Abstract:
First, second and third sets of cooling holes are provided in a turbine airfoil. The first set of holes adjacent a leading edge have turbulators commencing at a predetermined distance from the root of the airfoil and terminating short of the airfoil tip. A second set of cooling holes have turbulators commencing at a greater distance from the platform than the turbulators of the first set and terminating short of the airfoil tip at a greater distance from the tip than the turbulators of the first set of holes. A third set of holes adjacent the trailing edge has smooth bores. The size, location, style and configuration of the cooling holes increases bulk creep part life and overall efficiency of the turbine.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     The present invention relates to an airfoil for a bucket of a stage of a gas turbine and particularly relates to a stage two bucket airfoil having an optimized number, location, style and size of cooling holes for flowing a cooling medium, e.g., air, through the airfoil.  
         [0002]     Many different types, numbers and locations of passages for flowing a cooling medium, e.g., air, through an airfoil of a turbine bucket for cooling the airfoil have been proposed and constructed. Where air is used as the cooling medium, it will be appreciated that the air is derived from the compressor and therefore results in a debit to the overall efficiency of the turbine. In prior cooling configurations for turbine buckets, compressor discharge air is supplied to the airfoil through cooling passages formed integrally within the bucket. Insufficient cooling, however, affects bulk creep part life which in turn limits the life of the part to a predetermined number of hours of turbine operation. Accordingly, a more effective cooling scheme which decreases the bulk temperature of the bucket and increases the bucket&#39;s bulk creep life is deemed necessary.  
       BRIEF DESCRIPTION OF THE INVENTION  
       [0003]     In accordance with a preferred embodiment of the present invention, there is provided a bucket having an airfoil in which the number, location, style and size of the cooling holes or passages through the airfoil which convey the cooling medium increase the overall efficiency of the turbine and meet bucket life requirements, particularly by increasing the bulk creep part life. To accomplish the foregoing, the cooling holes are arranged optimally within the airfoil in accordance with X, Y coordinates set forth in Table I below. The size of the holes limits the amount of air flow based on a pressure difference across the bucket airfoil. The location of the holes determines the temperature of every finite element making up the bucket airfoil. The style reflects the way in which the heat transfer occurs along the walls of each cooling hole, i.e., turbulators at selected locations are used to enhance heat transfer. These attributes together create an efficient optimal cooling scheme for the turbine bucket.  
         [0004]     In a preferred embodiment according to the present invention, there is provided an air cooled bucket for a turbine comprising an airfoil having a plurality of cooling holes extending between root and tip portions of the airfoil and exiting at the tip of the airfoil, the plurality of cooling holes including first, second and third sets of holes with each set of holes having at least two holes, the first set of holes extending adjacent a leading edge of the airfoil, the second set of holes extending intermediate the first and third sets of holes and the third set of holes extending adjacent the trailing edge, the two holes of each of the first, second and third sets of holes including at least two of the holes numbered  1 - 4 ,  5 - 7  and  8 - 10 , respectively, and located in accordance with X, Y Cartesian coordinate values set forth in Table I below at tip and root portions of the airfoil.  
         [0005]     In a further preferred embodiment according to the present invention, there is provided an air cooled bucket for a turbine comprising an airfoil having a plurality of cooling holes extending between root and tip portions of the airfoil and exiting at the tip of the airfoil, the plurality of cooling holes including first, second and third sets of holes with each set of holes having at least two holes, the first set of holes extending adjacent a leading edge of the airfoil, the second set of holes extending intermediate the first and third sets of holes and the third set of holes extending adjacent the trailing edge, the two holes of one of the first set of holes and the second set of holes having turbulators spaced one from the other along the holes and terminating short of the root and tip portions of the airfoil. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0006]      FIG. 1  is a schematic representation of a hot gas path through multiple stages of a gas turbine and illustrates a second stage bucket airfoil according to a preferred embodiment of the present invention;  
         [0007]      FIG. 2  is a side elevational view of the second stage bucket illustrated from the pressure side of the airfoil, with the side of the bucket broken away to illustrate internal cooling passages through the bucket; in accordance with a preferred embodiment of the present invention;  
         [0008]      FIG. 3  is an enlarged radial inward view of the airfoil tip shroud illustrating the locations of the cooling hole exits;  
         [0009]      FIG. 4  is an enlarged cross-sectional view thereof taken generally about on line  4 - 4  in  FIG. 2 ;  
         [0010]      FIG. 5  is a radially outward view of the bucket illustrating inlets for the cooling passages in the dovetail of the bucket;  
         [0011]      FIG. 6  is a cross-sectional view about line  6 - 6  in  FIG. 2 ;  
         [0012]      FIG. 7  is an enlarged cross-sectional view taken in  FIG. 6 ;  
         [0013]      FIG. 8  is an enlarged cross-sectional view taken about on line  8 - 8  in  FIG. 2 ;  
         [0014]      FIG. 9  is an enlarged cross-sectional view of a portion of the airfoil and passage of  FIG. 8 ; and  
         [0015]      FIG. 10  is a schematic representation of an airfoil profile section along the bucket of  FIG. 2 . 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0016]     Referring now to the drawing figures, particularly to  FIG. 1 , there is illustrated a hot gas path, generally designated  11 , of a gas turbine  12  including a plurality of turbine stages. Three stages are illustrated. For example, the first stage comprises a plurality of circumferentially spaced nozzles  14  and buckets  16 . The nozzles are circumferentially spaced one from the other and fixed about the axis of the rotor. The first stage buckets  16 , of course, are mounted on a turbine rotor wheel  17 . A second stage of the turbine  12  is also illustrated, including a plurality of circumferentially spaced nozzles  18  and a plurality of circumferentially spaced buckets  20  mounted on a rotor wheel  21 . The third stage is also illustrated including a plurality of circumferentially spaced nozzles  22  and buckets  24  mounted on the rotor. It will be appreciated that the nozzles and buckets lie in the hot gas path  10  of the turbine  12 , the direction of flow of the hot gas through the hot gas path  10  being indicated by the arrow  26 .  
         [0017]     Referring to  FIG. 2 , each bucket  20  of the second stage is provided with a platform  30 , a shank  32  and a dovetail  34  for connection with a complementary-shaped mating dovetail on rotor wheel  21  forming part of the rotor. Each of the second stage buckets  20  also includes an airfoil  36  having an airfoil profile at any cross-section along the airfoil from the platform to the airfoil tip, as schematically illustrated by the profile section  38  in  FIG. 10 .  
         [0018]     Each of the second stage buckets  20  is also provided with a tip shroud, generally designated  40  ( FIG. 2 ). The tip shrouds  40  are preferably formed integrally with the buckets and each tip shroud engages at opposite ends adjacent tip shrouds of adjacent buckets to form a generally annular ring or shroud circumscribing the hot gas path at the axial location of the second stage buckets.  
         [0019]     As best illustrated in  FIG. 2 , the bucket  20  includes a plurality of cooling holes extending between the dovetail  34  and the tip  44  of the airfoil  36 . Thus, as best illustrated in  FIG. 5 , the dovetail  34  has a plurality of inlets  46  in communication with respective holes  42 . Tip  44 , as illustrated in  FIG. 3 , includes a plurality of outlets  48  through the tip shroud  40  in communication with respective holes  42 . Accordingly, the cooling medium, e.g., air from the turbine compressor, enters the inlets  46 , passes through the cooling holes  42  and exits from the tip  44  of the airfoil through shroud  40  into the hot gas stream.  
