Patent application title:

Airfoil profile

Publication number:

-

Publication date:
Application number:

17/185,659

Filed date:

2021-02-25

βœ… Patent granted

Patent number:

US 11,293,286 B1

Grant date:

2022-04-05

PCT filing:

-

PCT publication:

-

Examiner:

Eric J Zamora Alvarez

Agent:

Shook, Hardy & Bacon, L.L.P.

Adjusted expiration:

2041-02-25

Abstract:

Compressor components, such as blades and vanes, having an airfoil portion with an uncoated, nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1. X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance in inches. The profile sections at the Z distances are joined smoothly with one another to form a complete airfoil shape.

Inventors:

Assignee:

Applicant:

Interested in similar patents?

Get notified when new applications in this technology area are published.

Classification:

F01D5/141 »  CPC main

Blades; Blade-carrying members ; Heating, heat-insulating, cooling or antivibration means on the blades or the members; Blades; Form or construction Shape, i.e. outer, aerodynamic form

F04D29/324 »  CPC further

Details, component parts, or accessories; Rotors specially for elastic fluids for axial flow pumps for axial flow compressors Blades

F05D2220/3216 »  CPC further

Application in turbines in gas turbines for a special turbine stage for a special compressor stage

F05D2240/301 »  CPC further

Components; Rotors; Characteristics of rotor blades, i.e. of any element transforming dynamic fluid energy to or from rotational energy and being attached to a rotor Cross-sectional characteristics

F05D2250/74 »  CPC further

Geometry; Shape given by a set or table of xyz-coordinates

F01D5/14 IPC

Blades; Blade-carrying members ; Heating, heat-insulating, cooling or antivibration means on the blades or the members; Blades Form or construction

F04D29/32 IPC

Details, component parts, or accessories; Rotors specially for elastic fluids for axial flow pumps

Description

TECHNICAL FIELD

The present invention generally relates to axial compressor components having an airfoil. More specifically, the present invention relates to an airfoil profile for compressor components, such as blades and/or vanes, that have a variable thickness and three-dimensional (β€œ3D”) shape along the airfoil span in order to raise the natural frequency, improve airfoil mean stress and dynamic stress capabilities of the compressor component, and minimize risk of failure due to cracks caused by excitation of the component.

BACKGROUND

Gas turbine engines, such as those used for power generation or propulsion, include a compressor section. The compressor section includes a casing and a rotor that rotates about an axis within the casing. In axial-flow compressors, the rotor typically includes a plurality of rotor discs that rotate about the axis. A plurality of compressor blades extend away from, and are radially spaced around, an outer circumferential surface of each of the rotor discs. Typically, following each plurality of compressor blades is a plurality of compressor vanes. The plurality of compressor vanes usually extend from, and are radially spaced around, the casing. Each set of a rotor disc, a plurality of compressor blades extending from the rotor disc, and a plurality of compressor vanes immediately following the plurality of compressor blades is generally referred to as a compressor stage. The radial height of each successive compressor stage decreases because the blades and vanes increase the density, pressure and temperature of air passing through the stage. Specialized shapes of compressor blades and compressor vanes aid in compressing fluid as it passes through the compressor.

Compressor components, such as compressor blades and stator vanes, have an inherent natural frequency. When these components are excited by the passing air, as would occur during normal operating conditions of a gas turbine engine, the compressor components vibrate at different orders of engine rotational frequency. When the natural frequency of a compressor component coincides with or crosses an engine order, the compressor component can exhibit resonant vibration that in turn can cause cracking and ultimately failure of the compressor component.

SUMMARY

This summary is intended to introduce a selection of concepts in a simplified form that are further described below in the detailed description section of this disclosure. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in isolation to determine the scope of the claimed subject matter.

In brief, and at a high level, this disclosure describes gas turbine engine components, e.g., compressor components such as blades and vanes, having airfoil portions that optimize the interaction with other compressor stages, provide for aerodynamic efficiency, and meet aeromechanical life objectives. More specifically, the compressor components described herein have unique airfoil thicknesses, chord lengths, and 3D shaping that results in the desired natural frequency of the respective compressor component. Further, the airfoil thicknesses and 3D shaping at specified radial distances along the airfoil span may provide an acceptable level of mean stress in the airfoil sections, and also provide improved vane aerodynamics and efficiency while maintaining the desired vane natural frequency. The airfoil portion of the compressor components disclosed herein, such as blades or vanes, have a particular shape or profile as specified herein. For example, one such airfoil profile may be defined by at least some of the Cartesian coordinate values of X, Y, and Z set forth in Table 1. In this example, the Z coordinate values are distances measured perpendicular to the compressor centerline and the X and Y coordinate values for each Z distance define an airfoil section when the coordinate values are connected with smooth continuing arcs. In this example, the airfoil sections at each Z distance are further joined with smooth continuing arcs to define the 3D shape of the airfoil portion of the compressor component.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments disclosed herein relate to compressor component airfoil designs and are described in detail with reference to the attached drawing figures, which illustrate non-limiting examples of the disclosed subject matter, wherein:

FIG. 1 depicts a schematic view of a gas turbine engine, in accordance with aspects hereof;

FIG. 2 depicts a perspective view of a set of compressor vanes coupled to a compressor casing, in accordance with aspects hereof;

FIG. 3 depicts a perspective view of a portion of the compressor casing of FIG. 2 and a compressor vane coupled thereto, in accordance with aspects hereof;

FIG. 4 depicts a top view of a compressor component, in accordance with aspects hereof;

FIG. 5 depicts a perspective view of a pressure side of the compressor component of FIG. 4, in accordance with aspects hereof;

FIG. 6 depicts a perspective view of a suction side of the compressor component of FIG. 4, in accordance with aspects hereof;

FIG. 7 depicts a cross-section of the compressor component of FIG. 4 taken along cut-line 7-7 in FIG. 5, in accordance with aspects hereof; and

FIG. 8 depicts a perspective view of the airfoil sections defined by the Cartesian coordinate values of X, Y, and Z set forth in Table 1, in accordance with aspects hereof.

DETAILED DESCRIPTION

The subject matter of this disclosure is described herein to meet statutory requirements. However, this description is not intended to limit the scope of the invention. Rather, the claimed subject matter may be embodied in other ways, to include different steps, combinations of steps, features, and/or combinations of features, similar to those described in this disclosure, and in conjunction with other present or future technologies.

In brief, and at a high level, this disclosure describes gas turbine engine components, e.g., compressor components such as blades and vanes, having airfoil portions that may optimize the interaction with other compressor stages, provide for aerodynamic efficiency, and improve aeromechanical life objectives. More specifically, the compressor components described herein may have, in different disclosed aspects, unique airfoil thicknesses, chord lengths, and 3D shaping that results in different performance characteristics being achieved, such as, e.g., an altered natural frequency of the associated compressor component. Further, the airfoil thicknesses and 3D shaping at specified radial distances along the airfoil span may provide an acceptable level of mean stress in the airfoil sections, and also provide improved vane aerodynamics and efficiency. The airfoil portion of the compressor components disclosed herein, such as blades or vanes, have a particular shape or profile as specified herein. For example, one such airfoil profile may be defined by the Cartesian coordinate values of X, Y, and Z set forth in Table 1. In this example, the Z coordinate values are distances measured perpendicular from the compressor centerline and the X and Y coordinate values at each Z distance define an airfoil section when the coordinate values are connected with smooth continuing arcs. In this example, the airfoil sections at each Z distance may be joined with smooth continuing arcs to define the 3D shape of the airfoil portion of the compressor component.

Referring now to FIG. 1, there is illustrated a portion of a compressor 10 having multiple compressor stages, including a stage zero 12 at the front of the compressor 10. Each compressor stage includes a rotor disc 14, a plurality of circumferentially spaced compressor blades 16 coupled to the rotor disc 14, and a plurality of compressor vanes 18 adjacent to, and following, the plurality of circumferentially spaced compressor blades 16. The plurality of compressor vanes 18 are circumferentially spaced around, and extend from, a casing 20 of the compressor 10.

One aspect of a compressor component is a compressor vane 16A, as depicted in FIGS. 2-6. As best seen in FIG. 3, the compressor vane 16A includes a root portion 22 configured to be coupled to the casing 20, and an airfoil portion 26 extending from the root portion 22 to a tip 28. As best seen in FIGS. 5 and 6, the airfoil portion 26 generally includes a leading edge 30, a trailing edge 32, and a pressure side wall 34 and a suction side wall 36 each extending between the leading edge 30 and the trailing edge 32. The pressure side wall 34 generally presents a convex surface along the span of the airfoil portion 26. The suction side wall 36 generally presents a concave surface along the span of the airfoil portion 26.

A compressor component may be used in a land-based compressor in connection with a land-based gas turbine engine. Typically, compressor components in such a compressor only experience temperatures below approximately 850 degrees Fahrenheit. As such, these types of compressor components may be fabricated from a relatively low temperature alloy. For example, these compressor components may be made from a stainless-steel alloy.

A cross-section of one aspect of the airfoil portion 26 is depicted in FIG. 7. As seen in FIG. 7, a chord 40 is shown for this radial section of the airfoil portion 26. The thickness of the airfoil portion 26 (e.g., the distance between the pressure side wall 34 and the suction side wall 36) varies at each point along the chord 40. As is evident from FIGS. 4-6, the length and orientation of the chord 40 changes along the span of the airfoil portion 26.

By changing the airfoil thickness, chord, 3D shaping, and/or the distribution of material along the span of the airfoil portion 26 of the compressor component, the natural frequency of the compressor component may be altered. This may be advantageous for the operation of the compressor 10. For example, during operation of the compressor 10, the compressor component may move (e.g., vibrate) at various modes due to the geometry, temperature, and aerodynamic forces being applied to the compressor component. These modes may include bending, torsion, and various higher-order modes.

If excitation of the compressor component occurs for a prolonged period of time with a sufficiently high amplitude then the compressor component can fail due to high cycle fatigue. For example, a critical first bending mode frequency of a compressor component may be approximately twice the 60 Hz rotation frequency of the gas turbine engine. For this mode, the first bending mode must avoid the critical frequency ranges of 55-65 Hz and 110-130 Hz to prevent resonance of the bending mode with the excitation associated with compressor (or engine) rotation. Modifying the thickness, chord, and/or the 3D shape of the compressor component, and in particular that of the airfoil portion thereof, results in altering the natural frequency of the compressor component. Continuing with the above example, modifying the thickness, chord, and/or the 3D shape of the compressor component in accordance with the disclosure herein may result in the first bending natural frequency being shifted to be between 65 Hz and 110 Hz, in accordance with some aspects. In other aspects, the first bending natural frequency may be shifted to be between about 70 Hz to about 105 Hz. This first bending natural frequency of the compressor component will therefore be between the 1st and 2nd engine order excitation frequencies when the compressor is rotating at 60 Hz. More specifically, a compressor component having the thickness, chord, and/or the 3D shape as defined by the Cartesian coordinates set forth in Table 1 will have a natural frequency of first bending between 1st and 2nd engine order excitations. In other aspects, a compressor component having the thickness, chord, and/or the 3D shape as defined by the Cartesian coordinates set forth in Table 1 will have a natural frequency of first bending at least 5-10% greater than 1st engine order excitations and at least 5-10% less than 2nd engine order excitations. In fact, a compressor component having the thickness, chord, and/or the 3D shape as defined by the Cartesian coordinates set forth in Table 1 will have a natural frequency for the lowest few vibration modes of at least 5-10% less than or greater than each engine order excitation. For example, the compressor component may have a natural frequency 12% less than the 2nd engine order excitation when the compressor is rotating at 60 Hz.

