive and negative values for the X and Y coordinates as typically used in Cartesian coordinate systems. 
         [0021]    The Table 1 values are generated and shown to three decimal places for determining the profile of the airfoil. There are typical manufacturing tolerances, which may be accounted for in the airfoil profile. Accordingly, the values for the profile given in Table 1 are for a nominal airfoil. It will therefore be appreciated that ±typical manufacturing tolerances are additive to the X and Y values given in Table 1 below. Accordingly, a distance of ±0.100 inches in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular nozzle airfoil design and turbine. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 The coordinate values given below provide the preferred 
               
               
                 nominal profile envelope. 
               
             
          
           
               
                 X 
                 Y 
                 Z 
               
               
                   
               
             
          
           
               
                 0.184 
                 0.804 
                 51.017 
               
               
                 −0.245 
                 0.936 
                 51.017 
               
               
                 1.861 
                 −0.073 
                 51.017 
               
               
                 −0.228 
                 0.985 
                 51.017 
               
               
                 3.043 
                 −0.864 
                 51.017 
               
               
                 2.473 
                 −1.578 
                 51.017 
               
               
                 1.74 
                 −0.65 
                 51.017 
               
               
                 0.927 
                 0.081 
                 51.017 
               
               
                 −0.172 
                 0.879 
                 51.017 
               
               
                 0.927 
                 0.437 
                 51.017 
               
               
                 −0.247 
                 0.962 
                 51.017 
               
               
                 2.411 
                 −0.414 
                 51.017 
               
               
                 2.837 
                 −2.238 
                 51.017 
               
               
                 −0.188 
                 0.986 
                 51.017 
               
               
                 3.443 
                 −1.194 
                 51.017 
               
               
                 2.188 
                 −1.172 
                 51.017 
               
               
                 1.427 
                 −0.344 
                 51.017 
               
               
                 0.487 
                 0.414 
                 51.017 
               
               
                 −0.236 
                 0.924 
                 51.017 
               
               
                 1.579 
                 0.089 
                 51.017 
               
               
                 −0.236 
                 0.979 
                 51.017 
               
               
                 2.836 
                 −0.708 
                 51.017 
               
               
                 2.602 
                 −1.79 
                 51.017 
               
               
                 3.741 
                 −1.476 
                 51.017 
               
               
                 1.89 
                 −0.811 
                 51.017 
               
               
                 1.097 
                 −0.057 
                 51.017 
               
               
                 −0.057 
                 0.8 
                 51.017 
               
               
                 0.556 
                 0.622 
                 51.017 
               
               
                 −0.249 
                 0.952 
                 51.017 
               
               
                 2.138 
                 −0.24 
                 51.017 
               
               
                 −0.208 
                 0.99 
                 51.017 
               
               
                 3.246 
                 −1.025 
                 51.017 
               
               
                 2.335 
                 −1.372 
                 51.017 
               
               
                 1.586 
                 −0.494 
                 51.017 
               
               
                 0.754 
                 0.215 
                 51.017 
               
               
                 −0.223 
                 0.914 
                 51.017 
               
               
                 −0.243 
                 0.971 
                 51.017 
               
               
                 1.294 
                 0.245 
                 51.017 
               
               
                 2.626 
                 −0.559 
                 51.017 
               
               
                 2.724 
                 −2.012 
                 51.017 
               
               
                 3.594 
                 −1.333 
                 51.017 
               
               
                 2.034 
                 −0.978 
                 51.017 
               
               
                 1.264 
                 −0.199 
                 51.017 
               
               
                 0.217 
                 0.609 
                 51.017 
               
               
                 3.347 
                 −3.781 
                 51.017 
               
               
                 3.035 
                 −2.699 
                 51.017 
               
               
                 3.884 
                 −1.623 
                 51.017 
               
               
                 4.466 
                 −2.388 
                 51.017 
               
               
                 4.846 
                 −3.229 
                 51.017 
               
               
                 3.437 
                 −4.438 
                 51.017 
               
               
                 3.248 
                 −3.353 
                 51.017 
               
               
                 4.15 
                 −1.934 
                 51.017 
               
               
                 4.643 
                 −2.715 
                 51.017 
               
               
                 3.385 
                 −3.998 
                 51.017 
               
               
                 3.121 
                 −2.933 
                 51.017 
               
               
                 4.367 
                 −2.232 
                 51.017 
               
               
                 4.787 
                 −3.055 
                 51.017 
               
               
                 3.45 
                 −4.658 
                 51.017 
               
               
                 3.301 
                 −3.566 
                 51.017 
               
               
                 2.941 
                 −2.467 
                 51.017 
               
               
                 4.02 
                 −1.776 
                 51.017 
               
               
                 4.558 
