Airfoil profile for a turbine nozzle

TECHNICAL FIELD

This application relates to airfoils for a gas turbine and more particularly to an airfoil profile for a turbine nozzle of a gas turbine.

BACKGROUND

Turbines are machines that obtain rotational force by impulsive or reaction force using a flow of a compressible fluid such as steam or gas, and include a steam turbine using steam, a gas turbine using hot combustion gas, and so on.

The gas turbine includes a compressor, a combustor, and a turbine. The compressor includes an air inlet into which air is introduced, and a plurality of compressor vanes and a plurality of compressor blades which are alternately arranged in a compressor housing. The introduced air is compressed by the compressor vanes and the compressor blades while passing through an inside of the compressor.

The combustor supplies fuel to air compressed by the compressor and ignites a fuel-air mixture with an igniter to produce high-temperature and high-pressure combustion gas.

The turbine includes a plurality of turbine vanes and a plurality of turbine blades which are alternately arranged in a turbine housing. In addition, a rotor is arranged to pass through centers of the compressor, the combustor, the turbine, and an exhaust chamber.

The rotor is rotatably supported at both ends thereof by bearings. A plurality of disks are fixed to the rotor, and a plurality of blades are connected to each of the disks while a drive shaft of a generator is connected to an end of the exhaust chamber.

In a gas turbine, many system requirements should be met at each stage of the gas turbine to meet design goals. The design goals may include overall improved efficiency and airfoil loading capability. For example, a turbine nozzle airfoil profile should achieve thermal and mechanical operating requirements for that particular stage. There is thus a desire for an improved turbine nozzle airfoil profile for use in a turbine and the like.

SUMMARY

Aspects of one or more exemplary embodiments provide a unique airfoil profile for the nozzles of a turbine stage capable of enhancing aeromechanics and reducing thermal and mechanical stresses.

Additional aspects will be set forth in part in the description which follows and, in part, will become apparent from the description, or may be learned by practice of the exemplary embodiments.

According to an aspect of an exemplary embodiment, there is provided a turbine nozzle including: an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1. Here, the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections at each Z distance, and the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

The airfoil shape may lie within an envelope of +1-0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.

The X and Y coordinate values are scalable as a function of a same constant or number, and a set of corresponding nominal Z coordinate values are scalable as a function of the same constant or number to provide at least one of a scaled up or a scaled down airfoil.

The airfoil shape may include a leaned airfoil section to reduce a secondary flow effect.

The turbine nozzle may further include a coating applied to the airfoil shape, the coating having a thickness of less than or equal to 0.010 inches.

According to an aspect of another exemplary embodiment, there is provided a turbine including: a turbine nozzle extending from a platform to an end wall and having an airfoil-shaped cross section having a leading edge, a trailing edge, and a pressure side and a suction side each of which extends from the leading edge to the trailing edge, wherein the turbine nozzle may include an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1. Here, the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections at each Z distance, and the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

According to an aspect of another exemplary embodiment, there is provided a gas turbine including: a compressor configured to compress air; a combustor configured to mix compressed air supplied from the compressor with fuel for combustion; and a turbine including a plurality of turbine nozzles and a plurality of turbine blades rotated by combustion gas to generate power, wherein each of the turbine nozzles extending from a platform to an end wall and having an airfoil-shaped cross section having a leading edge, a trailing edge, and a pressure side and a suction side each of which extends from the leading edge to the trailing edge, and wherein the turbine nozzle may include an airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1. Here, the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections at each Z distance, and the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects will become more apparent from the following description of the exemplary embodiments with reference to the accompanying drawings, in which:

FIG. 1 is a partially cutaway perspective view illustrating a gas turbine according to an exemplary embodiment;

FIG. 2 is a cross-sectional view illustrating a schematic structure of the gas turbine according to the exemplary embodiment;

FIG. 3 is a schematic diagram of a turbine according to an exemplary embodiment;

FIG. 4 is an aft view of a turbine nozzle including an airfoil according to an exemplary embodiment;

FIG. 5 is a forward view of a turbine nozzle including an airfoil according to an exemplary embodiment; and

FIG. 6 is an airfoil shape including a leaned airfoil section according to an exemplary embodiment.

DETAILED DESCRIPTION

Various modifications and various embodiments will be described below in detail with reference to the accompanying drawings so that those skilled in the art can easily carry out the disclosure. It should be understood, however, that the various embodiments are not for limiting the scope of the disclosure to the specific embodiment, but they should be interpreted to include all modifications, equivalents, and alternatives of the embodiments included within the spirit and scope disclosed herein.

Hereinafter, exemplary embodiments will be described in detail with reference to the accompanying drawings. Throughout the disclosure, like reference numerals refer to like parts throughout the various figures and exemplary embodiments. In certain embodiments, a detailed description of functions and configurations well known in the art may be omitted to avoid obscuring appreciation of the disclosure by a person of ordinary skill in the art. For the same reason, some components may be exaggerated, omitted, or schematically illustrated in the accompanying drawings.

FIG. 1 is a partially cutaway perspective view illustrating a gas turbine according to an exemplary embodiment. FIG. 2 is a cross-sectional view illustrating a schematic structure of the gas turbine according to the exemplary embodiment.

Referring to FIGS. 1 and 2, the gas turbine 1000 may include a compressor 1100, a combustor 1200, and a turbine 1300. Based on a flow direction of gas (e.g., compressed air or combustion gas), the compressor 1100 is disposed at an upstream side of the gas turbine 1000, and the turbine 1300 is disposed at a downstream side of the gas turbine 1000. The combustor 1200 is disposed between the compressor 1100 and the turbine 1300.

The compressor 1100 includes compressor vanes 1120 and compressor rotors in a compressor housing. The turbine 1300 includes turbine vane 1320 and turbine rotors in a turbine housing. The compressor vanes 1120 and the compressor rotors are arranged in a multi-stage arrangement along the flow direction of compressed air. The turbine vanes 1320 and the turbine rotors are arranged in a multi-stage arrangement along the flow direction of combustion gas. The compressor 1100 is designed such that an internal space is gradually decreased in size from a front stage to a rear stage so that air drawn into the compressor 1100 can be compressed. On the contrary, the turbine 1300 is designed such that an internal space is gradually increased in size from a front stage to a rear stage so that combustion gas received from the combustor 1200 can expand.

A torque tube for transmitting a rotational torque generated by the turbine 1300 to the compressor 1100 is disposed between a compressor rotor that is located at the rearmost stage of the compressor 1100 and a turbine rotor that is located at the foremost stage of the turbine 1300. FIG. 2 illustrates a case in which the torque tube includes multiple torque tube disks arranged in a three-stage arrangement, but it is understood that this is only an example and other exemplary embodiments are not limited thereto. For example, the torque tube may include multiple torque tube disks arranged in an arrangement of equal to or greater than four stages or an arrangement of equal to or less than two stages.

Each of the compressor rotors includes a compressor rotor disk and a compressor blade 1110 fastened to the compressor disk. That is, the compressor 1100 includes a plurality of compressor rotor disks, and respective compressor rotor disks are coupled to each other by a tie rod to prevent axial separation in an axial direction. The compressor rotor disks are arranged in the axial direction with the tie rod extending through centers of the compressor disks. Adjacent compressor rotor disks are arranged such that opposing surfaces thereof are in tight contact with each other by being tightly fastened by the tie rod so that the adjacent compressor rotor disks cannot rotate relative to each other. Each of the compressor rotor disks has a plurality of compressor blades 1110 radially coupled to an outer circumferential surface thereof.

The compressor blades 1110 (or referred to as buckets) are radially coupled to an outer circumferential surface of each of the compressor rotor disks in a row. The compressor vanes 1120 (or referred to as nozzles) are provided on an inner circumferential surface of the compressor housing in an annular row in each stage, and rows of the compressor vanes 1120 are arranged between rows of the compressor blades 1110. While the compressor disks rotate along with a rotation of the tie rod, the compressor vanes 1120 fixed to the housing do not rotate. The compressor vanes 1120 guide the flow of compressed air moved from front-stage compressor blades to rear-stage compressor blades.

The tie rod is disposed to pass through centers of the plurality of compressor rotor disks and turbine rotor disks. One end of the tie rod is fastened to a compressor disk located at the foremost stage of the compressor 1100, and the other end thereof is fastened in the torque tube by a fastening nut.

It is understood that the tie rod is not limited to the example illustrated in FIG. 2, and may be changed or vary according to one or more other exemplary embodiments. For example, a single tie rod may be disposed to pass through the centers of the rotor disks, a plurality of tie rods may be arranged circumferentially, or a combination thereof may be used.

Also, a deswirler serving as a guide vane may be provided in the compressor 1100 to adjust an actual inflow angle of the fluid entering into an inlet of the combustor 1200 to a designed inflow angle.

The combustor 1200 mixes the introduced compressed air with fuel, burns a fuel-air mixture to produce high-temperature and high-pressure combustion gas with high energy, and increases the temperature of the combustion gas to a temperature at which the combustor and the turbine components are able to withstand an isobaric combustion process.

A plurality of combustors constituting the combustor 1200 of the gas turbine may be arranged in the housing in a form of a cell. The combustor 1200 may include a plurality of chambers 1210 and fuel nozzle modules 1220 arranged annually.

The high-temperature and high-pressure combustion gas supplied from the combustor 1200 flows into the turbine 1300 and expands while passing through the inside of the turbine 1300, thereby applying an impulsive force or reaction force to the turbine blades 1310 to generate a rotational torque. A portion of the rotational torque is transmitted to the compressor via the torque tube, and a remaining portion which is an excessive torque is used to drive a generator to produce power.

The turbine 1300 basically has a structure similar to the compressor 1100. That is, the turbine 1300 may include a plurality of turbine rotors similar to the compressor rotors, and each of the turbine rotor may include a turbine rotor disk and a turbine blade 1310 fastened to the turbine rotor disk. A plurality of turbine blades 1310 (or referred to as buckets) are radially disposed. A plurality of turbine vanes 1320 (or referred to as nozzles) are fixedly arranged on an inner circumferential surface of the turbine housing in an annular row in each stage, and rows of the turbine vanes 1320 are arranged between rows of the turbine blades 1310. The turbine vanes 1320 guide the flow direction of combustion gas passing through the turbine blades 1310.