In one embodiment disclosed herein, a nominal 3D shape of an airfoil portion, such as the airfoil portion 26 shown in FIGS. 5 and 6, of a gas turbine engine component, such as a compressor component of a gas turbine engine, may be defined by a set of X, Y, and Z coordinate values measured in a Cartesian coordinate system. For example, one such set of coordinate values are set forth, in inches, in Table 1 below. The Cartesian coordinate system includes orthogonally related X, Y, and Z axes. The positive X, Y, and Z directions are axial toward the exhaust end of the compressor, tangential in the direction of engine rotation, and radially outward toward the static case, respectively. Each Z distance is measured from an axially-extending centerline of the compressor 10 (which, in aspects, may also be a centerline of the gas turbine engine). The X and Y coordinates for each distance Z may be joined smoothly (e.g., such as by smooth continuing arcs, splines, or the like) to thereby define a section of the airfoil portion of the compressor component at the respective Z distance. Each of the sections of the airfoil portion from the coordinate values set forth in Table 1 below is shown in FIG. 8. Each of the defined sections of the airfoil profile is joined smoothly with an adjacent section of the airfoil profile in the Z direction to form a complete nominal 3D shape of the airfoil portion.

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

Further, the compressor component 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 compressor component may have a series of manufacturing tolerances for the position, profile, twist, and chord that can cause the compressor component to vary from the nominal 3D shape defined by the coordinate values set forth in Table 1. This manufacturing tolerance may be, for example, +/βˆ’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 other aspects, the manufacturing tolerances may be +/βˆ’0.080 inches. In still other aspects, the manufacturing tolerances may be +/βˆ’0.020 inches.

In addition to manufacturing tolerances affecting the overall size of the compressor component, 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 compressor component uniformly in the X, Y, and Z directions. However, since the Z values in Table 1 are measured from a centerline of the compressor rather than a point on the compressor component, the scaling of the Z values must be relative to the minimum Z value in Table 1. For example, the first (i.e., radially innermost) profile section is positioned approximately 23.819 inches from the compressor centerline and the second profile section is positioned approximately 25.152 inches from the engine centerline. Thus, if the compressor component was to be scaled 20% larger, each of the X and Y values in Table 1 may simply be multiplied by 1.2. However, each of the Z values must first be adjusted to a relative scale by subtracting the distance from the compressor centerline to the first profile section (e.g., the Z coordinates for the first profile section become Z=0, the Z coordinates for the second profile section become Z=1.333 inches, etc.). This adjustment creates a nominal Z value. After this adjustment, then the nominal Z values may be multiplied by the same constant or number as were the X and Y coordinates (1.2 in this example).

The Z values set forth in Table 1 may assume a compressor sized to operate at 60 Hz. In other aspects, the compressor component described herein may also be used in different size compressors (e.g., a compressor sized to operate at 50 Hz, etc.). In these aspects, the compressor component defined by the X, Y, and Z values set forth in Table 1 may still be used, however, the Z values would be offset to account for the radial spacing of the differently sized compressors and components thereof (e.g., rotors, discs, blades, casing, etc.). The Z values may be offset radially inwardly or radially outwardly, depending upon whether the compressor is smaller or larger than the compressor envisioned by Table 1. For example, the casing to which a vane is affixed may spaced farther from the compressor centerline (e.g., 20%) than that envisioned by Table 1. In such a case, the minimum Z values (i.e., the radially innermost profile section) would be offset a distance equal to the difference in casing size (e.g., the radially innermost profile section would be positioned approximately 28.583 inches from the engine centerline instead of 23.819 inches) and the remainder of the Z values would maintain their relative spacing to one another from Table 1 with the same scale factor as being applied to X and Y (e.g., if the scale factor is one then the second profile section would be positioned approximately 29.916 inches from the engine centerlineβ€”still 1.333 inches radially outward from the first profile section). Stated another way, the difference in spacing of the casing from the centerline would be added to all of the scaled Z values in Table 1.

Equation (1) provides another way to determine new Z values (e.g., scaled or translated) from the Z values listed in Table 1 when changing the relative size and/or position of the component defined by Table 1. In equation (1), Z1 is the Z value from Table 1, Z1min is the minimum Z value from Table 1, scale is the scaling factor, Z2min is the minimum Z value of the component as scaled and/or translated, and Z2 is the resultant Z value for the component as scaled and/or translated. Of note, when merely translating the component, the scaling factor in equation (1) is 1.00.
Z2=[(Z1βˆ’Z1min)*scale+Z2min]  (1)

In yet another aspect, the airfoil profile may be defined by a portion of the set of X, Y, and Z coordinate values set forth in Table 1 (e.g., at least 85% of said coordinate values).

