OPTIMIZED AERODYNAMIC PROFILE FOR A TURBINE VANE, IN PARTICULAR FOR A NOZZLE OF THE FIRST STAGE OF A TURBINE

Information

  • Patent Application
  • 20180016904
  • Publication Number
    20180016904
  • Date Filed
    December 29, 2016
    7 years ago
  • Date Published
    January 18, 2018
    6 years ago
Abstract
When cold and in the non-coated state, the aerodynamic profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y, Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H where D is the distance of the point under consideration from a first reference plane P0 situated at the base of the nominal profile, and H is the height of said profile measured from the first reference plane to a second reference plane P1. The measurements D and H are taken radially relative to the axis of the turbine, while the X coordinate is measured in the axial direction of the turbine.
Description
FIELD OF THE DISCLOSURE

The present invention relates to an aerodynamic profile for a turbine vane.


INTRODUCTION

In particular, the invention relates to the aerodynamic profile of a nozzle vane forming a portion of the stator of a gas turbine, and more particularly of a low pressure turbine of the type used in a turbojet of an aircraft.


The invention relates in particular to a nozzle vane of the first stage of a turbine having a plurality of stages, preferably seven stages.


Such a profile should enable the turbine to provide the desired efficiency, and in order to do that it must be such that the flow of air around the profile is sound over the working spectrum of the turbine, i.e. substantially such that it does not give rise to turbulence, which is harmful for overall efficiency.


It must be capable of being installed properly in the environment of the engine, and in particular, for a nozzle vane forming a portion of the stator of the turbine, it must be capable of being fastened easily to the sectors of the foot platform (the zone of the vane that is furthest from the axis of rotation of the turbine) and of the head platform (the zone that is closest to said axis). Furthermore, this part must present a profile enabling it to be manufactured in a reliable and cost-effective manner by available manufacturing methods, such as casting, forging, machining, additive fabrication, or else weaving, without this list being limitative.


Furthermore, the profile of the vane must enable it to withstand the mechanical stresses, to which the vane is subjected, by enabling those stresses to be spread over the entire vane in such a manner as to avoid premature wear thereof. This spreading must apply both in static mode and in dynamic mode.


An object of the invention is to propose an aerodynamic profile for a turbine vane that is optimized, and capable of satisfying those objectives.


This object is achieved by the fact that when cold and in a non-coated state, said profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H where D is the distance of the point P under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane that is the intersection of the stacking axis of the set of vanes and the axisymmetric surface of the hub, out to a second reference plane that is the intersection of said stacking axis with the axisymmetric surface of the casing, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.


This profile has been determined as a result of numerous tests and simulations. It is defined cold, i.e. at an ambient temperature of 20° C. That is a reference temperature at which the profile is geometrically determined. The above-mentioned objectives of aerodynamics and mechanical optimization are naturally valid for the conditions of use of this aerodynamic profile, i.e. when hot, at a temperature that is stabilized when the engine of which the turbine forms a part is being used under cruising conditions.


Furthermore, the aerodynamic profile of the invention is defined in the non-coated state. Since turbine vanes are subjected to high temperature gradients, it is common practice for them to be provided with a coating having thermal properties enabling them more easily to withstand such temperature variations. The profile is determined prior to installing such a coating.


It is stated above that the profile of the invention is “substantially identical” to the nominal profile. This means that the profile may depart very slightly from said nominal profile.


The aerodynamic profile is thus preferably defined within an envelope of ±1 millimeter (mm) in a direction normal to the surface of the nominal profile.


This variation takes account in particular of manufacturing tolerances of the profile.


It is also preferable for the X,Y coordinates of the aerodynamic profile to lie within a range of ±5% relative to the X,Y coordinates of the nominal profile.


This variation takes account of the setting of the profile to adapt to the environment when in operation.


With a nozzle vane, i.e. a portion of the stator of a turbine, the profile serves to orient the fluid correctly for the turbine blades that are situated downstream, and that belong in particular to the rotary wheel of the first stage of the turbine.





BRIEF DESCRIPTION OF THE DRAWINGS

The invention can be better understood and its advantages appear better on reading the following detailed description of an embodiment given by way of non-limiting example. The description refers to the accompanying drawings, in which:



FIG. 1 is a fragmentary axial section view of a turbine including a vane of profile that corresponds to that of the invention;



FIG. 2 is an enlarged view of FIG. 1, showing the first stage of the turbine.





DETAILED DESCRIPTION

The turbine shown in axial section in FIG. 1 comprises seven stages referenced respectively S1 to S7. In the direction DF going from upstream to downstream, each stage comprises a nozzle that forms a portion of the stator of the turbine and that has a plurality of radially-oriented vanes, and a rotary wheel that forms a portion of the rotor of the turbine and that likewise includes a plurality of radially-oriented blades.


In FIG. 1, the vanes of the nozzles of stages S1 to S7 are given references N1 to N7, whereas the blades of rotary wheels of stages S1 to S7 are given respective references W1 to W7.


In known manner, the vanes of the nozzles are fastened at both ends to stationary structure portions, while the blades of the rotary wheels are fastened to a rotary disk via their roots that are formed at their radially-inner ends closer to the axis of the rotation A of the turbine. The disks d1 to d7 forming parts of the wheels W1 to W7 are constrained to rotate together.


The invention relates in particular to a vane N1 which is a vane of the nozzle of the first stage S1 of the turbine that, as mentioned above, preferably comprises seven stages as shown, without this number being limiting.


As best seen in FIG. 2, via its foot 10, which is its end remote from the axis of rotation A, the vane N1 is fastened to the outer ring 12 of the turbine, which ring is stationary in rotation. Via its head 14, formed by its end closer to the axis of rotation A, the vane is fastened to an inner shroud 16 of the turbine. By convention, the aerodynamic profile 18 of the vane is the entire portion of said vane that extends radially outwards from its head 14 to its foot 10 without incorporating the fastenings respectively to the outer ring 12 and to the inner shroud 16.


In FIG. 2, there can be seen a frame of reference comprising Cartesian coordinates X,Y,Z. The radial direction Z is the height direction of the vane, which extends radially from its head to its foot. This direction Z is perpendicular to the axial direction X which is the direction of the axis of rotation A of the turbine. The direction Y is perpendicular to the X,Z plane and is therefore tangential to the direction of rotation of the turbine.


The nominal profile from which the aerodynamic profile of the invention is determined is defined in following Table 1 of coordinates, in which the coordinate Zadim, measured along the axis Z is non-dimensional, whereas the dimensions X and Y, respectively measured along the axes X and Y, are expressed in millimeters.