         [0020]     As illustrated in  FIG. 2 , the cooling holes  42  extend between a root portion  50  and the tip  44  of the airfoil and continue through the shank  32  and dovetail  34 . The plurality of cooling holes  42  through the airfoil includes first, second and third sets of holes  54 ,  56  and  58 , respectively. The first set of holes  54  extends adjacent a leading edge  57  of the airfoil. The second set of holes  56  extends intermediate the first and third sets of holes  54  and  58 , respectively. The third set of holes  58  extends adjacent the trailing edge  59 . Each of the first, second and third sets of the plurality of cooling holes  42  includes at least two holes. For convenience, the holes of the plurality of holes  42  are numbered  1  through  10  in Table I below. As indicated, the first set of holes  54  comprises holes numbered  1 - 4 , the second set of holes  56  comprises numbered holes  5 - 7  and the third set of holes  58  comprise numbered holes  8 - 10  in Table I and as illustrated in  FIGS. 3-5 .  
         [0021]     Each of the holes  42  of the first set of holes  54  includes a plurality of turbulators  60  at spaced locations from one another along predetermined portions of each hole between the root and tip portions of the airfoil. Similarly, each of the holes  42  of the second set of holes  56  includes a plurality of turbulators  62  at spaced locations from one another along predetermined portions of the holes between the root and tip portions of the airfoil. The third set of holes  58  do not include turbulators and have smooth bores between the root and tip portions of the airfoil.  
         [0022]     The turbulators  60  of the first set of holes  54  include radially inwardly projecting annular ribs  61  at spaced locations along predetermined portions of the holes  54 . The turbulators  62  of the second set of holes  56  likewise include radially inwardly projecting annular ribs  63  at spaced locations along predetermined portions of the holes between the root and tip portions of the airfoils. It will be appreciated that while radially inwardly projecting annular ribs are disclosed as forming turbulators  60 ,  62 , other types of turbulators may be utilized. For example, interrupted annular ribs, pins projecting radially into the bores or dimpled or roughened surfaces may be utilized.  
         [0023]     As noted above, the turbulators  60  and  62  of the first and second sets of openings  54  and  56 , respectively, are provided along predetermined portions of the respective holes. The turbulators  60  and  62  are located along holes  42  and terminate short of the root  50  and tip  44  of the airfoil  36 . More particularly, the turbulators  60  of the first set of holes  54  commence at a distance of about 30-40% and, more preferably, about 36% of the length of the airfoil from the root to the tip. The turbulators  60  of the first set of holes  54  terminate or end at about 75-85% of the airfoil length, preferably about 80% of the airfoil length from the root to the tip. The turbulators  62  of the second set of holes  56  commence at about 45-55% of the length of the airfoil from root to tip, and preferably at about 51% of the length of the airfoil from root to tip. The turbulators  62  of the second set of holes  56  terminate at about 70-80% of the airfoil length, preferably at about 74% of the length from root to tip.  
         [0024]     With reference to  FIGS. 6 and 7 , the diameter of the first set of holes  54  is larger than the diameter of the second set of holes  56 . In a preferred embodiment, the diameters of (i) the smooth bore portion of the first set of holes  54  between the root portion of the airfoil and the commencement of turbulators  60  and (ii) the smooth bore portion from the outermost turbulator  60  to the tip  44  are about 0.090 inches. The outer diameter of the turbulated holes  54  between ribs  61  is about 0.115 inches. The inner diameter of the ribs  61  is about 0.097 inches. The ribs  61  have a thickness or axial depth, preferably about 0.009 inches and are equally spaced one from the other a distance about 0.090 inches. With reference to  FIGS. 8 and 9 , the diameters of (i) the smooth bore portion of the second set of holes  56  from the root to the commencement of the turbulators  62  and (ii) the smooth bore portion from the last outboard turbulator  62  to the tip of the airfoil are about 0.065 inches. Ribs  6  are equally spaced from one another about 0.060 inches. The outer diameter of the turbulators  62  between ribs  63  of the second set of holes  56  is about 0.085 inches. The inner diameter of the ribs  63  is about 0.070 inches. The ribs  63  have a thickness or axial depth preferably about 0.006 inches. The ribs  63  are equally spaced from one another along the bore of the second set of holes  56  a distance of about 0.060 inches. The ribs are equally spaced one from the other.  
         [0025]     In a preferred aspect of the invention having ninety-two second stage buckets, a datum U ( FIG. 2 ) is established passing through the dovetail  34  at 24.100 inches from the engine centerline. The root portion  50  of the airfoil is 2.487 inches radially outwardly of datum U, i.e., 26.587 inches from the engine centerline. The turbulators  60  commence preferably about 5.591 inches from datum U and terminate preferably 9.400 inches from datum U. The smooth bore portion of the second set of holes  56  extends from the datum preferably about 6.899 inches to the first turbulator  62 . The last of the turbulators  62  of the second set of holes  56  is preferably about 8.900 inches from the datum U. From a review of  FIG. 2 , it will be appreciated that the holes  42  in the shank  32  and dovetail  34  of the bucket have smooth bores.  
         [0026]     The location of the cooling holes numbered  1 - 10  are given in Table I in a Cartesian coordinate system using X and Y values at the tip and root portions of the airfoil. Also, the X and Y coordinate values for the inlet openings  46  through the dovetail  34  of the holes  42  are also given in Table I. The hole diameter from the root portion of the airfoil to the inlet openings  46  is about 0.140 inches.  
                                                                                                               TABLE I                           Hole   Hole Diameter From   Nominal Hole Diameter   Tip   Root   Inlet 46            Number   Tip to Root   From Root To Inlet 46   “X”   “Y”   “X”   “Y”   “X”   “Y”                    1   See  FIG. 6     0.140   −0.596   1.319   −1.111   −0.142   −1.240   0.468       2           −0.389   1.185   −0.857   0.197   −1.011   0.355       3           −0.235   0.990   −0.514   0.446   −0.794   0.253       4           −0.120   0.793   −0.109   0.433   −0.583   0.183       5   See  FIG. 8         0.174   0.339   0.149   0.285   −0.355   0.129       6           0.225   0.227   0.338   0.106   −0.119   0.079       7           0.268   0.111   0.531   −0.069   0.117   0.028       8   0.060       0.315   −0.003   0.702   −0.265   0.355   −0.020       9           0.371   −0.111   0.843   −0.483   0.597   −0.066       10           0.430   −0.217   0.979   −0.704   0.840   −0.111                  
 
         [0027]     To define the airfoil shape of each second stage bucket airfoil, there is a unique set or loci of points in space that meet the stage requirements and can be manufactured. This unique loci of points meets the requirements for stage efficiency and reduced thermal and mechanical stresses. The loci of points are arrived at by iteration between aerodynamic and mechanical loadings enabling the turbine to run in an efficient, safe and smooth manner. The loci which defines the bucket airfoil profile comprises a set of 1320 points relative to the axis of rotation of the turbine. A Cartesian coordinate system of X, Y and Z values given in Table II below define the profile of the bucket airfoil at various locations along its length. The coordinate values for the X and Y coordinates are set forth in inches in Table II although other units of dimensions may be used when the values are appropriately converted. The Z values are set forth in Table II in non-dimensional form from 0.088 to 0.92. These values exclude the fillet regions of the platform and the tip shroud. To convert the Z value to a Z coordinate value, e.g., in inches, the non-dimensional Z value given in Table II is multiplied by the height of airfoil in inches. The Cartesian coordinate system has orthogonally-related X, Y and Z axes and the X axis lies parallel to the turbine rotor centerline, i.e., the rotary axis and a positive X coordinate value is axial toward the aft, i.e., exhaust end of the turbine. The positive Y coordinate value looking aft extends tangentially in the direction of rotation of the rotor and the positive Z coordinate value is radially outwardly toward the bucket tip.  
