Abstract:
A turbine bucket including a bucket airfoil having an airfoil shape is provided. The airfoil shape has a nominal profile according to the tables set forth in the specification. The X and Y coordinate are smoothly joined by an arc of radius R defining airfoil profile sections at each distance Z. The profile sections at the Z distances are joined smoothly with one another to form a complete airfoil shape.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    The present invention relates to turbines, particularly steam turbines, and more particularly relates to last-stage steam turbine buckets having improved aerodynamic, thermodynamic and mechanical properties. 
         [0002]    Last-stage buckets for turbines have for some time been the subject of substantial developmental work. It is highly desirable to optimize the performance of these last-stage buckets to reduce aerodynamic losses and to improve the thermodynamic performance of the turbine. Last-stage buckets are exposed to a wide range of flows, loads and strong dynamic forces. Factors that affect the final bucket profile design include the active length of the bucket, the pitch diameter and the high operating speed in both supersonic and subsonic flow regions. Damping and bucket fatigue are factors which must also be considered in the mechanical design of the bucket and its profile. These mechanical and dynamic response properties of the buckets, as well as others, such as aero-thermodynamic properties or material selection, all influence the optimum bucket profile. The last-stage steam turbine buckets require, therefore, a precisely defined bucket profile for optimal performance with minimal losses over a wide operating range. 
         [0003]    Adjacent rotor buckets are typically connected together by some form of cover bands or shroud bands around the periphery to confine the working fluid within a well-defined path and to increase the rigidity of the buckets. Grouped buckets, however, can be stimulated by a number of stimuli known to exist in the working fluid to vibrate at the natural frequencies of the bucket-cover assembly. If the vibration is sufficiently large, fatigue damage to the bucket material can occur and lead to crack initiation and eventual failure of the bucket components. Also, last-stage buckets operate in a wet steam environment and are subject to potential erosion by water droplets. A method of erosion protection sometimes used, is to either weld or braze a protective shield to the leading edge of each bucket at its upper active length. These shields, however, may be subject to stress corrosion cracking or departure from the buckets due to deterioration of the bonding material as in the case of a brazed shield. 
       BRIEF DESCRIPTION OF THE INVENTION 
       [0004]    In one aspect of the present invention, a turbine bucket including a bucket airfoil having an airfoil shape is provided. The airfoil has a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z and arc coordinate R as set forth in Tables 1-19. The X, Y, Z and R distances are in inches, and an arc of radius R smoothly joins the X and Y coordinate values. The airfoil profile sections are defined at each distance Z. The profile sections at the Z distances are joined smoothly with one another to form a complete airfoil shape. 
         [0005]    In another aspect of the present invention, a turbine wheel having a plurality of buckets is provided. The buckets include an airfoil having an airfoil shape defined by a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z and arc coordinate R as set forth in Tables 1-19. The X, Y, Z and R distances are in inches, and an arc of radius R smoothly joins the X and Y coordinate values. The airfoil profile sections are defined at each distance Z. The profile sections at the Z distances are joined smoothly with one another to form a complete airfoil shape. 
         [0006]    In yet another aspect of the present invention, a turbine including a turbine wheel having a plurality of buckets is provided. The buckets include an airfoil having an airfoil shape defined by a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z and arc coordinate R as set forth in Tables 1-19. The X, Y, Z and R distances are in inches, and an arc of radius R smoothly joins the X and Y coordinate values. The airfoil profile sections are defined at each distance Z. The profile sections at the Z distances are joined smoothly with one another to form a complete airfoil shape. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0007]      FIG. 1  is a perspective partial cut away illustration of a steam turbine. 
           [0008]      FIG. 2  is a perspective illustration of a turbine bucket that may be used with the steam turbine shown in  FIG. 1 . 
           [0009]      FIG. 3  is a graph illustrating a representative airfoil section of the bucket profile as defined by the tables set forth in the following specification. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0010]      FIG. 1  is a perspective partial cut away view of a steam turbine  10  including a rotor  12  that includes a shaft  14  and a low-pressure (LP) turbine  16 . LP turbine  16  includes a plurality of axially spaced rotor wheels  18 . A plurality of buckets  20  are mechanically coupled to each rotor wheel  18 . More specifically, buckets  20  are arranged in rows that extend circumferentially around each rotor wheel  18 . A plurality of stationary nozzles  22  extend circumferentially around shaft  14  and are axially positioned between adjacent rows of buckets  20 . Nozzles  22  cooperate with buckets  20  to form a turbine stage and to define a portion of a steam flow path through turbine  10 . 
         [0011]    In operation, steam  24  enters an inlet  26  of turbine  10  and is channeled through nozzles  22 . Nozzles  22  direct steam  24  downstream against buckets  20 . Steam  24  passes through the remaining stages imparting a force on buckets  20  causing rotor  12  to rotate. At least one end of turbine  10  may extend axially away from rotor  12  and may be attached to a load or machinery (not shown), such as, but not limited, to, a generator, and/or another turbine. Accordingly, a large steam turbine unit may actually include several turbines that are all co-axially coupled to the same shaft  14 . Such a unit may, for example, include a high-pressure turbine coupled to an intermediate-pressure turbine, which is coupled to a low-pressure turbine. 
         [0012]      FIG. 2  is a perspective view of a turbine bucket  20  that may be used with turbine  10 . Bucket  20  includes a blade portion  102  that includes a trailing edge  104  and a leading edge  106 , wherein steam flows generally from leading edge  106  to trailing edge  104 . Bucket  20  also includes a first concave sidewall  108  and a second convex sidewall  110 . First sidewall  108  and second sidewall  110  are connected axially at trailing edge  104  and leading edge  106 , and extend radially between a rotor blade root  112  and a rotor blade tip  114 . A blade chord distance  116  is a distance measured from trailing edge  104  to leading edge  106  at any point along a radial length  118  of blade  102 . In the exemplary embodiment, radial length  118  is approximately forty-five inches. Although radial length  118  is described herein as being equal to approximately forty-five inches, it will be understood that radial length  118  may be any suitable length depending on the desired application. Root  112  includes a dovetail  121  used for coupling bucket  20  to a rotor disc  122  along shaft  14 , and a blade platform  124  that determines a portion of a flow path through each bucket  20 . In the exemplary embodiment, dovetail  121  is a curved axial entry dovetail that engages a mating slot  125  defined in rotor disc  122 . However, in other embodiments, dovetail  121  could also be a straight axial entry dovetail, angled-axial entry dovetail, or any other suitable type of dovetail configuration. 
         [0013]    In the exemplary embodiment, first and second sidewalls,  108  and  110 , each include a mid-blade connection point  126  positioned between blade root  112  and blade tip  114  and used to couple adjacent buckets  20  together. In one embodiment, mid-blade connection point  126  is used to couple adjacent buckets  20  together with tie wires (not shown) to facilitate improving a vibratory response of buckets  20  in a mid region between root  112  and tip  114 . The mid-blade connection point can also be referred to as the mid-span or part-span shroud. The part-span shroud can be located at about 45% to about 65% of the radial length  118 , as measured from the blade platform  124 . 
