Abstract:
A fan or rotor design where the surface profile may be configured to desired dimensions particular to a given operating environment is disclosed.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present application claims the priority benefit of U.S. provisional patent application No. 60/827,677 filed Sep. 29, 2006 and entitled “Axial Flow Fan” and U.S. provisional patent application No. 60/950,610 filed Jul. 19, 2007 and entitled “Surface Profile for a Quiet Rotor or Stator.” The disclosure of these commonly owned applications are incorporated herein by reference. 
         [0002]    This application is related to U.S. Pat. No. 5,934,877 for a “Rotor with Logarithmic Scaled Shape” and U.S. Pat. No. 6,702,552 for an “Impeller Having Blade(s) Conforming to the Golden Section of a Logarithmic Curve.” The disclosures of these commonly owned patents are incorporated herein by reference. 
     
    
     BACKGROUND OF THE INVENTION 
       [0003]    1. Field of the Invention 
         [0004]    The present invention generally concerns axial flow fans and rotors. More specifically, the present invention concerns a surface profile for axial flow fans and rotors used in environments requiring high output in conjunction with constrained fan size including but not limited to electronics cooling. 
         [0005]    2. Description of the Related Art 
         [0006]    Fan and rotor design has undergone little change over the past century. As a result, fans and rotors remain relatively inefficient. A part of this inefficiency is the result of fans and rotors generating a considerable amount of noise and turbulence. Similarly, fans and rotors used in liquid environments typically result in cavitation. Noise, turbulence, and cavitation reduce the operational efficiency of the fan and rotor. 
         [0007]    A chart illustrating inefficiencies with respect to flow and sound in a series of 92×38 mm computer fans as found in the prior art are shown in  FIG. 1A . A similar chart illustrating inefficiencies with respect to flow and torque in prior art fan design is shown in  FIG. 1B .  FIG. 1B  illustrates, specifically, a 22″ best-in-class A/C fan with a standard bell shroud operating at 850 rpm. 
         [0008]    Much of the noise, turbulence, and unwanted torque in prior art fan design may be attributable to the surface design of the fan or rotor. In many instances, fans and rotors are implemented in a particular operating environment based on a pre-existing design. These pre-existing designs are not necessarily designed or intended for that particular operating environment. Nevertheless, these pre-existing designs may achieve results that are adequate or ‘good enough’ for that particular environment. 
         [0009]    Determining which pre-existing design is adequate or ‘good enough’ for a particular environment is a never-ending exercise. Trial and error will continually redefine the best adequate or ‘good enough’ design implementation. Notwithstanding these adequate results, some degree of the aforementioned noise, turbulence, and/or unwanted torque will inevitably remain. 
         [0010]    There is, therefore, a need in the art for fan and rotor design where the surface profile may be configured to desired dimensions particular to a given operating environment. 
       SUMMARY OF THE INVENTION 
       [0011]    Embodiments of the present invention provide for an axial flow fan that is quieter for the same or better output throughout a range of operating points compared to prior art fan designs. References to an axial flow fan or any fan are meant to be inclusive with respect to rotors and other blade designs. 
         [0012]    In one exemplary embodiment, a method for constructing an axial fan is disclosed. In this exemplary method, a spline is drafted to connect a plurality of points along a radius cut sketch to form a blade surface. The blade surface is then offset by a constant amount and filled to form a single blade. The single blade is oriented with respect to a hub and patterned along with a total number of blades to be affixed to the hub. The single blade and remaining blades are then attached to the hub. 
         [0013]    In another embodiment, a fan apparatus is disclosed. The fan apparatus includes a hub a blade coupled to the hub, the blade including a blade surface. The blade surface is created by drafting a spline to connect a plurality of points along a radius cut sketch. The blade is created by offsetting the blade surface by a constant amount and filling the blade surface to form a single blade. 
         [0014]    Another exemplary method provides for constructing an axial fan. The exemplary method includes drafting a spline to connect a plurality of points along a radius cut sketch to form a blade surface. A complimentary airfoil shape is then created. The airfoil is then lofted into a solid. 
         [0015]    A computer-readable storage medium is also disclosed. The medium has embodied thereon a program being executable by a processor to perform a method for constructing an axial fan. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0016]      FIG. 1A  is a chart exhibiting flow and sound inefficiencies in prior art fan design. 
           [0017]      FIG. 1B  is a chart exhibiting flow and torque inefficiencies in prior art fan design. 
           [0018]      FIG. 2A  is a chart exhibiting flow and sound efficiency of a fan as may be designed in accordance with an exemplary embodiment of the present invention as compared to the inefficiencies of prior art fans like those shown in  FIG. 1A . 
           [0019]      FIG. 2B  is a chart exhibiting flow and torque efficiency of a fan as may be designed in accordance with an exemplary embodiment of the present invention as compared to the inefficiencies of a prior art fan like that shown in  FIG. 1B . 
           [0020]      FIG. 3  illustrates an exemplary fan and surface profile according to an embodiment of the present invention. 
           [0021]      FIG. 4  illustrates an exemplary surface profile of a fan blade according to an alternative embodiment of the present invention. 
           [0022]      FIG. 5  illustrates an exemplary method for constructing a blade surface according to an embodiment of the present invention. 
           [0023]      FIG. 6  illustrates a method for forming a blade according to an embodiment of the present invention. 
           [0024]      FIG. 7  illustrates an alternative method for forming a blade according to an embodiment of the present invention. 
           [0025]      FIG. 8  illustrates an exemplary method for constructing a fan according to an embodiment of the present invention. 
           [0026]      FIGS. 9A-9E  illustrate exemplary fans constructed utilizing the surface profile disclosed with respect to  FIG. 3 . 
           [0027]      FIGS. 10A-10E  illustrate exemplary fans constructed utilizing the surface profile disclosed with respect to  FIG. 4 . 
       
