# Patent

## Title
Air cooled bucket for a turbine

## Abstract

A bucket for a turbine is described. The bucket includes a dovetail portion configured to couple the bucket to a turbine wheel, the dovetail portion having a lower surface. The bucket also includes a shank portion that extends from the dovetail portion and an airfoil having a root and a tip portion, an airfoil shape, and a nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table I. The bucket also includes a plurality of cooling passages. The plurality includes no more than five cooling passages that extend between the root and the tip portion of the airfoil. Each of the cooling passages exits the airfoil at the tip portion, the plurality of cooling passages are positioned in a camber line pattern.

## Background
CROSS REFERENCE TO RELATED APPLICATIONS
This application claims the benefit of U.S. Provisional Patent Application Ser. No. 60/976,238, filed on Sep. 28, 2007 titled Turbine Bucket Airfoil Cooling Hole Location, Style, and Configuration.


BACKGROUND OF THE INVENTION
The field of the invention relates generally to turbine buckets and, more particularly, to a turbine bucket that includes a cooling circuit with cooling holes sized and positioned to facilitate optimizing cooling ability and turbine efficiency.
In known gas turbine engines, combustion gases cause rotation of a turbine which drives a compressor. The compressor supplies pressurized air to a combustor which generates the combustion gases. Because such engines operate at relatively high temperatures, the capacity of such an engine may be limited by the materials used in fabricating the turbine blades, sometimes referred to herein as “buckets.” More specifically, higher temperatures may cause thermal stresses to develop within the blades which may limit their operation. Such stresses may be more severe in industrial gas turbine engines because of the relatively large size of the turbine blades.
Turbines are designed to operate at a predetermined temperature that facilitates a desired performance and efficiency. Typically, newer turbines are designed to operate at higher temperatures, which necessitates greater cooling of the blades than blades used in turbines operating at lower temperatures. After continued exposure to high temperatures, turbine blades may require replacement.
To enable the turbines to operate with higher operating temperatures and increased engine efficiency without risking blade failure, at least some turbines use hollow, convectively-cooled turbine blades. At least some of such blades include interior cooling passageways which provide cooling flow to the interior of the blades to facilitate maintaining the blade at a relatively uniform temperature. Turbine air flow is diverted from a compressor into the interior passageways within the blades. When turbine blades are replaced, it may be desirable to maintain a substantially similar level of cooling flow as was previously present.
BRIEF DESCRIPTION OF THE INVENTION
In one aspect, a bucket for a turbine is provided. The bucket includes a dovetail portion configured to couple the bucket to a turbine wheel. The dovetail portion includes a lower surface. The bucket also includes a shank portion extending from the dovetail portion and an airfoil that includes a root portion, a tip portion, an airfoil shape, and a nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table I. Z is a distance from the lower surface of the dovetail portion, and X and Y are coordinates defining the profile at each distance Z from the lower surface. The bucket also includes a plurality of cooling passages. The plurality of cooling passages includes no more than five cooling passages that extend between the root and the tip portion of the airfoil. Each of the cooling passages exits at said tip portion, and the plurality of cooling passages are positioned in a camber line pattern.
In another aspect, a gas turbine engine is provided. The gas turbine engine includes a rotor including at least one rotor wheel, and a plurality of buckets extending radially from the at least one rotor wheel. Each of the plurality of buckets includes a dovetail portion, a shank portion, an airfoil, and a plurality of cooling passages extending therethrough. The airfoil has a nominal profile formed substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table I, wherein Z is a distance from a lower surface of the dovetail portion, and X and Y are coordinates defining the profile at each distance Z from the lower surface. The plurality of cooling passages each extend between the lower surface of the dovetail portion and a tip portion of each airfoil. The plurality of cooling passages include no more than five cooling passages positioned in a camber line pattern.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic cross-sectional illustration of an exemplary turbine including a second stage turbine wheel;
FIG. 2 is a front view of an exemplary turbine bucket that may be used within the turbine shown in FIG. 1;
FIG. 3 is a side view of the turbine bucket shown in FIG. 2;
FIG. 4 illustrates a perspective view of the turbine bucket shown in FIG. 2 and illustrates a Cartesian coordinate system for X, Y, and Z values set forth in Table I;
FIG. 5 is a diagram of cross-sections of the turbine bucket taken along lines shown in FIG. 4.
FIG. 6 is a cross-sectional view of the turbine bucket shown in FIG. 2 taken along line 1-1;
FIG. 7 is a cross-sectional view of the turbine bucket shown in FIG. 2 and taken along line 2-2; and
FIG. 8 is a cross-sectional view of the turbine bucket shown in FIG. 2 and taken along line 3-3.



DETAILED DESCRIPTION OF THE INVENTION
FIG. 1 illustrates a cross-sectional view of an exemplary turbine 10. In the exemplary embodiment, turbine 10 includes a rotor 12 having respective first, second, and third stage rotor wheels 14, 16, and 18 that include respective buckets 20, 22, and 24 and respective stator vanes 26, 28, and 30. Each row of buckets 20, 22, and 24 and stator vanes 26, 28, and 30, defines a subsequent stage of turbine 10. In the exemplary embodiment, turbine 10 is a three stage turbine. Alternatively, turbine 10 may include more or less than three stages. In one embodiment, turbine 10 is a General Electric 6B gas turbine, manufactured by General Electric Company of Schenectady, N.Y.
Within the second turbine stage, rotor wheel 16 includes buckets 22 which are mounted in axially opposition to the upstream stator vanes 30. Buckets 22 are spaced circumferentially about the second stage wheel 16. In the exemplary embodiment, second stage wheel 16 includes ninety-two buckets 22.
FIGS. 2 and 3 illustrate a perspective front view and a side view of an exemplary turbine bucket 22. In the exemplary embodiment, bucket 22 includes an airfoil 40 extending outward from a platform 42, and a shank 44 that extends outward from an opposite side of platform 42. The radial inner end of shank 44 extends from a dovetail 46 used for coupling the bucket 22 to turbine wheel 16 (shown in FIG. 1). As is known, dovetail 46 mates in corresponding dovetail openings (not shown) defined in turbine wheel 16. Bucket 22 also includes wheel space seals, i.e., angel wings 52, that extend axially outward from shank 44. In an example embodiment, airfoil 40 is fabricated from a known nickel-based superalloy, such as Alloy 738.
FIG. 4 illustrates a perspective view of turbine bucket 22 shown in FIG. 2 and illustrates a Cartesian coordinate system 54 for X, Y, and Z values set forth in Table I which follows. The Cartesian coordinate system 54 has orthogonally related X, Y, and Z axes with the Z axis or datum lying substantially perpendicular to the platform 42 and extending generally in a radial direction through airfoil 40. A first section 58, a second section 60, a third section 62, a fourth section 64, a fifth section 66, a sixth section 68, a seventh section 70, an eighth section 72, a ninth section 74, and a tenth section 76 of airfoil 40 are illustrated.
FIG. 5 is a diagram of cross-sections of airfoil 40 taken at first section 58, second section 60, third section 62, fourth section 64, fifth section 66, sixth section 68, seventh section 70, eighth section 72, ninth section 74, and tenth section 76. The Y axis extends substantially parallel to a centerline of the turbine, i.e., the rotary axis. By defining X and Y coordinate values at selected locations in the radial direction, i.e., in a Z direction, the profile of the airfoil 40 can be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section at each radial distance Z is fixed. The surface profiles at the various surface locations between the radial distances Z can be ascertained by connecting adjacent profiles. The X and Y coordinates for determining the airfoil section profile at each radial location or airfoil height Z are tabulated in the following Table I, wherein Z equals zero at a lower surface 78 of the bucket 22. These tabular values are given in inches and represent actual airfoil profiles at ambient, non-operating or non-hot conditions, and are for an uncoated airfoil. Airfoil 40 may be at least partially covered with a coating (not shown in FIG. 4), which may increase the dimensions of airfoil 40. In an exemplary embodiment, the coating protects airfoil 40 from corrosion and/or oxidation. Additionally, the sign convention used in Table I assigns a positive value to the value Z and positive and negative values for the coordinates X and Y, as typically used in a Cartesian coordinate system.
The values in Table 1 are computer-generated and shown to four decimal places. However, in view of manufacturing constraints, actual values useful for forming airfoil 40 are considered valid to only three decimal places for determining the profile of the airfoil 40. Moreover, there are typical manufacturing tolerances to be accounted for in the profile of airfoil 40. Accordingly, the values for the profile given in Table I are for a nominal airfoil. It should therefore be appreciated that plus or minus typical manufacturing tolerances are applicable to the X, Y, and Z values and that an airfoil having a profile substantially in accordance with those values includes such tolerances. For example, a manufacturing tolerance of about ±0.010 inches is within design limits for the airfoil and preferably a manufacturing tolerance of about ±0.008 inches is maintained. Accordingly, the values of X and Y carried to three decimal places and having a manufacturing tolerance about ±0.010 inches and preferably about ±0.008 inches are acceptable to define the profile of airfoil 40 at each radial position throughout its entire length.
Airfoil 40 imparts kinetic energy to the airflow and therefore contributes to a desired flow across a compressor (not shown). Airfoil 40 turns the fluid flow, slows relative velocity of the fluid flow, in the respective airfoil frame of reference, and yields a rise in the static pressure of the fluid flow. Airfoil 40, along with its interaction with surrounding airfoils and peripheral surfaces, facilitates, in certain exemplary embodiments: stage airflow efficiency, enhanced aeromechanics, smooth laminar flow from stage to stage, reduced thermal stresses, enhanced interrelation of the stages to effectively pass the airflow from stage to stage, and reduced mechanical stresses. Typically, multiple rows of airfoil stages, such as, but not limited to, rotor/stator airfoils, are oriented to achieve a desired discharge-to-inlet pressure ratio. Airfoils 40 can be coupled to wheels using dovetail 46 (shown in FIGS. 2 and 3).
The orientation of airfoil 40, and any interaction with surrounding airfoils, facilitates providing desirable fluid flow dynamics and laminar flow. Fluid flow intersects with airfoil 40 and is enhanced, and more specifically, the fluid dynamics and laminar flow from airfoil 40 are enhanced. As such, a smooth transition fluid flow to adjacent/downstream airfoils is facilitated. Moreover, flow from each airfoil 40 proceeds downstream towards the adjacent/downstream airfoils and is enhanced due to the enhanced laminar fluid flow from airfoil 40. Therefore, the orientation of airfoil 40 assists in preventing turbulent fluid flow in the unit comprising airfoil 40.
In the exemplary embodiment, the configuration of airfoil 40 (with or without fluid flow interaction) can be determined using various design processes and practices. Such design processes and practices may include any of, but also are not limited to only including: computational Fluid Dynamics (CFD); traditional fluid dynamics analysis; Euler and Navier-Stokes equations; manual positioning, flow testing (for example in wind tunnels), and modification of the airfoil; in-situ testing; modeling; application of scientific principles to design or develop the airfoils, machines, apparatus, or manufacturing processes; and airfoil flow testing and modification.
As noted above, the configuration of airfoil 40, and the interaction of airfoil 40 with surrounding airfoils and peripheral surfaces, facilitates stage airflow efficiency, enhanced aeromechanics, smooth laminar flow from stage-to-stage, reduced thermal stresses, enhanced interrelation of the stages to effectively pass the airflow from stage-to-stage, and reduced mechanical stresses, among other desirable effects, compared to other similar airfoils, which have like applications. In the exemplary embodiment, airfoil 40 facilitates increasing the efficiency of the turbine operation as compared to turbines using known airfoils. The increased efficiency provides, in addition to the above-noted advantages, an increased power output with a decrease in the amount of fuel required. As such, emissions produced from the engine are decreased.
As noted previously, airfoil 40 may also be coated for protection against corrosion and oxidation after airfoil 40 is manufactured, according to the values of Table I and within the tolerances explained above. Consequently, in addition to the manufacturing tolerances for the X and Y values set forth in Table I, there may also be an addition to those values to account for the coating thicknesses.