TABLE 1
X Y Z
βˆ’1.569 βˆ’1.386 23.819
βˆ’1.591 βˆ’1.409 23.819
βˆ’1.606 βˆ’1.397 23.819
βˆ’1.589 βˆ’1.370 23.819
βˆ’1.388 βˆ’1.113 23.819
βˆ’1.125 βˆ’0.805 23.819
βˆ’0.844 βˆ’0.511 23.819
βˆ’0.547 βˆ’0.235 23.819
βˆ’0.234 0.023 23.819
0.096 0.259 23.819
0.445 0.465 23.819
0.814 0.634 23.819
1.199 0.763 23.819
1.594 0.853 23.819
1.917 0.897 23.819
1.926 0.892 23.819
1.925 0.882 23.819
1.802 0.854 23.819
1.418 0.747 23.819
1.045 0.607 23.819
0.685 0.436 23.819
0.340 0.236 23.819
0.012 0.011 23.819
βˆ’0.308 βˆ’0.227 23.819
βˆ’0.619 βˆ’0.477 23.819
βˆ’0.920 βˆ’0.738 23.819
βˆ’1.210 βˆ’1.011 23.819
βˆ’1.487 βˆ’1.297 23.819
βˆ’1.574 βˆ’1.392 23.819
βˆ’1.599 βˆ’1.412 23.819
βˆ’1.603 βˆ’1.390 23.819
βˆ’1.576 βˆ’1.353 23.819
βˆ’1.324 βˆ’1.035 23.819
βˆ’1.056 βˆ’0.730 23.819
βˆ’0.772 βˆ’0.440 23.819
βˆ’0.471 βˆ’0.169 23.819
βˆ’0.153 0.084 23.819
0.181 0.314 23.819
0.536 0.511 23.819
0.909 0.670 23.819
1.297 0.789 23.819
1.694 0.870 23.819
1.920 0.897 23.819
1.927 0.889 23.819
1.922 0.880 23.819
1.705 0.830 23.819
1.323 0.715 23.819
0.953 0.567 23.819
0.597 0.389 23.819
0.257 0.182 23.819
βˆ’0.069 βˆ’0.048 23.819
βˆ’0.387 βˆ’0.289 23.819
βˆ’0.695 βˆ’0.541 23.819
βˆ’0.994 βˆ’0.805 23.819
βˆ’1.281 βˆ’1.081 23.819
βˆ’1.555 βˆ’1.371 23.819
βˆ’1.580 βˆ’1.398 23.819
βˆ’1.606 βˆ’1.412 23.819
βˆ’1.598 βˆ’1.383 23.819
βˆ’1.514 βˆ’1.272 23.819
βˆ’1.259 βˆ’0.957 23.819
βˆ’0.987 βˆ’0.656 23.819
βˆ’0.698 βˆ’0.371 23.819
βˆ’0.393 βˆ’0.103 23.819
βˆ’0.071 0.144 23.819
0.268 0.367 23.819
0.628 0.554 23.819
1.005 0.703 23.819
1.395 0.813 23.819
1.795 0.884 23.819
1.922 0.896 23.819
1.927 0.887 23.819
1.920 0.879 23.819
1.609 0.805 23.819
1.230 0.681 23.819
0.863 0.526 23.819
0.510 0.340 23.819
0.174 0.126 23.819
βˆ’0.149 βˆ’0.107 23.819
βˆ’0.465 βˆ’0.351 23.819
βˆ’0.771 βˆ’0.606 23.819
βˆ’1.066 βˆ’0.873 23.819
βˆ’1.350 βˆ’1.152 23.819
βˆ’1.585 βˆ’1.404 23.819
βˆ’1.608 βˆ’1.404 23.819
βˆ’1.594 βˆ’1.376 23.819
βˆ’1.452 βˆ’1.192 23.819
βˆ’1.192 βˆ’0.880 23.819
βˆ’0.916 βˆ’0.583 23.819
βˆ’0.623 βˆ’0.302 23.819
βˆ’0.314 βˆ’0.040 23.819
0.012 0.202 23.819
0.356 0.417 23.819
0.720 0.595 23.819
1.101 0.734 23.819
1.495 0.834 23.819
1.896 0.895 23.819
1.925 0.894 23.819
1.926 0.884 23.819
1.899 0.875 23.819
1.513 0.777 23.819
1.137 0.645 23.819
0.773 0.482 23.819
0.425 0.289 23.819
0.093 0.069 23.819
βˆ’0.229 βˆ’0.167 23.819
βˆ’0.542 βˆ’0.413 23.819
βˆ’0.846 βˆ’0.671 23.819
βˆ’1.139 βˆ’0.942 23.819
βˆ’1.419 βˆ’1.224 23.819
βˆ’1.669 βˆ’1.322 25.152
βˆ’1.693 βˆ’1.343 25.152
βˆ’1.708 βˆ’1.330 25.152
βˆ’1.689 βˆ’1.304 25.152
βˆ’1.473 βˆ’1.050 25.152
βˆ’1.189 βˆ’0.747 25.152
βˆ’0.888 βˆ’0.460 25.152
βˆ’0.570 βˆ’0.194 25.152
βˆ’0.234 0.050 25.152
0.119 0.269 25.152
0.489 0.457 25.152
0.875 0.612 25.152
1.272 0.734 25.152
1.677 0.824 25.152
2.006 0.875 25.152
2.017 0.869 25.152
2.016 0.857 25.152
1.891 0.823 25.152
1.500 0.706 25.152
1.119 0.563 25.152
0.747 0.397 25.152
0.386 0.208 25.152
0.036 βˆ’0.001 25.152
βˆ’0.305 βˆ’0.224 25.152
βˆ’0.638 βˆ’0.459 25.152
βˆ’0.963 βˆ’0.705 25.152
βˆ’1.277 βˆ’0.964 25.152
βˆ’1.580 βˆ’1.237 25.152
βˆ’1.675 βˆ’1.328 25.152
βˆ’1.701 βˆ’1.347 25.152
βˆ’1.704 βˆ’1.323 25.152
βˆ’1.675 βˆ’1.287 25.152
βˆ’1.404 βˆ’0.973 25.152
βˆ’1.116 βˆ’0.673 25.152
βˆ’0.810 βˆ’0.392 25.152
βˆ’0.487 βˆ’0.131 25.152
βˆ’0.147 0.108 25.152
0.210 0.319 25.152
0.584 0.499 25.152
0.973 0.645 25.152
1.372 0.759 25.152
1.779 0.842 25.152
2.010 0.875 25.152
2.019 0.866 25.152
2.013 0.855 25.152
1.792 0.796 25.152
1.404 0.673 25.152
1.025 0.524 25.152
0.656 0.352 25.152
0.298 0.157 25.152
βˆ’0.050 βˆ’0.056 25.152
βˆ’0.389 βˆ’0.282 25.152
βˆ’0.720 βˆ’0.519 25.152
βˆ’1.042 βˆ’0.768 25.152
βˆ’1.354 βˆ’1.031 25.152
βˆ’1.653 βˆ’1.307 25.152
βˆ’1.681 βˆ’1.333 25.152
βˆ’1.709 βˆ’1.346 25.152
βˆ’1.699 βˆ’1.317 25.152
βˆ’1.609 βˆ’1.207 25.152
βˆ’1.333 βˆ’0.896 25.152
βˆ’1.041 βˆ’0.601 25.152
βˆ’0.731 βˆ’0.325 25.152
βˆ’0.404 βˆ’0.069 25.152
βˆ’0.060 0.163 25.152
0.302 0.367 25.152
0.680 0.538 25.152
1.072 0.677 25.152
1.473 0.783 25.152
1.882 0.858 25.152
2.013 0.874 25.152
2.019 0.863 25.152
2.010 0.853 25.152
1.695 0.768 25.152
1.308 0.638 25.152
0.932 0.483 25.152
0.565 0.305 25.152
0.210 0.106 25.152
βˆ’0.135 βˆ’0.111 25.152
βˆ’0.472 βˆ’0.340 25.152
βˆ’0.801 βˆ’0.580 25.152
βˆ’1.121 βˆ’0.833 25.152
βˆ’1.430 βˆ’1.099 25.152
βˆ’1.687 βˆ’1.339 25.152
βˆ’1.710 βˆ’1.338 25.152
βˆ’1.694 βˆ’1.310 25.152
βˆ’1.541 βˆ’1.128 25.152
βˆ’1.262 βˆ’0.821 25.152
βˆ’0.965 βˆ’0.530 25.152
βˆ’0.651 βˆ’0.259 25.152
βˆ’0.320 βˆ’0.008 25.152
0.029 0.217 25.152
0.395 0.413 25.152
0.777 0.576 25.152
1.171 0.706 25.152
1.575 0.805 25.152
1.985 0.872 25.152
2.015 0.872 25.152
2.018 0.860 25.152
1.989 0.848 25.152
1.597 0.738 25.152
1.213 0.601 25.152
0.839 0.441 25.152
0.475 0.257 25.152
0.123 0.053 25.152
βˆ’0.220 βˆ’0.168 25.152
βˆ’0.555 βˆ’0.399 25.152
βˆ’0.882 βˆ’0.642 25.152
βˆ’1.200 βˆ’0.898 25.152
βˆ’1.505 βˆ’1.167 25.152
βˆ’1.743 βˆ’1.259 26.455
βˆ’1.770 βˆ’1.280 26.455
βˆ’1.785 βˆ’1.265 26.455
βˆ’1.764 βˆ’1.238 26.455
βˆ’1.536 βˆ’0.985 26.455
βˆ’1.235 βˆ’0.685 26.455
βˆ’0.915 βˆ’0.405 26.455
βˆ’0.577 βˆ’0.149 26.455
βˆ’0.221 0.082 26.455
0.153 0.285 26.455
0.540 0.459 26.455
0.939 0.604 26.455
1.347 0.722 26.455
1.762 0.814 26.455
2.099 0.869 26.455
2.112 0.862 26.455
2.110 0.848 26.455
1.982 0.809 26.455
1.586 0.682 26.455
1.196 0.535 26.455
0.814 0.370 26.455
0.440 0.188 26.455
0.073 βˆ’0.009 26.455
βˆ’0.287 βˆ’0.219 26.455
βˆ’0.639 βˆ’0.441 26.455
βˆ’0.985 βˆ’0.674 26.455
βˆ’1.321 βˆ’0.919 26.455
βˆ’1.647 βˆ’1.178 26.455
βˆ’1.750 βˆ’1.265 26.455
βˆ’1.778 βˆ’1.282 26.455
βˆ’1.780 βˆ’1.258 26.455
βˆ’1.750 βˆ’1.221 26.455
βˆ’1.463 βˆ’0.908 26.455
βˆ’1.157 βˆ’0.613 26.455
βˆ’0.833 βˆ’0.339 26.455
βˆ’0.489 βˆ’0.088 26.455
βˆ’0.129 0.136 26.455
0.248 0.332 26.455
0.639 0.498 26.455
1.041 0.636 26.455
1.450 0.747 26.455
1.867 0.832 26.455
2.103 0.869 26.455
2.113 0.859 26.455
2.107 0.845 26.455
1.883 0.780 26.455
1.488 0.647 26.455
1.100 0.496 26.455
0.720 0.326 26.455
0.347 0.140 26.455
βˆ’0.018 βˆ’0.061 26.455
βˆ’0.375 βˆ’0.274 26.455
βˆ’0.726 βˆ’0.498 26.455
βˆ’1.069 βˆ’0.734 26.455
βˆ’1.403 βˆ’0.983 26.455
βˆ’1.727 βˆ’1.245 26.455
βˆ’1.756 βˆ’1.270 26.455
βˆ’1.786 βˆ’1.281 26.455
βˆ’1.775 βˆ’1.251 26.455
βˆ’1.680 βˆ’1.141 26.455
βˆ’1.388 βˆ’0.832 26.455
βˆ’1.078 βˆ’0.542 26.455
βˆ’0.748 βˆ’0.274 26.455