FIG. 3 is a schematic diagram of the turbine 1300 according to an exemplary embodiment. FIG. 4 is an aft view of a turbine nozzle including an airfoil according to an exemplary embodiment. FIG. 5 is a forward view of a turbine nozzle including an airfoil according to an exemplary embodiment.

Referring to FIG. 3, the turbine 1300 may include a plurality of turbine stages employing a plurality of nozzles and a plurality of buckets. For example, a first stage comprises a plurality of circumferentially spaced nozzles 20 and buckets 10. The nozzles are circumferentially spaced one from the other and fixed about the axis of the rotor. The first stage buckets 10 are mounted on the turbine rotor 17. A second stage of the turbine 1300 includes a plurality of circumferentially spaced nozzles 26 and buckets 16 mounted on the rotor 17. A third stage of the turbine 1300 includes a plurality of circumferentially spaced nozzles 32 and buckets 22 mounted on rotor 17. Although three stages are illustrated in FIG. 3, it is to be understood that any number of stages may be used.

Referring to FIGS. 4 and 5, the turbine nozzle 1320 according to the exemplary embodiment includes an airfoil extending from a platform 1340 to an end wall 1342. The turbine vane airfoil 1330 has an airfoil-shaped cross section having a leading edge 1331, a trailing edge 1332, a pressure side 1333, and a suction side 1334. The pressure side 1333 and the suction side 1334 are formed to extend from the leading edge 1331 to the trailing edge 1332.

The airfoil shape may be defined by a loci of points in space that meet stage design requirements. These points are unique and specific to the system. The list of X, Y, and Z coordinates for the airfoil, which are included as Table 1, has been optimized for stage efficiency, aerodynamic efficiency, and thermal and mechanical life requirements. In one exemplary embodiment, the points may be arrived at by iteration between aerodynamic and mechanical design optimization. Accordingly, these are the only loci of points that allow the gas turbine to run at the most efficient, safe and smooth manner.

Referring to FIGS. 4 and 5, the airfoil shape of the exemplary embodiment is defined by a unique set or loci of points in space that may be delineated. As shown in Table 1, the loci that defines the shape of the airfoil may include a set of approximately 1,440 points with X, Y and Z coordinates. The X, Y and Z coordinates, which represent the airfoil shape, are created in a coordinate system which is defined relative to the cold rotor centerline axis of the gas turbine (i.e., X coordinate axis). The origin of the coordinate system on the cold rotor centerline axis is defined as X=0.0, Y=0.0 and Z=0.0. For example, the coordinate system is set relative to the airfoil and is fully defined by points A, B and C. Points A and B are both located 41.650 inches above the cold rotor centerline axis. Point A lies at an intersection of the airfoil mean camber line and the leading-edge airfoil surface. Point B lies at an intersection of the airfoil mean camber line and the trailing-edge airfoil surface. Point C is located 46.100 inches above the cold rotor centerline axis and lies at the intersection of the airfoil mean camber line and the airfoil trailing-edge surface. Here, a coordinate system origin is located at point A. Points A and B define the positive X-axis. Points A, B and C define the positive X-Z plane. The Y-axis is then defined using the right-hand rule methodology. The coordinate values for the X, Y and Z coordinates are set forth in inches in Table 1, although other units of dimensions may be used if the values are appropriately converted.

The Cartesian coordinate system of X, Y and Z values given in Table 1 below defines the shape of the airfoil according to an exemplary embodiment. More specifically, the shape of the airfoil is defined by the cloud of points listed such that airfoil could be constructed by defining approximately smooth sheet surfaces through the listed points. As one of ordinary skill in the art will appreciate, Table 1 values are generated and shown to three decimal places for determining the profile of airfoil. All of the 1440 points represent a nominal cold or room temperature shape of the airfoil. It will be appreciated that as the nozzle heats up in operation, mechanical loading and temperature will cause a change in X, Y and Z coordinates. Accordingly, values for the airfoil shape given in Table 1 represent ambient, non-operating or non-hot conditions.

The coordinate values set forth in Table 1 below are for a cold condition of the turbine nozzle (e.g., non-rotating state and at room temperature). Further, the coordinate values set forth in Table 1 are for an uncoated nominal three-dimensional (3D) shape of the turbine nozzle. In some aspects, a coating (e.g., corrosion protective coating) may be applied to the turbine nozzle. The coating thickness may up to about 0.010 inches thick.

Further, the turbine nozzle 1320 may be fabricated using a variety of manufacturing techniques, such as forging, casting, milling, electro-chemical machining, electric-discharge machining, and the like. As such, the turbine nozzle may have a series of manufacturing tolerances for the position, profile, twist, and chord that can cause the turbine nozzle to vary from the nominal 3D shape defined by the coordinate values set forth in Table 1. This manufacturing tolerance may be, for example, +1-0.120 inches in a direction away from any of the coordinate values of Table 1 without departing from the scope of the subject matter described herein.

In addition to manufacturing tolerances affecting the overall size of the turbine nozzle, it is also possible to scale the airfoil to a larger or smaller airfoil size. In order to maintain the benefits of this 3D shape, in terms of stiffness and stress, it is necessary to scale the turbine nozzle uniformly in the X, Y, and Z directions.

The Table 1 values are generated and shown for determining the profile of the airfoil. There are typical manufacturing tolerances as well as coatings which must be accounted for in the actual profile of the airfoil. Each section is joined smoothly with the other sections to form the complete airfoil shape. It will therefore be appreciated that +/−typical manufacturing tolerances, i.e., +/−values, including any coating thicknesses, are additive to the X, Y and Z values given in Table 1 below.