    
    
     DETAILED DESCRIPTION 
       [0028]    Embodiments of the present invention provide for a fan that is quieter for the same or better output throughout a range of operating points compared to prior art fan designs.  FIG. 2A  is a chart exhibiting flow and sound efficiency of an exemplary fan as may be designed in accordance with the present invention compared to the inefficiencies of a prior art fan like that found in  FIG. 1A .  FIG. 2B , in turn, is a chart exhibiting flow and torque efficiency of an exemplary surface profile as may be designed for a fan in accordance with the present invention compared to the inefficiencies of a prior art fan like that found in  FIG. 1B . 
         [0029]      FIG. 3  illustrates a portion of an exemplary fan  300  and surface profile  330  according to an embodiment of the present invention. Fan  300  may be motor driven or subject to the natural flow of a fluid (e.g., liquid or gas). Fan  300  includes a hub  310 , which may be approximately cylindrical or conical in shape. Hub  310  may be hollowed like that of  FIG. 9A  or solid as is shown in  FIG. 10E . Hub  310  may also include a cap like that shown in  FIG. 9B . Hub  310  may be altered with radii, chamfers, and/or blends with symmetry about the Y-axis as illustrated throughout  FIGS. 9 and 10 . Hub  310  may be configured to an appropriate height and diameter in order to incorporate a desired motor and hub-tip ratio as illustrated throughout  FIGS. 9 and 10 . 
         [0030]    Blades  320  are circularly patterned around hub  310 . Blades  320  may be permanently or temporarily coupled or affixed to the hub  310  through various techniques as known in the art. The surface profile  330  of blades  320  may be configured in accordance with the various profiles described in U.S. Pat. Nos. 5,934,877 and 6,702,552, the disclosure of which has been previously incorporated herein by reference. For example, a portion of the surface profile  330  of fan blade  320  may conform to a logarithmic spiral. The radius of that particular logarithmic spiral may unfold at a constant order of growth when measured at equiangular radii, which may sometimes be referred to as the Golden Section. 
         [0031]    Surface profile  330  configurations may also correspond to external or internal shell configurations as found in nature. For example, the surface profile  330  of blade  320  may conform to the shell of the phylum Mollusca, class Cephalopoda, genus  Nautilus . An alternative surface profile-to-shell configuration may be inclusive of the shell shaping of the phylum Mollusca, class Gastropoda, genus  Conus, Conidae, Turbinidea , or  Volutidae . Shell configurations from other members of phylum Mollusca, class Gastropoda or Cephalopoda may also be implemented with respect to the surface profile  330  of blade  320 . 
         [0032]    Various other surface configurations may be implemented in accordance with embodiments of the present invention. For example, surface profile  330  of blade  320  may be defined by the following tables. In Tables I-IX, Cartesian points are taken at even intervals along the span of the blade, which corresponds to an 87 mm diameter fan. In the context of  FIG. 3 , axis Y represents the hub axis and serves as the zero reference for all radial measurements. All dimensions in Tables I-IX are in millimeters. The blade surface may be constructed through a method like that disclosed in the context of  FIG. 5 . 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE I 
               
             
             
               
                   
               
               
                 22.5 mm Radius 
               
             
          
           
               
                   
                 Pt # 
                 X 
                 Y 
                 Z 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 −5.389 
                 −2.463 
                 21.845 
               
               
                   
                 2 
                 −2.804 
                 −0.447 
                 22.325 
               
               
                   
                 3 
                 −1.548 
                 0.621 
                 22.447 
               
               
                   
                 4 
                 −0.338 
                 1.725 
                 22.497 
               
               
                   
                 5 
                 4.187 
                 6.381 
                 22.107 
               
               
                   
                 6 
                 6.236 
                 8.883 
                 21.619 
               
               
                   
                 7 
                 8.171 
                 11.467 
                 20.964 
               
               
                   
                 8 
                 9.981 
                 14.098 
                 20.165 
               
               
                   
                 9 
                 11.645 
                 16.791 
                 19.252 
               
               
                   
                 10 
                 12.675 
                 18.611 
                 18.590 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE II 
               
             
             
               
                   
               
               
                 25 mm Radius 
               
             
          
           
               
                   
                 Pt# 
                 X 
                 Y 
                 Z 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 −6.755 
                 −3.085 
                 24.070 
               
               
                   
                 2 
                 −5.230 
                 −1.984 
                 24.447 
               
               
                   
                 3 
                 −3.708 
                 −0.850 
                 24.723 
               
               
                   
                 4 
                 −2.209 
                 0.344 
                 24.902 
               
               
                   
                 5 
                 −0.743 
                 1.590 
                 24.989 
               
               
                   
                 6 
                 0.680 
                 2.866 
                 24.991 
               
               
                   
                 7 
                 2.072 
                 4.159 
                 24.914 
               
               
                   
                 8 
                 4.740 
                 6.826 
                 24.547 
               
               
                   
                 9 
                 7.203 
                 9.653 
                 23.940 
               
               
                   
                 10 
                 9.536 
                 12.571 
                 23.110 
               
               
                   
                 11 
                 11.695 
                 15.578 
                 22.096 
               
               
                   
                 12 
                 13.656 
                 18.668 
                 20.941 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE III 
               
             
             
               
                   
               
               
                 27.5 mm Radius 
               
             
          
           
               
                   
                 Pt # 
                 X 
                 Y 
                 Z 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 −8.339 
                 −3.663 
                 26.205 
               
               
                   
                 2 
                 −6.681 
                 −2.508 
                 26.676 
               
               
                   