         [0028]     By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the profile section of the bucket airfoil, e.g., the profile section  38  illustrated in  FIG. 10 , at each Z distance along the length of the airfoil can be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section  38  at each distance Z is fixed. The airfoil profiles of the various surface locations between the distances Z are determined by smoothly connecting the adjacent profile sections  38  to one another to form the airfoil profile. These values represent the airfoil profiles at ambient, non-operating or non-hot conditions and are for an uncoated airfoil.  
         [0029]     The Table II values are generated and shown to three decimal places for determining the profile of the airfoil. There are typical manufacturing tolerances as well as coatings which must be accounted for in the actual profile of the airfoil. Accordingly, the values for the profile given in Table II are for a nominal airfoil. It will therefore be appreciated that ±typical manufacturing tolerances, i.e., ±values, including any coating thicknesses, are additive to the X and Y values given in Table II. Accordingly, a distance of ±0.160 inches in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular bucket airfoil design and turbine, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in Table II below at the same temperature. The bucket airfoil design is robust to this range of variation without impairment of mechanical and aerodynamic functions.  
         [0030]     The coordinate values given in Table II below provide the preferred nominal profile envelope.  
                                                                                     TABLE II                       X   Y   Z′   X   Y   Z′   X   Y   Z′                                −1.291   −0.288   0.088   0.492   0.262   0.088   0.901   −0.765   0.088       −1.313   −0.230   0.088   0.533   0.214   0.088   0.859   −0.718   0.088       −1.317   −0.167   0.088   0.573   0.165   0.088   0.816   −0.672   0.088       −1.312   −0.104   0.088   0.612   0.115   0.088   0.772   −0.626   0.088       −1.300   −0.042   0.088   0.650   0.065   0.088   0.728   −0.581   0.088       −1.282   0.018   0.088   0.687   0.014   0.088   0.684   −0.537   0.088       −1.260   0.077   0.088   0.722   −0.038   0.088   0.638   −0.493   0.088       −1.233   0.135   0.088   0.757   −0.091   0.088   0.592   −0.450   0.088       −1.203   0.190   0.088   0.792   −0.144   0.088   0.544   −0.408   0.088       −1.169   0.243   0.088   0.825   −0.197   0.088   0.496   −0.368   0.088       −1.132   0.294   0.088   0.858   −0.251   0.088   0.447   −0.328   0.088       −1.092   0.343   0.088   0.890   −0.306   0.088   0.397   −0.290   0.088       −1.050   0.390   0.088   0.922   −0.360   0.088   0.346   −0.253   0.088       −1.004   0.434   0.088   0.953   −0.415   0.088   0.293   −0.218   0.088       −0.957   0.475   0.088   0.984   −0.470   0.088   0.240   −0.185   0.088       −0.907   0.513   0.088   1.014   −0.525   0.088   0.185   −0.153   0.088       −0.854   0.549   0.088   1.045   −0.581   0.088   0.129   −0.124   0.088       −0.800   0.581   0.088   1.075   −0.636   0.088   0.072   −0.097   0.088       −0.744   0.610   0.088   1.105   −0.692   0.088   0.014   −0.073   0.088       −0.686   0.635   0.088   1.135   −0.747   0.088   −0.046   −0.051   0.088       −0.627   0.657   0.088   1.164   −0.803   0.088   −0.106   −0.033   0.088       −0.566   0.675   0.088   1.194   −0.859   0.088   −0.167   −0.018   0.088       −0.505   0.688   0.088   1.224   −0.914   0.088   −0.230   −0.007   0.088       −0.442   0.698   0.088   1.253   −0.970   0.088   −0.292   0.001   0.088       −0.380   0.702   0.088   1.282   −1.026   0.088   −0.355   0.005   0.088       −0.317   0.703   0.088   1.312   −1.082   0.088   −0.418   0.006   0.088       −0.254   0.698   0.088   1.341   −1.138   0.088   −0.481   0.003   0.088       −0.191   0.689   0.088   1.371   −1.193   0.088   −0.544   −0.004   0.088       −0.130   0.675   0.088   1.394   −1.251   0.088   −0.606   −0.015   0.088       −0.069   0.657   0.088   1.353   −1.289   0.088   −0.668   −0.029   0.088       −0.010   0.635   0.088   1.306   −1.249   0.088   −0.728   −0.047   0.088       0.048   0.610   0.088   1.267   −1.199   0.088   −0.788   −0.068   0.088       0.104   0.581   0.088   1.227   −1.151   0.088   −0.846   −0.092   0.088       0.159   0.549   0.088   1.187   −1.102   0.088   −0.903   −0.119   0.088       0.211   0.515   0.088   1.147   −1.053   0.088   −0.959   −0.148   0.088       0.262   0.478   0.088   1.107   −1.004   0.088   −1.013   −0.180   0.088       0.312   0.438   0.088   1.066   −0.956   0.088   −1.067   −0.214   0.088       0.359   0.397   0.088   1.026   −0.908   0.088   −1.120   −0.248   0.088       0.405   0.353   0.088   0.985   −0.860   0.088   −1.174   −0.281   0.088       0.449   0.308   0.088   0.943   −0.812   0.088   −1.232   −0.303   0.088       −1.252   0.091   0.10   −0.173   0.686   0.10   1.022   −0.550   0.10       −1.218   −0.282   0.10   −0.089   −0.026   0.10   0.910   −0.777   0.10       −1.305   −0.217   0.10   −0.488   0.693   0.10   0.731   −0.060   0.10       −1.274   0.032   0.10   −0.299   0.703   0.10   1.194   −1.116   0.10       −1.194   0.203   0.10   −0.028   −0.046   0.10   0.952   −0.824   0.10       −1.106   −0.225   0.10   −0.464   0.019   0.10   0.783   −0.636   0.10       −1.309   −0.154   0.10   −0.337   0.019   0.10   1.142   −0.773   0.10       −1.159   0.257   0.10   −0.112   0.670   0.10   1.201   −0.884   0.10       −1.279   −0.273   0.10   0.031   −0.068   0.10   0.649   −0.501   0.10       −1.305   −0.091   0.10   −0.274   0.013   0.10   0.993   −0.872   0.10       −1.122   0.308   0.10   −0.425   0.701   0.10   1.172   −0.829   0.10       −1.292   −0.029   0.10   −0.236   0.697   0.10   0.866   −0.275   0.10       −1.160   −0.258   0.10   −0.400   0.021   0.10   1.115   −1.018   0.10       −1.225   0.148   0.10   0.372   0.380   0.10   0.800   −0.167   