Patent Publication Number: US-9890790-B2

Title: Adjusted rotating airfoil

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related by subject matter to the non-provisional patent application Ser. No. 14/087,946 entitled “ADJUSTED STATIONARY AIRFOIL” and assigned to the same assignee. 
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not Applicable. 
     TECHNICAL FIELD 
     The present invention relates generally to gas turbine engines and more specifically to an airfoil profile having an improved design. 
     BACKGROUND OF THE INVENTION 
     A gas turbine engine typically comprises a multi-stage compressor that takes air, which has been drawn into the engine, and compresses it into a higher pressure and temperature. A majority of this air passes to the combustion system, which mixes the compressed and heated air with fuel and contains the resulting reaction that generates the hot combustion gases. These gases then pass through a multi-stage turbine, which, in turn drives the compressor, and possibly a shaft of an electrical generator. Exhaust from the turbine can also be channeled to provide thrust for propulsion of a vehicle. 
     Typical compressors and turbines comprise a plurality of alternating rows of rotating and stationary airfoils. The stationary airfoils, or vanes, direct the flow of air in a compressor or hot combustion gases in a turbine onto a subsequent row of rotating airfoils, or blades, at the proper orientation in order to maximize the output of the compressor or turbine. The performance of the gas turbine engine is dependent on the mass of air entering the engine. Generally, the greater the amount of air that enters the engine, the more power that is produced. 
     SUMMARY OF THE INVENTION 
     The present invention is defined by the claims below. Embodiments of the present invention solve at least the above problems by providing a system and method for, among other things, increasing airflow throughout a plurality of assemblies in a gas turbine engine. 
     In accordance with the present invention, there is provided a novel and improved airfoil for a compressor component having a redefined airfoil profile. The surface area of the rotor blade is adjusted to allow for increased air flow. The chord length of the rotor blade is increased at the root with the amount of increase tapering towards the tip. By increasing the surface area of the rotor blade, more air may be captured and harnessed by the airfoil, thus increasing the performance of the compressor and the gas turbine engine. 
     In an embodiment of the present invention, a compressor component having an attachment, a platform, and an airfoil extending radially outward from the platform is disclosed. The airfoil has an uncoated profile substantially in accordance with Cartesian coordinate values of X and Z, for each distance Y in inches as set forth in Table 1, carried to three decimal places. 
     In another embodiment, an airfoil for a compressor blade is disclosed having an uncoated profile substantially in accordance with Cartesian coordinate values X, Y, and Z as set forth in Table 1, carried to three decimal places, where Y is a distance measured in inches, the X and Z coordinate values being joined in smooth continuing splines to form airfoil sections and the airfoil sections joined smoothly to form the profile. 
     In another embodiment, a compressor is disclosed in which the compressor comprises a compressor disk having a plurality of compressor blades extending radially outward from the compressor disk. The compressor blades each have an airfoil with an uncoated nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z, set forth in inches in Table 1, with the Y coordinate values at perpendicular distances from planes normal to a radius from an engine centerline, wherein airfoil sections are defined at each distance Y by connecting the X and Z coordinate values with smooth continuing splines, and the airfoil sections are joined smoothly to form the airfoil profile, where the compressor blades are rotating blades located adjacent to inlet guide vanes of the compressor, the inlet guide vanes being shaped to compliment the profile of the compressor blades. 
     Although disclosed as an airfoil that is uncoated, it is envisioned that an alternate embodiment of the present invention can include an airfoil that is at least partially coated with an erosion resistant coating, corrosion resistant coating, or a combination thereof. In this case, the coordinates of the airfoil as listed in Table 1 would be prior to a coating being applied to any portion of the airfoil. 
     Additional advantages and features of the present invention will be set forth in part in a description which follows, and in part will become apparent to those skilled in the art upon examination of the following, or may be learned from practice of the invention. The instant invention will now be described with particular reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       The present invention is described in detail below with reference to the attached drawing figures, wherein: 
         FIG. 1  is a front elevation view of a compressor blade having an airfoil in accordance with an embodiment of the present invention; 
         FIG. 2  is a side elevation view of the compressor blade of  FIG. 1 ; 
         FIG. 3  is a top elevation view of the compressor blade of  FIG. 1 ; 
         FIG. 4  is a perspective view illustrating a plurality of airfoil sections of a compressor blade generated by the Cartesian coordinates of Table 1; 
         FIG. 5  is a perspective view of a comparison between the airfoil of a compressor blade generated by airfoil sections in accordance with the Cartesian coordinates of Table 1 and a prior art airfoil; 
         FIGS. 6-8  are enlarged cross sectional views at various radial heights of cross sections overlaying an airfoil of a compressor blade in accordance with an embodiment of the present invention with an airfoil of the prior art; and 
         FIG. 9  is a cross-sectional view of a portion of a turbine engine showing the centerline of a turbine engine. 
     