TABLE I









Section 1
Section 2
Section 3
















Point
X
Y
Z
X
Y
Z
X
Y
Z





1
−1.2863
−0.5237
4.3045
−0.4461
−0.1553
5.1101
0.0433
−0.0905
5.9156


2
−1.1988
−0.3007
4.3045
−0.8739
0.1801
5.1101
−1.115
−0.15
5.9156


3
−0.1846
−0.1543
4.3045
−0.6366
−0.2319
5.1101
−1.1211
−0.3644
5.9156


4
−0.2999
0.5367
4.3045
−0.1212
−0.1009
5.1101
−1.1587
−0.2834
5.9156


5
−0.9855
0.0244
4.3045
−1.0812
−0.1065
5.1101
−0.5176
−0.1255
5.9156


6
−0.6967
0.3164
4.3045
−1.2004
−0.3626
5.1101
−1.0141
−0.3555
5.9156


7
−0.8939
−0.428
4.3045
−1.1163
−0.5101
5.1101
−0.2816
0.5688
5.9156


8
−1.2639
−0.6589
4.3045
−0.1882
0.5598
5.1101
−0.771
−0.2363
5.9156


9
−1.2719
−0.6549
4.3045
−1.2158
−0.4704
5.1101
−0.5587
0.4798
5.9156


10
−0.4196
0.4898
4.3045
−0.7806
0.2746
5.1101
−0.8064
0.2978
5.9156


11
−1.1477
−0.6294
4.3045
−0.9349
−0.4075
5.1101
−0.1371
−0.0659
5.9156


12
−1.2949
−0.597
4.3045
−0.4733
0.4797
5.1101
−1.0184
0.0305
5.9156


13
−0.0521
0.5832
4.3045
−0.7337
0.3155
5.1101
−1.1401
−0.2134
5.9156


14
−1.2455
−0.6631
4.3045
−0.3166
−0.1218
5.1101
−1.0873
−0.3701
5.9156


15
−1.2657
−0.4528
4.3045
−0.9637
0.0706
5.1101
−0.11
0.5753
5.9156


16
0.0245
−0.1483
4.3045
0.0048
−0.1069
5.1101
−1.1605
−0.3137
5.9156


17
−1.1298
−0.1801
4.3045
−1.1475
−0.2315
5.1101
−0.9348
−0.3211
5.9156


18
−0.3224
−0.176
4.3045
−1.1692
−0.5137
5.1101
−0.3938
0.5452
5.9156


19
−0.8772
0.1494
4.3045
−0.0133
0.564
5.1101
−0.6463
−0.1763
5.9156


20
−0.7018
−0.312
4.3045
−1.2149
−0.4228
5.1101
−0.6617
0.4179
5.9156


21
−0.5587
−0.2471
4.3045
−1.0615
−0.4867
5.1101
−0.5825
−0.1494
5.9156


22
−0.5908
0.3938
4.3045
−0.3051
0.5382
5.1101
−0.3024
−0.0742
5.9156


23
−1.0273
−0.5304
4.3045
−1.208
−0.4903
5.1101
−0.8986
0.197
5.9156


24
−1.2844
−0.6415
4.3045
−1.0355
−0.4718
5.1101
−0.0163
−0.0784
5.9156


25
−0.2381
0.5547
4.3045
−0.8245
−0.3362
5.1101
−1.0856
−0.0883
5.9156


26
−1.1909
−0.6545
4.3045
−0.5813
0.4235
5.1101
−1.1364
−0.3565
5.9156


27
−1.2928
−0.5601
4.3045
−0.5094
−0.1772
5.1101
0.0615
0.5472
5.9156


28
−1.2233
−0.3504
4.3045
−0.8254
0.2315
5.1101
−1.1551
−0.2646
5.9156


29
−0.115
−0.1487
4.3045
−0.0694
0.5664
5.1101
−1.0416
−0.3639
5.9156


30
−1.0363
−0.0419
4.3045
−0.1842
−0.1036
5.1101
−0.2245
0.5748
5.9156


31
−0.4813
−0.219
4.3045
−1.0443
−0.046
5.1101
−0.8323
−0.2683
5.9156


32
−0.7595
0.2636
4.3045
−1.1891
−0.3291
5.1101
−0.5044
0.5057
5.9156


33
−0.8316
−0.3865
4.3045
−1.1339
−0.5141
5.1101
−0.4648
−0.1089
5.9156


34
−0.4783
0.4608
4.3045
−0.1289
0.565
5.1101
−0.7563
0.3441
5.9156


35
−1.123
−0.6106
4.3045
−1.2173
−0.4598
5.1101
0.0036
0.5606
5.9156


36
−1.2933
−0.6154
4.3045
−0.9848
−0.4402
5.1101
−0.1924
−0.0654
5.9156


37
−0.1139
0.578
4.3045
−0.4184
0.5025
5.1101
−0.9809
0.0877
5.9156


38
−1.2269
−0.6637
4.3045
−0.7004
−0.2644
5.1101
−1.1282
−0.1814
5.9156


39
−1.2771
−0.488
4.3045
−0.6849
0.3542
5.1101
−1.1046
−0.3688
5.9156


40
−1.1724
−0.2519
4.3045
−0.3818
−0.1368
5.1101
−0.053
0.5698
5.9156


41
−0.2538
−0.1634
4.3045
−0.92
0.1264
5.1101
−1.1606
−0.3024
5.9156


42
−0.9322
0.0886
4.3045
−0.0581
−0.102
5.1101
−0.9872
−0.3449
5.9156


43
−0.6345
−0.2793
4.3045
−1.1157
−0.1683
5.1101
−0.3381
0.5589
5.9156


44
−0.6445
0.3563
4.3045
−1.1859
−0.5078
5.1101
−0.4112
−0.0947
5.9156


45
−0.9543
−0.4721
4.3045
0.0425
0.5581
5.1101
−0.709
−0.2054
5.9156


46
−1.2788
−0.6489
4.3045
−1.2098
−0.3967
5.1101
−0.6111
0.4505
5.9156


47
−0.3604
0.515
4.3045
−1.0883
−0.4999
5.1101
−0.3571
−0.0831
5.9156


48
−1.1741
−0.6461
4.3045
−0.247
0.5509
5.1101
−1.1554
−0.3358
5.9156


49
−1.2946
−0.5785
4.3045
−1.2129
−0.4808
5.1101
−0.8538
0.2486
5.9156


50
0.0099
0.5841
4.3045
−0.885
−0.3746
5.1101
−0.0765
−0.0702
5.9156


51
−1.2457
−0.4011
4.3045
−0.5269
0.4538
5.1101
−1.0534
−0.0281
5.9156


52
−0.0453
−0.1467
4.3045
−0.5715
−0.2021
5.1101
−1.1495
−0.3451
5.9156


53
−1.0844
−0.11
4.3045
−0.2507
−0.1106
5.1101
−1.1504
−0.2461
5.9156


54
−0.4024
−0.1953
4.3045
−1.0051
0.0131
5.1101
−1.0699
−0.3691
5.9156


55
−1.099
−0.5906
4.3045
−1.1762
−0.2961
5.1101
−0.1673
0.577
5.9156


56
−0.8197
0.2078
4.3045
−1.1516
−0.5157
5.1101
−1.1589
−0.325
5.9156


57
−0.7676
−0.3478
4.3045
−1.2174
−0.4492
5.1101
−0.4485
0.5278
5.9156


58
−0.5353
0.4287
4.3045
−0.3623
0.5221
5.1101
−0.71
0.3823
5.9156


59
−1.2902
−0.6289
4.3045
−1.2012
−0.498
5.1101
−0.8833
−0.2952
5.9156


60
−0.1753
0.5686
4.3045
−0.763
−0.2993
5.1101
−0.2475
−0.0683
5.9156


61
−1.2086
−0.6607
4.3045
−0.634
0.3902
5.1101
−0.941
0.1433
5.9156


62
0.1332
0.5721
4.3045
1.2154
−0.9757
5.1101
1.2034
−1.0493
5.9156


63
1.3681
−0.8619
4.3045
0.6142
0.2446
5.1101
1.209
−1.0301
5.9156


64
0.1593
−0.1619
4.3045
1.2621
−0.9892
5.1101
0.3262
−0.2069
5.9156


65
0.4104
0.4721
4.3045
0.3675
0.4441
5.1101
0.5892
−0.4104
5.9156


66
1.3064
−0.9038
4.3045
0.1909
−0.145
5.1101
0.9255
−0.3487
5.9156


67
0.6542
0.2873
4.3045
1.291
−0.9507
5.1101
0.9136
−0.7676
5.9156


68
1.2324
−0.8528
4.3045
0.0977
0.5486
5.1101
1.1262
−1.0195
5.9156


69
0.9218
−0.032
4.3045
0.4816
−0.2792
5.1101
1.1804
−0.9489
5.9156


70
0.9982
−0.6024
4.3045
1.2605
−0.8676
5.1101
1.1396
−1.0351
5.9156


71
1.2437
−0.5656
4.3045
0.8101
−0.5358
5.1101
0.6386
0.1329
5.9156


72
0.6659
−0.3466
4.3045
1.0211
−0.3656
5.1101
0.4757
0.3121
5.9156


73
1.3692
−0.8165
4.3045
1.1577
−0.9065
5.1101
1.1793
−1.0629
5.9156


74
0.3516
−0.2061
4.3045
0.7601
0.0683
5.1101
0.7188
0.0211
5.9156


75
0.2501
0.5429
4.3045
1.2322
−0.9882
5.1101
0.1595
−0.1259
5.9156


76
1.3496
−0.8873
4.3045
0.5125
0.3407
5.1101
0.174
0.5089
5.9156


77
0.5118
0.407
4.3045
1.2788
−0.9786
5.1101
1.0665
−0.6643
5.9156


78
1.2767
−0.8963
4.3045
0.2613
0.4976
5.1101
1.1613
−1.0577
5.9156


79
0.7403
0.1979
4.3045
0.3111
−0.1895
5.1101
0.2281
0.4844
5.9156


80
1.1917
−0.8056
4.3045
1.2876
−0.9286
5.1101
0.7087
−0.5318
5.9156


81
1.059
−0.2403
4.3045
0.6076
−0.3652
5.1101
0.9744
−0.4531
5.9156


82
0.8574
−0.4793
4.3045
1.1785
−0.6871
5.1101
1.0832
−0.9694
5.9156


83
1.3298
−0.7316
4.3045
0.9767
−0.7022
5.1101
1.1528
−0.8781
5.9156


84
0.5428
−0.2807
4.3045
0.9057
−0.1565
5.1101
1.1531
−1.0511
5.9156


85
0.0718
0.5804
4.3045
1.2082
−0.9677
5.1101
0.5609
0.2258
5.9156


86
1.3725
−0.8468
4.3045
0.0673
−0.1156
5.1101
0.7604
−0.0438