βˆ’0.401 βˆ’0.030 26.455
βˆ’0.036 0.187 26.455
0.345 0.376 26.455
0.738 0.535 26.455
1.142 0.667 26.455
1.554 0.771 26.455
1.971 0.850 26.455
2.106 0.868 26.455
2.114 0.855 26.455
2.104 0.844 26.455
1.783 0.748 26.455
1.390 0.611 26.455
1.004 0.455 26.455
0.626 0.281 26.455
0.255 0.091 26.455
βˆ’0.108 βˆ’0.113 26.455
βˆ’0.464 βˆ’0.329 26.455
βˆ’0.813 βˆ’0.556 26.455
βˆ’1.154 βˆ’0.795 26.455
βˆ’1.485 βˆ’1.047 26.455
βˆ’1.763 βˆ’1.275 26.455
βˆ’1.787 βˆ’1.273 26.455
βˆ’1.770 βˆ’1.245 26.455
βˆ’1.609 βˆ’1.062 26.455
βˆ’1.312 βˆ’0.758 26.455
βˆ’0.997 βˆ’0.473 26.455
βˆ’0.663 βˆ’0.211 26.455
βˆ’0.311 0.027 26.455
0.058 0.237 26.455
0.442 0.418 26.455
0.838 0.571 26.455
1.245 0.695 26.455
1.658 0.793 26.455
2.076 0.866 26.455
2.110 0.866 26.455
2.113 0.851 26.455
2.083 0.838 26.455
1.684 0.716 26.455
1.293 0.574 26.455
0.909 0.413 26.455
0.533 0.235 26.455
0.164 0.041 26.455
βˆ’0.197 βˆ’0.166 26.455
βˆ’0.552 βˆ’0.384 26.455
βˆ’0.899 βˆ’0.614 26.455
βˆ’1.238 βˆ’0.857 26.455
βˆ’1.566 βˆ’1.112 26.455
βˆ’1.776 βˆ’1.211 27.771
βˆ’1.805 βˆ’1.230 27.771
βˆ’1.820 βˆ’1.214 27.771
βˆ’1.800 βˆ’1.186 27.771
βˆ’1.567 βˆ’0.926 27.771
βˆ’1.255 βˆ’0.623 27.771
βˆ’0.920 βˆ’0.345 27.771
βˆ’0.564 βˆ’0.095 27.771
βˆ’0.189 0.124 27.771
0.202 0.315 27.771
0.605 0.479 27.771
1.018 0.616 27.771
1.438 0.728 27.771
1.864 0.817 27.771
2.209 0.873 27.771
2.224 0.865 27.771
2.222 0.849 27.771
2.091 0.808 27.771
1.686 0.677 27.771
1.287 0.529 27.771
0.895 0.365 27.771
0.508 0.187 27.771
0.128 βˆ’0.004 27.771
βˆ’0.246 βˆ’0.207 27.771
βˆ’0.614 βˆ’0.421 27.771
βˆ’0.975 βˆ’0.647 27.771
βˆ’1.328 βˆ’0.884 27.771
βˆ’1.673 βˆ’1.133 27.771
βˆ’1.783 βˆ’1.216 27.771
βˆ’1.813 βˆ’1.233 27.771
βˆ’1.816 βˆ’1.206 27.771
βˆ’1.785 βˆ’1.168 27.771
βˆ’1.491 βˆ’0.848 27.771
βˆ’1.173 βˆ’0.551 27.771
βˆ’0.833 βˆ’0.280 27.771
βˆ’0.472 βˆ’0.037 27.771
βˆ’0.092 0.175 27.771
0.302 0.359 27.771
0.708 0.515 27.771
1.122 0.646 27.771
1.544 0.753 27.771
1.971 0.836 27.771
2.213 0.873 27.771
2.225 0.861 27.771
2.219 0.846 27.771
1.989 0.777 27.771
1.586 0.641 27.771
1.189 0.489 27.771
0.797 0.321 27.771
0.413 0.140 27.771
0.034 βˆ’0.054 27.771
βˆ’0.339 βˆ’0.259 27.771
βˆ’0.705 βˆ’0.476 27.771
βˆ’1.064 βˆ’0.705 27.771
βˆ’1.415 βˆ’0.945 27.771
βˆ’1.758 βˆ’1.197 27.771
βˆ’1.790 βˆ’1.221 27.771
βˆ’1.821 βˆ’1.231 27.771
βˆ’1.811 βˆ’1.199 27.771
βˆ’1.714 βˆ’1.086 27.771
βˆ’1.414 βˆ’0.771 27.771
βˆ’1.090 βˆ’0.480 27.771
βˆ’0.745 βˆ’0.216 27.771
βˆ’0.379 0.018 27.771
0.005 0.223 27.771
0.402 0.400 27.771
0.810 0.551 27.771
1.227 0.675 27.771
1.650 0.776 27.771
2.078 0.854 27.771
2.217 0.871 27.771
2.225 0.857 27.771
2.215 0.844 27.771
1.888 0.744 27.771
1.486 0.605 27.771
1.090 0.448 27.771
0.701 0.277 27.771
0.317 0.093 27.771
βˆ’0.060 βˆ’0.104 27.771
βˆ’0.431 βˆ’0.312 27.771
βˆ’0.795 βˆ’0.532 27.771
βˆ’1.152 βˆ’0.764 27.771
βˆ’1.502 βˆ’1.007 27.771
βˆ’1.797 βˆ’1.226 27.771
βˆ’1.823 βˆ’1.222 27.771
βˆ’1.805 βˆ’1.193 27.771
βˆ’1.641 βˆ’1.005 27.771
βˆ’1.335 βˆ’0.696 27.771
βˆ’1.006 βˆ’0.412 27.771
βˆ’0.655 βˆ’0.155 27.771
βˆ’0.284 0.072 27.771
0.103 0.270 27.771
0.503 0.440 27.771
0.914 0.584 27.771
1.332 0.703 27.771
1.757 0.797 27.771
2.186 0.870 27.771
2.221 0.869 27.771
2.224 0.852 27.771
2.193 0.837 27.771
1.787 0.711 27.771
1.386 0.567 27.771
0.992 0.407 27.771
0.604 0.232 27.771
0.222 0.045 27.771
βˆ’0.153 βˆ’0.155 27.771
βˆ’0.523 βˆ’0.366 27.771
βˆ’0.885 βˆ’0.589 27.771
βˆ’1.240 βˆ’0.824 27.771
βˆ’1.587 βˆ’1.070 27.771
βˆ’1.797 βˆ’1.181 29.086
βˆ’1.828 βˆ’1.200 29.086
βˆ’1.845 βˆ’1.181 29.086
βˆ’1.824 βˆ’1.151 29.086
βˆ’1.590 βˆ’0.882 29.086
βˆ’1.270 βˆ’0.573 29.086
βˆ’0.923 βˆ’0.295 29.086
βˆ’0.551 βˆ’0.050 29.086
βˆ’0.160 0.161 29.086
0.246 0.344 29.086
0.662 0.501 29.086
1.087 0.634 29.086
1.518 0.744 29.086
1.954 0.832 29.086
2.307 0.888 29.086
2.323 0.880 29.086
2.322 0.861 29.086
2.188 0.817 29.086
1.775 0.681 29.086
1.368 0.530 29.086
0.966 0.365 29.086
0.570 0.187 29.086
0.179 βˆ’0.001 29.086
βˆ’0.207 βˆ’0.200 29.086
βˆ’0.587 βˆ’0.411 29.086
βˆ’0.960 βˆ’0.634 29.086
βˆ’1.327 βˆ’0.866 29.086
βˆ’1.689 βˆ’1.106 29.086
βˆ’1.804 βˆ’1.186 29.086
βˆ’1.837 βˆ’1.202 29.086
βˆ’1.841 βˆ’1.173 29.086
βˆ’1.809 βˆ’1.133 29.086
βˆ’1.513 βˆ’0.802 29.086
βˆ’1.186 βˆ’0.500 29.086
βˆ’0.832 βˆ’0.231 29.086
βˆ’0.455 0.006 29.086
βˆ’0.059 0.209 29.086
0.349 0.385 29.086
0.768 0.536 29.086
1.194 0.663 29.086
1.626 0.768 29.086
2.063 0.851 29.086
2.312 0.888 29.086
2.325 0.875 29.086
2.318 0.857 29.086
2.084 0.785 29.086
1.673 0.645 29.086
1.267 0.490 29.086
0.867 0.322 29.086
0.472 0.141 29.086
0.082 βˆ’0.050 29.086
βˆ’0.303 βˆ’0.252 29.086
βˆ’0.681 βˆ’0.466 29.086
βˆ’1.052 βˆ’0.691 29.086
βˆ’1.418 βˆ’0.926 29.086
βˆ’1.778 βˆ’1.168 29.086
βˆ’1.812 βˆ’1.191 29.086
βˆ’1.845 βˆ’1.198 29.086
βˆ’1.835 βˆ’1.166 29.086
βˆ’1.738 βˆ’1.047 29.086
βˆ’1.434 βˆ’0.723 29.086
βˆ’1.100 βˆ’0.430 29.086
βˆ’0.740 βˆ’0.169 29.086
βˆ’0.358 0.059 29.086
0.042 0.256 29.086
0.453 0.425 29.086
0.873 0.570 29.086
1.302 0.692 29.086
1.735 0.791 29.086
2.173 0.869 29.086
2.316 0.886 29.086
2.325 0.870 29.086
2.314 0.855 29.086
1.981 0.751 29.086
1.571 0.608 29.086
1.167 0.449 29.086
0.768 0.278 29.086
0.374 0.094 29.086
βˆ’0.015 βˆ’0.099 29.086
βˆ’0.398 βˆ’0.304 29.086
βˆ’0.774 βˆ’0.521 29.086
βˆ’1.144 βˆ’0.749 29.086
βˆ’1.508 βˆ’0.985 29.086
βˆ’1.820 βˆ’1.196 29.086
βˆ’1.847 βˆ’1.190 29.086
βˆ’1.830 βˆ’1.159 29.086
βˆ’1.665 βˆ’0.964 29.086
βˆ’1.353 βˆ’0.647 29.086
βˆ’1.012 βˆ’0.362 29.086
βˆ’0.646 βˆ’0.108 29.086
βˆ’0.259 0.111 29.086
0.143 0.300 29.086
0.557 0.464 29.086
0.980 0.603 29.086
1.409 0.718 29.086
1.844 0.812 29.086
2.283 0.885 29.086
2.320 0.884 29.086
2.324 0.865 29.086
2.292 0.849 29.086
1.878 0.717 29.086
1.469 0.569 29.086
1.066 0.408 29.086
0.669 0.233 29.086
0.276 0.047 29.086
βˆ’0.111 βˆ’0.149 29.086
βˆ’0.493 βˆ’0.357 29.086
βˆ’0.867 βˆ’0.577 29.086
βˆ’1.236 βˆ’0.807 29.086
βˆ’1.599 βˆ’1.046 29.086
βˆ’1.819 βˆ’1.168 30.390
βˆ’1.852 βˆ’1.186 30.390
βˆ’1.871 βˆ’1.166 30.390
βˆ’1.850 βˆ’1.134 30.390
βˆ’1.615 βˆ’0.855 30.390
βˆ’1.288 βˆ’0.539 30.390
βˆ’0.930 βˆ’0.260 30.390
βˆ’0.545 βˆ’0.017 30.390
βˆ’0.141 0.190 30.390
0.278 0.369 30.390
0.705 0.524 30.390
1.140 0.655 30.390
1.581 0.765 30.390
2.027 0.855 30.390
2.388 0.913 30.390
2.407 0.904 30.390
2.405 0.882 30.390
2.268 0.836 30.390
1.849 0.693 30.390
1.434 0.536 30.390
