USPatent applicationPatented

Turbine nozzle airfoil profile

Granted 19 Apr 2022 · 1 office action

Life of the application

10 dated events
⤢ drag to zoom20202022202420262028203020322034203620382040ProsecutionOwnershipTerm & fees
ProsecutionOwnershipTerm & feeshover for detail · click to open

Abstract

A turbine nozzle includes an airfoil shape. The airfoil shape may have a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z. The airfoil profile sections at Z distances may be joined smoothly with one another to form a complete airfoil shape.

Description

7 parts
›FIELD

The present application relates generally to a turbine nozzle for a gas turbine engine, and more particularly relates to a turbine nozzle airfoil profile for a turbine nozzle.

›BACKGROUND

Some aircraft and/or power plant systems, for example certain jet aircraft, nuclear, simple cycle and combined cycle power plant systems, employ turbines (also referred to as turbomachines) in their design and operation. Some of these turbines employ airfoils (e.g., stator vanes or nozzles and rotor blades) which during operation are exposed to fluid flows. These airfoils are configured to aerodynamically interact with the fluid flows and generate energy (e.g., creating thrust, turning kinetic energy to mechanical energy, converting thermal energy to mechanical energy, etc.) from these fluid flows as part of power generation. As a result of this interaction and conversion, the aerodynamic characteristics and losses of these airfoils have an impact on system and turbine operation, performance, thrust, efficiency, and power.

›BRIEF DESCRIPTION

Aspects and advantages of the turbines and turbine nozzles in accordance with the present disclosure will be set forth in part in the following description, or may be obvious from the description, or may be learned through practice of the technology.

In accordance with one embodiment, the present application provides a turbine nozzle including an airfoil shape. The airfoil shape may have a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z. The airfoil profile sections at Z distances may be joined smoothly with one another to form a complete airfoil shape.

In accordance with another embodiment, the present application provides a turbine nozzle including an airfoil having a suction-side uncoated nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance. The airfoil profile sections at the Z distances may be joined smoothly with one another to form a complete (uncoated) suction-side airfoil shape. The X, Y and Z distances are scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.

In accordance with another embodiment, the present application provides a turbine with a plurality of turbine nozzles, each having an airfoil having an airfoil shape. The airfoils each have a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance. The airfoil profile sections at the Z distances may be joined smoothly with one another to form a complete airfoil shape.

These and other features, aspects and advantages of the present turbines and turbine nozzles will become better understood with reference to the following description and appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the technology and, together with the description, serve to explain the principles of the technology.

›BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of the present turbines and turbine nozzles, including the best mode of making and using the present systems and methods, directed to one of ordinary skill in the art, is set forth in the specification, which makes reference to the appended figures, in which:

FIG. 1 is a schematic representation of an exemplary turbine having multiple stages with each stage including, in alternating relationship, a row of turbine rotor blades and a row of turbine nozzles, according to at least one embodiment of the present disclosure;

FIG. 2 is a perspective view of an exemplary turbine nozzle according to at least one embodiment of the present disclosure; and

FIG. 3 provides a cross-sectional view of an airfoil portion of the turbine nozzle of FIG. 2 .

›DETAILED DESCRIPTION · 1 of 3

Reference now will be made in detail to embodiments of the present turbines and turbine nozzles, one or more examples of which are illustrated in the drawings. Each example is provided by way of explanation, rather than limitation of, the technology. In fact, it will be apparent to those skilled in the art that various modifications and variations can be made in the present technology without departing from the scope or spirit of the claimed technology. For instance, features illustrated or described as part of one embodiment can be used with another embodiment to yield a still further embodiment. Thus, it is intended that the present disclosure covers such modifications and variations as come within the scope of the appended claims and their equivalents.

The detailed description uses numerical and letter designations to refer to features in the drawings. Like or similar designations in the drawings and description have been used to refer to like or similar parts of the invention. As used herein, the terms “first”, “second”, and “third” may be used interchangeably to distinguish one component from another and are not intended to signify location or importance of the individual components.

Referring now to the drawings, particularly to FIG. 1 , there is illustrated an exemplary turbine 10 of a gas turbine 12 including a plurality of turbine stages arranged in serial flow order. Each stage of the turbine includes a row of stationary turbine nozzles or vanes disposed axially adjacent to a corresponding row of rotating turbine rotor blades. Four stages are illustrated in FIG. 1 . The exact number of stages of the turbine 10 is a choice of engineering design and may be more or less than the four stages illustrated in FIG. 1 . The four stages are merely exemplary of one turbine design and are not intended to limit the presently claimed turbine rotor blade in any manner.

The first stage comprises a plurality of turbine nozzles or vanes 100 and a plurality of turbine rotor blades 150 . The turbine nozzles 100 are annularly arranged about an axis of a turbine rotor 14 . The turbine rotor blades 150 are annularly arranged about and coupled to the turbine rotor 14 . A second stage of the turbine 12 includes a plurality of turbine nozzles 200 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 250 annularly arranged about and coupled to the turbine rotor 14 . The turbine nozzles 200 may be coupled to a casing of the turbine 12 .

As shown in FIG. 1 , a third stage of the turbine 12 includes a plurality of turbine nozzles 300 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 350 annularly arranged about and coupled to the turbine rotor 14 . The turbine nozzles 300 may be coupled to the casing of the turbine 12 . In particular embodiments, the turbine 12 includes a fourth stage, which includes plurality of turbine nozzles 400 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 450 annularly arranged about and coupled to the turbine rotor 14 . The fourth stage turbine nozzles 400 may be coupled to the casing of the turbine 12 .

It will be appreciated that the turbine nozzles 100 , 200 , 300 and 400 and turbine rotor blades 150 , 250 , 350 and 450 are disposed or at least partially disposed within a hot gas path 18 of the turbine 12 . The various stages of the turbine 12 at least partially define the hot gas path 18 through which combustion gases, as indicated by arrows 20 , flow during operation of the gas turbine 12 .

FIG. 2 provides a perspective view of an exemplary turbine nozzle 50 as may be incorporated in any stage of the turbine 12 . FIG. 3 provides a cross-sectional top view of an airfoil 52 of the turbine nozzle 50 shown in FIG. 2 . In one embodiment, the turbine nozzle 50 as provided in Table I below is representative of one or more turbine nozzles 100 of the plurality of turbine nozzles 100 of the first stage as shown in FIG. 1 . As shown in FIGS. 2 and 3 collectively, the turbine nozzle 50 airfoil 52 includes a pressure-side wall 54 and an opposing suction-side wall 56 . The pressure-side wall 54 and the suction-side wall 56 meet or intersect at a leading edge 58 and at a trailing edge 60 of the airfoil 52 . A chord line 62 extends between the leading edge 58 and the trailing edge 60 such that pressure- and suction-side walls 54 , 56 can be said to extend in chord or chordwise between the leading edge 58 and the trailing edge 60 .

As shown in FIG. 2 , the airfoil 52 includes a root or first end 64 , which intersects with and extends radially outwardly from an inner band 66 of the turbine nozzle 50 . The airfoil 52 terminates radially at a second end or tip 68 of the airfoil 52 . The second end 68 intersects with and extends radially inwardly from an outer band 70 of the turbine nozzle 50 . The pressure- and suction-side walls 54 , 56 can be said to extend in height and/or span or in a span-wise direction 72 between the root 64 and/or the inner band 66 and the second end 68 or the outer band 70 . In other words, each turbine nozzle 50 includes an airfoil 52 having opposing pressure- and suction-side walls 54 , 56 that extend in chord or chordwise 62 between opposing leading and trailing edges 58 , 60 and that extend in span or span-wise direction 72 between the root 64 and the second end 68 of the airfoil 52 .

In particular configurations, the airfoil 52 may include a fillet 74 formed between the inner band 66 and the airfoil 52 proximate to the root 64 . The fillet 74 can include a weld or braze fillet, which can be formed via conventional MIG welding, TIG welding, brazing, etc., and can include a profile that can reduce fluid dynamic losses as a result of the presence of fillet 74 . In particular embodiments, the inner band 66 , airfoil 52 and the fillet 74 can be formed as a single component, such as by casting and/or machining and/or 3D printing and/or any other suitable technique now known or later developed and/or discovered.

›DETAILED DESCRIPTION · 2 of 3

The airfoil 52 of the turbine nozzle 50 has a profile at any cross-section taken between the inner band 66 or the root 64 and the second end 68 . The X, Y, and Z values are given in Table I as percentage values of the airfoil length or height/span. As one example only, the height or radial span of the airfoil 52 of turbine nozzle 50 may be from about 2 inches to about 50 inches (about 5 centimeters to about 130 centimeters). However, it is to be understood that heights below or above this range may also be employed as desired in the specific application.

The gas turbine hot gas path 18 requires airfoils 52 that meet system requirements of aerodynamic and mechanical blade loading and efficiency. To define the airfoil shape of each turbine nozzle airfoil 52 , there is a unique set or loci of points in space that meet the stage requirements and that can be manufactured. These unique loci of points meet the requirements for stage efficiency and are arrived at by iteration between aerodynamic and mechanical loadings enabling the turbine to run in an efficient, safe and smooth manner. These points are unique and specific to the system.