5.9156


87
0.2241
−0.1735
4.3045
0.6613
0.1929
5.1101
1.197
−1.0564
5.9156


88
0.2882
−0.1883
4.3045
1.2523
−0.9912
5.1101
0.333
0.4242
5.9156


89
0.3585
0.4992
4.3045
0.129
−0.1282
5.1101
1.0212
−0.5584
5.9156


90
1.3218
−0.9018
4.3045
1.2891
−0.9616
5.1101
0.2815
0.4559
5.9156


91
0.6086
0.3293
4.3045
0.1523
0.5356
5.1101
0.8404
−0.6808
5.9156


92
1.253
−0.8761
4.3045
0.4262
−0.2467
5.1101
1.1329
−1.0272
5.9156


93
0.8641
0.0469
4.3045
1.279
−0.9076
5.1101
0.6749
0.0844
5.9156


94
1.0648
−0.6681
4.3045
0.7446
−0.4766
5.1101
0.8
−0.1101
5.9156


95
1.1844
−0.4559
4.3045
1.0751
−0.472
5.1101
1.17
−1.0617
5.9156


96
0.7252
−0.3835
4.3045
1.1073
−0.8474
5.1101
0.2722
−0.1766
5.9156


97
1.3635
−0.802
4.3045
0.8111
−0.005
5.1101
0.102
−0.1064
5.9156


98
0.4141
−0.2269
4.3045
0.4178
0.4124
5.1101
1.2076
−1.0406
5.9156


99
0.1939
0.5592
4.3045
1.2233
−0.9829
5.1101
0.3786
−0.24
5.9156


100
1.3602
−0.8757
4.3045
0.5647
0.294
5.1101
1.1957
−0.9884
5.9156


101
0.0941
−0.1536
4.3045
1.2712
−0.9848
5.1101
1.2034
−1.0091
5.9156


102
0.4605
0.442
4.3045
0.3152
0.4726
5.1101
0.65
−0.4701
5.9156


103
1.291
−0.902
4.3045
0.2516
−0.1655
5.1101
0.9864
−0.8547
5.9156


104
0.698
0.2434
4.3045
1.2903
−0.9396
5.1101
0.5261
−0.3531
5.9156


105
1.2122
−0.8291
4.3045
0.5356
−0.314
5.1101
0.8378
−0.1774
5.9156


106
0.9921
−0.135
4.3045
1.2281
−0.7958
5.1101
1.1461
−1.0432
5.9156


107
0.9291
−0.5393
4.3045
0.8948
−0.6176
5.1101
0.6006
0.1801
5.9156


108
1.3015
−0.6761
4.3045
0.9648
−0.2603
5.1101
1.1887
−1.0611
5.9156


109
0.6051
−0.3122
4.3045
1.2012
−0.9594
5.1101
1.1104
−0.7708
5.9156


110
1.3728
−0.8315
4.3045
0.7061
0.1392
5.1101
0.3826
0.3895
5.9156


111
0.305
0.5229
4.3045
1.2424
−0.991
5.1101
0.2167
−0.1495
5.9156


112
1.3366
−0.8961
4.3045
0.4661
0.3779
5.1101
0.1183
0.5299
5.9156


113
0.5612
0.3693
4.3045
1.2849
−0.9706
5.1101
0.4786
−0.3135
5.9156


114
1.2642
−0.8871
4.3045
0.2058
0.519
5.1101
1.2071
−1.0195
5.9156


115
1.3571
−0.7877
4.3045
0.3693
−0.2167
5.1101
0.4294
−0.2757
5.9156


116
0.8038
0.1237
4.3045
1.2837
−0.918
5.1101
0.7659
−0.595
5.9156


117
1.1291
−0.736
4.3045
0.6771
−0.4195
5.1101
0.8739
−0.2456
5.9156


118
1.123
−0.3473
4.3045
1.1275
−0.5792
5.1101
1.1995
−0.9987
5.9156


119
0.7828
−0.423
4.3045
1.0561
−0.789
5.1101
0.5193
0.2699
5.9156


120
0.4791
−0.2523
4.3045
0.8595
−0.0801
5.1101
0.4302
0.352
5.9156


Hole 1
−0.663
−0.0626
4.3045
−0.2702
0.1279
5.1101
−0.5863
0.0714
5.9156


Hole 2
−0.2928
0.102
4.3045
−0.6246
0.0044
5.1101
−0.2477
0.1538
5.9156


Hole 3
0.4613
0.0371
4.3045
0.8424
−0.3783
5.1101
0.4303
−0.0478
5.9156


Hole 4
0.8746
−0.3089
4.3045
0.4458
−0.0054
5.1101
0.8101
−0.4478
5.9156


Hole 5
0.0875
0.1167
4.3045
0.0965
0.0998
5.1101
0.1055
0.0828
5.9156














Section 4
Section 5
Section 6
















Point
X
Y
Z
X
Y
Z
X
Y
Z





1
−0.9981
−0.2284
6.7212
−0.6613
−0.04
7.5267
−1.0043
0.1373
8.3323


2
−1.1125
−0.1884
6.7212
−0.6656
0.4981
7.5267
−1.0263
0.0535
8.3323


3
−0.7868
−0.1582
6.7212
−0.8611
0.3293
7.5267
−0.6842
0.0523
8.3323


4
−0.7015
0.4419
6.7212
−1.0014
0.1286
7.5267
−0.6058
0.5504
8.3323


5
−0.9052
0.2461
6.7212
−1.0396
−0.1022
7.5267
−0.798
0.4131
8.3323


6
−1.0705
−0.0172
6.7212
−1.0629
−0.0184
7.5267
−0.8663
0.3425
8.3323


7
−1.0596
−0.228
6.7212
−0.962
−0.1145
7.5267
−0.951
0.2319
8.3323


8
−1.1146
−0.1586
6.7212
−1.0635
−0.0781
7.5267
−1.0123
0.0196
8.3323


9
−1.1033
−0.2055
6.7212
−1.0528
−0.0933
7.5267
−1.0205
0.0935
8.3323


10
−0.6617
−0.1106
6.7212
−0.8337
−0.086
7.5267
−0.9584
0.0019
8.3323


11
−0.5739
0.5197
6.7212
−0.5213
0.5678
7.5267
−1.0226
0.0351
8.3323


12
−0.7891
0.37
6.7212
−0.5361
−0.018
7.5267
−0.8292
0.0219
8.3323


13
−0.9728
0.1551
6.7212
−0.7526
0.4354
7.5267
−0.5752
0.065
8.3323


14
−1.0954
−0.0785
6.7212
−0.9243
0.2501
7.5267
−0.683
0.5052
8.3323


15
−0.5339
−0.0713
6.7212
−1.0369
0.057
7.5267
−0.9908
0.1652
8.3323


16
−1.026
−0.2307
6.7212
−1.0101
−0.1126
7.5267
−0.9923
0.0079
8.3323


17
−1.1144
−0.1785
6.7212
−1.0675
−0.0499
7.5267
−1.0261
0.0629
8.3323


18
−0.9439
−0.2157
6.7212
−0.9305
−0.1102
7.5267
−0.9194
0.004
8.3323


19
−0.8387
−0.1788
6.7212
−0.7191
−0.0539
7.5267
−0.7411
0.0416
8.3323


20
−0.6605
0.4702
6.7212
−0.6192
0.5248
7.5267
−0.5651
0.5693
8.3323


21
−0.8685
0.2892
6.7212
−0.8658
−0.0949
7.5267
−0.7614
0.4459
8.3323


22
−1.0411
0.042
6.7212
−0.8268
0.3666
7.5267
−0.9245
0.27
8.3323


23
−1.0755
−0.2233
6.7212
−0.9774
0.1702
7.5267
−0.9813
0.0047
8.3323


24
−1.1111
−0.1341
6.7212
−1.0589
−0.0029
7.5267
−1.0158
0.1084
8.3323


25
−0.9708
−0.223
6.7212
−0.978
−0.1152
7.5267
−0.9699
0.0028
8.3323


26
−1.1089
−0.1976
6.7212
−1.0663
−0.0689
7.5267
−1.0253
0.0442
8.3323


27
−0.7244
−0.1338
6.7212
−0.5989
−0.0275
7.5267
−0.8608
0.0148
8.3323


28
−0.5286
0.5404
6.7212
−0.7102
0.4682
7.5267
−0.6268
0.0603
8.3323


29
−0.7463
0.4072
6.7212
−0.898
−0.1032
7.5267
−0.6451
0.5289
8.3323


30
−0.94
0.2013
6.7212
−0.8936
0.2904
7.5267
−0.833
0.3786
8.3323


31
−1.0836
−0.0476
6.7212
−1.0235
0.086
7.5267
−0.9757
0.1924
8.3323


32
−1.0429
−0.2303
6.7212
−1.0659
−0.034
7.5267
−1.0028
0.0128
8.3323


33
−1.115
−0.1685
6.7212
−0.9462
−0.1128
7.5267
−1.024
0.0784
8.3323


34
−0.8909
−0.1984
6.7212
−1.059
−0.0865
7.5267
−0.9468
0.0019
8.3323


35
−0.5982
−0.0896
6.7212
−0.7765
−0.0696
7.5267
−1.0184
0.0267
8.3323


36
−0.6179
0.4962
6.7212
−0.571
0.5481
7.5267
−0.8925
0.0082
8.3323


37
−0.8298
0.3306
6.7212
−1.0253
−0.1085
7.5267
−0.7976
0.0292
8.3323


38
−1.0085
0.0994
6.7212
−0.7906
0.4021
7.5267
−0.7231
0.4767
8.3323


39
−1.0903
−0.216
6.7212
−0.9517
0.2107
7.5267
−0.8962
0.3069
8.3323


40
−1.1053
−0.11
6.7212
−1.0488
0.0274
7.5267
0.0185
0.5357
8.3323


41
−0.2405
0.6006
6.7212
−0.9942
−0.1147
7.5267
0.0299
−0.0727
8.3323


42
−0.482
0.5583
6.7212
−1.0675
−0.0594
7.5267
−0.1377
0.0051
8.3323


43
−0.4686
−0.0563
6.7212
−0.3458
−0.0095
7.5267
−0.1876
0.6104
8.3323


44
0.0509
0.548
6.7212
−0.0338
−0.0688
7.5267
−0.3925
0.617
8.3323


45
−0.0929
0.5879
6.7212
−0.011
0.5591
7.5267
−0.4718
0.0677
8.3323


46
−0.3379
0.5933
6.7212
−0.3211
0.6074
7.5267
−0.0624
0.5735
8.3323


47
−0.1578
−0.0417
6.7212
−0.2706
0.6084
7.5267
−0.2691
0.621
8.3323


48
−0.1916
0.5996
6.7212
−0.2191
−0.0221
7.5267
