# Patent

## Title
Third stage turbine airfoil

## Abstract

The present invention provides an airfoil for a third stage blade 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 No. 60/755,497 filed Dec. 29, 2005, which is incorporated herein by reference.


FIELD OF INVENTION
The present invention relates to improved airfoil geometry, and more particularly to a high efficiency turbine airfoil for 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 the third stage turbine airfoil.
SUMMARY
The present invention provides an airfoil having an external surface with first and second side 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.
In another aspect of the present invention, a turbine blade for a gas turbine engine can be formed with a platform having an upper surface and a lower surface. The upper surface of the platform can partially define an inner flow path wall and the lower surface of the platform can have a connecting joint extending radially inward from the platform. The root of the blade is connectable to a rotatable disk, wherein the rotatable disk has an axis of rotation along a longitudinal axis of the gas turbine engine. An airfoil can extend radially outward from the upper surface of the platform relative to the axis of rotation. The airfoil includes an external surface having first and second sides extending between a hub and a tip in a spanwise direction and between a leading edge and a trailing edge in a streamwise direction. The external surface of the airfoil is substantially defined by a Cartesian coordinate array having X, Y and Z axis coordinates listed in Table 1 of the specification, wherein the Z axis generally extends radially outward from at least one of the upper surface of the platform and 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.
Another aspect of the present invention provides a method of forming an airfoil for a turbine blade having a contoured three-dimensional external surface. The external surface of the airfoil is defined by Cartesian (X, Y and Z) coordinates listed in the specification as Table 1, wherein the Z axis coordinates are generally measured radially from a platform or 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 a method of forming an airfoil for a turbine blade having a contoured three-dimensional external surface. The external surface of the airfoil is defined by Cartesian (X, Y and Z) coordinates listed in the specification as Table 1, wherein the Z axis coordinates are generally measured radially 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 third stage turbine blade illustrated in FIG. 2;
FIG. 4 is a front view of the third stage turbine blade illustrated in FIG. 3;
FIG. 5 is a back view of the third stage turbine blade illustrated in FIG. 3;
FIG. 6 is a right view of the third stage turbine blade illustrated in FIG. 3;
FIG. 7 is a left view of the third stage turbine blade illustrated in FIG. 3;
FIG. 8 is a top view of the third stage turbine blade illustrated in FIG. 3; and
FIG. 9 is a bottom view of the third stage turbine blade 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 bums 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 is 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 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 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 rotatingly drives 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 can also be connected to the first stage turbine assembly 42 and therefore further increases the power delivered to the shaft 22. The third stage turbine blades 136 will be the described in more detail below.
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 convective 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 third stage blade 136 will be described in more detail. As partially described previously, each blade 136 includes an inner shroud or platform 144 wherein an outer surface 350 of the platform defines a portion of the inner flow path wall 31 at that particular location in the engine 10. The airfoil 138 extends radially outward from the outer surface 350 of the platform 144 from a hub 352 toward a tip 354. The airfoil 138 is attached to the platform 144 proximate the hub 352 of the airfoil 138. The airfoil 138 can be integrally formed with the platform 144 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 146 can be attached to the airfoil 138 proximate the tip 354 of the airfoil 138. The outer shroud 146 includes an inner surface 356 which forms a portion of the outer flow path 33 in the turbine section 18. An outer surface 358 of the outer shroud 146 can include at least one knife seal 360 and in this particular embodiment includes two knife seals 360. The knife seals 360 are operable for engaging a blade track seal (not shown) to minimize leakage of working fluid from the outer flow path 33.
An attachment member 370 extends radially inward from an inner surface 372 of the platform 144. The attachment member 370 includes a connecting joint 374 operable to provide a mechanical connection between the third stage turbine blade 136 and the third turbine disk 134. The connecting joint 374 can be formed from common connections such as a dovetail joint, or as this particular embodiment discloses a “fir tree” design as it is commonly referred to by engineers in this field of endeavor. A stalk 376 extends between the connecting joint 374 and the inner surface 372 of the platform 144. The stalk 376 may include one or more seal members sometimes referred to as angel wings 378. The angel wing seals 378 may extend axially upstream and/or axially downstream of the third turbine assembly 130. The angel wing seals 378 minimize the space between the rotating turbine wheel 132 and adjacent static components (not shown in FIG. 3). The minimized space reduces leakage of working fluid through the inner flow path wall 31. An axial abutment 380 can be positioned adjacent a lower portion of the attachment member 370 to provide alignment and proper positioning of the turbine blade 136 with respect to the third stage turbine disk 134 during assembly.
The third stage turbine airfoil 138 of the present invention is substantially defined by Table 1 listed below. Table 1 lists data points in Cartesian coordinates that define the external surface of the airfoil 138 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 platform 144 of the airfoil 138. The Z axis defines an imaginary stacking axis from which the contoured external surface is formed. The stacking axis, as it is typically used by aerodynamic design engineers, is nominally defined normal to the platform radially from an 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 normal plane. 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 138 defined by Table 1 improves the third stage turbine efficiency by 2.09% over prior art designs.
While the external surface of airfoil 138 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 138. 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 blade is integrally cast as a one-piece component. Alternatively the turbine blade can be formed in multiple pieces and bonded together. In another form the turbine blade 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 third stage turbine airfoils (in)