TABLE 1

X
Y
Z

Section 1

Point 1
5.994
−0.345
−0.677

Point 2
5.903
−0.290
−0.673

Point 3
5.786
−0.323
−0.676

Point 4
5.669
−0.356
−0.678

Point 5
5.551
−0.388
−0.680

Point 6
5.434
−0.420
−0.683

Point 7
5.316
−0.451
−0.685

Point 8
5.199
−0.481
−0.687

Point 9
5.081
−0.510
−0.689

Point 10
4.962
−0.538
−0.692

Point 11
4.844
−0.565
−0.694

Point 12
4.725
−0.590
−0.695

Point 13
4.606
−0.614
−0.697

Point 14
4.486
−0.636
−0.699

Point 15
4.366
−0.656
−0.700

Point 16
4.246
−0.674
−0.702

Point 17
4.125
−0.690
−0.703

Point 18
4.005
−0.703
−0.704

Point 19
3.884
−0.715
−0.705

Point 20
3.762
−0.724
−0.705

Point 21
3.641
−0.730
−0.706

Point 22
3.519
−0.734
−0.706

Point 23
3.398
−0.735
−0.706

Point 24
3.276
−0.734
−0.706

Point 25
3.155
−0.729
−0.706

Point 26
3.034
−0.722
−0.705

Point 27
2.912
−0.711
−0.704

Point 28
2.792
−0.698
−0.703

Point 29
2.671
−0.682
−0.702

Point 30
2.551
−0.663
−0.701

Point 31
2.431
−0.641
−0.699

Point 32
2.312
−0.617
−0.697

Point 33
2.194
−0.589
−0.695

Point 34
2.076
−0.559
−0.693

Point 35
1.959
−0.527
−0.691

Point 36
1.843
−0.492
−0.688

Point 37
1.727
−0.455
−0.685

Point 38
1.612
−0.415
−0.682

Point 39
1.498
−0.374
−0.679

Point 40
1.384
−0.331
−0.676

Point 41
1.271
−0.286
−0.673

Point 42
1.158
−0.241
−0.670

Point 43
1.046
−0.194
−0.666

Point 44
0.934
−0.146
−0.663

Point 45
0.823
−0.098
−0.659

Point 46
0.711
−0.051
−0.656

Point 47
0.598
−0.005
−0.652

Point 48
0.484
0.038
−0.649

Point 49
0.369
0.075
−0.646

Point 50
0.250
0.101
−0.644

Point 51
0.129
0.103
−0.644

Point 52
0.013
0.068
−0.647

Point 53
−0.092
0.007
−0.651

Point 54
−0.177
−0.078
−0.658

Point 55
−0.239
−0.183
−0.665

Point 56
−0.285
−0.295
−0.674

Point 57
−0.318
−0.411
−0.682

Point 58
−0.341
−0.530
−0.691

Point 59
−0.355
−0.651
−0.700

Point 60
−0.357
−0.772
−0.709

Point 61
−0.349
−0.893
−0.718

Point 62
−0.331
−1.013
−0.727

Point 63
−0.303
−1.131
−0.735

Point 64
−0.264
−1.246
−0.744

Point 65
−0.214
−1.356
−0.752

Point 66
−0.153
−1.460
−0.760

Point 67
−0.080
−1.557
−0.767

Point 68
0.004
−1.645
−0.773

Point 69
0.097
−1.723
−0.779

Point 70
0.198
−1.791
−0.784

Point 71
0.305
−1.848
−0.788

Point 72
0.417
−1.894
−0.792

Point 73
0.533
−1.932
−0.795

Point 74
0.651
−1.960
−0.797

Point 75
0.771
−1.981
−0.798

Point 76
0.892
−1.996
−0.799

Point 77
1.013
−2.003
−0.800

Point 78
1.134
−2.006
−0.800

Point 79
1.256
−2.004
−0.800

Point 80
1.377
−1.997
−0.799

Point 81
1.498
−1.987
−0.799

Point 82
1.619
−1.973
−0.798

Point 83
1.740
−1.956
−0.796

Point 84
1.860
−1.937
−0.795

Point 85
1.979
−1.915
−0.793

Point 86
2.098
−1.891
−0.792

Point 87
2.217
−1.865
−0.790

Point 88
2.335
−1.837
−0.788

Point 89
2.453
−1.807
−0.785

Point 90
2.571
−1.776
−0.783

Point 91
2.688
−1.743
−0.781

Point 92
2.804
−1.709
−0.778

Point 93
2.921
−1.674
−0.776

Point 94
3.037
−1.637
−0.773

Point 95
3.152
−1.600
−0.770

Point 96
3.267
−1.561
−0.767

Point 97
3.382
−1.522
−0.764

Point 98
3.497
−1.481
−0.761

Point 99
3.611
−1.440
−0.758

Point 100
3.726
−1.398
−0.755

Point 101
3.839
−1.356
−0.752

Point 102
3.953
−1.312
−0.749

Point 103
4.066
−1.268
−0.746

Point 104
4.179
−1.224
−0.742

Point 105
4.292
−1.179
−0.739

Point 106
4.405
−1.133
−0.736

Point 107
4.517
−1.087
−0.732

Point 108
4.629
−1.040
−0.729

Point 109
4.741
−0.993
−0.725

Point 110
4.853
−0.945
−0.722

Point 111
4.965
−0.897
−0.718

Point 112
5.076
−0.849
−0.715

Point 113
5.187
−0.800
−0.711

Point 114
5.299
−0.751
−0.707

Point 115
5.409
−0.701
−0.704

Point 116
5.520
−0.651
−0.700

Point 117
5.631
−0.601
−0.696

Point 118
5.741
−0.550
−0.692

Point 119
5.852
−0.499
−0.689

Point 120
5.961
−0.447
−0.685

Section 2

Point 1
6.172
−0.042
−0.103

Point 2
6.078
0.005
−0.100

Point 3
5.960
−0.028
−0.102

Point 4
5.841
−0.062
−0.105

Point 5
5.722
−0.095
−0.107

Point 6
5.603
−0.127
−0.110

Point 7
5.484
−0.159
−0.112

Point 8
5.365
−0.190
−0.114

Point 9
5.245
−0.220
−0.117

Point 10
5.125
−0.249
−0.119

Point 11
5.005
−0.277
−0.121

Point 12
4.885
−0.304
−0.123

Point 13
4.765
−0.330
−0.125

Point 14
4.644
−0.355
−0.127

Point 15
4.523
−0.378
−0.128

Point 16
4.401
−0.400
−0.130

Point 17
4.280
−0.421
−0.131

Point 18
4.158
−0.440
−0.133

Point 19
4.036
−0.458
−0.134

Point 20
3.914
−0.474
−0.135

Point 21
3.791
−0.489
−0.136

Point 22
3.669
−0.501
−0.137

Point 23
3.546
−0.512
−0.138

Point 24
3.423
−0.521
−0.139

Point 25
3.300
−0.527
−0.139

Point 26
3.176
−0.532
−0.140

Point 27
3.053
−0.534
−0.140

Point 28
2.930
−0.534
−0.140

Point 29
2.807
−0.532
−0.140

Point 30
2.683
−0.527
−0.139

Point 31
2.560
−0.520
−0.139

Point 32
2.437
−0.510
−0.138

Point 33
2.315
−0.498
−0.137

Point 34
2.192
−0.482
−0.136

Point 35
2.070
−0.464
−0.135

Point 36
1.949
−0.443
−0.133

Point 37
1.828
−0.420
−0.131

Point 38
1.707
−0.393
−0.129

Point 39
1.588
−0.364
−0.127

Point 40
1.468
−0.332
−0.125

Point 41
1.350
−0.298
−0.122

Point 42
1.233
−0.261
−0.120

Point 43
1.116
−0.221
−0.117

Point 44
1.000
−0.180
−0.114

Point 45
0.884
−0.137
−0.110

Point 46
0.769
−0.093
−0.107

Point 47
0.654
−0.050
−0.104

Point 48
0.537
−0.008
−0.101

Point 49
0.420
0.029
−0.098

Point 50
0.299
0.054
−0.096

Point 51
0.176
0.060
−0.096

Point 52
0.056
0.034
−0.098

Point 53
−0.053
−0.022
−0.102

Point 54
−0.139
−0.110
−0.108

Point 55
−0.199
−0.217
−0.116

Point 56
−0.242
−0.332
−0.125

Point 57
−0.271
−0.451
−0.134

Point 58
−0.289
−0.573
−0.143

Point 59
−0.296
−0.696
−0.152

Point 60
−0.293
−0.819
−0.161

Point 61
−0.280
−0.941
−0.170

Point 62
−0.257
−1.062
−0.179

Point 63
−0.224
−1.180
−0.188

Point 64
−0.179
−1.294
−0.196

Point 65
−0.123
−1.404
−0.204

Point 66
−0.054
−1.506
−0.212

Point 67
0.026
−1.599
−0.219

Point 68
0.117
−1.682
−0.225

Point 69
0.218
−1.753
−0.230

Point 70
0.326
−1.812
−0.234

Point 71
0.440
−1.858
−0.238

Point 72
0.558
−1.893
−0.240

Point 73
0.679
−1.918
−0.242

Point 74
0.801
−1.934
−0.243

Point 75
0.924
−1.942
−0.244

Point 76
1.047
−1.943
−0.244

Point 77
1.171
−1.939
−0.244

Point 78
1.294
−1.929
−0.243

Point 79
1.416
−1.915
−0.242

Point 80
1.538
−1.897
−0.241

Point 81
1.660
−1.875
−0.239

Point 82
1.780
−1.851
−0.237

Point 83
1.901
−1.824
−0.235

Point 84
2.021
−1.795
−0.233

Point 85
2.140
−1.764
−0.231

Point 86
2.259
−1.731
−0.228

Point 87
2.377
−1.696
−0.226

Point 88
2.495
−1.660
−0.223

Point 89
2.612
−1.623
−0.220

Point 90
2.729
−1.584
−0.217

Point 91
2.846
−1.544
−0.214

Point 92
2.962
−1.503
−0.211

Point 93
3.078
−1.461
−0.208

Point 94
3.194
−1.418
−0.205

Point 95
3.309
−1.374
−0.202

Point 96
3.424
−1.330
−0.199

Point 97
3.539
−1.285
−0.195

Point 98
3.653
−1.239
−0.192

Point 99
3.767
−1.193
−0.189

Point 100
3.882
−1.146
−0.185

Point 101
3.995
−1.099
−0.182

Point 102
4.109
−1.051
−0.178

Point 103
4.222
−1.003
−0.174

Point 104
4.336
−0.955
−0.171

Point 105
4.449
−0.906
−0.167

Point 106
4.562
−0.856
−0.164

Point 107
4.675
−0.807
−0.160

Point 108
4.787
−0.757
−0.156

Point 109
4.900
−0.707
−0.153

Point 110
5.012
−0.656
−0.149

Point 111
5.124
−0.605
−0.145

Point 112
5.237
−0.554
−0.141

Point 113
5.349
−0.503
−0.137

Point 114
5.461
−0.451
−0.134

Point 115
5.573
−0.399
−0.130

Point 116
5.684
−0.347
−0.126

Point 117
5.796
−0.295
−0.122

Point 118
5.908
−0.243
−0.118

Point 119
6.019
−0.190
−0.114

Point 120
6.130
−0.139
−0.111

Section 3

Point 1
6.283
0.139
0.461

Point 2
6.239
0.043
0.454

Point 3
6.283
0.139
0.461

Point 4
6.185
0.179
0.464

Point 5