−0.4806
0.5992
8.3323


49
−0.4345
0.5732
6.7212
0.0819
−0.1171
7.5267
−0.3175
0.053
8.3323


50
−0.2825
−0.036
6.7212
−0.114
0.5897
7.5267
−0.0237
−0.044
8.3323


51
−0.22
−0.0368
6.7212
−0.3714
0.6029
7.5267
0.0573
0.5135
8.3323


52
0.0738
−0.0985
6.7212
−0.4094
−0.0088
7.5267
−0.1475
0.6013
8.3323


53
−0.0442
0.5774
6.7212
−0.0947
−0.0495
7.5267
−0.3515
0.621
8.3323


54
−0.2893
0.5985
6.7212
0.0389
0.5389
7.5267
−0.1967
0.0246
8.3323


55
0.0181
−0.0791
6.7212
−0.2201
0.6059
7.5267
−0.0214
0.5558
8.3323


56
−0.407
−0.0459
6.7212
0.0874
0.5155
7.5267
−0.2282
0.617
8.3323


57
−0.0961
−0.0508
6.7212
−0.4703
0.5836
7.5267
−0.4369
0.6096
8.3323


58
−0.1421
0.5953
6.7212
−0.2823
−0.0139
7.5267
−0.3687
0.0605
8.3323


59
−0.3861
0.585
6.7212
0.0247
−0.0913
7.5267
−0.1045
0.5888
8.3323


60
−0.3449
−0.039
6.7212
−0.062
0.5761
7.5267
−0.3103
0.6223
8.3323


61
0.0038
0.5641
6.7212
−0.4729
−0.0117
7.5267
−0.5234
0.5857
8.3323


62
−0.0386
−0.0632
6.7212
−0.1565
−0.0339
7.5267
−0.4201
0.0654
8.3323


63
0.5121
−0.4022
6.7212
−0.1668
0.5997
7.5267
−0.5235
0.0675
8.3323


64
0.2335
−0.1761
6.7212
−0.4212
0.595
7.5267
−0.08
−0.0178
8.3323


65
0.3917
0.332
6.7212
0.4302
0.2293
7.5267
−0.2567
0.0406
8.3323


66
0.3803
−0.2798
6.7212
0.2284
0.4257
7.5267
0.2785
−0.2628
8.3323


67
0.4698
−0.3597
6.7212
0.239
−0.2112
7.5267
0.5138
−0.5433
8.3323


68
0.1812
−0.1469
6.7212
0.4538
−0.4053
7.5267
0.5465
−0.0571
8.3323


69
0.5219
0.1929
6.7212
0.5477
0.0694
7.5267
0.3347
0.2649
8.3323


70
0.3023
0.4075
6.7212
0.3546
0.3135
7.5267
0.1311
0.4634
8.3323


71
0.1043
0.5261
6.7212
0.1362
0.4883
7.5267
0.1322
−0.1386
8.3323


72
0.1282
−0.1211
6.7212
0.3296
−0.2834
7.5267
0.3684
−0.3588
8.3323


73
0.4336
0.2912
6.7212
0.5435
−0.5097
7.5267
0.4555
0.0973
8.3323


74
0.2063
0.4727
6.7212
0.4656
0.185
7.5267
0.2527
0.3563
8.3323


75
0.333
−0.2429
6.7212
0.2719
0.3908
7.5267
0.2307
−0.2179
8.3323


76
0.1561
0.5009
6.7212
0.4138
−0.3632
7.5267
0.4518
−0.4607
8.3323


77
0.568
−0.4627
6.7212
0.5858
0.0096
7.5267
0.5884
−0.1363
8.3323


78
0.5675
0.1353
6.7212
0.3932
0.2722
7.5267
0.3772
0.2107
8.3323


79
0.3479
0.3709
6.7212
0.1832
0.4583
7.5267
0.1734
0.4297
8.3323


80
0.4259
−0.3189
6.7212
0.2852
−0.2463
7.5267
0.0819
−0.1043
8.3323


81
0.2841
−0.2082
6.7212
0.4923
−0.4486
7.5267
0.3244
−0.3099
8.3323


82
0.4739
0.2485
6.7212
0.5077
0.128
7.5267
0.5738
−0.6275
8.3323


83
0.2548
0.4417
6.7212
0.3141
0.3531
7.5267
0.5023
0.0209
8.3323


84
1.0795
−0.9325
6.7212
0.1374
−0.1463
7.5267
0.2898
0.317
8.3323


85
0.7891
−0.7435
6.7212
0.3725
−0.3225
7.5267
0.0948
0.4893
8.3323


86
0.8312
−0.3115
6.7212
0.1911
−0.1786
7.5267
0.1806
−0.1754
8.3323


87
1.0547
−1.0798
6.7212
0.5929
−0.5723
7.5267
0.4108
−0.4092
8.3323


88
0.6106
0.0759
6.7212
0.957
−1.0719
7.5267
0.4173
0.1548
8.3323


89
1.0965
−1.1181
6.7212
0.6219
−0.0513
7.5267
0.2139
0.394
8.3323


90
1.128
−1.1008
6.7212
1.0589
−1.1462
7.5267
0.9995
−1.1718
8.3323


91
1.1193
−1.0513
6.7212
1.0188
−1.1509
7.5267
0.9609
−1.0505
8.3323


92
0.988
−0.681
6.7212
1.0584
−1.1001
7.5267
0.738
−0.4617
8.3323


93
0.7466
−0.1453
6.7212
0.9722
−0.8543
7.5267
0.8329
−1.0105
8.3323


94
1.0714
−1.0984
6.7212
0.6882
−0.7001
7.5267
0.9435
−1.182
8.3323


95
1.1101
−1.1178
6.7212
0.7458
−0.2913
7.5267
0.9818
−1.194
8.3323


96
1.1292
−1.0815
6.7212
0.9995
−1.129
7.5267
0.9922
−1.1364
8.3323


97
1.1032
−1.0022
6.7212
1.0653
−1.1297
7.5267
0.8756
−0.8134
8.3323


98
0.7235
−0.6552
6.7212
0.8819
−0.6122
7.5267
0.6327
−0.7126
8.3323


99
0.8868
−0.4333
6.7212
0.874
−0.959
7.5267
0.6664
−0.2975
8.3323


100
1.0129
−1.0317
6.7212
0.6656
−0.1301
7.5267
0.8861
−1.0922
8.3323


101
1.0903
−1.1154
6.7212
1.0115
−1.1443
7.5267
0.9996
−1.1622
8.3323


102
0.6515
0.0151
6.7212
1.0525
−1.1524
7.5267
0.9566
−1.1934
8.3323


103
1.1233
−1.1089
6.7212
0.6409
−0.6359
7.5267
0.9961
−1.1809
8.3323


104
0.6216
−0.5254
6.7212
1.0618
−1.1099
7.5267
0.9742
−1.0874
8.3323


105
1.1227
−1.0613
6.7212
1.0356
−1.1575
7.5267
0.7855
−0.5783
8.3323


106
1.0348
−0.8064
6.7212
1.0152
−0.9763
7.5267
0.8061
−0.9698
8.3323


107
0.9661
−0.9761
6.7212
0.783
−0.3733
7.5267
0.9387
−1.1746
8.3323


108
0.8544
−0.8319
6.7212
0.9938
−1.1212
7.5267
0.9734
−1.1964
8.3323


109
0.7901
−0.2278
6.7212
1.0271
−1.1557
7.5267
0.9964
−1.1492
8.3323


110
1.0629
−1.0892
6.7212
1.0633
−1.1384
7.5267
0.9189
−0.9315
8.3323


111
1.1033
−1.1189
6.7212
0.8338
−0.4922
7.5267
0.7028
−0.3793
8.3323


112
1.1301
−1.0918
6.7212
1.0551
−1.0904
7.5267
0.8596
−1.0513
8.3323


113
1.1161
−1.0413
6.7212
0.9278
−0.733
7.5267
0.99
−1.1886
8.3323


114
0.9209
−0.9194
6.7212
1.0518
−1.0809
7.5267
0.9878
−1.124
8.3323


115
0.6733
−0.5897
6.7212
0.7812
−0.8295
7.5267
0.8313
−0.6956
8.3323


116
0.9389
−0.5565
6.7212
0.7067
−0.2102
7.5267
0.9494
−1.1884
8.3323


117
0.7006
−0.0642
6.7212
1.0053
−1.1368
7.5267
0.7199
−0.8408
8.3323


118
1.1166
−1.1149
6.7212
1.0445
−1.1563
7.5267
0.6283
−0.2165
8.3323


119
1.0804
−1.1074
6.7212
1.0645
−1.1198
7.5267
0.9125
−1.1333
8.3323


120
1.1263
−1.0713
6.7212
1.0386
−1.0435
7.5267
0.9648
−1.1962
8.3323


Hole 1
−0.5479
0.1383
6.7212
−0.5096
0.2053
7.5267
−0.18
0.2314
8.3323


Hole 2
−0.2251
0.1797
6.7212
−0.2026
0.2056
7.5267
−0.4713
0.2723
8.3323


Hole 3
0.4148
−0.0903
6.7212
0.3993
−0.1327
7.5267
0.3838
−0.1752
8.3323


Hole 4
0.1145
0.0659
6.7212
0.1236
0.0489
7.5267
0.1326
0.0319
8.3323


Hole 5
0.7778
−0.5172
6.7212
0.7455
−0.5867
7.5267
0.7132
−0.6561
8.3323














Section 7
Section 8
Section 9
















Point
X
Y
Z
X
Y
Z
X
Y
Z





1
−0.9264
0.1336
9.1378
−0.8565
0.4588
9.9434
−0.6547
0.4314
10.7489


2
−0.9854
0.1605
9.1378
−0.5619
0.6317
9.9434
−0.5888
0.7092
10.7489


3
−0.7311
0.1622
9.1378
−0.675
0.5858
9.9434
−0.8107
0.4492
10.7489


4
−0.6348
0.5555
9.1378
−0.7539
0.2871
9.9434
−0.7585
0.6433
10.7489


5
−0.8293
0.4179
9.1378
−0.9004
0.2828
9.9434
−0.8868
0.4674
10.7489


6
−0.9569
0.267
9.1378
−0.946
0.3286
9.9434
−0.8708
0.5568
10.7489


7
−0.9604
0.1375
9.1378
−0.9427
0.3014
9.9434
−0.9023
0.5093
10.7489


8
−0.8709
0.1391
9.1378
−0.9159
0.3908
9.9434
−0.8995
0.4782
10.7489


9
−0.6287
0.1735
9.1378
−0.7871
0.5171
9.9434
−0.9035
0.4856
10.7489


10
−0.5199
0.6052
9.1378
−0.6004
0.6185
9.9434