TABLE 1





X
Y
Zadim

















−6.04024
−0.8485
−0.17699


−6.08596
−0.88175
−0.17699


−6.14277
−0.94109
−0.17699


−6.2014
−1.05354
−0.17699


−6.2252
−1.22861
−0.17699


−6.18793
−1.45632
−0.17699


−6.08271
−1.72447
−0.17699


−5.90833
−2.02526
−0.17699


−5.66284
−2.35213
−0.17699


−5.34406
−2.69821
−0.17699


−4.94954
−3.05531
−0.17699


−4.47686
−3.41324
−0.17699


−3.92373
−3.75872
−0.17699


−3.29055
−4.07833
−0.17699


−2.57836
−4.35393
−0.17699


−1.79171
−4.56621
−0.17699


−0.9393
−4.69584
−0.17699


−0.03429
−4.72479
−0.17699


0.905962
−4.63858
−0.17699


1.861215
−4.42871
−0.17699


2.810998
−4.09498
−0.17699


3.737497
−3.64501
−0.17699


4.626885
−3.09131
−0.17699


5.46979
−2.44923
−0.17699


6.2612
−1.73549
−0.17699


7.001274
−0.96833
−0.17699


7.691772
−0.16367
−0.17699


8.332183
0.666957
−0.17699


8.924397
1.511698
−0.17699


9.473898
2.357796
−0.17699


9.982047
3.196599
−0.17699


10.44952
4.020653
−0.17699


10.88046
4.82131
−0.17699


11.27686
5.591927
−0.17699


11.63924
6.327288
−0.17699


11.96998
7.021887
−0.17699


12.27026
7.671472
−0.17699


12.54075
8.272695
−0.17699


12.78314
8.822442
−0.17699


12.99809
9.318784
−0.17699


13.18654
9.760438
−0.17699


13.34947
10.1469
−0.17699


13.48794
10.47847
−0.17699


13.60305
10.75636
−0.17699


13.69619
10.98258
−0.17699


13.7684
11.16028
−0.17699


13.79894
11.30026
−0.17699


13.75926
11.39206
−0.17699


13.71379
11.43584
−0.17699


13.67157
11.45963
−0.17699


13.63143
11.47281
−0.17699


13.57673
11.47884
−0.17699


13.49123
11.46176
−0.17699


13.39739
11.37932
−0.17699


13.31297
11.23495
−0.17699


13.20801
11.04926
−0.17699


13.07848
10.82124
−0.17699


12.92302
10.54924
−0.17699


12.74057
10.23235
−0.17699


12.53026
9.870365
−0.17699


12.29148
9.463698
−0.17699


12.02402
9.013294
−0.17699


11.7273
8.521005
−0.17699


11.40143
7.988925
−0.17699


11.04576
7.420241
−0.17699


10.6598
6.818646
−0.17699


10.24435
6.187564
−0.17699


9.799157
5.531618
−0.17699


9.325084
4.855183
−0.17699


8.823
4.163054
−0.17699


8.292622
3.461331
−0.17699


7.733816
2.756509
−0.17699


7.149655
2.052955
−0.17699


6.540128
1.357881
−0.17699


5.903684
0.680488
−0.17699


5.237341
0.032751
−0.17699


4.53758
−0.57019
−0.17699


3.802484
−1.11193
−0.17699


3.034185
−1.57673
−0.17699


2.239078
−1.94798
−0.17699


1.429184
−2.21077
−0.17699


0.621746
−2.35373
−0.17699


−0.16213
−2.37591
−0.17699


−0.90265
−2.28903
−0.17699


−1.58639
−2.11653
−0.17699


−2.20897
−1.88936
−0.17699


−2.77385
−1.64011
−0.17699


−3.28773
−1.39776
−0.17699


−3.75647
−1.18382
−0.17699


−4.18503
−1.01016
−0.17699


−4.57455
−0.88048
−0.17699


−4.92153
−0.79402
−0.17699


−5.22207
−0.74582
−0.17699


−5.47345
−0.72928
−0.17699


−5.67479
−0.73602
−0.17699


−5.82683
−0.76104
−0.17699


−5.93224
−0.7944
−0.17699


−9.54258
−0.71217
−0.0885


−9.58876
−0.74769
−0.0885


−9.64557
−0.81047
−0.0885


−9.70297
−0.92788
−0.0885


−9.72452
−1.10868
−0.0885


−9.68502
−1.34317
−0.0885


−9.5776
−1.61992
−0.0885


−9.40119
−1.9318
−0.0885


−9.1538
−2.2728
−0.0885


−8.83307
−2.63649
−0.0885


−8.43618
−3.01493
−0.0885


−7.96001
−3.39786
−0.0885


−7.40195
−3.77241
−0.0885


−6.76043
−4.12276
−0.0885


−6.03603
−4.43036
−0.0885


−5.23222
−4.67329
−0.0885


−4.3573
−4.8285
−0.0885


−3.42534
−4.87583
−0.0885


−2.45545
−4.7973
−0.0885


−1.47052
−4.58313
−0.0885


−0.4937
−4.23358
−0.0885


0.455359
−3.75816
−0.0885


1.362267
−3.17228
−0.0885


2.218126
−2.49407
−0.0885


3.018843
−1.74233
−0.0885


3.764828
−0.93592
−0.0885


4.458084
−0.09126
−0.0885


5.099352
0.778877
−0.0885


5.691753
1.661735
−0.0885


6.240475
2.54487
−0.0885


6.747345
3.419285
−0.0885


7.214056
4.2769
−0.0885


7.644536
5.109229
−0.0885


8.040847
5.909573
−0.0885


8.403993
6.672414
−0.0885


8.736275
7.392265
−0.0885


9.038622
8.064953
−0.0885


9.311772
8.687055
−0.0885


9.557133
9.255547
−0.0885


9.775304
9.768504
−0.0885


9.967016
10.22472
−0.0885


10.13318
10.62372
−0.0885


10.2747
10.96593
−0.0885


10.39257
11.25263
−0.0885


10.4881
11.48595
−0.0885


10.5626
11.66905
−0.0885


10.59355
11.81342
−0.0885


10.55228
11.90787
−0.0885


10.50507
11.95262
−0.0885


10.46125
11.97658
−0.0885


10.4196
11.98947
−0.0885


10.36302
11.99441
−0.0885


10.27535
11.97414
−0.0885


10.18126
11.88604
−0.0885


10.09633
11.73579
−0.0885


9.988891
11.54368
−0.0885


9.856484
11.30765
−0.0885


9.697833
11.02596
−0.0885


9.511991
10.69754
−0.0885


9.298208
10.32211
−0.0885


9.056047
9.89998
−0.0885


8.785362
9.432058
−0.0885


8.485814
8.920082
−0.0885


8.157597
8.366135
−0.0885


7.800365
7.773255
−0.0885


7.413807
7.145051
−0.0885


6.998851
6.484931
−0.0885


6.555212
5.797567
−0.0885


6.083129
5.087797
−0.0885


5.582899
4.360898
−0.0885


5.054843
3.622573
−0.0885


4.498232
2.879745
−0.0885


3.913231
2.139241
−0.0885


3.299662
1.408715
−0.0885


2.656431
0.697272
−0.0885


1.981378
0.016233
−0.0885


1.270555
−0.61898
−0.0885


0.521936
−1.19165
−0.0885


−0.26235
−1.68546
−0.0885


−1.07561
−2.08441
−0.0885


−1.90712
−2.37121
−0.0885


−2.73965
−2.53293
−0.0885


−3.55088
−2.56848
−0.0885


−4.31949
−2.49202
−0.0885


−5.03038
−2.32561
−0.0885


−5.67618
−2.09697
−0.0885


−6.25726
−1.83544
−0.0885


−6.77917
−1.56777
−0.0885


−7.24898
−1.31531
−0.0885


−7.67307
−1.09282
−0.0885


−8.0556
−0.90927
−0.0885


−8.39775
−0.7696
−0.0885


−8.69843
−0.67541
−0.0885


−8.95473
−0.62486
−0.0885


−9.16305
−0.61161
−0.0885


−9.32169
−0.62514
−0.0885


−9.43173
−0.6553
−0.0885


−12.9761
−0.59091
0


−13.0221
−0.62878
0


−13.0781
−0.6949
0


−13.1334
−0.81662
0


−13.1527
−1.0019
0


−13.112
−1.24176
0


−13.0044
−1.52575
0


−12.8286
−1.84742
0


−12.5825
−2.20124
0


−12.2634
−2.58115
0


−11.8684
−2.97959
0


−11.3932
−3.38578
0


−10.8346
−3.78681
0


−10.1904
−4.16644
0


−9.45915
−4.50341
0


−8.64408
−4.77486
0


−7.75295
−4.95454
0


−6.8003
−5.01662
0


−5.80771
−4.94036
0


−4.80111
−4.71657
0


−3.80632
−4.34645
0


−2.84421
−3.84283
0


−1.93209
−3.21982
0


−1.07713
−2.50071
0


−0.28038
−1.70843
0


0.458773
−0.86183
0


1.142826
0.022377
0


1.77399
0.930397
0


2.356692
1.848855
0


2.895678
2.765885
0


3.393213
3.672324
0


3.852012
4.55962
0


4.276073
5.419398
0


4.666768
6.245336
0


5.025434
7.031757
0


5.354332
7.773206
0


5.654287
8.465537
0


5.926101
9.105279
0


6.170877
9.689534
0


6.389122
10.2164
0


6.581351
10.68475
0


6.748382
11.09418
0


6.890922
11.4452
0


7.009876
11.73917
0


7.106429
11.97835
0


7.182137
12.16589
0


7.212787
12.3138
0


7.170519
12.41041
0


7.122144
12.45611
0


7.077119
12.48026
0


7.034255
12.49283
0


6.976203
12.49661
0


6.887113
12.47291
0


6.793961
12.37932
0


6.709554
12.22397
0


6.60113
12.02625
0


6.467687
11.78323
0


6.308056
11.49303
0


6.121415
11.15449
0


5.907151
10.76722
0


5.665
10.33142
0


5.394887
9.847968
0


5.096725
9.318473
0


4.770802
8.74499
0


4.417087
8.130399
0


4.03543
7.478222
0


3.626444
6.792097
0


3.18995
6.076634
0


2.726055
5.33677
0


2.23529
4.577624
0


1.716353
3.805967
0


1.168802
3.028523
0


0.592508
2.25231
0


−0.01431
1.486174
0


−0.65349
0.739914
0


−1.32635
0.024112
0


−2.03815
−0.64463
0


−2.79155
−1.24867
0


−3.58469
−1.77066
0


−4.41014
−2.19472
0


−5.25629
−2.5055
0


−6.1066
−2.69039
0


−6.93936
−2.74469
0


−7.73132
−2.67891
0


−8.46428
−2.51513
0


−9.12885
−2.28317
0


−9.72349
−2.01159
0


−10.2526
−1.72644
0


−10.7233
−1.44884
0


−11.1426
−1.19422
0


−11.5149
−0.9717
0


−11.8441
−0.78831
0


−12.1319
−0.64743
0


−12.3798
−0.55231
0


−12.5871
−0.50492
0


−12.75
−0.50325
0


−12.8636
−0.53079
0


−16.2281
−0.49077
0.088496


−16.2736
−0.53091
0.088496


−16.3283
−0.60013
0.088496


−16.3811
−0.72559
0.088496


−16.3979
−0.91447
0.088496


−16.3564
−1.15864
0.088496


−16.2491
−1.44862
0.088496


−16.0749
−1.77861
0.088496


−15.8312
−2.14353
0.088496


−15.5153
−2.53758
0.088496


−15.1235
−2.95312
0.088496


−14.6523
−3.3809
0.088496


−14.0964
−3.80634
0.088496


−13.452
−4.21171
0.088496


−12.7176
−4.5758
0.088496


−11.8943
−4.87069
0.088496


−10.9904
−5.06949
0.088496


−10.0212
−5.1415
0.088496


−9.01077
−5.06309
0.088496


−7.9886
−4.82391
0.088496


−6.9838
−4.42643
0.088496


−6.01961
−3.88555
0.088496


−5.109
−3.22573
0.088496


−4.25737
−2.4719
0.088496


−3.46822
−1.64379
0.088496


−2.73988
−0.76141
0.088496


−2.06867
0.157688
0.088496


−1.4508
1.098772
0.088496


−0.88071
2.048073
0.088496


−0.35416
2.994321
0.088496


0.131669
3.928168
0.088496


0.580375
4.840737
0.088496


0.994739
5.724368
0.088496


1.377007
6.572354
0.088496


1.729014
7.37882
0.088496


2.05283
8.138434
0.088496


2.348929
8.847198
0.088496


2.618151
9.501616
0.088496


2.861245
10.09893
0.088496


3.078605
10.63727
0.088496


3.270516
11.11561
0.088496


3.437694
11.53358
0.088496


3.580644
11.8918
0.088496


3.700167
12.19171
0.088496


3.797337
12.43566
0.088496


3.873895
12.62678
0.088496


3.903782
12.77763
0.088496


3.860549
12.87589
0.088496


3.811265