6.066
0.143
0.462

Point 6
5.946
0.109
0.459

Point 7
5.826
0.076
0.457

Point 8
5.706
0.044
0.454

Point 9
5.585
0.012
0.452

Point 10
5.464
−0.019
0.450

Point 11
5.344
−0.049
0.448

Point 12
5.222
−0.079
0.445

Point 13
5.101
−0.108
0.443

Point 14
4.979
−0.135
0.441

Point 15
4.858
−0.162
0.439

Point 16
4.736
−0.188
0.437

Point 17
4.614
−0.213
0.435

Point 18
4.491
−0.237
0.434

Point 19
4.369
−0.260
0.432

Point 20
4.246
−0.282
0.430

Point 21
4.123
−0.303
0.429

Point 22
4.000
−0.323
0.427

Point 23
3.877
−0.341
0.426

Point 24
3.753
−0.358
0.425

Point 25
3.630
−0.374
0.424

Point 26
3.506
−0.389
0.422

Point 27
3.382
−0.402
0.422

Point 28
3.257
−0.413
0.421

Point 29
3.133
−0.423
0.420

Point 30
3.009
−0.431
0.419

Point 31
2.884
−0.437
0.419

Point 32
2.760
−0.441
0.419

Point 33
2.635
−0.444
0.418

Point 34
2.510
−0.444
0.418

Point 35
2.386
−0.441
0.419

Point 36
2.261
−0.437
0.419

Point 37
2.137
−0.429
0.419

Point 38
2.012
−0.420
0.420

Point 39
1.888
−0.407
0.421

Point 40
1.764
−0.391
0.422

Point 41
1.641
−0.372
0.424

Point 42
1.519
−0.350
0.425

Point 43
1.396
−0.325
0.427

Point 44
1.275
−0.296
0.429

Point 45
1.155
−0.264
0.432

Point 46
1.035
−0.228
0.434

Point 47
0.917
−0.190
0.437

Point 48
0.799
−0.149
0.440

Point 49
0.682
−0.106
0.443

Point 50
0.565
−0.064
0.447

Point 51
0.447
−0.024
0.449

Point 52
0.326
0.007
0.452

Point 53
0.202
0.020
0.453

Point 54
0.079
0.000
0.451

Point 55
−0.031
−0.056
0.447

Point 56
−0.116
−0.147
0.440

Point 57
−0.175
−0.256
0.432

Point 58
−0.217
−0.373
0.424

Point 59
−0.244
−0.494
0.415

Point 60
−0.260
−0.617
0.406

Point 61
−0.265
−0.742
0.396

Point 62
−0.260
−0.866
0.387

Point 63
−0.246
−0.989
0.378

Point 64
−0.220
−1.111
0.369

Point 65
−0.184
−1.230
0.360

Point 66
−0.136
−1.345
0.352

Point 67
−0.076
−1.453
0.344

Point 68
−0.003
−1.554
0.336

Point 69
0.083
−1.645
0.330

Point 70
0.180
−1.723
0.324

Point 71
0.286
−1.787
0.319

Point 72
0.400
−1.838
0.315

Point 73
0.519
−1.875
0.313

Point 74
0.641
−1.901
0.311

Point 75
0.764
−1.916
0.310

Point 76
0.889
−1.922
0.309

Point 77
1.014
−1.921
0.309

Point 78
1.138
−1.914
0.310

Point 79
1.262
−1.900
0.311

Point 80
1.385
−1.883
0.312

Point 81
1.508
−1.861
0.314

Point 82
1.630
−1.836
0.315

Point 83
1.752
−1.808
0.318

Point 84
1.873
−1.777
0.320

Point 85
1.993
−1.744
0.322

Point 86
2.113
−1.709
0.325

Point 87
2.232
−1.673
0.328

Point 88
2.350
−1.634
0.330

Point 89
2.469
−1.595
0.333

Point 90
2.586
−1.554
0.336

Point 91
2.704
−1.512
0.339

Point 92
2.821
−1.469
0.343

Point 93
2.937
−1.425
0.346

Point 94
3.054
−1.380
0.349

Point 95
3.170
−1.334
0.353

Point 96
3.285
−1.288
0.356

Point 97
3.401
−1.241
0.359

Point 98
3.516
−1.193
0.363

Point 99
3.631
−1.145
0.367

Point 100
3.746
−1.096
0.370

Point 101
3.860
−1.047
0.374

Point 102
3.975
−0.998
0.377

Point 103
4.089
−0.948
0.381

Point 104
4.203
−0.898
0.385

Point 105
4.317
−0.847
0.389

Point 106
4.431
−0.797
0.392

Point 107
4.544
−0.746
0.396

Point 108
4.658
−0.694
0.400

Point 109
4.771
−0.643
0.404

Point 110
4.885
−0.591
0.408

Point 111
4.998
−0.539
0.411

Point 112
5.111
−0.487
0.415

Point 113
5.224
−0.434
0.419

Point 114
5.337
−0.382
0.423

Point 115
5.450
−0.329
0.427

Point 116
5.563
−0.276
0.431

Point 117
5.676
−0.223
0.435

Point 118
5.789
−0.170
0.439

Point 119
5.902
−0.117
0.443

Point 120
6.014
−0.064
0.446

Section 4

Point 1
6.366
0.218
1.019

Point 2
6.267
0.257
1.022

Point 3
6.146
0.222
1.019

Point 4
6.025
0.188
1.017

Point 5
5.903
0.154
1.014

Point 6
5.781
0.122
1.012

Point 7
5.659
0.090
1.009

Point 8
5.537
0.059
1.007

Point 9
5.414
0.029
1.005

Point 10
5.292
0.000
1.003

Point 11
5.169
−0.029
1.001

Point 12
5.046
−0.057
0.999

Point 13
4.923
−0.084
0.997

Point 14
4.799
−0.110
0.995

Point 15
4.676
−0.135
0.993

Point 16
4.552
−0.159
0.991

Point 17
4.428
−0.183
0.989

Point 18
4.304
−0.205
0.988

Point 19
4.180
−0.227
0.986

Point 20
4.055
−0.247
0.984

Point 21
3.931
−0.267
0.983

Point 22
3.806
−0.285
0.982

Point 23
3.681
−0.303
0.980

Point 24
3.556
−0.319
0.979

Point 25
3.431
−0.334
0.978

Point 26
3.306
−0.347
0.977

Point 27
3.180
−0.359
0.976

Point 28
3.054
−0.370
0.975

Point 29
2.929
−0.380
0.975

Point 30
2.803
−0.388
0.974

Point 31
2.677
−0.394
0.974

Point 32
2.551
−0.398
0.973

Point 33
2.425
−0.400
0.973

Point 34
2.299
−0.401
0.973

Point 35
2.172
−0.399
0.973

Point 36
2.046
−0.395
0.974

Point 37
1.921
−0.389
0.974

Point 38
1.795
−0.379
0.975

Point 39
1.669
−0.367
0.976

Point 40
1.544
−0.352
0.977

Point 41
1.419
−0.333
0.978

Point 42
1.295
−0.311
0.980

Point 43
1.172
−0.285
0.982

Point 44
1.049
−0.254
0.984

Point 45
0.928
−0.220
0.986

Point 46
0.808
−0.183
0.989

Point 47
0.689
−0.142
0.992

Point 48
0.570
−0.099
0.995

Point 49
0.451
−0.057
0.998

Point 50
0.330
−0.023
1.001

Point 51
0.205
−0.009
1.002

Point 52
0.081
−0.030
1.000

Point 53
−0.030
−0.089
0.996

Point 54
−0.115
−0.181
0.989

Point 55
−0.174
−0.292
0.981

Point 56
−0.216
−0.411
0.972

Point 57
−0.244
−0.533
0.963

Point 58
−0.260
−0.658
0.954

Point 59
−0.266
−0.783
0.945

Point 60
−0.261
−0.909
0.936

Point 61
−0.246
−1.034
0.926

Point 62
−0.220
−1.157
0.917

Point 63
−0.183
−1.277
0.908

Point 64
−0.134
−1.393
0.900

Point 65
−0.072
−1.502
0.892

Point 66
0.005
−1.602
0.884

Point 67
0.094
−1.691
0.878

Point 68
0.196
−1.765
0.872

Point 69
0.307
−1.825
0.868

Point 70
0.424
−1.870
0.864

Point 71
0.546
−1.901
0.862

Point 72
0.671
−1.920
0.861

Point 73
0.797
−1.928
0.860

Point 74
0.923
−1.929
0.860

Point 75
1.049
−1.922
0.861

Point 76
1.174
−1.909
0.862

Point 77
1.299
−1.891
0.863

Point 78
1.423
−1.869
0.865

Point 79
1.547
−1.843
0.866

Point 80
1.669
−1.814
0.869

Point 81
1.792
−1.783
0.871

Point 82
1.913
−1.749
0.873

Point 83
2.034
−1.713
0.876

Point 84
2.154
−1.675
0.879

Point 85
2.274
−1.636
0.882

Point 86
2.393
−1.595
0.885

Point 87
2.512
−1.553
0.888

Point 88
2.631
−1.510
0.891

Point 89
2.749
−1.466
0.894

Point 90
2.866
−1.421
0.898

Point 91
2.984
−1.375
0.901

Point 92
3.101
−1.328
0.905

Point 93
3.218
−1.281
0.908

Point 94
3.334
−1.232
0.912

Point 95
3.450
−1.184
0.915

Point 96
3.567
−1.135
0.919

Point 97
3.682
−1.085
0.922

Point 98
3.798
−1.035
0.926

Point 99
3.914
−0.985
0.930

Point 100
4.029
−0.934
0.934

Point 101
4.144
−0.883
0.937

Point 102
4.259
−0.832
0.941

Point 103
4.374
−0.780
0.945

Point 104
4.489
−0.728
0.949

Point 105
4.604
−0.676
0.953

Point 106
4.719
−0.624
0.957

Point 107
4.833
−0.571
0.960

Point 108
4.948
−0.519
0.964

Point 109
5.062
−0.466
0.968

Point 110
5.177
−0.413
0.972

Point 111
5.291
−0.360
0.976

Point 112
5.405
−0.306
0.980

Point 113
5.519
−0.253
0.984

Point 114
5.634
−0.199
0.988

Point 115
5.748
−0.146
0.992

Point 116
5.862
−0.092
0.996

Point 117
5.976
−0.038
1.000

Point 118
6.090
0.015
1.004

Point 119
6.204
0.069
1.008

Point 120
6.318
0.123
1.012

Section 5

Point 1
6.459
0.245
1.572

Point 2
6.410
0.150
1.565

Point 3
6.459
0.245
1.572

Point 4
6.359
0.283
1.575

Point 5
6.236
0.248
1.573

Point 6
6.113
0.213
1.570

Point 7
5.990
0.180
1.568

Point 8
5.867
0.147
1.565

Point 9
5.743
0.115
1.563

Point 10
5.619
0.084
1.560

Point 11
5.495
0.053
1.558

Point 12
5.371
0.024
1.556

Point 13
5.247
−0.005
1.554

Point 14
5.122
−0.033
1.552

Point 15
4.997
−0.061
1.550

Point 16
4.872
−0.087
1.548

Point 17
4.747
−0.113
1.546

Point 18
4.622
−0.138
1.544

Point 19