−0.661
0.6882
10.7489


11
−0.9813
0.1523
9.1378
−0.5956
0.289
9.9434
−0.855
0.4565
10.7489


12
−0.7175
0.5058
9.1378
−0.8441
0.2822
9.9434
−0.8136
0.6075
10.7489


13
−0.8933
0.3526
9.1378
−0.9226
0.2871
9.9434
−0.8913
0.5303
10.7489


14
−0.9776
0.2261
9.1378
−0.9402
0.3477
9.9434
−0.9051
0.4937
10.7489


15
−0.9434
0.1343
9.1378
−0.6409
0.2902
9.9434
−0.6105
0.4245
10.7489


16
−0.9877
0.1694
9.1378
−0.8777
0.4373
9.9434
−0.5502
0.7167
10.7489


17
−0.782
0.1542
9.1378
−0.711
0.5665
9.9434
−0.7884
0.4466
10.7489


18
−0.5256
0.1759
9.1378
−0.6861
0.2898
9.9434
−0.7269
0.6602
10.7489


19
−0.5914
0.5768
9.1378
−0.8892
0.282
9.9434
−0.8765
0.4628
10.7489


20
−0.7948
0.4479
9.1378
−0.9471
0.3187
9.9434
−0.8591
0.5689
10.7489


21
−0.9404
0.2927
9.1378
−0.9372
0.295
9.9434
−0.8991
0.5165
10.7489


22
−0.9683
0.1409
9.1378
−0.9267
0.3742
9.9434
−0.5665
0.4161
10.7489


23
−0.9866
0.1969
9.1378
−0.8228
0.489
9.9434
−0.627
0.6993
10.7489


24
−0.9093
0.1345
9.1378
−0.6381
0.6031
9.9434
−0.8329
0.4524
10.7489


25
−0.68
0.1688
9.1378
−0.5504
0.2861
9.9434
−0.789
0.6246
10.7489


26
−0.6768
0.5317
9.1378
−0.8215
0.2832
9.9434
−0.8816
0.544
10.7489


27
−0.8622
0.3861
9.1378
−0.9116
0.2844
9.9434
−0.9044
0.5018
10.7489


28
−0.9714
0.2401
9.1378
−0.9435
0.3382
9.9434
−0.8938
0.4721
10.7489


29
−0.988
0.1878
9.1378
−0.946
0.3088
9.9434
−0.7215
0.4396
10.7489


30
−0.952
0.1355
9.1378
−0.8976
0.4147
9.9434
−0.6943
0.6751
10.7489


31
−0.9884
0.1786
9.1378
−0.7498
0.543
9.9434
−0.8658
0.4592
10.7489


32
−0.8328
0.1454
9.1378
−0.8666
0.2817
9.9434
−0.837
0.589
10.7489


33
−0.5771
0.1759
9.1378
−0.9304
0.2903
9.9434
−0.8954
0.5235
10.7489


34
−0.556
0.5919
9.1378
−0.9361
0.3569
9.9434
0.0006
0.5009
10.7489


35
−0.7569
0.4778
9.1378
−0.0697
0.0944
9.9434
−0.2626
0.2926
10.7489


36
−0.9224
0.3173
9.1378
−0.2807
0.2208
9.9434
−0.1441
0.6273
10.7489


37
−0.9755
0.1458
9.1378
−0.5054
0.2812
9.9434
−0.0741
0.1363
10.7489


38
−0.9827
0.2117
9.1378
−0.4838
0.6511
9.9434
−0.3066
0.7033
10.7489


39
−0.2522
0.6356
9.1378
−0.2899
0.6556
9.9434
−0.4718
0.7241
10.7489


40
−0.4457
0.6258
9.1378
−0.1117
0.5972
9.9434
−0.3956
0.3629
10.7489


41
−0.4741
0.1733
9.1378
0.0428
−0.0072
9.9434
−0.0543
0.5561
10.7489


42
−0.2295
0.1207
9.1378
0.0461
0.4817
9.9434
−0.1813
0.2339
10.7489


43
−0.0071
0.0027
9.1378
−0.1521
0.1529
9.9434
−0.2073
0.6644
10.7489


44
0.0503
0.5047
9.1378
−0.3703
0.2529
9.9434
−0.4798
0.3936
10.7489


45
−0.1345
0.6081
9.1378
−0.4048
0.6607
9.9434
−0.0102
0.0662
10.7489


46
−0.331
0.6394
9.1378
−0.2163
0.6395
9.9434
−0.3719
0.7176
10.7489


47
−0.3721
0.1602
9.1378
−0.0458
0.5572
9.9434
0.0264
0.4717
10.7489


48
−0.1386
0.0815
9.1378
−0.0307
0.0622
9.9434
−0.3055
0.3185
10.7489


49
0.0783
−0.0645
9.1378
−0.2375
0.201
9.9434
−0.1142
0.6061
10.7489


50
−0.022
0.5546
9.1378
−0.4606
0.2743
9.9434
−0.1079
0.1696
10.7489


51
−0.2123
0.6294
9.1378
−0.5228
0.6427
9.9434
−0.2747
0.6932
10.7489


52
−0.4078
0.6328
9.1378
−0.3274
0.6599
9.9434
0.0616
−0.0235
10.7489


53
−0.2763
0.1366
9.1378
−0.1456
0.6136
9.9434
−0.4384
0.7239
10.7489


54
−0.0523
0.033
9.1378
0.0167
0.5085
9.9434
−0.4373
0.3793
10.7489


55
0.0842
0.4767
9.1378
−0.1102
0.1247
9.9434
−0.0263
0.529
10.7489


56
−0.097
0.5933
9.1378
−0.4164
0.2651
9.9434
−0.2212
0.2643
10.7489


57
−0.2924
0.6389
9.1378
−0.2528
0.6488
9.9434
−0.1752
0.6468
10.7489


58
−0.4831
0.6166
9.1378
−0.325
0.2382
9.9434
−0.0416
0.1017
10.7489


59
−0.4229
0.1682
9.1378
−0.4444
0.6571
9.9434
−0.3391
0.7114
10.7489


60
−0.1835
0.1023
9.1378
−0.0789
0.5787
9.9434
−0.5111
0.7217
10.7489


61
0.0364
−0.0298
9.1378
0.0068
0.0283
9.9434
0.0512
0.4417
10.7489


62
0.0149
0.5307
9.1378
−0.1955
0.1788
9.9434
−0.3499
0.342
10.7489


63
−0.173
0.6202
9.1378
−0.3651
0.6615
9.9434
−0.0836
0.5818
10.7489


64
−0.3696
0.6374
9.1378
−0.1806
0.6277
9.9434
−0.1428
0.2016
10.7489


65
−0.3239
0.1498
9.1378
−0.0139
0.5337
9.9434
−0.2405
0.6799
10.7489


66
−0.0948
0.0584
9.1378
0.1338
0.386
9.9434
−0.5229
0.4058
10.7489


67
−0.0605
0.576
9.1378
0.4935
−0.2518
9.9434
0.0201
0.0298
10.7489


68
0.3243
−0.3366
9.1378
0.4529
−0.5959
9.9434
−0.4051
0.7218
10.7489


69
0.5626
−0.6994
9.1378
0.2308
−0.2382
9.9434
0.3255
−0.0116
10.7489


70
0.5815
−0.2938
9.1378
0.25
0.2203
9.9434
0.1531
0.2994
10.7489


71
0.3869
0.0883
9.1378
0.5896
−0.4744
9.9434
0.2123
−0.2477
10.7489


72
0.2168
0.3377
9.1378
0.4428
−0.1417
9.9434
0.4555
−0.687
10.7489


73
0.1167
0.447
9.1378
0.3293
−0.3873
9.9434
0.458
−0.3011
10.7489


74
0.202
−0.1863
9.1378
0.1599
−0.1423
9.9434
0.2575
0.1206
10.7489


75
0.3991
−0.4422
9.1378
0.1011
0.4245
9.9434
0.0869
0.3954
10.7489


76
0.4931
−0.1086
9.1378
0.3898
−0.0326
9.9434
0.3019
−0.4002
10.7489


77
0.3233
0.191
9.1378
0.5119
−0.7018
9.9434
0.5614
−0.8989
10.7489


78
0.1478
0.416
9.1378
0.1945
0.305
9.9434
0.5883
−0.6229
10.7489


79
0.2851
−0.2853
9.1378
0.2645
−0.2873
9.9434
0.3714
−0.1073
10.7489


80
0.5094
−0.6128
9.1378
0.1649
0.346
9.9434
0.1841
0.2499
10.7489


81
0.4169
0.0357
9.1378
0.3157
0.108
9.9434
0.1764
−0.1905
10.7489


82
0.254
0.2901
9.1378
0.3535
0.0381
9.9434
0.4009
−0.5819
10.7489


83
0.1576
−0.1392
9.1378
0.5697
−0.8084
9.9434
0.4992
−0.3989
10.7489


84
0.3622
−0.389
9.1378
0.5424
−0.3627
9.9434
0.2921
0.0548
10.7489


85
0.5382
−0.2008
9.1378
0.3922
−0.491
9.9434
0.1208
0.348
10.7489


86
0.3558
0.1401
9.1378
0.0835
−0.0507
9.9434
0.2578
−0.3236
10.7489


87
0.1777
0.3837
9.1378
0.196
−0.1898
9.9434
0.5089
−0.7927
10.7489


88
0.2444
−0.2351
9.1378
0.0742
0.4537
9.9434
0.1013
−0.0781
10.7489


89
0.4551
−0.5269
9.1378
0.2228
0.263
9.9434
0.4154
−0.2039
10.7489


90
0.4459
−0.0174
9.1378
0.2973
−0.337
9.9434
0.2216
0.1858
10.7489


91
0.2895
0.2411
9.1378
0.1225
−0.0958
9.9434
0.1395
−0.1339
10.7489


92
0.1187
−0.101
9.1378
0.2762
0.1769
9.9434
0.3448
−0.4775
10.7489


93
0.7775
−0.7689
9.1378
0.7838
−1.2108
9.9434
0.5392
−0.4971
10.7489


94
0.898
−1.2423
9.1378
0.818
−1.2734
9.9434
0.7649
−1.3145
10.7489


95
0.8703
−1.2172
9.1378
0.7205
−0.809
9.9434
0.8002
−1.3298
10.7489


96
0.9167
−1.2391
9.1378
0.8611
−1.2165
9.9434
0.8188
−1.3044
10.7489


97
0.9314
−1.2067
9.1378
0.8713
−1.2698
9.9434
0.8073
−1.259
10.7489


98
0.8826
−1.0597
9.1378
0.7573