12.92237
0.088496


3.765283
12.94669
0.088496


3.721533
12.95896
0.088496


3.662411
12.96164
0.088496


3.572549
12.93485
0.088496


3.480509
12.83699
0.088496


3.397026
12.67768
0.088496


3.288368
12.47565
0.088496


3.154806
12.22725
0.088496


2.995288
11.93048
0.088496


2.809117
11.58409
0.088496


2.595825
11.18758
0.088496


2.355333
10.74105
0.088496


2.087646
10.24536
0.088496


1.792936
9.701971
0.088496


1.471604
9.112897
0.088496


1.123954
8.480841
0.088496


0.750049
7.809214
0.088496


0.349922
7.101995
0.088496


−0.07658
6.363768
0.088496


−0.52906
5.599291
0.088496


−1.00773
4.814118
0.088496


−1.51427
4.015188
0.088496


−2.04916
3.209195
0.088496


−2.61405
2.404163
0.088496


−3.21223
1.610041
0.088496


−3.84564
0.836873
0.088496


−4.51674
0.096454
0.088496


−5.22729
−0.59817
0.088496


−5.97783
−1.23213
0.088496


−6.76907
−1.78591
0.088496


−7.59812
−2.23727
0.088496


−8.45353
−2.56782
0.088496


−9.31676
−2.7644
0.088496


−10.1636
−2.82537
0.088496


−10.9695
−2.76176
0.088496


−11.7158
−2.59865
0.088496


−12.3926
−2.36479
0.088496


−12.9977
−2.08895
0.088496


−13.534
−1.7951
0.088496


−14.0063
−1.50194
0.088496


−14.4212
−1.22473
0.088496


−14.7857
−0.97612
0.088496


−15.1055
−0.76495
0.088496


−15.3854
−0.59774
0.088496


−15.6277
−0.4784
0.088496


−15.8338
−0.41268
0.088496


−15.9991
−0.40106
0.088496


−16.1151
−0.42711
0.088496


−18.42
−0.42485
0.176991


−18.4639
−0.4673
0.176991


−18.5159
−0.53933
0.176991


−18.565
−0.66736
0.176991


−18.5798
−0.85782
0.176991


−18.5391
−1.10399
0.176991


−18.4353
−1.39761
0.176991


−18.2662
−1.73341
0.176991


−18.0294
−2.10663
0.176991


−17.7216
−2.51171
0.176991


−17.3388
−2.94127
0.176991


−16.8762
−3.38507
0.176991


−16.3284
−3.82912
0.176991


−15.6908
−4.25524
0.176991


−14.9603
−4.64015
0.176991


−14.1379
−4.95625
0.176991


−13.2295
−5.16592
0.176991


−12.2532
−5.23891
0.176991


−11.2362
−5.14938
0.176991


−10.2115
−4.88806
0.176991


−9.2104
−4.46063
0.176991


−8.25628
−3.88622
0.176991


−7.362
−3.19089
0.176991


−6.53321
−2.39985
0.176991


−5.76963
−1.53684
0.176991


−5.06827
−0.62224
0.176991


−4.42425
0.326245
0.176991


−3.83244
1.293653
0.176991


−3.28665
2.266491
0.176991


−2.78337
3.234314
0.176991


−2.31902
4.187653
0.176991


−1.88934
5.117585
0.176991


−1.49036
6.016138
0.176991


−1.12188
6.87766
0.176991


−0.78171
7.69621
0.176991


−0.46815
8.466684
0.176991


−0.18088
9.185168
0.176991


0.081087
9.848127
0.176991


0.318146
10.45296
0.176991


0.530632
10.99784
0.176991


0.718627
11.4818
0.176991


0.882739
11.90455
0.176991


1.023307
12.26675
0.176991


1.141029
12.56993
0.176991


1.236859
12.81648
0.176991


1.312603
13.00956
0.176991


1.340605
13.16192
0.176991


1.297454
13.26108
0.176991


1.248172
13.30828
0.176991


1.201891
13.33285
0.176991


1.157916
13.34489
0.176991


1.098561
13.34667
0.176991


1.009179
13.31726
0.176991


0.9194
13.21672
0.176991


0.838239
13.05554
0.176991


0.731799
12.85146
0.176991


0.601098
12.60046
0.176991


0.445179
12.3005
0.176991


0.263451
11.95026
0.176991


0.055561
11.54917
0.176991


−0.17842
11.09727
0.176991


−0.43848
10.59538
0.176991


−0.72424
10.04487
0.176991


−1.03531
9.447749
0.176991


−1.37127
8.806644
0.176991


−1.7321
8.124957
0.176991


−2.11594
7.405643
0.176991


−2.52413
6.65385
0.176991


−2.95678
5.874538
0.176991


−3.41427
5.073249
0.176991


−3.89876
4.25703
0.176991


−4.4105
3.432289
0.176991


−4.95174
2.607188
0.176991


−5.52626
1.791665
0.176991


−6.13569
0.995203
0.176991


−6.78316
0.229634
0.176991


−7.47332
−0.48974
0.176991


−8.2089
−1.14583
0.176991


−8.98875
−1.72104
0.176991


−9.80979
−2.19323
0.176991


−10.6614
−2.54173
0.176991


−11.5245
−2.75211
0.176991


−12.3735
−2.82236
0.176991


−13.1826
−2.7646
0.176991


−13.9324
−2.60483
0.176991


−14.6121
−2.37209
0.176991


−15.2191
−2.09497
0.176991


−15.7562
−1.79823
0.176991


−16.2285
−1.50139
0.176991


−16.6419
−1.219
0.176991


−17.002
−0.96159
0.176991


−17.3157
−0.73909
0.176991


−17.5877
−0.55742
0.176991


−17.8242
−0.42504
0.176991


−18.0273
−0.3484
0.176991


−18.1926
−0.33059
0.176991


−18.309
−0.35696
0.176991


−19.7523
−0.39184
0.265487


−19.7951
−0.43585
0.265487


−19.8452
−0.5096
0.265487


−19.8921
−0.63902
0.265487


−19.9056
−0.83035
0.265487


−19.8652
−1.07756
0.265487


−19.7625
−1.37293
0.265487


−19.5955
−1.7114
0.265487


−19.3614
−2.08838
0.265487


−19.0568
−2.49844
0.265487


−18.6777
−2.93436
0.265487


−18.2192
−3.38611
0.265487


−17.6758
−3.83987
0.265487


−17.0428
−4.27829
0.265487


−16.3154
−4.67591
0.265487


−15.4935
−5.00275
0.265487


−14.5838
−5.22306
0.265487


−13.6039
−5.30116
0.265487


−12.5831
−5.20858
0.265487


−11.5571
−4.93548
0.265487


−10.5595
−4.48912
0.265487


−9.61438
−3.89168
0.265487


−8.73435
−3.17122
0.265487


−7.92556
−2.35328
0.265487


−7.18278
−1.46629
0.265487


−6.5039
−0.52918
0.265487


−5.88289
0.439986
0.265487


−5.31344
1.425964
0.265487


−4.78929
2.415681
0.265487


−4.30707
3.399024
0.265487


−3.8623
4.366319
0.265487


−3.45062
5.308834
0.265487


−3.06947
6.219356
0.265487


−2.71718
7.091666
0.265487


−2.39134
7.919832
0.265487


−2.09064
8.698981
0.265487


−1.81474
9.42522
0.265487


−1.56261
10.09503
0.265487


−1.33407
10.70591
0.265487


−1.12885
11.25606
0.265487


−0.94699
11.74458
0.265487


−0.78798
12.1712
0.265487


−0.6516
12.53666
0.265487


−0.53724
12.84251
0.265487


−0.44405
13.0912
0.265487


−0.37032
13.28595
0.265487


−0.34397
13.43923
0.265487


−0.38526
13.53964
0.265487


−0.43367
13.58813
0.265487


−0.47983
13.61337
0.265487


−0.52382
13.62537
0.265487


−0.5832
13.62617
0.265487


−0.67131
13.59313
0.265487


−0.75728
13.4893
0.265487


−0.83568
13.32675
0.265487


−0.93855
13.12083
0.265487


−1.06479
12.86753
0.265487


−1.21528
12.56478
0.265487


−1.39053
12.21123
0.265487


−1.59085
11.80627
0.265487


−1.81606
11.3499
0.265487


−2.06616
10.84294
0.265487


−2.34072
10.28671
0.265487


−2.63928
9.683184
0.265487


−2.96147
9.034996
0.265487


−3.30719
8.345471
0.265487


−3.67581
7.61818
0.265487


−4.06827
6.857992
0.265487


−4.48394
6.069425
0.265487


−4.92424
5.258497
0.265487


−5.39079
4.43182
0.265487


−5.88406
3.595828
0.265487


−6.40651
2.758621
0.265487


−6.96248
1.930264
0.265487


−7.55397
1.120301
0.265487


−8.18354
0.33981
0.265487


−8.85577
−0.39648
0.265487


−9.57674
−1.06869
0.265487


−10.3468
−1.65716
0.265487


−11.1614
−2.14054
0.265487


−12.0089
−2.49917
0.265487


−12.8701
−2.71689
0.265487


−13.7185
−2.79338
0.265487


−14.5281
−2.74114
0.265487


−15.2786
−2.58496
0.265487


−15.9595
−2.35558
0.265487


−16.568
−2.08142
0.265487


−17.1063
−1.78704
0.265487


−17.5791
−1.49089
0.265487


−17.9919
−1.20752
0.265487


−18.3499
−0.94716
0.265487


−18.66
−0.71954
0.265487


−18.9258
−0.5289
0.265487


−19.1609
−0.39397
0.265487


−19.3624
−0.31307
0.265487


−19.5274
−0.2929
0.265487


−19.6434
−0.32064
0.265487


−20.5539
−0.37652
0.353982


−20.5953
−0.4222
0.353982


−20.6433
−0.49777
0.353982


−20.6877
−0.62867
0.353982


−20.6997
−0.82089
0.353982


−20.6592
−1.06914
0.353982


−20.5575
−1.36623
0.353982


−20.3921
−1.70723
0.353982


−20.16
−2.0876
0.353982


−19.8576
−2.50192
0.353982


−19.4808
−2.94292
0.353982


−19.0243
−3.40045
0.353982


−18.4833
−3.8617
0.353982


−17.8516
−4.3075
0.353982


−17.1242
−4.71227
0.353982


−16.3006
−5.04496
0.353982


−15.3877
−5.26851
0.353982


−14.4037
−5.34571
0.353982


−13.3792
−5.247
0.353982


−12.3516
−4.96283
0.353982


−11.3558
−4.50166
0.353982


−10.4155
−3.88819
0.353982


−9.54274
−3.15157
0.353982


−8.74483
−2.31641
0.353982


−8.01449
−1.41297
0.353982


−7.348
−0.46114
0.353982


−6.73938
0.521474
0.353982


−6.18166
1.519547
0.353982


−5.66897
2.520469
0.353982


−5.19789
3.514231
0.353982


−4.76327
4.490964
0.353982


−4.36071
5.442043
0.353982


−3.98806
6.360499
0.353982


−3.64331
7.240006
0.353982


−3.32393
8.074639
0.353982


−3.02895
8.859677
0.353982


−2.75792
9.59118
0.353982


−2.50983
10.26566
0.353982


−2.28465
10.88067
0.353982


−2.08215
11.43442
0.353982


−1.90247
11.92605
0.353982


−1.74516
12.35531
0.353982


−1.61008
12.72298
0.353982


−1.49672
13.03065
0.353982


−1.40425
13.28078
0.353982


−1.33117
13.47669
0.353982


−1.30697
13.63098
0.353982


−1.34839
13.73182
0.353982


−1.39666
13.78085
0.353982


−1.44286
13.80648
0.353982


−1.48685
13.81863
0.353982


−1.54629
13.81937
0.353982


−1.63424
13.78563
0.353982


−1.71986
13.68134
0.353982


−1.7976
13.51826
0.353982


−1.89902
13.31137
0.353982


−2.02342
13.05684
0.353982


−2.17166
12.75261
0.353982


−2.34422
12.39728
0.353982


−2.54138
11.99026
0.353982


−2.76285
11.53149
0.353982


−3.0087
11.02182
0.353982


−3.27843
10.46253
0.353982


−3.57157
9.855601
0.353982


−3.88776
9.203649
0.353982


−4.22688
8.509983
0.353982


−4.58836
7.778194
0.353982


−4.97311
7.013108
0.353982


−5.38091
6.219422
0.353982


−5.81246
5.40275
0.353982


−6.2702
4.57006