1.025 0.367 30.390
0.620 0.187 30.390
0.219 βˆ’0.003 30.390
βˆ’0.177 βˆ’0.201 30.390
βˆ’0.566 βˆ’0.413 30.390
βˆ’0.949 βˆ’0.635 30.390
βˆ’1.328 βˆ’0.865 30.390
βˆ’1.705 βˆ’1.098 30.390
βˆ’1.827 βˆ’1.174 30.390
βˆ’1.862 βˆ’1.187 30.390
βˆ’1.867 βˆ’1.157 30.390
βˆ’1.836 βˆ’1.115 30.390
βˆ’1.537 βˆ’0.772 30.390
βˆ’1.201 βˆ’0.466 30.390
βˆ’0.836 βˆ’0.196 30.390
βˆ’0.446 0.038 30.390
βˆ’0.037 0.237 30.390
0.384 0.410 30.390
0.813 0.559 30.390
1.250 0.685 30.390
1.693 0.790 30.390
2.139 0.874 30.390
2.393 0.913 30.390
2.409 0.898 30.390
2.401 0.879 30.390
2.163 0.801 30.390
1.745 0.655 30.390
1.331 0.495 30.390
0.923 0.323 30.390
0.519 0.141 30.390
0.120 βˆ’0.051 30.390
βˆ’0.275 βˆ’0.253 30.390
βˆ’0.662 βˆ’0.468 30.390
βˆ’1.044 βˆ’0.692 30.390
βˆ’1.423 βˆ’0.923 30.390
βˆ’1.799 βˆ’1.156 30.390
βˆ’1.835 βˆ’1.178 30.390
βˆ’1.870 βˆ’1.184 30.390
βˆ’1.862 βˆ’1.149 30.390
βˆ’1.765 βˆ’1.026 30.390
βˆ’1.456 βˆ’0.692 30.390
βˆ’1.113 βˆ’0.395 30.390
βˆ’0.740 βˆ’0.134 30.390
βˆ’0.345 0.090 30.390
0.067 0.283 30.390
0.490 0.449 30.390
0.922 0.592 30.390
1.360 0.713 30.390
1.804 0.813 30.390
2.252 0.893 30.390
2.399 0.911 30.390
2.409 0.893 30.390
2.396 0.876 30.390
2.058 0.766 30.390
1.641 0.616 30.390
1.229 0.453 30.390
0.822 0.279 30.390
0.419 0.093 30.390
0.021 βˆ’0.101 30.390
βˆ’0.372 βˆ’0.305 30.390
βˆ’0.758 βˆ’0.523 30.390
βˆ’1.139 βˆ’0.749 30.390
βˆ’1.517 βˆ’0.981 30.390
βˆ’1.844 βˆ’1.183 30.390
βˆ’1.873 βˆ’1.175 30.390
βˆ’1.856 βˆ’1.142 30.390
βˆ’1.691 βˆ’0.939 30.390
βˆ’1.373 βˆ’0.614 30.390
βˆ’1.022 βˆ’0.326 30.390
βˆ’0.643 βˆ’0.075 30.390
βˆ’0.243 0.141 30.390
0.172 0.326 30.390
0.597 0.487 30.390
1.031 0.625 30.390
1.471 0.740 30.390
1.915 0.834 30.390
2.364 0.910 30.390
2.403 0.908 30.390
2.408 0.887 30.390
2.374 0.869 30.390
1.953 0.730 30.390
1.537 0.577 30.390
1.127 0.411 30.390
0.721 0.233 30.390
0.319 0.046 30.390
βˆ’0.078 βˆ’0.151 30.390
βˆ’0.469 βˆ’0.359 30.390
βˆ’0.854 βˆ’0.579 30.390
βˆ’1.234 βˆ’0.807 30.390
βˆ’1.611 βˆ’1.039 30.390
βˆ’1.845 βˆ’1.170 31.704
βˆ’1.881 βˆ’1.187 31.704
βˆ’1.901 βˆ’1.164 31.704
βˆ’1.881 βˆ’1.130 31.704
βˆ’1.645 βˆ’0.841 31.704
βˆ’1.312 βˆ’0.517 31.704
βˆ’0.944 βˆ’0.235 31.704
βˆ’0.548 0.008 31.704
βˆ’0.132 0.214 31.704
0.298 0.392 31.704
0.736 0.546 31.704
1.181 0.678 31.704
1.632 0.789 31.704
2.088 0.880 31.704
2.456 0.940 31.704
2.478 0.930 31.704
2.476 0.906 31.704
2.336 0.856 31.704
1.910 0.706 31.704
1.488 0.543 31.704
1.071 0.368 31.704
0.659 0.184 31.704
0.250 βˆ’0.009 31.704
βˆ’0.155 βˆ’0.210 31.704
βˆ’0.553 βˆ’0.423 31.704
βˆ’0.946 βˆ’0.647 31.704
βˆ’1.336 βˆ’0.875 31.704
βˆ’1.726 βˆ’1.102 31.704
βˆ’1.854 βˆ’1.175 31.704
βˆ’1.891 βˆ’1.187 31.704
βˆ’1.897 βˆ’1.155 31.704
βˆ’1.866 βˆ’1.110 31.704
βˆ’1.566 βˆ’0.756 31.704
βˆ’1.223 βˆ’0.443 31.704
βˆ’0.847 βˆ’0.170 31.704
βˆ’0.445 0.063 31.704
βˆ’0.025 0.261 31.704
0.406 0.433 31.704
0.847 0.581 31.704
1.294 0.708 31.704
1.746 0.813 31.704
2.202 0.900 31.704
2.463 0.940 31.704
2.480 0.924 31.704
2.472 0.901 31.704
2.229 0.819 31.704
1.804 0.666 31.704
1.384 0.500 31.704
0.968 0.323 31.704
0.556 0.136 31.704
0.148 βˆ’0.058 31.704
βˆ’0.255 βˆ’0.262 31.704
βˆ’0.652 βˆ’0.479 31.704
βˆ’1.043 βˆ’0.704 31.704
βˆ’1.433 βˆ’0.932 31.704
βˆ’1.824 βˆ’1.158 31.704
βˆ’1.863 βˆ’1.180 31.704
βˆ’1.900 βˆ’1.183 31.704
βˆ’1.892 βˆ’1.146 31.704
βˆ’1.795 βˆ’1.018 31.704
βˆ’1.484 βˆ’0.674 31.704
βˆ’1.132 βˆ’0.371 31.704
βˆ’0.749 βˆ’0.109 31.704
βˆ’0.342 0.115 31.704
0.082 0.306 31.704
0.516 0.472 31.704
0.958 0.615 31.704
1.406 0.736 31.704
1.860 0.837 31.704
2.317 0.919 31.704
2.469 0.938 31.704
2.481 0.917 31.704
2.466 0.899 31.704
2.122 0.782 31.704
1.698 0.626 31.704
1.279 0.457 31.704
0.865 0.277 31.704
0.454 0.088 31.704
0.047 βˆ’0.108 31.704
βˆ’0.355 βˆ’0.315 31.704
βˆ’0.750 βˆ’0.534 31.704
βˆ’1.141 βˆ’0.761 31.704
βˆ’1.531 βˆ’0.989 31.704
βˆ’1.872 βˆ’1.184 31.704
βˆ’1.903 βˆ’1.174 31.704
βˆ’1.886 βˆ’1.138 31.704
βˆ’1.722 βˆ’0.928 31.704
βˆ’1.399 βˆ’0.594 31.704
βˆ’1.039 βˆ’0.302 31.704
βˆ’0.649 βˆ’0.049 31.704
βˆ’0.237 0.166 31.704
0.189 0.350 31.704
0.626 0.510 31.704
1.069 0.647 31.704
1.519 0.763 31.704
1.974 0.859 31.704
2.432 0.937 31.704
2.474 0.935 31.704
2.479 0.911 31.704
2.443 0.891 31.704
2.016 0.744 31.704
1.593 0.584 31.704
1.175 0.413 31.704
0.762 0.231 31.704
0.352 0.040 31.704
βˆ’0.054 βˆ’0.159 31.704
βˆ’0.454 βˆ’0.369 31.704
βˆ’0.848 βˆ’0.591 31.704
βˆ’1.238 βˆ’0.818 31.704
βˆ’1.629 βˆ’1.046 31.704
βˆ’1.878 βˆ’1.183 33.019
βˆ’1.917 βˆ’1.199 33.019
βˆ’1.938 βˆ’1.173 33.019
βˆ’1.918 βˆ’1.137 33.019
βˆ’1.682 βˆ’0.838 33.019
βˆ’1.344 βˆ’0.505 33.019
βˆ’0.967 βˆ’0.218 33.019
βˆ’0.561 0.028 33.019
βˆ’0.134 0.235 33.019
0.306 0.413 33.019
0.755 0.567 33.019
1.211 0.699 33.019
1.672 0.810 33.019
2.138 0.902 33.019
2.514 0.963 33.019
2.538 0.951 33.019
2.536 0.925 33.019
2.393 0.872 33.019
1.961 0.714 33.019
1.532 0.544 33.019
1.108 0.364 33.019
0.688 0.175 33.019
0.271 βˆ’0.021 33.019
βˆ’0.143 βˆ’0.224 33.019
βˆ’0.550 βˆ’0.440 33.019
βˆ’0.952 βˆ’0.666 33.019
βˆ’1.352 βˆ’0.894 33.019
βˆ’1.755 βˆ’1.117 33.019
βˆ’1.887 βˆ’1.188 33.019
βˆ’1.927 βˆ’1.199 33.019
βˆ’1.935 βˆ’1.164 33.019
βˆ’1.904 βˆ’1.117 33.019
βˆ’1.602 βˆ’0.751 33.019
βˆ’1.253 βˆ’0.429 33.019
βˆ’0.868 βˆ’0.152 33.019
βˆ’0.456 0.083 33.019
βˆ’0.025 0.282 33.019
0.418 0.454 33.019
0.868 0.602 33.019
1.326 0.729 33.019
1.788 0.835 33.019
2.255 0.922 33.019
2.521 0.963 33.019
2.540 0.945 33.019
2.532 0.920 33.019
2.285 0.834 33.019
1.853 0.672 33.019
1.426 0.500 33.019
1.003 0.317 33.019
0.583 0.127 33.019
0.167 βˆ’0.071 33.019
βˆ’0.245 βˆ’0.277 33.019
βˆ’0.651 βˆ’0.496 33.019
βˆ’1.052 βˆ’0.723 33.019
βˆ’1.452 βˆ’0.950 33.019
βˆ’1.857 βˆ’1.172 33.019
βˆ’1.897 βˆ’1.193 33.019
βˆ’1.936 βˆ’1.193 33.019
βˆ’1.930 βˆ’1.155 33.019
βˆ’1.833 βˆ’1.021 33.019
βˆ’1.519 βˆ’0.666 33.019
βˆ’1.160 βˆ’0.356 33.019
βˆ’0.767 βˆ’0.090 33.019
βˆ’0.350 0.136 33.019
0.085 0.327 33.019
0.530 0.493 33.019
0.982 0.636 33.019
1.441 0.757 33.019
1.905 0.859 33.019
2.372 0.941 33.019
2.528 0.961 33.019
2.541 0.938 33.019
2.526 0.917 33.019
2.176 0.794 33.019
1.746 0.630 33.019
1.320 0.455 33.019
0.897 0.270 33.019
0.479 0.078 33.019
0.063 βˆ’0.122 33.019
βˆ’0.347 βˆ’0.330 33.019
βˆ’0.751 βˆ’0.552 33.019
βˆ’1.152 βˆ’0.780 33.019
βˆ’1.553 βˆ’1.006 33.019
βˆ’1.907 βˆ’1.196 33.019
βˆ’1.940 βˆ’1.184 33.019
βˆ’1.924 βˆ’1.146 33.019