         [0014]    An extension  128  is formed on a portion of blade  102  to alter the vibratory response of blade  102 . Extension  128  may be formed on blade  102  after a design of blade  102  has been fabricated, and has undergone production testing. At a particular point along radial length  118 , a chord distance  116  defines a shape of blade  102 . In one embodiment, extension  128  is formed by adding blade material to blade  102  such that at radial distance  118  where the blade material is added, chord distance  116  is extended past leading edge  106  and/or trailing edge  104  of blade  102  as originally formed. In another embodiment, blade material is removed from blade  102  such that at radial distance  118  where blade material has not been removed, chord distance  116  extends past leading edge  106  and/or trailing edge  104  of blade  102  as modified by removing material. In a further embodiment, extension  128  is formed integrally and material at extension  128  may be removed to tune each bucket as dictated by testing. Extension  128  is formed to coincide with an aerodynamic shape of blade  102  so as to facilitate minimizing a flow disturbance of steam  24  as it passes extension  128 . 
         [0015]    During design and manufacture of bucket  20 , a profile of blade  102  is determined and implemented. A profile is a cross-sectional view of blade  102  taken at radial distance  118 . A series of profiles of blade  102  taken at subdivisions of radial distance  118  define a shape of blade  102 . The shape of blade  102  is a component of an aerodynamic performance of blade  102 . After blade  102  has been manufactured the shape of blade  102  is relatively fixed, in that altering the shape of blade  102  may alter the vibratory response in an undesired way. In some known instances, it may be desirable to alter the vibratory response of blade  102  after blade  102  has been manufactured, such as during a post-manufacturing testing process. In order to maintain a predetermined performance of blade  102 , the shape of blade  102  may be modified in such a way, as determined by analysis, such as by computer analysis or by empirical study to add mass to blade  102  that alters the vibratory response of blade  102 . The analysis determines an optimum amount of mass needed to achieve a desired alteration of the vibratory response of blade  102 . Modifying blade  102  with extension  128  to add mass to blade  102 , tends to decrease the natural frequency of blade  102 . Modifying blade  102  with extension  128  to remove mass from blade  102 , tends to increase the natural frequency of blade  102 . Extension  128  may also be crafted to alter an aeromechanical characteristic of blade  102  such that an aerodynamic response of blade  102  to a flow of steam  24  past extension  128  will create a desirable change in the vibratory response of blade  102 . Thus, the addition of extension  128  may alter the vibratory response of blade  102  in at least two ways, a change of mass of blade  102  and a modification of the airfoil shape of blade  102 . Extension  128  may be designed to utilize both aspects of adding mass and changing airfoil shape to effect a change in the vibratory response of blade  102 . 
         [0016]    In operation, blade  102  undergoes a testing process to validate design requirements were met during the manufacturing process. One known test indicates a natural frequency of blade  102 . Modern design and manufacturing techniques are tending toward buckets  20  that are thinner in profile. A thinner profile tends to lower the overall natural frequencies of blade  102 . Lowering the natural frequency of blade  102  into the domain of the vibratory forces present in turbine  10 , may cause a resonance condition in any number or in an increased number of system modes that each will be de-tuned. To modify the natural frequency of blade  102 , mass may be added to or removed from blade  102 . To facilitate limiting lowering the natural frequency of blade  102  into the domain of the vibratory forces present in turbine  10 , a minimum amount of mass is added to blade  102 . In the exemplary embodiment, extension  128  is machined from a forged material envelope of leading edge  106  of blade  102 . In other embodiments, extension  128  may be coupled to blade  102  using other processes. In the exemplary embodiment, extension  128  is coupled to blade  102  between connection point  126  and blade tip  114 . In other embodiments, extension  128  may be coupled to leading edge  106  between blade root  112  and blade tip  114 , to trailing edge  104  between blade root  112  and blade tip  114 , or may be added to sidewalls  108  and/or  110 . 
         [0017]    The above-described turbine rotor blade extension is cost effective and highly reliable. The turbine rotor blade includes a first and second sidewall coupled to each other at their respective leading edge and trailing edge. An extension coupled to the blade, or removed from the blade forged material envelope alters the blade natural frequency and improves reliability. The amount of material in the extension is facilitated to be minimized by analysis or testing of the rotor blade. Minimizing this mass addition reduces to total weight of the blade, thus minimizing both blade and disk stress and improves reliability. As a result, the turbine rotor blade extension facilitates operating a steam turbine in a cost effective and reliable manner. 
         [0018]    Referring now to  FIG. 3 , there is illustrated a representative bucket section profile at a predetermined distance “Z” (in inches) or radial distance  118  from surface  124 . Each profile section at that radial distance is defined in X-Y coordinates by adjacent points identified by representative numerals, for example, the illustrated numerals  1  through  15 , and which adjacent points are connected one to the other along the arcs of circles having radii R. Thus, the arc connecting points  10  and  11  constitutes a portion of a circle having a radius Rat a center  310  as illustrated. Values of the X-Y coordinates and the radii R for each bucket section profile taken at specific radial locations or heights “Z” from the blade platform  124  are tabulated in the following tables numbered  1  through  19 . The tables identify the various points along a profile section at the given heights “Z” from the blade platform  124  by their X-Y coordinates and it will be seen that the tables have anywhere from 13 to 27 representative X-Y coordinate points, depending upon the profile section height from the datum line. These values are given in inches and represent actual bucket configurations at ambient, non-operating conditions (with the exception of the coordinate points noted below for the theoretical blade profiles at the root, mid-point and tip of the bucket). The value for each radius R provides the length of the radius defining the arc of the circle between two of the adjacent points identified by the X-Y coordinates. The sign convention assigns a positive value to the radius R when the adjacent two points are connected in a clockwise direction and a negative value to the radius R when the two adjacent points are connected in a counterclockwise direction. By providing X-Y coordinates for spaced points about the blade profile at selected radial positions or heights Z from blade platform  124  and defining the radii R of circles connecting adjacent points, the profile of the bucket is defined at each radial position and thus the bucket profile is defined throughout its entire length. 
         [0019]    Table 1 represents the theoretical profile of the bucket at the blade platform  124  (i.e., Z=0). The actual profile at that location includes the fillets in the root section connecting the airfoil and dovetail sections, the fillets fairing the profiled bucket into the structural base of the bucket. The actual profile of the bucket at the blade platform  124  is not given but the theoretical profile of the bucket at the blade platform  124  is given in Table 1. Similarly, the profile given in Table 19 is also a theoretical profile, as this section is joined to the tip shroud. The actual profile includes the fillets in the tip section connecting the airfoil and tip-shroud sections. In the middle portion of the blade, a part-span shroud may also be incorporated into the bucket. The tables below do not define the shape of the part-span shroud. 
         [0020]    It will be appreciated that having defined the profile of the bucket at various selected heights from the root, properties of the bucket such as the maximum and minimum moments of inertia, the area of the bucket at each section, the twist, torsional stiffness, shear centers and vane width can be ascertained. Accordingly, Tables 2-18 identify the actual profile of a bucket; Tables 1 and 19 identify the theoretical profiles of a bucket at the designated locations therealong. 
         [0021]    Also, in one preferred embodiment, the turbine includes 49 buckets, each of the profiles provided by the Tables 2-18 and having the theoretical profile given by the X, Y and R values at the radial distances of Tables 1 and 19. However, it is to be understood that any number of buckets (e.g., more or less than 49) could be employed and the X, Y and R values would be appropriately scaled to obtain the desired bucket profile. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 1 
               