0.353982


−6.75449
3.7277
0.353982


−7.26763
2.883582
0.353982


−7.8144
2.047915
0.353982


−8.39699
1.230277
0.353982


−9.01799
0.441699
0.353982


−9.68139
−0.30391
0.353982


−10.3932
−0.98722
0.353982


−11.1559
−1.58654
0.353982


−11.9663
−2.07874
0.353982


−12.8108
−2.44667
0.353982


−13.6705
−2.67426
0.353982


−14.519
−2.75948
0.353982


−15.3299
−2.71709
0.353982


−16.0833
−2.57087
0.353982


−16.7678
−2.35018
0.353982


−17.38
−2.08285
0.353982


−17.9212
−1.79231
0.353982


−18.3954
−1.49753
0.353982


−18.808
−1.21308
0.353982


−19.1649
−0.95049
0.353982


−19.4728
−0.71933
0.353982


−19.7371
−0.52588
0.353982


−19.9677
−0.38306
0.353982


−20.1668
−0.29588
0.353982


−20.3316
−0.27255
0.353982


−20.4474
−0.30163
0.353982


−20.3319
−0.38536
0.442478


−20.3713
−0.43257
0.442478


−20.4164
−0.50975
0.442478


−20.4572
−0.64154
0.442478


−20.4672
−0.83348
0.442478


−20.4275
−1.08134
0.442478


−20.3288
−1.37875
0.442478


−20.1679
−1.72105
0.442478


−19.9416
−2.10384
0.442478


−19.6456
−2.52146
0.442478


−19.2756
−2.96671
0.442478


−18.8263
−3.42946
0.442478


−18.2909
−3.89496
0.442478


−17.6638
−4.34453
0.442478


−16.94
−4.75223
0.442478


−16.1187
−5.08577
0.442478


−15.2068
−5.3054
0.442478


−14.2239
−5.37034
0.442478


−13.2037
−5.25157
0.442478


−12.1851
−4.9441
0.442478


−11.2026
−4.46031
0.442478


−10.2788
−3.82616
0.442478


−9.42444
−3.07188
0.442478


−8.64198
−2.22542
0.442478


−7.92808
−1.31194
0.442478


−7.2779
−0.35176
0.442478


−6.68477
0.637535
0.442478


−6.14077
1.640504
0.442478


−5.64053
2.645146
0.442478


−5.1809
3.641787
0.442478


−4.75619
4.620494
0.442478


−4.36299
5.573203
0.442478


−3.99942
6.493117
0.442478


−3.66251
7.373596
0.442478


−3.3499
8.208845
0.442478


−3.06099
8.994311
0.442478


−2.79509
9.726005
0.442478


−2.55141
10.40053
0.442478


−2.32992
11.01546
0.442478


−2.13056
11.56907
0.442478


−1.95347
12.0605
0.442478


−1.79824
12.48953
0.442478


−1.66484
12.85697
0.442478


−1.5528
13.1644
0.442478


−1.46135
13.41433
0.442478


−1.38929
13.61017
0.442478


−1.36818
13.76458
0.442478


−1.41014
13.86497
0.442478


−1.45808
13.91413
0.442478


−1.50399
13.94003
0.442478


−1.54765
13.95241
0.442478


−1.60674
13.95344
0.442478


−1.69425
13.92012
0.442478


−1.78013
13.81707
0.442478


−1.85723
13.65487
0.442478


−1.95681
13.44859
0.442478


−2.07892
13.19481
0.442478


−2.22443
12.89146
0.442478


−2.39378
12.53717
0.442478


−2.58726
12.13134
0.442478


−2.80457
11.6739
0.442478


−3.0458
11.16571
0.442478


−3.31054
10.60809
0.442478


−3.59832
10.00299
0.442478


−3.90903
9.353127
0.442478


−4.24176
8.661411
0.442478


−4.59475
7.930828
0.442478


−4.9701
7.1667
0.442478


−5.36862
6.374194
0.442478


−5.79135
5.559036
0.442478


−6.23927
4.727376
0.442478


−6.71335
3.88578
0.442478


−7.21515
3.041633
0.442478


−7.74973
2.205078
0.442478


−8.31968
1.385777
0.442478


−8.92633
0.593516
0.442478


−9.57611
−0.15614
0.442478


−10.275
−0.84433
0.442478


−11.0226
−1.45366
0.442478


−11.8159
−1.9629
0.442478


−12.6451
−2.35141
0.442478


−13.493
−2.60176
0.442478


−14.3338
−2.70975
0.442478


−15.1408
−2.688
0.442478


−15.8927
−2.5593
0.442478


−16.5775
−2.35367
0.442478


−17.1905
−2.09816
0.442478


−17.732
−1.81604
0.442478


−18.2056
−1.52632
0.442478


−18.616
−1.24387
0.442478


−18.9692
−0.9806
0.442478


−19.2728
−0.74761
0.442478


−19.5329
−0.55181
0.442478


−19.7569
−0.40165
0.442478


−19.9511
−0.30703
0.442478


−20.1139
−0.27744
0.442478


−20.2289
−0.30689
0.442478


−19.5066
−0.4278
0.530974


−19.5437
−0.4762
0.530974


−19.5858
−0.55422
0.530974


−19.6235
−0.68571
0.530974


−19.6324
−0.87609
0.530974


−19.5945
−1.12209
0.530974


−19.5002
−1.41818
0.530974


−19.3452
−1.75971
0.530974


−19.1248
−2.14163
0.530974


−18.8344
−2.55794
0.530974


−18.4699
−3.0014
0.530974


−18.0263
−3.46211
0.530974


−17.4978
−3.92641
0.530974


−16.8774
−4.37424
0.530974


−16.1604
−4.7799
0.530974


−15.345
−5.10794
0.530974


−14.4385
−5.31612
0.530974


−13.463
−5.36628
0.530974


−12.4537
−5.23014
0.530974


−11.4499
−4.90511
0.530974


−10.4875
−4.40202
0.530974


−9.58793
−3.74994
0.530974


−8.75849
−2.98231
0.530974


−7.99981
−2.12736
0.530974


−7.30981
−1.20784
0.530974


−6.68326
−0.24366
0.530974


−6.1121
0.747304
0.530974


−5.58879
1.750426
0.530974


−5.10963
2.754852
0.530974


−4.66984
3.750336
0.530974


−4.26265
4.726759
0.530974


−3.88447
5.676214
0.530974


−3.53405
6.592324
0.530974


−3.20909
7.468845
0.530974


−2.90744
8.300148
0.530974


−2.62863
9.081798
0.530974


−2.37172
9.809762
0.530974


−2.1361
10.48077
0.530974


−1.92176
11.09241
0.530974


−1.72872
11.64302
0.530974


−1.55709
12.13174
0.530974


−1.40654
12.55837
0.530974


−1.27709
12.92373
0.530974


−1.16828
13.22941
0.530974


−1.07947
13.47792
0.530974


−1.00987
13.67278
0.530974


−0.99191
13.82628
0.530974


−1.03286
13.92608
0.530974


−1.07958
13.97561
0.530974


−1.12469
14.00204
0.530974


−1.16766
14.01478
0.530974


−1.22601
14.01609
0.530974


−1.31225
13.9826
0.530974


−1.39666
13.8805
0.530974


−1.47224
13.72001
0.530974


−1.56823
13.51513
0.530974


−1.68596
13.26309
0.530974


−1.82627
12.96185
0.530974


−1.98963
12.61005
0.530974


−2.17626
12.20709
0.530974


−2.38597
11.75294
0.530974


−2.61894
11.2485
0.530974


−2.87476
10.69504
0.530974


−3.15275
10.09442
0.530974


−3.45223
9.449029
0.530974


−3.77357
8.76232
0.530974


−4.1153
8.037382
0.530974


−4.47842
7.278913
0.530974


−4.86332
6.491782
0.530974


−5.2705
5.681322
0.530974


−5.70295
4.854545
0.530974


−6.16203
4.018152
0.530974


−6.64817
3.178763
0.530974


−7.16599
2.346022
0.530974


−7.71889
1.529839
0.530974


−8.30801
0.739666
0.530974


−8.93865
−0.01042
0.530974


−9.6163
−0.70297
0.530974


−10.342
−1.32007
0.530974


−11.1133
−1.84156
0.530974


−11.9228
−2.24532
0.530974


−12.7537
−2.51368
0.530974


−13.5807
−2.64327
0.530974


−14.378
−2.64329
0.530974


−15.1239
−2.53576
0.530974


−15.8046
−2.34779
0.530974


−16.4146
−2.10679
0.530974


−16.9531
−1.83501
0.530974


−17.4221
−1.55098
0.530974


−17.8263
−1.27045
0.530974


−18.1721
−1.00638
0.530974


−18.4686
−0.77177
0.530974


−18.7232
−0.57543
0.530974


−18.9442
−0.4265
0.530974


−19.136
−0.33232
0.530974


−19.2976
−0.30906
0.530974


−19.4094
−0.34474
0.530974


−18.6023
−0.46622
0.59292


−18.6366
−0.51597
0.59292


−18.6755
−0.59471
0.59292


−18.7106
−0.72563
0.59292


−18.7186
−0.91432
0.59292


−18.6815
−1.15816
0.59292


−18.5891
−1.45186
0.59292


−18.4365
−1.79075
0.59292


−18.2198
−2.17017
0.59292


−17.9344
−2.58432
0.59292


−17.575
−3.02521
0.59292


−17.136
−3.48234
0.59292


−16.6115
−3.94153
0.59292


−15.9954
−4.38332
0.59292


−15.2823
−4.78047
0.59292


−14.472
−5.09997
0.59292


−13.5724
−5.30024
0.59292


−12.6054
−5.3417
0.59292


−11.6068
−5.19521
0.59292


−10.6174
−4.85772
0.59292


−9.67112
−4.34533
0.59292


−8.78867
−3.68701
0.59292


−7.97792
−2.91449
0.59292


−7.23863
−2.05642
0.59292


−6.56728
−1.13611
0.59292


−5.95834
−0.17307
0.59292


−5.40348
0.815201
0.59292


−4.89517
1.814467
0.59292


−4.42951
2.814075
0.59292


−4.00189
3.804071
0.59292


−3.60635
4.774888
0.59292


−3.23972
5.718898
0.59292


−2.90038
6.629657
0.59292


−2.58524
7.500718
0.59292


−2.29257
8.3267
0.59292


−2.02196
9.103236
0.59292


−1.77238
9.826321
0.59292


−1.54334
10.49276
0.59292


−1.33486
11.1002
0.59292


−1.14705
11.64701
0.59292


−0.97993
12.13231
0.59292


−0.8333
12.55595
0.59292


−0.70715
12.91874
0.59292


−0.60107
13.22224
0.59292


−0.51449
13.469
0.59292


−0.44703
13.66262
0.59292


−0.43167
13.81498
0.59292


−0.47189
13.91404
0.59292


−0.5175
13.96375
0.59292


−0.56181
13.99059
0.59292


−0.6041
14.00368
0.59292


−0.66174
14.00537
0.59292


−0.74687
13.97219
0.59292


−0.83039
13.87141
0.59292


−0.90476
13.71273
0.59292


−0.99793
13.50958
0.59292


−1.11222
13.25968
0.59292


−1.24846
12.961
0.59292


−1.40709
12.61223
0.59292


−1.58835
12.21275
0.59292


−1.79202
11.76252
0.59292


−2.01809
11.26235
0.59292


−2.26619
10.71352
0.59292


−2.53587
10.11794
0.59292


−2.82697
9.478221
0.59292


−3.13972
8.797683
0.59292


−3.47327
8.07967
0.59292


−3.82763
7.328352
0.59292


−4.20464
6.549232
0.59292


−4.60461
5.747492
0.59292


−5.02839
4.928998
0.59292


−5.4776
4.100423
0.59292


−5.95437
3.269241
0.59292


−6.46163
2.443998
0.59292


−7.00274
1.634343
0.59292


−7.57944
0.849898
0.59292


−8.19583
0.103466
0.59292


−8.8575
−0.58812
0.59292


−9.56596
−1.20739
0.59292


−10.3197
−1.73437
0.59292


−11.1121
−2.14715
0.59292


−11.9269
−2.4298
0.59292


−12.7412
−2.57479
0.59292


−13.5286
−2.59188
0.59292


−14.2674
−2.50097
0.59292


−14.9435
−2.32894
0.59292


−15.5502
−2.10138
0.59292


−16.0861
−1.84085
0.59292


−16.5529
−1.56616
0.59292


−16.9545
−1.2922
0.59292


−17.2983
−1.03419
0.59292


−17.5922
−0.80373
0.59292


−17.8428
−0.60857
0.59292


−18.0569
−0.45559
0.59292


−18.2444
−0.35939
0.59292


−18.4041
−0.33607
0.59292


−18.5123
−0.37745
0.59292