βˆ’1.759 βˆ’0.928 33.019
βˆ’1.433 βˆ’0.584 33.019
βˆ’1.064 βˆ’0.285 33.019
βˆ’0.665 βˆ’0.030 33.019
βˆ’0.242 0.187 33.019
0.195 0.371 33.019
0.642 0.531 33.019
1.096 0.668 33.019
1.557 0.784 33.019
2.021 0.881 33.019
2.489 0.960 33.019
2.534 0.957 33.019
2.540 0.931 33.019
2.502 0.909 33.019
2.068 0.755 33.019
1.639 0.588 33.019
1.214 0.410 33.019
0.793 0.223 33.019
0.375 0.028 33.019
βˆ’0.040 βˆ’0.173 33.019
βˆ’0.449 βˆ’0.385 33.019
βˆ’0.851 βˆ’0.609 33.019
βˆ’1.252 βˆ’0.837 33.019
βˆ’1.654 βˆ’1.062 33.019
βˆ’1.917 βˆ’1.205 34.335
βˆ’1.958 βˆ’1.219 34.335
βˆ’1.981 βˆ’1.192 34.335
βˆ’1.962 βˆ’1.153 34.335
βˆ’1.725 βˆ’0.844 34.335
βˆ’1.382 βˆ’0.502 34.335
βˆ’0.998 βˆ’0.207 34.335
βˆ’0.583 0.044 34.335
βˆ’0.146 0.254 34.335
0.304 0.433 34.335
0.764 0.587 34.335
1.230 0.719 34.335
1.702 0.830 34.335
2.178 0.922 34.335
2.563 0.983 34.335
2.589 0.970 34.335
2.587 0.941 34.335
2.441 0.884 34.335
2.002 0.718 34.335
1.567 0.542 34.335
1.136 0.355 34.335
0.708 0.162 34.335
0.283 βˆ’0.038 34.335
βˆ’0.139 βˆ’0.244 34.335
βˆ’0.555 βˆ’0.462 34.335
βˆ’0.966 βˆ’0.690 34.335
βˆ’1.376 βˆ’0.918 34.335
βˆ’1.790 βˆ’1.140 34.335
βˆ’1.927 βˆ’1.210 34.335
βˆ’1.969 βˆ’1.219 34.335
βˆ’1.978 βˆ’1.181 34.335
βˆ’1.947 βˆ’1.132 34.335
βˆ’1.644 βˆ’0.754 34.335
βˆ’1.290 βˆ’0.424 34.335
βˆ’0.897 βˆ’0.140 34.335
βˆ’0.476 0.100 34.335
βˆ’0.035 0.301 34.335
0.418 0.473 34.335
0.880 0.622 34.335
1.348 0.749 34.335
1.821 0.855 34.335
2.298 0.942 34.335
2.571 0.983 34.335
2.592 0.963 34.335
2.582 0.935 34.335
2.331 0.844 34.335
1.893 0.675 34.335
1.459 0.496 34.335
1.028 0.308 34.335
0.601 0.112 34.335
0.177 βˆ’0.089 34.335
βˆ’0.244 βˆ’0.297 34.335
βˆ’0.658 βˆ’0.519 34.335
βˆ’1.068 βˆ’0.747 34.335
βˆ’1.479 βˆ’0.974 34.335
βˆ’1.895 βˆ’1.193 34.335
βˆ’1.937 βˆ’1.214 34.335
βˆ’1.978 βˆ’1.213 34.335
βˆ’1.973 βˆ’1.172 34.335
βˆ’1.877 βˆ’1.033 34.335
βˆ’1.559 βˆ’0.667 34.335
βˆ’1.195 βˆ’0.348 34.335
βˆ’0.794 βˆ’0.076 34.335
βˆ’0.367 0.154 34.335
0.078 0.346 34.335
0.533 0.513 34.335
0.996 0.656 34.335
1.466 0.777 34.335
1.940 0.878 34.335
2.418 0.961 34.335
2.578 0.980 34.335
2.593 0.955 34.335
2.575 0.932 34.335
2.221 0.803 34.335
1.784 0.631 34.335
1.351 0.450 34.335
0.921 0.259 34.335
0.495 0.062 34.335
0.071 βˆ’0.140 34.335
βˆ’0.348 βˆ’0.351 34.335
βˆ’0.761 βˆ’0.575 34.335
βˆ’1.171 βˆ’0.804 34.335
βˆ’1.583 βˆ’1.030 34.335
βˆ’1.947 βˆ’1.217 34.335
βˆ’1.982 βˆ’1.203 34.335
βˆ’1.968 βˆ’1.162 34.335
βˆ’1.803 βˆ’0.937 34.335
βˆ’1.472 βˆ’0.583 34.335
βˆ’1.097 βˆ’0.276 34.335
βˆ’0.689 βˆ’0.015 34.335
βˆ’0.257 0.205 34.335
0.191 0.390 34.335
0.648 0.551 34.335
1.113 0.688 34.335
1.584 0.804 34.335
2.059 0.901 34.335
2.537 0.979 34.335
2.584 0.976 34.335
2.591 0.948 34.335
2.552 0.924 34.335
2.111 0.761 34.335
1.675 0.587 34.335
1.243 0.403 34.335
0.814 0.211 34.335
0.389 0.012 34.335
βˆ’0.034 βˆ’0.191 34.335
βˆ’0.452 βˆ’0.406 34.335
βˆ’0.863 βˆ’0.633 34.335
βˆ’1.273 βˆ’0.861 34.335
βˆ’1.686 βˆ’1.085 34.335
βˆ’1.955 βˆ’1.233 35.651
βˆ’1.999 βˆ’1.247 35.651
βˆ’2.024 βˆ’1.217 35.651
βˆ’2.006 βˆ’1.175 35.651
βˆ’1.768 βˆ’0.857 35.651
βˆ’1.422 βˆ’0.504 35.651
βˆ’1.032 βˆ’0.200 35.651
βˆ’0.610 0.057 35.651
βˆ’0.164 0.272 35.651
0.297 0.452 35.651
0.766 0.608 35.651
1.243 0.740 35.651
1.726 0.851 35.651
2.212 0.941 35.651
2.605 1.002 35.651
2.634 0.988 35.651
2.632 0.956 35.651
2.483 0.895 35.651
2.037 0.722 35.651
1.596 0.538 35.651
1.158 0.346 35.651
0.723 0.147 35.651
0.291 βˆ’0.057 35.651
βˆ’0.140 βˆ’0.266 35.651
βˆ’0.563 βˆ’0.487 35.651
βˆ’0.983 βˆ’0.717 35.651
βˆ’1.402 βˆ’0.946 35.651
βˆ’1.826 βˆ’1.168 35.651
βˆ’1.966 βˆ’1.238 35.651
βˆ’2.011 βˆ’1.245 35.651
βˆ’2.022 βˆ’1.206 35.651
βˆ’1.991 βˆ’1.153 35.651
βˆ’1.687 βˆ’0.764 35.651
βˆ’1.328 βˆ’0.423 35.651
βˆ’0.929 βˆ’0.131 35.651
βˆ’0.500 0.115 35.651
βˆ’0.050 0.320 35.651
0.413 0.494 35.651
0.885 0.643 35.651
1.363 0.770 35.651
1.847 0.875 35.651
2.334 0.961 35.651
2.613 1.001 35.651
2.637 0.980 35.651
2.626 0.950 35.651
2.371 0.853 35.651
1.926 0.677 35.651
1.486 0.491 35.651
1.049 0.297 35.651
0.615 0.096 35.651
0.183 βˆ’0.109 35.651
βˆ’0.246 βˆ’0.320 35.651
βˆ’0.669 βˆ’0.544 35.651
βˆ’1.088 βˆ’0.775 35.651
βˆ’1.508 βˆ’1.003 35.651
βˆ’1.933 βˆ’1.222 35.651
βˆ’1.977 βˆ’1.242 35.651
βˆ’2.020 βˆ’1.239 35.651
βˆ’2.017 βˆ’1.195 35.651
βˆ’1.921 βˆ’1.052 35.651
βˆ’1.602 βˆ’0.674 35.651
βˆ’1.232 βˆ’0.346 35.651
βˆ’0.824 βˆ’0.066 35.651
βˆ’0.389 0.170 35.651
0.065 0.365 35.651
0.531 0.533 35.651
1.004 0.677 35.651
1.484 0.798 35.651
1.968 0.898 35.651
2.456 0.980 35.651
2.621 0.999 35.651
2.638 0.971 35.651
2.619 0.945 35.651
2.259 0.810 35.651
1.816 0.632 35.651
1.376 0.443 35.651
0.940 0.247 35.651
0.507 0.045 35.651
0.075 βˆ’0.160 35.651
βˆ’0.352 βˆ’0.375 35.651
βˆ’0.773 βˆ’0.602 35.651
βˆ’1.192 βˆ’0.832 35.651
βˆ’1.614 βˆ’1.058 35.651
βˆ’1.988 βˆ’1.245 35.651
βˆ’2.025 βˆ’1.228 35.651
βˆ’2.012 βˆ’1.185 35.651
βˆ’1.846 βˆ’0.953 35.651
βˆ’1.513 βˆ’0.587 35.651
βˆ’1.133 βˆ’0.271 35.651
βˆ’0.718 βˆ’0.003 35.651
βˆ’0.277 0.222 35.651
0.181 0.410 35.651
0.648 0.571 35.651
1.123 0.709 35.651
1.605 0.825 35.651
2.090 0.920 35.651
2.579 0.998 35.651
2.628 0.994 35.651
2.636 0.963 35.651
2.595 0.937 35.651
2.148 0.767 35.651
1.705 0.585 35.651
1.267 0.395 35.651
0.831 0.197 35.651
0.399 βˆ’0.006 35.651
βˆ’0.033 βˆ’0.213 35.651
βˆ’0.458 βˆ’0.431 35.651
βˆ’0.878 βˆ’0.659 35.651
βˆ’1.297 βˆ’0.889 35.651
βˆ’1.720 βˆ’1.114 35.651
βˆ’1.989 βˆ’1.266 36.953
βˆ’2.036 βˆ’1.278 36.953
βˆ’2.063 βˆ’1.246 36.953
βˆ’2.045 βˆ’1.202 36.953
βˆ’1.808 βˆ’0.874 36.953
βˆ’1.459 βˆ’0.509 36.953
βˆ’1.065 βˆ’0.195 36.953
βˆ’0.636 0.070 36.953
βˆ’0.183 0.290 36.953
0.287 0.474 36.953
0.767 0.631 36.953
1.253 0.764 36.953
1.745 0.874 36.953
2.242 0.963 36.953
2.643 1.022 36.953
2.674 1.007 36.953
2.672 0.972 36.953
2.520 0.909 36.953
2.068 0.729 36.953
1.621 0.538 36.953
1.177 0.339 36.953
0.736 0.134 36.953
0.297 βˆ’0.075 36.953
βˆ’0.140 βˆ’0.288 36.953
βˆ’0.570 βˆ’0.513 36.953
βˆ’0.998 βˆ’0.746 36.953
βˆ’1.425 βˆ’0.977 36.953
βˆ’1.857 βˆ’1.201 36.953
βˆ’2.000 βˆ’1.271 36.953
βˆ’2.047 βˆ’1.276 36.953
βˆ’2.060 βˆ’1.234 36.953
βˆ’2.031 βˆ’1.179 36.953
βˆ’1.726 βˆ’0.778 36.953
βˆ’1.365 βˆ’0.426 36.953
βˆ’0.961 βˆ’0.125 36.953
βˆ’0.525 0.129 36.953
βˆ’0.066 0.339 36.953
0.406 0.515 36.953
0.888 0.666 36.953
1.376 0.793 36.953
1.869 0.898 36.953
2.366 0.983 36.953
2.652 1.022 36.953