             
             
               
                   
               
               
                 Z = 0″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 8.14269 
                 −5.20398 
                 0 
               
               
                   
                 2 
                 8.05234 
                 −5.07557 
                 −16.2182 
               
               
                   
                 3 
                 6.88009 
                 −3.59989 
                 0 
               
               
                   
                 4 
                 6.79455 
                 −3.50419 
                 −12.0433 
               
               
                   
                 5 
                 5.46936 
                 −2.23195 
                 −10.2247 
               
               
                   
                 6 
                 4.00875 
                 −1.22859 
                 −11.486 
               
               
                   
                 7 
                 2.36161 
                 −0.46126 
                 −10.6965 
               
               
                   
                 8 
                 0.71906 
                 0.00551 
                 −12.9835 
               
               
                   
                 9 
                 −0.76065 
                 0.21312 
                 −11.3455 
               
               
                   
                 10 
                 −2.66242 
                 0.20915 
                 −12.0758 
               
               
                   
                 11 
                 −4.40123 
                 −0.06964 
                 −9.38671 
               
               
                   
                 12 
                 −6.75505 
                 −0.9736 
                 −6.95049 
               
               
                   
                 13 
                 −8.05266 
                 −1.89219 
                 0.14286 
               
               
                   
                 14 
                 −8.27779 
                 −1.72609 
                 1.90355 
               
               
                   
                 15 
                 −8.02488 
                 −1.32011 
                 8.87163 
               
               
                   
                 16 
                 −6.84361 
                 −0.12142 
                 7.90759 
               
               
                   
                 17 
                 −5.7334 
                 0.65761 
                 8.50374 
               
               
                   
                 18 
                 −3.27442 
                 1.61214 
                 9.94464 
               
               
                   
                 19 
                 −0.50286 
                 1.81863 
                 9.35978 
               
               
                   
                 20 
                 2.70352 
                 1.02294 
                 8.56383 
               
               
                   
                 21 
                 4.18539 
                 0.1734 
                 8.94235 
               
               
                   
                 22 
                 6.17556 
                 −1.78429 
                 11.93268 
               
               
                   
                 23 
                 6.58317 
                 −2.37131 
                 61.30643 
               
               
                   
                 24 
                 7.34792 
                 −3.57674 
                 141.7845 
               
               
                   
                 25 
                 7.69087 
                 −4.13434 
                 0 
               
               
                   
                 26 
                 8.28597 
                 −5.11004 
                 0.08572 
               
               
                   
                 27 
                 8.14269 
                 −5.20398 
                 0 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 2 
               
             
             
               
                   
               
               
                 Z = 4.552″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 6.86668 
                 −5.96371 
                 −14.0609 
               
               
                   
                 2 
                 5.47222 
                 −3.91188 
                 −20.4525 
               
               
                   
                 3 
                 3.4143 
                 −1.73999 
                 −8.60622 
               
               
                   
                 4 
                 1.24007 
                 −0.29415 
                 −7.37985 
               
               
                   
                 5 
                 −1.09022 
                 0.35078 
                 −7.68903 
               
               
                   
                 6 
                 −3.2812 
                 0.26831 
                 −8.90384 
               
               
                   
                 7 
                 −5.52553 
                 −0.45946 
                 −4.54205 
               
               
                   
                 8 
                 −5.849 
                 −0.63065 
                 −10.2262 
               
               
                   
                 9 
                 −6.25351 
                 −0.87879 
                 0.54072 
               
               
                   
                 10 
                 −6.39112 
                 −0.94237 
                 0.15144 
               
               
                   
                 11 
                 −6.58268 
                 −0.76502 
                 0.54072 
               
               
                   
                 12 
                 −6.52934 
                 −0.62194 
                 4.49951 
               
               
                   
                 13 
                 −5.1571 
                 0.91336 
                 6.429 
               
               
                   
                 14 
                 −2.91267 
                 1.91118 
                 7.1473 
               
               
                   
                 15 
                 −0.99193 
                 2.08605 
                 4.61171 
               
               
                   
                 16 
                 0.52219 
                 1.75807 
                 8.01567 
               
               
                   
                 17 
                 2.66566 
                 0.4777 
                 11.41873 
               
               
                   
                 18 
                 4.68621 
                 −1.71265 
                 17.92081 
               
               
                   
                 19 
                 5.45598 
                 −2.90119 
                 16.79805 
               
               
                   
                 20 
                 5.99933 
                 −3.89214 
                 0 
               
               
                   
                 21 
                 7.0082 
                 −5.88854 
                 0.08015 
               
               
                   
                 22 
                 6.86668 
                 −5.96371 
                 11.93268 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 3 
               
             
             
               
                   
               
               
                 Z = 9.1028″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 5.26358 
                 −6.07395 
                 −0.72114 
               
               
                   
                 2 
                 5.20983 
                 −5.9376 
                 −40.2462 
               
               
                   
                 3 
                 4.69365 
                 −4.97198 
                 −14.6591 
               
               
                   
                 4 
                 2.34221 
                 −1.80943 
                 −7.38262 
               
               
                   
                 5 
                 0.04359 
                 −0.21632 
                 −5.12742 
               
               
                   
                 6 
                 −1.24096 
                 0.15948 
                 −8.71006 
               
               
                   
                 7 
                 −2.98287 
                 0.25262 
                 −8.1828 
               
               
                   
                 8 
                 −3.83361 
                 0.16799 
                 −18.9473 
               