A. Section Height 9.330709











X1 = −0.692949
Y1 = −0.034168
Z1 = 9.330709



X2 = −0.61762
Y2 = −0.120494
Z2 = 9.330709



X3 = −0.513774
Y3 = −0.173097
Z3 = 9.330709



X4 = −0.401212
Y4 = −0.20346
Z4 = 9.330709



X5 = −0.285281
Y5 = −0.216337
Z5 = 9.330709



X6 = −0.168675
Y6 = −0.212886
Z6 = 9.330709



X7 = −0.053614
Y7 = −0.193656
Z7 = 9.330709



X8 = 0.057952
Y8 = −0.15954
Z8 = 9.330709



X9 = 0.164684
Y9 = −0.112391
Z9 = 9.330709



X10 = 0.26592
Y10 = −0.054338
Z10 = 9.330709



X11 = 0.360854
Y11 = 0.013518
Z11 = 9.330709



X12 = 0.44907
Y12 = 0.089941
Z12 = 9.330709



X13 = 0.530902
Y13 = 0.17316
Z13 = 9.330709



X14 = 0.606706
Y14 = 0.261924
Z14 = 9.330709



X15 = 0.678199
Y15 = 0.35421
Z15 = 9.330709



X16 = 0.730665
Y16 = 0.425062
Z16 = 9.330709



X17 = 0.731839
Y17 = 0.427173
Z17 = 9.330709



X18 = 0.732613
Y18 = 0.429462
Z18 = 9.330709



X19 = 0.732928
Y19 = 0.431857
Z19 = 9.330709



X20 = 0.732781
Y20 = 0.434268
Z20 = 9.330709



X21 = 0.732221
Y21 = 0.436619
Z21 = 9.330709



X22 = 0.731266
Y22 = 0.438839
Z22 = 9.330709



X23 = 0.729923
Y23 = 0.440846
Z23 = 9.330709



X24 = 0.728223
Y24 = 0.442565
Z24 = 9.330709



X25 = 0.726213
Y25 = 0.443902
Z25 = 9.330709



X26 = 0.723964
Y26 = 0.444779
Z26 = 9.330709



X27 = 0.721576
Y27 = 0.445148
Z27 = 9.330709



X28 = 0.719169
Y28 = 0.444982
Z28 = 9.330709



X29 = 0.716855
Y29 = 0.444289
Z29 = 9.330709



X30 = 0.71474
Y30 = 0.443125
Z30 = 9.330709



X31 = 0.674765
Y31 = 0.40935
Z31 = 9.330709



X32 = 0.595305
Y32 = 0.345009
Z32 = 9.330709



X33 = 0.512982
Y33 = 0.284387
Z33 = 9.330709



X34 = 0.427156
Y34 = 0.228842
Z34 = 9.330709



X35 = 0.337839
Y35 = 0.179114
Z35 = 9.330709



X36 = 0.244992
Y36 = 0.136352
Z36 = 9.330709



X37 = 0.149
Y37 = 0.101214
Z37 = 9.330709



X38 = 0.050608
Y38 = 0.073474
Z38 = 9.330709



X39 = −0.049452
Y39 = 0.052524
Z39 = 9.330709



X40 = −0.150634
Y40 = 0.037882
Z40 = 9.330709



X41 = −0.252393
Y41 = 0.027953
Z41 = 9.330709



X42 = −0.354378
Y42 = 0.020621
Z42 = 9.330709



X43 = −0.456415
Y43 = 0.014049
Z43 = 9.330709



X44 = −0.558385
Y44 = 0.006522
Z44 = 9.330709



X45 = −0.659699
Y45 = −0.006744
Z45 = 9.330709



X46 = −0.684591
Y46 = −0.016079
Z46 = 9.330709



X47 = −0.685842
Y47 = −0.016911
Z47 = 9.330709



X48 = −0.687011
Y48 = −0.017853
Z48 = 9.330709



X49 = −0.68808
Y49 = −0.018907
Z49 = 9.330709



X50 = −0.689046
Y50 = −0.020057
Z50 = 9.330709



X51 = −0.689914
Y51 = −0.021283
Z51 = 9.330709



X52 = −0.690689
Y52 = −0.02257
Z52 = 9.330709



X53 = −0.691367
Y53 = −0.02391
Z53 = 9.330709



X54 = −0.691942
Y54 = −0.025297
Z54 = 9.330709



X55 = −0.692407
Y55 = −0.026725
Z55 = 9.330709



X56 = −0.692755
Y56 = −0.028186
Z56 = 9.330709



X57 = −0.692982
Y57 = −0.029671
Z57 = 9.330709



X58 = −0.693085
Y58 = −0.031169
Z58 = 9.330709



X59 = −0.693071
Y59 = −0.032671
Z59 = 9.330709



X60 = −0.692949
Y60 = −0.034168
Z60 = 9.330709







B. Section Height 9.814398











X1 = −0.675827
Y1 = −0.026703
Z1 = 9.814398



X2 = −0.60045
Y2 = −0.112613
Z2 = 9.814398



X3 = −0.500061
Y3 = −0.168814
Z3 = 9.814398



X4 = −0.389519
Y4 = −0.201256
Z4 = 9.814398



X5 = −0.27499
Y5 = −0.214355
Z5 = 9.814398



X6 = −0.159804
Y6 = −0.209471
Z6 = 9.814398



X7 = −0.046645
Y7 = −0.187385
Z7 = 9.814398



X8 = 0.062315
Y8 = −0.149642
Z8 = 9.814398



X9 = 0.165758
Y9 = −0.098639
Z9 = 9.814398



X10 = 0.262924
Y10 = −0.036489
Z10 = 9.814398



X11 = 0.352536
Y11 = 0.03613
Z11 = 9.814398



X12 = 0.435539
Y12 = 0.116268
Z12 = 9.814398



X13 = 0.512914
Y13 = 0.201853
Z13 = 9.814398



X14 = 0.58527
Y14 = 0.291736
Z14 = 9.814398



X15 = 0.654501
Y15 = 0.384057
Z15 = 9.814398



X16 = 0.705893
Y16 = 0.454455
Z16 = 9.814398



X17 = 0.707068
Y17 = 0.456592
Z17 = 9.814398



X18 = 0.707832
Y18 = 0.458909
Z18 = 9.814398



X19 = 0.708126
Y19 = 0.46133
Z19 = 9.814398



X20 = 0.707947
Y20 = 0.463762
Z20 = 9.814398



X21 = 0.707344
Y21 = 0.466127
Z21 = 9.814398



X22 = 0.706338
Y22 = 0.46835
Z22 = 9.814398



X23 = 0.704939
Y23 = 0.470346
Z23 = 9.814398



X24 = 0.703181
Y24 = 0.472039
Z24 = 9.814398



X25 = 0.701116
Y25 = 0.473334
Z25 = 9.814398



X26 = 0.698822
Y26 = 0.474158
Z26 = 9.814398



X27 = 0.696402
Y27 = 0.474465
Z27 = 9.814398



X28 = 0.693977
Y28 = 0.474235
Z28 = 9.814398



X29 = 0.691658
Y29 = 0.473478
Z29 = 9.814398



X30 = 0.68955
Y30 = 0.472254
Z30 = 9.814398



X31 = 0.650527
Y31 = 0.43724
Z31 = 9.814398



X32 = 0.574492
Y32 = 0.368625
Z32 = 9.814398



X33 = 0.497037
Y33 = 0.301625
Z33 = 9.814398



X34 = 0.416543
Y34 = 0.238316
Z34 = 9.814398



X35 = 0.333197
Y35 = 0.178811
Z35 = 9.814398



X36 = 0.246616
Y36 = 0.124135
Z36 = 9.814398



X37 = 0.1564
Y37 = 0.075706
Z37 = 9.814398



X38 = 0.062518
Y38 = 0.034854
Z38 = 9.814398



X39 = −0.034913
Y39 = 0.003461
Z39 = 9.814398



X40 = −0.135405
Y40 = −0.015976
Z40 = 9.814398



X41 = −0.237494
Y41 = −0.023461
Z41 = 9.814398



X42 = −0.33984
Y42 = −0.020577
Z42 = 9.814398



X43 = −0.441782
Y43 = −0.010836
Z43 = 9.814398



X44 = −0.543478
Y44 = 0.00129
Z44 = 9.814398



X45 = −0.64558
Y45 = 0.003515
Z45 = 9.814398



X46 = −0.67013
Y46 = −0.006563
Z46 = 9.814398



X47 = −0.671323
Y47 = −0.007609
Z47 = 9.814398



X48 = −0.672413
Y48 = −0.008761
Z48 = 9.814398



X49 = −0.673377
Y49 = −0.010021
Z49 = 9.814398



X50 = −0.674214
Y50 = −0.011369
Z50 = 9.814398



X51 = −0.674931
Y51 = −0.012784
Z51 = 9.814398



X52 = −0.675537
Y52 = −0.014251
Z52 = 9.814398



X53 = −0.676029
Y53 = −0.015759
Z53 = 9.814398



X54 = −0.676401
Y54 = −0.017302
Z54 = 9.814398



X55 = −0.676644
Y55 = −0.018869
Z55 = 9.814398



X56 = −0.676752
Y56 = −0.020452
Z56 = 9.814398



X57 = −0.676722
Y57 = −0.022038
Z57 = 9.814398



X58 = −0.676552
Y58 = −0.023616
Z58 = 9.814398



X59 = −0.676249
Y59 = −0.025173
Z59 = 9.814398



X60 = −0.675827
Y60 = −0.026703
Z60 = 9.814398







C. Section Height 10.298088











X1 = −0.659356
Y1 = −0.036652
Z1 = 10.298088



X2 = −0.58367
Y2 = −0.122169
Z2 = 10.298088



X3 = −0.485265
Y3 = −0.180835
Z3 = 10.298088



X4 = −0.375482
Y4 = −0.214038
Z4 = 10.298088



X5 = −0.261301
Y5 = −0.22568
Z5 = 10.298088



X6 = −0.146852
Y6 = −0.216828
Z6 = 10.298088



X7 = −0.03548
Y7 = −0.188944
Z7 = 10.298088



X8 = 0.070524
Y8 = −0.144773
Z8 = 10.298088



X9 = 0.170138
Y9 = −0.087573
Z9 = 10.298088



X10 = 0.262658
Y10 = −0.01949
Z10 = 10.298088



X11 = 0.347154
Y11 = 0.058352
Z11 = 10.298088



X12 = 0.425516
Y12 = 0.142404
Z12 = 10.298088



X13 = 0.498925
Y13 = 0.230819
Z13 = 10.298088



X14 = 0.568485
Y14 = 0.322305
Z14 = 10.298088



X15 = 0.635126
Y15 = 0.415938
Z15 = 10.298088



X16 = 0.683107
Y16 = 0.48828
Z16 = 10.298088



X17 = 0.684154
Y17 = 0.490487
Z17 = 10.298088



X18 = 0.684779
Y18 = 0.492849
Z18 = 10.298088



X19 = 0.684922