0.10       −0.589   0.004   0.10   0.411   −0.294   0.10   1.112   −0.717   0.10       −0.841   0.560   0.10   0.255   −0.185   0.10   1.052   −0.606   0.10       −0.772   −0.047   0.10   0.557   −0.415   0.10   0.868   −0.729   0.10       −0.944   −0.126   0.10   0.089   −0.094   0.10   0.898   −0.329   0.10       −0.611   0.664   0.10   0.583   0.145   0.10   0.696   −0.008   0.10       −1.082   0.356   0.10   0.325   0.423   0.10   0.833   −0.221   0.10       −0.999   −0.157   0.10   0.509   −0.373   0.10   1.155   −1.067   0.10       −0.944   0.487   0.10   0.461   0.290   0.10   1.075   −0.969   0.10       −0.712   −0.026   0.10   0.360   −0.256   0.10   0.659   0.044   0.10       −1.038   0.402   0.10   0.277   0.463   0.10   0.991   −0.495   0.10       −0.786   0.591   0.10   0.603   −0.458   0.10   0.766   −0.113   0.10       −0.651   −0.009   0.10   0.201   −0.153   0.10   0.826   −0.683   0.10       −0.671   0.644   0.10   0.503   0.243   0.10   0.694   −0.545   0.10       −0.831   −0.070   0.10   0.064   0.600   0.10   0.960   −0.439   0.10       −0.550   0.681   0.10   0.226   0.501   0.10   0.739   −0.591   0.10       −0.992   0.446   0.10   0.174   0.537   0.10   1.349   −1.164   0.10       −0.527   0.014   0.10   0.460   −0.333   0.10   1.369   −1.277   0.10       −0.894   0.525   0.10   0.622   0.095   0.10   1.234   −1.165   0.10       −0.729   0.619   0.10   0.417   0.336   0.10   1.261   −0.996   0.10       −1.053   −0.190   0.10   0.145   −0.122   0.10   1.379   −1.220   0.10       −0.888   −0.096   0.10   0.120   0.570   0.10   1.313   −1.264   0.10       −0.052   0.651   0.10   0.308   −0.220   0.10   1.369   −1.277   0.10       −0.362   0.704   0.10   0.544   0.194   0.10   1.231   −0.940   0.10       −0.150   −0.009   0.10   1.082   −0.661   0.10   1.319   −1.108   0.10       −0.212   0.004   0.10   0.929   −0.384   0.10   1.274   −1.214   0.10       0.007   0.627   0.10   1.034   −0.921   0.10   1.290   −1.052   0.10       −1.170   0.232   0.20   −0.258   0.126   0.20   0.794   −0.651   0.20       −1.139   0.284   0.20   −0.378   0.143   0.20   1.167   −0.912   0.20       −1.246   0.004   0.20   −0.446   0.717   0.20   1.204   −1.175   0.20       −1.236   0.063   0.20   −0.199   0.112   0.20   0.690   −0.070   0.20       −1.219   0.122   0.20   −0.084   0.074   0.20   1.195   −0.966   0.20       −1.196   0.178   0.20   −0.317   0.136   0.20   0.833   −0.697   0.20       −1.165   −0.125   0.20   −0.265   0.711   0.20   0.909   −0.791   0.20       −1.222   −0.111   0.20   0.021   0.616   0.20   0.755   −0.604   0.20       −1.246   −0.057   0.20   −0.498   0.143   0.20   0.908   −0.433   0.20       −1.107   −0.108   0.20   −0.147   0.685   0.20   1.020   −0.935   0.20       −0.941   0.511   0.20   −0.205   0.701   0.20   0.755   −0.172   0.20       −0.791   0.070   0.20   −0.385   0.720   0.20   0.967   −0.539   0.20       −1.003   −0.045   0.20   0.398   0.316   0.20   0.848   −0.328   0.20       −0.737   0.641   0.20   0.466   −0.295   0.20   1.110   −0.806   0.20       −0.618   0.126   0.20   0.552   −0.380   0.20   0.657   −0.020   0.20       −0.681   0.665   0.20   0.268   0.443   0.20   1.130   −1.079   0.20       −0.846   0.045   0.20   0.594   −0.423   0.20   1.167   −1.127   0.20       −0.565   0.699   0.20   0.622   0.031   0.20   0.716   −0.558   0.20       −0.791   0.614   0.20   0.183   −0.067   0.20   0.996   −0.592   0.20       −1.105   0.335   0.20   0.233   −0.102   0.20   0.938   −0.486   0.20       −0.843   0.583   0.20   0.438   0.270   0.20   0.871   −0.744   0.20       −1.068   0.382   0.20   0.329   −0.175   0.20   0.946   −0.839   0.20       −0.559   0.137   0.20   0.282   −0.138   0.20   0.676   −0.513   0.20       −0.899   0.017   0.20   0.074   0.586   0.20   1.057   −0.983   0.20       −0.893   0.548   0.20   0.477   0.224   0.20   1.223   −1.020   0.20       −1.028   0.428   0.20   0.222   0.482   0.20   0.818   −0.276   0.20       −0.952   −0.013   0.20   0.080   −0.004   0.20   1.025   −0.645   0.20       −0.624   0.684   0.20   0.125   0.554   0.20   1.139   −0.859   0.20       −1.055   −0.077   0.20   0.515   0.177   0.20   0.723   −0.121   0.20       −0.986   0.471   0.20   0.376   −0.214   0.20   1.082   −0.752   0.20       −0.734   0.092   0.20   0.635   −0.468   0.20   0.787   −0.224   0.20       −0.677   0.111   0.20   0.552   0.129   0.20   1.053   −0.699   0.20       −0.325   0.718   0.20   0.174   0.519   0.20   0.983   −0.887   0.20       −0.141   0.095   0.20   0.313   0.402   0.20   0.878   −0.381   0.20       −0.506   0.710   0.20   0.132   −0.035   0.20   1.294   −1.234   0.20       0.027   0.025   0.20   0.356   0.359   0.20   1.251   −1.074   0.20       −0.089   0.666   0.20   0.509   −0.337   0.20   1.307   −1.181   0.20       −0.033   0.643   0.20   0.421   −0.254   0.20   1.240   −1.224   0.20       −0.438   0.145   0.20   0.588   0.080   0.20   1.294   −1.234   0.20       −0.028   0.051   0.20   1.094   −1.031   0.20   1.279   −1.127   0.20       −1.113   0.033   0.30   −0.406   0.750   0.30   0.931   −0.851   0.30       −1.144   0.272   0.30   −0.468   0.270   0.30   0.688   −0.526   0.30       −1.182   0.163   0.30   −0.078   0.172   0.30   1.210   −1.087   0.30       −1.187   0.105   0.30   −0.070   0.669   0.30   1.033   −0.992   0.30       −1.118   0.324   0.30   −0.295   0.251   0.30   1.077   −0.829   0.30       −1.166   0.219   0.30   −0.234   0.728   0.30   0.897   −0.804   0.30       −1.166   0.053   0.30   −0.130   0.197   0.30   1.134   −1.133   0.30       −1.054   0.421   0.30   −0.239   0.236   0.30   0.652   −0.480   0.30       −0.793   0.648   0.30   0.031   0.612   0.30   0.759   −0.617   0.30       −1.017   0.465   0.30   −0.410   0.268   0.30   0.999   −0.945   0.30       −0.803   0.185   0.30   −0.184   0.218   0.30   0.648   −0.072   0.30       −1.005   0.071   0.30   0.300   −0.095   0.30   1.168   −1.180   0.30       −0.695   0.229   0.30   0.126   0.545   0.30   0.968   −0.624   0.30       −0.742   0.676   0.30   0.584   0.025   0.30   1.157   −0.984   0.30       −0.977   0.507   0.30   0.337   0.346   0.30   0.679   −0.121   0.30       −0.854   0.158   0.30   0.464   −0.259   0.30   0.884   −0.472   0.30       −0.526   0.267   0.30   0.424   −0.217   0.30   1.184   −1.035   0.30       −0.583   0.259   0.30   0.616   −0.435   0.30   0.798   −0.320   0.30       −0.689   0.699   0.30   0.551   0.073   0.30   0.828   −0.710   0.30       −0.935   0.547   0.30   0.616   −0.024   0.30   1.221   −1.189   0.30       −0.904   0.129   0.30   0.375   0.303   0.30   0.965   −0.898   0.30       −0.640   0.246   0.30   0.079   0.580   0.30   1.104   −0.881   0.30       −0.635   0.719   0.30   0.171   0.509   0.30   0.995   −0.675   0.30       −0.843   0.618   0.30   0.383   −0.176   0.30   0.709   −0.171   0.30       −0.890   0.584   0.30   0.256   −0.057   0.30   0.863   −0.757   0.30       −1.057   0.045   0.30   0.579   −0.390   0.30   0.794   −0.664   0.30       −0.954   0.100   0.30   0.518   0.120   0.30   0.940   −0.573   0.30       −1.088   0.373   0.30   0.483   0.167   0.30   1.022   −0.727   0.30       −0.750   0.209   0.30   0.412   0.258   0.30   0.739   −0.220   0.30       −0.578   0.733   0.30   0.448   0.213   0.30   1.130   −0.932   0.30       −0.290   0.739   0.30   0.503   −0.302   0.30   0.827   −0.371   0.30       0.024   0.116   0.30   0.297   0.389   0.30   1.100   −1.086   0.30       −0.464   0.749   0.30   0.215   0.470   0.30   1.066   −1.039   0.30       −0.019   0.642   0.30   0.120   0.052   0.30   0.856   −0.421   0.30       −0.352   0.262   0.30   0.342   −0.135   0.30   1.050   −0.778   0.30       −0.026   0.146   0.30   0.212   −0.019   0.30   0.724   −0.571   0.30       −0.123   0.692   0.30   0.541   −0.346   0.30   1.221   −1.189   0.30       −0.348   0.747   0.30   0.167   0.017   0.30   0.769   −0.270   0.30       −0.521   0.744   0.30   0.257   0.430   0.30   0.912   −0.522   0.30       −0.178   0.712   0.30   0.073   0.085   0.30   1.237   −1.138   0.30       −1.118   0.333   0.40   −0.332   0.374   0.40   0.279   0.385   0.40       −1.116   0.226   0.40   −0.278   0.359   0.40   0.449   0.166   0.40       −1.130   0.279   0.40   −0.497   0.391   0.40   0.603   −0.066   0.40       −0.742   0.725   0.40   −0.203   0.751   0.40   0.881   −0.547   0.40       −0.607   0.378   0.40   −0.310   0.781   0.40   1.011   −0.792   0.40       −1.070   0.433   0.40   −0.226   0.340   0.40   0.967   −0.948   0.40       −0.913   0.248   0.40   0.016   0.204   0.40   1.138   −1.039   0.40       −0.966   0.563   0.40   −0.053   0.679   0.40   0.651   −0.490   0.40       −0.883   0.637   0.40   −0.386   0.384   0.40   0.905   −0.856   0.40       −0.531   0.791   0.40   −0.152   0.730   0.40   0.717   −0.256   0.40       −0.838   0.670   0.40   −0.175   0.318   0.40   0.986   −0.743   0.40       −0.692   0.748   0.40   0.226   0.023   0.40   0.999   −0.993   0.40       −0.661   0.364   0.40   0.484   −0.268   0.40   1.113   −0.990   0.40       −0.864   0.275   0.40   0.304   −0.057   0.40   0.874   −0.810   0.40       −0.586   0.781   0.40   0.103   0.135   0.40   0.684   −0.536   0.40       −1.039   0.479   0.40   0.242   0.427   0.40   0.854   −0.498   0.40       −0.815   0.300   0.40   0.417   0.211   0.40   0.689   −0.208   0.40       −1.070   0.198   0.40   0.573   −0.019   0.40   0.960   −0.694   0.40       −0.639   0.767   0.40   0.519   −0.312   0.40   1.030   −1.039   0.40       −1.097   0.384   0.40   0.341   −0.098   0.40   0.716   −0.581   0.40       −0.552   0.387   0.40   0.204   0.467   0.40   0.827   −0.449   0.40       −0.765   0.324   0.40   0.383   0.256   0.40   1.088   −0.940   0.40       −1.015   0.203   0.40   0.543   0.028   0.40   0.661   −0.161   0.40       −0.791   0.699   0.40   0.186   0.061   0.40   0.800   −0.401   0.40       −0.714   0.346   0.40   0.165   0.507   0.40   0.934   −0.645   0.40       −1.004   0.522   0.40   0.552   −0.356   0.40   1.062   −1.085   0.40       −0.926   0.601   0.40   0.349   0.299   0.40   1.145   −1.138   0.40       −0.963   0.224   0.40   0.512   0.074   0.40   0.748   −0.626   0.40       −0.441   0.390   0.40   0.378   −0.140   0.40   1.094   −1.130   0.40       −0.476   0.796   0.40   0.586   −0.401   0.40   0.773   −0.353   0.40       −0.039   0.616   0.40   0.414   −0.182   0.40   0.907   −0.596   0.40       −0.125   0.293   0.40   0.124   0.545   0.40   1.063   −0.891   0.40       −0.420   0.796   0.40   0.314   0.343   0.40   1.037   −0.842   0.40       −0.030   0.235   0.40   0.481   0.120   0.40   0.936   −0.902   0.40       −0.256   0.768   0.40   0.145   0.099   0.40   1.163   −1.089   0.40       0.060   0.170   0.40   0.632   −0.113   0.40   0.779   −0.672   0.40       −0.102   0.706   0.40   0.619   −0.445   0.40   1.145   −1.138   0.40       −0.006   0.649   0.40   0.265   −0.017   0.40   0.811   −0.718   0.40       −0.365   0.791   0.40   0.082   0.582   0.40   0.842   −0.764   0.40       −0.077   0.265   0.40   0.450   −0.225   0.40   0.745   −0.304   0.40       −0.783   0.446   0.50   −0.368   0.494   0.50   0.326   −0.061   0.50       −0.992   0.603   0.50   −0.429   0.853   0.50   0.153   0.141   0.50       −0.786   0.769   0.50   −0.175   0.780   0.50   0.352   0.263   0.50       −0.734   0.466   0.50   −0.083   0.726   0.50   0.154   0.514   0.50       −0.535   0.851   0.50   −0.084   0.354   0.50   0.289   0.349   0.50       −0.981   0.371   0.50   −0.317   0.479   0.50   0.637   −0.186   0.50       −1.025   0.561   0.50   −0.482   0.855   0.50   0.499   0.041   0.50       −0.832   0.742   0.50   −0.041   0.322   0.50   0.956   −0.984   0.50       −0.587   0.842   0.50   −0.267   0.460   0.50   1.015   −0.889   0.50       −0.683   0.483   0.50   0.042   0.627   0.50   0.810   −0.761   0.50       −0.579   0.506   0.50   0.118   0.553   0.50   0.767   −0.418   0.50       −0.930   0.384   0.50   0.359   −0.103   0.50   1.065   −1.077   0.50       −1.052   0.515   0.50   0.189   0.101   0.50   0.665   −0.539   0.50       −0.876   0.711   0.50   0.470   0.086   0.50   0.818   −0.511   0.50       −0.639   0.830   