4.497
−0.162
1.542

Point 20
4.371
−0.185
1.541

Point 21
4.245
−0.207
1.539

Point 22
4.119
−0.229
1.537

Point 23
3.993
−0.249
1.536

Point 24
3.867
−0.269
1.534

Point 25
3.741
−0.287
1.533

Point 26
3.614
−0.304
1.532

Point 27
3.488
−0.321
1.531

Point 28
3.361
−0.336
1.529

Point 29
3.234
−0.350
1.528

Point 30
3.107
−0.362
1.527

Point 31
2.980
−0.374
1.527

Point 32
2.852
−0.384
1.526

Point 33
2.725
−0.392
1.525

Point 34
2.597
−0.399
1.525

Point 35
2.470
−0.403
1.524

Point 36
2.342
−0.407
1.524

Point 37
2.214
−0.408
1.524

Point 38
2.087
−0.406
1.524

Point 39
1.959
−0.403
1.524

Point 40
1.832
−0.397
1.525

Point 41
1.704
−0.387
1.526

Point 42
1.577
−0.375
1.526

Point 43
1.450
−0.359
1.528

Point 44
1.324
−0.340
1.529

Point 45
1.199
−0.317
1.531

Point 46
1.074
−0.289
1.533

Point 47
0.950
−0.257
1.535

Point 48
0.828
−0.220
1.538

Point 49
0.707
−0.180
1.541

Point 50
0.587
−0.137
1.544

Point 51
0.466
−0.094
1.547

Point 52
0.344
−0.057
1.550

Point 53
0.218
−0.039
1.551

Point 54
0.093
−0.060
1.550

Point 55
−0.020
−0.119
1.545

Point 56
−0.105
−0.213
1.538

Point 57
−0.165
−0.326
1.530

Point 58
−0.207
−0.446
1.521

Point 59
−0.234
−0.570
1.512

Point 60
−0.250
−0.696
1.503

Point 61
−0.255
−0.824
1.493

Point 62
−0.250
−0.951
1.484

Point 63
−0.234
−1.077
1.475

Point 64
−0.208
−1.202
1.465

Point 65
−0.170
−1.323
1.456

Point 66
−0.119
−1.440
1.448

Point 67
−0.055
−1.551
1.440

Point 68
0.023
−1.651
1.432

Point 69
0.114
−1.740
1.426

Point 70
0.218
−1.814
1.420

Point 71
0.332
−1.872
1.416

Point 72
0.452
−1.915
1.413

Point 73
0.576
−1.943
1.411

Point 74
0.703
−1.960
1.409

Point 75
0.830
−1.966
1.409

Point 76
0.958
−1.964
1.409

Point 77
1.085
−1.955
1.410

Point 78
1.212
−1.940
1.411

Point 79
1.338
−1.919
1.412

Point 80
1.463
−1.895
1.414

Point 81
1.588
−1.867
1.416

Point 82
1.712
−1.836
1.418

Point 83
1.835
−1.803
1.421

Point 84
1.958
−1.767
1.424

Point 85
2.080
−1.729
1.426

Point 86
2.201
−1.689
1.429

Point 87
2.322
−1.648
1.432

Point 88
2.442
−1.606
1.436

Point 89
2.562
−1.562
1.439

Point 90
2.682
−1.517
1.442

Point 91
2.801
−1.472
1.445

Point 92
2.920
−1.425
1.449

Point 93
3.038
−1.377
1.452

Point 94
3.156
−1.329
1.456

Point 95
3.274
−1.280
1.460

Point 96
3.392
−1.231
1.463

Point 97
3.510
−1.181
1.467

Point 98
3.627
−1.131
1.471

Point 99
3.744
−1.080
1.474

Point 100
3.861
−1.029
1.478

Point 101
3.978
−0.977
1.482

Point 102
4.094
−0.925
1.486

Point 103
4.211
−0.873
1.490

Point 104
4.327
−0.820
1.494

Point 105
4.443
−0.768
1.497

Point 106
4.559
−0.715
1.501

Point 107
4.676
−0.662
1.505

Point 108
4.792
−0.608
1.509

Point 109
4.907
−0.555
1.513

Point 110
5.023
−0.501
1.517

Point 111
5.139
−0.447
1.521

Point 112
5.255
−0.393
1.525

Point 113
5.370
−0.339
1.529

Point 114
5.486
−0.285
1.533

Point 115
5.602
−0.231
1.537

Point 116
5.717
−0.177
1.541

Point 117
5.833
−0.122
1.545

Point 118
5.948
−0.068
1.549

Point 119
6.063
−0.013
1.553

Point 120
6.179
0.041
1.557

Section 6

Point 1
6.563
0.239
2.123

Point 2
6.512
0.143
2.116

Point 3
6.563
0.239
2.123

Point 4
6.461
0.276
2.126

Point 5
6.337
0.240
2.123

Point 6
6.212
0.205
2.121

Point 7
6.088
0.171
2.118

Point 8
5.962
0.139
2.116

Point 9
5.837
0.106
2.114

Point 10
5.712
0.075
2.111

Point 11
5.586
0.044
2.109

Point 12
5.460
0.014
2.107

Point 13
5.334
−0.015
2.105

Point 14
5.208
−0.043
2.103

Point 15
5.082
−0.071
2.101

Point 16
4.955
−0.098
2.099

Point 17
4.829
−0.124
2.097

Point 18
4.702
−0.149
2.095

Point 19
4.575
−0.174
2.093

Point 20
4.448
−0.198
2.091

Point 21
4.321
−0.221
2.089

Point 22
4.193
−0.243
2.088

Point 23
4.066
−0.264
2.086

Point 24
3.938
−0.284
2.085

Point 25
3.810
−0.304
2.083

Point 26
3.682
−0.322
2.082

Point 27
3.554
−0.340
2.081

Point 28
3.426
−0.356
2.079

Point 29
3.297
−0.371
2.078

Point 30
3.168
−0.385
2.077

Point 31
3.040
−0.398
2.076

Point 32
2.911
−0.409
2.075

Point 33
2.782
−0.419
2.075

Point 34
2.653
−0.427
2.074

Point 35
2.524
−0.433
2.074

Point 36
2.394
−0.437
2.073

Point 37
2.265
−0.440
2.073

Point 38
2.136
−0.440
2.073

Point 39
2.006
−0.438
2.073

Point 40
1.877
−0.433
2.074

Point 41
1.748
−0.425
2.074

Point 42
1.619
−0.414
2.075

Point 43
1.491
−0.399
2.076

Point 44
1.363
−0.380
2.078

Point 45
1.235
−0.358
2.079

Point 46
1.109
−0.330
2.081

Point 47
0.984
−0.298
2.084

Point 48
0.860
−0.262
2.086

Point 49
0.737
−0.220
2.089

Point 50
0.616
−0.176
2.093

Point 51
0.495
−0.131
2.096

Point 52
0.372
−0.091
2.099

Point 53
0.245
−0.069
2.101

Point 54
0.117
−0.086
2.099

Point 55
0.003
−0.145
2.095

Point 56
−0.084
−0.240
2.088

Point 57
−0.145
−0.354
2.080

Point 58
−0.186
−0.476
2.071

Point 59
−0.213
−0.602
2.061

Point 60
−0.227
−0.730
2.052

Point 61
−0.231
−0.859
2.042

Point 62
−0.224
−0.988
2.033

Point 63
−0.208
−1.116
2.023

Point 64
−0.181
−1.242
2.014

Point 65
−0.142
−1.365
2.005

Point 66
−0.091
−1.483
1.996

Point 67
−0.027
−1.595
1.988

Point 68
0.052
−1.698
1.980

Point 69
0.144
−1.788
1.974

Point 70
0.248
−1.864
1.968

Point 71
0.363
−1.924
1.964

Point 72
0.484
−1.968
1.960

Point 73
0.610
−1.997
1.958

Point 74
0.738
−2.014
1.957

Point 75
0.868
−2.020
1.956

Point 76
0.997
−2.017
1.957

Point 77
1.126
−2.007
1.957

Point 78
1.254
−1.991
1.958

Point 79
1.382
−1.970
1.960

Point 80
1.508
−1.945
1.962

Point 81
1.635
−1.916
1.964

Point 82
1.760
−1.883
1.966

Point 83
1.884
−1.849
1.969

Point 84
2.008
−1.812
1.972

Point 85
2.131
−1.773
1.975

Point 86
2.254
−1.732
1.978

Point 87
2.376
−1.689
1.981

Point 88
2.498
−1.646
1.984

Point 89
2.619
−1.601
1.987

Point 90
2.740
−1.555
1.991

Point 91
2.861
−1.508
1.994

Point 92
2.981
−1.460
1.998

Point 93
3.100
−1.411
2.001

Point 94
3.220
−1.362
2.005

Point 95
3.339
−1.312
2.009

Point 96
3.458
−1.261
2.012

Point 97
3.577
−1.210
2.016

Point 98
3.695
−1.158
2.020

Point 99
3.814
−1.106
2.024

Point 100
3.932
−1.054
2.028

Point 101
4.050
−1.002
2.032

Point 102
4.168
−0.949
2.036

Point 103
4.286
−0.895
2.040

Point 104
4.403
−0.842
2.043

Point 105
4.521
−0.788
2.047

Point 106
4.639
−0.734
2.051

Point 107
4.756
−0.680
2.055

Point 108
4.873
−0.626
2.059

Point 109
4.991
−0.571
2.063

Point 110
5.108
−0.517
2.068

Point 111
5.225
−0.462
2.072

Point 112
5.342
−0.407
2.076

Point 113
5.459
−0.353
2.080

Point 114
5.576
−0.298
2.084

Point 115
5.693
−0.243
2.088

Point 116
5.810
−0.188
2.092

Point 117
5.927
−0.132
2.096

Point 118
6.044
−0.077
2.100

Point 119
6.161
−0.022
2.104

Point 120
6.278
0.033
2.108

Section 7

Point 1
6.670
0.209
2.673

Point 2
6.566
0.246
2.675

Point 3
6.440
0.210
2.673

Point 4
6.314
0.175
2.670

Point 5
6.187
0.142
2.668

Point 6
6.061
0.109
2.665

Point 7
5.934
0.077
2.663

Point 8
5.807
0.046
2.661

Point 9
5.679
0.015
2.658

Point 10
5.552
−0.014
2.656

Point 11
5.424
−0.043
2.654

Point 12
5.296
−0.072
2.652

Point 13
5.168
−0.099
2.650

Point 14
5.040
−0.126
2.648

Point 15
4.911
−0.152
2.646

Point 16
4.783
−0.177
2.644

Point 17
4.654
−0.202
2.642

Point 18
4.526
−0.226
2.641

Point 19
4.397
−0.249
2.639

Point 20
4.268
−0.271
2.637

Point 21
4.138
−0.293
2.636

Point 22
4.009
−0.313
2.634

Point 23
3.880
−0.333
2.633

Point 24
3.750
−0.352
2.631

Point 25
3.620
−0.369
2.630

Point 26
3.490
−0.386
2.629

Point 27
3.360
−0.402
2.628

Point 28
3.230
−0.416
2.626

Point 29
3.100
−0.429
2.625

Point 30
2.969
−0.441
2.625

Point 31
2.839
−0.451
2.624

Point 32
2.708
−0.460
2.623