                 3 
                 −5.014 
                 −1.334 
                 27.039 
               
               
                   
                 4 
                 −3.379 
                 −0.118 
                 27.292 
               
               
                   
                 5 
                 −1.774 
                 1.140 
                 27.443 
               
               
                   
                 6 
                 −0.200 
                 2.438 
                 27.499 
               
               
                   
                 7 
                 1.360 
                 3.757 
                 27.466 
               
               
                   
                 8 
                 2.898 
                 5.107 
                 27.347 
               
               
                   
                 9 
                 4.395 
                 6.508 
                 27.147 
               
               
                   
                 10 
                 5.841 
                 7.963 
                 26.873 
               
               
                   
                 11 
                 7.233 
                 9.452 
                 26.532 
               
               
                   
                 12 
                 9.896 
                 12.488 
                 25.658 
               
               
                   
                 13 
                 12.351 
                 15.634 
                 24.571 
               
               
                   
                 14 
                 14.594 
                 18.869 
                 23.308 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE IV 
               
             
             
               
                   
               
               
                 30 mm Radius 
               
             
          
           
               
                   
                 Pt # 
                 X 
                 Y 
                 Z 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 −10.052 
                 −4.175 
                 28.266 
               
               
                   
                 2 
                 −8.259 
                 −2.972 
                 28.841 
               
               
                   
                 3 
                 −6.454 
                 −1.744 
                 29.298 
               
               
                   
                 4 
                 −2.895 
                 0.799 
                 29.860 
               
               
                   
                 5 
                 −1.145 
                 2.119 
                 29.978 
               
               
                   
                 6 
                 0.589 
                 3.464 
                 29.994 
               
               
                   
                 7 
                 2.300 
                 4.847 
                 29.912 
               
               
                   
                 8 
                 3.968 
                 6.289 
                 29.736 
               
               
                   
                 9 
                 5.597 
                 7.786 
                 29.473 
               
               
                   
                 10 
                 7.177 
                 9.315 
                 29.129 
               
               
                   
                 11 
                 10.171 
                 12.444 
                 28.223 
               
               
                   
                 12 
                 11.578 
                 14.055 
                 27.676 
               
               
                   
                 13 
                 12.919 
                 15.705 
                 27.076 
               
               
                   
                 14 
                 15.426 
                 19.108 
                 25.730 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE V 
               
             
             
               
                   
               
               
                 32.5 mm Radius 
               
             
          
           
               
                   
                 Pt # 
                 X 
                 Y 
                 Z 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 −11.904 
                 −4.628 
                 30.241 
               
               
                   
                 2 
                 −8.077 
                 −2.121 
                 31.480 
               
               
                   
                 3 
                 −6.134 
                 −0.832 
                 31.916 
               
               
                   
                 4 
                 −4.200 
                 0.476 
                 32.227 
               
               
                   
                 5 
                 −0.387 
                 3.180 
                 32.498 
               
               
                   
                 6 
                 3.326 
                 6.035 
                 32.329 
               
               
                   
                 7 
                 5.121 
                 7.551 
                 32.094 
               
               
                   
                 8 
                 6.879 
                 9.111 
                 31.764 
               
               
                   
                 9 
                 10.229 
                 12.302 
                 30.848 
               
               
                   
                 10 
                 13.307 
                 15.645 
                 29.651 
               
               
                   
                 11 
                 16.096 
                 19.177 
                 28.234 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE VI 
               
             
             
               
                   
               
               
                 35 mm Radius 
               
             
          
           
               
                   
                 Pt # 
                 X 
                 Y 
                 Z 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 −13.944 
                 −5.042 
                 32.102 
               
               
                   
                 2 
                 −11.950 
                 −3.756 
                 32.897 
               
               
                   
                 3 
                 −9.913 
                 −2.465 
                 33.567 
               
               
                   
                 4 
                 −7.835 
                 −1.168 
                 34.112 
               
               
                   
                 5 
                 −5.747 
                 0.160 
                 34.525 
               
               
                   
                 6 
                 −1.625 
                 2.908 
                 34.962 
               
               
                   
                 7 
                 2.419 
                 5.778 
                 34.916 
               
               
                   
                 8 
                 4.393 
                 7.286 
                 34.723 
               
               
                   
                 9 
                 6.319 
                 8.865 
                 34.425 
               
               
                   
                 10 
                 10.022 
                 12.110 
                 33.535 
               
               
                   
                 11 
                 11.778 
                 13.779 
                 32.959 
               
               
                   
                 12 
                 13.453 
                 15.502 
                 32.311 
               
               
                   
                 13 
                 15.045 
                 17.284 
                 31.602 
               
               
                   
                 14 
                 16.552 
                 19.129 
                 30.839 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE VII 
               
             
             
               
                   
               
               
                 37.5 mm Radius 
               
             
          
           
               
                   
                 Pt # 
                 X 
                 Y 
                 Z 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 −16.217 
                 −5.442 
                 33.812 
               
               
                   
                 2 
                 −14.137 
                 −4.107 
                 34.733 
               
               
                   
                 3 
                 −12.003 
                 −2.783 
                 35.527 
               
               
                   
                 4 
                 −9.813 
                 −1.473 
                 36.193 
               
               
                   
                 5 
                 −7.592 
                 −0.132 
                 36.724 
               
               
                   
                 6 
                 −3.163 
                 2.655 
                 37.366 
               
               
                   
                 7 
                 1.205 
                 5.545 
                 37.481 
               
               
                   
                 8 
                 3.361 
                 7.039 
                 37.349 
               
               
                   
                 9 
                 5.468 
                 8.607 
                 37.099 
               
               
                   
                 10 
                 7.519 
                 10.247 
                 36.738 
               
               
                   