Y19 = 0.495287
Z19 = 10.298088



X20 = 0.684586
Y20 = 0.497706
Z20 = 10.298088



X21 = 0.683825
Y21 = 0.500028
Z21 = 10.298088



X22 = 0.682664
Y22 = 0.502178
Z22 = 10.298088



X23 = 0.681121
Y23 = 0.504071
Z23 = 10.298088



X24 = 0.67924
Y24 = 0.505631
Z24 = 10.298088



X25 = 0.677083
Y25 = 0.506773
Z25 = 10.298088



X26 = 0.674732
Y26 = 0.507432
Z26 = 10.298088



X27 = 0.672293
Y27 = 0.507575
Z27 = 10.298088



X28 = 0.669883
Y28 = 0.507193
Z28 = 10.298088



X29 = 0.667608
Y29 = 0.506302
Z29 = 10.298088



X30 = 0.665565
Y30 = 0.504967
Z30 = 10.298088



X31 = 0.628522
Y31 = 0.467888
Z31 = 10.298088



X32 = 0.556608
Y32 = 0.395018
Z32 = 10.298088



X33 = 0.48274
Y33 = 0.324134
Z33 = 10.298088



X34 = 0.406342
Y34 = 0.255985
Z34 = 10.298088



X35 = 0.327495
Y35 = 0.190689
Z35 = 10.298088



X36 = 0.245778
Y36 = 0.129028
Z36 = 10.298088



X37 = 0.160564
Y37 = 0.072313
Z37 = 10.298088



X38 = 0.071326
Y38 = 0.022188
Z38 = 10.298088



X39 = −0.022478
Y39 = −0.018669
Z39 = 10.298088



X40 = −0.121107
Y40 = −0.045761
Z40 = 10.298088



X41 = −0.222704
Y41 = −0.057581
Z41 = 10.298088



X42 = −0.324966
Y42 = −0.054554
Z42 = 10.298088



X43 = −0.426318
Y43 = −0.040338
Z43 = 10.298088



X44 = −0.526699
Y44 = −0.020203
Z44 = 10.298088



X45 = −0.628045
Y45 = −0.007181
Z45 = 10.298088



X46 = −0.653464
Y46 = −0.014747
Z46 = 10.298088



X47 = −0.654809
Y47 = −0.015846
Z47 = 10.298088



X48 = −0.656035
Y48 = −0.017076
Z48 = 10.298088



X49 = −0.657116
Y49 = −0.018435
Z49 = 10.298088



X50 = −0.658048
Y50 = −0.019901
Z50 = 10.298088



X51 = −0.65884
Y51 = −0.021447
Z51 = 10.298088



X52 = −0.659498
Y52 = −0.023055
Z52 = 10.298088



X53 = −0.660021
Y53 = −0.024712
Z53 = 10.298088



X54 = −0.660398
Y54 = −0.026408
Z54 = 10.298088



X55 = −0.660621
Y55 = −0.028131
Z55 = 10.298088



X56 = −0.660684
Y56 = −0.029867
Z56 = 10.298088



X57 = −0.660585
Y57 = −0.031601
Z57 = 10.298088



X58 = −0.660324
Y58 = −0.033318
Z58 = 10.298088



X59 = −0.65991
Y59 = −0.035005
Z59 = 10.298088



X60 = −0.659356
Y60 = −0.036652
Z60 = 10.298088







D. Section Height 10.781777











X1 = −0.646233
Y1 = −0.065726
Z1 = 10.781777



X2 = −0.571741
Y2 = −0.152202
Z2 = 10.781777



X3 = −0.473776
Y3 = −0.211208
Z3 = 10.781777



X4 = −0.363476
Y4 = −0.241988
Z4 = 10.781777



X5 = −0.249064
Y5 = −0.248817
Z5 = 10.781777



X6 = −0.135473
Y6 = −0.233311
Z6 = 10.781777



X7 = −0.026366
Y7 = −0.198004
Z7 = 10.781777



X8 = 0.076204
Y8 = −0.146634
Z8 = 10.781777



X9 = 0.171624
Y9 = −0.082902
Z9 = 10.781777



X10 = 0.259329
Y10 = −0.008908
Z10 = 10.781777



X11 = 0.338926
Y11 = 0.073773
Z11 = 10.781777



X12 = 0.412573
Y12 = 0.161829
Z12 = 10.781777



X13 = 0.482031
Y13 = 0.253233
Z13 = 10.781777



X14 = 0.548466
Y14 = 0.346862
Z14 = 10.781777



X15 = 0.613027
Y15 = 0.441794
Z15 = 10.781777



X16 = 0.660376
Y16 = 0.514455
Z16 = 10.781777



X17 = 0.661467
Y17 = 0.516685
Z17 = 10.781777



X18 = 0.662118
Y18 = 0.519081
Z18 = 10.781777



X19 = 0.662266
Y19 = 0.521558
Z19 = 10.781777



X20 = 0.661914
Y20 = 0.524016
Z20 = 10.781777



X21 = 0.661122
Y21 = 0.526369
Z21 = 10.781777



X22 = 0.659917
Y22 = 0.52854
Z22 = 10.781777



X23 = 0.658321
Y23 = 0.530441
Z23 = 10.781777



X24 = 0.656384
Y24 = 0.531994
Z24 = 10.781777



X25 = 0.654172
Y25 = 0.533118
Z25 = 10.781777



X26 = 0.651771
Y26 = 0.533747
Z26 = 10.781777



X27 = 0.649292
Y27 = 0.533856
Z27 = 10.781777



X28 = 0.646847
Y28 = 0.533433
Z28 = 10.781777



X29 = 0.644548
Y29 = 0.532499
Z29 = 10.781777



X30 = 0.642489
Y30 = 0.531111
Z30 = 10.781777



X31 = 0.606295
Y31 = 0.493636
Z31 = 10.781777



X32 = 0.536525
Y32 = 0.419613
Z32 = 10.781777



X33 = 0.465772
Y33 = 0.346533
Z33 = 10.781777



X34 = 0.393
Y34 = 0.275464
Z34 = 10.781777



X35 = 0.317829
Y35 = 0.206942
Z35 = 10.781777



X36 = 0.239848
Y36 = 0.141641
Z36 = 10.781777



X37 = 0.158568
Y37 = 0.080503
Z37 = 10.781777



X38 = 0.073464
Y38 = 0.024825
Z38 = 10.781777



X39 = −0.016377
Y39 = −0.022755
Z39 = 10.781777



X40 = −0.111971
Y40 = −0.057225
Z40 = 10.781777



X41 = −0.211811
Y41 = −0.076093
Z41 = 10.781777



X42 = −0.313403
Y42 = −0.078683
Z42 = 10.781777



X43 = −0.414559
Y43 = −0.068449
Z43 = 10.781777



X44 = −0.51467
Y44 = −0.050449
Z44 = 10.781777



X45 = −0.615334
Y45 = −0.036888
Z45 = 10.781777



X46 = −0.640588
Y46 = −0.044147
Z46 = 10.781777



X47 = −0.641891
Y47 = −0.045245
Z47 = 10.781777



X48 = −0.643079
Y48 = −0.046468
Z48 = 10.781777



X49 = −0.644123
Y49 = −0.047815
Z49 = 10.781777



X50 = −0.64502
Y50 = −0.049265
Z50 = 10.781777



X51 = −0.645781
Y51 = −0.05079
Z51 = 10.781777



X52 = −0.646413
Y52 = −0.052374
Z52 = 10.781777



X53 = −0.646912
Y53 = −0.054004
Z53 = 10.781777



X54 = −0.64727
Y54 = −0.055671
Z54 = 10.781777



X55 = −0.647479
Y55 = −0.057362
Z55 = 10.781777



X56 = −0.647534
Y56 = −0.059066
Z56 = 10.781777



X57 = −0.647432
Y57 = −0.060768
Z57 = 10.781777



X58 = −0.647175
Y58 = −0.062453
Z58 = 10.781777



X59 = −0.64677
Y59 = −0.064109
Z59 = 10.781777



X60 = −0.646233
Y60 = −0.065727
Z60 = 10.781777







E. Section Height 11.265467











X1 = −0.636756
Y1 = −0.117631
Z1 = 11.265467



X2 = −0.560254
Y2 = −0.20202
Z2 = 11.265467



X3 = −0.458991
Y3 = −0.254859
Z3 = 11.265467



X4 = −0.34675
Y4 = −0.277067
Z4 = 11.265467



X5 = −0.23227
Y5 = −0.274026
Z5 = 11.265467



X6 = −0.120587
Y6 = −0.248513
Z6 = 11.265467



X7 = −0.014922
Y7 = −0.204135
Z7 = 11.265467



X8 = 0.083344
Y8 = −0.145086
Z8 = 11.265467



X9 = 0.174047
Y9 = −0.074926
Z9 = 11.265467



X10 = 0.257029
Y10 = 0.004221
Z10 = 11.265467



X11 = 0.332265
Y11 = 0.090792
Z11 = 11.265467



X12 = 0.402135
Y12 = 0.181772
Z12 = 11.265467



X13 = 0.468053
Y13 = 0.275661
Z13 = 11.265467



X14 = 0.531098
Y14 = 0.371507
Z14 = 11.265467



X15 = 0.59263
Y15 = 0.468333
Z15 = 11.265467



X16 = 0.6379
Y16 = 0.542235
Z16 = 11.265467



X17 = 0.638949
Y17 = 0.544492
Z17 = 11.265467



X18 = 0.639551
Y18 = 0.546908
Z18 = 11.265467



X19 = 0.639643
Y19 = 0.549394
Z19 = 11.265467



X20 = 0.639229
Y20 = 0.551849
Z20 = 11.265467



X21 = 0.638371
Y21 = 0.554187
Z21 = 11.265467



X22 = 0.637099
Y22 = 0.556327
Z22 = 11.265467



X23 = 0.63544
Y23 = 0.558183
Z23 = 11.265467



X24 = 0.63345
Y24 = 0.559678
Z24 = 11.265467



X25 = 0.631197
Y25 = 0.560735
Z25 = 11.265467



X26 = 0.628772
Y26 = 0.561294
Z26 = 11.265467



X27 = 0.626284
Y27 = 0.561337
Z27 = 11.265467



X28 = 0.623843
Y28 = 0.560856
Z28 = 11.265467



X29 = 0.621556
Y29 = 0.559872
Z29 = 11.265467



X30 = 0.619517
Y30 = 0.558446
Z30 = 11.265467



X31 = 0.584157
Y31 = 0.520358
Z31 = 11.265467



X32 = 0.516883
Y32 = 0.444415
Z32 = 11.265467



X33 = 0.449265
Y33 = 0.368778
Z33 = 11.265467



X34 = 0.380236
Y34 = 0.294428
Z34 = 11.265467



X35 = 0.308668
Y35 = 0.222526
Z35 = 11.265467



X36 = 0.233939
Y36 = 0.153919
Z36 = 11.265467



X37 = 0.155764
Y37 = 0.08927
Z37 = 11.265467



X38 = 0.073889
Y38 = 0.029383
Z38 = 11.265467



X39 = −0.012401
Y39 = −0.023895
Z39 = 11.265467



X40 = −0.10463
Y40 = −0.065968
Z40 = 11.265467



X41 = −0.201995
Y41 = −0.094141
Z41 = 11.265467



X42 = −0.302554
Y42 = −0.106814
Z42 = 11.265467



X43 = −0.403965
Y43 = −0.106488
Z43 = 11.265467



X44 = −0.504969
Y44 = −0.097144
Z44 = 11.265467



X45 = −0.605895
Y45 = −0.087522
Z45 = 11.265467



X46 = −0.631321
Y46 = −0.09443
Z46 = 11.265467



X47 = −0.63275
Y47 = −0.095588
Z47 = 11.265467



X48 = −0.634047
Y48 = −0.096894
Z48 = 11.265467



X49 = −0.635179
Y49 = −0.098343
Z49 = 11.265467



X50 = −0.636144
Y50 = −0.09991
Z50 = 11.265467



X51 = −0.636951
Y51 = −0.101564
Z51 = 11.265467



X52 = −0.637604
Y52 = −0.103284
Z52 = 11.265467



X53 = −0.638102
Y53 = −0.105055
Z53 = 11.265467



X54 = −0.638433
Y54 = −0.106865
Z54 = 11.265467



X55 = −0.63859
Y55 = −0.108698
Z55 = 11.265467



X56 = −0.638569
Y56 = −0.110538
Z56 = 11.265467



X57 = −0.638369
Y57 = −0.112367
Z57 = 11.265467



X58 = −0.637992
Y58 = −0.114168
Z58 = 11.265467



X59 = −0.63745
Y59 = −0.115927
Z59 = 11.265467



X60 = −0.636756
Y60 = −0.117631
Z60 = 11.265467







F. Section Height 11.749156











X1 = −0.630702
Y1 = −0.181619
Z1 = 11.749156



X2 = −0.550173
Y2 = −0.261439
Z2 = 11.749156



X3 = −0.443623
Y3 = −0.303256
Z3 = 11.749156



X4 = −0.329374
Y4 = −0.313234
Z4 = 11.749156



X5 = −0.215583
Y5 = −0.298071
Z5 = 11.749156



X6 = −0.106678
Y6 = −0.261607
Z6 = 11.749156



X7 = −0.004973
Y7 = −0.208158
Z7 = 11.749156



X8 = 0.088908
Y8 = −0.141869
Z8 = 11.749156



X9 = 0.175105
Y9 = −0.065821
Z9 = 11.749156



X10 = 0.253882
Y10 = 0.017898
Z10 = 11.749156



X11 = 0.325555
Y11 = 0.107793
Z11 = 11.749156



X12 = 0.392021
Y12 = 0.20162
Z12 = 11.749156



X13 = 0.454548
Y13 = 0.298121
Z13 = 11.749156



X14 = 0.514337
Y14 = 0.396348
Z14 = 11.749156



X15 = 0.572619
Y15 = 0.495476
Z15 = 11.749156



X16 = 0.615648
Y16 = 0.570942
Z16 = 11.749156



X17 = 0.616627
Y17 = 0.573248
Z17 = 11.749156



X18 = 0.617146
Y18 = 0.575698
Z18 = 11.749156



X19 = 0.617144
Y19 = 0.578202
Z19 = 11.749156



X20 = 0.616629
Y20 = 0.580653
Z20 = 11.749156



X21 = 0.615667
Y21 = 0.582967
Z21 = 11.749156



X22 = 0.614294
Y22 = 0.585062
Z22 = 11.749156



X23 = 0.612542
Y23 = 0.586853
Z23 = 11.749156



X24 = 0.610474
Y24 = 0.588264
Z24 = 11.749156



X25 = 0.608161
Y25 = 0.589225
Z25 = 11.749156



X26 = 0.605699
Y26 = 0.589683
Z26 = 11.749156



X27 = 0.603195
Y27 = 0.589623
Z27 = 11.749156



X28 = 0.600759
Y28 = 0.589044
Z28 = 11.749156



X29 = 0.598497
Y29 = 0.58797
Z29 = 11.749156



X30 = 0.596497
Y30 = 0.586462
Z30 = 11.749156



X31 = 0.562297
Y31 = 0.54709
Z31 = 11.749156



X32 = 0.497346
Y32 = 0.468703
Z32 = 11.749156



X33 = 0.432726
Y33 = 0.390041
Z33 = 11.749156



X34 = 0.366992
Y34 = 0.312309
Z34 = 11.749156



X35 = 0.298636
Y35 = 0.236882
Z35 = 11.749156



X36 = 0.226618
Y36 = 0.164948
Z36 = 11.749156



X37 = 0.150807
Y37 = 0.097025
Z37 = 11.749156



X38 = 0.071393
Y38 = 0.033351
Z38 = 11.749156



X39 = −0.012004
Y39 = −0.024982
Z39 = 11.749156



X40 = −0.100818
Y40 = −0.074621
Z40 = 11.749156



X41 = −0.194947
Y41 = −0.113216
Z41 = 11.749156



X42 = −0.293393
Y42 = −0.1388
Z42 = 11.749156



X43 = −0.39425
Y43 = −0.152348
Z43 = 11.749156



X44 = −0.495937
Y44 = −0.155974
Z44 = 11.749156



X45 = −0.597675
Y45 = −0.153024
Z45 = 11.749156



X46 = −0.623485
Y46 = −0.15927
Z46 = 11.749156



X47 = −0.624992
Y47 = −0.160285
Z47 = 11.749156



X48 = −0.626381
Y48 = −0.161456
Z48 = 11.749156



X49 = −0.627621
Y49 = −0.162784
Z49 = 11.749156



X50 = −0.628704
Y50 = −0.164243
Z50 = 11.749156



X51 = −0.629637
Y51 = −0.165802
Z51 = 11.749156



X52 = −0.630423
Y52 = −0.16744
Z52 = 11.749156



X53 = −0.631059
Y53 = −0.169142
Z53 = 11.749156



X54 = −0.631532
Y54 = −0.170897
Z54 = 11.749156



X55 = −0.631833
Y55 = −0.172688
Z55 = 11.749156



X56 = −0.631957
Y56 = −0.174501
Z56 = 11.749156



X57 = −0.6319
Y57 = −0.176317
Z57 = 11.749156



X58 = −0.631664
Y58 = −0.178119
Z58 = 11.749156



X59 = −0.63126
Y59 = −0.179891
Z59 = 11.749156



X60 = −0.630702
Y60 = −0.18162
Z60 = 11.749156







G. Section Height 12.232846











X1 = −0.622996
Y1 = −0.251076
Z1 = 12.232846



X2 = −0.537655
Y2 = −0.324245
Z2 = 12.232846



X3 = −0.426214
Y3 = −0.351918
Z3 = 12.232846



X4 = −0.311244
Y4 = −0.34804
Z4 = 12.232846



X5 = −0.199479
Y5 = −0.320326
Z5 = 12.232846



X6 = −0.094295
Y6 = −0.273324
Z6 = 12.232846



X7 = 0.003031
Y7 = −0.2116
Z7 = 12.232846



X8 = 0.092508
Y8 = −0.138925
Z8 = 12.232846



X9 = 0.174447
Y9 = −0.057821
Z9 = 12.232846



X10 = 0.249413
Y10 = 0.029781
Z10 = 12.232846



X11 = 0.317975
Y11 = 0.122492
Z11 = 12.232846



X12 = 0.381389
Y12 = 0.218808
Z12 = 12.232846



X13 = 0.440771
Y13 = 0.317667
Z13 = 12.232846



X14 = 0.497438
Y14 = 0.418111
Z14 = 12.232846



X15 = 0.552609
Y15 = 0.519385
Z15 = 12.232846



X16 = 0.593607
Y16 = 0.596262
Z16 = 12.232846



X17 = 0.594525
Y17 = 0.598608
Z17 = 12.232846



X18 = 0.594973
Y18 = 0.601087
Z18 = 12.232846



X19 = 0.594889
Y19 = 0.603604
Z19 = 12.232846



X20 = 0.594286
Y20 = 0.60605
Z20 = 12.232846



X21 = 0.593235
Y21 = 0.608341
Z21 = 12.232846



X22 = 0.591776
Y22 = 0.610395
Z22 = 12.232846



X23 = 0.589947
Y23 = 0.612128
Z23 = 12.232846



X24 = 0.587813
Y24 = 0.613467
Z24 = 12.232846



X25 = 0.585452
Y25 = 0.614345
Z25 = 12.232846



X26 = 0.582961
Y26 = 0.614715
Z26 = 12.232846



X27 = 0.580446
Y27 = 0.614569
Z27 = 12.232846



X28 = 0.578016
Y28 = 0.613906
Z28 = 12.232846



X29 = 0.575775
Y29 = 0.612755
Z29 = 12.232846



X30 = 0.573811
Y30 = 0.611177
Z30 = 12.232846



X31 = 0.54055
Y31 = 0.57051
Z31 = 12.232846



X32 = 0.477607
Y32 = 0.489542
Z32 = 12.232846



X33 = 0.415602
Y33 = 0.40785
Z33 = 12.232846



X34 = 0.352749
Y34 = 0.326811
Z34 = 12.232846



X35 = 0.28724
Y35 = 0.247912
Z35 = 12.232846



X36 = 0.217665
Y36 = 0.172584
Z36 = 12.232846



X37 = 0.143941
Y37 = 0.101306
Z37 = 12.232846



X38 = 0.06662
Y38 = 0.033946
Z38 = 12.232846



X39 = −0.014304
Y39 = −0.029029
Z39 = 12.232846



X40 = −0.09987
Y40 = −0.085505
Z40 = 12.232846



X41 = −0.190334
Y41 = −0.133736
Z41 = 12.232846



X42 = −0.285383
Y42 = −0.172102
Z42 = 12.232846



X43 = −0.384035
Y43 = −0.199996
Z43 = 12.232846



X44 = −0.484991
Y44 = −0.217702
Z44 = 12.232846



X45 = −0.587344
Y45 = −0.223709
Z45 = 12.232846



X46 = −0.613637
Y46 = −0.229345
Z46 = 12.232846



X47 = −0.615258
Y47 = −0.230208
Z47 = 12.232846



X48 = −0.616776
Y48 = −0.231241
Z48 = 12.232846



X49 = −0.61816
Y49 = −0.232447
Z49 = 12.232846



X50 = −0.619399
Y50 = −0.233803
Z50 = 12.232846



X51 = −0.620496