                 −2.549 
                 51.017 
               
               
                 4.899 
                 −3.414 
                 51.017 
               
               
                 3.415 
                 −4.218 
                 51.017 
               
               
                 3.188 
                 −3.142 
                 51.017 
               
               
                 4.261 
                 −2.081 
                 51.017 
               
               
                 4.72 
                 −2.884 
                 51.017 
               
               
                 4.975 
                 −3.792 
                 51.017 
               
               
                 3.782 
                 −7.259 
                 51.017 
               
               
                 5.002 
                 −4.797 
                 51.017 
               
               
                 3.515 
                 −7.19 
                 51.017 
               
               
                 4.802 
                 −5.835 
                 51.017 
               
               
                 3.316 
                 −6.945 
                 51.017 
               
               
                 4.517 
                 −6.558 
                 51.017 
               
               
                 3.279 
                 −6.568 
                 51.017 
               
               
                 4.221 
                 −7.005 
                 51.017 
               
               
                 3.405 
                 −5.638 
                 51.017 
               
               
                 4.858 
                 −5.632 
                 51.017 
               
               
                 3.952 
                 −7.215 
                 51.017 
               
               
                 3.671 
                 −7.251 
                 51.017 
               
               
                 4.947 
                 −5.217 
                 51.017 
               
               
                 3.419 
                 −7.115 
                 51.017 
               
               
                 4.698 
                 −6.142 
                 51.017 
               
               
                 3.284 
                 −6.803 
                 51.017 
               
               
                 4.388 
                 −6.782 
                 51.017 
               
               
                 3.303 
                 −6.337 
                 51.017 
               
               
                 4.114 
                 −7.11 
                 51.017 
               
               
                 3.447 
                 −5.149 
                 51.017 
               
               
                 4.942 
                 −3.602 
                 51.017 
               
               
                 3.84 
                 −7.252 
                 51.017 
               
               
                 5.014 
                 −4.18 
                 51.017 
               
               
                 5.015 
                 −4.586 
                 51.017 
               
               
                 3.565 
                 −7.216 
                 51.017 
               
               
                 3.342 
                 −7.006 
                 51.017 
               
               
                 4.573 
                 −6.442 
                 51.017 
               
               
                 3.276 
                 −6.646 
                 51.017 
               
               
                 4.269 
                 −6.948 
                 51.017 
               
               
                 3.367 
                 −5.911 
                 51.017 
               
               
                 4.005 
                 −7.187 
                 51.017 
               
               
                 4.999 
                 −3.986 
                 51.017 
               
               
                 3.726 
                 −7.258 
                 51.017 
               
               
                 4.979 
                 −5.007 
                 51.017 
               
               
                 3.469 
                 −7.159 
                 51.017 
               
               
                 4.753 
                 −5.989 
                 51.017 
               
               
                 3.297 
                 −6.88 
                 51.017 
               
               
                 4.455 
                 −6.672 
                 51.017 
               
               
                 3.285 
                 −6.49 
                 51.017 
               
               
                 4.169 
                 −7.059 
                 51.017 
               
               
                 3.431 
                 −5.393 
                 51.017 
               
               
                 3.897 
                 −7.236 
                 51.017 
               
               
                 5.019 
                 −4.374 
                 51.017 
               
               
                 3.617 
                 −7.236 
                 51.017 
               
               
                 4.907 
                 −5.425 
                 51.017 
               
               
                 3.376 
                 −7.064 
                 51.017 
               
               
                 4.639 
                 −6.293 
                 51.017 
               
               
                 3.277 
                 −6.725 
                 51.017 
               
               
                 4.315 
                 −6.888 
                 51.017 
               
               
                 3.325 
                 −6.184 
                 51.017 
               
               
                 4.055 
                 −7.156 
                 51.017 
               
               
                 3.454 
                 −4.903 
                 51.017 
               
               
                 0.918 
                 −0.008 
                 49.687 
               
               
                 −0.159 
                 0.775 
                 49.687 
               
               
                 0.892 
                 0.35 
                 49.687 
               
               
                 −0.242 
                 0.856 
                 49.687 
               
               
                 2.332 
                 −0.473 
                 49.687 
               
               
                 −0.182 
                 0.888 
                 49.687 
               
               
                 3.335 
                 −1.218 
                 49.687 
               
               
                 2.264 
                 −1.388 
                 49.687 
               
               
                 1.47 
                 −0.484 
                 49.687 
               
               
                 0.468 
                 0.334 
                 49.687 
               
               
                 −0.221 
                 0.818 
                 49.687 
               
               
                 1.522 
                 0.012 
                 49.687 
               
               
                 −0.236 
                 0.874 
                 49.687 
               
               