−17.5321
−0.50149
0.646018


−17.5628
−0.55278
0.646018


−17.5977
−0.63234
0.646018


−17.6297
−0.76256
0.646018


−17.6369
−0.94926
0.646018


−17.6006
−1.19055
0.646018


−17.5097
−1.48131
0.646018


−17.3595
−1.81689
0.646018


−17.1467
−2.19317
0.646018


−16.8678
−2.60527
0.646018


−16.5148
−3.04346
0.646018


−16.0817
−3.49689
0.646018


−15.563
−3.95144
0.646018


−14.9533
−4.3883
0.646018


−14.2464
−4.77901
0.646018


−13.4424
−5.08918
0.646018


−12.5507
−5.27955
0.646018


−11.5936
−5.30884
0.646018


−10.6081
−5.14836
0.646018


−9.6358
−4.79571
0.646018


−8.70834
−4.27304
0.646018


−7.84463
−3.60944
0.646018


−7.05277
−2.83457
0.646018


−6.33212
−1.97652
0.646018


−5.67833
−1.05855
0.646018


−5.08501
−0.10008
0.646018


−4.54416
0.882142
0.646018


−4.04915
1.874711
0.646018


−3.59629
2.867261
0.646018


−3.18006
3.849612
0.646018


−2.79534
4.812731
0.646018


−2.43893
5.749093
0.646018


−2.10892
6.65224
0.646018


−1.8021
7.515785
0.646018


−1.51713
8.334559
0.646018


−1.25355
9.104239
0.646018


−1.01029
9.820864
0.646018


−0.78696
10.48131
0.646018


−0.5836
11.08325
0.646018


−0.40037
11.6251
0.646018


−0.23725
12.10598
0.646018


−0.09409
12.52575
0.646018


0.02912
12.88522
0.646018


0.132738
13.18595
0.646018


0.217315
13.43045
0.646018


0.282732
13.62245
0.646018


0.295513
13.77342
0.646018


0.255789
13.87145
0.646018


0.21121
13.92112
0.646018


0.167745
13.94827
0.646018


0.126322
13.96169
0.646018


0.069661
13.96397
0.646018


−0.01429
13.93192
0.646018


−0.09739
13.83361
0.646018


−0.17052
13.67755
0.646018


−0.26078
13.47714
0.646018


−0.37154
13.23063
0.646018


−0.50359
12.93603
0.646018


−0.65741
12.59204
0.646018


−0.83331
12.19811
0.646018


−1.03108
11.7542
0.646018


−1.25059
11.26104
0.646018


−1.49159
10.71996
0.646018


−1.75381
10.13289
0.646018


−2.03873
9.503145
0.646018


−2.34466
8.833125
0.646018


−2.67191
8.126638
0.646018


−3.02171
7.388382
0.646018


−3.39334
6.622575
0.646018


−3.78585
5.83369
0.646018


−4.20103
5.027925
0.646018


−4.6409
4.212048
0.646018


−5.10682
3.392951
0.646018


−5.60118
2.57863
0.646018


−6.1269
1.778087
0.646018


−6.6878
1.002045
0.646018


−7.28939
0.264222
0.646018


−7.93808
−0.41783
0.646018


−8.63197
−1.03008
0.646018


−9.3722
−1.54937
0.646018


−10.1509
−1.95403
0.646018


−10.9496
−2.23309
0.646018


−11.7462
−2.3849
0.646018


−12.5184
−2.41655
0.646018


−13.2464
−2.34311
0.646018


−13.9147
−2.18571
0.646018


−14.5142
−1.96863
0.646018


−15.042
−1.71606
0.646018


−15.5013
−1.4487
0.646018


−15.8984
−1.18304
0.646018


−16.2392
−0.933
0.646018


−16.5336
−0.71332
0.646018


−16.7867
−0.53027
0.646018


−17.0032
−0.38992
0.646018


−17.2004
−0.32331
0.646018


−17.3569
−0.34356
0.646018


−17.4525
−0.40583
0.646018


−16.2716
−0.5439
0.707964


−16.298
−0.59657
0.707964


−16.3282
−0.67669
0.707964


−16.3567
−0.80575
0.707964


−16.3631
−0.98977
0.707964


−16.3278
−1.22765
0.707964


−16.2392
−1.51449
0.707964


−16.092
−1.84562
0.707964


−15.8853
−2.2182
0.707964


−15.6129
−2.62591
0.707964


−15.268
−3.06019
0.707964


−14.8426
−3.50843
0.707964


−14.3308
−3.95585
0.707964


−13.7279
−4.38336
0.707964


−13.0289
−4.76383
0.707964


−12.2342
−5.06315
0.707964


−11.3533
−5.24064
0.707964


−10.4097
−5.25547
0.707964


−9.44115
−5.08179
0.707964


−8.48799
−4.72056
0.707964


−7.58283
−4.19001
0.707964


−6.74321
−3.52117
0.707964


−5.97456
−2.74569
0.707964


−5.27563
−1.8907
0.707964


−4.6427
−0.97799
0.707964


−4.06859
−0.0269
0.707964


−3.54551
0.946517
0.707964


−3.06642
1.929045
0.707964


−2.62775
2.910675
0.707964


−2.22393
3.881492
0.707964


−1.85057
4.832971
0.707964


−1.50438
5.757694
0.707964


−1.18384
6.649469
0.707964


−0.88569
7.502002
0.707964


−0.60891
8.31033
0.707964


−0.35291
9.07015
0.707964


−0.11663
9.777563
0.707964


0.100294
10.42951
0.707964


0.297831
11.02371
0.707964


0.475803
11.55859
0.707964


0.634268
12.03328
0.707964


0.773344
12.44766
0.707964


0.893055
12.8025
0.707964


0.993714
13.09938
0.707964


1.075838
13.34076
0.707964


1.138666
13.53054
0.707964


1.148577
13.67953
0.707964


1.10974
13.77625
0.707964


1.066534
13.82585
0.707964


1.024198
13.8534
0.707964


0.984273
13.86716
0.707964


0.929373
13.87045
0.707964


0.847346
13.84101
0.707964


0.764649
13.74748
0.707964


0.693084
13.59643
0.707964


0.606923
13.40143
0.707964


0.501177
13.1616
0.707964


0.37494
12.87505
0.707964


0.227731
12.54054
0.707964


0.059125
12.15759
0.707964


−0.13109
11.72634
0.707964


−0.34312
11.24764
0.707964


−0.57718
10.72299
0.707964


−0.83262
10.1541
0.707964


−1.10875
9.543214
0.707964


−1.40551
8.893381
0.707964


−1.72392
8.208638
0.707964


−2.06451
7.493243
0.707964


−2.42731
6.751632
0.707964


−2.81096
5.987967
0.707964


−3.21584
5.207604
0.707964


−3.64362
4.416908
0.707964


−4.09772
3.623716
0.707964


−4.58058
2.835963
0.707964


−5.09632
2.063407
0.707964


−5.64755
1.315998
0.707964


−6.23661
0.604902
0.707964


−6.86617
−0.0563
0.707964


−7.53868
−0.65072
0.707964


−8.25436
−1.15803
0.707964


−9.00703
−1.5573
0.707964


−9.78181
−1.83264
0.707964


−10.5572
−1.97571
0.707964


−11.3078
−1.9949
0.707964


−12.0124
−1.9096
0.707964


−12.6578
−1.74791
0.707964


−13.2389
−1.53775
0.707964


−13.7573
−1.30471
0.707964


−14.2173
−1.06899
0.707964


−14.6232
−0.8446
0.707964


−14.9795
−0.64186
0.707964


−15.2909
−0.46872
0.707964


−15.5625
−0.33467
0.707964


−15.8012
−0.25712
0.707964


−16.0012
−0.27859
0.707964


−16.1312
−0.36104
0.707964


−16.2057
−0.4427
0.707964


−15.0461
−0.58771
0.769912


−15.0681
−0.64139
0.769912


−15.0932
−0.72181
0.769912


−15.1172
−0.84952
0.769912


−15.1243
−1.0306
0.769912


−15.0965
−1.26637
0.769912


−15.0219
−1.55451
0.769912


−14.8875
−1.88855
0.769912


−14.6847
−2.25978
0.769912


−14.4096
−2.66004
0.769912


−14.0606
−3.08229
0.769912


−13.6347
−3.51814
0.769912


−13.1262
−3.95434
0.769912


−12.5285
−4.37048
0.769912


−11.836
−4.73857
0.769912


−11.0491
−5.02305
0.769912


−10.1788
−5.18243
0.769912


−9.25033
−5.1855
0.769912


−8.29892
−5.00624
0.769912


−7.36356
−4.64332
0.769912


−6.47719
−4.11295
0.769912


−5.65689
−3.44666
0.769912


−4.90723
−2.67628
0.769912


−4.22682
−1.82832
0.769912


−3.6117
−0.9243
0.769912


−3.05398
0.016514
0.769912


−2.54617
0.978634
0.769912


−2.08156
1.949316
0.769912


−1.65649
2.918721
0.769912


−1.26541
3.877142
0.769912


−0.90104
4.815096
0.769912


−0.5635
5.726692
0.769912


−0.25075
6.605635
0.769912


0.039375
7.446125
0.769912


0.308599
8.243018
0.769912


0.557457
8.992109
0.769912


0.787
9.689566
0.769912


0.997523
10.3324
0.769912


1.18913
10.91832
0.769912


1.361665
11.44579
0.769912


1.515227
11.91392
0.769912


1.649932
12.32261
0.769912


1.765852
12.67259
0.769912


1.863273
12.96542
0.769912


1.942643
13.20356
0.769912


2.002434
13.39106
0.769912


2.009591
13.53788
0.769912


1.972203
13.63342
0.769912


1.930708
13.68316
0.769912


1.889714
13.7113
0.769912


1.851648
13.72548
0.769912


1.798928
13.72976
0.769912


1.719489
13.70263
0.769912


1.637983
13.61458
0.769912


1.568329
13.46967
0.769912


1.487499
13.28119
0.769912


1.388195
13.04943
0.769912


1.269286
12.77267
0.769912


1.130137
12.44981
0.769912


0.970155
12.08045
0.769912


0.788016
11.66523
0.769912


0.582164
11.20557
0.769912


0.351376
10.70341
0.769912


0.097276
10.15998
0.769912


−0.17772
9.576648
0.769912


−0.46974
8.954556
0.769912


−0.78248
8.298883
0.769912


−1.11944
7.615209
0.769912


−1.4794
6.907259
0.769912


−1.86058
6.178832
0.769912


−2.26191
5.434388
0.769912


−2.68526
4.680272
0.769912


−3.13456
3.924508
0.769912


−3.61397
3.176042
0.769912


−4.12703
2.44445
0.769912


−4.67512
1.738966
0.769912


−5.2591
1.069667
0.769912


−5.88244
0.451002
0.769912


−6.54693
−0.10031
0.769912


−7.25051
−0.56631
0.769912


−7.98574
−0.9291
0.769912


−8.7389
−1.17183
0.769912


−9.48751
−1.28964
0.769912


−10.2085
−1.28893
0.769912


−10.883
−1.18669
0.769912


−11.4974
−1.00938
0.769912


−12.0489
−0.79158
0.769912


−12.5441
−0.56305
0.769912


−12.9935
−0.3476
0.769912


−13.4114
−0.17416
0.769912


−13.8032
−0.06734
0.769912


−14.1568
−0.04401
0.769912


−14.4484
−0.09417
0.769912


−14.6687
−0.18809
0.769912


−14.8241
−0.29723
0.769912


−14.9269
−0.40089
0.769912


−14.9901
−0.48571
0.769912


−14.1184
−0.6264
0.823009


−14.1409
−0.6795
0.823009


−14.165
−0.75988
0.823009


−14.1864
−0.88724
0.823009


−14.1884
−1.06693
0.823009


−14.1539
−1.29881
0.823009


−14.0703
−1.5792
0.823009


−13.9311
−1.90422
0.823009


−13.7307
−2.26904
0.823009


−13.4638
−2.66647
0.823009


−13.1243
−3.08682
0.823009


−12.7056
−3.51854
0.823009


−12.201
−3.94646
0.823009


−11.6053
−4.34968
0.823009


−10.9156
−4.70152
0.823009


−10.135
−4.97002
0.823009


−9.27549
−5.11994
0.823009


−8.35995
−5.11601
0.823009


−7.42293
−4.93382
0.823009


−6.50249
−4.57175
0.823009


−5.6291
−4.04757
0.823009


−4.82097
−3.38906
0.823009


−4.08177
−2.62885