    
    
     DETAILED DESCRIPTION 
     The subject matter of the present invention is described with specificity herein to meet statutory requirements. However, the description itself is not intended to limit the scope of this patent. Rather, the inventors have contemplated that the claimed subject matter might also be embodied in other ways, to include different components, combinations of components, steps, or combinations of steps similar to the ones described in this document, in conjunction with other present or future technologies. 
     Referring initially to  FIGS. 1-3 , a compressor blade  100  is shown in accordance with an embodiment of the present invention. The compressor blade  100  comprises an attachment  102 , which can also be referred to as a root. The attachment  102  utilizes one or more attachment surfaces  104  that are oriented so as to correspond with a slot in a compressor disk (not depicted) having a matching profile. Such an engagement maintains the blade within the disk, preventing it from moving radially outward due to radial pulling forces associated with the rotation of the compressor disk. For the compressor blade  100 , the upper surface of the attachment  102  serves as a platform  106 , which aligns with an adjacent surface on an outer diameter of the blade disk to provide a uniform inner wall surface for the incoming air flow to the compressor. 
     Extending radially outward from the platform  106  is an airfoil  108  having a tip  112 , with the tip  112  located at an end of the airfoil  108  opposite of the platform  106 . For the compressor blade  100 , the airfoil is solid, and fabricated from a material such as a martenestic steel alloy. The airfoil has an uncoated profile substantially in accordance with Cartesian coordinate values of X and Z, for each distance Y, in inches, as set forth in Table 1 below, and carried to three decimal places. The distance Y is measured from the engine centerline, shown in  FIG. 9 . The X and Z coordinates are distances relative to a coordinate plane origin established at each of the radial Y heights. 
     A plurality of airfoil sections  110  are established by applying smooth continuing splines between the X, Z coordinate values at each Y height. Smoothly joining each of the airfoil section  110  together form the profile of the airfoil  108 . The airfoil  108  can be fabricated by a variety of manufacturing techniques such as forging, casting, milling, and electro-chemical machining (ECM). As such, the airfoil has a series of manufacturing tolerance for the position, profile, twist, and chord that can cause the airfoil  108  to vary by as much as approximately +/−0.012 inches from a nominal state. 
     The compressor blade  100  is generally fabricated from a steel alloy such as 15-5PH, which is a precipitation-hardened, martensitic stainless steel alloy that is used on parts requiring corrosion resistance and high strength at temperatures up to approximately 600 deg. F. While other alloys could be used, it is preferred that a high-temperature steel alloy be selected because of the operating conditions. Although the compressor blade has been discussed as having an attachment, a platform, and an airfoil, it is to be understood that all of these features of the blade are typically fabricated from the same material and are most likely integral with one another. 
     In addition to manufacturing tolerances affecting the overall size of the airfoil  108 , it is also possible to scale the airfoil  108  to a larger or smaller airfoil size. However, in order to maintain the benefits of this airfoil shape and size, in terms of stiffness and stress, as will be discussed further below, it is necessary to scale the airfoil uniformly in X and Z directions, but Y direction may be scaled separately. 
     As previously discussed, the profile generated by the X, Y, and Z coordinates of Table 1 is an uncoated profile. While an embodiment of the present invention is an uncoated compressor blade  100 , it is possible to add a coating to at least a portion of the airfoil  108  in an alternate embodiment. This coating would have a thickness of up to approximately 0.010 inches. Such coatings can be applied to the airfoil to improve resistance to erosion or to increase temperature capability. 
     Referring to  FIG. 3 , positioned at the tip of the blade, opposite of the platform, is a squealer tip  113 , which includes a recessed portion so as to minimize the amount of metal located at the blade tip  112 . By minimizing the amount of metal, compressor blade  100  can be sized radially to have a tighter fit with the surrounding compressor case such that tolerances can be decreased and efficiency of the compressor increase. Should the squealer tip  113  contact the compressor case and begin to rub the case, the blade will not get as hot due to the smaller amount of material at the blade tip  112 . 