−1.1615
9.9434
0.6814
−0.8765
10.7489


99
0.7024
−0.5769
9.1378
0.8233
−1.2801
9.9434
0.7386
−1.2618
10.7489


100
0.7484
−1.0111
9.1378
0.8009
−1.2421
9.9434
0.7761
−1.327
10.7489


101
0.8814
−1.2331
9.1378
0.6266
−0.9155
9.9434
0.81
−1.324
10.7489


102
0.9297
−1.2252
9.1378
0.8005
−1.0332
9.9434
0.8155
−1.2858
10.7489


103
0.9244
−1.1813
9.1378
0.8616
−1.2833
9.9434
0.7913
−1.2078
10.7489


104
0.8135
−0.8654
9.1378
0.6785
−0.6976
9.9434
0.7608
−1.3071
10.7489


105
0.6232
−0.3876
9.1378
0.8571
−1.2045
9.9434
0.792
−1.3313
10.7489


106
0.8557
−1.1922
9.1378
0.8375
−1.2886
9.9434
0.8175
−1.3125
10.7489


107
0.9076
−1.2422
9.1378
0.8459
−1.2892
9.9434
0.8101
−1.2679
10.7489


108
0.916
−1.157
9.1378
0.8726
−1.2617
9.9434
0.7253
−1.0042
10.7489


109
0.7405
−0.6727
9.1378
0.7102
−1.0733
9.9434
0.6794
−1.1409
10.7489


110
0.6559
−0.855
9.1378
0.7612
−0.9209
9.9434
0.7699
−1.3214
10.7489


111
0.8753
−1.2256
9.1378
0.865
−1.2285
9.9434
0.8054
−1.3274
10.7489


112
0.9244
−1.2331
9.1378
0.8675
−1.2772
9.9434
0.8178
−1.2951
10.7489


113
0.9282
−1.1938
9.1378
0.8299
−1.2854
9.9434
0.8045
−1.25
10.7489


114
0.6635
−0.4819
9.1378
0.8718
−1.2533
9.9434
0.6357
−0.7494
10.7489


115
0.8487
−0.9622
9.1378
0.7923
−1.2265
9.9434
0.7499
−1.2844
10.7489


116
0.8408
−1.1673
9.1378
0.6352
−0.5867
9.9434
0.7836
−1.3305
10.7489


117
0.9321
−1.213
9.1378
0.8093
−1.2578
9.9434
0.8138
−1.3198
10.7489


118
0.889
−1.239
9.1378
0.8291
−1.1188
9.9434
0.8129
−1.2768
10.7489


119
0.9316
−1.2193
9.1378
0.8541
−1.2874
9.9434
0.7675
−1.1325
10.7489


120
0.9203
−1.169
9.1378
0.8687
−1.2408
9.9434
0.6205
−1.0199
10.7489


Hole 1
−0.1575
0.2573
9.1378
−0.1349
0.2832
9.9434
−0.1124
0.3091
10.7489


Hole 2
−0.4329
0.3392
9.1378
−0.3946
0.4062
9.9434
−0.3563
0.4732
10.7489


Hole 3
0.3684
−0.2177
9.1378
0.3529
−0.2601
9.9434
0.3374
−0.3026
10.7489


Hole 4
0.1416
0.015
9.1378
0.1506
−0.002
9.9434
0.1596
−0.019
10.7489


Hole 5
0.6809
−0.7256
9.1378
0.6486
−0.795
9.9434
0.6163
−0.8645
10.7489












Section 10












Point
X
Y
Z







 1
−0.8551
0.6867
11.5545



 2
−0.6417
0.8365
11.5545



 3
−0.8138
0.6581
11.5545



 4
−0.7705
0.7968
11.5545



 5
−0.8241
0.6627
11.5545



 6
−0.843
0.7436
11.5545



 7
−0.8601
0.7104
11.5545



 8
−0.8435
0.6743
11.5545



 9
−0.5776
0.5807
11.5545



10
−0.5519
0.8422
11.5545



11
−0.6627
0.6108
11.5545



12
−0.7003
0.8236
11.5545



13
−0.8094
0.7738
11.5545



14
−0.7494
0.6365
11.5545



15
−0.8518
0.7312
11.5545



16
−0.8588
0.6945
11.5545



17
−0.6119
0.8402
11.5545



18
−0.75
0.8062
11.5545



19
−0.8328
0.7548
11.5545



20
−0.8583
0.7177
11.5545



21
−0.834
0.6681
11.5545



22
−0.5361
0.563
11.5545



23
−0.8498
0.6799
11.5545



24
−0.6199
0.5965
11.5545



25
−0.6712
0.831
11.5545



26
−0.7904
0.786
11.5545



27
−0.706
0.624
11.5545



28
−0.8605
0.7026
11.5545



29
−0.7711
0.643
11.5545



30
−0.7926
0.6501
11.5545



31
−0.5819
0.8421
11.5545



32
−0.7289
0.8144
11.5545



33
−0.8215
0.7648
11.5545



34
−0.8554
0.7246
11.5545



35
−0.8477
0.7375
11.5545



36
−0.4889
0.8369
11.5545



37
−0.4175
0.4985
11.5545



38
−0.1576
0.2676
11.5545



39
0.0226
0.4372
11.5545



40
−0.4956
0.5434
11.5545



41
0.0335
0.0037
11.5545



42
−0.1127
0.6179
11.5545



43
−0.226
0.3422
11.5545



44
−0.2472
0.7394
11.5545



45
−0.3966
0.815
11.5545



46
−0.0831
0.1741
11.5545



47
−0.0308
0.515
11.5545



48
−0.3
0.4113
11.5545



49
−0.3044
0.7748
11.5545



50
−0.4577
0.8314
11.5545



51
−0.164
0.6712
11.5545



52
−0.38
0.4734
11.5545



53
−0.1911
0.3056
11.5545



54
0.0482
0.3975
11.5545



55
−0.456
0.5219
11.5545



56
−0.014
0.0765
11.5545



57
−0.0885
0.5897
11.5545



58
−0.22
0.7194
11.5545



59
−0.3651
0.8035
11.5545



60
−0.5203
0.8405
11.5545



61
−0.1196
0.2215
11.5545



62
−0.0036
0.4764
11.5545



63
−0.1378
0.6451
11.5545



64
−0.2753
0.7579
11.5545



65
−0.4269
0.8241
11.5545



66
−0.2623
0.3775
11.5545



67
−0.048
0.1257
11.5545



68
−0.059
0.5528
11.5545



69
−0.1914
0.696
11.5545



70
−0.3393
0.4433
11.5545



71
−0.3343
0.7901
11.5545



72
0.4329
−0.3671
11.5545



73
0.2249
0.0873
11.5545



74
0.2483
−0.3739
11.5545



75
0.4973
−0.8811
11.5545



76
0.5585
−0.6944
11.5545



77
0.3485
−0.1702
11.5545



78
0.14
0.2444
11.5545



79
0.1231
−0.1452
11.5545



80
0.342
−0.5579
11.5545



81
0.4728
−0.4665
11.5545



82
0.265
0.0075
11.5545



83
0.2075
−0.2972
11.5545



84
0.4463
−0.773
11.5545



85
0.3915
−0.2683
11.5545



86
0.1832
0.1663
11.5545



87
0.079
−0.0703
11.5545



88
0.2883
−0.4511
11.5545



89
0.5615
−1.0191
11.5545



90
0.5113
−0.5665
11.5545



91
0.3038
−0.0729
11.5545



92
0.095
0.3215
11.5545



93
0.1658
−0.2209
11.5545



94
0.3946
−0.6652
11.5545



95
0.6812
−1.2788
11.5545



96
0.718
−1.3559
11.5545



97
0.749
−1.3652
11.5545



98
0.7661
−1.3342
11.5545



99
0.7473
−1.2692
11.5545



100 
0.7083
−1.3385
11.5545



101 
0.7278
−1.3644
11.5545



102 
0.7614
−1.3562
11.5545



103 
0.762
−1.3175
11.5545



104 
0.6895
−1.0818
11.5545



105 
0.6251
−1.1572
11.5545



106 
0.7144
−1.3503
11.5545



107 
0.7417
−1.3667
11.5545



108 
0.7665
−1.3427
11.5545



109 
0.757
−1.3012
11.5545



110 
0.6038
−0.823
11.5545



111 
0.7055
−1.3325
11.5545



112 
0.7224
−1.3607
11.5545



113 
0.7559
−1.3615
11.5545



114 
0.7643
−1.3257
11.5545



115 
0.73
−1.212
11.5545



116 
0.7112
−1.3444
11.5545



117 
0.7341
−1.3664
11.5545



118 
0.765
−1.3498
11.5545



119 
0.7595
−1.3093
11.5545



120 
0.6475
−0.9521
11.5545



Hole 1
−0.3179
0.5402
11.5545



Hole 2
−0.0898
0.335
11.5545



Hole 3
0.3219
−0.345
11.5545



Hole 4
0.1687
−0.0359
11.5545



Hole 5
0.584
−0.934
11.5545










FIG. 5 is an illustration of cross-sections of turbine bucket 22. As shown in FIG. 2, bucket 22 includes a plurality of cooling fluid medium passages 100, which may also be referred to as cooling passages. In an exemplary embodiment, the cooling fluid medium is air. Alternatively, any cooling fluid medium may be used that facilitates cooling of turbine bucket 22 as described herein. In the exemplary embodiment, the plurality of cooling passages 100 include a first cooling passage 102, a second cooling passage 104, a third cooling passage 106, a fourth cooling passage 108, and a fifth cooling passage 110. To enhance the cooling of airfoil 40, passages 100 extend through airfoil 40 from a root portion 120 of airfoil 40 to a tip portion 122 of airfoil 40. The passages 100 extend substantially linearly through the compound curved airfoil 40 and continue through platform 42, shank section 44, and dovetail section 46.