The loci that defines the turbine nozzle airfoil profile includes a set of about 2,200 points with X, Y and Z dimensions relative to a reference origin coordinate system. The Cartesian coordinate system of X, Y and Z values given in Table I below defines the profile of the turbine nozzle airfoil at various locations along its height. Table I lists data for a non-coated airfoil. The envelope/tolerance for the coordinates is about +/−5% in a direction normal to any airfoil surface location and/or about +/−5% of the chord 62 in a direction nominal to any airfoil surface location. The point data origin 76 is defined at or proximate to the leading edge 58 of the airfoil 52 and at or proximate to the root 64 .

The coordinate values for the X, Y and Z coordinates are set forth in non-dimensionalized units by the values provided in Table I, although other units of dimensions may be used when the values are appropriately converted. The X, Y and Z values set forth in Table I are also expressed in non-dimensional form (X, Y, and Z) from 0% to 100% of the height or span of the airfoil 52 . As one example only, the Cartesian coordinate values of X, Y and Z may be convertible to dimensional distances by multiplying the X, Y and Z values by a height of the airfoil at the leading edge 58 and multiplying by a constant number (e.g., 100). As one example only, the Cartesian coordinate values of X, Y and Z may be convertible to dimensional distances by multiplying the X, Y and Z values by a height of the airfoil at the trailing edge 60 and multiplying by a constant number (e.g., 100).

To convert the Z value to a Z coordinate value, e.g., in inches, the non-dimensional Z value given in Table I is multiplied by the Z height of the airfoil in inches. As described above, the Cartesian coordinate system has orthogonally-related X, Y and Z axes, and the X axis lies generally parallel to the turbine rotor centerline, i.e., the rotary axis, and a positive X coordinate value is axial toward an exhaust end of the turbine 14 . The positive Y coordinate value extends tangentially in the direction of rotation of the rotor shaft 14 , and the positive Z coordinate value is radially outwardly toward the second end 68 of the airfoil 52 . All the values in Table I are given at room temperature and are non-filleted.

By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the profile section or airfoil shape of the airfoil 52 of the turbine nozzle 50 , at each Z distance along the height of the airfoil 52 can be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section at each distance Z is fixed. The airfoil profiles of the various surface locations between the distances Z are determined by smoothly connecting the adjacent profile sections to one another to form the airfoil profile.

The Table I values are generated and shown to four decimal places for determining the profile of the airfoil. As the turbine nozzle surface heats up during operation of the turbine 14 , mechanical stresses and elevated temperatures will cause a change in the X, Y and Z values. Accordingly, the values for the profile given in Table I represent the profile of an uncoated airfoil at ambient, non-operating or non-hot conditions (e.g., room temperature).

There are typical manufacturing tolerances as well as coatings that must be accounted for in the actual profile of the airfoil 52 . Each section is joined smoothly with the other sections to form the complete airfoil shape. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/− values, including any coating thicknesses, are additive to the X and Y values given in Table I below. Accordingly, a distance of +/−5% in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular turbine nozzle airfoil design and turbine, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in the Table below at the same temperature. The data is scalable (i.e., by uniform geometric scaling), and the geometry pertains to all aerodynamic scales, at above and/or below 3000 RPM. The design of the airfoil 52 of the turbine nozzle 50 is robust to this range of variation without impairment of mechanical and aerodynamic functions.

It will also be appreciated that the airfoil 52 disclosed in the above Table I may be scaled up or down geometrically for use in other similar turbine designs using uniform geometric scaling. Consequently, the coordinate values set forth in Table I may be scaled upwardly or downwardly such that the airfoil profile shape remains unchanged. A scaled version of the coordinates in Table I would be represented by X, Y and Z coordinate values of Table I, with the X, Y and Z non-dimensional coordinate values converted to inches, multiplied or divided by the same constant number.

›DETAILED DESCRIPTION · 3 of 3

An important term in this disclosure is “profile”. The profile is the range of the variation between measured points on an airfoil surface and the ideal position listed in Table I. The actual profile on a manufactured turbine nozzle will be different than those in Table I, and the design is robust to this variation meaning that mechanical and aerodynamic function are not impaired. As noted above, a + or −5% profile tolerance is used herein. The X, Y and Z values are all non-dimensionalized relative to the airfoil height.

The disclosed airfoil shape optimizes and is specific to the machine conditions and specifications. It provides a unique profile to achieve 1) interaction among other stages in the turbine 10 ; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical nozzle or airfoil loadings. The disclosed loci of points defined in Table I allow the gas turbine 12 or any other suitable turbine to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil 52 may be adopted as long as 1) interaction among other stages in the pressure turbine 10 ; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical nozzle or airfoil loadings are maintained in the scaled turbine.

The airfoil 52 described herein thus improves overall gas turbine 12 efficiency. Specifically, the airfoil 52 provides a desired turbine efficiency lapse rate (ISO, hot, cold, part load, etc.). The airfoil 52 also meets all aeromechanic and stress requirements. The turbine nozzle 50 described herein has very specific aerodynamic design requirements such as an upstream bucket radial back pressure (i.e., work splits) and radial velocity triangles for the downstream turbine rotors 150 , 250 , 350 and 450 . Significant cross-functional design effort was required to meet these design goals. The airfoil 52 of the turbine nozzle 50 thus is of a specific shape to meet aerodynamic, mechanical, and heat transfer requirements in an efficient and cost-effective manner.

This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims or if they include equivalent structural elements with insubstantial differences from the literal language of the claims.