     Depending on the blade configuration, it is possible that a second platform can be positioned proximate the tip  112  of the airfoil  108 . A second platform located at the tip  112 , is commonly referred to as a shroud and interlocks with a shroud of an adjacent blade. The shrouds provide an outer air path seal that increases efficiency by preventing air from passing over the blade tip  112  and also serves to reduce the vibration of the airfoils  108 . The use of a second platform, or a shroud, is common in airfoils having a relatively long radial length. 
     In an alternate embodiment of the invention, a compressor comprises at least one compressor disk (not depicted) having a plurality of compressor blades  100  that extend radially outward from the compressor disk. As one skilled in the art understands, a compressor typically comprises a plurality of alternating stages of rotating and stationary airfoils that raise the pressure and temperature of a fluid passing through. While the compressor blade  100  having the airfoil  108  can operate in a variety of locations within a compressor, depending on the compressor size, one such location that suits this blade, is adjacent an inlet of the compressor. 
     For compressor blades in this location, a common durability issue exhibited by prior art blades is erosion of the blade leading edge. The leading edge of the blade (see  114  in  FIGS. 1 and 2 ) is the generally radially extending edge at the forward or upstream end of the blade where the concave and convex surfaces of the airfoil come together. This edge first receives the oncoming air flow, and therefore, is also first impacted by anything entering the compressor. Over time, this leading edge can erode away and weaken the airfoil. 
     As one skilled in the art understands, as a compressor blade is rotated by a compressor disk, and the weight of the blade pulls radially outward on the disk. However, because of blade design issues such as desired compression of the airflow, blade materials, and compressor size, rarely is the only load a truly radial pulling load. For large unshrouded blades there is usually a substantial amount of blade twist from airfoil root to airfoil tip. Due to the blade&#39;s pulling load, the airfoil will tend to untwist or try to straighten itself out. The compression of the airflow also creates load on the airfoil that tries to bend the blade where the airfoil attaches to the platform. Blade pull, untwist, and aero loading result in concentrated steady stress that can occur near the blade&#39;s airfoil root leading edge and the blade attachment, as seen with blades of prior art. Airfoil unsteady stress can occur due to the vibratory nature of the blade. Specific vibratory shapes for the blade result in stress concentrations on the airfoil. Blade failure can occur when the blade steady and unsteady stress concentrations occur together. If erosion forms at a location of high steady and unsteady stress then the chance of blade failure is increased. 
     For a compressor blade, increasing the surface area near the root of the compressor blade may allow for the compressor blade to take in a larger amount of air than the prior art. By taking in a larger amount of air, more air may be compressed and consequently, more power may be produced by the engine. However, due to the fixed geometry of the compressor case, where an airfoil of a compressor blade increases in axial length, there generally must also be a corresponding decrease in the axial length of an adjacent vane, thereby reducing the surface area of the vane. Decreasing the surface area of the stator vane allows for the stator vane to clear the compressor blade. 
     Referring to  FIG. 4 , a perspective view illustrating a plurality of airfoil sections  110  of a compressor blade generated by the Cartesian coordinates of Table 1 is shown. The modifications to the prior art airfoil, in terms of the increased chord length of the compressor blade, can be seen in more detail in  FIGS. 5-8 .  FIG. 5  is a perspective view depicting the present invention airfoil  108  of a compressor blade with solid lines compared to the prior art airfoil  200 , shown in dashed lines. From  FIG. 5  it can be determined the areas of the airfoil  108  having an increased chord length.  FIGS. 6-8  are enlargements of specific sections of the compressor blade depicted in  FIG. 5 , with  FIG. 6  taken at a radial height of approximately Y=25,  FIG. 7  taken at a radial height of approximately Y=32, and  FIG. 8  taken at a radial height of approximately Y=38 where Y is measured from the engine centerline. 
     