                 11 
                 9.510 
                 11.916 
                 36.274 
               
               
                   
                 12 
                 11.447 
                 13.606 
                 35.710 
               
               
                   
                 13 
                 13.311 
                 15.339 
                 35.058 
               
               
                   
                 14 
                 15.077 
                 17.149 
                 34.335 
               
               
                   
                 15 
                 16.736 
                 19.050 
                 33.558 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE VIII 
               
             
             
               
                   
               
               
                 40 mm Radius 
               
             
          
           
               
                   
                 Pt # 
                 X 
                 Y 
                 Z 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 −18.694 
                 −5.801 
                 35.363 
               
               
                   
                 2 
                 −16.540 
                 −4.436 
                 36.420 
               
               
                   
                 3 
                 −14.332 
                 −3.083 
                 37.344 
               
               
                   
                 4 
                 −12.065 
                 −1.755 
                 38.137 
               
               
                   
                 5 
                 −9.759 
                 −0.412 
                 38.791 
               
               
                   
                 6 
                 −7.428 
                 0.970 
                 39.304 
               
               
                   
                 7 
                 −5.073 
                 2.390 
                 39.677 
               
               
                   
                 8 
                 −0.382 
                 5.301 
                 39.998 
               
               
                   
                 9 
                 4.225 
                 8.324 
                 39.776 
               
               
                   
                 10 
                 6.454 
                 9.943 
                 39.476 
               
               
                   
                 11 
                 8.614 
                 11.644 
                 39.062 
               
               
                   
                 12 
                 10.707 
                 13.380 
                 38.540 
               
               
                   
                 13 
                 12.752 
                 15.132 
                 37.913 
               
               
                   
                 14 
                 14.711 
                 16.945 
                 37.197 
               
               
                   
                 15 
                 16.538 
                 18.880 
                 36.421 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE IX 
               
             
             
               
                   
               
               
                 42.5 mm Radius 
               
             
          
           
               
                   
                 Pt # 
                 X 
                 Y 
                 Z 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 −21.317 
                 −6.090 
                 36.767 
               
               
                   
                 2 
                 −19.109 
                 −4.701 
                 37.962 
               
               
                   
                 3 
                 −16.842 
                 −3.324 
                 39.020 
               
               
                   
                 4 
                 −12.129 
                 −0.612 
                 40.732 
               
               
                   
                 5 
                 −9.709 
                 0.774 
                 41.376 
               
               
                   
                 6 
                 −7.262 
                 2.199 
                 41.875 
               
               
                   
                 7 
                 −2.365 
                 5.103 
                 42.434 
               
               
                   
                 8 
                 0.080 
                 6.575 
                 42.500 
               
               
                   
                 9 
                 2.514 
                 8.074 
                 42.426 
               
               
                   
                 10 
                 4.912 
                 9.640 
                 42.215 
               
               
                   
                 11 
                 7.231 
                 11.300 
                 41.880 
               
               
                   
                 12 
                 9.460 
                 13.033 
                 41.434 
               
               
                   
                 13 
                 11.633 
                 14.797 
                 40.877 
               
               
                   
                 14 
                 13.759 
                 16.584 
                 40.211 
               
               
                   
                 15 
                 15.754 
                 18.503 
                 39.472 
               
               
                   
                   
               
             
          
         
       
     
         [0033]      FIG. 4  illustrates an exemplary surface profile  410  of a fan blade  400  according to an alternative embodiment of the present invention. Surface profile  410  may correspond to a blade coupled or affixed to a hub like the fan  300  shown in  FIG. 3 . The surface profile  410  of fan blade  400  in  FIG. 4  has been defined by the Cartesian points as referenced in Tables X-XXVI (below) and taken at even intervals along the axis of the fan blade  400 . The X, Y, and Z axis are orthogonal to one another and oriented as shown in  FIG. 4 . Like tables I-IX, all dimensions are in millimeters. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE X 
               
             
             
               
                   
               
               
                 z = 0 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −15.143 
                 −23.188 
               
               
                   
                 −14.326 
                 −22.832 
               
               
                   
                 −13.543 
                 −22.424 
               
               
                   
                 −12.092 
                 −21.431 
               
               
                   
                 −10.769 
                 −20.241 
               
               
                   
                 −9.567 
                 −18.931 
               
               
                   
                 −8.467 
                 −17.536 
               
               
                   
                 −7.442 
                 −16.078 
               
               
                   
                 −5.577 
                 −13.054 
               
               
                   
                 −3.900 
                 −9.921 
               
               
                   
                 −2.423 
                 −6.683 
               
               
                   
                 −1.140 
                 −3.369 
               
               
                   
                 0.000 
                 0.000 
               
               
                   
                 1.470 
                 5.110 
               
               
                   
                 2.078 
                 7.697 
               
               
                   
                 2.576 
                 10.311 
               
               
                   
                 3.158 
                 15.563 
               
               
                   
                 3.063 
                 20.820 
               
               
                   
                 2.698 
                 23.451 
               
               
                   
                 2.425 
                 24.763 
               
               
                   
                 2.094 
                 26.055 
               
               
                   
                 0.214 
                 31.012 
               
               
                   
                 −0.392 
                 32.199 
               
               
                   
                 −1.055 
                 33.364 
               
               
                   
                 −2.543 
                 35.567 
               
               
                   
                 −4.264 
                 37.579 
               
               
                   
                 −6.176 
                 39.433 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XI 
               
             
             
               
                   
               
               
                 z = 5 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −11.448 
                 −21.282 
               
               
                   
                 −10.262 
                 −20.347 
               
               
                   
                 −9.220 
                 −19.270 
               
               
                   
                 −8.278 
                 −18.093 
               
               
                   