›Tables in the description — 1
TABLE I
SUCTION-SIDEPRESSURE-SIDE
X (%)Y (%)Z (%)X (%)Y (%)Z (%)
0.00000.00000.00000.00000.00000.0000
0.7518−2.69770.0000−0.33512.17790.0000
1.8343−5.25370.0000−0.43824.36440.0000
3.2562−7.65930.0000−0.30506.55960.0000
4.9658−9.86730.00000.06018.74180.0000
6.9161−11.85620.00000.627210.86820.0000
9.0940−13.60880.00001.387512.93440.0000
11.4309−15.12520.00002.341214.92330.0000
13.8666−16.41820.00003.479516.79630.0000
16.3839−17.52650.00004.764018.56180.0000
18.9742−18.48450.00006.147220.25860.0000
21.6203−19.30920.00007.594821.90390.0000
24.3095−20.00520.00009.085423.51910.0000
27.0244−20.56360.000010.597525.10850.0000
29.7521−20.96740.000012.122526.68930.0000
32.5014−21.19940.000013.656128.25720.0000
35.2807−21.23800.000015.198229.82090.0000
38.0601−21.05760.000016.740431.37590.0000
40.7964−20.64090.000018.291232.92670.0000
43.4770−19.97510.000019.846234.47310.0000
46.1016−19.04720.000021.405636.01530.0000
48.6275−17.87450.000022.969237.55320.0000
51.0116−16.47410.000024.537139.08670.0000
53.2669−14.86750.000026.109440.61600.0000
55.4019−13.08050.000027.685942.14100.0000
57.4037−11.14740.000029.266743.66600.0000
59.2723−9.11120.000030.847545.18660.0000
61.0293−6.98050.000032.428446.70730.0000
62.6874−4.76820.000034.009248.23230.0000
64.2682−2.48290.000035.585749.75300.0000
65.7674−0.15040.000037.162251.28230.0000
67.19362.22090.000038.730252.81150.0000
68.55114.61790.000040.293854.34940.0000
69.84847.03640.000041.848955.89590.0000
71.09419.48060.000043.395357.44230.0000
72.292611.93780.000044.933259.00170.0000
73.443914.41640.000046.462560.56530.0000
74.565116.90790.000047.983262.13750.0000
75.651919.40810.000049.495363.71410.0000
76.712921.92530.000050.994565.29920.0000
77.748224.44690.000052.480866.89290.0000
78.757726.98140.000053.954268.49950.0000
79.745729.52450.000055.419070.11470.0000
80.716532.07610.000056.866771.73850.0000
81.665934.63640.000058.297273.37510.0000
82.598037.20090.000059.714875.02040.0000
83.513039.76970.000061.119576.68280.0000
84.410842.35150.000062.502778.35390.0000
85.295844.93320.000063.873080.03780.0000
86.167847.52350.000065.230581.73460.0000
87.022650.11810.000066.566483.44430.0000
87.864652.72130.000067.889585.16690.0000
88.698055.32450.000069.191186.89810.0000
89.514257.93630.000070.479888.64640.0000
90.321760.54810.000071.751490.40340.0000
91.120863.16850.000073.005792.17750.0000
91.906965.79320.000074.242993.96020.0000
92.680168.41790.000075.467295.76010.0000
93.444771.05120.000076.674397.56860.0000
94.200873.68440.000077.864299.39000.0000
94.939676.31770.000079.0369101.22430.0000
95.674278.95960.000080.1924103.06710.0000
96.391681.60140.000081.3351104.92720.0000
97.100484.24330.000082.4606106.79580.0000
97.800686.88950.000083.5646108.68160.0000
98.487989.53990.000084.6557110.57610.0000
99.162392.19040.000085.7339112.48340.0000
99.823994.84510.000086.7950114.40350.0000
100.476897.50420.000087.8431116.33230.0000
101.1169100.16320.000088.8784118.26970.0000
101.7484102.82660.000089.9008120.21990.0000
102.3626105.48990.000090.9103122.17450.0000
102.9640108.15760.000091.9112124.13760.0000
103.5569110.82950.000092.9035126.10510.0000
104.1325113.50570.000093.8829128.07680.0000
104.6952116.18200.000094.8494130.05280.0000
105.2494118.86250.000095.8031132.03320.0000
105.7863121.54300.000096.7438134.02210.0000
106.3147124.22780.000097.6717136.01960.0000
106.8302126.91700.000098.5781138.02140.0000
107.3371129.60610.000099.4630140.03610.0000
107.8397132.29950.0000100.3265142.06370.0000
108.3337134.99290.0000101.1641144.09980.0000
108.8320137.68630.0000101.9760146.14890.0000
109.3346140.37970.0000102.7664148.20650.0000
109.8458143.06890.0000103.5354150.27280.0000
110.3699145.75370.0000104.2828152.34760.0000
110.9111148.43850.0000105.0174154.42240.0000
111.4653151.11470.0000105.7348156.50590.0000
112.0280153.79100.0000106.4436158.59360.0000
112.5865156.47150.0000107.1481160.68560.0000
113.1277159.15630.0000107.8440162.77760.0000
113.6432161.84970.0000108.5485164.86960.0000
114.1200164.54740.0000109.2659166.95300.0000
114.5496167.24090.0000110.0047169.02790.0000
114.7429168.59400.0000110.7608171.09840.0000
114.9362169.94720.0000111.2548172.43870.0000
115.1768171.71270.0000111.8132173.74890.0000
115.1682173.46110.0000112.8313174.68960.0000
113.9310174.65530.0000113.9310174.65530.0000
−0.07730.081610.0004−0.07730.081610.0004
0.1224−0.807610.0004−0.23411.520710.0004
0.3222−1.696810.0004−0.39092.959710.0004
0.6057−2.650510.0004−0.39313.681410.0004
0.8720−3.432310.0004−0.39524.403110.0004
1.5679−5.111910.0004−0.20196.645510.0004
1.6410−5.266510.00040.23638.857810.0004
3.0199−7.723710.00040.889211.005610.0004
4.7038−9.979010.00041.735513.093310.0004
6.6455−12.019410.00042.775015.082310.0004
8.7976−13.836510.00044.012216.955210.0004
11.1216−15.421610.00045.399718.716410.0004
13.5788−16.796310.00046.881720.396110.0004
16.1347−17.973310.00048.428222.024110.0004
18.7680−18.978510.000410.009023.617910.0004
21.4528−19.824710.000411.615625.190110.0004
24.1806−20.524910.000413.239426.745110.0004
26.9384−21.079110.000414.863228.291610.0004
29.7264−21.474310.000416.495629.833810.0004
32.5358−21.697710.000418.127931.371610.0004
35.3495−21.727710.000419.764632.909510.0004
38.1589−21.543010.000421.397034.447410.0004
40.9425−21.122010.000423.033635.980910.0004
43.6789−20.460510.000424.666037.523110.0004
46.3422−19.549810.000426.302739.061010.0004
48.9110−18.394310.000427.930840.607410.0004
51.3596−17.002410.000429.558842.153910.0004
53.6750−15.400110.000431.182643.704610.0004
55.8529−13.617410.000432.802145.259710.0004
57.8977−11.684410.000434.408746.823310.0004
59.8136−9.622410.000436.006748.395510.0004
61.6092−7.453110.000437.591849.976410.0004
63.2974−5.197810.000439.164151.570110.0004
64.8868−2.873810.000440.723453.172410.0004
66.3860−0.489710.000442.265654.787610.0004
67.81221.937410.000443.790556.415710.0004
69.16534.407410.000445.302658.052310.0004
70.45846.907510.000446.801859.701910.0004
71.69559.437710.000448.283961.364310.0004
72.885411.989310.000449.748763.035410.0004
74.023814.562510.000451.200764.723610.0004
75.127817.157110.000452.631166.420410.0004
76.188819.764610.000454.048768.134410.0004
77.215522.385010.000455.444869.861210.0004
78.216425.018310.000456.823771.601010.0004
79.183027.660110.000458.185573.353710.0004
80.128030.314910.000459.525875.123510.0004
81.047332.973910.000460.848876.901910.0004
81.945135.645910.000462.154778.701810.0004
82.825738.317810.000463.443480.510310.0004
83.680641.002610.000464.710782.336010.0004
84.522543.687410.000465.960784.174610.0004
85.343046.380910.000467.193686.026010.0004
86.150649.078610.000468.405087.890410.0004
86.941051.780610.000469.599289.771910.0004
87.718554.486910.000470.776291.666310.0004
88.483257.197510.000471.940493.569310.0004
89.234959.912410.000473.083095.489510.0004
89.973862.627310.000474.217197.422610.0004
90.699865.350710.000475.329799.364210.0004
91.412968.074210.000476.4294101.314510.0004
92.117470.797710.000477.5162103.277610.0004
92.809073.529810.000478.5901105.253710.0004
93.492076.261910.000479.6469107.234010.0004
94.162178.993910.000480.6865109.222910.0004
94.823781.734610.000481.7174111.220410.0004
95.472384.471010.000482.7269113.222210.0004
96.112487.215910.000483.7278115.236910.0004
96.739689.960910.000484.7158117.251610.0004
97.362492.705910.000485.6867119.274910.0004
97.968195.455110.000486.6489121.298210.0004
98.565298.204410.000487.6026123.330010.0004
99.1537100.957910.000488.5519125.366210.0004
99.7337103.715810.000489.4884127.402410.0004
100.3007106.473610.000490.4206129.442810.0004
100.8591109.231510.000491.3484131.487610.0004
101.4090111.993610.000492.2677133.536710.0004
101.9460114.760110.000493.1784135.590010.0004
102.4743117.526510.000494.0805137.643410.0004
102.9898120.293010.000494.9740139.705310.0004
103.4924123.063710.000495.8589141.767310.0004
103.9821125.834410.000496.7267143.837810.0004
104.4590128.609510.000497.5772145.916910.0004
104.9229131.388810.000498.4106148.000310.0004
105.3782134.168110.000499.2225150.092410.0004
105.8293136.947510.0004100.0129152.197310.0004
106.2760139.726810.0004100.7818154.302210.0004
106.7228142.506110.0004101.5293156.419910.0004
107.1824145.285510.0004102.2595158.542010.0004
107.6550148.060510.0004102.9683160.672710.0004
108.1490150.831210.0004103.6685162.807710.0004
108.6645153.602010.0004104.3644164.942710.0004
109.1971156.364110.0004105.0518167.081910.0004
109.7427159.126310.0004105.7477169.216910.0004
110.2882161.888410.0004106.4522171.351910.0004
110.8209164.654810.0004107.1653173.478210.0004
111.8046170.196310.0004108.6602177.718110.0004
112.2428172.979910.0004109.4162179.827310.0004
112.6509175.767910.0004111.1560181.206210.0004
111.9034178.487010.0004111.9034178.487010.0004
−0.18900.481120.0009−0.18900.481120.0009
0.4468−2.354120.0009−0.36081.950320.0009
1.4648−5.077520.0009−0.42963.419420.0009
2.8352−7.612020.0009−0.41024.154020.0009
4.5449−9.966120.0009−0.39094.888520.0009
6.5252−12.092420.0009−0.12467.165320.0009
8.7289−13.974020.00090.39099.399020.0009
11.1173−15.636420.00091.125511.564120.0009
13.6217−17.084120.00092.057613.651820.0009
16.2120−18.334120.00093.196015.640720.0009
18.8668−19.416620.00094.523417.496520.0009
21.5817−20.357420.00095.996819.236220.0009
24.3567−21.152120.00097.573320.894420.0009
27.1833−21.796520.00099.205722.496720.0009
30.0357−22.269020.000910.876824.060320.0009