Y51 = −0.235276
Z51 = 12.232846



X52 = −0.62145
Y52 = −0.236845
Z52 = 12.232846



X53 = −0.622256
Y53 = −0.238495
Z53 = 12.232846



X54 = −0.622901
Y54 = −0.240214
Z54 = 12.232846



X55 = −0.623372
Y55 = −0.241989
Z55 = 12.232846



X56 = −0.623661
Y56 = −0.243803
Z56 = 12.232846



X57 = −0.623764
Y57 = −0.245636
Z57 = 12.232846



X58 = −0.623681
Y58 = −0.247471
Z58 = 12.232846



X59 = −0.623421
Y59 = −0.249289
Z59 = 12.232846



X60 = −0.622996
Y60 = −0.251076
Z60 = 12.232846







H. Section Height 12.716535











X1 = −0.609536
Y1 = −0.316629
Z1 = 12.716535



X2 = −0.520238
Y2 = −0.382551
Z2 = 12.716535



X3 = −0.405962
Y3 = −0.395899
Z3 = 12.716535



X4 = −0.291999
Y4 = −0.378843
Z4 = 12.716535



X5 = −0.183473
Y5 = −0.339775
Z5 = 12.716535



X6 = −0.082659
Y6 = −0.283609
Z6 = 12.716535



X7 = 0.01007
Y7 = −0.214853
Z7 = 12.716535



X8 = 0.095184
Y8 = −0.136839
Z8 = 12.716535



X9 = 0.173081
Y9 = −0.051601
Z9 = 12.716535



X10 = 0.244407
Y10 = 0.039218
Z10 = 12.716535



X11 = 0.309821
Y11 = 0.13439
Z11 = 12.716535



X12 = 0.370153
Y12 = 0.232871
Z12 = 12.716535



X13 = 0.426477
Y13 = 0.333702
Z13 = 12.716535



X14 = 0.48022
Y14 = 0.435937
Z14 = 12.716535



X15 = 0.532574
Y15 = 0.538891
Z15 = 12.716535



X16 = 0.571917
Y16 = 0.616777
Z16 = 12.716535



X17 = 0.572792
Y17 = 0.619155
Z17 = 12.716535



X18 = 0.573186
Y18 = 0.621658
Z18 = 12.716535



X19 = 0.573039
Y19 = 0.624187
Z19 = 12.716535



X20 = 0.572367
Y20 = 0.62663
Z20 = 12.716535



X21 = 0.571247
Y21 = 0.628904
Z21 = 12.716535



X22 = 0.56972
Y22 = 0.630926
Z22 = 12.716535



X23 = 0.567829
Y23 = 0.632613
Z23 = 12.716535



X24 = 0.565643
Y24 = 0.633895
Z24 = 12.716535



X25 = 0.563244
Y25 = 0.634708
Z25 = 12.716535



X26 = 0.560728
Y26 = 0.635009
Z26 = 12.716535



X27 = 0.558203
Y27 = 0.634792
Z27 = 12.716535



X28 = 0.555778
Y28 = 0.634061
Z28 = 12.716535



X29 = 0.553555
Y29 = 0.632845
Z29 = 12.716535



X30 = 0.551621
Y30 = 0.631208
Z30 = 12.716535



X31 = 0.519248
Y31 = 0.589335
Z31 = 12.716535



X32 = 0.458331
Y32 = 0.505878
Z32 = 12.716535



X33 = 0.398673
Y33 = 0.421513
Z33 = 12.716535



X34 = 0.33833
Y34 = 0.337639
Z34 = 12.716535



X35 = 0.275505
Y35 = 0.255615
Z35 = 12.716535



X36 = 0.208594
Y36 = 0.176898
Z36 = 12.716535



X37 = 0.137411
Y37 = 0.102018
Z37 = 12.716535



X38 = 0.062586
Y38 = 0.030774
Z38 = 12.716535



X39 = −0.015672
Y39 = −0.036677
Z39 = 12.716535



X40 = −0.09797
Y40 = −0.099121
Z40 = 12.716535



X41 = −0.184632
Y41 = −0.155344
Z41 = 12.716535



X42 = −0.275634
Y42 = −0.204207
Z42 = 12.716535



X43 = −0.370909
Y43 = −0.24409
Z43 = 12.716535



X44 = −0.46978
Y44 = −0.27391
Z44 = 12.716535



X45 = −0.571772
Y45 = −0.289858
Z45 = 12.716535



X46 = −0.598417
Y46 = −0.295243
Z46 = 12.716535



X47 = −0.60013
Y47 = −0.296001
Z47 = 12.716535



X48 = −0.601753
Y48 = −0.296936
Z48 = 12.716535



X49 = −0.603254
Y49 = −0.298056
Z49 = 12.716535



X50 = −0.604621
Y50 = −0.299338
Z50 = 12.716535



X51 = −0.605851
Y51 = −0.300751
Z51 = 12.716535



X52 = −0.606944
Y52 = −0.302273
Z52 = 12.716535



X53 = −0.607892
Y53 = −0.303889
Z53 = 12.716535



X54 = −0.608679
Y54 = −0.305589
Z54 = 12.716535



X55 = −0.609291
Y55 = −0.307359
Z55 = 12.716535



X56 = −0.609718
Y56 = −0.309183
Z56 = 12.716535



X57 = −0.609954
Y57 = −0.311042
Z57 = 12.716535



X58 = −0.609997
Y58 = −0.312915
Z58 = 12.716535



X59 = −0.609854
Y59 = −0.314783
Z59 = 12.716535



X60 = −0.609536
Y60 = −0.316629
Z60 = 12.716535







I. Section Height 13.200225











X1 = −0.587823
Y1 = −0.371438
Z1 = 13.200225



X2 = −0.496224
Y2 = −0.43084
Z2 = 13.200225



X3 = −0.38141
Y3 = −0.431778
Z3 = 13.200225



X4 = −0.269995
Y4 = −0.403313
Z4 = 13.200225



X5 = −0.16568
Y5 = −0.35467
Z5 = 13.200225



X6 = −0.069737
Y6 = −0.290979
Z6 = 13.200225



X7 = 0.018156
Y7 = −0.216527
Z7 = 13.200225



X8 = 0.098787
Y8 = −0.134243
Z8 = 13.200225



X9 = 0.172629
Y9 = −0.045807
Z9 = 13.200225



X10 = 0.240181
Y10 = 0.047532
Z10 = 13.200225



X11 = 0.302032
Y11 = 0.144748
Z11 = 13.200225



X12 = 0.358932
Y12 = 0.244949
Z12 = 13.200225



X13 = 0.4121
Y13 = 0.347184
Z13 = 13.200225



X14 = 0.462988
Y14 = 0.450577
Z14 = 13.200225



X15 = 0.512751
Y15 = 0.554517
Z15 = 13.200225



X16 = 0.550801
Y16 = 0.632825
Z16 = 13.200225



X17 = 0.551651
Y17 = 0.635228
Z17 = 13.200225



X18 = 0.55201
Y18 = 0.637752
Z18 = 13.200225



X19 = 0.551819
Y19 = 0.640292
Z19 = 13.200225



X20 = 0.551098
Y20 = 0.642737
Z20 = 13.200225



X21 = 0.549925
Y21 = 0.645001
Z21 = 13.200225



X22 = 0.548345
Y22 = 0.647002
Z22 = 13.200225



X23 = 0.546405
Y23 = 0.648655
Z23 = 13.200225



X24 = 0.544177
Y24 = 0.649893
Z24 = 13.200225



X25 = 0.541745
Y25 = 0.650654
Z25 = 13.200225



X26 = 0.539207
Y26 = 0.650899
Z26 = 13.200225



X27 = 0.536673
Y27 = 0.650624
Z27 = 13.200225



X28 = 0.53425
Y28 = 0.649836
Z28 = 13.200225



X29 = 0.532041
Y29 = 0.648564
Z29 = 13.200225



X30 = 0.530132
Y30 = 0.646875
Z30 = 13.200225



X31 = 0.498762
Y31 = 0.604077
Z31 = 13.200225



X32 = 0.440238
Y32 = 0.518614
Z32 = 13.200225



X33 = 0.382956
Y33 = 0.432309
Z33 = 13.200225



X34 = 0.325003
Y34 = 0.346454
Z34 = 13.200225



X35 = 0.264874
Y35 = 0.262115
Z35 = 13.200225



X36 = 0.201037
Y36 = 0.180555
Z36 = 13.200225



X37 = 0.13307
Y37 = 0.1024
Z37 = 13.200225



X38 = 0.061337
Y38 = 0.027688
Z38 = 13.200225



X39 = −0.013953
Y39 = −0.043438
Z39 = 13.200225



X40 = −0.093015
Y40 = −0.11034
Z40 = 13.200225



X41 = −0.176028
Y41 = −0.172268
Z41 = 13.200225



X42 = −0.262926
Y42 = −0.228607
Z42 = 13.200225



X43 = −0.354163
Y43 = −0.277573
Z43 = 13.200225



X44 = −0.449723
Y44 = −0.317434
Z44 = 13.200225



X45 = −0.549692
Y45 = −0.344014
Z45 = 13.200225



X46 = −0.57623
Y46 = −0.350312
Z46 = 13.200225



X47 = −0.577944
Y47 = −0.351053
Z47 = 13.200225



X48 = −0.579573
Y48 = −0.351967
Z48 = 13.200225



X49 = −0.581085
Y49 = −0.353062
Z49 = 13.200225



X50 = −0.582468
Y50 = −0.354318
Z50 = 13.200225



X51 = −0.583721
Y51 = −0.355702
Z51 = 13.200225



X52 = −0.584842
Y52 = −0.357196
Z52 = 13.200225



X53 = −0.585823
Y53 = −0.358785
Z53 = 13.200225



X54 = −0.58665
Y54 = −0.36046
Z54 = 13.200225



X55 = −0.587307
Y55 = −0.362208
Z55 = 13.200225



X56 = −0.587784
Y56 = −0.364013
Z56 = 13.200225



X57 = −0.588073
Y57 = −0.365858
Z57 = 13.200225



X58 = −0.588171
Y58 = −0.367723
Z58 = 13.200225



X59 = −0.588084
Y59 = −0.369589
Z59 = 13.200225



X60 = −0.587823
Y60 = −0.371438
Z60 = 13.200225







J. Section Height 13.683915











X1 = −0.561105
Y1 = −0.415586
Z1 = 13.683915



X2 = −0.468349
Y2 = −0.469781
Z2 = 13.683915



X3 = −0.354471
Y3 = −0.459831
Z3 = 13.683915



X4 = −0.246629
Y4 = −0.42133
Z4 = 13.683915



X5 = −0.147077
Y5 = −0.364541
Z5 = 13.683915



X6 = −0.056183
Y6 = −0.294637