               
                   
                 9 
                 −5.02122 
                 −0.05216 
                 0.71644 
               
               
                   
                 10 
                 −5.18645 
                 −0.06858 
                 0.18234 
               
               
                   
                 11 
                 −5.33788 
                 0.21051 
                 0.71644 
               
               
                   
                 12 
                 −5.23152 
                 0.34254 
                 6.18288 
               
               
                   
                 13 
                 −3.78337 
                 1.39581 
                 5.71719 
               
               
                   
                 14 
                 −2.0806 
                 1.97082 
                 5.12201 
               
               
                   
                 15 
                 −0.51004 
                 1.99265 
                 3.3534 
               
               
                   
                 16 
                 0.69203 
                 1.57999 
                 4.60877 
               
               
                   
                 17 
                 1.83358 
                 0.65404 
                 10.65731 
               
               
                   
                 18 
                 3.13974 
                 −1.15978 
                 27.97914 
               
               
                   
                 19 
                 3.97105 
                 −2.72845 
                 22.23978 
               
               
                   
                 20 
                 4.54028 
                 −3.98787 
                 0 
               
               
                   
                 21 
                 5.38821 
                 −6.03076 
                 0.06608 
               
               
                   
                 22 
                 5.26358 
                 −6.07395 
                 11.93268 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 4 
               
             
             
               
                   
               
               
                 Z = 11.3776″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 4.48709 
                 −6.06174 
                 0 
               
               
                   
                 2 
                 4.40741 
                 −5.89542 
                 −19.0432 
               
               
                   
                 3 
                 4.18165 
                 −5.43992 
                 −32.6737 
               
               
                   
                 4 
                 3.47323 
                 −4.13153 
                 −15.0586 
               
               
                   
                 5 
                 2.74312 
                 −2.9782 
                 −10.9154 
               
               
                   
                 6 
                 1.5228 
                 −1.52024 
                 −7.98608 
               
               
                   
                 7 
                 0.22255 
                 −0.46521 
                 −5.82226 
               
               
                   
                 8 
                 −0.28202 
                 −0.17194 
                 −7.2406 
               
               
                   
                 9 
                 −1.62911 
                 0.36013 
                 −9.98687 
               
               
                   
                 10 
                 −3.26816 
                 0.67925 
                 −14.3215 
               
               
                   
                 11 
                 −4.62007 
                 0.7622 
                 0.22265 
               
               
                   
                 12 
                 −4.77165 
                 1.14497 
                 0.59033 
               
               
                   
                 13 
                 −4.64949 
                 1.23571 
                 7.98942 
               
               
                   
                 14 
                 −3.28705 
                 1.83803 
                 6.15608 
               
               
                   
                 15 
                 −2.03335 
                 2.11627 
                 4.60122 
               
               
                   
                 16 
                 −0.88106 
                 2.10286 
                 3.51239 
               
               
                   
                 17 
                 0.34231 
                 1.69496 
                 3.27678 
               
               
                   
                 18 
                 0.80173 
                 1.38672 
                 4.52434 
               
               
                   
                 19 
                 1.50883 
                 0.67831 
                 7.59899 
               
               
                   
                 20 
                 2.13789 
                 −0.24063 
                 15.16049 
               
               
                   
                 21 
                 2.75458 
                 −1.41608 
                 32.16122 
               
               
                   
                 22 
                 3.53705 
                 −3.22258 
                 55.39263 
               
               
                   
                 23 
                 3.86564 
                 −4.06988 
                 0 
               
               
                   
                 24 
                 4.59621 
                 −6.01523 
                 0.05938 
               
               
                   
                 25 
                 4.48709 
                 −6.06174 
                 0 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 5 
               
             
             
               
                   
               
               
                 Z = 13.6522″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 3.77201 
                 −5.97958 
                 −56.57 
               
               
                   
                 2 
                 2.2127 
                 −3.09834 
                 −10.9567 
               
               
                   
                 3 
                 1.4095 
                 −1.90098 
                 −9.75049 
               
               
                   
                 4 
                 0.05471 
                 −0.46967 
                 −8.82884 
               
               
                   
                 5 
                 −1.48754 
                 0.59729 
                 −11.1118 
               
               
                   
                 6 
                 −1.99767 
                 0.85836 
                 −39.815 
               
               
                   
                 7 
                 −2.98203 
                 1.31411 
                 0 
               
               
                   
                 8 
                 −3.55102 
                 1.56681 
                 73.40256 
               
               
                   
                 9 
                 −3.87176 
                 1.71185 
                 16.35228 
               
               
                   
                 10 
                 −4.02287 
                 1.78156 
                 0.15137 
               
               
                   
                 11 
                 −4.03202 
                 2.05114 
                 3.41315 
               
               
                   
                 12 
                 −2.79565 
                 2.45215 
                 4.46469 
               
               
                   
                 13 
                 −1.31032 
                 2.38493 
                 3.96666 
               
               
                   
                 14 
                 0.02726 
                 1.82519 
                 4.44377 
               
               
                   
                 15 
                 1.14632 
                 0.77496 
                 5.21119 
               
               
                   
                 16 
                 1.57629 
                 0.09917 
                 11.48497 
               
               
                   
                 17 
                 2.08053 
                 −0.9777 
                 42.38902 
               
               
                   
                 18 
                 2.56189 
                 −2.21708 
                 79.22593 
               
               
                   
                 19 
                 3.13967 
                 −3.83014 
                 0 
               
               
                   
                 20 
                 3.86922 
                 −5.93846 
                 0.05291 
               
               
                   
                 21 
                 3.77201 
                 −5.97958 
                 32.16122 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 6 
               
             
             
               
                   
               
               
                 Z = 15.9221″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 3.20634 
                 −5.94189 
                 0 
               
               
                   
                 2 
                 2.3248 
                 −4.33582 
                 16.8259 
               
               
                   
                 3 
                 2.04392 
                 −3.79165 
                 −16.8259 
               
               
                   
                 4 
                 1.38492 
                 −2.58312 
                 −14.0679 
               
               
                   
                 5 
                 0.29629 
                 −1.01864 
                 −12.9619 
               
               
                   
                 6 
                 −0.94587 
                 0.32452 
                 −22.2454 
               
               
                   
                 7 
                 −1.84901 
                 1.12731 
                 22.24539 
               
               
                   
                 8 
                 −3.00019 
                 2.16658 
                 8.94741 
               
               
                   
                 9 
                 −3.13559 
                 2.30049 
                 13.50015 
               
               
                   
                 10 
                 −3.29841 
                 2.46786 
                 0.14302 
               
               
                   
                 11 
                 −3.24651 
                 2.70013 
                 2.47322 
               