                 1.972 
                 −1.012 
                 49.687 
               
               
                 2.747 
                 −0.756 
                 49.687 
               
               
                 2.643 
                 −2 
                 49.687 
               
               
                 3.624 
                 −1.482 
                 49.687 
               
               
                 1.106 
                 −0.162 
                 49.687 
               
               
                 −0.059 
                 0.707 
                 49.687 
               
               
                 0.536 
                 0.531 
                 49.687 
               
               
                 −0.24 
                 0.841 
                 49.687 
               
               
                 2.066 
                 −0.305 
                 49.687 
               
               
                 −0.201 
                 0.893 
                 49.687 
               
               
                 3.144 
                 −1.058 
                 49.687 
               
               
                 2.399 
                 −1.585 
                 49.687 
               
               
                 1.644 
                 −0.654 
                 49.687 
               
               
                 0.726 
                 0.141 
                 49.687 
               
               
                 −0.208 
                 0.809 
                 49.687 
               
               
                 1.247 
                 0.164 
                 49.687 
               
               
                 −0.24 
                 0.865 
                 49.687 
               
               
                 2.541 
                 −0.612 
                 49.687 
               
               
                 2.753 
                 −2.216 
                 49.687 
               
               
                 3.482 
                 −1.348 
                 49.687 
               
               
                 2.122 
                 −1.197 
                 49.687 
               
               
                 1.291 
                 −0.321 
                 49.687 
               
               
                 0.206 
                 0.522 
                 49.687 
               
               
                 0.177 
                 0.71 
                 49.687 
               
               
                 −0.233 
                 0.828 
                 49.687 
               
               
                 1.796 
                 −0.144 
                 49.687 
               
               
                 −0.221 
                 0.888 
                 49.687 
               
               
                 2.948 
                 −0.904 
                 49.687 
               
               
                 2.524 
                 −1.788 
                 49.687 
               
               
                 1.811 
                 −0.829 
                 49.687 
               
               
                 4.341 
                 −2.355 
                 49.687 
               
               
                 4.727 
                 −3.164 
                 49.687 
               
               
                 3.343 
                 −4.543 
                 49.687 
               
               
                 3.2 
                 −3.495 
                 49.687 
               
               
                 2.853 
                 −2.436 
                 49.687 
               
               
                 4.023 
                 −1.917 
                 49.687 
               
               
                 4.519 
                 −2.667 
                 49.687 
               
               
                 4.826 
                 −3.53 
                 49.687 
               
               
                 3.31 
                 −4.122 
                 49.687 
               
               
                 3.091 
                 −3.086 
                 49.687 
               
               
                 4.135 
                 −2.058 
                 49.687 
               
               
                 4.241 
                 −2.204 
                 49.687 
               
               
                 4.666 
                 −2.994 
                 49.687 
               
               
                 3.348 
                 −4.779 
                 49.687 
               
               
                 3.244 
                 −3.703 
                 49.687 
               
               
                 2.944 
                 −2.658 
                 49.687 
               
               
                 3.895 
                 −1.766 
                 49.687 
               
               
                 4.434 
                 −2.509 
                 49.687 
               
               
                 4.782 
                 −3.346 
                 49.687 
               
               
                 3.331 
                 −4.332 
                 49.687 
               
               
                 3.149 
                 −3.289 
                 49.687 
               
               
                 4.596 
                 −2.829 
                 49.687 
               
               
                 3.281 
                 −3.912 
                 49.687 
               
               
                 3.027 
                 −2.885 
                 49.687 
               
               
                 3.762 
                 −1.622 
                 49.687 
               
               
                 4.364 
                 −6.391 
                 49.687 
               
               
                 4.032 
                 −6.836 
                 49.687 
               
               
                 3.271 
                 −5.665 
                 49.687 
               
               
                 3.741 
                 −7.032 
                 49.687 
               
               
                 4.9 
                 −4.088 
                 49.687 
               
               
                 3.47 
                 −7.037 
                 49.687 
               
               
                 4.829 
                 −5.097 
                 49.687 
               
               
                 3.246 
                 −6.89 
                 49.687 
               
               
                 4.559 
                 −5.992 
                 49.687 
               
               
                 3.147 
                 −6.618 
                 49.687 
               
               
                 4.229 
                 −6.601 
                 49.687 
               
               
                 3.183 
                 −6.165 
                 49.687 
               
               
                 3.893 
                 −6.952 
                 49.687 
               
               
                 3.325 
                 −5.252 
                 49.687 
               
               
                 3.63 
                 −7.057 
                 49.687 
               
               
                 4.902 
                 −4.483 
                 49.687 
               
               
                 3.37 
                 −6.993 