Z6 = 13.683915



X7 = 0.026867
Y7 = −0.215538
Z7 = 13.683915



X8 = 0.103052
Y8 = −0.12979
Z8 = 13.683915



X9 = 0.172903
Y9 = −0.038801
Z9 = 13.683915



X10 = 0.236662
Y10 = 0.056561
Z10 = 13.683915



X11 = 0.294767
Y11 = 0.155475
Z11 = 13.683915



X12 = 0.348125
Y12 = 0.257035
Z12 = 13.683915



X13 = 0.398177
Y13 = 0.36027
Z13 = 13.683915



X14 = 0.446266
Y14 = 0.464436
Z14 = 13.683915



X15 = 0.493609
Y15 = 0.568944
Z15 = 13.683915



X16 = 0.53059
Y16 = 0.647345
Z16 = 13.683915



X17 = 0.531422
Y17 = 0.649769
Z17 = 13.683915



X18 = 0.531754
Y18 = 0.652311
Z18 = 13.683915



X19 = 0.531528
Y19 = 0.654863
Z19 = 13.683915



X20 = 0.530764
Y20 = 0.657311
Z20 = 13.683915



X21 = 0.529545
Y21 = 0.659567
Z21 = 13.683915



X22 = 0.527919
Y22 = 0.661549
Z22 = 13.683915



X23 = 0.525934
Y23 = 0.663172
Z23 = 13.683915



X24 = 0.523668
Y24 = 0.66437
Z24 = 13.683915



X25 = 0.521206
Y25 = 0.665083
Z25 = 13.683915



X26 = 0.518649
Y26 = 0.665275
Z26 = 13.683915



X27 = 0.516107
Y27 = 0.664947
Z27 = 13.683915



X28 = 0.513686
Y28 = 0.664105
Z28 = 13.683915



X29 = 0.511489
Y29 = 0.662783
Z29 = 13.683915



X30 = 0.509604
Y30 = 0.661046
Z30 = 13.683915



X31 = 0.479352
Y31 = 0.617587
Z31 = 13.683915



X32 = 0.423522
Y32 = 0.530622
Z32 = 13.683915



X33 = 0.368777
Y33 = 0.442964
Z33 = 13.683915



X34 = 0.313185
Y34 = 0.355843
Z34 = 13.683915



X35 = 0.255561
Y35 = 0.270057
Z35 = 13.683915



X36 = 0.194509
Y36 = 0.186682
Z36 = 13.683915



X37 = 0.12928
Y37 = 0.106536
Z37 = 13.683915



X38 = 0.059813
Y38 = 0.030035
Z38 = 13.683915



X39 = −0.013742
Y39 = −0.042545
Z39 = 13.683915



X40 = −0.09112
Y40 = −0.111034
Z40 = 13.683915



X41 = −0.171916
Y41 = −0.17546
Z41 = 13.683915



X42 = −0.25555
Y42 = −0.236159
Z42 = 13.683915



X43 = −0.342117
Y43 = −0.292585
Z43 = 13.683915



X44 = −0.432055
Y44 = −0.343459
Z44 = 13.683915



X45 = −0.526147
Y45 = −0.386043
Z45 = 13.683915



X46 = −0.551229
Y46 = −0.39625
Z46 = 13.683915



X47 = −0.552689
Y47 = −0.397039
Z47 = 13.683915



X48 = −0.554067
Y48 = −0.397962
Z48 = 13.683915



X49 = −0.55534
Y49 = −0.399026
Z49 = 13.683915



X50 = −0.556498
Y50 = −0.400214
Z50 = 13.683915



X51 = −0.557544
Y51 = −0.401502
Z51 = 13.683915



X52 = −0.558481
Y52 = −0.402871
Z52 = 13.683915



X53 = −0.559303
Y53 = −0.404312
Z53 = 13.683915



X54 = −0.560001
Y54 = −0.405817
Z54 = 13.683915



X55 = −0.560562
Y55 = −0.407378
Z55 = 13.683915



X56 = −0.560977
Y56 = −0.408985
Z56 = 13.683915



X57 = −0.561238
Y57 = −0.410623
Z57 = 13.683915



X58 = −0.561342
Y58 = −0.412279
Z58 = 13.683915



X59 = −0.561293
Y59 = −0.413937
Z59 = 13.683915



X60 = −0.561105
Y60 = −0.415586
Z60 = 13.683915







K. Section Height 14.167604











X1 = −0.533329
Y1 = −0.452651
Z1 = 14.167604



X2 = −0.438676
Y2 = −0.499995
Z2 = 14.167604



X3 = −0.326709
Y3 = −0.480162
Z3 = 14.167604



X4 = −0.223002
Y4 = −0.432791
Z4 = 14.167604



X5 = −0.12846
Y5 = −0.368908
Z5 = 14.167604



X6 = −0.042537
Y6 = −0.293769
Z6 = 14.167604



X7 = 0.035865
Y7 = −0.210783
Z7 = 14.167604



X8 = 0.107787
Y8 = −0.122107
Z8 = 14.167604



X9 = 0.173781
Y9 = −0.028931
Z9 = 14.167604



X10 = 0.233861
Y10 = 0.068166
Z10 = 14.167604



X11 = 0.28833
Y11 = 0.168523
Z11 = 14.167604



X12 = 0.33833
Y12 = 0.271187
Z12 = 14.167604



X13 = 0.385462
Y13 = 0.375203
Z13 = 14.167604



X14 = 0.430892
Y14 = 0.479975
Z14 = 14.167604



X15 = 0.475956
Y15 = 0.584906
Z15 = 14.167604



X16 = 0.511823
Y16 = 0.663385
Z16 = 14.167604



X17 = 0.512631
Y17 = 0.66583
Z17 = 14.167604



X18 = 0.512932
Y18 = 0.668387
Z18 = 14.167604



X19 = 0.512666
Y19 = 0.670947
Z19 = 14.167604



X20 = 0.511858
Y20 = 0.673393
Z20 = 14.167604



X21 = 0.510593
Y21 = 0.675636
Z21 = 14.167604



X22 = 0.508921
Y22 = 0.677595
Z22 = 14.167604



X23 = 0.506893
Y23 = 0.679183
Z23 = 14.167604



X24 = 0.504591
Y24 = 0.680337
Z24 = 14.167604



X25 = 0.502103
Y25 = 0.680999
Z25 = 14.167604



X26 = 0.499531
Y26 = 0.681135
Z26 = 14.167604



X27 = 0.496985
Y27 = 0.680751
Z27 = 14.167604



X28 = 0.494572
Y28 = 0.679854
Z28 = 14.167604



X29 = 0.492394
Y29 = 0.678479
Z29 = 14.167604



X30 = 0.490537
Y30 = 0.676695
Z30 = 14.167604



X31 = 0.461371
Y31 = 0.632459
Z31 = 14.167604



X32 = 0.408122
Y32 = 0.54382
Z32 = 14.167604



X33 = 0.355804
Y33 = 0.454624
Z33 = 14.167604



X34 = 0.302463
Y34 = 0.366036
Z34 = 14.167604



X35 = 0.24716
Y35 = 0.278664
Z35 = 14.167604



X36 = 0.188688
Y36 = 0.193385
Z36 = 14.167604



X37 = 0.126027
Y37 = 0.111142
Z37 = 14.167604



X38 = 0.058657
Y38 = 0.032713
Z38 = 14.167604



X39 = −0.013421
Y39 = −0.041415
Z39 = 14.167604



X40 = −0.089604
Y40 = −0.11132
Z40 = 14.167604



X41 = −0.168921
Y41 = −0.177657
Z41 = 14.167604



X42 = −0.250234
Y42 = −0.241539
Z42 = 14.167604



X43 = −0.332872
Y43 = −0.303699
Z43 = 14.167604



X44 = −0.417098
Y44 = −0.363683
Z44 = 14.167604



X45 = −0.503647
Y45 = −0.420261
Z45 = 14.167604



X46 = −0.526208
Y46 = −0.434959
Z46 = 14.167604



X47 = −0.527336
Y47 = −0.435843
Z47 = 14.167604



X48 = −0.528388
Y48 = −0.436815
Z48 = 14.167604



X49 = −0.529345
Y49 = −0.437881
Z49 = 14.167604



X50 = −0.530203
Y50 = −0.439029
Z50 = 14.167604



X51 = −0.530968
Y51 = −0.44024
Z51 = 14.167604



X52 = −0.531645
Y52 = −0.441503
Z52 = 14.167604



X53 = −0.532232
Y53 = −0.44281
Z53 = 14.167604



X54 = −0.532723
Y54 = −0.444157
Z54 = 14.167604



X55 = −0.53311
Y55 = −0.445536
Z55 = 14.167604



X56 = −0.533386
Y56 = −0.446942
Z56 = 14.167604



X57 = −0.533544
Y57 = −0.448366
Z57 = 14.167604



X58 = −0.533583
Y58 = −0.449799
Z58 = 14.167604



X59 = −0.533507
Y59 = −0.451229
Z59 = 14.167604



X60 = −0.533329
Y60 = −0.452651
Z60 = 14.167604







L. Section Height 14.651293











X1 = −0.508331
Y1 = −0.486316
Z1 = 14.651293



X2 = −0.409413
Y2 = −0.523401
Z2 = 14.651293



X3 = −0.300056
Y3 = −0.493153
Z3 = 14.651293



X4 = −0.200711
Y4 = −0.437718
Z4 = 14.651293



X5 = −0.110952
Y5 = −0.367692
Z5 = 14.651293



X6 = −0.029613
Y6 = −0.28799
Z6 = 14.651293



X7 = 0.044561
Y7 = −0.201557
Z7 = 14.651293



X8 = 0.112578
Y8 = −0.110189
Z8 = 14.651293



X9 = 0.174963
Y9 = −0.014885
Z9 = 14.651293



X10 = 0.231657
Y10 = 0.083912
Z10 = 14.651293



X11 = 0.282947
Y11 = 0.185625
Z11 = 14.651293



X12 = 0.330114
Y12 = 0.289321
Z12 = 14.651293



X13 = 0.374695
Y13 = 0.394158
Z13 = 14.651293



X14 = 0.417711
Y14 = 0.499648
Z14 = 14.651293



X15 = 0.460619
Y15 = 0.605182
Z15 = 14.651293



X16 = 0.495053
Y16 = 0.684077
Z16 = 14.651293



X17 = 0.495815
Y17 = 0.686543
Z17 = 14.651293



X18 = 0.496066
Y18 = 0.689112
Z18 = 14.651293



X19 = 0.495746
Y19 = 0.691672
Z19 = 14.651293



X20 = 0.494883
Y20 = 0.694105
Z20 = 14.651293



X21 = 0.493565
Y21 = 0.696324
Z21 = 14.651293



X22 = 0.491844
Y22 = 0.698248
Z22 = 14.651293