       
         
           
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 X 
                 Y 
                 Z 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 −1.462 
                 25.000 
                 3.116 
               
               
                 −1.351 
                 25.000 
                 3.016 
               
               
                 −1.242 
                 25.000 
                 2.913 
               
               
                 −1.134 
                 25.000 
                 2.809 
               
               
                 −1.028 
                 25.000 
                 2.703 
               
               
                 −0.925 
                 25.000 
                 2.594 
               
               
                 −0.824 
                 25.000 
                 2.483 
               
               
                 −0.726 
                 25.000 
                 2.370 
               
               
                 −0.629 
                 25.000 
                 2.256 
               
               
                 −0.533 
                 25.000 
                 2.140 
               
               
                 −0.440 
                 25.000 
                 2.023 
               
               
                 −0.348 
                 25.000 
                 1.904 
               
               
                 −0.259 
                 25.000 
                 1.784 
               
               
                 −0.172 
                 25.000 
                 1.662 
               
               
                 −0.087 
                 25.000 
                 1.539 
               
               
                 −0.004 
                 25.000 
                 1.414 
               
               
                 0.077 
                 25.000 
                 1.287 
               
               
                 0.155 
                 25.000 
                 1.159 
               
               
                 0.230 
                 25.000 
                 1.030 
               
               
                 0.302 
                 25.000 
                 0.898 
               
               
                 0.370 
                 25.000 
                 0.765 
               
               
                 0.435 
                 25.000 
                 0.630 
               
               
                 0.496 
                 25.000 
                 0.493 
               
               
                 0.554 
                 25.000 
                 0.355 
               
               
                 0.608 
                 25.000 
                 0.215 
               
               
                 0.658 
                 25.000 
                 0.073 
               
               
                 0.705 
                 25.000 
                 −0.069 
               
               
                 0.748 
                 25.000 
                 −0.213 
               
               
                 0.787 
                 25.000 
                 −0.357 
               
               
                 0.824 
                 25.000 
                 −0.503 
               
               
                 0.857 
                 25.000 
                 −0.649 
               
               
                 0.887 
                 25.000 
                 −0.796 
               
               
                 0.914 
                 25.000 
                 −0.943 
               
               
                 0.938 
                 25.000 
                 −1.091 
               
               
                 0.960 
                 25.000 
                 −1.239 
               
               
                 0.979 
                 25.000 
                 −1.388 
               
               
                 0.995 
                 25.000 
                 −1.537 
               
               
                 1.009 
                 25.000 
                 −1.686 
               
               
                 1.021 
                 25.000 
                 −1.836 
               
               
                 1.030 
                 25.000 
                 −1.985 
               
               
                 1.038 
                 25.000 
                 −2.135 
               
               
                 1.043 
                 25.000 
                 −2.285 
               
               
                 1.047 
                 25.000 
                 −2.435 
               
               
                 1.049 
                 25.000 
                 −2.585 
               
               
                 1.049 
                 25.000 
                 −2.734 
               
               
                 1.048 
                 25.000 
                 −2.884 
               
               
                 1.045 
                 25.000 
                 −3.034 
               
               
                 1.041 
                 25.000 
                 −3.184 
               
               
                 1.037 
                 25.000 
                 −3.334 
               
               
                 1.033 
                 25.000 
                 −3.484 
               
               
                 −1.486 
                 25.000 
                 3.135 
               
               
                 −1.512 
                 25.000 
                 3.148 
               
               
                 −1.541 
                 25.000 
                 3.156 
               
               
                 −1.570 
                 25.000 
                 3.156 
               
               
                 −1.598 
                 25.000 
                 3.144 
               
               
                 −1.616 
                 25.000 
                 3.121 
               
               
                 −1.623 
                 25.000 
                 3.092 
               
               
                 −1.623 
                 25.000 
                 3.063 
               
               
                 −1.616 
                 25.000 
                 3.034 
               
               