                 49.687 
               
               
                 4.733 
                 −5.497 
                 49.687 
               
               
                 3.190 
                 −6.797 
                 49.687 
               
               
                 4.424 
                 −6.281 
                 49.687 
               
               
                 3.145 
                 −6.465 
                 49.687 
               
               
                 4.095 
                 −6.770 
                 49.687 
               
               
                 3.241 
                 −5.841 
                 49.687 
               
               
                 3.794 
                 −7.010 
                 49.687 
               
               
                 4.885 
                 −3.901 
                 49.687 
               
               
                 3.522 
                 −7.051 
                 49.687 
               
               
                 4.863 
                 −4.894 
                 49.687 
               
               
                 3.283 
                 −6.930 
                 49.687 
               
               
                 4.618 
                 −5.844 
                 49.687 
               
               
                 3.157 
                 −6.694 
                 49.687 
               
               
                 4.299 
                 −6.498 
                 49.687 
               
               
                 3.160 
                 −6.313 
                 49.687 
               
               
                 3.965 
                 −6.897 
                 49.687 
               
               
                 3.298 
                 −5.489 
                 49.687 
               
               
                 3.686 
                 −7.048 
                 49.687 
               
               
                 4.906 
                 −4.276 
                 49.687 
               
               
                 3.419 
                 −7.017 
                 49.687 
               
               
                 3.576 
                 −7.058 
                 49.687 
               
               
                 4.785 
                 −5.298 
                 49.687 
               
               
                 3.215 
                 −6.846 
                 49.687 
               
               
                 4.495 
                 −6.138 
                 49.687 
               
               
                 3.143 
                 −6.542 
                 49.687 
               
               
                 4.154 
                 −6.701 
                 49.687 
               
               
                 3.209 
                 −6.017 
                 49.687 
               
               
                 3.844 
                 −6.983 
                 49.687 
               
               
                 3.342 
                 −5.015 
                 49.687 
               
               
                 4.861 
                 −3.715 
                 49.687 
               
               
                 4.672 
                 −5.694 
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                 41.707 
               
               
                 2.522 
                 −5.277 
                 41.707 
               
               
                 2.757 
                 −5.84 
                 41.707 
               
               
                 2.51 
                 −5.477 
                 41.707 
               
               
                 2.716 
                 −5.825 
                 41.707 
               
               
                 2.581 
                 −5.723 
                 41.707 
               
               
                 2.557 
                 −5.687 
                 41.707 
               
               
                 3.394 
                 −5.553 
                 41.707 
               
               
                 2.56 
                 −4.99 
                 41.707 
               
               
                 2.512 
                 −5.52 
                 41.707 
               
               
                 3.115 
                 −5.785 
                 41.707 
               
               
                 2.609 
                 −5.755 
                 41.707 
               
               
                 2.642 
                 −5.782 
                 41.707 
               
               
                 2.848 
                 −5.857 
                 41.707 
               
               
                 2.526 
                 −5.607 
                 41.707 
               
               
                 2.531 
                 −5.199 
                 41.707 
               
               
                 2.514 
                 −5.356 
                 41.707 
               
               
                 3 
                 −5.836 
                 41.707 
               
               
                 3.511 
                 −5.409 
                 41.707 
               
               
                 3.236 
                 −5.703 
                 41.707 
               
               
                 1.849 
                 −1.884 
                 40.377 
               
               
                 1.306 
                 −1.155 
                 40.377 
               
               
                 3.163 
                 −1.876 
                 40.377 
               
               
                 1.181 
                 −1.018 
                 40.377 
               
               
                 0.503 
                 −0.388 
                 40.377 
               
               
                 1.752 
                 −1.732 
                 40.377 
               
               
                 −0.192 
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                 40.377 
               
               
                 1.107 
                 −0.477 
                 40.377 
               
               
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                 −0.304 
                 40.377 
               
               
                 −0.197 
                 0.177 
                 40.377 
               
               
                 2.121 
                 −1.074 
                 40.377 
               
               
                 2.029 
                 −2.202 
                 40.377 
               
               
                 −0.138 
                 0.203 
                 40.377 
               
               
                 1.54 
                 −1.438 
                 40.377 
               
               
                 0.116 
                 −0.085 
                 40.377 
               
               
                 2.627 
                 −1.418 
                 40.377 
               
               
                 1.416 
                 −0.653 
                 40.377 
               
               
                 2.25 
                 −2.701 
                 40.377 
               
               
                 −0.182 
                 0.199 
                 40.377 
               
               
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                 0.038 
                 40.377 
               