In the exemplary embodiment, a cooling medium, for example, air, may be provided to the plurality of cooling passages 100 that extend through airfoil 40. Wheel 16, on which the bucket 22 is mounted, includes a single plenum which opens into cooling passages 100 when dovetail 46 is secured to wheel 16. Consequently, as wheel 16 rotates, cooling medium is supplied from the single plenum in wheel 16 to cooling passages 100 for flow radially outwardly through passages 100 prior to being discharged through cooling hole exit locations defined in the tip portion 122 of airfoil 40.
Turbines are designed to operate at a predetermined temperature that provides a desired performance and efficiency. Typically, newer turbines are designed to operate at a higher temperature than older turbines and newer turbine components are designed to withstand the higher temperatures. To withstand higher temperatures, the shape of an airfoil may be changed and/or the material the bucket is constructed from may be changed. In another example, buckets are provided with larger cooling passages to maintain suitable temperatures throughout the airfoil. However, diverting a larger amount of air from the compressor and into the cooling passages may lower the efficiency of the turbine. Changing the amount of air diverted from the compressor and into the cooling passages may also trigger government regulatory requirements and force a turbine operator to fulfill reporting requirements and/or take other actions. Therefore, when replacing worn or damaged buckets, it is not always necessary or beneficial to replace the bucket with a bucket designed for use in a new, higher temperature turbine. When replacing a worn or damaged bucket, it is beneficial to maintain the supply conditions, bucket life expectancy, and the repair strategy of the original bucket. This includes maintaining a substantially similar level of blade cooling as was previously present. However, it is also beneficial for a replacement bucket to have a modified shape and material if that shape and material improves performance of the turbine.
As described above, FIG. 2 is a front cross-sectional view of turbine bucket 22 and illustrates an exemplary orientation of cooling passages 100. FIG. 6 is a cross-sectional view of airfoil 40 taken along line 1-1 (shown in FIG. 2). FIG. 7 is a cross-sectional view of airfoil 40 taken along line 2-2 (shown in FIG. 2). FIG. 8 is a cross-sectional view of airfoil 40 taken along line 3-3 (shown in FIG. 2). The exemplary orientation of cooling passages 100 facilitates airfoil 40 maintaining and/or improving turbine performance and bucket life.
To facilitate the replacement of an original four-hole stage 2 bucket, with bucket 22 described herein, air passages 100 in the exemplary embodiment extend in a camber line pattern 140 (shown in FIG. 5) of airfoil 40. More specifically, in the exemplary embodiment, the camber line pattern 140 extends generally along a mean camber line 142 (shown in FIG. 5) of airfoil 40. Mean camber line 142 is equidistant at all points between a suction side surface 144 (shown in FIG. 5) and a pressure side surface 146 (shown in FIG. 5) of airfoil 40. In the exemplary embodiment, a distance between edges of air passages 100 and either suction side surface 144 and/or pressure side surface 146 of airfoil 40 is no less than about 0.050 inches. Alternatively, the locations of air passages 100 may be adjusted in airfoil 40 to enable passage diameter adjustments without violating minimum wall thickness requirements. Moreover, in alternative embodiments, the camber line pattern 140 may shift slightly or vary from mean camber line 142 to facilitate effective cooling of the airfoil.
As shown, the plurality of cooling passages 100 includes first 102, second 104, third 106, fourth 108, and fifth 110 cooling passages, that each extend through the airfoil section 40. For reference, first cooling passage 102 is positioned closest to a leading edge 150 (shown in FIG. 6) and fifth cooling passage 110 is positioned closest to a trailing edge 152 (shown in FIG. 6). In an exemplary embodiment, diameters 160, 162, 164, and 166 of the first 102, second 104, third 106, and fourth 108 cooling passages, respectively, are approximately 0.070 inches through airfoil 40. In other words, in the exemplary embodiment, diameters 160, 162, 164, and 166 are approximately 0.070 inches between line 2-2 (i.e., root 120, shown in FIG. 2) and line 3-3 (i.e., tip 122, shown in FIG. 2). In the exemplary embodiment, a diameter 168 of the fifth cooling passage 110 through airfoil 40 is approximately 0.050 inches. In an example embodiment, diameters of the cooling passages have a dimensional tolerance of about ±0.005 inches.
In an exemplary embodiment, first 102, second 104, third 106, fourth 108, and fifth 110 cooling passages also extend through shank 44 and dovetail 46. In the exemplary embodiment, the diameters 160, 162, 164, 166, and 168 are larger between line 1-1 and line 2-2 (shown in FIG. 2). In the exemplary embodiment, diameters 160, 162, 164, and 166 are 0.140 inches between line 1-1 and line 2-2, and diameter 168 is 0.100 inches between line 1-1 and line 2-2.
Airfoil section 40 cooling passage exit locations are relocated to allow for diameter maximization without violation of minimum wall thickness requirements on one side while leaving excessive margin on the other. The exit locations are defined at the lower surface 78 of bucket 22 and at the tip 122 of the airfoil section 40.
Table II provides exemplary cooling passage locations and hole diameters within turbine bucket 22. Locations and diameters are provided in inches, and also provided in millimeters (e.g., the first passage 102 has diameter 160 from line 1-1 to line 2-2 of 0.140 inches or 3.56 millimeters).