X23 = 0.489774
Y23 = 0.69979
Z23 = 14.651293



X24 = 0.487439
Y24 = 0.70089
Z24 = 14.651293



X25 = 0.484929
Y25 = 0.701491
Z25 = 14.651293



X26 = 0.482349
Y26 = 0.701563
Z26 = 14.651293



X27 = 0.479807
Y27 = 0.701114
Z27 = 14.651293



X28 = 0.477412
Y28 = 0.700153
Z28 = 14.651293



X29 = 0.475265
Y29 = 0.69872
Z29 = 14.651293



X30 = 0.473451
Y30 = 0.696885
Z30 = 14.651293



X31 = 0.445299
Y31 = 0.651513
Z31 = 14.651293



X32 = 0.39429
Y32 = 0.560632
Z32 = 14.651293



X33 = 0.344222
Y33 = 0.469224
Z33 = 14.651293



X34 = 0.293196
Y34 = 0.378349
Z34 = 14.651293



X35 = 0.240364
Y35 = 0.288513
Z35 = 14.651293



X36 = 0.184797
Y36 = 0.200346
Z36 = 14.651293



X37 = 0.12543
Y37 = 0.114699
Z37 = 14.651293



X38 = 0.061372
Y38 = 0.032507
Z38 = 14.651293



X39 = −0.007669
Y39 = −0.045545
Z39 = 14.651293



X40 = −0.081156
Y40 = −0.119431
Z40 = 14.651293



X41 = −0.158052
Y41 = −0.189772
Z41 = 14.651293



X42 = −0.23718
Y42 = −0.257599
Z42 = 14.651293



X43 = −0.317575
Y43 = −0.323922
Z43 = 14.651293



X44 = −0.399397
Y44 = −0.388468
Z44 = 14.651293



X45 = −0.482846
Y45 = −0.450903
Z45 = 14.651293



X46 = −0.503718
Y46 = −0.468181
Z46 = 14.651293



X47 = −0.504677
Y47 = −0.469203
Z47 = 14.651293



X48 = −0.505553
Y48 = −0.470295
Z48 = 14.651293



X49 = −0.506328
Y49 = −0.471462
Z49 = 14.651293



X50 = −0.506999
Y50 = −0.472692
Z50 = 14.651293



X51 = −0.507575
Y51 = −0.473969
Z51 = 14.651293



X52 = −0.508062
Y52 = −0.475283
Z52 = 14.651293



X53 = −0.508459
Y53 = −0.476627
Z53 = 14.651293



X54 = −0.508761
Y54 = −0.477995
Z54 = 14.651293



X55 = −0.508962
Y55 = −0.479381
Z55 = 14.651293



X56 = −0.509056
Y56 = −0.480779
Z56 = 14.651293



X57 = −0.509037
Y57 = −0.48218
Z57 = 14.651293



X58 = −0.508905
Y58 = −0.483575
Z58 = 14.651293



X59 = −0.508666
Y59 = −0.484955
Z59 = 14.651293



X60 = −0.508331
Y60 = −0.486316
Z60 = 14.651293







M. Section Height 15.134983











X1 = −0.488738
Y1 = −0.51767
Z1 = 15.134983



X2 = −0.384464
Y2 = −0.540973
Z2 = 15.134983



X3 = −0.278091
Y3 = −0.500296
Z3 = 15.134983



X4 = −0.182731
Y4 = −0.437613
Z4 = 15.134983



X5 = −0.096995
Y5 = −0.362198
Z5 = 15.134983



X6 = −0.019437
Y6 = −0.278352
Z6 = 15.134983



X7 = 0.051263
Y7 = −0.188631
Z7 = 15.134983



X8 = 0.116001
Y8 = −0.09451
Z8 = 15.134983



X9 = 0.175225
Y9 = 0.003179
Z9 = 15.134983



X10 = 0.229065
Y10 = 0.103936
Z10 = 15.134983



X11 = 0.277956
Y11 = 0.20719
Z11 = 15.134983



X12 = 0.323101
Y12 = 0.312141
Z12 = 15.134983



X13 = 0.36566
Y13 = 0.41817
Z13 = 15.134983



X14 = 0.406587
Y14 = 0.524841
Z14 = 15.134983



X15 = 0.447486
Y15 = 0.631522
Z15 = 15.134983



X16 = 0.480097
Y16 = 0.711458
Z16 = 15.134983



X17 = 0.480786
Y17 = 0.713946
Z17 = 15.134983



X18 = 0.48096
Y18 = 0.716522
Z18 = 15.134983



X19 = 0.480564
Y19 = 0.719072
Z19 = 15.134983



X20 = 0.47963
Y20 = 0.721479
Z20 = 15.134983



X21 = 0.478247
Y21 = 0.72366
Z21 = 15.134983



X22 = 0.47647
Y22 = 0.725534
Z22 = 15.134983



X23 = 0.474356
Y23 = 0.727016
Z23 = 15.134983



X24 = 0.471989
Y24 = 0.728047
Z24 = 15.134983



X25 = 0.469462
Y25 = 0.728574
Z25 = 15.134983



X26 = 0.46688
Y26 = 0.728569
Z26 = 15.134983



X27 = 0.464352
Y27 = 0.728042
Z27 = 15.134983



X28 = 0.461987
Y28 = 0.727008
Z28 = 15.134983



X29 = 0.459885
Y29 = 0.725508
Z29 = 15.134983



X30 = 0.45813
Y30 = 0.723614
Z30 = 15.134983



X31 = 0.430928
Y31 = 0.676671
Z31 = 15.134983



X32 = 0.381692
Y32 = 0.582874
Z32 = 15.134983



X33 = 0.333728
Y33 = 0.488416
Z33 = 15.134983



X34 = 0.285166
Y34 = 0.394264
Z34 = 15.134983



X35 = 0.234977
Y35 = 0.300971
Z35 = 15.134983



X36 = 0.182535
Y36 = 0.208926
Z36 = 15.134983



X37 = 0.127047
Y37 = 0.118691
Z37 = 15.134983



X38 = 0.067508
Y38 = 0.03108
Z38 = 15.134983



X39 = 0.003225
Y39 = −0.053108
Z39 = 15.134983



X40 = −0.06579
Y40 = −0.133463
Z40 = 15.134983



X41 = −0.139125
Y41 = −0.209898
Z41 = 15.134983



X42 = −0.216193
Y42 = −0.28257
Z42 = 15.134983



X43 = −0.296416
Y43 = −0.351749
Z43 = 15.134983



X44 = −0.380034
Y44 = −0.416765
Z44 = 15.134983



X45 = −0.465814
Y45 = −0.478915
Z45 = 15.134983



X46 = −0.486435
Y46 = −0.497281
Z46 = 15.134983



X47 = −0.487398
Y47 = −0.498499
Z47 = 15.134983



X48 = −0.488251
Y48 = −0.499796
Z48 = 15.134983



X49 = −0.488973
Y49 = −0.50117
Z49 = 15.134983



X50 = −0.489562
Y50 = −0.502606
Z50 = 15.134983



X51 = −0.490031
Y51 = −0.504086
Z51 = 15.134983



X52 = −0.490386
Y52 = −0.505598
Z52 = 15.134983



X53 = −0.490628
Y53 = −0.507131
Z53 = 15.134983



X54 = −0.49075
Y54 = −0.508679
Z54 = 15.134983



X55 = −0.490745
Y55 = −0.510231
Z55 = 15.134983



X56 = −0.490607
Y56 = −0.511778
Z56 = 15.134983



X57 = −0.490334
Y57 = −0.513306
Z57 = 15.134983



X58 = −0.489924
Y58 = −0.514803
Z58 = 15.134983



X59 = −0.489388
Y59 = −0.51626
Z59 = 15.134983



X60 = −0.488738
Y60 = −0.51767
Z60 = 15.134983







N. Section Height 15.618673











X1 = −0.475619
Y1 = −0.544522
Z1 = 15.618673



X2 = −0.367092
Y2 = −0.553501
Z2 = 15.618673



X3 = −0.263626
Y3 = −0.503161
Z3 = 15.618673



X4 = −0.171565
Y4 = −0.433888
Z4 = 15.618673



X5 = −0.088791
Y5 = −0.353673
Z5 = 15.618673



X6 = −0.013974
Y6 = −0.26595
Z6 = 15.618673



X7 = 0.054168
Y7 = −0.172935
Z7 = 15.618673



X8 = 0.116382
Y8 = −0.075851
Z8 = 15.618673



X9 = 0.172994
Y9 = 0.024608
Z9 = 15.618673



X10 = 0.224579
Y10 = 0.127742
Z10 = 15.618673



X11 = 0.271908
Y11 = 0.232902
Z11 = 15.618673



X12 = 0.315881
Y12 = 0.339511
Z12 = 15.618673



X13 = 0.35698
Y13 = 0.447262
Z13 = 15.618673



X14 = 0.396088
Y14 = 0.555754
Z14 = 15.618673



X15 = 0.435137
Y15 = 0.664266
Z15 = 15.618673



X16 = 0.465701
Y16 = 0.74587
Z16 = 15.618673



X17 = 0.466289
Y17 = 0.748383
Z17 = 15.618673



X18 = 0.466362
Y18 = 0.750963
Z18 = 15.618673



X19 = 0.465871
Y19 = 0.753495
Z19 = 15.618673



X20 = 0.46485
Y20 = 0.755865
Z20 = 15.618673



X21 = 0.46339
Y21 = 0.757995
Z21 = 15.618673



X22 = 0.46155
Y22 = 0.759804
Z22 = 15.618673



X23 = 0.459388
Y23 = 0.761213
Z23 = 15.618673



X24 = 0.456988
Y24 = 0.762163
Z24 = 15.618673



X25 = 0.454446
Y25 = 0.762604
Z25 = 15.618673



X26 = 0.451867
Y26 = 0.76251
Z26 = 15.618673



X27 = 0.44936
Y27 = 0.761895
Z27 = 15.618673



X28 = 0.447035
Y28 = 0.760776
Z28 = 15.618673



X29 = 0.44499
Y29 = 0.759201
Z29 = 15.618673



X30 = 0.443307
Y30 = 0.757245
Z30 = 15.618673



X31 = 0.417003
Y31 = 0.708434
Z31 = 15.618673



X32 = 0.369081
Y32 = 0.6113
Z32 = 15.618673



X33 = 0.323249
Y33 = 0.513155
Z33 = 15.618673



X34 = 0.277173
Y34 = 0.415125
Z34 = 15.618673



X35 = 0.229209
Y35 = 0.318008
Z35 = 15.618673



X36 = 0.178807
Y36 = 0.222134
Z36 = 15.618673



X37 = 0.125624
Y37 = 0.127775
Z37 = 15.618673



X38 = 0.068939
Y38 = 0.035483
Z38 = 15.618673



X39 = 0.007873
Y39 = −0.053967