0.50   0.321   0.306   0.50   0.843   −0.558   0.50       −0.880   0.404   0.50   0.610   −0.140   0.50   0.742   −0.371   0.50       −1.072   0.466   0.50   0.555   −0.049   0.50   0.868   −0.605   0.50       −0.917   0.678   0.50   0.441   0.131   0.50   0.985   −1.028   0.50       −0.690   0.813   0.50   0.412   0.175   0.50   0.991   −0.841   0.50       −0.832   0.425   0.50   0.391   −0.146   0.50   0.839   −0.806   0.50       −1.071   0.414   0.50   0.224   0.062   0.50   0.694   −0.583   0.50       −0.739   0.793   0.50   0.582   −0.095   0.50   0.716   −0.325   0.50       −0.632   0.497   0.50   0.293   −0.020   0.50   1.016   −1.071   0.50       −0.956   0.642   0.50   0.576   −0.406   0.50   0.967   −0.794   0.50       −0.526   0.511   0.50   0.423   −0.188   0.50   0.781   −0.717   0.50       −1.034   0.377   0.50   0.259   0.021   0.50   0.868   −0.851   0.50       −0.128   0.754   0.50   0.079   0.216   0.50   0.723   −0.628   0.50       −0.273   0.821   0.50   0.257   0.391   0.50   0.690   −0.279   0.50       0.002   0.662   0.50   0.606   −0.450   0.50   1.065   −1.077   0.50       0.000   0.288   0.50   0.455   −0.231   0.50   0.943   −0.746   0.50       −0.219   0.438   0.50   0.116   0.179   0.50   0.898   −0.895   0.50       −0.473   0.510   0.50   0.223   0.433   0.50   1.063   −0.984   0.50       −0.324   0.836   0.50   0.382   0.219   0.50   0.752   −0.672   0.50       −0.223   0.802   0.50   0.527   −0.004   0.50   0.893   −0.652   0.50       0.040   0.253   0.50   0.516   −0.318   0.50   1.085   −1.032   0.50       −0.173   0.412   0.50   0.081   0.591   0.50   0.663   −0.232   0.50       −0.420   0.505   0.50   0.546   −0.362   0.50   0.793   −0.465   0.50       −0.040   0.695   0.50   0.635   −0.494   0.50   0.918   −0.699   0.50       −0.376   0.847   0.50   0.189   0.474   0.50   0.927   −0.940   0.50       −0.127   0.384   0.50   0.486   −0.275   0.50   1.039   −0.937   0.50       −0.849   0.572   0.60   −0.259   0.562   0.60   0.638   −0.236   0.60       −0.603   0.635   0.60   −0.056   0.411   0.60   0.406   0.159   0.60       −0.728   0.885   0.60   0.046   0.651   0.60   0.379   0.202   0.60       −0.530   0.929   0.60   −0.146   0.817   0.60   0.237   0.413   0.60       −0.680   0.902   0.60   −0.401   0.619   0.60   0.086   0.264   0.60       −0.976   0.712   0.60   −0.378   0.918   0.60   0.080   0.614   0.60       −0.898   0.559   0.60   −0.305   0.585   0.60   0.245   0.066   0.60       −0.653   0.627   0.60   −0.094   0.445   0.60   0.324   0.288   0.60       −0.942   0.750   0.60   −0.105   0.788   0.60   0.392   −0.142   0.60       −0.949   0.556   0.60   −0.329   0.906   0.60   0.532   −0.355   0.60       −0.703   0.616   0.60   0.538   −0.059   0.60   0.783   −0.505   0.60       −0.775   0.865   0.60   0.563   −0.103   0.60   0.662   −0.281   0.60       −0.904   0.784   0.60   0.266   0.372   0.60   0.640   −0.527   0.60       −0.994   0.576   0.60   0.113   0.575   0.60   0.990   −1.003   0.60       −0.752   0.602   0.60   0.214   0.106   0.60   0.776   −0.743   0.60       −0.501   0.636   0.60   0.363   −0.100   0.60   0.923   −0.776   0.60       −0.631   0.914   0.60   0.504   −0.312   0.60   0.912   −0.957   0.60       −0.863   0.814   0.60   0.433   0.116   0.60   0.807   −0.550   0.60       −1.016   0.620   0.60   0.295   0.330   0.60   0.721   −0.657   0.60       −0.800   0.587   0.60   0.146   0.536   0.60   0.687   −0.325   0.60       −0.552   0.638   0.60   0.183   0.146   0.60   0.748   −0.700   0.60       −0.581   0.924   0.60   0.334   −0.058   0.60   0.946   −0.822   0.60       −0.820   0.841   0.60   0.613   −0.484   0.60   0.885   −0.914   0.60       −1.003   0.669   0.60   0.512   −0.015   0.60   0.830   −0.595   0.60       −0.352   0.604   0.60   0.588   −0.147   0.60   0.711   −0.370   0.60       −0.133   0.477   0.60   0.460   0.073   0.60   0.968   −0.868   0.60       0.052   0.302   0.60   0.177   0.495   0.60   0.858   −0.871   0.60       −0.065   0.756   0.60   0.151   0.186   0.60   0.854   −0.640   0.60       −0.281   0.889   0.60   0.305   −0.017   0.60   0.735   −0.415   0.60       −0.173   0.508   0.60   0.449   −0.227   0.60   0.694   −0.613   0.60       0.017   0.339   0.60   0.586   −0.441   0.60   0.991   −0.913   0.60       −0.027   0.723   0.60   0.613   −0.192   0.60   0.830   −0.828   0.60       −0.234   0.868   0.60   0.486   0.029   0.60   0.877   −0.685   0.60       −0.479   0.930   0.60   0.352   0.245   0.60   0.990   −1.003   0.60       −0.450   0.630   0.60   0.477   −0.269   0.60   0.759   −0.460   0.60       −0.216   0.536   0.60   0.207   0.455   0.60   0.667   −0.570   0.60       −0.019   0.375   0.60   0.119   0.225   0.60   1.011   −0.960   0.60       0.010   0.688   0.60   0.275   0.025   0.60   0.803   −0.785   0.60       −0.190   0.844   0.60   0.421   −0.184   0.60   0.900   −0.731   0.60       −0.429   0.926   0.60   0.559   −0.398   0.60   0.943   −0.998   0.60       −0.793   0.755   0.70   −0.065   0.465   0.70   0.372   0.187   0.70       −0.613   1.015   0.70   −0.051   0.777   0.70   0.231   0.081   0.70       −0.844   0.948   0.70   −0.241   0.928   0.70   0.244   0.393   0.70       −0.599   0.768   0.70   −0.468   1.010   0.70   0.364   −0.122   0.70       −0.503   0.755   0.70   −0.282   0.658   0.70   0.106   0.593   0.70       −0.841   0.748   0.70   −0.098   0.500   0.70   0.544   −0.411   0.70       −0.565   1.017   0.70   0.060   0.316   0.70   0.620   −0.535   0.70       −0.889   0.747   0.70   −0.018   0.742   0.70   0.633   −0.279   0.70       −0.801   0.970   0.70   −0.200   0.902   0.70   0.517   −0.066   0.70       −0.648   0.769   0.70   −0.420   1.000   0.70   0.397   0.145   0.70       −0.959   0.803   0.70   −0.205   0.600   0.70   0.203   0.121   0.70       −0.516   1.015   0.70   −0.323   0.684   0.70   0.270   0.352   0.70       −0.934   0.763   0.70   0.541   −0.108   0.70   0.338   −0.081   0.70       −0.756   0.987   0.70   0.422   0.104   0.70   0.135   0.554   0.70       −0.696   0.766   0.70   0.175   0.160   0.70   