Point 33
2.577
−0.467
2.623

Point 34
2.447
−0.472
2.622

Point 35
2.316
−0.476
2.622

Point 36
2.185
−0.477
2.622

Point 37
2.054
−0.475
2.622

Point 38
1.923
−0.471
2.622

Point 39
1.792
−0.464
2.623

Point 40
1.662
−0.453
2.624

Point 41
1.531
−0.439
2.625

Point 42
1.402
−0.421
2.626

Point 43
1.273
−0.399
2.628

Point 44
1.145
−0.371
2.630

Point 45
1.018
−0.338
2.632

Point 46
0.893
−0.300
2.635

Point 47
0.769
−0.257
2.638

Point 48
0.647
−0.209
2.642

Point 49
0.525
−0.161
2.645

Point 50
0.402
−0.117
2.649

Point 51
0.274
−0.093
2.650

Point 52
0.144
−0.108
2.649

Point 53
0.027
−0.166
2.645

Point 54
−0.062
−0.261
2.638

Point 55
−0.124
−0.376
2.629

Point 56
−0.165
−0.499
2.620

Point 57
−0.191
−0.627
2.611

Point 58
−0.204
−0.757
2.601

Point 59
−0.207
−0.888
2.592

Point 60
−0.199
−1.018
2.582

Point 61
−0.181
−1.148
2.572

Point 62
−0.154
−1.275
2.563

Point 63
−0.115
−1.400
2.554

Point 64
−0.064
−1.520
2.545

Point 65
0.001
−1.634
2.536

Point 66
0.079
−1.739
2.529

Point 67
0.170
−1.832
2.522

Point 68
0.275
−1.910
2.516

Point 69
0.390
−1.973
2.511

Point 70
0.512
−2.019
2.508

Point 71
0.639
−2.050
2.506

Point 72
0.769
−2.068
2.504

Point 73
0.900
−2.075
2.504

Point 74
1.031
−2.073
2.504

Point 75
1.161
−2.063
2.505

Point 76
1.291
−2.047
2.506

Point 77
1.420
−2.026
2.507

Point 78
1.549
−2.000
2.509

Point 79
1.676
−1.970
2.512

Point 80
1.803
−1.938
2.514

Point 81
1.929
−1.902
2.517

Point 82
2.055
−1.864
2.519

Point 83
2.179
−1.825
2.522

Point 84
2.304
−1.783
2.525

Point 85
2.427
−1.740
2.529

Point 86
2.550
−1.695
2.532

Point 87
2.673
−1.650
2.535

Point 88
2.795
−1.603
2.539

Point 89
2.917
−1.555
2.542

Point 90
3.039
−1.507
2.546

Point 91
3.160
−1.457
2.549

Point 92
3.281
−1.407
2.553

Point 93
3.402
−1.356
2.557

Point 94
3.522
−1.305
2.561

Point 95
3.642
−1.253
2.565

Point 96
3.762
−1.201
2.568

Point 97
3.882
−1.148
2.572

Point 98
4.002
−1.095
2.576

Point 99
4.121
−1.042
2.580

Point 100
4.241
−0.988
2.584

Point 101
4.360
−0.934
2.588

Point 102
4.479
−0.880
2.592

Point 103
4.598
−0.826
2.596

Point 104
4.717
−0.771
2.600

Point 105
4.836
−0.716
2.604

Point 106
4.955
−0.662
2.608

Point 107
5.074
−0.607
2.612

Point 108
5.193
−0.552
2.616

Point 109
5.311
−0.496
2.621

Point 110
5.430
−0.441
2.625

Point 111
5.549
−0.386
2.629

Point 112
5.667
−0.330
2.633

Point 113
5.786
−0.275
2.637

Point 114
5.904
−0.219
2.641

Point 115
6.023
−0.164
2.645

Point 116
6.141
−0.108
2.649

Point 117
6.260
−0.053
2.653

Point 118
6.378
0.003
2.657

Point 119
6.497
0.058
2.662

Point 120
6.616
0.114
2.666

Section 8

Point 1
6.770
0.161
3.221

Point 2
6.665
0.197
3.223

Point 3
6.538
0.162
3.221

Point 4
6.410
0.128
3.218

Point 5
6.282
0.094
3.216

Point 6
6.153
0.062
3.213

Point 7
6.025
0.031
3.211

Point 8
5.896
0.000
3.209

Point 9
5.767
−0.030
3.207

Point 10
5.638
−0.059
3.204

Point 11
5.508
−0.087
3.202

Point 12
5.379
−0.115
3.200

Point 13
5.249
−0.142
3.198

Point 14
5.119
−0.168
3.196

Point 15
4.989
−0.193
3.194

Point 16
4.859
−0.218
3.193

Point 17
4.729
−0.242
3.191

Point 18
4.599
−0.266
3.189

Point 19
4.468
−0.288
3.187

Point 20
4.338
−0.310
3.186

Point 21
4.207
−0.331
3.184

Point 22
4.076
−0.351
3.183

Point 23
3.945
−0.370
3.181

Point 24
3.814
−0.389
3.180

Point 25
3.683
−0.406
3.179

Point 26
3.551
−0.423
3.177

Point 27
3.420
−0.438
3.176

Point 28
3.288
−0.452
3.175

Point 29
3.156
−0.465
3.174

Point 30
3.024
−0.477
3.173

Point 31
2.892
−0.488
3.173

Point 32
2.760
−0.496
3.172

Point 33
2.628
−0.504
3.172

Point 34
2.496
−0.509
3.171

Point 35
2.363
−0.513
3.171

Point 36
2.231
−0.514
3.171

Point 37
2.098
−0.513
3.171

Point 38
1.966
−0.509
3.171

Point 39
1.834
−0.502
3.172

Point 40
1.702
−0.492
3.172

Point 41
1.570
−0.479
3.173

Point 42
1.439
−0.461
3.175

Point 43
1.308
−0.438
3.176

Point 44
1.179
−0.410
3.178

Point 45
1.051
−0.377
3.181

Point 46
0.924
−0.337
3.184

Point 47
0.800
−0.292
3.187

Point 48
0.678
−0.241
3.191

Point 49
0.556
−0.188
3.195

Point 50
0.433
−0.141
3.198

Point 51
0.304
−0.114
3.200

Point 52
0.173
−0.128
3.199

Point 53
0.053
−0.184
3.195

Point 54
−0.040
−0.277
3.188

Point 55
−0.103
−0.392
3.180

Point 56
−0.145
−0.518
3.170

Point 57
−0.171
−0.647
3.161

Point 58
−0.184
−0.779
3.151

Point 59
−0.185
−0.911
3.141

Point 60
−0.177
−1.042
3.132

Point 61
−0.159
−1.173
3.122

Point 62
−0.130
−1.302
3.112

Point 63
−0.091
−1.428
3.103

Point 64
−0.040
−1.550
3.094

Point 65
0.024
−1.665
3.086

Point 66
0.102
−1.772
3.078

Point 67
0.193
−1.868
3.071

Point 68
0.297
−1.949
3.065

Point 69
0.412
−2.014
3.060

Point 70
0.535
−2.063
3.056

Point 71
0.663
−2.097
3.054

Point 72
0.794
−2.117
3.052

Point 73
0.926
−2.125
3.052

Point 74
1.059
−2.124
3.052

Point 75
1.191
−2.115
3.052

Point 76
1.322
−2.100
3.053

Point 77
1.453
−2.079
3.055

Point 78
1.583
−2.053
3.057

Point 79
1.712
−2.024
3.059

Point 80
1.840
−1.991
3.062

Point 81
1.968
−1.956
3.064

Point 82
2.095
−1.918
3.067

Point 83
2.221
−1.878
3.070

Point 84
2.347
−1.836
3.073

Point 85
2.472
−1.793
3.076

Point 86
2.597
−1.748
3.079

Point 87
2.721
−1.703
3.083

Point 88
2.845
−1.656
3.086

Point 89
2.968
−1.608
3.090

Point 90
3.091
−1.559
3.093

Point 91
3.214
−1.509
3.097

Point 92
3.336
−1.459
3.101

Point 93
3.458
−1.408
3.105

Point 94
3.580
−1.356
3.108

Point 95
3.702
−1.304
3.112

Point 96
3.823
−1.251
3.116

Point 97
3.945
−1.198
3.120

Point 98
4.066
−1.145
3.124

Point 99
4.187
−1.092
3.128

Point 100
4.308
−1.038
3.132

Point 101
4.429
−0.984
3.136

Point 102
4.549
−0.929
3.140

Point 103
4.670
−0.875
3.144

Point 104
4.790
−0.820
3.148

Point 105
4.911
−0.765
3.152

Point 106
5.031
−0.710
3.156

Point 107
5.152
−0.655
3.160

Point 108
5.272
−0.600
3.164

Point 109
5.392
−0.545
3.168

Point 110
5.513
−0.489
3.173

Point 111
5.633
−0.434
3.177

Point 112
5.753
−0.379
3.181

Point 113
5.873
−0.323
3.185

Point 114
5.993
−0.267
3.189

Point 115
6.113
−0.212
3.193

Point 116
6.233
−0.156
3.197

Point 117
6.354
−0.101
3.201

Point 118
6.474
−0.045
3.205

Point 119
6.594
0.010
3.210

Point 120
6.714
0.066
3.214

Section 9

Point 1
6.858
0.098
3.767

Point 2
6.752
0.134
3.770

Point 3
6.624
0.099
3.768

Point 4
6.494
0.066
3.765

Point 5
6.365
0.034
3.763

Point 6
6.235
0.002
3.760

Point 7
6.105
−0.028
3.758

Point 8
5.975
−0.058
3.756

Point 9
5.844
−0.086
3.754

Point 10
5.714
−0.114
3.752

Point 11
5.583
−0.142
3.750

Point 12
5.452
−0.168
3.748

Point 13
5.321
−0.194
3.746

Point 14
5.190
−0.219
3.744

Point 15
5.059
−0.244
3.742

Point 16
4.927
−0.268
3.740

Point 17
4.796
−0.291
3.739

Point 18
4.664
−0.313
3.737

Point 19
4.532
−0.335
3.735

Point 20
4.401
−0.356
3.734

Point 21
4.269
−0.376
3.732

Point 22
4.136
−0.395
3.731

Point 23
4.004
−0.414
3.730

Point 24
3.872
−0.431
3.728

Point 25
3.739
−0.448
3.727

Point 26
3.607
−0.464
3.726

Point 27
3.474
−0.479
3.725

Point 28
3.341
−0.492
3.724

Point 29
3.208
−0.505
3.723

Point 30
3.075
−0.516
3.722

Point 31
2.942
−0.526
3.721

Point 32
2.809
−0.534
3.721

Point 33
2.675
−0.541
3.720

Point 34
2.542
−0.546
3.720

Point 35
2.408
−0.550
3.720

Point 36
2.275
−0.551
3.719

Point 37
2.141
−0.550
3.720

Point 38
2.008
−0.547
3.720

Point 39
1.874
−0.540
3.720

Point 40
1.741
−0.530
3.721

Point 41
1.608
−0.517
3.722

Point 42
1.476
−0.499
3.723

Point 43
1.344
−0.477
3.725

Point 44
1.214
−0.449
3.727

Point 45
1.085
−0.415
3.730

Point 46
0.957
−0.374