                 −1.603 
                 25.000 
                 3.007 
               
               
                 −1.538 
                 25.000 
                 2.881 
               
               
                 −1.473 
                 25.000 
                 2.754 
               
               
                 −1.410 
                 25.000 
                 2.627 
               
               
                 −1.348 
                 25.000 
                 2.499 
               
               
                 −1.288 
                 25.000 
                 2.370 
               
               
                 −1.230 
                 25.000 
                 2.240 
               
               
                 −1.173 
                 25.000 
                 2.110 
               
               
                 −1.117 
                 25.000 
                 1.979 
               
               
                 −1.063 
                 25.000 
                 1.848 
               
               
                 −1.009 
                 25.000 
                 1.716 
               
               
                 −0.956 
                 25.000 
                 1.584 
               
               
                 −0.903 
                 25.000 
                 1.452 
               
               
                 −0.851 
                 25.000 
                 1.320 
               
               
                 −0.800 
                 25.000 
                 1.187 
               
               
                 −0.749 
                 25.000 
                 1.054 
               
               
                 −0.700 
                 25.000 
                 0.921 
               
               
                 −0.651 
                 25.000 
                 0.788 
               
               
                 −0.604 
                 25.000 
                 0.654 
               
               
                 −0.557 
                 25.000 
                 0.519 
               
               
                 −0.511 
                 25.000 
                 0.385 
               
               
                 −0.467 
                 25.000 
                 0.250 
               
               
                 −0.423 
                 25.000 
                 0.115 
               
               
                 −0.380 
                 25.000 
                 −0.021 
               
               
                 −0.337 
                 25.000 
                 −0.157 
               
               
                 −0.295 
                 25.000 
                 −0.292 
               
               
                 −0.252 
                 25.000 
                 −0.428 
               
               
                 −0.210 
                 25.000 
                 −0.563 
               
               
                 −0.167 
                 25.000 
                 −0.699 
               
               
                 −0.124 
                 25.000 
                 −0.834 
               
               
                 −0.080 
                 25.000 
                 −0.970 
               
               
                 −0.037 
                 25.000 
                 −1.105 
               
               
                 0.007 
                 25.000 
                 −1.240 
               
               
                 0.051 
                 25.000 
                 −1.376 
               
               
                 0.095 
                 25.000 
                 −1.511 
               
               
                 0.140 
                 25.000 
                 −1.646 
               
               
                 0.185 
                 25.000 
                 −1.780 
               
               
                 0.231 
                 25.000 
                 −1.915 
               
               
                 0.276 
                 25.000 
                 −2.050 
               
               
                 0.323 
                 25.000 
                 −2.184 
               
               
                 0.369 
                 25.000 
                 −2.318 
               
               
                 0.416 
                 25.000 
                 −2.453 
               
               
                 0.463 
                 25.000 
                 −2.587 
               
               
                 0.510 
                 25.000 
                 −2.721 
               
               
                 0.558 
                 25.000 
                 −2.855 
               
               
                 0.605 
                 25.000 
                 −2.989 
               
               
                 0.653 
                 25.000 
                 −3.123 
               
               
                 0.701 
                 25.000 
                 −3.256 
               
               
                 0.750 
                 25.000 
                 −3.390 
               
               
                 0.800 
                 25.000 
                 −3.523 
               
               
                 0.815 
                 25.000 
                 −3.555 
               
               
                 0.837 
                 25.000 
                 −3.582 
               
               
                 0.866 
                 25.000 
                 −3.602 
               
               
                 0.900 
                 25.000 
                 −3.613 
               
               
                 0.935 
                 25.000 
                 −3.614 
               
               
                 0.968 
                 25.000 
                 −3.602 
               
               
                 0.995 
                 25.000 
                 −3.580 
               
               
                 1.016 
                 25.000 
                 −3.552 
               
               
                 1.029 
                 25.000 
                 −3.519 
               
               
                 −1.807 
                 26.650 
                 2.976 
               
               
                 −1.731 
                 26.650 