               
                   
                 12 
                 −2.1218 
                 2.85473 
                 3.43836 
               
               
                   
                 13 
                 −0.83989 
                 2.47108 
                 3.69043 
               
               
                   
                 14 
                 0.03854 
                 1.82382 
                 5.62144 
               
               
                   
                 15 
                 0.87199 
                 0.76604 
                 6.03234 
               
               
                   
                 16 
                 1.22537 
                 0.09439 
                 13.84047 
               
               
                   
                 17 
                 1.65159 
                 −0.97328 
                 12.52819 
               
               
                   
                 18 
                 1.72337 
                 −1.1832 
                 107.7916 
               
               
                   
                 19 
                 1.92655 
                 −1.80142 
                 0 
               
               
                   
                 20 
                 2.67719 
                 −4.09716 
                 37.75222 
               
               
                   
                 21 
                 2.73307 
                 −4.26423 
                 −37.7522 
               
               
                   
                 22 
                 2.81755 
                 −4.51586 
                 0 
               
               
                   
                 23 
                 3.28953 
                 −5.90528 
                 0.04563 
               
               
                   
                 24 
                 3.20634 
                 −5.94189 
                 0.05938 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 7 
               
             
             
               
                   
               
               
                 Z = 18.2012″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 2.72769 
                 −5.84753 
                 0 
               
               
                   
                 2 
                 1.96568 
                 −4.63648 
                 3.91954 
               
               
                   
                 3 
                 1.87284 
                 −4.47872 
                 0 
               
               
                   
                 4 
                 0.60228 
                 −2.15846 
                 −64.8003 
               
               
                   
                 5 
                 −0.28818 
                 −0.60873 
                 −16.8873 
               
               
                   
                 6 
                 −0.77465 
                 0.16319 
                 −35.8688 
               
               
                   
                 7 
                 −1.53008 
                 1.24913 
                 35.86876 
               
               
                   
                 8 
                 −2.0302 
                 1.95843 
                 6.45422 
               
               
                   
                 9 
                 −2.58539 
                 2.93782 
                 0.18456 
               
               
                   
                 10 
                 −2.43795 
                 3.19791 
                 2.23922 
               
               
                   
                 11 
                 −1.3505 
                 3.04842 
                 3.04942 
               
               
                   
                 12 
                 −0.29159 
                 2.3309 
                 2.86304 
               
               
                   
                 13 
                 0.09546 
                 1.82427 
                 6.52936 
               
               
                   
                 14 
                 0.52895 
                 0.96455 
                 6.03718 
               
               
                   
                 15 
                 0.68048 
                 0.55872 
                 71.58372 
               
               
                   
                 16 
                 1.13699 
                 −0.86141 
                 6.38032 
               
               
                   
                 17 
                 1.16995 
                 −0.97125 
                 −6.38032 
               
               
                   
                 18 
                 1.1988 
                 −1.0677 
                 0 
               
               
                   
                 19 
                 1.50673 
                 −2.09944 
                 −84.7491 
               
               
                   
                 20 
                 1.98755 
                 −3.59073 
                 −19.412 
               
               
                   
                 21 
                 2.18539 
                 −4.15615 
                 0 
               
               
                   
                 22 
                 2.79457 
                 −5.81467 
                 0.03747 
               
               
                   
                 23 
                 2.72769 
                 −5.84753 
                 0.04563 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 8 
               
             
             
               
                   
               
               
                 Z = 20.4775″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 2.30728 
                 −5.82104 
                 0 
               
               
                   
                 2 
                 1.87407 
                 −5.11416 
                 4.06378 
               
               
                   
                 3 
                 1.75979 
                 −4.91494 
                 10.80126 
               
               
                   
                 4 
                 1.58846 
                 −4.58198 
                 0 
               
               
                   
                 5 
                 0.78939 
                 −2.93817 
                 −9.10586 
               
               
                   
                 6 
                 0.70437 
                 −2.76957 
                 0 
               
               
                   
                 7 
                 −0.17713 
                 −1.02349 
                 37.38615 
               
               
                   
                 8 
                 −1.28734 
                 1.34369 
                 26.74437 
               
               
                   
                 9 
                 −2.07022 
                 3.40951 
                 0.20171 
               
               
                   
                 10 
                 −1.86439 
                 3.67435 
                 1.12707 
               
               
                   
                 11 
                 −1.45991 
                 3.56748 
                 2.16793 
               
               
                   
                 12 
                 −0.97706 
                 3.25227 
                 2.6963 
               
               
                   
                 13 
                 −0.51512 
                 2.73639 
                 6.86141 
               
               
                   
                 14 
                 0.03467 
                 1.77828 
                 5.26443 
               
               
                   
                 15 
                 0.21824 
                 1.33803 
                 23.56335 
               
               
                   
                 16 
                 0.54362 
                 0.38279 
                 19.69941 
               
               
                   
                 17 
                 0.76215 
                 −0.35674 
                 −19.6994 
               
               
                   
                 18 
                 0.86791 
                 −0.72794 
                 0 
               
               
                   
                 19 
                 1.49937 
                 −2.9549 
                 17.51244 
               
               
                   
                 20 
                 1.5854 
                 −3.25112 
                 −17.5124 
               
               
                   
                 21 
                 1.71651 
                 −3.69524 
                 0 
               
               
                   
                 22 
                 2.36646 
                 −5.79424 
                 0.03275 
               
               
                   
                 23 
                 2.30728 
                 −5.82104 
                 0.04563 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 9 
               
             
             
               
                   
               
               
                 Z = 22.7558″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 2.01086 
                 −5.78492 
                 0 
               
               
                   
                 2 
                 1.77127 
                 −5.39305 
                 6.83794 
               
               
                   
                 3 
                 1.4921 
                 −4.89008 
                 9.57775 
               
               
                   
                 4 
                 1.24813 
                 −4.36421 
                 0 
               
               
                   
                 5 
                 1.19473 
                 −4.23931 
                 6.59464 
               
               
                   
                 6 
                 1.12336 
                 −4.06564 
                 0 
               
               
                   
                 7 
                 0.57085 
                 −2.66454 
                 −10.3976 
               
               
                   
                 8 
                 0.475 
                 −2.42989 
                 0 
               
               
                   
                 9 
                 0.3274 
                 −2.08079 
                 −10.244 
               
               
                   
                 10 
                 0.27183 
                 −1.95185 
                 0 
               
               
                   
                 11 
                 −0.31059 
                 −0.62528 
                 59.9572 
               
               
                   
                 12 
                 −0.67265 
                 0.21681 
                 22.75803 
               
               
                   
                 13 
                 −1.20831 
                 1.61659 
                 11.7057 
               