32.8966−22.552520.000912.573625.598220.0009
35.7747−22.625520.000914.283327.123220.0009
38.6743−22.458020.000915.997328.639520.0009
41.5353−22.028420.000917.711230.151620.0009
44.3232−21.323920.000919.420931.668020.0009
47.0338−20.344520.000921.126333.193020.0009
49.6499−19.081620.000922.827434.722320.0009
52.1242−17.582420.000924.520036.264420.0009
54.4353−15.868420.000926.208237.810920.0009
56.6176−13.961120.000927.887839.366020.0009
58.6580−11.899120.000929.558840.929620.0009
60.5481−9.725520.000931.217042.506120.0009
62.3094−7.457420.000932.862244.095520.0009
63.9589−5.111920.000934.490345.702120.0009
65.5140−2.697720.000936.101247.321620.0009
66.9874−0.219120.000937.694948.954020.0009
68.38352.306820.000939.262950.603520.0009
69.71094.871320.000940.813652.270320.0009
70.97817.466020.000942.342953.954220.0009
72.189510.086320.000943.846455.646720.0009
73.345112.728220.000945.332757.360720.0009
74.457715.391620.000946.797559.083320.0009
75.527318.076420.000948.240960.827420.0009
76.558320.769820.000949.667162.580020.0009
77.554923.480420.000951.071864.354120.0009
78.521426.199620.000952.455066.136920.0009
79.453628.927420.000953.821067.936820.0009
80.360031.659420.000955.165669.753920.0009
81.244934.404420.000956.488771.579520.0009
82.104037.153720.000957.790373.422420.0009
82.941739.907220.000959.079075.282420.0009
83.762242.669420.000960.341977.155420.0009
84.561245.435820.000961.587779.036920.0009
85.343048.206520.000962.812080.939920.0009
86.111950.981620.000964.023482.851520.0009
86.859453.765220.000965.209084.780320.0009
87.594056.548820.000966.381786.717620.0009
88.319959.336720.000967.537388.672220.0009
89.028762.133320.000968.671390.639620.0009
89.728964.929820.000969.792592.615720.0009
90.416367.726320.000970.896594.604620.0009
91.090770.531420.000971.983396.606420.0009
91.756573.336520.000973.057398.616820.0009
92.409576.145920.000974.1140100.640120.0009
93.049578.955320.000975.1579102.667620.0009
93.681081.769020.000976.1888104.703820.0009
94.299684.582720.000977.2026106.748620.0009
94.909687.400720.000978.2078108.797620.0009
95.511090.218720.000979.2001110.851020.0009
96.103893.040920.000980.1796112.908620.0009
96.683795.863220.000981.1461114.974920.0009
97.259398.685520.000982.0997117.045420.0009
97.8221101.512120.000983.0448119.115920.0009
98.3762104.338720.000983.9813121.195120.0009
98.9218107.169620.000984.9048123.282820.0009
99.4587110.000420.000985.8198125.370520.0009
99.9828112.835620.000986.7305127.458220.0009
100.5026115.670820.000987.6326129.554520.0009
101.0095118.505920.000988.5347131.650820.0009
101.5078121.345420.000989.4282133.747220.0009
101.9932124.184920.000990.3217135.847820.0009
102.4700127.028720.000991.2110137.948420.0009
102.9383129.872420.000992.0959140.049020.0009
103.3979132.720520.000992.9722142.153920.0009
103.8447135.568520.000993.8485144.258820.0009
104.2828138.416620.000994.7120146.372320.0009
104.7167141.269020.000995.5625148.485820.0009
105.1506144.121320.000996.4002150.603520.0009
105.5844146.973720.000997.2250152.734220.0009
106.0312149.821720.000998.0283154.864920.0009
106.4908152.669820.000998.8187157.008520.0009
106.9677155.513620.000999.5833159.152020.0009
107.4745158.348720.0009100.3308161.308520.0009
107.9986161.183920.0009101.0610163.469220.0009
108.5442164.014820.0009101.7741165.634320.0009
109.0983166.845720.0009102.4700167.807920.0009
109.6482169.680820.0009103.1531169.985820.0009
110.1808172.520320.0009103.8361172.163820.0009
110.6749175.359820.0009104.5191174.341720.0009
111.1259178.203520.0009105.2236176.515320.0009
111.5426181.051620.0009105.9625178.671820.0009
111.8347182.898720.0009107.4917182.967520.0009
112.0967184.754520.0009108.2220185.136820.0009
111.5082186.459920.0009109.6009186.846520.0009
110.5546186.653220.0009110.5546186.653220.0009
−0.33510.919330.0013−0.33510.919330.0013
0.2534−1.976030.0013−0.47682.418530.0013
1.2372−4.764030.0013−0.51123.917730.0013
2.5946−7.388630.0013−0.43395.412630.0013
4.2828−9.811430.0013−0.27066.566030.0013
6.2675−12.002230.0013−0.10747.719430.0013
8.4883−13.948230.00130.46399.983230.0013
10.8896−15.675130.00131.267212.161230.0013
13.4112−17.212930.00132.285314.261830.0013
16.0273−18.591930.00133.505316.246430.0013
18.7121−19.829030.00134.914318.093630.0013
21.4528−20.937330.00136.473619.820430.0013
24.2407−21.908230.00138.127521.461430.0013
27.0845−22.724330.00139.845823.046530.0013
29.9712−23.355830.001311.602724.580130.0013
32.8966−23.776830.001313.385526.087930.0013
35.8435−23.944330.001315.176827.582830.0013
38.7989−23.836930.001316.968129.077730.0013
41.7243−23.420330.001318.755130.576930.0013
44.5852−22.681430.001320.533532.089030.0013
47.3431−21.616030.001322.303433.614030.0013
49.9635−20.254330.001324.056035.151930.0013
52.4335−18.630530.001325.800136.702630.0013
54.7360−16.779130.001327.527038.270530.0013
56.8796−14.742930.001329.240939.855730.0013
58.8771−12.565030.001330.937841.458030.0013
60.7371−10.271130.001332.613143.081730.0013
62.4726−7.878330.001334.271244.727030.0013
64.1007−5.412630.001335.907946.389430.0013
65.6343−2.882430.001337.514548.077730.0013
67.0819−0.305030.001339.099649.778830.0013
68.45652.311130.001340.654751.505630.0013
69.76674.961630.001342.179653.245430.0013
71.01257.642130.001343.678955.006730.0013
72.206710.344130.001345.152356.785130.0013
73.345113.071930.001346.599958.585030.0013
74.440515.816830.001348.021860.402130.0013
75.497218.579030.001349.426562.232130.0013
76.511021.354030.001350.805464.079230.0013
77.499024.137630.001352.162965.943630.0013
78.452726.938430.001353.494667.825130.0013
79.380629.743530.001354.809169.719530.0013
80.278432.557230.001356.106471.626830.0013
81.159035.379530.001357.377973.547030.0013
82.009538.210430.001358.632275.484330.0013
82.842941.045630.001359.869477.434630.0013
83.659143.889330.001361.085179.397730.0013
84.453846.733130.001362.283681.373830.0013
85.227049.585530.001363.464983.362730.0013
85.987452.442130.001364.629185.368830.0013
86.734855.303130.001365.776087.383530.0013
87.465158.168330.001366.905889.406830.0013
88.182561.033530.001368.018491.442930.0013
88.882763.903130.001369.118193.492030.0013
89.574366.776930.001370.200695.545330.0013
90.253069.655130.001371.270297.611630.0013
90.923172.533230.001372.322799.682130.0013
91.580475.415630.001373.3623101.761230.0013
92.224878.298030.001374.3889103.844730.0013
92.860581.184830.001375.4027105.936730.0013
93.483484.075830.001376.3993108.028730.0013
94.097786.966830.001377.3873110.133630.0013
94.703489.857830.001378.3668112.238530.0013
95.300592.753130.001379.3290114.347730.0013
95.884795.652730.001380.2827116.465530.0013
96.456098.552330.001381.2277118.583330.0013
97.0231101.452030.001382.1642120.709730.0013
97.5772104.355930.001383.0921122.836030.0013
98.1228107.259830.001384.0070124.971030.0013
98.6597110.168030.001384.9177127.106030.0013
99.1881113.076230.001385.8241129.245230.0013
99.7079115.984430.001386.7176131.388830.0013
100.2191118.896930.001387.6112133.532430.0013
100.7217121.809430.001388.4961135.680230.0013
101.2157124.721930.001389.3810137.828130.0013
101.7011127.634330.001390.2573139.980230.0013
102.1779130.551130.001391.1336142.132430.0013
102.6462133.472230.001392.0057144.284530.0013
103.1015136.393330.001392.8734146.436730.0013
103.5526139.314430.001393.7368148.593230.0013
103.9950142.235530.001394.5917150.753930.0013
104.4332145.156630.001395.4422152.914630.0013
104.8713148.082030.001396.2756155.084030.0013
105.3138151.003030.001397.1004157.253330.0013
105.7649153.924130.001397.9037159.435530.0013
106.2331156.840930.001398.6941161.617830.0013
106.7185159.757730.001399.4630163.812930.0013
107.2254162.670230.0013100.2105166.012330.0013
107.7581165.578430.0013100.9451168.216030.0013
108.3036168.482330.0013101.6581170.428330.0013
108.8664171.381930.0013102.3583172.644930.0013
109.4334174.285830.0013103.0414174.865830.0013
109.9918177.185430.0013103.7244177.086630.0013
110.5245180.093630.0013104.4117179.307530.0013
111.0142183.010430.0013105.1334181.515530.0013
111.4524185.931530.0013105.9023183.706330.0013
111.7359187.821630.0013106.7056185.888630.0013
111.9765189.720330.0013107.4745188.083730.0013
111.1903191.361330.0013108.2650190.261630.0013
109.9790191.662030.0013109.9790191.662030.0013
−0.46391.275840.0017−0.46391.275840.0017
0.0644−1.718340.0017−0.57562.800840.0017
1.0181−4.609340.0017−0.56274.312940.0017
2.3455−7.315640.0017−0.44255.825040.0017
4.0423−9.845840.0017−0.24706.991340.0017
6.0398−12.131140.0017−0.05158.157640.0017
8.2907−14.163040.00170.592810.425740.0017
10.7350−15.975840.00171.464812.607940.0017
13.2909−17.629640.00172.560214.699940.0017
15.9156−19.141740.00173.861816.671740.0017
18.6090−20.537840.00175.348218.497440.0017
21.3669−21.817940.00176.976220.198540.0017
24.1849−22.964940.00178.703121.809440.0017
27.0587−23.940040.001710.494423.360140.0017
29.9841−24.704740.001712.324424.863640.0017
32.9696−25.224540.001714.167326.341340.0017
36.0153−25.452140.001716.014427.819140.0017
39.0395−25.340440.001717.853029.301140.0017
42.0293−24.867940.001719.683030.796040.0017
44.9590−24.008840.001721.500132.308140.0017
47.7254−22.801740.001723.295733.841740.0017
50.3243−21.293940.001725.078435.392440.0017
52.7815−19.502640.001726.839636.960440.0017
55.0582−17.483640.001728.583738.549840.0017
57.1631−15.297040.001730.306340.160740.0017
59.1220−12.973140.001732.007441.797340.0017
60.9519−10.541740.001733.687043.455540.0017
62.6530−8.028740.001735.340945.139440.0017
64.2467−5.459940.001736.973246.849140.0017
65.7502−2.839540.001738.584148.588940.0017
67.1721−0.176140.001740.165050.350140.0017
68.52962.521640.001741.715752.141440.0017
69.82265.253740.001743.236453.949940.0017
71.06408.020140.001744.722755.784240.0017
72.249710.812340.001746.183357.631340.0017
73.383713.621740.001747.613759.500040.0017
74.474816.448340.001749.018461.385840.0017
75.527319.283540.001750.393163.284540.0017
76.541122.131540.001751.746265.196140.0017
77.524824.988240.001753.077967.124940.0017
78.482827.857740.001754.388169.070840.0017
79.414930.731640.001755.672571.025440.0017
80.317033.618340.001756.939772.997140.0017
81.201936.509340.001758.181274.981740.0017
82.061139.404640.001759.405576.975040.0017
82.898742.308540.001760.612678.981140.0017
83.719245.221040.001761.798281.000040.0017
84.522548.137840.001762.966683.031940.0017
85.308651.058940.001764.117985.072440.0017
86.077653.988640.001765.251987.125740.0017
86.833656.918340.001766.373189.183440.0017
87.568259.852240.001767.472891.253940.0017
88.294262.790540.001768.563993.337340.0017
89.007365.733140.001769.637995.425140.0017
89.707568.675640.001770.694697.525740.0017
90.390571.622540.001771.742899.630640.0017
91.069274.569440.001772.7737101.748440.0017
91.730777.520540.001773.7918103.870440.0017
92.383780.471740.001774.8013106.001140.0017
93.028183.427140.001775.7979108.136140.0017
93.659586.382640.001776.7816110.275440.0017
94.282489.342340.001777.7568112.418940.0017
94.892492.302140.001778.7190114.571140.0017
95.498195.261840.001779.6727116.723240.0017
96.090998.225940.001780.6177118.879740.0017
96.6708101.194240.001781.5499121.044740.0017
97.2464104.162540.001782.4778123.209840.0017
97.8092107.130940.001783.3928125.374840.0017
98.3633110.099240.001784.3034127.548440.0017
98.9089113.076240.001785.2056129.726440.0017
99.4459116.048840.001786.0991131.904340.0017
99.9742119.025740.001786.9926134.082240.0017
100.4940122.002740.001787.8775136.264440.0017
101.0052124.983940.001788.7581138.451040.0017
101.5078127.965140.001789.6344140.633240.0017
102.0018130.946340.001790.5108142.819740.0017
102.4872133.931940.001791.3828145.010540.0017
102.9683136.917440.001792.2505147.197040.0017
103.4366139.907240.001793.1183149.392240.0017
103.9005142.892740.001793.9774151.583040.0017
104.3602145.882640.001794.8323153.778140.0017
104.8155148.876740.001795.6785155.977540.0017
105.2708151.866540.001796.5162158.176940.0017
105.7262154.856340.001797.3410160.380640.0017
106.1944157.846140.001798.1571162.592940.0017
106.6798160.831740.001798.9561164.809540.0017
107.1867163.812940.001799.7380167.030440.0017
107.7151166.789840.0017100.5069169.255640.0017
108.2736169.758240.0017101.2501171.489340.0017
108.8535172.726540.0017101.9803173.731740.0017
109.4506175.694840.0017102.6891175.978340.0017
110.0520178.658940.0017103.3893178.229340.0017
110.6319181.631540.0017104.0852180.480340.0017
111.1646184.604140.0017104.7983182.726940.0017
111.6371187.589740.0017105.5372184.965040.0017
112.1010190.579540.0017106.3276187.181640.0017
112.2600191.546040.0017107.1481189.389640.0017
112.4189192.512640.0017107.9514191.606240.0017
112.2256194.407040.0017108.7847193.805640.0017
110.5331195.201740.0017110.5331195.201740.0017
−0.54991.563650.0021−0.54991.563650.0021
−0.1461−1.482050.0021−0.61863.097250.0021
0.7346−4.459050.0021−0.53704.622250.0021
2.0061−7.255550.0021−0.36086.138650.0021
3.6428−9.880150.0021−0.12247.304950.0021
5.5973−12.277250.00210.11608.471250.0021
7.8311−14.403550.00210.850610.730750.0021
10.2668−16.315150.00211.817112.895750.0021
12.8141−18.080750.00213.002714.953450.0021
15.4173−19.725950.00214.394516.886550.0021
18.0850−21.268150.00215.958218.669250.0021
20.8256−22.698650.00217.659320.323050.0021
23.6393−23.991650.00219.463521.882450.0021
26.5261−25.108550.002111.319223.385950.0021
29.4772−26.006350.002113.205024.859350.0021
32.4928−26.642050.002115.090926.324250.0021
35.5857−26.955650.002116.972427.797650.0021
38.6700−26.891250.002118.836729.283950.0021
41.7243−26.414450.002120.688230.791750.0021
44.6969−25.512350.002122.518132.325350.0021
47.5020−24.227850.002124.330933.880350.0021
50.1482−22.608450.002126.126635.456850.0021
52.6054−20.718250.002127.896437.054950.0021
54.8735−18.617650.002129.649038.674350.0021
56.9741−16.340950.002131.375940.323950.0021
58.9244−13.931050.002133.085641.999250.0021
60.7328−11.439550.002134.769543.700350.0021
62.4168−8.883550.002136.427745.422950.0021
64.0062−6.263250.002138.051547.171350.0021
65.5054−3.595550.002139.649548.941150.0021
66.9273−0.884950.002141.213150.736750.0021
68.28471.860050.002142.742452.549550.0021
69.58634.643750.002144.241654.383850.0021
70.83217.457450.002145.710756.239550.0021
72.026310.292550.002147.154158.112550.0021
73.173213.149250.002148.567460.006950.0021
74.277216.018750.002149.954961.922850.0021
75.342618.901250.002151.316663.851550.0021
76.369321.792250.002152.656965.797550.0021
77.365924.691850.002153.975767.756350.0021
78.336727.604350.002155.273069.732450.0021
79.277530.521150.002156.544571.725650.0021
80.196733.446550.002157.798973.731750.0021
81.094536.380450.002159.031775.750750.0021
81.966639.323050.002160.247477.782650.0021
82.821442.269950.002161.441679.827350.0021
83.654845.221050.002162.614481.885050.0021
84.475348.176550.002163.774283.959850.0021
85.274351.140550.002164.916986.043250.0021
86.060454.108950.002166.038188.139550.0021
86.829357.081550.002167.146490.244450.0021
87.581160.062750.002168.237592.357950.0021
88.319963.043950.002169.311494.484350.0021
89.045966.029550.002170.372496.615050.0021
89.759069.015050.002171.416398.749950.0021
90.463572.009150.002172.4473100.897850.0021
91.150874.998950.002173.4611103.050050.0021
91.829577.997350.002174.4620105.206450.0021
92.495480.995750.002175.4500107.367250.0021
93.152683.994250.002176.4294109.532250.0021
93.801386.996950.002177.3959111.705850.0021
94.437090.003950.002178.3539113.879550.0021
95.064293.006650.002179.2989116.061750.0021
95.682896.017950.002180.2354118.243950.0021
96.292899.029250.002181.1676120.434750.0021
96.8899102.040550.002182.0869122.625550.0021
97.4827105.051850.002183.0018124.820750.0021
98.0626108.067450.002183.9082127.015850.0021
98.6383111.087250.002184.8103129.219550.0021
99.2053114.107150.002185.7081131.423250.0021
99.7594117.127050.002186.5974133.626950.0021
100.3093120.151250.002187.4823135.834950.0021
100.8506123.175450.002188.3629138.042950.0021
101.3832126.199650.002189.2392140.255250.0021
101.9073129.228150.002190.1156142.467550.0021
102.4228132.256550.002190.9876144.679850.0021
102.9297135.289350.002191.8639146.892050.0021
103.4280138.317850.002192.7359149.104350.0021
103.9220141.350650.002193.6037151.316650.0021
104.4031144.383350.002194.4714153.533250.0021
104.8842147.420450.002195.3391155.749850.0021
105.3568150.453250.002196.1983157.966450.0021
105.8293153.490350.002197.0488160.187350.0021
106.3061156.527350.002197.8865162.416850.0021
106.7872159.560150.002198.7156164.646250.0021
107.2855162.592950.002199.5275166.880050.0021
107.8139165.621450.0021100.3265169.122450.0021
108.3681168.641350.0021101.1083171.369050.0021
108.9609171.656950.0021101.8729173.620050.0021
109.5837174.663950.0021102.6247175.879550.0021
110.2195177.675250.0021103.3635178.139150.0021
110.8424180.686550.0021104.0938180.402950.0021
111.4309183.706350.0021104.8284182.666850.0021
111.9722186.734850.0021105.5715184.926350.0021
112.4876189.759050.0021106.3448187.177350.0021
113.0160192.787550.0021107.1610189.411150.0021
113.1900193.773450.0021108.0201191.627650.0021
113.3640194.759250.0021108.8492193.861450.0021
113.1664196.692350.0021109.6868196.082350.0021
111.4524197.491350.0021111.4524197.491350.0021
−0.63151.855760.0026−0.63151.855760.0026
−0.3265−1.301660.0026−0.56063.397960.0026
0.4425−4.325860.0026−0.48974.940160.0026
1.6367−7.238360.0026−0.24066.465160.0026
3.2261−9.957560.00260.04947.620660.0026
5.1291−12.453360.00260.33948.776260.0026
7.3500−14.691460.00261.177011.014260.0026
9.7556−16.697560.00262.246713.149260.0026
12.2686−18.548960.00263.531115.163960.0026
14.8589−20.310260.00265.008817.036860.0026
17.5093−21.981260.00266.658418.768060.0026
20.2328−23.536260.00268.436820.361760.0026
23.0207−24.945260.002610.296821.856660.0026
25.8817−26.173860.002612.195523.304360.0026
28.8500−27.183360.002614.111424.734760.0026
31.9043−27.917960.002616.023026.165260.0026
35.0187−28.308860.002617.917427.617260.0026
38.1632−28.295960.002619.799029.086360.0026
41.2518−27.836260.002621.659030.585560.0026
44.2287−26.934160.002623.497632.110560.0026
47.0854−25.624060.002625.319033.656960.0026
49.7487−23.983060.002627.114635.229260.0026
52.2230−22.058560.002628.888736.827260.0026
54.5084−19.906460.002630.641438.451060.0026
56.6004−17.612460.002632.363940.104860.0026
58.5334−15.206860.002634.060741.784460.0026
60.3376−12.711060.002635.731843.494160.0026
62.0345−10.137960.002637.372745.229660.0026
63.6325−7.496060.002638.983646.995160.0026
65.1531−4.798360.002640.560248.782260.0026
66.5965−2.049160.002642.110950.599360.0026
67.97970.738960.002643.631652.442160.0026
69.29853.548360.002645.122254.306560.0026
70.55726.387760.002646.587156.196660.0026
71.76859.244460.002648.021858.103960.0026
72.928412.122560.002649.430860.032660.0026
74.049615.022160.002650.809761.982960.0026
75.132117.934660.002652.167263.946060.0026
76.180220.855760.002653.498965.930760.0026
77.198323.794060.002654.809167.928260.0026
78.190626.736560.002656.093569.942960.0026
79.152929.692060.002657.352171.970460.0026
80.093632.651760.002658.593674.010960.0026
81.012935.620160.002659.813676.064360.0026
81.906438.592760.002661.012178.130560.0026
82.782841.574060.002662.189180.209660.0026
83.637644.559560.002663.348982.297360.0026
84.475347.553660.002664.491684.393760.0026
85.295850.552060.002665.612886.502960.0026
86.099153.550460.002666.716888.620660.0026
86.885256.557460.002667.803690.747060.0026
87.658459.564460.002668.877592.882060.0026
88.414562.575760.002669.934395.021360.0026
89.157665.591360.002670.973897.173460.0026
89.887968.611260.002672.000599.329960.0026
90.609671.631160.002673.0143101.490660.0026
91.314174.655360.002674.0152103.660060.0026
92.014377.679560.002675.0032105.833660.0026
92.697380.707960.002675.9826108.011560.0026
93.376083.740760.002676.9492110.193760.0026
94.041886.773560.002677.9071112.384660.0026
94.699189.810660.002678.8565114.575460.0026
95.347792.847660.002679.7972116.770560.0026
95.992195.884760.002680.7251118.969960.0026
96.623698.926160.002681.6487121.173660.0026
97.2464101.967460.002682.5637123.377360.0026
97.8607105.013160.002683.4744125.585360.0026
98.4621108.063160.002684.3765127.797660.0026
99.0592111.108760.002685.2786130.009960.0026
99.6435114.163060.002686.1721132.222260.0026
100.2191117.212960.002687.0699134.438860.0026
100.7904120.267260.002687.9634136.651160.0026
101.3489123.321460.002688.8526138.867660.0026
101.9073126.380060.002689.7418141.084260.0026
102.4529129.434360.002690.6310143.300860.0026
102.9984132.492860.002691.5203145.517460.0026
103.5311135.551460.002692.4095147.734060.0026
104.0595138.614260.002693.2944149.954960.0026
104.5792141.672860.002694.1750152.171560.0026
105.0904144.739960.002695.0556154.392460.0026
105.5930147.802760.002695.9363156.613360.0026
106.0870150.869960.002696.8083158.834160.0026
106.5810153.937060.002697.6803161.059360.0026
107.0750157.004260.002698.5480163.284560.0026
107.5819160.071360.002699.4029165.514060.0026
108.1103163.129960.0026100.2492167.747860.0026
108.6688166.184160.0026101.0739169.990160.0026
109.2573169.234160.0026101.8772172.236860.0026
109.8801172.275460.0026102.6633174.492060.0026
110.5245175.316860.0026103.4366176.755960.0026
111.1775178.353960.0026104.2012179.015460.0026
111.8218181.391060.0026104.9701181.279360.0026
112.4361184.436660.0026105.7563183.534560.0026
113.0203187.486660.0026106.5596185.781260.0026
113.5788190.540860.0026107.3843188.019260.0026
114.1673193.595160.0026108.2263190.257360.0026
114.3327194.585260.0026109.0769192.486860.0026
114.4980195.575460.0026109.9360194.716360.0026
114.3133197.538660.0026110.8553196.924360.0026
112.5907198.384860.0026112.5907198.384860.0026
−0.69162.036270.0030−0.69162.036270.0030
−0.5241−1.061070.0030−0.61003.574070.0030
0.1117−4.093870.0030−0.42535.103370.0030
1.1341−7.014970.0030−0.12036.624070.0030
2.5645−9.764270.00300.21917.771070.0030
4.3172−12.315870.00300.55848.917970.0030
6.3791−14.626970.00301.473411.104470.0030
8.6645−16.718970.00302.624713.196470.0030
11.0787−18.664970.00303.986415.168270.0030
13.5702−20.512070.00305.532916.985370.0030
16.1132−22.277670.00307.242618.652070.0030
18.7250−23.948670.00309.081120.189970.0030
21.4142−25.490870.003011.001321.641870.0030
24.1935−26.865470.003012.960223.042270.0030
27.0630−28.042470.003014.923324.429770.0030
30.0185−28.970370.003016.886525.825970.0030
33.0512−29.580370.003018.832427.239170.0030
36.1442−29.816670.003020.756928.682570.0030
39.2285−29.623370.003022.659930.151670.0030
42.2527−28.978970.003024.537131.650870.0030
45.1609−27.913670.003026.392933.171570.0030
47.9144−26.483170.003028.227234.726670.0030
50.4704−24.743370.003030.031436.320370.0030
52.8373−22.750170.003031.809837.944170.0030
55.0324−20.559370.003033.558139.606570.0030
57.0772−18.226770.003035.276441.303370.0030
58.9802−15.778270.003036.956143.030270.0030
60.7629−13.239470.003038.597044.791470.0030
62.4425−10.631970.003040.195046.582870.0030
64.0234−7.968670.003041.754448.395570.0030
65.5269−5.262370.003043.279450.234170.0030
66.9616−2.517370.003044.770052.098570.0030
68.32770.266370.003046.230553.984370.0030
69.63363.075770.003047.661055.891670.0030
70.88795.910970.003049.061457.820470.0030
72.09078.767670.003050.436059.766370.0030
73.250611.645770.003051.780661.729570.0030
74.367514.541070.003053.103763.714170.0030
75.454317.444970.003054.396765.715970.0030
76.506720.361770.003055.668267.734970.0030
77.529123.287170.003056.918369.766770.0030
78.525726.221170.003058.142571.815870.0030
79.496529.163670.003059.349673.882070.0030
80.441632.110570.003060.535275.956970.0030
81.365235.070270.003061.703778.048970.0030
82.267338.034370.003062.854980.153870.0030
83.147941.002670.003063.984782.267370.0030
84.011343.979670.003065.101684.389470.0030
84.857646.960870.003066.201386.524370.0030
85.682449.946370.003067.283888.663670.0030
86.494352.936170.003068.349290.811570.0030
87.289055.934570.003069.405992.967970.0030
88.070858.937270.003070.441295.124470.0030
88.839761.944270.003071.467897.289470.0030
89.595864.955570.003072.485999.458770.0030
90.334667.966870.003073.4868101.636770.0030
91.064970.969570.003074.4791103.814670.0030
91.782373.985170.003075.4629106.001170.0030
92.512677.090970.003076.4337108.187670.0030
93.242880.239770.003077.3959110.382770.0030
93.955983.384270.003078.3539112.577970.0030
94.660486.520070.003079.2989114.781670.0030
95.352089.651670.003080.2397116.985370.0030
96.030892.783270.003081.1719119.193370.0030
96.700995.914870.003082.0997121.401370.0030
97.362499.050670.003083.0190123.613670.0030
98.0154102.190870.003083.9383125.830170.0030
98.6554105.335370.003084.8490128.046770.0030
99.2912108.484070.003085.7597130.263370.0030
99.9141111.632870.003086.6704132.479970.0030
100.5327114.790270.003087.5768134.696570.0030
101.1427117.943270.003088.4832136.917470.0030
101.7441121.100670.003089.3896139.134070.0030
102.3369124.262270.003090.2960141.354970.0030
102.9211127.419670.003091.2067143.571570.0030
103.4967130.581270.003092.1174145.788070.0030
104.0680133.742970.003093.0281148.004670.0030
104.6308136.904570.003093.9430150.221270.0030
105.1849140.070470.003094.8580152.437870.0030
105.7348143.236470.003095.7687154.654470.0030
106.2760146.398070.003096.6794156.871070.0030
106.8130149.568370.003097.5901159.087670.0030
107.3414152.734270.003098.4922161.308570.0030
107.8740155.904570.003099.3857163.533770.0030
108.4067159.070470.0030100.2663165.763170.0030
108.9609162.232170.0030101.1384167.992670.0030
109.5408165.393770.0030101.9932170.235070.0030
110.1551168.542570.0030102.8309172.477370.0030
110.8037171.686970.0030103.6600174.728370.0030
111.4782174.827170.0030104.4718176.983570.0030
112.1741177.963070.0030105.2751179.243170.0030
112.8614181.103170.0030106.0741181.502670.0030
113.5358184.243370.0030106.8774183.757970.0030
114.1845187.387870.0030107.6979186.008870.0030
114.8030190.536570.0030108.5442188.255570.0030
115.3830193.698270.0030109.4162190.485070.0030
115.5355194.722770.0030110.3011192.714570.0030
115.6880195.747270.0030111.1818194.939670.0030
115.6622197.779170.0030112.1010197.156270.0030
113.8580198.599670.0030113.8580198.599670.0030
−0.71741.924579.9991−0.71741.924579.9991
−0.6401−1.228679.9991−0.58423.470979.9991
−0.0988−4.330179.9991−0.33945.004579.9991
0.8591−7.328579.99910.02156.525279.9991
2.2252−10.168079.99910.39957.665779.9991
3.9435−12.809879.99910.77758.806279.9991
5.9796−15.211179.99911.774110.979979.9991
8.2435−17.406279.99913.011313.050479.9991
10.6448−19.451079.99914.450414.979279.9991
13.1277−21.392779.99916.069816.749079.9991
15.6708−23.257079.99917.856918.364279.9991
18.2869−25.014079.99919.759919.850579.9991
20.9975−26.637779.999111.744521.242379.9991
23.7983−28.081179.999113.759222.591279.9991
26.7022−29.318379.999115.778223.922879.9991
29.7049−30.284879.999117.797225.263179.9991
32.7892−30.920679.999119.803326.620679.9991
35.9337−31.156879.999121.787928.008179.9991
39.0781−30.954979.999123.751029.421479.9991
42.1539−30.289179.999125.684130.873379.9991
45.1050−29.189479.999127.591432.359679.9991
47.8972−27.716079.999129.468633.888979.9991
50.4919−25.933279.999131.315835.465479.9991
52.8975−23.901479.999133.124337.084979.9991
55.1269−21.671979.999134.898438.747479.9991
57.2018−19.296479.999136.625340.452879.9991
59.1391−16.804879.999138.304942.201179.9991
60.9562−14.223179.999139.933043.979679.9991
62.6702−11.577079.999141.518145.796679.9991
64.2854−8.875079.999143.051747.639579.9991
65.8233−6.121479.999144.550949.512479.9991
67.2881−3.333579.999146.015751.415479.9991
68.6842−0.506979.999147.446253.339979.9991
70.02022.345579.999148.842355.290279.9991
71.30465.227979.999150.212657.257679.9991
72.53758.131879.999151.552959.246579.9991
73.723111.052979.999152.863161.256979.9991
74.865813.991279.999154.147563.284579.9991
75.978316.946679.999155.410565.329379.9991
77.056619.906479.999156.647667.395579.9991
78.100422.879079.999157.867669.474679.9991
79.118525.864579.999159.061871.570979.9991
80.110828.854379.999160.238873.680179.9991
81.077431.852779.999161.394475.797979.9991
82.022434.859779.999162.532877.928679.9991
82.946037.871079.999163.649680.063679.9991
83.852440.890979.999164.753682.211479.9991
84.733043.915179.999165.840584.363679.9991
85.600846.947979.999166.914486.524379.9991
86.447049.985079.999167.975488.689479.9991
87.276153.026379.999169.023690.858779.9991
88.092356.072079.999170.058993.036679.9991
88.891359.122079.999171.085595.214679.9991
89.677462.176279.999172.099397.401179.9991
90.450665.234879.999173.108899.591979.9991
91.211068.297679.999174.1054101.787079.9991
91.958471.356279.999175.0934103.982179.9991
−0.7432−1.671089.9996−0.55843.110189.9996
−0.2663−4.862889.9996−0.26204.660989.9996
0.6444−7.925689.99960.14186.190189.9996
1.9846−10.868289.99960.55847.328589.9996
3.6900−13.595989.99960.97518.466989.9996
5.7262−16.083289.99962.057610.640589.9996
8.0072−18.377189.99963.380712.698189.9996
10.4257−20.520689.99964.897114.592689.9996
12.9215−22.556889.99966.602516.323789.9996
15.4947−24.511489.99968.471217.896089.9996
18.1537−26.349989.999610.447219.330789.9996
20.9030−28.033989.999612.479120.666789.9996
23.7467−29.515989.999614.545321.951189.9996
26.7108−30.770289.999616.620123.226989.9996
29.7994−31.741189.999618.690724.511489.9996
32.9739−32.342589.999620.748325.821689.9996
36.2043−32.505789.999622.775927.157589.9996
39.4218−32.205089.999624.773428.532289.9996
42.5491−31.423289.999626.732229.945489.9996
45.5432−30.190389.999628.656731.401789.9996
48.3354−28.596689.999630.534032.905289.9996
50.9515−26.689389.999632.372534.455989.9996
53.3700−24.541489.999634.163836.054089.9996
55.6038−22.213289.999635.912237.703589.9996
57.6915−19.743189.999637.613339.400389.9996
59.6374−17.165789.999639.267241.148789.9996
61.4545−14.523889.999640.878042.944389.9996
63.1556−11.830489.999642.446044.791489.9996
64.7708−9.089789.999643.975346.677389.9996
66.3044−6.310489.999645.465948.601789.9996
67.7649−3.492489.999646.917850.552089.9996
69.1610−0.644489.999648.331152.528089.9996
70.49702.229589.999649.705754.521289.9996
71.78575.137789.999651.050356.531689.9996
73.02298.063189.999652.360558.563589.9996
74.212811.014289.999653.640660.608389.9996
75.372713.982689.999654.895062.670289.9996
76.493816.968189.999656.123564.745089.9996
77.584919.966589.999657.330666.832889.9996
78.646022.977889.999658.516368.933489.9996
79.677026.002089.999659.684771.042689.9996
80.686529.030589.999660.831773.164789.9996
81.670232.071889.999661.961475.299689.9996
82.632435.113289.999663.074077.438989.9996
83.568938.163289.999664.173779.586889.9996
84.492541.221789.999665.256281.743289.9996
85.390344.280389.999666.330283.908289.9996
86.275247.347489.999667.391286.077689.9996
87.138650.423189.999668.439488.251289.9996
87.989253.498989.999669.483290.433489.9996
88.818256.583289.999670.514292.620089.9996
89.638759.667589.999671.536694.815189.9996
90.442062.760489.999672.550497.010289.9996
91.228165.853389.999673.555699.209689.9996
92.005768.950689.999674.5565101.413389.9996
92.770372.052189.999675.5488103.621389.9996
93.522175.153689.999676.5325105.829389.9996
94.265278.259489.999677.5119108.041689.9996
94.995581.365289.999678.4870110.253989.9996
95.717284.475389.999679.4579112.470589.9996
96.430387.589789.999680.4244114.691489.9996
97.130590.704189.999681.3867116.912289.9996
97.822193.818589.999682.3446119.133189.9996
98.505196.937289.999683.2983121.354089.9996
99.1838100.055889.999684.2519123.579289.9996
99.8496103.178889.999685.2013125.804489.9996
100.5112106.297589.999686.1506128.025389.9996
101.1641109.424889.999687.1000130.250489.9996
101.8128112.547889.999688.0493132.479989.9996
102.4529115.675189.999688.9987134.705189.9996
103.0800118.806689.999689.9480136.930389.9996
103.7029121.938289.999690.9017139.151289.9996
104.3172125.069889.999691.8553141.376389.9996
104.9186128.205789.999692.8090143.597289.9996
105.5157131.341689.999693.7669145.822489.9996
106.0999134.481789.999694.7249148.043389.9996
106.6755137.621989.999695.6871150.264289.9996
107.2426140.766489.999696.6493152.485189.9996
107.8053143.910889.999697.6073154.701789.9996
108.3681147.055389.999698.5652156.926889.9996
108.9308150.195589.999699.5189159.147789.9996
109.4935153.339989.9996100.4682161.372989.9996
110.0649156.484489.9996101.4090163.602489.9996
110.6448159.624689.9996102.3412165.836289.9996
111.2376162.760489.9996103.2604168.074289.9996
111.8519165.896389.9996104.1625170.320989.9996
112.4876169.023689.9996105.0432172.571889.9996
113.1492172.146689.9996105.9066174.831489.9996
113.8408175.265389.9996106.7529177.099589.9996
114.5668178.379789.9996107.5819179.372089.9996
115.3142181.485589.9996108.4067181.648789.9996
116.0617184.591389.9996109.2401183.916889.9996
116.7447187.714289.9996110.0992186.180789.9996
117.3375190.854489.9996110.9884188.431689.9996
117.9518193.990389.9996111.9077190.669789.9996
118.1580194.999889.9996112.8442192.899289.9996
118.3642196.009389.9996113.7549195.141589.9996
118.2310198.019789.9996114.6570197.379689.9996
116.4569198.857389.9996116.4569198.857389.9996
−0.74751.0310100.0000−0.74751.0310100.0000
−0.8634−1.0353100.0000−0.52842.5560100.0000
−0.7775−3.1058100.0000−0.19764.0766100.0000
−0.4983−5.1763100.00000.24495.5672100.0000
−0.0988−6.7400100.00000.68306.6820100.0000
0.3007−8.3036100.00001.12127.7967100.0000
1.5121−11.2591100.00002.22959.9145100.0000
3.1101−14.0642100.00003.569711.9163100.0000
5.0475−16.6459100.00005.103313.7549100.0000
7.2383−19.0043100.00006.813015.4216100.0000
9.5837−21.2208100.00008.681616.9380100.0000
12.0151−23.3429100.000010.662018.3212100.0000
14.5195−25.3619100.000012.706719.6014100.0000
17.1013−27.2692100.000014.790220.8299100.0000
19.7947−29.0348100.000016.877922.0456100.0000
22.6127−30.6156100.000018.957023.2785100.0000
25.5595−31.9687100.000021.018924.5414100.0000
28.6009−33.0255100.000023.046525.8516100.0000
31.7582−33.7300100.000025.039727.2048100.0000
34.9886−34.0135100.000026.998628.6095100.0000
38.2018−33.8159100.000028.918830.0657100.0000
41.3806−33.1243100.000030.804631.5821100.0000
44.3962−31.9816100.000032.647533.1586100.0000
47.2529−30.4480100.000034.451734.7867100.0000
49.9162−28.5966100.000036.200036.4706100.0000
52.3691−26.5003100.000037.901138.1975100.0000
54.6544−24.2021100.000039.546439.9674100.0000
56.7722−21.7621100.000041.140141.7716100.0000
58.7396−19.2319100.000042.682243.6187100.0000
60.5782−16.6287100.000044.185745.4959100.0000
62.3094−13.9611100.000045.646347.4075100.0000
63.9503−11.2376100.000047.068249.3449100.0000
65.5097−8.4669100.000048.451451.3123100.0000
67.0003−5.6575100.000049.808853.3056100.0000
68.4265−2.8137100.000051.131955.3202100.0000
69.79680.0687100.000052.429257.3607100.0000
71.11562.9855100.000053.700859.4184100.0000
72.38715.9238100.000054.946561.4889100.0000
73.61148.8835100.000056.170863.5766100.0000
74.797011.8605100.000057.373665.6729100.0000
75.948314.8460100.000058.554967.7778100.0000
77.065217.8487100.000059.719169.8956100.0000
78.156320.8557100.000060.866072.0177100.0000
79.217323.8756100.000062.000174.1527100.0000
80.252626.9041100.000063.117076.2876100.0000
81.262129.9411100.000064.216778.4355100.0000
82.254432.9868100.000065.307880.5834100.0000
83.220936.0411100.000066.386082.7441100.0000
84.170339.0996100.000067.455684.9048100.0000
85.098242.1668100.000068.512487.0742100.0000
86.008845.2339100.000069.556389.2435100.0000
86.898148.3096100.000070.595891.4215100.0000
87.774451.3897100.000071.622593.6037100.0000
88.637854.4740100.000072.644995.7902100.0000
89.479857.5626100.000073.658797.9767100.0000
90.313260.6512100.000074.6639100.1718100.0000
91.129363.7484100.000075.6648102.3669100.0000
91.936966.8457100.000076.6571104.5621100.0000
92.731669.9472100.000077.6494106.7658100.0000
93.513573.0530100.000078.6331108.9652100.0000
94.286776.1588100.000079.6125111.1732100.0000
95.051379.2689100.000080.5919113.3769100.0000
95.803182.3790100.000081.5671115.5849100.0000
96.550585.4934100.000082.5379117.7929100.0000
97.285188.6121100.000083.5044120.0052100.0000
98.006891.7307100.000084.4753122.2174100.0000
98.724294.8494100.000085.4418124.4254100.0000
99.433097.9724100.000086.4041126.6377100.0000
100.1332101.0997100.000087.3706128.8500100.0000
100.8205104.2270100.000088.3414131.0623100.0000
101.5035107.3543100.000089.3080133.2746100.0000
102.1779110.4858100.000090.2788135.4826100.0000
102.8438113.6174100.000091.2496137.6906100.0000
103.5010116.7490100.000092.2248139.8986100.0000
104.1497119.8849100.000093.2042142.1066100.0000
104.7940123.0207100.000094.1879144.3103100.0000
105.4298126.1566100.000095.1716146.5140100.0000
106.0613129.2968100.000096.1553148.7177100.0000
106.6798132.4370100.000097.1433150.9214100.0000
107.2941135.5814100.000098.1314153.1208100.0000
107.8998138.7259100.000099.1194155.3245100.0000
108.5012141.8704100.0000100.0988157.5282100.0000
109.0940145.0148100.0000101.0782159.7362100.0000
109.6868148.1636100.0000102.0534161.9442100.0000
110.2754151.3080100.0000103.0156164.1565100.0000
110.8725154.4568100.0000103.9649166.3774100.0000
111.4782157.5970100.0000104.9057168.5983100.0000
112.0967160.7414100.0000105.8293170.8278100.0000
112.7325163.8773100.0000106.7357173.0659100.0000
113.3983167.0089100.0000107.6292175.3082100.0000
114.1028170.1319100.0000108.5055177.5592100.0000
114.8374173.2463100.0000109.3733179.8144100.0000
115.6063176.3521100.0000110.2453182.0654100.0000
116.3882179.4579100.0000111.1259184.3120100.0000
117.1442182.5680100.0000112.0366186.5501100.0000
117.8487185.6910100.0000112.9817188.7710100.0000
118.5059188.8225100.0000113.9697190.9704100.0000
119.1546191.9498100.0000114.9491193.1784100.0000
119.6529195.1115100.0000115.8684195.4122100.0000
117.6382196.9286100.0000117.6382196.9286100.0000

Claims as granted

18 claims

Log in to read the claims of this application.

Log in to unlock

Classifications

6 codes
IPC · International Patent Classification
Section F — Mechanical engineering; lighting; heating; weapons
  • F01D9/04
  • F01D5/14
  • F04D29/44
  • F01D25/24
  • F01D5/32
  • F04D29/26

Claim changes

Soon
Coming soonHow the claims changed between publication and grant

See which claims were amended, added or cancelled during examination, with every added and removed word marked.

AmendedAddedCancelledUnchanged

The published claims of this application are not paired with the granted ones in what we hold.

File wrapper

⤢ drag to zoomOct 2019Jan 2020Apr 2020Jul 2020Oct 2020Jan 2021Apr 2021Jul 2021Oct 2021Jan 2022Apr 2022USPTOApplicantNon-final rejectionResponse after non-final
USPTOApplicanthover for detail · click to open
Pendency
2.5 y
916 days filing → grant
Office actions
1
non-final + final
Responses
1
no RCE
Examiner
Christopher Verdier
art unit 3745 · TC 3700
Citations: 18 back · 1 forward

See the full prosecution history — every USPTO and applicant action on this file, in order.

Log in to unlock

Documents

Log in to open the documents of this file: the application as filed, every office action and response, the notice of allowance.

Log in to unlock

Chain of title

⤢ drag to zoom20202022202420262028203020322034203620382040Owner 1Owner 2
Titlehover for detail · click to open

See the full assignment history — every owner this patent has passed through, with recordation dates and reel/frame numbers.

Log in to unlock