2.677 0.998 36.953
2.666 0.965 36.953
2.407 0.865 36.953
1.956 0.682 36.953
1.510 0.489 36.953
1.067 0.288 36.953
0.626 0.082 36.953
0.188 βˆ’0.127 36.953
βˆ’0.248 βˆ’0.343 36.953
βˆ’0.677 βˆ’0.571 36.953
βˆ’1.104 βˆ’0.804 36.953
βˆ’1.533 βˆ’1.034 36.953
βˆ’1.966 βˆ’1.255 36.953
βˆ’2.012 βˆ’1.275 36.953
βˆ’2.057 βˆ’1.269 36.953
βˆ’2.056 βˆ’1.223 36.953
βˆ’1.961 βˆ’1.074 36.953
βˆ’1.640 βˆ’0.685 36.953
βˆ’1.267 βˆ’0.346 36.953
βˆ’0.854 βˆ’0.057 36.953
βˆ’0.412 0.185 36.953
0.051 0.386 36.953
0.526 0.556 36.953
1.009 0.700 36.953
1.499 0.821 36.953
1.993 0.921 36.953
2.491 1.001 36.953
2.661 1.019 36.953
2.678 0.989 36.953
2.658 0.961 36.953
2.294 0.820 36.953
1.844 0.635 36.953
1.399 0.440 36.953
0.957 0.237 36.953
0.517 0.030 36.953
0.078 βˆ’0.180 36.953
βˆ’0.356 βˆ’0.399 36.953
βˆ’0.784 βˆ’0.629 36.953
βˆ’1.211 βˆ’0.862 36.953
βˆ’1.640 βˆ’1.090 36.953
βˆ’2.023 βˆ’1.278 36.953
βˆ’2.062 βˆ’1.258 36.953
βˆ’2.051 βˆ’1.212 36.953
βˆ’1.886 βˆ’0.973 36.953
βˆ’1.551 βˆ’0.596 36.953
βˆ’1.167 βˆ’0.269 36.953
βˆ’0.746 0.008 36.953
βˆ’0.298 0.239 36.953
0.169 0.430 36.953
0.646 0.594 36.953
1.131 0.733 36.953
1.622 0.848 36.953
2.117 0.943 36.953
2.616 1.019 36.953
2.668 1.014 36.953
2.676 0.980 36.953
2.634 0.952 36.953
2.181 0.775 36.953
1.732 0.587 36.953
1.288 0.390 36.953
0.846 0.186 36.953
0.407 βˆ’0.022 36.953
βˆ’0.031 βˆ’0.233 36.953
βˆ’0.463 βˆ’0.456 36.953
βˆ’0.891 βˆ’0.688 36.953
βˆ’1.318 βˆ’0.920 36.953
βˆ’1.749 βˆ’1.146 36.953
βˆ’2.016 βˆ’1.303 38.265
βˆ’2.065 βˆ’1.314 38.265
βˆ’2.095 βˆ’1.279 38.265
βˆ’2.079 βˆ’1.231 38.265
βˆ’1.842 βˆ’0.894 38.265
βˆ’1.493 βˆ’0.518 38.265
βˆ’1.096 βˆ’0.193 38.265
βˆ’0.662 0.082 38.265
βˆ’0.201 0.309 38.265
0.277 0.497 38.265
0.765 0.657 38.265
1.261 0.790 38.265
1.763 0.900 38.265
2.269 0.988 38.265
2.678 1.045 38.265
2.711 1.028 38.265
2.709 0.990 38.265
2.555 0.924 38.265
2.097 0.738 38.265
1.645 0.540 38.265
1.196 0.335 38.265
0.750 0.124 38.265
0.305 βˆ’0.091 38.265
βˆ’0.138 βˆ’0.309 38.265
βˆ’0.574 βˆ’0.540 38.265
βˆ’1.008 βˆ’0.777 38.265
βˆ’1.442 βˆ’1.011 38.265
βˆ’1.881 βˆ’1.237 38.265
βˆ’2.028 βˆ’1.307 38.265
βˆ’2.077 βˆ’1.311 38.265
βˆ’2.093 βˆ’1.267 38.265
βˆ’2.065 βˆ’1.208 38.265
βˆ’1.760 βˆ’0.795 38.265
βˆ’1.398 βˆ’0.431 38.265
βˆ’0.990 βˆ’0.119 38.265
βˆ’0.549 0.143 38.265
βˆ’0.083 0.359 38.265
0.398 0.540 38.265
0.889 0.692 38.265
1.386 0.820 38.265
1.889 0.924 38.265
2.396 1.007 38.265
2.688 1.044 38.265
2.715 1.019 38.265
2.703 0.983 38.265
2.440 0.879 38.265
1.984 0.689 38.265
1.532 0.490 38.265
1.084 0.283 38.265
0.638 0.070 38.265
0.194 βˆ’0.144 38.265
βˆ’0.247 βˆ’0.366 38.265
βˆ’0.683 βˆ’0.599 38.265
βˆ’1.116 βˆ’0.836 38.265
βˆ’1.552 βˆ’1.068 38.265
βˆ’1.992 βˆ’1.291 38.265
βˆ’2.040 βˆ’1.311 38.265
βˆ’2.088 βˆ’1.303 38.265
βˆ’2.089 βˆ’1.255 38.265
βˆ’1.995 βˆ’1.100 38.265
βˆ’1.675 βˆ’0.699 38.265
βˆ’1.300 βˆ’0.349 38.265
βˆ’0.882 βˆ’0.049 38.265
βˆ’0.434 0.201 38.265
0.036 0.407 38.265
0.520 0.580 38.265
1.012 0.727 38.265
1.512 0.848 38.265
2.016 0.947 38.265
2.523 1.025 38.265
2.697 1.041 38.265
2.716 1.009 38.265
2.694 0.978 38.265
2.325 0.832 38.265
1.871 0.640 38.265
1.420 0.439 38.265
0.972 0.230 38.265
0.527 0.017 38.265
0.083 βˆ’0.199 38.265
βˆ’0.357 βˆ’0.424 38.265
βˆ’0.791 βˆ’0.658 38.265
βˆ’1.225 βˆ’0.895 38.265
βˆ’1.661 βˆ’1.125 38.265
βˆ’2.052 βˆ’1.313 38.265
βˆ’2.093 βˆ’1.292 38.265
βˆ’2.085 βˆ’1.243 38.265
βˆ’1.921 βˆ’0.996 38.265
βˆ’1.585 βˆ’0.607 38.265
βˆ’1.199 βˆ’0.269 38.265
βˆ’0.773 0.018 38.265
βˆ’0.318 0.257 38.265
0.156 0.453 38.265
0.642 0.619 38.265
1.137 0.759 38.265
1.637 0.875 38.265
2.142 0.968 38.265
2.651 1.041 38.265
2.705 1.035 38.265
2.714 0.999 38.265
2.670 0.969 38.265
2.211 0.785 38.265
1.758 0.591 38.265
1.308 0.387 38.265
0.861 0.177 38.265
0.416 βˆ’0.037 38.265
βˆ’0.028 βˆ’0.254 38.265
βˆ’0.466 βˆ’0.482 38.265
βˆ’0.899 βˆ’0.718 38.265
βˆ’1.333 βˆ’0.953 38.265
βˆ’1.771 βˆ’1.182 38.265
βˆ’2.038 βˆ’1.341 39.583
βˆ’2.090 βˆ’1.351 39.583
βˆ’2.122 βˆ’1.314 39.583
βˆ’2.108 βˆ’1.263 39.583
βˆ’1.874 βˆ’0.915 39.583
βˆ’1.525 βˆ’0.527 39.583
βˆ’1.125 βˆ’0.191 39.583
βˆ’0.687 0.093 39.583
βˆ’0.220 0.328 39.583
0.265 0.521 39.583
0.762 0.684 39.583
1.267 0.819 39.583
1.778 0.928 39.583
2.293 1.014 39.583
2.710 1.068 39.583
2.745 1.050 39.583
2.743 1.009 39.583
2.586 0.940 39.583
2.124 0.748 39.583
1.666 0.544 39.583
1.213 0.332 39.583
0.762 0.114 39.583
0.312 βˆ’0.106 39.583
βˆ’0.135 βˆ’0.331 39.583
βˆ’0.576 βˆ’0.568 39.583
βˆ’1.015 βˆ’0.809 39.583
βˆ’1.456 βˆ’1.047 39.583
βˆ’1.902 βˆ’1.275 39.583
βˆ’2.051 βˆ’1.345 39.583
βˆ’2.103 βˆ’1.347 39.583
βˆ’2.121 βˆ’1.301 39.583
βˆ’2.094 βˆ’1.239 39.583
βˆ’1.792 βˆ’0.813 39.583
βˆ’1.429 βˆ’0.438 39.583
βˆ’1.019 βˆ’0.115 39.583
βˆ’0.572 0.156 39.583
βˆ’0.100 0.380 39.583
0.389 0.565 39.583
0.888 0.720 39.583
1.394 0.848 39.583
1.906 0.952 39.583
2.423 1.032 39.583
2.720 1.068 39.583
2.749 1.040 39.583
2.736 1.002 39.583
2.470 0.893 39.583
2.009 0.698 39.583
1.553 0.492 39.583
1.100 0.278 39.583
0.649 0.059 39.583
0.200 βˆ’0.162 39.583
βˆ’0.246 βˆ’0.390 39.583
βˆ’0.686 βˆ’0.628 39.583
βˆ’1.125 βˆ’0.869 39.583
βˆ’1.567 βˆ’1.105 39.583
βˆ’2.014 βˆ’1.330 39.583
βˆ’2.064 βˆ’1.349 39.583
βˆ’2.114 βˆ’1.339 39.583
βˆ’2.118 βˆ’1.288 39.583
βˆ’2.025 βˆ’1.128 39.583
βˆ’1.706 βˆ’0.715 39.583
βˆ’1.331 βˆ’0.352 39.583
βˆ’0.910 βˆ’0.042 39.583
βˆ’0.456 0.217 39.583
0.021 0.429 39.583
0.513 0.606 39.583
1.014 0.754 39.583
1.522 0.876 39.583
2.035 0.974 39.583
2.552 1.050 39.583
2.730 1.064 39.583
2.750 1.029 39.583
2.727 0.996 39.583
2.354 0.845 39.583
1.895 0.647 39.583
1.439 0.439 39.583
0.987 0.224 39.583
0.537 0.004 39.583
0.088 βˆ’0.217 39.583
βˆ’0.356 βˆ’0.449 39.583
βˆ’0.796 βˆ’0.688 39.583
βˆ’1.235 βˆ’0.929 39.583
βˆ’1.678 βˆ’1.162 39.583
βˆ’2.077 βˆ’1.351 39.583
βˆ’2.120 βˆ’1.328 39.583
βˆ’2.113 βˆ’1.276 39.583
βˆ’1.951 βˆ’1.020 39.583
βˆ’1.617 βˆ’0.619 39.583
βˆ’1.229 βˆ’0.270 39.583
βˆ’0.799 0.027 39.583
βˆ’0.339 0.274 39.583
0.143 0.476 39.583
0.637 0.646 39.583
1.140 0.787 39.583
1.650 0.903 39.583
2.164 0.995 39.583
2.682 1.065 39.583
2.739 1.058 39.583
2.748 1.019 39.583
2.702 0.987 39.583
2.239 0.797 39.583
1.780 0.596 39.583
1.326 0.385 39.583
0.874 0.169 39.583
0.425 βˆ’0.051 39.583
βˆ’0.024 βˆ’0.274 39.583
βˆ’0.466 βˆ’0.508 39.583
βˆ’0.905 βˆ’0.749 39.583
βˆ’1.345 βˆ’0.988 39.583
βˆ’1.790 βˆ’1.219 39.583