                 −7.405 
                 −16.861 
               
               
                   
                 −5.804 
                 −14.307 
               
               
                   
                 −4.345 
                 −11.667 
               
               
                   
                 −3.026 
                 −8.955 
               
               
                   
                 −1.861 
                 −6.181 
               
               
                   
                 −0.828 
                 −3.356 
               
               
                   
                 0.111 
                 −0.493 
               
               
                   
                 1.605 
                 4.777 
               
               
                   
                 2.219 
                 7.445 
               
               
                   
                 2.718 
                 10.142 
               
               
                   
                 3.285 
                 15.559 
               
               
                   
                 3.152 
                 20.975 
               
               
                   
                 2.756 
                 23.684 
               
               
                   
                 2.464 
                 25.033 
               
               
                   
                 2.110 
                 26.361 
               
               
                   
                 0.100 
                 31.441 
               
               
                   
                 −0.550 
                 32.655 
               
               
                   
                 −1.259 
                 33.838 
               
               
                   
                 −2.848 
                 36.059 
               
               
                   
                 −4.681 
                 38.070 
               
               
                   
                 −6.717 
                 39.906 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XII 
               
             
             
               
                   
               
               
                 z = 10 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −9.055 
                 −19.049 
               
               
                   
                 −8.218 
                 −18.097 
               
               
                   
                 −7.448 
                 −17.100 
               
               
                   
                 −6.051 
                 −15.004 
               
               
                   
                 −4.790 
                 −12.815 
               
               
                   
                 −3.650 
                 −10.566 
               
               
                   
                 −1.700 
                 −5.933 
               
               
                   
                 −0.091 
                 −1.161 
               
               
                   
                 1.427 
                 4.243 
               
               
                   
                 2.559 
                 9.716 
               
               
                   
                 3.150 
                 15.287 
               
               
                   
                 3.183 
                 18.115 
               
               
                   
                 3.003 
                 20.923 
               
               
                   
                 1.906 
                 26.433 
               
               
                   
                 1.465 
                 27.782 
               
               
                   
                 0.961 
                 29.098 
               
               
                   
                 −0.226 
                 31.637 
               
               
                   
                 −1.658 
                 34.046 
               
               
                   
                 −2.476 
                 35.197 
               
               
                   
                 −3.368 
                 36.305 
               
               
                   
                 −5.342 
                 38.334 
               
               
                   
                 −7.510 
                 40.159 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XIII 
               
             
             
               
                   
               
               
                 z = 15 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −7.636 
                 −16.833 
               
               
                   
                 −6.407 
                 −15.142 
               
               
                   
                 −5.294 
                 −13.382 
               
               
                   
                 −3.400 
                 −9.666 
               
               
                   
                 −1.841 
                 −5.788 
               
               
                   
                 −0.520 
                 −1.823 
               
               
                   
                 1.028 
                 3.721 
               
               
                   
                 2.187 
                 9.359 
               
               
                   
                 2.794 
                 15.067 
               
               
                   
                 2.623 
                 20.801 
               
               
                   
                 2.171 
                 23.646 
               
               
                   
                 1.454 
                 26.416 
               
               
                   
                 0.460 
                 29.106 
               
               
                   
                 −0.142 
                 30.420 
               
               
                   
                 −0.810 
                 31.697 
               
               
                   
                 −4.123 
                 36.335 
               
               
                   
                 −5.129 
                 37.364 
               
               
                   
                 −6.209 
                 38.335 
               
               
                   
                 −8.496 
                 40.128 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XIV 
               
             
             
               
                   
               
               
                 z = 20 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −6.748 
                 −14.747 
               
               
                   
                 −5.797 
                 −13.336 
               
               
                   
                 −4.930 
                 −11.879 
               
               
                   
                 −3.443 
                 −8.825 
               
               
                   
                 −1.117 
                 −2.431 
               
               
                   
                 0.442 
                 3.175 
               
               
                   
                 1.607 
                 8.854 
               
               
                   
                 2.225 
                 14.633 
               
               
                   
                 2.247 
                 17.565 
               
               
                   
                 2.033 
                 20.472 
               
               
                   
                 1.556 
                 23.345 
               
               
                   
                 1.212 
                 24.767 
               
               
                   
                 0.793 
                 26.176 
               
               
                   
                 −1.576 
                 31.479 
               
               
                   
                 −3.193 
                 33.910 
               
               
                   
                 −4.118 
                 35.055 
               
               
                   
                 −5.109 
                 36.129 
               
               
                   
                 −7.282 
                 38.061 
               
               
                   
                 −9.650 
                 39.775 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XV 
               
             
             
               
                   
               
               
                 z = 25 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −6.097 
                 −12.664 
               
               
                   
                 −5.414 
                 −11.525 
               
               
                   
                 −4.785 
                 −10.362 
               
               
                   
                 −3.674 
                 −7.973 
               
               
                   
                 −1.861 
                 −3.015 
               
               
                   
                 −0.288 
                 2.627 
               
               
                   
                 0.863 
                 8.346 
               
               
                   
                 1.461 
                 14.168 
               
               
                   
                 1.463 
                 17.118 
               
               
                   
                 1.220 
                 20.041 
               
               
                   
                 0.706 
                 22.931 
               
               
                   
                 −0.102 
                 25.770 
               
               
                   
                 −1.196 
                 28.484 
               
               
                   
                 −2.586 
                 31.057 
               
               
                   
                 −3.400 
                 32.287 
               
               
                   
                 −4.294 
                 33.466 
               
               
                   
                 −6.282 
                 35.609 
               
               
                   
                 −8.535 
                 37.464 
               
               
                   
                 −10.991 
                 39.098 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XVI 
               