3.733

Point 47
0.832
−0.328
3.736

Point 48
0.710
−0.275
3.740

Point 49
0.589
−0.219
3.744

Point 50
0.466
−0.167
3.748

Point 51
0.336
−0.135
3.750

Point 52
0.204
−0.145
3.750

Point 53
0.083
−0.199
3.746

Point 54
−0.014
−0.290
3.739

Point 55
−0.080
−0.406
3.730

Point 56
−0.124
−0.531
3.721

Point 57
−0.151
−0.662
3.711

Point 58
−0.165
−0.794
3.702

Point 59
−0.167
−0.927
3.692

Point 60
−0.159
−1.060
3.682

Point 61
−0.141
−1.192
3.672

Point 62
−0.112
−1.322
3.662

Point 63
−0.072
−1.449
3.653

Point 64
−0.020
−1.572
3.644

Point 65
0.044
−1.688
3.635

Point 66
0.122
−1.796
3.627

Point 67
0.213
−1.894
3.620

Point 68
0.317
−1.977
3.614

Point 69
0.432
−2.044
3.609

Point 70
0.555
−2.096
3.605

Point 71
0.684
−2.132
3.603

Point 72
0.815
−2.154
3.601

Point 73
0.949
−2.165
3.600

Point 74
1.082
−2.166
3.600

Point 75
1.215
−2.158
3.601

Point 76
1.348
−2.144
3.602

Point 77
1.480
−2.124
3.603

Point 78
1.611
−2.100
3.605

Point 79
1.742
−2.071
3.607

Point 80
1.872
−2.039
3.609

Point 81
2.000
−2.005
3.612

Point 82
2.129
−1.967
3.615

Point 83
2.256
−1.928
3.618

Point 84
2.383
−1.887
3.621

Point 85
2.510
−1.844
3.624

Point 86
2.636
−1.800
3.627

Point 87
2.761
−1.754
3.631

Point 88
2.886
−1.707
3.634

Point 89
3.011
−1.660
3.638

Point 90
3.135
−1.611
3.641

Point 91
3.259
−1.562
3.645

Point 92
3.383
−1.512
3.648

Point 93
3.506
−1.461
3.652

Point 94
3.630
−1.410
3.656

Point 95
3.753
−1.358
3.660

Point 96
3.876
−1.306
3.664

Point 97
3.998
−1.253
3.668

Point 98
4.121
−1.200
3.671

Point 99
4.243
−1.147
3.675

Point 100
4.366
−1.093
3.679

Point 101
4.488
−1.040
3.683

Point 102
4.610
−0.986
3.687

Point 103
4.732
−0.931
3.691

Point 104
4.854
−0.877
3.695

Point 105
4.976
−0.823
3.699

Point 106
5.097
−0.768
3.703

Point 107
5.219
−0.713
3.707

Point 108
5.341
−0.658
3.712

Point 109
5.463
−0.604
3.716

Point 110
5.584
−0.549
3.720

Point 111
5.706
−0.494
3.724

Point 112
5.827
−0.438
3.728

Point 113
5.949
−0.383
3.732

Point 114
6.071
−0.328
3.736

Point 115
6.192
−0.273
3.740

Point 116
6.314
−0.218
3.744

Point 117
6.435
−0.163
3.748

Point 118
6.557
−0.108
3.752

Point 119
6.678
−0.053
3.756

Point 120
6.800
0.002
3.760

Section 10

Point 1
6.936
0.022
4.313

Point 2
6.830
0.060
4.316

Point 3
6.700
0.026
4.314

Point 4
6.569
−0.006
4.311

Point 5
6.438
−0.037
4.309

Point 6
6.308
−0.067
4.307

Point 7
6.176
−0.097
4.305

Point 8
6.045
−0.125
4.303

Point 9
5.913
−0.152
4.300

Point 10
5.782
−0.179
4.299

Point 11
5.650
−0.205
4.297

Point 12
5.518
−0.230
4.295

Point 13
5.386
−0.254
4.293

Point 14
5.254
−0.278
4.291

Point 15
5.121
−0.301
4.289

Point 16
4.989
−0.324
4.288

Point 17
4.856
−0.346
4.286

Point 18
4.723
−0.367
4.285

Point 19
4.591
−0.387
4.283

Point 20
4.458
−0.407
4.282

Point 21
4.325
−0.426
4.280

Point 22
4.191
−0.444
4.279

Point 23
4.058
−0.461
4.278

Point 24
3.925
−0.478
4.276

Point 25
3.791
−0.493
4.275

Point 26
3.658
−0.508
4.274

Point 27
3.524
−0.522
4.273

Point 28
3.390
−0.534
4.272

Point 29
3.256
−0.546
4.271

Point 30
3.122
−0.556
4.271

Point 31
2.988
−0.565
4.270

Point 32
2.854
−0.573
4.269

Point 33
2.720
−0.579
4.269

Point 34
2.586
−0.584
4.269

Point 35
2.451
−0.587
4.268

Point 36
2.317
−0.588
4.268

Point 37
2.183
−0.586
4.268

Point 38
2.048
−0.582
4.269

Point 39
1.914
−0.575
4.269

Point 40
1.780
−0.565
4.270

Point 41
1.646
−0.552
4.271

Point 42
1.513
−0.534
4.272

Point 43
1.381
−0.512
4.274

Point 44
1.249
−0.484
4.276

Point 45
1.119
−0.451
4.278

Point 46
0.991
−0.410
4.281

Point 47
0.865
−0.363
4.285

Point 48
0.742
−0.309
4.289

Point 49
0.621
−0.251
4.293

Point 50
0.499
−0.195
4.297

Point 51
0.370
−0.158
4.300

Point 52
0.237
−0.164
4.300

Point 53
0.114
−0.216
4.296

Point 54
0.015
−0.306
4.289

Point 55
−0.055
−0.420
4.281

Point 56
−0.102
−0.545
4.271

Point 57
−0.131
−0.676
4.262

Point 58
−0.147
−0.809
4.252

Point 59
−0.151
−0.943
4.242

Point 60
−0.144
−1.077
4.232

Point 61
−0.126
−1.210
4.222

Point 62
−0.097
−1.340
4.213

Point 63
−0.057
−1.468
4.203

Point 64
−0.004
−1.591
4.194

Point 65
0.061
−1.709
4.185

Point 66
0.140
−1.817
4.177

Point 67
0.231
−1.915
4.170

Point 68
0.336
−1.999
4.164

Point 69
0.451
−2.068
4.159

Point 70
0.574
−2.122
4.155

Point 71
0.703
−2.160
4.152

Point 72
0.835
−2.184
4.150

Point 73
0.969
−2.197
4.149

Point 74
1.103
−2.200
4.149

Point 75
1.237
−2.195
4.149

Point 76
1.371
−2.183
4.150

Point 77
1.504
−2.164
4.152

Point 78
1.636
−2.141
4.153

Point 79
1.768
−2.114
4.155

Point 80
1.899
−2.083
4.158

Point 81
2.029
−2.050
4.160

Point 82
2.158
−2.013
4.163

Point 83
2.287
−1.975
4.166

Point 84
2.415
−1.935
4.169

Point 85
2.543
−1.893
4.172

Point 86
2.670
−1.849
4.175

Point 87
2.797
−1.804
4.178

Point 88
2.923
−1.758
4.182

Point 89
3.049
−1.711
4.185

Point 90
3.174
−1.664
4.189

Point 91
3.299
−1.615
4.192

Point 92
3.424
−1.566
4.196

Point 93
3.549
−1.516
4.200

Point 94
3.673
−1.465
4.203

Point 95
3.798
−1.414
4.207

Point 96
3.922
−1.362
4.211

Point 97
4.046
−1.310
4.215

Point 98
4.169
−1.258
4.219

Point 99
4.293
−1.206
4.223

Point 100
4.417
−1.153
4.226

Point 101
4.540
−1.100
4.230

Point 102
4.663
−1.047
4.234

Point 103
4.787
−0.993
4.238

Point 104
4.910
−0.940
4.242

Point 105
5.033
−0.886
4.246

Point 106
5.156
−0.832
4.250

Point 107
5.279
−0.778
4.254

Point 108
5.402
−0.724
4.258

Point 109
5.525
−0.670
4.262

Point 110
5.648
−0.616
4.266

Point 111
5.771
−0.562
4.270

Point 112
5.894
−0.507
4.274

Point 113
6.016
−0.453
4.278

Point 114
6.139
−0.399
4.282

Point 115
6.262
−0.344
4.286

Point 116
6.385
−0.290
4.290

Point 117
6.508
−0.236
4.294

Point 118
6.631
−0.182
4.298

Point 119
6.754
−0.127
4.302

Point 120
6.877
−0.073
4.306

Section 11

Point 1
7.010
−0.062
4.859

Point 2
6.904
−0.023
4.862

Point 3
6.773
−0.055
4.859

Point 4
6.641
−0.086
4.857

Point 5
6.510
−0.116
4.855

Point 6
6.377
−0.145
4.853

Point 7
6.245
−0.172
4.851

Point 8
6.113
−0.199
4.849

Point 9
5.980
−0.224
4.847

Point 10
5.847
−0.250
4.845

Point 11
5.714
−0.274
4.843

Point 12
5.581
−0.297
4.841

Point 13
5.448
−0.320
4.840

Point 14
5.315
−0.343
4.838

Point 15
5.182
−0.364
4.836

Point 16
5.048
−0.385
4.835

Point 17
4.914
−0.405
4.833

Point 18
4.781
−0.425
4.832

Point 19
4.647
−0.443
4.830

Point 20
4.513
−0.461
4.829

Point 21
4.379
−0.479
4.828

Point 22
4.245
−0.495
4.827

Point 23
4.111
−0.511
4.825

Point 24
3.976
−0.526
4.824

Point 25
3.842
−0.540
4.823

Point 26
3.708
−0.554
4.822

Point 27
3.573
−0.566
4.821

Point 28
3.438
−0.577
4.821

Point 29
3.304
−0.588
4.820

Point 30
3.169
−0.597
4.819

Point 31
3.034
−0.605
4.819

Point 32
2.899
−0.611
4.818

Point 33
2.764
−0.616
4.818

Point 34
2.629
−0.620
4.817

Point 35
2.494
−0.622
4.817

Point 36
2.359
−0.622
4.817

Point 37
2.224
−0.620
4.817

Point 38
2.089
−0.615
4.818

Point 39
1.954
−0.608
4.818

Point 40
1.819
−0.597
4.819

Point 41
1.685
−0.583
4.820

Point 42
1.551
−0.566
4.821

Point 43
1.417
−0.543
4.823

Point 44
1.285
−0.516
4.825

Point 45
1.154
−0.483
4.828

Point 46
1.025
−0.443
4.831

Point 47
0.899
−0.396
4.834

Point 48
0.775
−0.341
4.838

Point 49
0.653
−0.282
4.842

Point 50
0.531
−0.224
4.847

Point 51
0.403
−0.183
4.850

Point 52
0.269
−0.186
4.849

Point 53
0.145
−0.238
4.846

Point 54
0.045
−0.327
4.839

Point 55
−0.027
−0.441
4.831

Point 56
−0.077
−0.566
4.821

Point 57
−0.110
−0.697
4.812

Point 58
−0.129
−0.830
4.802

Point 59
−0.136
−0.965