0.467   −0.287   0.70       −0.949   0.850   0.70   0.296   0.311   0.70   0.594   −0.494   0.70       −0.959   0.803   0.70   0.312   −0.041   0.70   0.697   −0.659   0.70       −0.709   1.000   0.70   0.163   0.514   0.70   0.826   −0.864   0.70       −0.745   0.761   0.70   0.442   −0.246   0.70   0.896   −0.799   0.70       −0.921   0.890   0.70   0.569   −0.452   0.70   0.789   −0.581   0.70       −0.661   1.010   0.70   0.564   −0.151   0.70   0.678   −0.365   0.70       −0.885   0.922   0.70   0.446   0.061   0.70   0.671   −0.617   0.70       −0.551   0.764   0.70   0.147   0.200   0.70   0.801   −0.823   0.70       −0.132   0.535   0.70   0.322   0.270   0.70   0.917   −0.842   0.70       0.030   0.354   0.70   0.285   0.000   0.70   0.811   −0.624   0.70       −0.168   0.568   0.70   0.190   0.474   0.70   0.701   −0.408   0.70       0.015   0.706   0.70   0.416   −0.204   0.70   0.645   −0.576   0.70       −0.160   0.874   0.70   0.493   −0.328   0.70   0.775   −0.782   0.70       −0.374   0.988   0.70   0.587   −0.193   0.70   0.929   −0.888   0.70       −0.366   0.706   0.70   0.470   0.019   0.70   0.832   −0.668   0.70       −0.001   0.392   0.70   0.118   0.239   0.70   0.723   −0.451   0.70       0.046   0.669   0.70   0.347   0.229   0.70   0.749   −0.740   0.70       −0.123   0.843   0.70   0.258   0.040   0.70   0.897   −0.921   0.70       −0.328   0.971   0.70   0.217   0.434   0.70   0.854   −0.711   0.70       −0.243   0.630   0.70   0.390   −0.163   0.70   0.745   −0.494   0.70       −0.033   0.429   0.70   0.076   0.631   0.70   0.723   −0.700   0.70       −0.411   0.726   0.70   0.518   −0.370   0.70   0.854   −0.904   0.70       −0.086   0.811   0.70   0.610   −0.236   0.70   0.875   −0.755   0.70       −0.284   0.951   0.70   0.494   −0.023   0.70   0.767   −0.537   0.70       −0.456   0.742   0.70   0.089   0.278   0.70   0.656   −0.322   0.70       −0.713   1.119   0.80   −0.186   0.641   0.80   0.199   0.111   0.80       −0.888   0.951   0.80   −0.361   0.796   0.80   0.255   0.356   0.80       −0.758   1.109   0.80   −0.392   1.075   0.80   0.371   0.154   0.80       −0.526   1.116   0.80   −0.194   0.952   0.80   0.273   −0.008   0.80       −0.711   0.914   0.80   −0.032   0.784   0.80   0.148   0.190   0.80       −0.618   0.905   0.80   −0.010   0.423   0.80   0.483   −0.052   0.80       −0.850   0.925   0.80   −0.154   0.606   0.80   0.592   −0.259   0.80       −0.802   1.093   0.80   −0.323   0.768   0.80   0.613   −0.568   0.80       −0.573   1.123   0.80   −0.025   0.710   0.80   0.491   −0.368   0.80       −0.572   0.895   0.80   −0.436   1.092   0.80   0.371   −0.168   0.80       −0.804   0.918   0.80   −0.231   0.981   0.80   0.123   0.230   0.80       −0.843   1.070   0.80   −0.062   0.820   0.80   0.106   0.595   0.80       −0.619   1.126   0.80   0.206   0.437   0.80   0.231   0.397   0.80       −0.527   0.881   0.80   0.325   0.235   0.80   0.322   −0.088   0.80       −0.757   0.916   0.80   0.097   0.269   0.80   0.348   0.194   0.80       −0.877   1.038   0.80   0.439   0.031   0.80   0.461   −0.011   0.80       −0.664   0.911   0.80   0.549   −0.176   0.80   0.571   −0.218   0.80       −0.666   1.125   0.80   0.539   −0.449   0.80   0.249   0.032   0.80       −0.897   0.996   0.80   0.419   −0.248   0.80   0.637   −0.608   0.80       0.053   0.672   0.80   0.298   −0.048   0.80   0.515   −0.409   0.80       0.018   0.385   0.80   0.182   0.476   0.80   0.395   −0.208   0.80       −0.124   0.571   0.80   0.302   0.276   0.80   0.656   −0.384   0.80       −0.287   0.739   0.80   0.417   0.072   0.80   0.759   −0.594   0.80       −0.483   0.864   0.80   0.224   0.072   0.80   0.662   −0.648   0.80       −0.481   1.105   0.80   0.527   −0.135   0.80   0.856   −0.807   0.80       −0.269   1.008   0.80   0.635   −0.343   0.80   0.835   −0.846   0.80       −0.093   0.855   0.80   0.174   0.151   0.80   0.739   −0.552   0.80       −0.045   0.346   0.80   0.564   −0.489   0.80   0.687   −0.687   0.80       −0.094   0.534   0.80   0.443   −0.288   0.80   0.840   −0.764   0.80       −0.252   0.708   0.80   0.071   0.307   0.80   0.719   −0.510   0.80       −0.441   0.844   0.80   0.157   0.516   0.80   0.712   −0.727   0.80       −0.309   1.033   0.80   0.278   0.316   0.80   0.820   −0.721   0.80       −0.125   0.889   0.80   0.394   0.113   0.80   0.698   −0.468   0.80       −0.066   0.498   0.80   0.080   0.633   0.80   0.736   −0.767   0.80       −0.159   0.921   0.80   0.505   −0.093   0.80   0.800   −0.679   0.80       −0.218   0.675   0.80   0.614   −0.301   0.80   0.791   −0.843   0.80       −0.400   0.821   0.80   0.588   −0.529   0.80   0.677   −0.426   0.80       −0.350   1.055   0.80   0.467   −0.328   0.80   0.761   −0.807   0.80       −0.003   0.747   0.80   0.346   −0.128   0.80   0.780   −0.637   0.80       −0.037   0.460   0.80   0.132   0.555   0.80   0.835   −0.846   0.80       −0.508   1.226   0.90   0.022   0.358   0.90   0.604   −0.336   0.90       −0.705   1.070   0.90   −0.068   0.845   0.90   0.504   −0.133   0.90       −0.730   1.251   0.90   −0.215   1.017   0.90   0.401   0.069   0.90       −0.498   0.981   0.90   −0.388   1.164   0.90   0.294   0.269   0.90       −0.749   1.080   0.90   −0.425   0.927   0.90   0.142   0.166   0.90       −0.685   1.257   0.90   −0.267   0.764   0.90   0.181   0.466   0.90       −0.536   1.005   0.90   −0.129   0.584   0.90   0.259   −0.028   0.90       −0.792   1.093   0.90   −0.003   0.396   0.90   0.062   0.659   0.90       −0.640   1.257   0.90   −0.041   0.808   0.90   0.376   −0.223   0.90       −0.576   1.026   0.90   −0.184   0.984   0.90   0.493   −0.417   0.90       −0.830   1.168   0.90   −0.350   1.138   0.90   0.614   −0.609   0.90       −0.825   1.124   0.90   −0.461   0.955   0.90   0.624   −0.377   0.90       −0.595   1.252   0.90   −0.297   0.798   0.90   0.524   −0.173   0.90       −0.618   1.043   0.90   −0.156   0.621   0.90   0.422   0.029   0.90       −0.808   1.207   0.90   −0.028   0.434   0.90   0.315   0.229   0.90       −0.830   1.168   0.90   0.213   0.049   0.90   0.118   0.204   0.90       −0.551   1.241   0.90   0.111   0.582   0.90   0.204   0.427   0.90       −0.661   1.058   0.90   0.329   −0.145   0.90   0.236   0.010   0.90       −0.772   1.234   0.90   0.446   −0.339   0.90   0.086   0.621   0.90       −0.015   0.771   0.90   0.565   −0.533   0.90   0.353   −0.184   0.90       −0.154   0.951   0.90   0.565   −0.255   0.90   0.470   −0.378   0.90       −0.315   1.110   0.90   0.463   −0.052   0.90   0.590   −0.571   0.90       −0.327   0.832   0.90   0.358   0.149   0.90   0.544   −0.214   0.90       −0.183   0.658   0.90   0.070   0.281   0.90   0.442   −0.012   0.90       −0.052   0.472   0.90   0.249   0.348   0.90   0.337   0.189   0.90       0.011   0.734   0.90   0.189   0.088   0.90   0.094   0.243   0.90       −0.124   0.916   0.90   0.134   0.544   0.90   0.227   0.388   0.90       −0.280   1.080   0.90   0.306   −0.106   0.90   0.686   −0.724   0.90       −0.466   1.208   0.90   0.423   −0.301   0.90   0.759   −0.664   0.90       −0.359   0.865   0.90   0.541   −0.494   0.90   0.663   −0.459   0.90       −0.210   0.694   0.90   0.585   −0.295   0.90   0.662   −0.686   0.90       −0.078   0.510   0.90   0.483   −0.092   0.90   0.777   −0.706   0.90       0.046   0.320   0.90   0.380   0.109   0.90   0.682   −0.500   0.90       0.037   0.697   0.90   0.272   0.309   0.90   0.785   −0.749   0.90       −0.096   0.881   0.90   0.165   0.127   0.90   0.701   −0.541   0.90       −0.247   1.049   0.90   0.158   0.505   0.90   0.752   −0.778   0.90       −0.426   1.187   0.90   0.283   −0.067   0.90   0.720   −0.582   0.90       −0.391   0.896   0.90   0.399   −0.262   0.90   0.713   −0.761   0.90       −0.238   0.729   0.90   0.517   −0.456   0.90   0.740   −0.623   0.90       −0.103   0.547   0.90   0.638   −0.647   0.90   0.644   −0.418   0.90       −0.815   1.203   0.92   0.308   −0.119   0.92   0.367   0.129   0.92       −0.812   1.158   0.92   0.331   −0.157   0.92   0.346   0.168   0.92       −0.783   1.126   0.92   0.354   −0.196   0.92   0.325   0.208   0.92       −0.740   1.112   0.92   0.377   −0.234   0.92   0.304   0.247   0.92       −0.697   1.100   0.92   0.400   −0.273   0.92   0.282   0.287   0.92       −0.655   1.086   0.92   0.424   −0.311   0.92   0.260   0.326   0.92       −0.613   1.070   0.92   0.447   −0.349   0.92   0.239   0.365   0.92       −0.573   1.050   0.92   0.470   −0.387   0.92   0.216   0.404   0.92       −0.534   1.028   0.92   0.494   −0.425   0.92   0.194   0.442   0.92       −0.497   1.003   0.92   0.517   −0.463   0.92   0.171   0.481   0.92       −0.462   0.975   0.92   0.541   −0.501   0.92   0.148   0.519   0.92       −0.428   0.946   0.92   0.565   −0.539   0.92   0.125   0.558   0.92       −0.396   0.915   0.92   0.589   −0.577   0.92   0.101   0.596   0.92       −0.365   0.883   0.92   0.613   −0.614   0.92   0.077   0.633   0.92       −0.335   0.849   0.92   0.637   −0.652   0.92   0.053   0.671   0.92       −0.305   0.815   0.92   0.661   −0.690   0.92   0.028   0.708   0.92       −0.277   0.781   0.92   0.685   −0.728   0.92   0.003   0.745   0.92       −0.249   0.746   0.92   0.715   −0.761   0.92   −0.022   0.782   0.92       −0.222   0.710   0.92   0.757   −0.757   0.92   −0.048   0.819   0.92       −0.195   0.674   0.92   0.774   −0.718   0.92   −0.075   0.855   0.92       −0.169   0.638   0.92   0.758   −0.676   0.92   −0.102   0.891   0.92       −0.143   0.602   0.92   0.739   −0.636   0.92   −0.129   0.926   0.92       −0.118   0.565   0.92   0.720   −0.595   0.92   −0.157   0.961   0.92       −0.093   0.528   0.92   0.701   −0.554   0.92   −0.186   0.995   0.92       −0.068   0.490   0.92   0.683   −0.514   0.92   −0.216   1.028   0.92       −0.044   0.453   0.92   0.664   −0.473   0.92   −0.247   1.061   0.92       −0.019   0.415   0.92   0.645   −0.433   0.92   −0.278   1.092   0.92       0.005   0.377   0.92   0.626   −0.392   0.92   −0.311   1.123   0.92       0.029   0.340   0.92   0.607   −0.352   0.92   −0.345   1.152   0.92       0.052   0.302   0.92   0.587   −0.311   0.92   −0.380   1.179   0.92       0.076   0.264   0.92   0.568   −0.271   0.92   −0.417   1.204   0.92       0.099   0.226   0.92   0.548   −0.231   0.92   −0.456   1.227   0.92       0.123   0.187   0.92   0.529   −0.191   0.92   −0.496   1.247   0.92       0.146   0.149   0.92   0.509   −0.151   0.92   −0.538   1.263   0.92       0.169   0.111   0.92   0.489   −0.110   0.92   −0.581   1.276   0.92       0.193   0.073   0.92   0.469   −0.070   0.92   −0.625   1.284   0.92       0.216   0.034   0.92   0.449   −0.030   0.92   −0.669   1.286   0.92       0.239   −0.004   0.92   0.428   0.010   0.92   −0.714   1.281   0.92       0.262   −0.042   0.92   0.408   0.049   0.92   −0.756   1.266   0.92       0.285   −0.081   0.92   0.387   0.089   0.92   −0.792   1.240   0.92                  
 
         [0031]     The origin of the X, Y coordinate values of Table I are identical to the origin of the X, Y coordinate values of Table II.  
         [0032]     In the preferred embodiment of the second stage bucket hereof, the datum U is 24.100 inches from the engine or rotor centerline. The bucket radial height is 11.280 inches from the datum to the cutter tooth on the tip shroud  40 . Consequently, the bucket radial height from the engine centerline is 35.380 inches. The airfoil sections start at Z=0% span, which is 2.221 inch from datum U (26.321 inches from the engine centerline). The airfoil sections end at Z=100% span, which is 11.122 inches from datum U (35.22 inches from the engine centerline). With respect to the non-dimensionalized value Z in Table I, Z=0.088 or 8.8% span, which corresponds to 3.005 inches from datum U (27.15 inches from the engine centerline). The Z value of Table I at 0.92 or 92% span corresponds to a distance of 10.410 inches from datum U (34.510 inches from the engine centerline).  
         [0033]     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, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.