0.823009


−3.41071
−1.79232
0.823009


−2.80336
−0.90095
0.823009


−2.25218
0.026479
0.823009


−1.75029
0.97503
0.823009


−1.2919
1.932502
0.823009


−0.87275
2.888817
0.823009


−0.48706
3.834262
0.823009


−0.13189
4.761137
0.823009


0.195969
5.66223
0.823009


0.499523
6.530996
0.823009


0.781927
7.361375
0.823009


1.043697
8.148727
0.823009


1.285722
8.88879
0.823009


1.50909
9.577782
0.823009


1.714029
10.21278
0.823009


1.900617
10.79153
0.823009


2.068666
11.31254
0.823009


2.218308
11.77492
0.823009


2.349602
12.17857
0.823009


2.46264
12.52424
0.823009


2.557636
12.81347
0.823009


2.635028
13.04867
0.823009


2.69279
13.23401
0.823009


2.697119
13.37895
0.823009


2.660027
13.47315
0.823009


2.619591
13.52259
0.823009


2.579608
13.551
0.823009


2.543032
13.56528
0.823009


2.492192
13.57089
0.823009


2.414515
13.54809
0.823009


2.332237
13.46609
0.823009


2.263499
13.3267
0.823009


2.185564
13.14445
0.823009


2.089846
12.92033
0.823009


1.975169
12.65273
0.823009


1.840887
12.34058
0.823009


1.68633
11.98356
0.823009


1.509992
11.58236
0.823009


1.310156
11.13848
0.823009


1.085129
10.65404
0.823009


0.836357
10.1303
0.823009


0.566533
9.568414
0.823009


0.273085
8.972532
0.823009


−0.04227
8.345206
0.823009


−0.38323
7.6922
0.823009


−0.74951
7.017669
0.823009


−1.13767
6.324356
0.823009


−1.54342
5.614774
0.823009


−1.96868
4.895173
0.823009


−2.41794
4.1738
0.823009


−2.89767
3.46094
0.823009


−3.41326
2.767549
0.823009


−3.96907
2.105933
0.823009


−4.5679
1.489791
0.823009


−5.20997
0.934067
0.823009


−5.89189
0.454372
0.823009


−6.60616
0.066071
0.823009


−7.34077
−0.21751
0.823009


−8.08014
−0.39019
0.823009


−8.80672
−0.45294
0.823009


−9.50119
−0.42
0.823009


−10.1491
−0.31519
0.823009


−10.7474
−0.17297
0.823009


−11.3018
−0.02652
0.823009


−11.8188
0.095687
0.823009


−12.2993
0.169576
0.823009


−12.735
0.180004
0.823009


−13.1095
0.127166
0.823009


−13.4073
0.027831
0.823009


−13.6286
−0.09162
0.823009


−13.7932
−0.21572
0.823009


−13.9159
−0.33598
0.823009


−14.0023
−0.44087
0.823009


−14.0585
−0.52189
0.823009


−13.8594
−0.62186
0.853496


−13.8773
−0.6799
0.853496


−13.8963
−0.76246
0.853496


−13.9121
−0.88862
0.853496


−13.912
−1.06544
0.853496


−13.8825
−1.29396
0.853496


−13.8118
−1.57089
0.853496


−13.6901
−1.89412
0.853496


−13.5066
−2.25973
0.853496


−13.2477
−2.65675
0.853496


−12.9026
−3.07032
0.853496


−12.4683
−3.48863
0.853496


−11.9468
−3.90004
0.853496


−11.3394
−4.28846
0.853496


−10.6473
−4.63387
0.853496


−9.87191
−4.90511
0.853496


−9.02088
−5.0658
0.853496


−8.1138
−5.07533
0.853496


−7.17867
−4.90825
0.853496


−6.25551
−4.55971
0.853496


−5.3805
−4.04803
0.853496


−4.57127
−3.39923
0.853496


−3.834
−2.64512
0.853496


−3.16662
−1.81321
0.853496


−2.56423
−0.92571
0.853496


−2.01684
−0.00296
0.853496


−1.51818
0.940614
0.853496


−1.06378
1.893296
0.853496


−0.64692
2.844169
0.853496


−0.26388
3.784601
0.853496


0.088309
4.706381
0.853496


0.412271
5.602716
0.853496


0.709296
6.467436
0.853496


0.982837
7.294451
0.853496


1.235316
8.078757
0.853496


1.469582
8.815724
0.853496


1.686747
9.501598
0.853496


1.88701
10.13323
0.853496


2.069567
10.70731
0.853496


2.234377
11.22423
0.853496


2.381277
11.68306
0.853496


2.510286
12.08371
0.853496


2.621422
12.42691
0.853496


2.714811
12.71418
0.853496


2.790873
12.94787
0.853496


2.847332
13.13217
0.853496


2.850759
13.27632
0.853496


2.814243
13.37006
0.853496


2.774522
13.41959
0.853496


2.735215
13.44828
0.853496


2.699564
13.46269
0.853496


2.649938
13.46892
0.853496


2.573209
13.44778
0.853496


2.491122
13.36867
0.853496


2.422864
13.23217
0.853496


2.346789
13.05315
0.853496


2.253553
12.83307
0.853496


2.141982
12.57039
0.853496


2.011591
12.26413
0.853496


1.862002
11.91389
0.853496


1.693111
11.51922
0.853496


1.501185
11.08147
0.853496


1.284693
10.60393
0.853496


1.04345
10.08838
0.853496


0.778128
9.536725
0.853496


0.484837
8.95323
0.853496


0.166704
8.340025
0.853496


−0.17729
7.701694
0.853496


−0.54692
7.042703
0.853496


−0.93884
6.365949
0.853496


−1.34853
5.673581
0.853496


−1.77688
4.9706
0.853496


−2.23095
4.265411
0.853496


−2.71571
3.570369
0.853496


−3.23506
2.898908
0.853496


−3.79655
2.267241
0.853496


−4.4166
1.681795
0.853496


−5.08571
1.171389
0.853496


−5.7966
0.752826
0.853496


−6.53476
0.439336
0.853496


−7.28954
0.234864
0.853496


−8.02294
0.139589
0.853496


−8.73498
0.135702
0.853496


−9.41536
0.201507
0.853496


−10.0551
0.307372
0.853496


−10.6547
0.420995
0.853496


−11.2191
0.512426
0.853496


−11.7482
0.553169
0.853496


−12.231
0.528951
0.853496


−12.6487
0.44009
0.853496


−12.9878
0.304258
0.853496


−13.2456
0.147268
0.853496


−13.4349
−0.00966
0.853496


−13.5819
−0.16601
0.853496


−13.6915
−0.31056
0.853496


−13.765
−0.42698
0.853496


−13.8112
−0.51242
0.853496


−14.102
−0.57233
0.884956


−14.1175
−0.66916
0.884956


−14.1286
−0.77334
0.884956


−14.1349
−0.89198
0.884956


−14.1329
−1.06627
0.884956


−14.1115
−1.29009
0.884956


−14.0571
−1.56348
0.884956


−13.9535
−1.88173
0.884956


−13.7837
−2.2393
0.884956


−13.5317
−2.62585
0.884956


−13.1857
−3.02885
0.884956


−12.744
−3.43383
0.884956


−12.2137
−3.83092
0.884956


−11.5984
−4.20706
0.884956


−10.9022
−4.54745
0.884956


−10.1259
−4.82689
0.884956


−9.27336
−5.01093
0.884956


−8.36119
−5.06008
0.884956


−7.41377
−4.93943
0.884956


−6.47439
−4.6326
0.884956


−5.57784
−4.15201
0.884956


−4.74485
−3.52778
0.884956


−3.98279
−2.79243
0.884956


−3.29114
−1.97449
0.884956


−2.66703
−1.09634
0.884956


−2.10215
−0.1787
0.884956


−1.58976
0.762788
0.884956


−1.12462
1.71563
0.884956


−0.70039
2.668376
0.884956


−0.30967
3.610499
0.884956


0.050174
4.534371
0.884956


0.380273
5.433534
0.884956


0.680526
6.302265
0.884956


0.954147
7.134503
0.884956


1.206189
7.924034
0.884956


1.44043
8.665671
0.884956


1.657845
9.3557
0.884956


1.85863
9.991228
0.884956


2.041773
10.57035
0.884956


2.207115
11.09157
0.884956


2.354435
11.55411
0.884956


2.483762
11.95789
0.884956


2.595141
12.30366
0.884956


2.688714
12.59299
0.884956


2.764824
12.82831
0.884956


2.820981
13.01392
0.884956


2.825517
13.15887
0.884956


2.790235
13.2535
0.884956


2.751071
13.30401
0.884956


2.711987
13.33356
0.884956


2.676461
13.34847
0.884956


2.626872
13.35521
0.884956


2.549729
13.33409
0.884956


2.468467
13.25504
0.884956


2.400387
13.11875
0.884956


2.325277
12.93945
0.884956


2.233083
12.71894
0.884956


2.12241
12.45574
0.884956


1.99261
12.1488
0.884956


1.843025
11.79779
0.884956


1.673627
11.40277
0.884956


1.479484
10.96656
0.884956


1.259336
10.49108
0.884956


1.012364
9.978687
0.884956


0.737962
9.432249
0.884956


0.43593
8.85498
0.884956


0.106279
8.250296
0.884956


−0.25053
7.621976
0.884956


−0.63369
6.973932
0.884956


−1.04177
6.310033
0.884956


−1.47287
5.634161
0.884956


−1.92672
4.951536
0.884956


−2.40792
4.271128
0.884956


−2.9253
3.606214
0.884956


−3.48522
2.970692
0.884956


−4.09177
2.379816
0.884956


−4.7458
1.849718
0.884956


−5.44553
1.399066
0.884956


−6.18363
1.046277
0.884956


−6.94622
0.806787
0.884956


−7.71297
0.682363
0.884956


−8.46198
0.662568
0.884956


−9.17883
0.720125
0.884956


−9.85649
0.821336
0.884956


−10.4953
0.926814
0.884956


−11.0972
1.005367
0.884956


−11.6599
1.03121
0.884956


−12.1761
0.990734
0.884956


−12.6351
0.886795
0.884956


−13.028
0.73039
0.884956


−13.3496
0.537072
0.884956


−13.5997
0.32673
0.884956


−13.7834
0.118703
0.884956


−13.9101
−0.07075
0.884956


−13.9919
−0.22967
0.884956


−14.0413
−0.35156
0.884956


−14.0699
−0.43894
0.884956


−14.858
−0.49509
0.914841


−14.8634
−0.56389
0.914841


−14.867
−0.65379
0.914841


−14.8663
−0.78055
0.914841


−14.855
−0.95695
0.914841


−14.8236
−1.18476
0.914841


−14.7597
−1.46397
0.914841


−14.6484
−1.79102
0.914841


−14.4729
−2.16032
0.914841


−14.2166
−2.56111
0.914841


−13.8658
−2.97844
0.914841


−13.4168
−3.39141
0.914841


−12.8749
−3.78426
0.914841


−12.243
−4.14767
0.914841


−11.5296
−4.47637
0.914841


−10.7364
−4.75506
0.914841


−9.8696
−4.95966
0.914841


−8.94319
−5.05631
0.914841


−7.97447
−5.009
0.914841


−6.99838
−4.78564
0.914841


−6.05091
−4.37388
0.914841


−5.15992
−3.80253
0.914841


−4.33983
−3.10335
0.914841


−3.59576
−2.30592
0.914841


−2.92669
−1.43556
0.914841


−2.32489
−0.5176
0.914841


−1.7826
0.429818
0.914841


−1.29279
1.392226
0.914841


−0.84889
2.357107
0.914841


−0.44333
3.313192
0.914841


−0.07132
4.251685
0.914841


0.269514
5.165607
0.914841


0.580711
6.048721
0.914841


0.866145
6.894629
0.914841


1.129122
7.697278
0.914841


1.372141
8.451629
0.914841


1.596432
9.153827
0.914841


1.802451
9.801131
0.914841


1.989732
10.39282
0.914841


2.158443
10.92522
0.914841


2.308479
11.39767
0.914841


2.439928
11.81007
0.914841


2.553043
12.16313
0.914841


2.648058
12.45848
0.914841


2.725262
12.69866
0.914841


2.782046