                 2.852 
               
               
                 −1.655 
                 26.650 
                 2.728 
               
               
                 −1.580 
                 26.650 
                 2.604 
               
               
                 −1.505 
                 26.650 
                 2.479 
               
               
                 −1.430 
                 26.650 
                 2.354 
               
               
                 −1.357 
                 26.650 
                 2.228 
               
               
                 −1.284 
                 26.650 
                 2.102 
               
               
                 −1.212 
                 26.650 
                 1.976 
               
               
                 −1.141 
                 26.650 
                 1.849 
               
               
                 −1.070 
                 26.650 
                 1.722 
               
               
                 −1.000 
                 26.650 
                 1.594 
               
               
                 −0.931 
                 26.650 
                 1.466 
               
               
                 −0.861 
                 26.650 
                 1.338 
               
               
                 −0.793 
                 26.650 
                 1.210 
               
               
                 −0.725 
                 26.650 
                 1.081 
               
               
                 −0.658 
                 26.650 
                 0.952 
               
               
                 −0.592 
                 26.650 
                 0.823 
               
               
                 −0.527 
                 26.650 
                 0.692 
               
               
                 −0.463 
                 26.650 
                 0.561 
               
               
                 −0.401 
                 26.650 
                 0.430 
               
               
                 −0.340 
                 26.650 
                 0.298 
               
               
                 −0.280 
                 26.650 
                 0.165 
               
               
                 −0.221 
                 26.650 
                 0.032 
               
               
                 −0.163 
                 26.650 
                 −0.101 
               
               
                 −0.105 
                 26.650 
                 −0.235 
               
               
                 −0.048 
                 26.650 
                 −0.369 
               
               
                 0.009 
                 26.650 
                 −0.503 
               
               
                 0.066 
                 26.650 
                 −0.636 
               
               
                 0.123 
                 26.650 
                 −0.770 
               
               
                 0.181 
                 26.650 
                 −0.904 
               
               
                 0.238 
                 26.650 
                 −1.038 
               
               
                 0.296 
                 26.650 
                 −1.171 
               
               
                 0.353 
                 26.650 
                 −1.305 
               
               
                 0.412 
                 26.650 
                 −1.438 
               
               
                 0.470 
                 26.650 
                 −1.571 
               
               
                 0.529 
                 26.650 
                 −1.705 
               
               
                 0.588 
                 26.650 
                 −1.837 
               
               
                 0.648 
                 26.650 
                 −1.970 
               
               
                 0.709 
                 26.650 
                 −2.102 
               
               
                 0.770 
                 26.650 
                 −2.235 
               
               
                 0.831 
                 26.650 
                 −2.367 
               
               
                 0.893 
                 26.650 
                 −2.498 
               
               
                 0.955 
                 26.650 
                 −2.630 
               
               
                 1.018 
                 26.650 
                 −2.761 
               
               
                 1.081 
                 26.650 
                 −2.892 
               
               
                 1.145 
                 26.650 
                 −3.023 
               
               
                 1.210 
                 26.650 
                 −3.153 
               
               
                 1.276 
                 26.650 
                 −3.283 
               
               
                 1.343 
                 26.650 
                 −3.412 
               
               
                 −1.818 
                 26.650 
                 2.995 
               
               
                 −1.824 
                 26.650 
                 3.016 
               
               
                 −1.825 
                 26.650 
                 3.038 
               
               
                 −1.820 
                 26.650 
                 3.059 
               
               
                 −1.808 
                 26.650 
                 3.077 
               
               
                 −1.788 
                 26.650 
                 3.085 
               
               
                 −1.766 
                 26.650 
                 3.086 
               
               
                 −1.745 
                 26.650 
                 3.081 
               
               
                 −1.725 
                 26.650 
                 3.072 
               
               
                 −1.708 
                 26.650 
                 3.058 
               
               
                 −1.596 
                 26.650 
                 2.957 
               
               
                 −1.483 
                 26.650 
                 2.856 
               
               