4.792

Point 60
−0.131
−1.100
4.782

Point 61
−0.114
−1.233
4.772

Point 62
−0.085
−1.365
4.762

Point 63
−0.045
−1.493
4.753

Point 64
0.008
−1.617
4.744

Point 65
0.075
−1.735
4.735

Point 66
0.154
−1.843
4.727

Point 67
0.247
−1.941
4.720

Point 68
0.353
−2.025
4.713

Point 69
0.468
−2.095
4.708

Point 70
0.592
−2.150
4.704

Point 71
0.721
−2.189
4.701

Point 72
0.853
−2.216
4.699

Point 73
0.987
−2.230
4.698

Point 74
1.122
−2.235
4.698

Point 75
1.257
−2.232
4.698

Point 76
1.392
−2.221
4.699

Point 77
1.526
−2.204
4.700

Point 78
1.660
−2.183
4.702

Point 79
1.792
−2.157
4.704

Point 80
1.924
−2.128
4.706

Point 81
2.055
−2.095
4.708

Point 82
2.186
−2.060
4.711

Point 83
2.316
−2.023
4.714

Point 84
2.445
−1.984
4.717

Point 85
2.574
−1.943
4.720

Point 86
2.702
−1.900
4.723

Point 87
2.830
−1.856
4.726

Point 88
2.957
−1.811
4.729

Point 89
3.084
−1.765
4.733

Point 90
3.211
−1.719
4.736

Point 91
3.337
−1.671
4.740

Point 92
3.463
−1.622
4.743

Point 93
3.589
−1.573
4.747

Point 94
3.715
−1.524
4.751

Point 95
3.840
−1.473
4.754

Point 96
3.965
−1.423
4.758

Point 97
4.090
−1.372
4.762

Point 98
4.215
−1.321
4.766

Point 99
4.340
−1.269
4.769

Point 100
4.465
−1.217
4.773

Point 101
4.589
−1.165
4.777

Point 102
4.714
−1.113
4.781

Point 103
4.838
−1.060
4.785

Point 104
4.963
−1.008
4.789

Point 105
5.087
−0.955
4.793

Point 106
5.211
−0.902
4.797

Point 107
5.336
−0.849
4.800

Point 108
5.460
−0.796
4.804

Point 109
5.584
−0.743
4.808

Point 110
5.708
−0.690
4.812

Point 111
5.832
−0.637
4.816

Point 112
5.957
−0.584
4.820

Point 113
6.081
−0.530
4.824

Point 114
6.205
−0.477
4.828

Point 115
6.329
−0.424
4.832

Point 116
6.453
−0.370
4.836

Point 117
6.577
−0.317
4.840

Point 118
6.701
−0.264
4.844

Point 119
6.825
−0.211
4.848

Point 120
6.950
−0.157
4.852

Section 12

Point 1
7.086
−0.151
5.404

Point 2
6.980
−0.111
5.407

Point 3
6.848
−0.142
5.404

Point 4
6.715
−0.172
5.402

Point 5
6.582
−0.200
5.400

Point 6
6.449
−0.227
5.398

Point 7
6.316
−0.253
5.396

Point 8
6.182
−0.278
5.394

Point 9
6.048
−0.302
5.392

Point 10
5.914
−0.325
5.391

Point 11
5.780
−0.347
5.389

Point 12
5.646
−0.369
5.387

Point 13
5.512
−0.390
5.386

Point 14
5.377
−0.411
5.384

Point 15
5.243
−0.430
5.383

Point 16
5.108
−0.449
5.382

Point 17
4.974
−0.468
5.380

Point 18
4.839
−0.485
5.379

Point 19
4.704
−0.502
5.378

Point 20
4.569
−0.518
5.376

Point 21
4.434
−0.534
5.375

Point 22
4.299
−0.549
5.374

Point 23
4.164
−0.563
5.373

Point 24
4.028
−0.576
5.372

Point 25
3.893
−0.588
5.371

Point 26
3.758
−0.600
5.370

Point 27
3.622
−0.610
5.370

Point 28
3.487
−0.620
5.369

Point 29
3.351
−0.629
5.368

Point 30
3.215
−0.636
5.368

Point 31
3.079
−0.643
5.367

Point 32
2.944
−0.648
5.367

Point 33
2.808
−0.651
5.367

Point 34
2.672
−0.653
5.366

Point 35
2.536
−0.654
5.366

Point 36
2.400
−0.653
5.366

Point 37
2.264
−0.649
5.367

Point 38
2.128
−0.643
5.367

Point 39
1.993
−0.635
5.368

Point 40
1.857
−0.624
5.369

Point 41
1.722
−0.609
5.370

Point 42
1.587
−0.591
5.371

Point 43
1.453
−0.568
5.373

Point 44
1.320
−0.541
5.375

Point 45
1.189
−0.507
5.377

Point 46
1.059
−0.468
5.380

Point 47
0.931
−0.421
5.384

Point 48
0.806
−0.368
5.388

Point 49
0.684
−0.309
5.392

Point 50
0.560
−0.251
5.396

Point 51
0.431
−0.211
5.399

Point 52
0.296
−0.216
5.399

Point 53
0.172
−0.270
5.395

Point 54
0.073
−0.362
5.388

Point 55
0.001
−0.476
5.380

Point 56
−0.052
−0.601
5.370

Point 57
−0.088
−0.732
5.361

Point 58
−0.110
−0.866
5.351

Point 59
−0.120
−1.001
5.341

Point 60
−0.117
−1.136
5.331

Point 61
−0.102
−1.271
5.321

Point 62
−0.074
−1.404
5.311

Point 63
−0.034
−1.533
5.301

Point 64
0.019
−1.658
5.292

Point 65
0.086
−1.775
5.283

Point 66
0.167
−1.884
5.275

Point 67
0.261
−1.982
5.268

Point 68
0.368
−2.066
5.262

Point 69
0.485
−2.135
5.257

Point 70
0.609
−2.190
5.253

Point 71
0.739
−2.230
5.250

Point 72
0.872
−2.257
5.248

Point 73
1.007
−2.273
5.247

Point 74
1.142
−2.279
5.246

Point 75
1.278
−2.276
5.246

Point 76
1.414
−2.267
5.247

Point 77
1.549
−2.251
5.248

Point 78
1.683
−2.231
5.250

Point 79
1.817
−2.206
5.252

Point 80
1.950
−2.178
5.254

Point 81
2.082
−2.146
5.256

Point 82
2.214
−2.112
5.259

Point 83
2.345
−2.076
5.261

Point 84
2.475
−2.038
5.264

Point 85
2.605
−1.998
5.267

Point 86
2.734
−1.956
5.270

Point 87
2.863
−1.913
5.273

Point 88
2.992
−1.869
5.277

Point 89
3.120
−1.824
5.280

Point 90
3.248
−1.778
5.283

Point 91
3.376
−1.732
5.287

Point 92
3.503
−1.684
5.290

Point 93
3.630
−1.636
5.294

Point 94
3.757
−1.587
5.297

Point 95
3.883
−1.538
5.301

Point 96
4.010
−1.488
5.305

Point 97
4.136
−1.438
5.308

Point 98
4.262
−1.388
5.312

Point 99
4.389
−1.337
5.316

Point 100
4.515
−1.287
5.320

Point 101
4.640
−1.236
5.323

Point 102
4.766
−1.184
5.327

Point 103
4.892
−1.133
5.331

Point 104
5.018
−1.081
5.335

Point 105
5.143
−1.029
5.339

Point 106
5.269
−0.978
5.342

Point 107
5.395
−0.926
5.346

Point 108
5.520
−0.874
5.350

Point 109
5.646
−0.822
5.354

Point 110
5.771
−0.770
5.358

Point 111
5.896
−0.717
5.362

Point 112
6.022
−0.665
5.366

Point 113
6.147
−0.613
5.369

Point 114
6.273
−0.561
5.373

Point 115
6.398
−0.508
5.377

Point 116
6.524
−0.456
5.381

Point 117
6.649
−0.404
5.385

Point 118
6.774
−0.352
5.389

Point 119
6.900
−0.299
5.393

Point 120
7.025
−0.247
5.396

FIG. 6 illustrates an airfoil shape including a leaned airfoil section 1360 according to an exemplary embodiment. As the nozzles come into direct contact with the high-temperature and high-pressure combustion gas, a secondary flow occurs. That is, secondary flows are flow effects that occur after the high-temperature and high-pressure combustion gas path flow contacts the nozzles. The effects are not good as they negatively affect aerodynamic performance, causing turbulence in the flow path. Further, the turbulences may increase the heat transfer coefficients on the gas path surface which also increases heat transfer/metal temperature rise by increasing the heat transfer coefficient of the gas path surface. In order to reduce losses caused by the secondary flows, a newly designed airfoil shape is needed. According to the newly designed airfoil shape of the exemplary embodiment which includes a leaned airfoil section 1360 as illustrated in FIG. 6, it is possible to reduce the secondary flow effects aerodynamically by changing the shape/contour of the airfoil.

While one or more exemplary embodiments have been described with reference to the accompanying drawings, it is to be understood by those skilled in the art that various modifications and changes in form and details can be made therein without departing from the spirit and scope as defined by the appended claims. Therefore, the description of the exemplary embodiments should be construed in a descriptive sense only and not to limit the scope of the claims, and many alternatives, modifications, and variations will be apparent to those skilled in the art.

Number	Name	Date	Kind
6887041	Coke	May 2005	B2
7329093	Vandeputte	Feb 2008	B2
7837445	Benjamin	Nov 2010	B2
9945232	Munoz	Apr 2018	B2
10190421	Ristau	Jan 2019	B2
10280774	Ryman	May 2019	B2
10480335	Ravanis	Nov 2019	B2
10590772	Parker	Mar 2020	B1
10590782	Parker	Mar 2020	B1
10598034	Tsifourdaris	Mar 2020	B2
11236628	Ristau	Feb 2022	B1

Airfoil profile for a turbine nozzle

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US Referenced Citations (11)