Z39 = 15.618673



X40 = −0.058125
Y40 = −0.139837
Z40 = 15.618673



X41 = −0.129331
Y41 = −0.221438
Z41 = 15.618673



X42 = −0.205576
Y42 = −0.298351
Z42 = 15.618673



X43 = −0.286408
Y43 = −0.370432
Z43 = 15.618673



X44 = −0.371954
Y44 = −0.436831
Z44 = 15.618673



X45 = −0.45846
Y45 = −0.501903
Z45 = 15.618673



X46 = −0.477102
Y46 = −0.523085
Z46 = 15.618673



X47 = −0.477883
Y47 = −0.524517
Z47 = 15.618673



X48 = −0.478534
Y48 = −0.526011
Z48 = 15.618673



X49 = −0.479034
Y49 = −0.527564
Z49 = 15.618673



X50 = −0.479383
Y50 = −0.529156
Z50 = 15.618673



X51 = −0.479597
Y51 = −0.530773
Z52 = 15.618673



X53 = −0.479648
Y53 = −0.534032
Z53 = 15.618673



X54 = −0.47948
Y54 = −0.535655
Z54 = 15.618673



X55 = −0.479177
Y55 = −0.537257
Z55 = 15.618673



X56 = −0.478734
Y56 = −0.538826
Z56 = 15.618673



X57 = −0.47815
Y57 = −0.540349
Z57 = 15.618673



X58 = −0.477428
Y58 = −0.541811
Z58 = 15.618673



X59 = −0.47658
Y59 = −0.543204
Z59 = 15.618673



X60 = −0.475619
Y60 = −0.544522
Z60 = 15.618673







O. Section Height 16.102362











X1 = −0.468649
Y1 = −0.565774
Z1 = 16.102362



X2 = −0.357413
Y2 = −0.561537
Z2 = 16.102362



X3 = −0.256795
Y3 = −0.502223
Z3 = 16.102362



X4 = −0.167427
Y4 = −0.426864
Z4 = 16.102362



X5 = −0.086875
Y5 = −0.342096
Z5 = 16.102362



X6 = −0.013989
Y6 = −0.250625
Z6 = 16.102362



X7 = 0.052333
Y7 = −0.154279
Z7 = 16.102362



X8 = 0.112628
Y8 = −0.054048
Z8 = 16.102362



X9 = 0.167072
Y9 = 0.049482
Z9 = 16.102362



X10 = 0.216858
Y10 = 0.155339
Z10 = 16.102362



X11 = 0.263254
Y11 = 0.262727
Z11 = 16.102362



X12 = 0.306695
Y12 = 0.371345
Z12 = 16.102362



X13 = 0.346762
Y13 = 0.481251
Z13 = 16.102362



X14 = 0.384208
Y14 = 0.592082
Z14 = 16.102362



X15 = 0.421522
Y15 = 0.702958
Z15 = 16.102362



X16 = 0.449962
Y16 = 0.786643
Z16 = 16.102362



X17 = 0.450432
Y17 = 0.789182
Z17 = 16.102362



X18 = 0.450387
Y18 = 0.791764
Z18 = 16.102362



X19 = 0.449783
Y19 = 0.794274
Z19 = 16.102362



X20 = 0.448663
Y20 = 0.796599
Z20 = 16.102362



X21 = 0.447116
Y21 = 0.798669
Z21 = 16.102362



X22 = 0.445205
Y22 = 0.800406
Z22 = 16.102362



X23 = 0.442989
Y23 = 0.80173
Z23 = 16.102362



X24 = 0.440552
Y24 = 0.802589
Z24 = 16.102362



X25 = 0.437995
Y25 = 0.802932
Z25 = 16.102362



X26 = 0.435419
Y26 = 0.80274
Z26 = 16.102362



X27 = 0.432937
Y27 = 0.802027
Z27 = 16.102362



X28 = 0.430657
Y28 = 0.800818
Z28 = 16.102362



X29 = 0.428675
Y29 = 0.799161
Z29 = 16.102362



X30 = 0.42707
Y30 = 0.79714
Z30 = 16.102362



X31 = 0.401646
Y31 = 0.746359
Z31 = 16.102362



X32 = 0.35472
Y32 = 0.645778
Z32 = 16.102362



X33 = 0.311182
Y33 = 0.543678
Z33 = 16.102362



X34 = 0.267545
Y34 = 0.441619
Z34 = 16.102362



X35 = 0.22111
Y35 = 0.340808
Z35 = 16.102362



X36 = 0.171119
Y36 = 0.241712
Z36 = 16.102362



X37 = 0.117726
Y37 = 0.144407
Z37 = 16.102362



X38 = 0.060881
Y38 = 0.049078
Z38 = 16.102362



X39 = −0.000082
Y39 = −0.043665
Z39 = 16.102362



X40 = −0.066038
Y40 = −0.132921
Z40 = 16.102362



X41 = −0.137379
Y41 = −0.217931
Z41 = 16.102362



X42 = −0.213925
Y42 = −0.298287
Z42 = 16.102362



X43 = −0.29473
Y43 = −0.374369
Z43 = 16.102362



X44 = −0.379816
Y44 = −0.445616
Z44 = 16.102362



X45 = −0.461962
Y45 = −0.519831
Z45 = 16.102362



X46 = −0.475514
Y46 = −0.545228
Z46 = 16.102362



X47 = −0.475854
Y47 = −0.546825
Z47 = 16.102362



X48 = −0.476062
Y48 = −0.548444
Z48 = 16.102362



X49 = −0.476119
Y49 = −0.550075
Z49 = 16.102362



X50 = −0.476031
Y50 = −0.551705
Z50 = 16.102362



X51 = −0.475814
Y51 = −0.553323
Z51 = 16.102362



X52 = −0.47548
Y52 = −0.55492
Z52 = 16.102362



X53 = −0.475032
Y53 = −0.55649
Z53 = 16.102362



X54 = −0.474467
Y54 = −0.558021
Z54 = 16.102362



X55 = −0.473782
Y55 = −0.559503
Z55 = 16.102362



X56 = −0.472977
Y56 = −0.560923
Z56 = 16.102362



X57 = −0.472053
Y57 = −0.562269
Z57 = 16.102362



X58 = −0.471016
Y58 = −0.563529
Z58 = 16.102362



X59 = −0.469877
Y59 = −0.564698
Z59 = 16.102362



X60 = −0.46865
Y60 = −0.565774
Z60 = 16.102362










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 discontinuities.

7. The airfoil of claim 6, wherein the discontinuities include through apertures formed in at least one of the sides to provide an outlet for cooling fluid to flow therethrough.

8. The airfoil of claim 1, wherein the airfoil is connected to a third stage turbine disk.

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

10. A turbine blade for a gas turbine engine comprising:
a platform having an upper surface and a lower surface, the upper surface of the platform partially defining an inner flow path wall, the lower surface having a root with a connecting joint extending radially inward from the platform, the root being connectable to a rotatable disk, wherein the rotatable disk has an axis of rotation along a longitudinal axis of the gas turbine engine;
an airfoil extending radially outward from the upper surface of the platform relative to the axis of rotation, 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 wherein
the first and second external surfaces of the airfoil is substantially defined by a Cartesian coordinate array having X, Y and Z axis coordinates listed in Table 1 of the specification, wherein the Z axis generally extends radially outward from at least one of the upper surface of the platform and 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.

11. The turbine blade 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 blade of claim 10, wherein the Z axis further defines a stacking axis as a reference line to facilitate design and manufacturing of the airfoil, and the stacking axis defines a tilt angle of the airfoil position relative to a reference base.

13. The turbine blade of claim 12, wherein the reference base is the blade platform and the stacking axis extends from the platform from between a normal position and 25 degrees from the normal position in any direction.

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

15. The turbine blade 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 blade of claim 14, wherein the coating is at least one of a thermal barrier coating and a radiation barrier coating.

17. The turbine blade of claim 10, wherein a portion of the external surface of the airfoil includes discontinuities.

18. The turbine blade of claim 10, wherein the airfoil includes an outer shroud formed adjacent the tip.

19. The turbine blade of claim 10, wherein the turbine blade is attached to a turbine disk.

20. A method of forming an airfoil for a turbine blade 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 radially from a platform or an engine centerline, 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 blade 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.