                 −1.372 
                 26.650 
                 2.754 
               
               
                 −1.261 
                 26.650 
                 2.651 
               
               
                 −1.151 
                 26.650 
                 2.547 
               
               
                 −1.043 
                 26.650 
                 2.442 
               
               
                 −0.935 
                 26.650 
                 2.335 
               
               
                 −0.829 
                 26.650 
                 2.228 
               
               
                 −0.724 
                 26.650 
                 2.119 
               
               
                 −0.620 
                 26.650 
                 2.009 
               
               
                 −0.518 
                 26.650 
                 1.898 
               
               
                 −0.416 
                 26.650 
                 1.786 
               
               
                 −0.317 
                 26.650 
                 1.672 
               
               
                 −0.219 
                 26.650 
                 1.556 
               
               
                 −0.123 
                 26.650 
                 1.439 
               
               
                 −0.029 
                 26.650 
                 1.321 
               
               
                 0.062 
                 26.650 
                 1.201 
               
               
                 0.151 
                 26.650 
                 1.078 
               
               
                 0.237 
                 26.650 
                 0.954 
               
               
                 0.320 
                 26.650 
                 0.827 
               
               
                 0.399 
                 26.650 
                 0.699 
               
               
                 0.475 
                 26.650 
                 0.568 
               
               
                 0.547 
                 26.650 
                 0.435 
               
               
                 0.615 
                 26.650 
                 0.300 
               
               
                 0.680 
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                 36.550 
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                 36.550 
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                 39.850 
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                 39.850 
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                 39.850 
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                 39.850 
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                 39.850 
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                 −1.046 
                 39.850 
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                 −1.335 
                 39.850 
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                 −1.480 
                 39.850 
                 1.292 
               
               
                 −1.625 
                 39.850 
                 1.377 
               
               
                 −1.770 
                 39.850 
                 1.461 
               
               
                 −1.916 
                 39.850 
                 1.544 
               
               
                 −2.063 
                 39.850 
                 1.626 
               
               
                 −2.209 
                 39.850 
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                 −2.357 
                 39.850 
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                 −2.505 
                 39.850 
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                 −2.654 
                 39.850 
                 1.944 
               
               
                 −2.803 
                 39.850 
                 2.020 
               
               
                 −2.954 
                 39.850 
                 2.095 
               
               
                 −3.105 
                 39.850 
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                 −3.258 
                 39.850 
                 2.237 
               
               
                 −3.261 
                 39.850 
                 2.238 
               
               
                 −3.264 
                 39.850 
                 2.239 
               
               
                 −3.267 
                 39.850 
                 2.239 
               
               
                 −3.270 
                 39.850 
                 2.238 
               
               
                 −3.272 
                 39.850 
                 2.236 
               
               
                 −3.273 
                 39.850 
                 2.233 
               
               
                 −3.272 
                 39.850 
                 2.231 
               
               
                 −3.270 
                 39.850 
                 2.228 
               
               
                 −3.268 
                 39.850 
                 2.226 
               
               
                   
               
            
           
         
       
     
     While the invention has been described in what is known as presently the preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment but, on the contrary, is intended to cover various modifications and equivalent arrangements within the scope of the following claims. The present invention has been described in relation to particular embodiments, which are intended in all respects to be illustrative rather than restrictive. 
     From the foregoing, it will be seen that this invention is well adapted to attain all the ends and objects set forth above, together with other advantages which are obvious and inherent to the system and method. It will be understood that certain features and sub-combinations are of utility and may be employed without reference to other features and sub-combinations. This is contemplated by and within the scope of the claims.