12.88809
0.914841


2.78789
13.03549
0.914841


2.753344
13.13232
0.914841


2.714355
13.18463
0.914841


2.675136
13.21555
0.914841


2.639151
13.23127
0.914841


2.588866
13.23851
0.914841


2.510141
13.21625
0.914841


2.428834
13.13464
0.914841


2.360307
12.99566
0.914841


2.28434
12.81273
0.914841


2.190748
12.58781
0.914841


2.077821
12.3195
0.914841


1.944673
12.00672
0.914841


1.789756
11.64948
0.914841


1.610974
11.2495
0.914841


1.404405
10.8102
0.914841


1.168263
10.33255
0.914841


0.902011
9.81905
0.914841


0.60601
9.272341
0.914841


0.281398
8.69509
0.914841


−0.07044
8.090234
0.914841


−0.44864
7.461244
0.914841


−0.85351
6.812291
0.914841


−1.28633
6.148756
0.914841


−1.74875
5.476585
0.914841


−2.24249
4.806935
0.914841


−2.77003
4.148365
0.914841


−3.34496
3.516493
0.914841


−3.97836
2.930925
0.914841


−4.67163
2.413855
0.914841


−5.40046
1.994908
0.914841


−6.17596
1.672809
0.914841


−6.96488
1.460521
0.914841


−7.74892
1.350183
0.914841


−8.52622
1.323858
0.914841


−9.28499
1.35809
0.914841


−10.0139
1.422311
0.914841


−10.7062
1.484667
0.914841


−11.3608
1.518287
0.914841


−11.9721
1.503402
0.914841


−12.5332
1.430826
0.914841


−13.0375
1.301516
0.914841


−13.4782
1.122805
0.914841


−13.85
0.907211
0.914841


−14.1503
0.672249
0.914841


−14.3826
0.435398
0.914841


−14.555
0.211031
0.914841


−14.6757
0.01349
0.914841


−14.7573
−0.15365
0.914841


−14.8091
−0.28667
0.914841


−14.8386
−0.38523
0.914841


−15.6882
−0.41277
0.946903


−15.6982
−0.47167
0.946903


−15.709
−0.5575
0.946903


−15.7174
−0.6903
0.946903


−15.714
−0.87625
0.946903


−15.686
−1.11729
0.946903


−15.6182
−1.41365
0.946903


−15.4939
−1.76014
0.946903


−15.2976
−2.14703
0.946903


−15.0157
−2.5602
0.946903


−14.6398
−2.98302
0.946903


−14.1678
−3.39888
0.946903


−13.6019
−3.7931
0.946903


−12.9471
−4.15509
0.946903


−12.2109
−4.48
0.946903


−11.3991
−4.75844
0.946903


−10.5183
−4.97589
0.946903


−9.57436
−5.10582
0.946903


−8.58252
−5.1112
0.946903


−7.56618
−4.95673
0.946903


−6.56234
−4.62174
0.946903


−5.60724
−4.11263
0.946903


−4.72363
−3.45536
0.946903


−3.92281
−2.68063
0.946903


−3.20526
−1.81961
0.946903


−2.56343
−0.9004
0.946903


−1.98847
0.055182
0.946903


−1.47152
1.029758
0.946903


−1.00578
2.009841
0.946903


−0.58347
2.983341
0.946903


−0.19771
3.940033
0.946903


0.155181
4.871969
0.946903


0.47836
5.772086
0.946903


0.776206
6.633546
0.946903


1.05042
7.451064
0.946903


1.302417
8.220007
0.946903


1.533706
8.936303
0.946903


1.745036
9.596744
0.946903


1.93678
10.19889
0.946903


2.109084
10.74109
0.946903


2.262085
11.22241
0.946903


2.395923
11.64275
0.946903


2.51102
12.00274
0.946903


2.607685
12.30398
0.946903


2.686166
12.54904
0.946903


2.743763
12.74241
0.946903


2.751111
12.89258
0.946903


2.717213
12.99188
0.946903


2.678322
13.04599
0.946903


2.638905
13.0783
0.946903


2.602452
13.0948
0.946903


2.551438
13.1026
0.946903


2.471134
13.07975
0.946903


2.389353
12.9958
0.946903


2.320314
12.85435
0.946903


2.243402
12.66814
0.946903


2.148293
12.43942
0.946903


2.032986
12.16689
0.946903


1.896188
11.84975
0.946903


1.735447
11.48845
0.946903


1.546833
11.08492
0.946903


1.327214
10.64155
0.946903


1.074303
10.16113
0.946903


0.787744
9.646146
0.946903


0.468802
9.098721
0.946903


0.11971
8.520839
0.946903


−0.25661
7.914448
0.946903


−0.65888
7.282863
0.946903


−1.08827
6.631412
0.946903


−1.54855
5.967752
0.946903


−2.04492
5.301471
0.946903


−2.58368
4.644503
0.946903


−3.17079
4.010982
0.946903


−3.81258
3.419007
0.946903


−4.5157
2.894189
0.946903


−5.27924
2.464149
0.946903


−6.09129
2.150803
0.946903


−6.92998
1.96194
0.946903


−7.77105
1.890915
0.946903


−8.59754
1.910174
0.946903


−9.39911
1.980261
0.946903


−10.1723
2.060498
0.946903


−10.9148
2.118128
0.946903


−11.6224
2.128736
0.946903


−12.2891
2.080263
0.946903


−12.9063
1.969728
0.946903


−13.4655
1.80239
0.946903


−13.9588
1.588368
0.946903


−14.3813
1.34113
0.946903


−14.7316
1.075945
0.946903


−15.012
0.807579
0.946903


−15.2281
0.549569
0.946903


−15.3886
0.313334
0.946903


−15.5031
0.106654
0.946903


−15.5815
−0.06576
0.946903


−15.6321
−0.20147
0.946903


−15.6625
−0.30115
0.946903


−16.541
−0.3055
1


−16.5449
−0.36779
1


−16.5461
−0.45747
1


−16.5505
−0.59379
1


−16.5518
−0.78306
1


−16.5335
−1.03081
1


−16.4778
−1.33638
1


−16.3647
−1.69566
1


−16.1795
−2.09895
1


−15.9124
−2.53449
1


−15.5553
−2.98818
1


−15.103
−3.44513
1


−14.5542
−3.88969
1


−13.9092
−4.3029
1


−13.1705
−4.66634
1


−12.3426
−4.96203
1


−11.4353
−5.17532
1


−10.4628
−5.29479
1


−9.4415
−5.30541
1


−8.38997
−5.18754
1


−7.3345
−4.92223
1


−6.30812
−4.4935
1


−5.34082
−3.90605
1


−4.45321
−3.18199
1


−3.65358
−2.35192
1


−2.94088
−1.446
1


−2.30659
−0.49096
1


−1.7416
0.492369
1


−1.23626
1.486853
1


−0.78191
2.478642
1


−0.36998
3.455844
1


0.004638
4.409377
1


0.345846
5.331499
1


0.658245
6.214988
1


0.944902
7.053858
1


1.207152
7.843348
1


1.446412
8.579276
1


1.664121
9.258121
1


1.863296
9.876529
1


2.041017
10.43376
1


2.19884
10.92843
1


2.336881
11.36044
1


2.45558
11.73042
1


2.555257
12.04003
1


2.636137
12.2919
1


2.695539
12.49066
1


2.705722
12.64465
1


2.672338
12.74728
1


2.633255
12.80361
1


2.593336
12.83753
1


2.556315
12.8548
1


2.504324
12.86345
1


2.422165
12.84142
1


2.337773
12.75593
1


2.267735
12.61152
1


2.189394
12.42128
1


2.092061
12.1878
1


1.973511
11.90983
1


1.831142
11.58712
1


1.661256
11.22077
1


1.459535
10.81306
1


1.222656
10.36675
1


0.948871
9.884633
1


0.637905
9.369358
1


0.290834
8.823337
1


−0.09066
8.249061
1


−0.5053
7.649715
1


−0.95347
7.03014
1


−1.43504
6.395345
1


−1.9552
5.755126
1


−2.52299
5.1244
1


−3.1516
4.527003
1


−3.84823
3.990246
1


−4.612
3.543713
1


−5.43193
3.211231
1


−6.29014
3.001359
1


−7.16744
2.91059
1


−8.04429
2.918118
1


−8.9071
2.987117
1


−9.74901
3.071615
1


−10.5673
3.130931
1


−11.3571
3.143688
1


−12.1122
3.097031
1


−12.8243
2.985264
1


−13.4841
2.809384
1


−14.0822
2.57637
1


−14.6112
2.297871
1


−15.0667
1.988345
1


−15.4479
1.663228
1


−15.7577
1.337284
1


−16.0012
1.02338
1


−16.1857
0.732034
1


−16.3196
0.471125
1


−16.4118
0.246263
1


−16.4713
0.061188
1


−16.5071
−0.0829
1


−16.5266
−0.18736
1


−17.2023
−0.22801
1.035398


−17.213
−0.29062
1.035398


−17.2249
−0.38144
1.035398


−17.2349
−0.52121
1.035398


−17.234
−0.71599
1.035398


−17.2101
−0.96932
1.035398


−17.1489
−1.28182
1.035398


−17.0363
−1.64954
1.035398


−16.858
−2.06481
1.035398


−16.6015
−2.51723
1.035398


−16.2555
−2.99524
1.035398


−15.8117
−3.48121
1.035398


−15.2658
−3.95612
1.035398


−14.6179
−4.39879
1.035398


−13.8721
−4.78809
1.035398


−13.0336
−5.10401
1.035398


−12.1114
−5.3283
1.035398


−11.1198
−5.44894
1.035398


−10.0771
−5.46107
1.035398


−9.00117
−5.35578
1.035398


−7.91544
−5.11745
1.035398


−6.84661
−4.73234
1.035398


−5.82253
−4.19646
1.035398


−4.87107
−3.51792
1.035398


−4.00625
−2.72121
1.035398


−3.23605
−1.83164
1.035398


−2.55356
−0.88053
1.035398


−1.94904
0.10724
1.035398


−1.41224
1.111866
1.035398


−0.93231
2.117024
1.035398


−0.4997
3.109615
1.035398


−0.10855
4.079731
1.035398


0.246536
5.018708
1.035398


0.570214
5.919069
1.035398


0.866226
6.774414
1.035398


1.137008
7.579478
1.035398


1.384338
8.329882
1.035398


1.607856
9.022591
1.035398


1.810134
9.654333
1.035398


1.992015
10.22314
1.035398


2.153471
10.7281
1.035398


2.294601
11.16912
1.035398


2.415913
11.54683
1.035398


2.517767
11.86292
1.035398


2.600395
12.12007
1.035398


2.661202
12.32298
1.035398


2.673381
12.47989
1.035398


2.640243
12.5851
1.035398


2.601092
12.64314
1.035398


2.560863
12.67837
1.035398


2.523268
12.69639
1.035398


2.470273
12.7057
1.035398


2.386452
12.68377
1.035398


2.300332
12.59592
1.035398


2.229951
12.44812
1.035398


2.150157
12.25387
1.035398


2.050658
12.01559
1.035398


1.928865
11.73217
1.035398


1.781145
11.40383
1.035398


1.603053
11.03206
1.035398


1.390002
10.61949
1.035398


1.138876
10.16898
1.035398


0.847955
9.683514
1.035398


0.516739
9.166095
1.035398


0.146122
8.619447
1.035398


−0.26295
8.046769
1.035398


−0.70949
7.451735
1.035398


−1.19367
6.839446
1.035398


−1.71754
6.217202
1.035398


−2.28833
5.598101
1.035398


−2.91988
5.005999
1.035398


−3.62268
4.472276
1.035398


−4.3959
4.028635
1.035398


−5.22924
3.702221
1.035398


−6.10689
3.507849
1.035398


−7.00809
3.444543
1.035398


−7.91326
3.49083
1.035398


−8.80532
3.602839
1.035398


−9.67845
3.731738
1.035398


−10.5325
3.831059
1.035398


−11.3654
3.867076
1.035398


−12.1709
3.82265
1.035398


−12.9366
3.692987
1.035398


−13.6495
3.48744
1.035398


−14.2997
3.220694
1.035398


−14.8808
2.908335
1.035398


−15.3892
2.565466
1.035398


−15.8238
2.206099
1.035398


−16.1852
1.842749
1.035398


−16.4758
1.487145
1.035398


−16.7015
1.150504
1.035398


−16.8704
0.842089
1.035398