               
                   
                 14 
                 −1.57838 
                 2.93257 
                 6.99237 
               
               
                   
                 15 
                 −1.71226 
                 3.80234 
                 0.22265 
               
               
                   
                 16 
                 −1.37201 
                 4.0108 
                 1.88442 
               
               
                   
                 17 
                 −1.01684 
                 3.72181 
                 2.93469 
               
               
                   
                 18 
                 −0.59502 
                 3.16271 
                 5.29042 
               
               
                   
                 19 
                 −0.26772 
                 2.49626 
                 9.96354 
               
               
                   
                 20 
                 0.03956 
                 1.62768 
                 33.73321 
               
               
                   
                 21 
                 0.35761 
                 0.50693 
                 0 
               
               
                   
                 22 
                 2.0648 
                 −5.76153 
                 0.02969 
               
               
                   
                 23 
                 2.01086 
                 −5.78492 
                 0.04563 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 10 
               
             
             
               
                   
               
               
                 Z = 25.0338″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 1.81505 
                 −5.76825 
                 15.72298 
               
               
                   
                 2 
                 1.56739 
                 −5.27717 
                 30 
               
               
                   
                 3 
                 0.65763 
                 −3.19351 
                 75 
               
               
                   
                 4 
                 −0.44402 
                 −0.1988 
                 26.63003 
               
               
                   
                 5 
                 −1.04084 
                 1.78431 
                 13.81459 
               
               
                   
                 6 
                 −1.43114 
                 4.06229 
                 0.74728 
               
               
                   
                 7 
                 −1.43357 
                 4.14851 
                 0.14272 
               
               
                   
                 8 
                 −1.20162 
                 4.25562 
                 0.74728 
               
               
                   
                 9 
                 −1.12652 
                 4.18644 
                 2.2833 
               
               
                   
                 10 
                 −0.72156 
                 3.59509 
                 12 
               
               
                   
                 11 
                 0.07255 
                 1.38392 
                 0 
               
               
                   
                 12 
                 1.86883 
                 −5.74766 
                 0.02901 
               
               
                   
                 13 
                 1.81505 
                 −5.76825 
                 11.7057 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 11 
               
             
             
               
                   
               
               
                 Z = 27.3109″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 1.66692 
                 −5.74133 
                 0 
               
               
                   
                 2 
                 1.12277 
                 −4.61262 
                 4.11497 
               
               
                   
                 3 
                 1.03508 
                 −4.40816 
                 23.74997 
               
               
                   
                 4 
                 0.84338 
                 −3.90929 
                 0 
               
               
                   
                 5 
                 0.63975 
                 −3.35834 
                 0.57106 
               
               
                   
                 6 
                 0.63603 
                 −3.34754 
                 5.45871 
               
               
                   
                 7 
                 0.62496 
                 −3.31401 
                 0 
               
               
                   
                 8 
                 −0.24726 
                 −0.6132 
                 32.48476 
               
               
                   
                 9 
                 −0.86584 
                 1.6598 
                 18.25371 
               
               
                   
                 10 
                 −1.1838 
                 3.39676 
                 21.93099 
               
               
                   
                 11 
                 −1.23945 
                 3.84972 
                 24.92753 
               
               
                   
                 12 
                 −1.28904 
                 4.33374 
                 0.14286 
               
               
                   
                 13 
                 −1.03331 
                 4.43369 
                 2.5686 
               
               
                   
                 14 
                 −0.68907 
                 3.82809 
                 12.43525 
               
               
                   
                 15 
                 −0.2081 
                 2.37275 
                 36.57981 
               
               
                   
                 16 
                 −0.03539 
                 1.69041 
                 134.69 
               
               
                   
                 17 
                 0.27682 
                 0.37637 
                 0 
               
               
                   
                 18 
                 1.04382 
                 −2.94283 
                 −147.62399 
               
               
                   
                 19 
                 1.16922 
                 −3.46869 
                 −108.15 
               
               
                   
                 20 
                 1.28126 
                 −3.9302 
                 0 
               
               
                   
                 21 
                 1.72041 
                 −5.72213 
                 0.02858 
               
               
                   
                 22 
                 1.66692 
                 −5.74133 
                 0.02969 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 12 
               
             
             
               
                   
               
               
                 Z = 29.5884″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 1.51597 
                 −5.71912 
                 139.3053 
               
               
                   
                 2 
                 0.98183 
                 −4.5066 
                 3.01844 
               
               
                   
                 3 
                 0.90988 
                 −4.32532 
                 10.77397 
               
               
                   
                 4 
                 0.75283 
                 −3.85543 
                 34.20319 
               
               
                   
                 5 
                 0.44357 
                 −2.79355 
                 0 
               
               
                   
                 6 
                 −0.0857 
                 −0.86034 
                 48.60234 
               
               
                   
                 7 
                 −0.87365 
                 2.47549 
                 17.30307 
               
               
                   
                 8 
                 −1.15438 
                 4.50507 
                 0.44337 
               
               
                   
                 9 
                 −1.15225 
                 4.59529 
                 0.08468 
               
               
                   
                 10 
                 −1.00934 
                 4.64551 
                 0.44337 
               
               
                   
                 11 
                 −0.94996 
                 4.57459 
                 2.57476 
               
               
                   
                 12 
                 −0.628 
                 3.90406 
                 29.46461 
               
               
                   
                 13 
                 −0.00641 
                 1.58567 
                 70 
               
               
                   
                 14 
                 0.1233 
                 0.99714 
                 0 
               
               
                   
                 15 
                 1.56932 
                 −5.70167 
                 0.02823 
               
               
                   
                 16 
                 1.51597 
                 −5.71912 
                 134.69 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 13 
               
             
             
               
                   
               
               
                 Z = 31.8659″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 1.37725 
                 −5.69672 
                 137.6895 
               
               
                   
                 2 
                 0.91796 
                 −4.60379 
                 1.70029 
               
               
                   
                 3 
                 0.8722 
                 −4.48025 
                 3.4118 
               
               
                   
                 4 
                 0.79678 
                 −4.21332 
                 97.0057 
               
               
                   
                 5 
                 0.47157 
                 −2.80704 
                 0 
               
               
                   
                 6 
                 −0.74575 
                 2.64135 
                 83.91212 
               
               
                   
                 7 
                 −0.92003 
                 3.4396 
                 14.02929 
               
               
                   
                 8 
                 −1.0334 
                 4.03385 
                 6.44655 
               
               
                   
                 9 
                 −1.11124 
                 4.71531 
                 0.32572 
               
               
                   
                 10 
                 −1.10944 
                 4.77442 
                 0.06221 
               
               
                   
                 11 
                 −1.00462 
                 4.81177 
                 0.32572 
               
               
                   
                 12 
                 −0.96456 
                 4.76533 
                 1.96955 
               
               
                   
                 13 
                 −0.74312 
                 4.35991 
                 7.94476 
               
               
                   
                 14 
                 −0.47464 
                 3.57668 
                 29.54417 
               
               
                   
                 15 
                 −0.17891 
                 2.45839 
                 23.99381 
               
               
                   
                 16 
                 0.04576 
                 1.44045 
                 143.30981 
               
               
                   
                 17 
                 0.1273 
                 1.02548 
                 185.80972 
               
               
                   
                 18 
                 0.14862 
                 0.91597 
                 0 
               
               
                   
                 19 
                 1.40035 
                 −5.52483 
                 136.64554 
               
               
                   
                 20 
                 1.4305 
                 −5.68046 
                 0.02801 
               
               
                   
                 21 
                 1.37725 
                 −5.69672 
                 0.02858 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 14 
               
             
             
               
                   
               
               
                 Z = 34.1435″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 1.30024 
                 −5.68367 
                 0 
               
               
                   
                 2 
                 0.81215 
                 −4.56682 
                 1.07849 
               
               
                   
                 3 
                 0.76343 
                 −4.43132 
                 3.20433 
               
               
                   
                 4 
                 0.72698 
                 −4.29204 
                 7.61968 
               
               
                   
                 5 
                 0.67477 
                 −4.05592 
                 0 
               
               
                   
                 6 
                 −0.8365 
                 3.33401 
                 16.85328 
               
               
                   
                 7 
                 −0.99746 
                 4.24892 
                 7.90627 
               
               
                   
                 8 
                 −1.07009 
                 4.9652 
                 0.06857 
               
               
                   
                 9 
                 −0.9417 
                 5.00231 
                 2.94371 
               
               
                   
                 10 
                 −0.7577 
                 4.60396 
                 6.35831 
               
               
                   
                 11 
                 −0.52553 
                 3.84073 
                 −94.7678 
               
               
                   
                 12 
                 −0.4565 
                 3.55126 
                 0 
               
               
                   
                 13 
                 −0.31732 
                 2.97168 
                 17.86547 
               
               
                   
                 14 
                 −0.12419 
                 2.06424 
                 0 
               
               
                   
                 15 
                 0.73398 
                 −2.55376 
                 −54.4051 
               
               
                   
                 16 
                 0.81808 
                 −2.99614 
                 0 
               
               
                   
                 17 
                 1.00508 
                 −3.95802 
                 −27.1624 
               
               
                   
                 18 
                 1.05339 
                 −4.20062 
                 0 
               
               
                   
                 19 
                 1.35238 
                 −5.66716 
                 0.02751 
               
               
                   
                 20 
                 1.30024 
                 −5.68367 
                 0.02801 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 15 
               
             
             
               
                   
               
               
                 Z = 36.4218″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 1.28721 
                 −5.67147 
                 0 
               
               
                   
                 2 
                 0.69127 
                 −4.42436 
                 0.48204 
               
               
                   
                 3 
                 0.65442 
                 −4.31543 
                 103.2697 
               
               
                   
                 4 
                 0.55332 
                 −3.8273 
                 −500 
               
               
                   
                 5 
                 −0.02683 
                 −1.03264 
                 0 
               
               
                   
                 6 
                 −0.4485 
                 0.96985 
                 38.35151 
               
               
                   
                 7 
                 −0.9102 
                 3.62048 
                 17.3778 
               
               
                   
                 8 
                 −1.05546 
                 5.1998 
                 0.06857 
               
               
                   
                 9 
                 −0.9233 
                 5.22842 
                 4.89375 
               
               
                   
                 10 
                 −0.72457 
                 4.6179 
                 17.18319 
               
               
                   
                 11 
                 −0.46267 
                 3.40691 
                 0 
               
               
                   
                 12 
                 −0.33716 
                 2.70483 
                 −176.212 
               
               
                   
                 13 
                 0.00372 
                 0.85533 
                 0 
               
               
                   
                 14 
                 0.35192 
                 −0.97896 
                 −134.032 
               
               
                   
                 15 
                 0.98865 
                 −4.12693 
                 −55.9761 
               
               
                   
                 16 
                 1.31427 
                 −5.55208 
                 0 
               
               
                   
                 17 
                 1.33874 
                 −5.65313 
                 0.02751 
               
               
                   
                 18 
                 1.28721 
                 −5.67147 
                 0 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 16 
               
             
             
               
                   
               
               
                 Z = 38.7016″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 1.25913 
                 −5.65294 
                 87.53835 
               
               
                   
                 2 
                 0.72125 
                 −4.54406 
                 1.47705 
               
               
                   
                 3 
                 0.66033 
                 −4.39601 
                 5.91333 
               
               
                   
                 4 
                 0.47172 
                 −3.73516 
                 82.38358 
               
               
                   
                 5 
                 −0.04808 
                 −1.22655 
                 10 
               
               
                   
                 6 
                 −0.08499 
                 −1.0218 
                 0 
               
               
                   
                 7 
                 −0.51202 
                 1.49661 
                 48.40389 
               
               
                   
                 8 
                 −0.82787 
                 3.6529 
                 23.04195 
               
               
                   
                 9 
                 −0.97661 
                 5.40196 
                 0.2199 
               
               
                   
                 10 
                 −0.97071 
                 5.46383 
                 0.042 
               
               
                   
                 11 
                 −0.89751 
                 5.48072 
                 0.2199 
               
               
                   
                 12 
                 −0.86487 
                 5.42716 
                 2.54425 
               
               
                   
                 13 
                 −0.72316 
                 4.99061 
                 24.25494 
               
               
                   
                 14 
                 −0.43944 
                 3.53951 
                 0 
               
               
                   
                 15 
                 0.11067 
                 0.18612 
                 −76.8724 
               
               
                   
                 16 
                 0.71254 
                 −3.04795 
                 −59.549 
               
               
                   
                 17 
                 1.31162 
                 −5.63353 
                 0.02814 
               
               
                   
                 18 
                 1.25913 
                 −5.65294 
                 0 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 17 
               
             
             
               
                   
               
               
                 Z = 40.9827″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 1.21987 
                 −5.65479 
                 0 
               
               
                   
                 2 
                 0.7985 
                 −4.87148 
                 31.42264 
               
               
                   
                 3 
                 0.741 
                 −4.7641 
                 1.23199 
               
               
                   
                 4 
                 0.65349 
                 −4.5559 
                 5.5107 
               
               
                   
                 5 
                 0.61644 
                 −4.43375 
                 16.09645 
               