TABLE II








Hole
Hole
Lower
Middle
Upper


Hole
Diameter
Diameter
Section
Section
Section















Number
from 1 to 2
from 2 to 3
X
Y
X
Y
X
Y


















102
0.140
0.070
−0.888
0.000
−0.682
0.096
−0.293
0.583



[3.56]
[1.78]
[22.56]
[0.0]
[17.32]
[2.44]
[7.44]
[14.81]


104
0.140
0.070
−0.420
0.000
−0.304
0.089
−0.075
0.352



[3.56]
[1.78]
[10.67]
[0.0]
[7.72]
[2.26]
[1.90]
[8.94]


106
0.140
0.070
0.083
0.000
0.083
0.125
0.174
−0.047



[3.56]
[1.78]
[2.11]
[0.0]
[2.11]
[3.18]
[4.42]
[1.19]


108
0.140
0.070
0.586
0.000
0.469
0.058
0.312
−0.372



[3.56]
[1.78]
[14.88]
[0.0]
[11.91]
[1.47]
[7.92]
[9.45]


110
0.100
0.050
0.905
0.000
0.891
−0.274
0.563
−0.978



[2.54]
[1.27]
[22.99]
[0.0]
[22.63]
[6.96]
[14.30]
[24.84]









With reference to FIGS. 6-8, the origin of the X, Y, Z Cartesian coordinate system referenced in Table II used to locate the cooling passages is the intersection of the S, T, and U datum planes. These datum planes are identified in the drawings. The distance X to the center of the holes is the distance from datum T and the distance Y is the distance from datum S. Values for a distance X and a distance Y are provided at three distances from datum U. More specifically, values for a distance X and a distance Y are provided at line 1-1 (i.e., lower section), at line 2-2 (i.e., middle section), and at line 3-3 (i.e., upper section). While the distance Z is the distance from datum U. Thus, the origin of the coordinate system lies at the intersection of datum S, T and U. FIG. 6 is a cross-sectional view of turbine bucket 22 taken along line 1-1. FIG. 7 is a cross-sectional view of turbine bucket 22 taken along line 2-2, which is also an intersection of the shank and airfoil cooling passages. FIG. 8 is a cross-sectional view of turbine bucket 22 taken along line 3-3. In the exemplary embodiment, passages 100 are formed using Shaped Tube Electrochemical Machining (STEM).
The above described embodiments of a turbine bucket provide a cost-effective and reliable replacement for currently-used stage 2 buckets. The above described buckets maintain original supply conditions and similar repair strategies as the buckets being replaced while maintaining and/or improving turbine performance and bucket life.
Exemplary embodiments of a bucket for a turbine and a turbine engine are described above in detail. The air cooled bucket and turbine engine are not limited to the specific embodiments described herein, but rather, components may be utilized independently and separately from other components described herein.
This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.

## Claims

1. A bucket for a turbine, said bucket comprising:
a dovetail portion configured to couple said bucket to a turbine wheel, said dovetail portion comprising a lower surface;
a shank portion extending from said dovetail portion;
an airfoil comprising a root portion, a tip portion, an airfoil shape, and a nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table I, wherein Z is a distance from said lower surface of said dovetail portion, and X and Y are coordinates defining the profile at each distance Z from said lower surface; and
a plurality of cooling passages, said plurality of cooling passages comprising no more than five cooling passages extending between said root and said tip portion of said airfoil, each of said cooling passages exits at said tip portion, said plurality of cooling passages are positioned in a camber line pattern.

2. A bucket in accordance with claim 1 wherein said plurality of cooling passages are positioned at said tip and root portions of said airfoil substantially in accordance with X and Y Cartesian coordinate values set forth in Table II.

3. A bucket in accordance with claim 1 wherein said plurality of cooling passages are aligned substantially parallel to each other.

4. A bucket in accordance with claim 1 wherein a first, a second, a third, and a fourth of said plurality of cooling passages each have a diameter of about 0.070 inches±0.005 inches from said root to said tip portion of said airfoil, and a fifth of said plurality of cooling passages has a diameter of about 0.050 inches±0.005 inches from said root to said airfoil tip portion.

5. A bucket in accordance with claim 4 wherein at least one of said first, second, third, fourth, and fifth cooling passages has a larger diameter defined within said dovetail and said shank portions than in said airfoil.

6. A bucket in accordance with claim 1 wherein said plurality of cooling passages facilitate extending a useful life of said airfoil.

7. A bucket in accordance with claim 1 wherein said plurality of cooling passages facilitate maintaining a desired airfoil temperature within said airfoil with a predetermined air flow through said plurality of cooling passages.

8. A bucket in accordance with claim 1 wherein said plurality of cooling passages facilitate increasing creep margins throughout said airfoil.

9. A bucket in accordance with claim 1 wherein said airfoil further comprises a coating extending at least partially over each side of said airfoil.

10. A bucket in accordance with claim 1 wherein said dovetail portion, said shank portion, and said airfoil are integrally cast together, said plurality of cooling passages are each defined adjacent to each of a pressure side and a suction side of said airfoil.

11. A bucket in accordance with claim 1 wherein said bucket is cast from a nickel-based superalloy.

12. A gas turbine engine comprising:
a rotor comprising at least one rotor wheel; and
a plurality of buckets extending radially from said at least one rotor wheel, each of said plurality of buckets comprises a dovetail portion, a shank portion, an airfoil, and a plurality of cooling passages extending therethrough, said airfoil has a nominal profile formed substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table I, wherein Z is a distance from a lower surface of said dovetail portion, and X and Y are coordinates defining the profile at each distance Z from a lower surface of said dovetail portion, said plurality of cooling passages each extend between said lower surface of said dovetail portion and a tip portion of each airfoil, said plurality of cooling passages comprise no more than five cooling passages positioned in a camber line pattern.

13. A gas turbine engine in accordance with claim 12 wherein said plurality of cooling passages are each positioned at said tip portion of said airfoil, at a root portion of said airfoil, and at said lower surface of said dovetail portion substantially in accordance with X and Y Cartesian coordinate values set forth in Table II.

14. A gas turbine engine in accordance with claim 12 wherein said plurality of cooling passages are substantially parallel to each other.

15. A gas turbine engine in accordance with claim 13 wherein a first, a second, a third, and a fourth of said plurality of cooling passages each have a diameter of about 0.070 inches±0.005 inches from said root portion to said tip portion of said airfoil, and a fifth of said plurality of cooling passages has a diameter of about 0.050 inches±0.005 inches from said root portion to said tip portion of said airfoil.

16. A gas turbine engine in accordance with claim 15 wherein at least one of said first, second, third, fourth, and fifth of said plurality of cooling passages has a larger diameter defined within said dovetail and shank portions than defined in said airfoil.

17. A gas turbine engine in accordance with claim 12 wherein said cooling passages facilitate extending a useful life of said airfoil, and facilitate increasing creep margins throughout said airfoil.

18. A gas turbine engine in accordance with claim 12 wherein said plurality of cooling passages facilitate maintaining a desired airfoil temperature within said airfoil with a predetermined air flow through said plurality of cooling passages.

19. A gas turbine engine in accordance with claim 12 wherein said dovetail portion, said shank portion, and said airfoil are integrally cast together to form each of said plurality of buckets, said plurality of cooling passages are each defined adjacent to each of a pressure side and a suction side of said airfoil.

20. A multi-stage gas turbine engine in accordance with claim 12 wherein said plurality of buckets are cast from a nickel-based superalloy.