Embodiment 1. A compressor component comprising a root portion, an airfoil portion extending from the root portion, the airfoil portion having an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, form an airfoil shape.

Embodiment 2. The compressor component of embodiment 1, wherein the root portion and the airfoil portion form at least part of a compressor vane.

Embodiment 3. The compressor component of any of embodiments 1-2, wherein the root portion is configured to couple with a casing of a compressor.

Embodiment 4. The compressor component of any of embodiments 1-3, wherein the airfoil shape lies within an envelope of +/βˆ’0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.

Embodiment 5. The compressor component of any of embodiments 1-4, wherein the airfoil shape lies within an envelope of +/βˆ’0.080 inches measured in a direction normal to any of the plurality of airfoil profile sections.

Embodiment 6. The compressor component of any of embodiments 1-5, wherein the airfoil shape lies within an envelope of +/βˆ’0.020 inches measured in a direction normal to any of the plurality of airfoil profile sections.

Embodiment 7. The compressor component of any of embodiments 1-6, wherein the airfoil profile is in accordance with at least 85% of the X, Y, and Z coordinate values listed in Table 1.

Embodiment 8. The compressor component of any of embodiments 1-7, further comprising a coating applied to the airfoil shape, the coating having a thickness of less than or equal to 0.010 inches.

Embodiment 9. A compressor vane, comprising 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, wherein the X, Y, and Z coordinate values are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

Embodiment 10. The compressor vane of embodiment 9, wherein 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.

Embodiment 11. The compressor vane of any of embodiments 9-10, wherein the compressor vane is configured to couple with a plurality of compressor casings each spaced away from a compressor centerline by a different amount, wherein the Z coordinate values set forth in Table 1 are offset by a distance equal to the difference in radial spacing of each said compressor casing to provide at least one of a radially outwardly offset or radially inwardly offset airfoil shape.

Embodiment 12. The compressor vane of any of embodiments 9-11, wherein the airfoil shape lies within an envelope of +/βˆ’0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.

Embodiment 13. The compressor vane of any of embodiments 9-12, wherein the airfoil shape provides the compressor vane with a first bending natural frequency between 65 Hz and 110 Hz when scaled for use in a compressor with a 60 Hz rotation speed.

Embodiment 14. The compressor vane of any of embodiments 9-13, wherein the airfoil shape provides the compressor vane with a first bending natural frequency that differs by at least 5% from 1st and 2nd engine order excitations.

Embodiment 15. The compressor vane of any of embodiments 9-14, wherein the airfoil profile is in accordance with at least 85% of the X, Y, and Z coordinate values listed in Table 1.

Embodiment 16. The compressor vane of any of embodiments 9-16, further comprising a coating applied to the airfoil shape, the coating having a thickness of less than or equal to 0.010 inches.

Embodiment 17. A compressor, comprising a casing, a plurality of compressor vanes coupled to the casing, the plurality of compressor vanes circumferentially spaced around the casing and extending towards a center axis of the compressor, wherein each compressor vane of the plurality of compressor vanes has an airfoil comprising 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, wherein the X, Y, and Z coordinate values are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

Embodiment 18. The compressor of embodiment 17, wherein the casing and the plurality of compressor vanes coupled thereto comprise a compressor stage zero.

Embodiment 19. The compressor of any of embodiments 17-18, wherein the airfoil shape lies within an envelope of +/βˆ’0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.

Embodiment 20. The compressor of any of embodiments 17-19, wherein the airfoil profile is in accordance with at least 85% of the X, Y, and Z coordinate values listed in Table 1

Embodiment 21. An airfoil, comprising an airfoil profile substantially in accordance with the X, Y, and Z coordinates listed in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

Embodiment 22. The airfoil of embodiment 21, wherein the airfoil is part of a vane of a gas turbine engine.

Embodiment 23. The airfoil of any of embodiments 21-22, wherein the vane is a compressor vane.

Embodiment 24. The airfoil of any of embodiments 21-23, wherein the airfoil shape lies within an envelope of +/βˆ’0.160 inches measured in a direction normal to any of the plurality of airfoil profile sections.

Embodiment 25. The airfoil of any of embodiments 21-24, wherein the airfoil shape lies within an envelope of +/βˆ’0.080 inches measured in a direction normal to any of the plurality of airfoil profile sections.

Embodiment 26. The airfoil of any of embodiments 21-25, wherein the airfoil shape lies within an envelope of +/βˆ’0.020 inches measured in a direction normal to any of the plurality of airfoil profile sections.

Embodiment 27. The airfoil of any of embodiments 21-26, wherein the airfoil profile is in accordance with at least 85% of the X, Y, and Z coordinates listed in Table 1.

Embodiment 28. The airfoil of any of embodiments 21-27 further comprising a coating.

Embodiment 29. A gas turbine engine vane, comprising an airfoil portion, comprising an airfoil profile substantially in accordance with the X, Y, and Z coordinates listed in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

Embodiment 30. The gas turbine engine vane of embodiment 29, wherein the airfoil shape defines an airfoil portion of a compressor vane.

Embodiment 31. The gas turbine engine blade of any of embodiments 29-30, wherein the gas turbine engine vane is one of a plurality of gas turbine engine vanes that are assembled about an axis of a gas turbine to form an assembled gas turbine engine stage.

Embodiment 32. The gas turbine engine blade of any of embodiments 29-31, wherein the airfoil shape lies within an envelope of +/βˆ’0.160 inches measured in a direction normal to any of the plurality of airfoil profile sections.

Embodiment 33. The gas turbine engine blade of any of embodiments 29-32, wherein the airfoil shape lies within an envelope of +/βˆ’0.080 inches measured in a direction normal to any of the plurality of airfoil profile sections.

Embodiment 34. The gas turbine engine blade of any of embodiments 29-33, wherein the airfoil shape lies within an envelope of +/βˆ’0.020 inches measured in a direction normal to any of the plurality of airfoil profile sections.

Embodiment 35. The gas turbine engine blade of any of embodiments 29-34, wherein the airfoil profile is in accordance with at least 85% of the X, Y, and Z coordinates listed in Table 1.

Embodiment 36. The gas turbine engine vane of any of embodiments 29-35 further comprising a coating.

Embodiment 37. A gas turbine engine, comprising a plurality of gas turbine engine vanes circumferentially assembled about a center axis of the gas turbine engine, wherein at least one of the plurality of gas turbine engine vanes has an airfoil comprising an airfoil profile substantially in accordance with the X, Y, and Z coordinates listed in Table 1, wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system, wherein, at each Z distance, the corresponding X and Y coordinates, when connected by a smooth continuous arc, define one of a plurality of airfoil profile sections, and wherein the plurality of airfoil profile sections, when joined together by smooth continuous arcs, define an airfoil shape.

Embodiment 38. The gas turbine engine of embodiment 37, wherein the plurality of gas turbine engine vanes form an assembled compressor stage.

Embodiment 39. The gas turbine engine of any of embodiments 37-38, wherein the airfoil shape lies within an envelope of +/βˆ’0.160 inches measured in a direction normal to any of the plurality of airfoil profile sections.

Embodiment 40. The gas turbine engine of any of embodiments 37-39, wherein the airfoil profile is in accordance with at least 85% of the X, Y, and Z coordinates listed in Table 1.

Embodiment 41. Any of the aforementioned embodiments 1-40, in any combination.

The subject matter of this disclosure has been described in relation to particular embodiments, which are intended in all respects to be illustrative rather than restrictive. Alternative embodiments will become apparent to those of ordinary skill in the art to which the present subject matter pertains without departing from the scope hereof. Different combinations of elements, as well as use of elements not shown, are also possible and contemplated.

Claims

What is claimed is:

1. A compressor component comprising:

a root portion; and

an airfoil portion extending from the root portion, the airfoil portion having an uncoated nominal profile in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1,

wherein the X, Y, and Z coordinates are distances in inches measured in a Cartesian coordinate system,

wherein at each Z distance, corresponding X and Y coordinates are connected by a smooth continuous arc to define one of a plurality of airfoil profile sections, and

wherein the plurality of airfoil profile sections are joined together by smooth continuous arcs to form the airfoil profile.

2. The compressor component of claim 1, wherein the root portion and the airfoil portion form at least part of a compressor vane.

3. The compressor component of claim 1, wherein the root portion is configured to couple with a casing of a compressor.

4. The compressor component of claim 1, wherein the airfoil profile lies within an envelope of +/βˆ’0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.

5. The compressor component of claim 1, wherein the airfoil profile lies within an envelope of +/βˆ’0.080 inches measured in a direction normal to any of the plurality of airfoil profile sections.

6. The compressor component of claim 1, wherein the airfoil profile lies within an envelope of +/βˆ’0.020 inches measured in a direction normal to any of the plurality of airfoil profile sections.

7. The compressor component of claim 1, further comprising a coating applied to the airfoil profile, the coating having a thickness of less than or equal to 0.010 inches.

8. A compressor vane, comprising:

an airfoil portion having an uncoated nominal profile in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1,

wherein the X, Y, and Z coordinate values are distances in inches measured in a Cartesian coordinate system,

wherein at each Z distance, corresponding X and Y coordinates are connected by a smooth continuous arc to define one of a plurality of airfoil profile sections, and

wherein the plurality of airfoil profile sections are joined together by smooth continuous arcs to define the airfoil profile.

9. The compressor vane of claim 8, wherein 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.

10. The compressor vane of claim 9, wherein the compressor vane is configured to couple with a plurality of compressor casings each spaced away from a compressor centerline by a different amount, wherein the Z coordinate values set forth in Table 1 are offset by a distance equal to a difference in radial spacing of each compressor casing to provide at least one of a radially outward offset or radially inward offset airfoil shape.

11. The compressor vane of claim 8, wherein the airfoil profile lies within an envelope of +/βˆ’0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.

12. The compressor vane of claim 8, wherein the airfoil profile provides the compressor vane with a first bending natural frequency between 65 Hz and 110 Hz when scaled for use in a compressor with a 60 Hz rotation speed.

13. The compressor vane of claim 8, wherein the airfoil profile provides the compressor vane with a first bending natural frequency that differs by at least 5% from 1st and 2nd engine order excitations.

14. The compressor vane of claim 8, further comprising a coating applied to the airfoil profile, the coating having a thickness of less than or equal to 0.010 inches.

15. A compressor, comprising:

a casing; and

a plurality of compressor vanes coupled to the casing, the plurality of compressor vanes circumferentially spaced around the casing and extending towards a center axis of the compressor, wherein each compressor vane of the plurality of compressor vanes has an airfoil comprising:

an airfoil portion having an uncoated nominal profile in accordance with Cartesian coordinate values of X, Y, and Z set forth in Table 1,

wherein the X, Y, and Z coordinate values are distances in inches measured in a Cartesian coordinate system,

wherein at each Z distance, corresponding X and Y coordinates are connected by a smooth continuous arc to define one of a plurality of airfoil profile sections, and

wherein the plurality of airfoil profile sections are joined together by smooth continuous arcs to define the airfoil profile.

16. The compressor of claim 15, wherein the casing and the plurality of compressor vanes coupled thereto comprise a compressor stage zero.

17. The compressor of claim 15, wherein the airfoil profile lies within an envelope of +/βˆ’0.120 inches measured in a direction normal to any of the plurality of airfoil profile sections.

Resources

Images & Drawings included:

Sources:

Similar patent applications:

Recent applications in this class:

Recent applications for this Assignee: