# Patent

## Title
Airfoil for a first stage nozzle guide vane

## Abstract

The present invention provides an airfoil for a first stage nozzle guide vane having an external surface with first and second sides. The external surface extends spanwise between a hub and a tip and streamwise between a leading edge and a trailing edge of the airfoil. The external surface includes a contour substantially defined by Table 1 as listed in the specification.

## Background
RELATED APPLICATIONS
The present application claims the benefit of U.S. patent application Ser. No. 60/755,498 filed Dec. 29, 2005, which is incorporated herein by reference.


FIELD OF THE INVENTION
The present invention relates to improved airfoil geometry, and more particularly to a high efficiency airfoil for a turbine nozzle guide vane in a gas turbine engine.
BACKGROUND
Gas turbine engine designers continuously work to improve engine efficiency, to reduce operating costs of the engine, and to reduce specific exhaust gas emissions such as NOx, CO2, CO, unburnt hydrocarbons, and particulate matter. The specific fuel consumption (SFC) of an engine is inversely proportional to the overall thermal efficiency of the engine, thus, as the SFC decreases the fuel efficiency of the engine increases. Furthermore, specific exhaust gas emissions typically decrease as the engine becomes more efficient. The thermal efficiency of the engine is a function of component efficiencies, cycle pressure ratio and turbine inlet temperature. The present invention contemplates increased thermal efficiency for a gas turbine engine by improving turbine efficiency through a new aerodynamic design of an airfoil for a first stage nozzle guide vane.
SUMMARY
The present invention provides an airfoil with an external surface having first and second sides, the external surface extends spanwise between a hub and a tip and streamwise between a leading edge and a trailing edge. The external surface has a contour substantially defined by Table 1 as listed in the specification.
In another aspect of the present invention, a turbine nozzle guide vane assembly for a gas turbine engine can include an inner shroud having an upper surface and a lower surface, the upper surface of the inner shroud partially defining an inner flow path wall. An airfoil can extend radially outward from the upper surface of the inner shroud relative to an axis of rotation of the gas turbine engine. The airfoil includes first and second three-dimensional external surfaces that extend between a hub and a tip in a spanwise direction and between a leading edge and a trailing edge in a streamwise direction. A Cartesian coordinate array having X,Y and Z axis coordinates listed in Table 1 of the specification defines the first and second external surfaces of the airfoil.
Another aspect of the present invention provides for a method of forming an airfoil for a turbine nozzle guide vane. The method includes forming a contoured three-dimensional external surface of an airfoil defined by Cartesian (X, Y and Z) coordinates listed in the specification as Table 1, wherein the Z axis coordinates are generally measured in a radial direction from a longitudinal axis, the X axis coordinates are generally measured normal to the Z axis in a streamwise direction, and the Y axis coordinates are generally measured normal to the Z axis and normal to the X axis.
Another aspect of the present invention provides for a method of forming an airfoil for a turbine nozzle guide vane. The method includes forming a contoured three-dimensional external surface of an airfoil defined by Cartesian (X, Y and Z) coordinates listed in the specification as Table 1, wherein the Z axis coordinates are generally measured from an engine centerline axis, the X axis coordinates are generally measured normal to the Z axis in a streamwise direction, and the Y axis coordinates are generally measured normal to the Z axis and normal to the X axis.



BRIEF DESCRIPTION OF THE DRAWINGS
The description herein makes reference to the accompanying drawings wherein like reference numerals refer to like parts throughout the several views, and wherein:
FIG. 1 is a schematic representation of a gas turbine engine;
FIG. 2 is a cross-sectional view of a turbine module for the gas turbine engine of FIG. 1;
FIG. 3 is a perspective view of a first stage turbine nozzle guide vane segment illustrated in FIG. 2;
FIG. 4 is a front view of the first stage turbine nozzle guide vane segment illustrated in FIG. 3;
FIG. 5 is a back view of the first stage turbine nozzle guide vane segment illustrated in FIG. 3;
FIG. 6 is a right view of the first stage turbine nozzle guide vane segment illustrated in FIG. 3;
FIG. 7 is a left view of the first stage turbine nozzle guide vane segment illustrated in FIG. 3;
FIG. 8 is a top view of the first stage turbine nozzle guide vane segment illustrated in FIG. 3; and
FIG. 9 is a bottom view of the first stage turbine nozzle guide vane segment illustrated in FIG. 3.



DETAILED DESCRIPTION
For purposes of promoting an understanding of the principles of the invention, reference will now be made to the embodiments illustrated in the drawings and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the invention is thereby intended, such alterations and further modifications in the illustrated device, and such further applications of the principles of the invention as illustrated therein being contemplated as would normally occur to one skilled in the art to which the invention relates.
Referring to FIG. 1, a schematic view of a gas turbine engine 10 is depicted. While the gas turbine engine 10 is illustrated with one spool (i.e. one shaft connecting a turbine and a compressor), it should be understood that the present invention is not limited to any particular engine design or configuration and as such may be used in multi spool engines of the aero or power generation type. The gas turbine engine 10 will be described generally, however significant details regarding general gas turbine engines will not be presented herein as it is believed that the theory of operation and general parameters of gas turbine engines are well known to those of ordinary skill in the art.
The gas turbine engine 10 includes an inlet section 12, a compressor section 14, a combustor section 16, a turbine section 18, and an exhaust section 20. In operation, air is drawn in through the inlet 12 and compressed to a high pressure relative to ambient pressure in the compressor section 14. The air is mixed with fuel in the combustor section 16 wherein the fuel/air mixture burns and produces a high temperature and pressure working fluid from which the turbine section 18 extracts power. The turbine section 18 is mechanically coupled to the compressor section 14 via a shaft 22. The shaft 22 rotates about a centerline axis 24 that extends axially along the longitudinal axis of the engine 10, such that as the turbine section 18 rotates due to the forces generated by the high pressure working fluid, the compressor section 14 is rotatingly driven by the turbine section 18 to produce compressed air. A portion of the power extracted from the turbine section 18 can be utilized to drive a secondary device 26, which in one embodiment can be an electrical generator. The electrical generator can be run at a substantially constant speed that is appropriate for a desired power grid frequency; a non-limiting example being 50 or 60 Hz. Alternatively the secondary device 26 can be in the form of a compressor or pump for use in fluid pipelines such as oil or natural gas lines.
Referring now to FIG. 2, a partial cross section of the turbine section 18 is shown therein. As the working fluid exits the combustor section 16, the working fluid is constrained between an inner flow path wall 31 and an outer flow path wall 33 as it flows through the turbine section 18. The turbine section 18 includes a turbine inlet or first stage nozzle guide vane (NGV) assembly 30. The first stage NGV assembly 30 includes a plurality of static vanes or airfoils 32 positioned circumferentially around a flow path annulus of the engine 10. The first stage NGV assembly 30 is operable for accelerating and turning the flow of working fluid to a desired direction, as the working fluid exits the combustor section 16 and enters the turbine section 18.
Each airfoil 32 of the first stage NGV assembly 30 extends between a leading edge 34 and a trailing edge 36 in the stream wise direction and between an inner shroud 38 and an outer shroud 40 in the spanwise direction. It should be understood that the terms leading edge and trailing edge are defined relative to the general flow path of the working fluid, such that the working fluid first passes the leading edge and subsequently passes the trailing edge of a particular airfoil. The inner and outer shrouds 38, 40 form a portion of the inner and outer flow path walls 31, 33 respectively at that location in the engine 10. The first stage NGV assembly 30 will be the described in more detail below.
The turbine section 18 further includes a first stage turbine assembly 42 positioned downstream of the first stage NGV assembly 30. The first stage turbine assembly 42 includes a first turbine wheel 44 which is comprised of a first turbine disk 46 having a plurality of first stage turbine blades 48 coupled thereto. It should be noted here that in one preferred embodiment the turbine blades 48 and the disk 46 can be separate components, but that the present invention contemplates other forms such as a turbine wheel having the blades and disk integrally formed together. This type of component is commonly called a “BLISK,” short for a “Bladed Disk,” by those working in the gas turbine engine industry.
Each turbine blade 48 includes an airfoil 50 that rotates with the turbine disk 46. Each airfoil 50 extends between a leading edge 52 and a trailing edge 54 in the stream wise direction and between an inner shroud or platform 56 and an outer shroud 58 in the spanwise direction. The disk 46 may include one or more seals 60 extending forward or aft in the streamwise direction. The seals 60, sometimes called rotating knife seals, limit the leakage of working fluid from the desired flowpath. The first stage turbine assembly 42 is operable for extracting energy from the working fluid via the airfoils 50 which in turn cause the turbine wheel 44 to rotate and drive the shaft 22.
Directly downstream of the first stage turbine assembly 42 is a second stage nozzle guide vane (NGV) assembly 70. The second stage NGV assembly 70 includes a plurality of static vanes or airfoils 72 positioned circumferentially around the flow path of the engine 10. The airfoils 72 of the second stage NGV assembly 70 are operable for accelerating and turning the working fluid flow to a desired direction as the working fluid exits the second stage NGV assembly 70. Each airfoil 72 extends between a leading edge 74 and a trailing edge 76 in the stream wise direction and between an inner shroud 78 and an outer shroud 80 in the spanwise direction. The inner and outer shrouds 78, 80 form a portion of the inner and outer flow path walls 31, 33 respectively at that location in the engine 10.
A second stage turbine assembly 82 is positioned downstream of the second stage NGV assembly 70. The second stage turbine assembly 82 includes a second turbine wheel 84 which is comprised of a second turbine disk 86 having a plurality of second stage turbine blades 88 coupled thereto. Each turbine blade 88 includes an airfoil 90 that rotates with the turbine disk 86 when the engine 10 is running. Each airfoil 90 extends between a leading edge 92 and a trailing edge 94 in the stream wise direction and between an inner shroud or platform 96 and an outer shroud 98 in the spanwise direction. The disk 86 may include one or more seals 100 extending forward or aft in the streamwise direction. In this particular embodiment of the invention, the second stage turbine assembly 82 is connected to the first stage turbine assembly 42 and therefore increases the power delivered to the shaft 22.
A third stage nozzle guide vane (NGV) assembly 110 is located downstream of the second stage turbine assembly 82. The third stage NGV assembly 110 includes a plurality of static vanes or airfoils 112 positioned circumferentially around the flowpath of the engine 10. The airfoils 112 of the third stage NGV assembly 110 are operable for accelerating and turning the working fluid flow to a desired direction as the working fluid exits the third stage NGV assembly 110. Each airfoil 112 extends between a leading edge 114 and a trailing edge 116 in the streamwise direction and between an inner shroud 118 and an outer shroud 120 in the spanwise direction. The inner and outer shrouds 118, 120 form a portion of the inner and outer flow path walls 31, 33 respectively at that location in the engine 10.
A third stage turbine assembly 130 is positioned downstream of the third stage NGV 110. The third stage turbine assembly 130 includes a third turbine wheel 132 which is comprised of a third turbine disk 134 having a plurality of third stage turbine blades 136 coupled thereto. Each turbine blade 136 includes an airfoil 138 that rotates with the turbine disk 134 when the engine 10 is running. Each airfoil 138 extends between a leading edge 140 and a trailing edge 142 in the stream wise direction and between an inner shroud or platform 144 and an outer shroud 146 in the spanwise direction. The third disk 134 may also include one or more seals 148 extending forward or aft of the disk 134 in the streamwise direction. Similar to the second stage turbine assembly 82, the third stage turbine assembly 130 is also connected to the first stage turbine assembly 42 and therefore further increases the power delivered to the shaft 22.
Although not shown in each of the drawings it should be understood that the airfoils for both the turbine blades and turbine nozzle guide vanes may include internal cooling flow passages and apertures extending through portions of the external surfaces of the airfoil. Pressurized cooling fluid can then flow from the internal passages through the apertures to cool the external surface of the airfoils as would be known to those skilled in the art. In this manner, the engine 10 may be run at the higher turbine inlet temperatures, and thus produce higher thermal efficiencies while still providing adequate component life as measured by such parameters as high cycle fatigue limits, low cycle fatigue limits, and creep, etc.
It should be further noted that the airfoils may include coatings to increase component life. The coatings can be of the thermal barrier type and/or the radiation barrier type. Thermal barrier coatings have relatively low heat transfer coefficients which help to reduce the heat load that the cooling fluid is required to dissipate. Thermal barrier coatings are typically ceramic based and can include mullite and zirconia based composites, although other types of coatings are contemplated herein. Radiation barrier coatings operate to reduce radiation heat transfer to the coated component by having highly reflective external surfaces such that radiation emanating from the high temperature exhaust gas is at least partially reflected away and not absorbed by the component. Radiation barrier coatings can include materials from high temperature chromium based alloys as is known to those skilled in the art. The radiation barrier coatings and thermal barrier coatings can be used to coat the entire airfoil, but alternate embodiments include a partial coating and/or a coating with intermittent discontinuities formed therein.
Referring now to FIGS. 3 through 9, the first stage nozzle guide vane assembly 30 will be described in more detail. As described previously, the nozzle guide vane assembly 30 includes an inner shroud 38 wherein an outer surface 150 of the shroud defines a portion of the inner flow path wall 31 at that particular location in the engine 10. A plurality of airfoils 32 extends radially outward from the outer surface 150 of the shroud 38 from a hub 152 toward a tip 154. Each airfoil 32 is attached to the shroud 38 proximate the hub 152 of the airfoil 32. The airfoils 32 can be integrally formed with the shroud 38 through a casting process or the like or alternatively may be mechanically joined via welding, brazing or by any other joining method known to those skilled in the art. An outer shroud 40 can be attached to the airfoil 32 proximate the tip 154 of the airfoil 32. The outer shroud 40 includes an inner surface 156 which forms a portion of the outer flow path 33 in the turbine section 18.
The first stage nozzle guide vane assembly 30 further includes an outer lug 160 positioned above each airfoil. The lugs 160 are operable for reacting torque loads produced by the airfoils through the frame (not shown) of the aircraft engine 10. A plurality of coolant inlets 162 can be formed in the outer shroud 40 to provide cooling fluid to each airfoil 32. The cooling fluid extracts heat load from each airfoil 32 and is ejected through coolant outlet holes 164 into the flow path of the working fluid.
Each airfoil 32 includes an external surface 161 having first and second sides 163, 165 sometimes called pressure and suction sides respectively. The external surface 161 of the airfoil 32 provides aerodynamic control of the flow of working fluid so as to optimize efficiency in the turbine section 18. The external surface 161 of the airfoil 32 is substantially defined by Table 1 listed below. Table 1 lists data points in Cartesian coordinates that define the external surface of the airfoil 32 at discrete locations. The Z axis coordinates are generally measured radially outward from a reference location. In one form the reference location is the engine centerline axis and in another form the reference location is the inner shroud 38 from the hub 152. The Z axis defines an imaginary stacking axis from which the contoured external surface is formed. The term “stacking axis,” as it is typically used by aerodynamic design engineers, is nominally defined normal to the inner shroud 38 or in a radial direction from the axis of rotation, but in practice can “lean” or “tilt” in a desired direction to satisfy mechanical design criteria as is known to those skilled in the art. The lean or tilt angle is typically within 10°-25° of the normal plane in any direction relative to the inner shroud 38, but can vary with larger angles as necessary to satisfy mechanical design criteria. The X axis coordinates are generally measured normal to the stacking axis in a streamwise direction. The Y axis coordinates are generally measured normal to the stacking axis and normal to the X axis. The airfoil 32 defined by Table 1 improves the first stage turbine nozzle guide vane efficiency by 0.94% over prior art designs.
While the external surface of airfoil 32 is defined by discrete points, the surface can be “smoothed” between these discrete points by parametric spline fit techniques and the like. One such method called numerical uniform rational B-spline (NURB-S) is employed by software run on Unigraphics® computer aided design workstations. The data splines can be formed in the streamwise direction and/or the spanwise direction of the airfoil 32. Other surface smoothing techniques known to those skilled in the art are also contemplated by the present invention.
The airfoils of the present invention can be formed from any manufacturing process known to those skilled in the art. One such process is an investment casting method whereby the entire first stage NGV assembly 30 is integrally cast as a one-piece component. Alternatively the first stage NGV assembly 30 can be formed in multiple pieces and bonded together. In another form, the first stage NGV assembly 30 can be formed from wrought material and finished machined to a desired specification.
The present invention includes airfoils having an external surface formed within a manufacturing tolerance of +/−0.025 inches with respect to any particular point in Table 1 or spline curve between discrete points. Furthermore, if the airfoil of the present invention has a material coating applied, the tolerance band can be increased to +/−0.050 inches.







TABLE 1





Coordinates for airfoils on the first stage nozzle guide vane (in).







A. Section height 11.75











X1 = −0.77808
Y1 = 0.42024
Z1 = 11.75000



X2 = −0.79849
Y2 = 0.44000
Z2 = 11.75000



X3 = −0.80884
Y3 = 0.46644
Z3 = 11.75000



X4 = −0.80727
Y4 = 0.49480
Z4 = 11.75000



X5 = −0.79406
Y5 = 0.51994
Z5 = 11.75000



X6 = −0.63813
Y6 = 0.61239
Z6 = 11.75000



X7 = −0.68171
Y7 = 0.59769
Z7 = 11.75000



X8 = −0.72325
Y8 = 0.57805
Z8 = 11.75000



X9 = −0.76086
Y9 = 0.55171
Z9 = 11.75000



X10 = −0.79406
Y10 = 0.51994
Z10 = 11.75000



X11 = 0.84940
Y11 = −0.90763
Z11 = 11.75000



X12 = 0.80838
Y12 = −0.79328
Z12 = 11.75000



X13 = 0.76302
Y13 = −0.68058
Z13 = 11.75000



X14 = 0.71490
Y14 = −0.56902
Z14 = 11.75000



X15 = 0.66489
Y15 = −0.45829
Z15 = 11.75000



X16 = 0.61286
Y16 = −0.34850
Z16 = 11.75000



X17 = 0.55811
Y17 = −0.24005
Z17 = 11.75000



X18 = 0.49988
Y18 = −0.13342
Z18 = 11.75000



X19 = 0.43746
Y19 = −0.02919
Z19 = 11.75000



X20 = 0.37011
Y20 = 0.07190
Z20 = 11.75000



X21 = 0.29690
Y21 = 0.16885
Z21 = 11.75000



X22 = 0.21777
Y22 = 0.26101
Z22 = 11.75000



X23 = 0.13239
Y23 = 0.34741
Z23 = 11.75000



X24 = 0.04001
Y24 = 0.42625
Z24 = 11.75000



X25 = −0.05947
Y25 = 0.49592
Z25 = 11.75000



X26 = −0.16587
Y26 = 0.55443
Z26 = 11.75000



X27 = −0.27882
Y27 = 0.59891
Z27 = 11.75000



X28 = −0.39720
Y28 = 0.62571
Z28 = 11.75000



X29 = −0.51837
Y29 = 0.63133
Z29 = 11.75000



X30 = −0.63813
Y30 = 0.61239
Z30 = 11.75000



X31 = 0.84940
Y31 = −0.90763
Z31 = 11.75000



X32 = 0.84911
Y32 = −0.91635
Z32 = 11.75000



X33 = 0.84299
Y33 = −0.92270
Z33 = 11.75000



X34 = 0.83430
Y34 = −0.92329
Z34 = 11.75000



X35 = 0.82752
Y35 = −0.91773
Z35 = 11.75000



X36 = −0.65696
Y36 = 0.38301
Z36 = 11.75000



X37 = −0.55257
Y37 = 0.35743
Z37 = 11.75000



X38 = −0.44921
Y38 = 0.32798
Z38 = 11.75000



X39 = −0.34757
Y39 = 0.29305
Z39 = 11.75000



X40 = −0.24847
Y40 = 0.25149
Z40 = 11.75000



X41 = −0.15293
Y41 = 0.20232
Z41 = 11.75000



X42 = −0.06214
Y42 = 0.14485
Z42 = 11.75000



X43 = 0.02370
Y43 = 0.08019
Z43 = 11.75000



X44 = 0.10618
Y44 = 0.01128
Z44 = 11.75000



X45 = 0.18564
Y45 = −0.06109
Z45 = 11.75000



X46 = 0.26184
Y46 = −0.13688
Z46 = 11.75000



X47 = 0.33542
Y47 = −0.21524
Z47 = 11.75000



X48 = 0.40658
Y48 = −0.29579
Z48 = 11.75000



X49 = 0.47506
Y49 = −0.37862
Z49 = 11.75000



X50 = 0.54079
Y50 = −0.46366
Z50 = 11.75000



X51 = 0.60352
Y51 = −0.55094
Z51 = 11.75000



X52 = 0.66313
Y52 = −0.64038
Z52 = 11.75000



X53 = 0.71980
Y53 = −0.73170
Z53 = 11.75000



X54 = 0.77420
Y54 = −0.82440
Z54 = 11.75000



X55 = 0.82752
Y55 = −0.91773
Z55 = 11.75000



X56 = −0.77808
Y56 = 0.42024
Z56 = 11.75000



X57 = −0.74932
Y57 = 0.40679
Z57 = 11.75000



X58 = −0.71885
Y58 = 0.39772
Z58 = 11.75000



X59 = −0.68793
Y59 = 0.39026
Z59 = 11.75000



X60 = −0.65696
Y60 = 0.38301
Z60 = 11.75000







B. Section height 12.25











X1 = −0.79201
Y1 = 0.46381
Z1 = 12.25000



X2 = −0.80457
Y2 = 0.43888
Z2 = 12.25000



X3 = −0.80588
Y3 = 0.41100
Z3 = 12.25000



X4 = −0.79570
Y4 = 0.38502
Z4 = 12.25000



X5 = −0.77576
Y5 = 0.36549
Z5 = 12.25000



X6 = −0.64788
Y6 = 0.55619
Z6 = 12.25000



X7 = −0.68803
Y7 = 0.53993
Z7 = 12.25000



X8 = −0.72638
Y8 = 0.51983
Z8 = 12.25000



X9 = −0.76141
Y9 = 0.49441
Z9 = 12.25000



X10 = −0.79201
Y10 = 0.46381
Z10 = 12.25000



X11 = 0.84952
Y11 = −0.94682
Z11 = 12.25000



X12 = 0.80824
Y12 = −0.83178
Z12 = 12.25000



X13 = 0.76305
Y13 = −0.71821
Z13 = 12.25000



X14 = 0.71507
Y14 = −0.60580
Z14 = 12.25000



X15 = 0.66478
Y15 = −0.49439
Z15 = 12.25000



X16 = 0.61203
Y16 = −0.38413
Z16 = 12.25000



X17 = 0.55638
Y17 = −0.27531
Z17 = 12.25000



X18 = 0.49730
Y18 = −0.16831
Z18 = 12.25000



X19 = 0.43428
Y19 = −0.06359
Z19 = 12.25000



X20 = 0.36660
Y20 = 0.03819
Z20 = 12.25000



X21 = 0.29350
Y21 = 0.13612
Z21 = 12.25000



X22 = 0.21444
Y22 = 0.22932
Z22 = 12.25000



X23 = 0.12897
Y23 = 0.31666
Z23 = 12.25000



X24 = 0.03631
Y24 = 0.39631
Z24 = 12.25000



X25 = −0.06395
Y25 = 0.46611
Z25 = 12.25000



X26 = −0.17186
Y26 = 0.52334
Z26 = 12.25000



X27 = −0.28681
Y27 = 0.56452
Z27 = 12.25000



X28 = −0.40702
Y28 = 0.58576
Z28 = 12.25000



X29 = −0.52901
Y29 = 0.58360
Z29 = 12.25000



X30 = −0.64788
Y30 = 0.55619
Z30 = 12.25000



X31 = 0.84952
Y31 = −0.94682
Z31 = 12.25000



X32 = 0.84925
Y32 = −0.95559
Z32 = 12.25000



X33 = 0.84306
Y33 = −0.96194
Z33 = 12.25000



X34 = 0.83430
Y34 = −0.96255
Z34 = 12.25000



X35 = 0.82743
Y35 = −0.95703
Z35 = 12.25000



X36 = −0.62568
Y36 = 0.31791
Z36 = 12.25000



X37 = −0.52382
Y37 = 0.29214
Z37 = 12.25000



X38 = −0.42300
Y38 = 0.26258
Z38 = 12.25000



X39 = −0.32421
Y39 = 0.22685
Z39 = 12.25000



X40 = −0.22808
Y40 = 0.18447
Z40 = 12.25000



X41 = −0.13539
Y41 = 0.13507
Z41 = 12.25000



X42 = −0.04712
Y42 = 0.07812
Z42 = 12.25000



X43 = 0.03686
Y43 = 0.01500
Z43 = 12.25000



X44 = 0.11765
Y44 = −0.05217
Z44 = 12.25000



X45 = 0.19547
Y45 = −0.12276
Z45 = 12.25000



X46 = 0.27033
Y46 = −0.19648
Z46 = 12.25000



X47 = 0.34261
Y47 = −0.27273
Z47 = 12.25000



X48 = 0.41237
Y48 = −0.35130
Z48 = 12.25000



X49 = 0.47946
Y49 = −0.43216
Z49 = 12.25000



X50 = 0.54382
Y50 = −0.51521
Z50 = 12.25000



X51 = 0.60541
Y51 = −0.60033
Z51 = 12.25000



X52 = 0.66420
Y52 = −0.68741
Z52 = 12.25000



X53 = 0.72037
Y53 = −0.77621
Z53 = 12.25000



X54 = 0.77441
Y54 = −0.86631
Z54 = 12.25000



X55 = 0.82743
Y55 = −0.95703
Z55 = 12.25000



X56 = −0.77576
Y56 = 0.36549
Z56 = 12.25000



X57 = −0.73999
Y57 = 0.34895
Z57 = 12.25000



X58 = −0.70222
Y58 = 0.33742
Z58 = 12.25000



X59 = −0.66401
Y59 = 0.32742
Z59 = 12.25000



X60 = −0.62568
Y60 = 0.31791
Z60 = 12.25000







C. Section height 12.75











X1 = −0.79009
Y1 = 0.40814
Z1 = 12.75000



X2 = −0.80217
Y2 = 0.38334
Z2 = 12.75000



X3 = −0.80322
Y3 = 0.35578
Z3 = 12.75000



X4 = −0.79305
Y4 = 0.33014
Z4 = 12.75000



X5 = −0.77337
Y5 = 0.31081
Z5 = 12.75000



X6 = −0.79009
Y6 = 0.40814
Z6 = 12.75000



X7 = −0.75933
Y7 = 0.43976
Z7 = 12.75000



X8 = −0.72335
Y8 = 0.46536
Z8 = 12.75000



X9 = −0.68446
Y9 = 0.48630
Z9 = 12.75000



X10 = −0.64382
Y10 = 0.50364
Z10 = 12.75000



X11 = −0.64382
Y11 = 0.50364
Z11 = 12.75000



X12 = −0.52602
Y12 = 0.53407
Z12 = 12.75000



X13 = −0.40446
Y13 = 0.53943
Z13 = 12.75000



X14 = −0.28422
Y14 = 0.52053
Z14 = 12.75000



X15 = −0.16914
Y15 = 0.48078
Z15 = 12.75000



X16 = −0.06135
Y16 = 0.42407
Z16 = 12.75000



X17 = 0.03844
Y17 = 0.35418
Z17 = 12.75000



X18 = 0.13040
Y18 = 0.27424
Z18 = 12.75000



X19 = 0.21518
Y19 = 0.18670
Z19 = 12.75000



X20 = 0.29350
Y20 = 0.09332
Z20 = 12.75000



X21 = 0.36595
Y21 = −0.00469
Z21 = 12.75000



X22 = 0.43333
Y22 = −0.10626
Z22 = 12.75000



X23 = 0.49639
Y23 = −0.21056
Z23 = 12.75000



X24 = 0.55574
Y24 = −0.31702
Z24 = 12.75000



X25 = 0.61181
Y25 = −0.42525
Z25 = 12.75000



X26 = 0.66487
Y26 = −0.53499
Z26 = 12.75000



X27 = 0.71523
Y27 = −0.64599
Z27 = 12.75000



X28 = 0.76304
Y28 = −0.75812
Z28 = 12.75000



X29 = 0.80805
Y29 = −0.87139
Z29 = 12.75000



X30 = 0.84963
Y30 = −0.98597
Z30 = 12.75000



X31 = 0.84963
Y31 = −0.98597
Z31 = 12.75000



X32 = 0.84941
Y32 = −0.99477
Z32 = 12.75000



X33 = 0.84322
Y33 = −1.00116
Z33 = 12.75000



X34 = 0.83443
Y34 = −1.00183
Z34 = 12.75000



X35 = 0.82748
Y35 = −0.99636
Z35 = 12.75000



X36 = 0.82748
Y36 = −0.99636
Z36 = 12.75000



X37 = 0.77282
Y37 = −0.90525
Z37 = 12.75000



X38 = 0.71707
Y38 = −0.81480
Z38 = 12.75000



X39 = 0.65922
Y39 = −0.72569
Z39 = 12.75000



X40 = 0.59883
Y40 = −0.63827
Z40 = 12.75000



X41 = 0.53572
Y41 = −0.55280
Z41 = 12.75000



X42 = 0.46986
Y42 = −0.46944
Z42 = 12.75000



X43 = 0.40119
Y43 = −0.38837
Z43 = 12.75000



X44 = 0.32970
Y44 = −0.30977
Z44 = 12.75000



X45 = 0.25550
Y45 = −0.23373
Z45 = 12.75000



X46 = 0.17851
Y46 = −0.16052
Z46 = 12.75000



X47 = 0.09856
Y47 = −0.09056
Z47 = 12.75000



X48 = 0.01553
Y48 = −0.02428
Z48 = 12.75000



X49 = −0.07100
Y49 = 0.03735
Z49 = 12.75000



X50 = −0.16181
Y50 = 0.09245
Z50 = 12.75000



X51 = −0.25659
Y51 = 0.14041
Z51 = 12.75000



X52 = −0.35445
Y52 = 0.18174
Z52 = 12.75000



X53 = −0.45496
Y53 = 0.21611
Z53 = 12.75000



X54 = −0.55740
Y54 = 0.24428
Z54 = 12.75000



X55 = −0.66038
Y55 = 0.27043
Z55 = 12.75000



X56 = −0.66038
Y56 = 0.27043
Z56 = 12.75000



X57 = −0.68944
Y57 = 0.27831
Z57 = 12.75000



X58 = −0.71830
Y58 = 0.28688
Z58 = 12.75000



X59 = −0.74660
Y59 = 0.29712
Z59 = 12.75000



X60 = −0.77337
Y60 = 0.31081
Z60 = 12.75000







D. Section height 13.25











X1 = −0.78853
Y1 = 0.35300
Z1 = 13.25000



X2 = −0.80026
Y2 = 0.32825
Z2 = 13.25000



X3 = −0.80110
Y3 = 0.30088
Z3 = 13.25000



X4 = −0.79089
Y4 = 0.27546
Z4 = 13.25000



X5 = −0.77133
Y5 = 0.25629
Z5 = 13.25000



X6 = −0.78853
Y6 = 0.35300
Z6 = 13.25000



X7 = −0.75795
Y7 = 0.38488
Z7 = 13.25000



X8 = −0.72193
Y8 = 0.41054
Z8 = 13.25000



X9 = −0.68302
Y9 = 0.43164
Z9 = 13.25000



X10 = −0.64247
Y10 = 0.44935
Z10 = 13.25000



X11 = −0.64247
Y11 = 0.44935
Z11 = 13.25000



X12 = −0.52558
Y12 = 0.48097
Z12 = 13.25000



X13 = −0.40467
Y13 = 0.48758
Z13 = 13.25000



X14 = −0.28484
Y14 = 0.46987
Z14 = 13.25000



X15 = −0.17002
Y15 = 0.43113
Z15 = 13.25000



X16 = −0.06252
Y16 = 0.37513
Z16 = 13.25000



X17 = 0.03696
Y17 = 0.30582
Z17 = 13.25000



X18 = 0.12864
Y18 = 0.22644
Z18 = 13.25000



X19 = 0.21316
Y19 = 0.13946
Z19 = 13.25000



X20 = 0.29120
Y20 = 0.04661
Z20 = 13.25000



X21 = 0.36340
Y21 = −0.05086
Z21 = 13.25000



X22 = 0.43072
Y22 = −0.15177
Z22 = 13.25000



X23 = 0.49395
Y23 = −0.25530
Z23 = 13.25000



X24 = 0.55363
Y24 = −0.36091
Z24 = 13.25000



X25 = 0.61010
Y25 = −0.46828
Z25 = 13.25000



X26 = 0.66356
Y26 = −0.57717
Z26 = 13.25000



X27 = 0.71421
Y27 = −0.68740
Z27 = 13.25000



X28 = 0.76223
Y28 = −0.79881
Z28 = 13.25000



X29 = 0.80748
Y29 = −0.91136
Z29 = 13.25000



X30 = 0.84974
Y30 = −1.02507
Z30 = 13.25000



X31 = 0.84974
Y31 = −1.02507
Z31 = 13.25000



X32 = 0.84960
Y32 = −1.03388
Z32 = 13.25000



X33 = 0.84347
Y33 = −1.04035
Z33 = 13.25000



X34 = 0.83468
Y34 = −1.04112
Z34 = 13.25000



X35 = 0.82765
Y35 = −1.03573
Z35 = 13.25000



X36 = 0.82765
Y36 = −1.03573
Z36 = 13.25000



X37 = 0.77319
Y37 = −0.94758
Z37 = 13.25000



X38 = 0.71771
Y38 = −0.86007
Z38 = 13.25000



X39 = 0.66040
Y39 = −0.77375
Z39 = 13.25000



X40 = 0.60082
Y40 = −0.68898
Z40 = 13.25000



X41 = 0.53877
Y41 = −0.60601
Z41 = 13.25000



X42 = 0.47414
Y42 = −0.52503
Z42 = 13.25000



X43 = 0.40684
Y43 = −0.44625
Z43 = 13.25000



X44 = 0.33684
Y44 = −0.36987
Z44 = 13.25000



X45 = 0.26415
Y45 = −0.29603
Z45 = 13.25000



X46 = 0.18877
Y46 = −0.22495
Z46 = 13.25000



X47 = 0.11063
Y47 = −0.15691
Z47 = 13.25000



X48 = 0.02962
Y48 = −0.09233
Z48 = 13.25000



X49 = −0.05456
Y49 = −0.03192
Z49 = 13.25000



X50 = −0.14240
Y50 = 0.02299
Z50 = 13.25000



X51 = −0.23384
Y51 = 0.07168
Z51 = 13.25000



X52 = −0.32822
Y52 = 0.11440
Z52 = 13.25000



X53 = −0.42524
Y53 = 0.15070
Z53 = 13.25000



X54 = −0.52456
Y54 = 0.18018
Z54 = 13.25000



X55 = −0.62484
Y55 = 0.20625
Z55 = 13.25000



X56 = −0.62484
Y56 = 0.20625
Z56 = 13.25000



X57 = −0.66241
Y57 = 0.21614
Z57 = 13.25000



X58 = −0.69984
Y58 = 0.22656
Z58 = 13.25000



X59 = −0.73667
Y59 = 0.23887
Z59 = 13.25000



X60 = −0.77133
Y60 = 0.25629
Z60 = 13.25000







E. Section height 13.75











X1 = −0.78730
Y1 = 0.29843
Z1 = 13.75000



X2 = −0.79882
Y2 = 0.27363
Z2 = 13.75000



X3 = −0.79947
Y3 = 0.24629
Z3 = 13.75000



X4 = −0.78913
Y4 = 0.22097
Z4 = 13.75000



X5 = −0.76951
Y5 = 0.20191
Z5 = 13.75000



X6 = −0.78730
Y6 = 0.29843
Z6 = 13.75000



X7 = −0.75545
Y7 = 0.33156
Z7 = 13.75000



X8 = −0.71767
Y8 = 0.35781
Z8 = 13.75000



X9 = −0.67688
Y9 = 0.37916
Z9 = 13.75000



X10 = −0.63435
Y10 = 0.39681
Z10 = 13.75000



X11 = −0.63435
Y11 = 0.39681
Z11 = 13.75000



X12 = −0.51812
Y12 = 0.42546
Z12 = 13.75000



X13 = −0.39846
Y13 = 0.42946
Z13 = 13.75000



X14 = −0.28026
Y14 = 0.41019
Z14 = 13.75000



X15 = −0.16708
Y15 = 0.37090
Z15 = 13.75000



X16 = −0.06101
Y16 = 0.31512
Z16 = 13.75000



X17 = 0.03739
Y17 = 0.24666
Z17 = 13.75000



X18 = 0.12836
Y18 = 0.16857
Z18 = 13.75000



X19 = 0.21234
Y19 = 0.08299
Z19 = 13.75000



X20 = 0.28987
Y20 = −0.00849
Z20 = 13.75000



X21 = 0.36169
Y21 = −0.10452
Z21 = 13.75000



X22 = 0.42876
Y22 = −0.20394
Z22 = 13.75000



X23 = 0.49185
Y23 = −0.30594
Z23 = 13.75000



X24 = 0.55150
Y24 = −0.40998
Z24 = 13.75000



X25 = 0.60805
Y25 = −0.51574
Z25 = 13.75000



X26 = 0.66170
Y26 = −0.62300
Z26 = 13.75000



X27 = 0.71262
Y27 = −0.73159
Z27 = 13.75000



X28 = 0.76096
Y28 = −0.84134
Z28 = 13.75000



X29 = 0.80669
Y29 = −0.95222
Z29 = 13.75000



X30 = 0.84982
Y30 = −1.06412
Z30 = 13.75000



X31 = 0.84982
Y31 = −1.06412
Z31 = 13.75000



X32 = 0.84981
Y32 = −1.07293
Z32 = 13.75000



X33 = 0.84381
Y33 = −1.07950
Z33 = 13.75000



X34 = 0.83505
Y34 = −1.08042
Z34 = 13.75000



X35 = 0.82795
Y35 = −1.07514
Z35 = 13.75000



X36 = −0.64316
Y36 = 0.15725
Z36 = 13.75000



X37 = −0.54266
Y37 = 0.13083
Z37 = 13.75000



X38 = −0.44308
Y38 = 0.10114
Z38 = 13.75000



X39 = −0.34575
Y39 = 0.06479
Z39 = 13.75000



X40 = −0.25111
Y40 = 0.02192
Z40 = 13.75000



X41 = −0.15926
Y41 = −0.02666
Z41 = 13.75000



X42 = −0.07058
Y42 = −0.08080
Z42 = 13.75000



X43 = 0.01478
Y43 = −0.14004
Z43 = 13.75000



X44 = 0.09706
Y44 = −0.20350
Z44 = 13.75000



X45 = 0.17646
Y45 = −0.27054
Z45 = 13.75000



X46 = 0.25307
Y46 = −0.34074
Z46 = 13.75000



X47 = 0.32697
Y47 = −0.41379
Z47 = 13.75000



X48 = 0.39816
Y48 = −0.48949
Z48 = 13.75000



X49 = 0.46663
Y49 = −0.56765
Z49 = 13.75000



X50 = 0.53243
Y50 = −0.64808
Z50 = 13.75000



X51 = 0.59564
Y51 = −0.73056
Z51 = 13.75000



X52 = 0.65641
Y52 = −0.81486
Z52 = 13.75000



X53 = 0.71503
Y53 = −0.90066
Z53 = 13.75000



X54 = 0.77197
Y54 = −0.98759
Z54 = 13.75000



X55 = 0.82795
Y55 = −1.07514
Z55 = 13.75000



X56 = −0.76951
Y56 = 0.20191
Z56 = 13.75000



X57 = −0.73964
Y57 = 0.18655
Z57 = 13.75000



X58 = −0.70796
Y58 = 0.17527
Z58 = 13.75000



X59 = −0.67564
Y59 = 0.16597
Z59 = 13.75000



X60 = −0.64316
Y60 = 0.15725
Z60 = 13.75000







F. Section height 14.25











X1 = −0.78638
Y1 = 0.24442
Z1 = 14.25000



X2 = −0.79786
Y2 = 0.21947
Z2 = 14.25000



X3 = −0.79834
Y3 = 0.19202
Z3 = 14.25000



X4 = −0.78777
Y4 = 0.16667
Z4 = 14.25000



X5 = −0.76792
Y5 = 0.14770
Z5 = 14.25000



X6 = −0.78638
Y6 = 0.24442
Z6 = 14.25000



X7 = −0.75683
Y7 = 0.27563
Z7 = 14.25000



X8 = −0.72171
Y8 = 0.30050
Z8 = 14.25000



X9 = −0.68360
Y9 = 0.32056
Z9 = 14.25000



X10 = −0.64379
Y10 = 0.33696
Z10 = 14.25000



X11 = −0.64379
Y11 = 0.33696
Z11 = 14.25000



X12 = −0.52804
Y12 = 0.36406
Z12 = 14.25000



X13 = −0.40913
Y13 = 0.36646
Z13 = 14.25000



X14 = −0.29181
Y14 = 0.34671
Z14 = 14.25000



X15 = −0.17925
Y15 = 0.30804
Z15 = 14.25000



X16 = −0.07333
Y16 = 0.25374
Z16 = 14.25000



X17 = 0.02552
Y17 = 0.18735
Z17 = 14.25000



X18 = 0.11744
Y18 = 0.11164
Z18 = 14.25000



X19 = 0.20242
Y19 = 0.02821
Z19 = 14.25000



X20 = 0.28088
Y20 = −0.06141
Z20 = 14.25000



X21 = 0.35357
Y21 = −0.15576
Z21 = 14.25000



X22 = 0.42137
Y22 = −0.25369
Z22 = 14.25000



X23 = 0.48506
Y23 = −0.35436
Z23 = 14.25000



X24 = 0.54525
Y24 = −0.45715
Z24 = 14.25000



X25 = 0.60240
Y25 = −0.56167
Z25 = 14.25000



X26 = 0.65677
Y26 = −0.66766
Z26 = 14.25000



X27 = 0.70863
Y27 = −0.77490
Z27 = 14.25000



X28 = 0.75809
Y28 = −0.88328
Z28 = 14.25000



X29 = 0.80513
Y29 = −0.99272
Z29 = 14.25000



X30 = 0.84986
Y30 = −1.10312
Z30 = 14.25000



X31 = 0.84986
Y31 = −1.10312
Z31 = 14.25000



X32 = 0.85006
Y32 = −1.11190
Z32 = 14.25000



X33 = 0.84425
Y33 = −1.11861
Z33 = 14.25000



X34 = 0.83554
Y34 = −1.11972
Z34 = 14.25000



X35 = 0.82837
Y35 = −1.11459
Z35 = 14.25000



X36 = −0.65970
Y36 = 0.10909
Z36 = 14.25000



X37 = −0.55900
Y37 = 0.08256
Z37 = 14.25000



X38 = −0.45944
Y38 = 0.05205
Z38 = 14.25000



X39 = −0.36209
Y39 = 0.01513
Z39 = 14.25000



X40 = −0.26745
Y40 = −0.02829
Z40 = 14.25000



X41 = −0.17559
Y41 = −0.07732
Z41 = 14.25000



X42 = −0.08652
Y42 = −0.13126
Z42 = 14.25000



X43 = −0.00027
Y43 = −0.18959
Z43 = 14.25000



X44 = 0.08317
Y44 = −0.25189
Z44 = 14.25000



X45 = 0.16377
Y45 = −0.31783
Z45 = 14.25000



X46 = 0.24152
Y46 = −0.38709
Z46 = 14.25000



X47 = 0.31658
Y47 = −0.45928
Z47 = 14.25000



X48 = 0.38899
Y48 = −0.53412
Z48 = 14.25000



X49 = 0.45873
Y49 = −0.61144
Z49 = 14.25000



X50 = 0.52580
Y50 = −0.69111
Z50 = 14.25000



X51 = 0.59024
Y51 = −0.77291
Z51 = 14.25000



X52 = 0.65226
Y52 = −0.85657
Z52 = 14.25000



X53 = 0.71222
Y53 = −0.94170
Z53 = 14.25000



X54 = 0.77070
Y54 = −1.02787
Z54 = 14.25000



X55 = 0.82837
Y55 = −1.11459
Z55 = 14.25000



X56 = −0.76792
Y56 = 0.14770
Z56 = 14.25000



X57 = −0.74232
Y57 = 0.13449
Z57 = 14.25000



X58 = −0.71526
Y58 = 0.12456
Z58 = 14.25000



X59 = −0.68757
Y59 = 0.11650
Z59 = 14.25000



X60 = −0.65970
Y60 = 0.10909
Z60 = 14.25000







G. Section height 14.75











X1 = −0.78588
Y1 = 0.19092
Z1 = 14.75000



X2 = −0.79741
Y2 = 0.16574
Z2 = 14.75000



X3 = −0.79777
Y3 = 0.13804
Z3 = 14.75000



X4 = −0.78690
Y4 = 0.11256
Z4 = 14.75000



X5 = −0.76667
Y5 = 0.09364
Z5 = 14.75000



X6 = −0.78588
Y6 = 0.19092
Z6 = 14.75000



X7 = −0.75225
Y7 = 0.22528
Z7 = 14.75000



X8 = −0.71190
Y8 = 0.25154
Z8 = 14.75000



X9 = −0.66807
Y9 = 0.27156
Z9 = 14.75000



X10 = −0.62218
Y10 = 0.28623
Z10 = 14.75000



X11 = −0.62218
Y11 = 0.28623
Z11 = 14.75000



X12 = −0.50725
Y12 = 0.30207
Z12 = 14.75000



X13 = −0.39136
Y13 = 0.29495
Z13 = 14.75000



X14 = −0.27818
Y14 = 0.26891
Z14 = 14.75000



X15 = −0.16978
Y15 = 0.22708
Z15 = 14.75000



X16 = −0.06735
Y16 = 0.17224
Z16 = 14.75000



X17 = 0.02915
Y17 = 0.10747
Z17 = 14.75000



X18 = 0.11964
Y18 = 0.03454
Z18 = 14.75000



X19 = 0.20347
Y19 = −0.04597
Z19 = 14.75000



X20 = 0.28103
Y20 = −0.13254
Z20 = 14.75000



X21 = 0.35309
Y21 = −0.22376
Z21 = 14.75000



X22 = 0.42024
Y22 = −0.31865
Z22 = 14.75000



X23 = 0.48320
Y23 = −0.41638
Z23 = 14.75000



X24 = 0.54268
Y24 = −0.51626
Z24 = 14.75000



X25 = 0.59929
Y25 = −0.61780
Z25 = 14.75000



X26 = 0.65348
Y26 = −0.72066
Z26 = 14.75000



X27 = 0.70562
Y27 = −0.82456
Z27 = 14.75000



X28 = 0.75569
Y28 = −0.92949
Z28 = 14.75000



X29 = 0.80381
Y29 = −1.03532
Z29 = 14.75000



X30 = 0.84987
Y30 = −1.14206
Z30 = 14.75000



X31 = 0.84987
Y31 = −1.14206
Z31 = 14.75000



X32 = 0.85034
Y32 = −1.15079
Z32 = 14.75000



X33 = 0.84477
Y33 = −1.15766
Z33 = 14.75000



X34 = 0.83613
Y34 = −1.15903
Z34 = 14.75000



X35 = 0.82888
Y35 = −1.15409
Z35 = 14.75000



X36 = −0.63239
Y36 = 0.05080
Z36 = 14.75000



X37 = −0.53411
Y37 = 0.02355
Z37 = 14.75000



X38 = −0.43776
Y38 = −0.00986
Z38 = 14.75000



X39 = −0.34375
Y39 = −0.04937
Z39 = 14.75000



X40 = −0.25239
Y40 = −0.09468
Z40 = 14.75000



X41 = −0.16372
Y41 = −0.14507
Z41 = 14.75000



X42 = −0.07730
Y42 = −0.19924
Z42 = 14.75000



X43 = 0.00701
Y43 = −0.25663
Z43 = 14.75000



X44 = 0.08899
Y44 = −0.31730
Z44 = 14.75000



X45 = 0.16831
Y45 = −0.38141
Z45 = 14.75000



X46 = 0.24478
Y46 = −0.44889
Z46 = 14.75000



X47 = 0.31879
Y47 = −0.51908
Z47 = 14.75000



X48 = 0.39043
Y48 = −0.59167
Z48 = 14.75000



X49 = 0.45960
Y49 = −0.66662
Z49 = 14.75000



X50 = 0.52618
Y50 = −0.74388
Z50 = 14.75000



X51 = 0.59026
Y51 = −0.82324
Z51 = 14.75000



X52 = 0.65202
Y52 = −0.90440
Z52 = 14.75000



X53 = 0.71194
Y53 = −0.98694
Z53 = 14.75000



X54 = 0.77066
Y54 = −1.07034
Z54 = 14.75000



X55 = 0.82888
Y55 = −1.15409
Z55 = 14.75000



X56 = −0.76667
Y56 = 0.09364
Z56 = 14.75000



X57 = −0.73476
Y57 = 0.07849
Z57 = 14.75000



X58 = −0.70100
Y58 = 0.06799
Z58 = 14.75000



X59 = −0.66672
Y59 = 0.05929
Z59 = 14.75000



X60 = −0.63239
Y60 = 0.05080
Z60 = 14.75000










While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment(s), but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims, which scope is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures as permitted under the law. Furthermore it should be understood that while the use of the word preferable, preferably, or preferred in the description above indicates that feature so described may be more desirable, it nonetheless may not be necessary and any embodiment lacking the same may be contemplated as within the scope of the invention, that scope being defined by the claims that follow. In reading the claims it is intended that when words such as “a,” “an,” “at least one” and “at least a portion” are used, there is no intention to limit the claim to only one item unless specifically stated to the contrary in the claim. Further, when the language “at least a portion” and/or “a portion” is used the item may include a portion and/or the entire item unless specifically stated to the contrary.

## Claims

1. An airfoil comprising:
an external surface having first and second sides, the external surface extending spanwise between a hub and a tip and streamwise between a leading edge and a trailing edge; and
the external surface having a contour substantially defined by Table 1 as listed in the specification.

2. The airfoil of claim 1, further comprising:
at least one coating formed on the external surface thereof.

3. The airfoil of claim 2, wherein the external surface including the at least one coating substantially meets the contour dimensions defined by Table 1.

4. The airfoil of claim 2, wherein an outer surface of the at least one coating extends outside of the contour dimensions as substantially defined by Table 1.

5. The airfoil of claim 2, wherein the coating includes at least one of a thermal barrier coating and a radiation barrier coating.

6. The airfoil of claim 1, wherein a portion of the external surface includes at least one discontinuity.

7. The airfoil of claim 6, wherein the at least one discontinuity includes a through aperture formed in at least one of the sides of the airfoil to provide an outlet path for cooling fluid to flow therethrough.

8. The airfoil of claim 1, wherein the airfoil is connected to a first stage turbine nozzle guide vane assembly.

9. The airfoil of claim 1, wherein the positional tolerance of the external surface is held to range of about +/−0.025 inches for each dimension listed in Table 1.

10. A turbine nozzle guide vane assembly for a gas turbine engine comprising:
an inner shroud having an upper surface and a lower surface, the upper surface of the inner shroud partially defining an inner flow path wall;
an airfoil extending radially outward from the upper surface of the inner shroud relative to an axis of rotation of the gas turbine engine, the airfoil having first and second three-dimensional external surfaces extending between a hub and a tip in a spanwise direction and between a leading edge and a trailing edge in a streamwise direction; and
a Cartesian coordinate array having X,Y and Z axis coordinates listed in Table 1 of the specification defining the first and second external surfaces of the airfoil, wherein the Z axis generally extends radially outward from at least one of the upper surface of the inner shroud or a longitudinal axis of the engine, the X axis generally extends normal to the Z axis in the streamwise direction, and the Y axis generally extends normal to both the X axis and the Z axis in a lateral direction.

11. The turbine nozzle guide vane assembly of claim 10, wherein the external surface of the airfoil is formed within a manufacturing tolerance of about +/−0.025 inches of each dimension listed in Table 1.

12. The turbine nozzle guide vane assembly of claim 10, wherein the Z axis further defines a stacking axis extending at a predefined angle from the inner shroud.

13. The turbine nozzle guide vane assembly of claim 12, wherein the angle of the stacking axis is located between a normal position and 25° from the normal position in any direction.

14. The turbine nozzle guide vane assembly of claim 10, further comprising:
at least one coating formed on the external surface of the airfoil.

15. The turbine nozzle guide vane assembly of claim 14, wherein the at least one coating is applied to the airfoil such that an outer surface of the coating is located within a tolerance of +/−0.050 inches of the coordinate dimensions defined in Table 1.

16. The turbine nozzle guide vane assembly of claim 14, wherein the coating is at least one of a thermal barrier coating and a radiation barrier coating.

17. The turbine nozzle guide vane assembly of claim 10, wherein a portion of the external surface of the airfoil includes at least one discontinuity.

18. The turbine nozzle guide vane assembly of claim 17, wherein the at least one discontinuity includes a through aperture formed in at least one of the sides of the airfoil to provide an outlet path for cooling fluid to flow therethrough.

19. The turbine nozzle guide vane assembly of claim 10, wherein the airfoil includes an outer shroud formed adjacent the tip.

20. A method of forming an airfoil for a turbine nozzle guide vane comprising:
forming a contoured three-dimensional external surface of an airfoil defined by Cartesian (X, Y and Z) coordinates listed in the specification as Table 1, wherein the Z axis coordinates are generally measured from an inner shroud or an engine centerline axis, the X axis coordinates are generally measured normal to the Z axis in a streamwise direction, and the Y axis coordinates are generally measured normal to the Z axis and normal to the X axis.

21. The method of claim 20, further comprising:
forming the airfoil from a casting process, wherein the casting process includes one of integrally casting the turbine nozzle guide vane in one piece and casting multiple pieces and subsequently bonding the cast pieces together.

22. The method of claim 20, further comprising:
forming the airfoil from a wrought material; and
machine processing a portion of the airfoil to meet a design specification.