               
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                 −0.831 
                 40.377 
               
               
                 2.508 
                 −1.333 
                 40.377 
               
               
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                 0.123 
                 40.377 
               
               
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                 −0.508 
                 40.377 
               
               
                 0.487 
                 −0.132 
                 40.377 
               
               
                 −0.198 
                 0.166 
                 40.377 
               
               
                 1.427 
                 −1.296 
                 40.377 
               
               
                 1.923 
                 −0.951 
                 40.377 
               
               
                 2.109 
                 −2.365 
                 40.377 
               
               
                 −0.153 
                 0.207 
                 40.377 
               
               
                 1.649 
                 −1.583 
                 40.377 
               
               
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                 40.377 
               
               
                 1.052 
                 −0.885 
                 40.377 
               
               
                 0.311 
                 −0.234 
                 40.377 
               
               
                 0.783 
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                 40.377 
               
               
                 3.078 
                 −1.793 
                 40.377 
               
               
                 2.743 
                 −1.507 
                 40.377 
               
               
                 −0.182 
                 0.132 
                 40.377 
               
               
                 −0.193 
                 0.188 
                 40.377 
               
               
                 2.316 
                 −1.201 
                 40.377 
               
               
                 1.942 
                 −2.041 
                 40.377 
               
               
                 −0.082 
                 0.061 
                 40.377 
               
               
                 2.969 
                 −1.693 
                 40.377 
               
               
                 2.857 
                 −1.598 
                 40.377 
               
               
                 0.919 
                 −0.756 
                 40.377 
               
               
                 −0.197 
                 0.154 
                 40.377 
               
               
                 −0.168 
                 0.206 
                 40.377 
               
               
                 2.183 
                 −2.532 
                 40.377 
               
               
                 3.544 
                 −2.343 
                 40.377 
               
               
                 3.838 
                 −2.999 
                 40.377 
               
               
                 2.492 
                 −4.671 
                 40.377 
               
               
                 2.503 
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                 40.377 
               
               
                 2.352 
                 −3.007 
                 40.377 
               
               
                 3.803 
                 −2.882 
                 40.377 
               
               
                 3.327 
                 −2.054 
                 40.377 
               
               
                 3.663 
                 −2.547 
                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
                 3.913 
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                 40.377 
               
               
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                 40.377 
               
               
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                 −2.148 
                 40.377 
               
               
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                 −3.235 
                 40.377 
               
               
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                 −3.355 
                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
                 2.482 
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
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                 40.377 
               
               
                 3.715 
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                 40.377 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
                 2.405 
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                 39.047 
               
               
                 3.78 
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                 39.047 
               
               
                 3.181 
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
                 3.723 
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                 39.047 
               
               
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                 39.047 
               
               
                 2.248 
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                 39.047 
               
               
                 3.329 
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                 39.047 
               
               
                 2.294 
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                 39.047 
               
               
                 3.616 
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                 39.047 
               
               
                 2.414 
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                 39.047 
               
               
                 2.417 
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                 39.047 
               
               
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                 39.047 
               
               
                 2.333 
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
                 3.726 
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                 39.047 
               
               
                 3.178 
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                 39.047 
               
               
                 3.566 
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                 39.047 
               
               
                 3.325 
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
                 3.222 
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
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                 39.047 
               
               
                 2.382 
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                 39.047 
               
               
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                 39.047 
               
               
                 3.264 
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                 39.047 
               
               
                 2.375 
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                 39.047 
               
               
                 3.381 
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                 39.047 
               
               
                 3.762 
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                 39.047 
               
               
                 2.369 
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                 39.047 
               
               
                 2.476 
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                 39.047 
               
               
                 2.424 
                 −5.32 
                 39.047 
               
               
                 3.433 
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                 39.047 
               
               
                 2.616 
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                 39.047 
               
               
                 2.392 
                 −5.248 
                 39.047 
               
               
                   
               
             
          
         
       
     
         [0022]    It will also be appreciated that the airfoil disclosed in Table 1 may be scaled up or down geometrically for use in similar turbine designs. Consequently, the coordinate values set forth in Table 1 may be scaled upwardly or downwardly such that the airfoil section shape remains unchanged. A scaled version of the coordinates in Table I would be represented by X, Y and, optionally, Z coordinate values (after the Z values have been converted to inches) multiplied or divided by the same constant or number. 
         [0023]    One or more specific embodiments of the present invention will be described below. In an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers&#39; specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure. 
         [0024]    While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment. On the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.