−16.9922
0.569213
1.035398


−17.0764
0.33639
1.035398


−17.1309
0.146911
1.035398


−17.1626
7.33E−05
1.035398


−17.1783
−0.1064
1.035398


−17.6984
−0.16988
1.061947


−17.6979
−0.24207
1.061947


−17.6976
−0.34472
1.061947


−17.7018
−0.49228
1.061947


−17.7175
−0.68735
1.061947


−17.7042
−0.93683
1.061947


−17.6524
−1.24748
1.061947


−17.5462
−1.61799
1.061947


−17.3691
−2.04024
1.061947


−17.1086
−2.50008
1.061947


−16.7574
−2.98362
1.061947


−16.3137
−3.47892
1.061947


−15.7756
−3.9752
1.061947


−15.1391
−4.4537
1.061947


−14.4001
−4.88454
1.061947


−13.5604
−5.23596
1.061947


−12.6284
−5.48016
1.061947


−11.6214
−5.60413
1.061947


−10.562
−5.60837
1.061947


−9.46962
−5.4969
1.061947


−8.36271
−5.26992
1.061947


−7.26399
−4.91166
1.061947


−6.20283
−4.409
1.061947


−5.20611
−3.76273
1.061947


−4.29264
−2.99168
1.061947


−3.47614
−2.11846
1.061947


−2.75319
−1.17418
1.061947


−2.1155
−0.18542
1.061947


−1.55215
0.825561
1.061947


−1.05133
1.840537
1.061947


−0.60253
2.845055
1.061947


−0.19719
3.827563
1.061947


0.16907
4.779568
1.061947


0.501695
5.693057
1.061947


0.805098
6.561244
1.061947


1.081503
7.378826
1.061947


1.334422
8.140762
1.061947


1.563626
8.843933
1.061947


1.769554
9.485713
1.061947


1.954692
10.06356
1.061947


2.118994
10.57657
1.061947


2.262555
11.02462
1.061947


2.385907
11.40839
1.061947


2.489467
11.72954
1.061947


2.573469
11.99081
1.061947


2.635429
12.19695
1.061947


2.64918
12.35614
1.061947


2.616168
12.46337
1.061947


2.576969
12.52273
1.061947


2.536505
12.55898
1.061947


2.498402
12.5776
1.061947


2.444529
12.58742
1.061947


2.359334
12.56549
1.061947


2.271859
12.4755
1.061947


2.201308
12.32471
1.061947


2.120214
12.12703
1.061947


2.018818
11.88466
1.061947


1.894155
11.59663
1.061947


1.741755
11.26351
1.061947


1.556687
10.88714
1.061947


1.334209
10.47036
1.061947


1.071116
10.0163
1.061947


0.765788
9.528073
1.061947


0.41772
9.008884
1.061947


0.027244
8.462019
1.061947


−0.40494
7.89109
1.061947


−0.87786
7.300073
1.061947


−1.39223
6.69491
1.061947


−1.95064
6.084095
1.061947


−2.55991
5.481696
1.061947


−3.23454
4.914938
1.061947


−3.98944
4.427664
1.061947


−4.82023
4.060552
1.061947


−5.70847
3.843353
1.061947


−6.6241
3.77954
1.061947


−7.54858
3.842532
1.061947


−8.46277
3.980712
1.061947


−9.36195
4.140256
1.061947


−10.2431
4.273356
1.061947


−11.1063
4.346435
1.061947


−11.9489
4.336282
1.061947


−12.7601
4.233538
1.061947


−13.5254
4.042562
1.061947


−14.2316
3.777572
1.061947


−14.87
3.457088
1.061947


−15.4367
3.099763
1.061947


−15.9307
2.721971
1.061947


−16.3529
2.336659
1.061947


−16.7041
1.954309
1.061947


−16.9868
1.58445
1.061947


−17.2055
1.236711
1.061947


−17.369
0.919929
1.061947


−17.488
0.641205
1.061947


−17.5727
0.404717
1.061947


−17.6303
0.214567
1.061947


−17.6655
0.072921
1.061947


−17.6853
−0.03172
1.061947


−17.6952
−0.11264
1.061947









In the above Table 1, the plane Zadim=0 corresponds to the reference plane P0 situated at the base of the profile. This plane P0 is the intersection of the stacking axis AE of the set of vanes with the axisymmetric surface of the hub, i.e. it passes via the intersection between the axis AE and the surface 16A where it is assembled with the inner shroud 16. The plane Zadim=1 corresponds to the reference plane P1 situated at the top of the profile. This plane P1 is the intersection between the axis AE and the axisymmetric surface of the casing, i.e. it passes via the intersection of the axis AE with the surface 12A where it is assembled with the outer ring 12.


By convention, the stacking axis AE of the set of vanes, for the vane of a nozzle, is the axis that extends in the radial direction Z and passes through the middle of the inter-vane throat. For a given vane, the inter-vane throat is the location where the distance between the trailing edge of the vane in question and the suction side of the preceding vane in the direction of rotation of the turbine is at a minimum.


This is the axis on which the various X,Y sections of the set of vanes are “stacked” when designing the set of vanes.


As mentioned at the beginning of the present description, the aerodynamic profile of the invention is substantially identical to the nominal profile defined in the above table, i.e. it departs from said nominal profile by very little at most, being defined in particular within an envelope of ±1 mm in a direction normal to the surface of the nominal profile, and/or having X,Y coordinates lying within a range of ±5% relative to the coordinates X,Y of the nominal profile.


The coordinate Zadim is non-dimensional, i.e. for a point P, situated at a distance D from the plane P0 (where D is measured along the axis Z), the value of Zadim is D/H, where H represents the total height of the profile as measured between the planes P0 and P1. Naturally, in the Table 1 above, by multiplying the coordinate Zadim by the height H, it is possible to obtain the complete coordinates of the vane.


By way of example, the total height H is preferably about 60 mm±10%. By way of example, the plane P0 is situated at a distance of about 335 mm±10% from the axis A.


In the above table, the profile is characterized by twenty-one section planes at constant Zadim coordinates, for which the coordinates X and Y are specified. These twenty-one section planes include seventeen section planes located between Zadim=0 and Zadim=1, and thus arranged in the fluid stream, these section planes being distributed from P0 to P1. The twenty-one section planes also include four section planes which are substantially outside the fluid stream (two section planes with Zadim<0, and two section planes with Zadim>1), these four section planes being provided for ensuring geometric continuity of the stacking, close to the head and the foot, respectively. In each section plane at constant coordinate Zadim, the section of the profile is given by a continuous and smooth curve, interconnecting all of the points (X,Y). In each section plane, the profile is interpolated so as to generate a uniform profile. Between the section planes, the profile is to be interpolated so as to generate a complete vane, as homogeneous as possible.


It is advantageous for the nozzle that includes the vane of the invention to have 110 to 130 vanes that present aerodynamic profiles as defined above.

Claims
  • 1. An aerodynamic profile for a turbine vane, the profile being, when cold and in a non-coated state, substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H, where D is the distance of the point under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane out to the end of the vane, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.
  • 2. The aerodynamic profile as claimed in claim 1, wherein said profile is defined within an envelope of ±1 mm in a direction normal to the surface of the nominal profile.
  • 3. The aerodynamic profile as claimed in claim 1, wherein the coordinates X,Y of said profile lie within a range of ±5% relative to the coordinates X,Y of the nominal profile.
  • 4. The aerodynamic profile as claimed in claim 1, wherein the vane is a nozzle vane forming a part of a stator of a turbine.
  • 5. The aerodynamic profile as claimed in claim 4, wherein the vane is a nozzle vane of the first stage of the turbine.
  • 6. The aerodynamic profile as claimed in claim 4, wherein the vane is a vane of the first stage nozzle of a turbine having seven stages.
  • 7. A turbine vane, presenting an aerodynamic profile as claimed in claim 1.
  • 8. A turbine, including turbine vanes presenting aerodynamic profiles as claimed in claim 1.
  • 9. A turbine as claimed in claim 8, including a nozzle that is stationary in rotation, having 110 to 130 vanes that present aerodynamic profiles comprising: when cold and in a non-coated state, substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H, where D is the distance of the point under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane out to the end of the vane, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.
  • 10. A turbine nozzle forming a portion of a turbine stator, wherein all the vanes of the nozzle present an aerodynamic profile as claimed in claim 1.
  • 11. A turbine nozzle as claimed in claim 10, including 110 to 130 vanes that present aerodynamic profiles comprising: when cold and in a non-coated state, substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H, where D is the distance of the point under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane out to the end of the vane, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.
CROSS-REFERENCE TO RELATED APPLICATION(S)

This patent application claims the benefit under 35 U.S.C. §119 to U.S. Provisional Application No. 62/361,567, filed on Jul. 13, 2016, the entirety of which is incorporated herein by reference.

Provisional Applications (1)
Number Date Country
62361567 Jul 2016 US