               
                   
                 6 
                 0.39827 
                 −3.60087 
                 38.31746 
               
               
                   
                 7 
                 0.08847 
                 −2.14769 
                 0 
               
               
                   
                 8 
                 −0.0106 
                 −1.6344 
                 25 
               
               
                   
                 9 
                 −0.21776 
                 −0.39414 
                 0 
               
               
                   
                 10 
                 −0.55542 
                 1.99575 
                 57.90813 
               
               
                   
                 11 
                 −0.81637 
                 4.12741 
                 28.68988 
               
               
                   
                 12 
                 −0.93501 
                 5.68442 
                 0.05714 
               
               
                   
                 13 
                 −0.83534 
                 5.7253 
                 0.1515 
               
               
                   
                 14 
                 −0.80286 
                 5.66679 
                 6.44268 
               
               
                   
                 15 
                 −0.65091 
                 5.02648 
                 0 
               
               
                   
                 16 
                 −0.54839 
                 4.46912 
                 18.5916 
               
               
                   
                 17 
                 −0.44348 
                 3.83789 
                 0 
               
               
                   
                 18 
                 0.2358 
                 −0.73448 
                 −9.19071 
               
               
                   
                 19 
                 0.2683 
                 −0.93753 
                 0 
               
               
                   
                 20 
                 0.35889 
                 −1.46572 
                 −33.5814 
               
               
                   
                 21 
                 0.47515 
                 −2.10628 
                 0 
               
               
                   
                 22 
                 0.52937 
                 −2.38933 
                 −43.2909 
               
               
                   
                 23 
                 0.98054 
                 −4.46727 
                 −60.9649 
               
               
                   
                 24 
                 1.11309 
                 −5.00222 
                 0 
               
               
                   
                 25 
                 1.27274 
                 −5.63426 
                 0.02858 
               
               
                   
                 26 
                 1.21987 
                 −5.65479 
                 0.08572 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 18 
               
             
             
               
                   
               
               
                 Z = 43.2654″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 1.18126 
                 −5.67467 
                 0 
               
               
                   
                 2 
                 0.84884 
                 −5.13531 
                 2.77432 
               
               
                   
                 3 
                 0.49882 
                 −4.26532 
                 70.5369 
               
               
                   
                 4 
                 −0.07838 
                 −1.2827 
                 38.55754 
               
               
                   
                 5 
                 −0.23221 
                 −0.30999 
                 63.44528 
               
               
                   
                 6 
                 −0.40931 
                 1.00769 
                 0 
               
               
                   
                 7 
                 −0.59561 
                 2.51326 
                 59.53784 
               
               
                   
                 8 
                 −0.79907 
                 4.40491 
                 30.89333 
               
               
                   
                 9 
                 −0.90043 
                 5.92769 
                 0.20122 
               
               
                   
                 10 
                 −0.89467 
                 5.98457 
                 0.03843 
               
               
                   
                 11 
                 −0.82759 
                 5.99959 
                 0.20122 
               
               
                   
                 12 
                 −0.79756 
                 5.94926 
                 1.6985 
               
               
                   
                 13 
                 −0.69912 
                 5.61953 
                 34.69339 
               
               
                   
                 14 
                 −0.41738 
                 3.91472 
                 0 
               
               
                   
                 15 
                 0.16104 
                 −0.22347 
                 −44.6866 
               
               
                   
                 16 
                 0.57547 
                 −2.68486 
                 −60.1787 
               
               
                   
                 17 
                 1.04914 
                 −4.87144 
                 0 
               
               
                   
                 18 
                 1.23371 
                 −5.65298 
                 0.02876 
               
               
                   
                 19 
                 1.18126 
                 −5.67467 
                 0 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE NO. 19 
               
             
             
               
                   
               
               
                 Z = 45.55″ 
               
             
          
           
               
                   
                 POINT NO. 
                 X 
                 Y 
                 R 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 1.12747 
                 −5.71414 
                 0 
               
               
                   
                 2 
                 0.57999 
                 −4.88189 
                 0.38633 
               
               
                   
                 3 
                 0.54175 
                 −4.80717 
                 0.60926 
               
               
                   
                 4 
                 0.5103 
                 −4.69162 
                 0 
               
               
                   
                 5 
                 0.28237 
                 −3.34203 
                 58.05177 
               
               
                   
                 6 
                 0.23511 
                 −3.05787 
                 0 
               
               
                   
                 7 
                 −0.05661 
                 −1.27676 
                 45.25879 
               
               
                   
                 8 
                 −0.08987 
                 −1.07069 
                 0 
               
               
                   
                 9 
                 −0.33632 
                 0.47871 
                 10 
               
               
                   
                 10 
                 −0.3961 
                 0.91688 
                 0 
               
               
                   
                 11 
                 −0.61081 
                 2.80034 
                 71.57434 
               
               
                   
                 12 
                 −0.79431 
                 4.61535 
                 33.18385 
               
               
                   
                 13 
                 −0.89791 
                 6.24806 
                 0.05714 
               
               
                   
                 14 
                 −0.78605 
                 6.26656 
                 6.16388 
               
               
                   
                 15 
                 −0.64595 
                 5.69765 
                 17.56455 
               
               
                   
                 16 
                 −0.56598 
                 5.26131 
                 4.03085 
               
               
                   
                 17 
                 −0.54606 
                 5.13154 
                 0 
               
               
                   
                 18 
                 0.26807 
                 −0.8145 
                 −7.68995 
               
               
                   
                 19 
                 0.29713 
                 −1.00833 
                 0 
               
               
                   
                 20 
                 0.40029 
                 −1.6413 
                 −23.6684 
               
               
                   
                 21 
                 0.45034 
                 −1.93659 
                 0 
               
               
                   
                 22 
                 0.55916 
                 −2.55494 
                 −25.0416 
               
               
                   
                 23 
                 0.61114 
                 −2.84055 
                 0 
               
               
                   
                 24 
                 0.74545 
                 −3.55509 
                 −15.7037 
               
               
                   
                 25 
                 0.7916 
                 −3.79061 
                 0 
               
               
                   
                 26 
                 1.17933 
                 −5.69274 
                 0.02858 
               
               
                   
                 27 
                 1.12747 
                 −5.71414 
                 0 
               
               
                   
                   
               
             
          
         
       
     
         [0022]    Exemplary embodiments of turbine rotor buckets are described above in detail. The turbine rotor buckets are not limited to the specific embodiments described herein, but rather, components of the turbine rotor bucket may be utilized independently and separately from other components described herein. Each turbine rotor bucket component can also be used in combination with other turbine rotor bucket components. 
         [0023]    While the invention has been described in terms of various specific embodiments, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the claims.