             
             
               
                   
               
               
                 z = 30 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −5.585 
                 −10.399 
               
               
                   
                 −4.067 
                 −7.100 
               
               
                   
                 −2.804 
                 −3.695 
               
               
                   
                 −1.189 
                 1.944 
               
               
                   
                 −0.064 
                 7.667 
               
               
                   
                 0.486 
                 13.491 
               
               
                   
                 0.463 
                 16.449 
               
               
                   
                 0.189 
                 19.383 
               
               
                   
                 −0.363 
                 22.272 
               
               
                   
                 −0.751 
                 23.699 
               
               
                   
                 −1.217 
                 25.108 
               
               
                   
                 −3.828 
                 30.353 
               
               
                   
                 −4.679 
                 31.560 
               
               
                   
                 −5.615 
                 32.715 
               
               
                   
                 −7.690 
                 34.793 
               
               
                   
                 −10.027 
                 36.564 
               
               
                   
                 −12.561 
                 38.097 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XVII 
               
             
             
               
                   
               
               
                 z = 35 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −5.162 
                 −7.551 
               
               
                   
                 −4.098 
                 −4.761 
               
               
                   
                 −2.368 
                 0.873 
               
               
                   
                 −1.217 
                 6.608 
               
               
                   
                 −0.708 
                 12.454 
               
               
                   
                 −0.704 
                 13.936 
               
               
                   
                 −0.758 
                 15.427 
               
               
                   
                 −1.060 
                 18.379 
               
               
                   
                 −1.647 
                 21.280 
               
               
                   
                 −2.058 
                 22.709 
               
               
                   
                 −2.552 
                 24.119 
               
               
                   
                 −3.772 
                 26.814 
               
               
                   
                 −5.307 
                 29.331 
               
               
                   
                 −6.199 
                 30.519 
               
               
                   
                 −7.177 
                 31.651 
               
               
                   
                 −9.340 
                 33.665 
               
               
                   
                 −11.769 
                 35.341 
               
               
                   
                 −14.399 
                 36.754 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XVIII 
               
             
             
               
                   
               
               
                 z = 40 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −4.536 
                 −2.789 
               
               
                   
                 −3.114 
                 2.520 
               
               
                   
                 −2.292 
                 7.928 
               
               
                   
                 −2.135 
                 10.675 
               
               
                   
                 −2.170 
                 13.441 
               
               
                   
                 −2.907 
                 18.884 
               
               
                   
                 −3.250 
                 20.222 
               
               
                   
                 −3.664 
                 21.546 
               
               
                   
                 −4.704 
                 24.098 
               
               
                   
                 −6.028 
                 26.505 
               
               
                   
                 −6.800 
                 27.653 
               
               
                   
                 −7.645 
                 28.755 
               
               
                   
                 −9.517 
                 30.760 
               
               
                   
                 −11.648 
                 32.479 
               
               
                   
                 −14.038 
                 33.894 
               
               
                   
                 −16.570 
                 35.051 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XIX 
               
             
             
               
                   
               
               
                 z = 45 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −3.952 
                 5.610 
               
               
                   
                 −3.744 
                 9.858 
               
               
                   
                 −4.047 
                 14.086 
               
               
                   
                 −4.411 
                 16.191 
               
               
                   
                 −4.929 
                 18.258 
               
               
                   
                 −6.455 
                 22.212 
               
               
                   
                 −6.949 
                 23.159 
               
               
                   
                 −7.488 
                 24.086 
               
               
                   
                 −8.690 
                 25.845 
               
               
                   
                 −10.056 
                 27.471 
               
               
                   
                 −11.599 
                 28.952 
               
               
                   
                 −13.298 
                 30.240 
               
               
                   
                 −15.124 
                 31.311 
               
               
                   
                 −17.062 
                 32.195 
               
               
                   
                 −19.063 
                 32.962 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XX 
               
             
             
               
                   
               
               
                 z = −5 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −19.764 
                 −24.408 
               
               
                   
                 −18.389 
                 −24.124 
               
               
                   
                 −17.077 
                 −23.624 
               
               
                   
                 −14.607 
                 −22.303 
               
               
                   
                 −12.354 
                 −20.650 
               
               
                   
                 −11.318 
                 −19.698 
               
               
                   
                 −10.354 
                 −18.686 
               
               
                   
                 −7.038 
                 −14.217 
               
               
                   
                 −5.603 
                 −11.812 
               
               
                   
                 −4.294 
                 −9.345 
               
               
                   
                 −2.231 
                 −4.690 
               
               
                   
                 −0.511 
                 0.098 
               
               
                   
                 0.964 
                 5.079 
               
               
                   
                 2.097 
                 10.148 
               
               
                   
                 2.738 
                 15.274 
               
               
                   
                 2.712 
                 20.412 
               
               
                   
                 2.387 
                 22.987 
               
               
                   
                 2.136 
                 24.271 
               
               
                   
                 1.829 
                 25.537 
               
               
                   
                 0.074 
                 30.408 
               
               
                   
                 −0.494 
                 31.579 
               
               
                   
                 −1.117 
                 32.730 
               
               
                   
                 −2.524 
                 34.917 
               
               
                   
                 −4.159 
                 36.924 
               
               
                   
                 −5.979 
                 38.785 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XXI 
               
             
             
               
                   
               
               
                 z = −10 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −21.148 
                 −24.550 
               
               
                   
                 −19.540 
                 −23.946 
               
               
                   
                 −17.984 
                 −23.240 
               
               
                   
                 −15.006 
                 −21.576 
               
               
                   
                 −13.608 
                 −20.570 
               
               
                   
                 −12.302 
                 −19.447 
               
               
                   
                 −9.977 
                 −16.914 
               
               
                   
                 −8.556 
                 −14.998 
               
               
                   
                 −7.262 
                 −13.011 
               
               
                   
                 −4.973 
                 −8.872 
               
               
                   
                 −3.030 
                 −4.542 
               
               
                   
                 −1.367 
                 −0.074 
               
               
                   
                 0.131 
                 4.783 
               
               
                   
                 1.301 
                 9.730 
               
               
                   
                 2.016 
                 14.737 
               
               
                   
                 2.087 
                 19.764 
               
               
                   
                 1.814 
                 22.288 
               
               
                   
                 1.591 
                 23.550 
               
               
                   
                 1.314 
                 24.796 
               
               
                   
                 −0.307 
                 29.601 
               
               
                   
                 −1.426 
                 31.897 
               
               
                   
                 −2.762 
                 34.067 
               
               
                   
                 −4.328 
                 36.060 
               
               
                   
                 −6.086 
                 37.906 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XXII 
               
             
             
               
                   
               
               
                 z = −15 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −21.794 
                 −24.790 
               
               
                   
                 −20.175 
                 −23.944 
               
               
                   
                 −18.591 
                 −23.032 
               
               
                   
                 −17.082 
                 −22.071 
               
               
                   
                 −15.621 
                 −21.055 
               
               
                   
                 −12.915 
                 −18.773 
               
               
                   
                 −10.552 
                 −16.093 
               
               
                   
                 −8.510 
                 −13.142 
               
               
                   
                 −5.128 
                 −6.869 
               
               
                   
                 −3.707 
                 −3.589 
               
               
                   
                 −2.436 
                 −0.232 
               
               
                   
                 −0.930 
                 4.469 
               
               
                   
                 0.255 
                 9.261 
               
               
                   
                 1.019 
                 14.115 
               
               
                   
                 1.181 
                 18.994 
               
               
                   
                 0.970 
                 21.446 
               
               
                   
                 0.540 
                 23.894 
               
               
                   
                 −0.937 
                 28.601 
               
               
                   
                 −1.982 
                 30.851 
               
               
                   
                 −3.246 
                 32.984 
               
               
                   
                 −4.740 
                 34.943 
               
               
                   
                 −6.430 
                 36.756 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XXIII 
               
             
             
               
                   
               
               
                 z = −20 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −22.214 
                 −26.282 
               
               
                   
                 −20.683 
                 −24.942 
               
               
                   
                 −19.172 
                 −23.578 
               
               
                   
                 −17.670 
                 −22.205 
               
               
                   
                 −16.180 
                 −20.819 
               
               
                   
                 −14.728 
                 −19.392 
               
               
                   
                 −13.353 
                 −17.905 
               
               
                   
                 −10.889 
                 −14.728 
               
               
                   
                 −8.742 
                 −11.328 
               
               
                   
                 −6.831 
                 −7.765 
               
               
                   
                 −3.661 
                 −0.323 
               
               
                   
                 −2.183 
                 4.174 
               
               
                   
                 −1.014 
                 8.742 
               
               
                   
                 −0.234 
                 13.401 
               
               
                   
                 −0.037 
                 15.773 
               
               
                   
                 −0.005 
                 18.144 
               
               
                   
                 −0.510 
                 22.827 
               
               
                   
                 −1.071 
                 25.139 
               
               
                   
                 −1.836 
                 27.393 
               
               
                   
                 −3.977 
                 31.617 
               
               
                   
                 −4.658 
                 32.603 
               
               
                   
                 −5.400 
                 33.542 
               
               
                   
                 −7.006 
                 35.315 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XXIV 
               
             
             
               
                   
               
               
                 z = −25 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −22.961 
                 −27.642 
               
               
                   
                 −22.018 
                 −26.664 
               
               
                   
                 −21.095 
                 −25.669 
               
               
                   
                 −19.289 
                 −23.642 
               
               
                   
                 −15.812 
                 −19.472 
               
               
                   
                 −12.680 
                 −15.049 
               
               
                   
                 −9.911 
                 −10.389 
               
               
                   
                 −8.345 
                 −7.520 
               
               
                   
                 −6.615 
                 −4.030 
               
               
                   
                 −5.102 
                 −0.441 
               
               
                   
                 −3.634 
                 3.837 
               
               
                   
                 −3.014 
                 6.011 
               
               
                   
                 −2.481 
                 8.210 
               
               
                   
                 −1.722 
                 12.644 
               
               
                   
                 −1.476 
                 17.128 
               
               
                   
                 −1.592 
                 19.393 
               
               
                   
                 −1.890 
                 21.635 
               
               
                   
                 −3.064 
                 25.986 
               
               
                   
                 −3.957 
                 28.073 
               
               
                   
                 −5.049 
                 30.035 
               
               
                   
                 −6.358 
                 31.855 
               
               
                   
                 −7.844 
                 33.558 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XXV 
               
             
             
               
                   
               
               
                 z = −30 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −4.440 
                 6.519 
               
               
                   
                 −3.341 
                 13.018 
               
               
                   
                 −3.243 
                 16.316 
               
               
                   
                 −3.330 
                 17.977 
               
               
                   
                 −3.515 
                 19.623 
               
               
                   
                 −4.193 
                 22.849 
               
               
                   
                 −4.700 
                 24.428 
               
               
                   
                 −5.326 
                 25.969 
               
               
                   
                 −6.933 
                 28.834 
               
               
                   
                 −8.986 
                 31.417 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE XXVI 
               
             
             
               
                   
               
               
                 z = −35 mm 
               
             
          
           
               
                   
                 X 
                 Y 
               
               
                   
                   
               
             
          
           
               
                   
                 −5.258 
                 14.085 
               
               
                   
                 −5.583 
                 18.053 
               
               
                   
                 −5.972 
                 20.003 
               
               
                   
                 −6.524 
                 21.926 
               
               
                   
                 −8.139 
                 25.532 
               
               
                   
                 −9.219 
                 27.183 
               
               
                   
                 −10.437 
                 28.755 
               
               
                   
                   
               
             
          
         
       
     
         [0034]    Both prototype and manufactured surfaces resulting from the application of Tables I-IX and Tables X-XXVI may conform to these points within reasonable process tolerances. 
         [0035]      FIG. 5  illustrates an exemplary method  500  for constructing a blade surface according to an embodiment of the present invention. In step  510 , a radius cut is sketched. Points are identified along that radius cut in step  520  and a spline is drafted to connect the aforementioned points in step  530 . In step  540 , each radius cut sketch is lofted in increasing radius order to form a surface. The surface may be extended or trimmed at the edges to reach the exact desired dimensions in step  550 . 
         [0036]      FIG. 6  illustrates a method  600  for forming a blade according to an embodiment of the present invention. In step  610 , the surface (as may be created through the method described with respect to  FIG. 5 ) is offset by a constant amount. In step  620 , the offset is filled to form a single blade. In optional step  630 , the bluntness of the leading and/or trailing edges may be altered for desired operating conditions. 
         [0037]      FIG. 7  illustrates an alternative method  700  for forming a blade according to an embodiment of the present invention. In step  710 , a complimentary airfoil shape is created. In step  720 , a semi- or fully-airfoil blade cross-section is created on one or both sides of the blade. This cross-section may then be lofted into a solid in step  730 . Alterations may also be made with respect to the bluntness of the leading and/or trailing edges for the purpose of desired operating conditions in step  740 . 
         [0038]      FIG. 8  illustrates an exemplary method  800  for constructing a fan according to an embodiment of the present invention. In step  810 , blades are oriented with respect to the hub, which may include rotating the in-tact blade surface about an axis to change the pitch, dihedral, or sweep angle as they pertain to desired fan performance. The blade is then patterned around the hub or other fixturing device in step  820  for the appropriate number of blades. Blades can be fully or partially attached to the hub in step  830  and radiused as desired. Alterations may also be made to the leading and/or trailing edge bluntness in order to achieve desired operation conditions. 
         [0039]    While Tables I-IX, for example, dictate an 87 mm diameter fan, the blade surface, full blade, and/or final fan may be scaled to change the size and output of the fan as may the measurements set forth in Tables X-XXVI. The resulting fan blade may be mirrored or run in either rotation. Additional attributes may be added to the fan including radii, mid-blade or blade-tip winglets (vertical extrusions out of the blade), full or partial-depth rings, extended or indented turbulators (bumps or cavities along the blade to change boundary layer behavior or noise), embossings, fastening devices, coatings and so forth. Additional surface features and/or strategic roughness may be employed. Furthermore, this blade surface may also be used in a similar fashion to make a non-rotating fan, or stator. 
         [0040]    The methods disclosed with respect to  FIGS. 5-8  may be embodied in computer software. A computer-readable storage medium may have embodied thereon a program. The program may be executable by a processor to perform the methods or combinations thereof as disclosed herein. These methods may be applicable in the field of computer-aided drafting or design, which may include three-dimensional design tools. The results of such computer-aided drafting and design may be rendered on a display device (e.g., a computer monitor) or printed to a tangible medium such as a computer printout. These results may be annotated with measurement information. 
         [0041]      FIGS. 9A-9E  illustrate exemplary fans constructed utilizing the surface profile disclosed with respect to  FIG. 3 . These fan configurations are exemplary and various elements thereof (e.g., hub, blade number, blade configuration, stators) may be interchangeably combined with one another and in conjunction with a particular surface profile to construct a fan in accordance with an embodiment of the present invention. 
         [0042]      FIG. 9A  illustrates an exemplary fan including five blades arranged about a cylindrical and hollowed hub. 
         [0043]      FIG. 9B  illustrates another exemplary fan including seven blades arranged about a cylindrical and capped hub. 
         [0044]      FIG. 9C  illustrates an exemplary fan including five blades with serrated edges and arranged about a conical hub. 
         [0045]      FIG. 9D  illustrates an exemplary fan including twelve blades with a notched edge and arranged about a cylindrical and capped hub. 
         [0046]      FIG. 9E  illustrates an exemplary fan including two blades and arranged about a cylindrical hub, the fan being enclosed within a stator. 
         [0047]      FIGS. 10A-10E  illustrate exemplary fans constructed utilizing the surface profile disclosed with respect to  FIG. 4 . These fan configurations are exemplary and various elements thereof (e.g., hub, blade number, blade configuration, stators) may be interchangeably combined with one another and in conjunction with a particular surface profile to construct a fan in accordance with an embodiment of the present invention. 
         [0048]      FIG. 10A  illustrates an exemplary fan including three blades extending outward in three-dimensions from an otherwise flat, two-dimensional hub. 
         [0049]      FIG. 10B  illustrates an exemplary fan including six blades and arranged about a cylindrical and solid hub, the fan being enclosed within a stator. 
         [0050]      FIG. 10C  illustrates an exemplary fan including three blades extending outward in three-dimensions from a conical hub. 
         [0051]      FIG. 10D  illustrates an exemplary fan including fourteen blades and arranged about a cylindrical hub, each of the blades being coupled to one another by intermediate ‘webbing.’ 
         [0052]      FIG. 10E  illustrates an exemplary fan including four blades and arranged about a cylindrical and solid hub. 
         [0053]    While the present invention has been described with reference to exemplary embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements or steps thereof without departing from the true spirit and scope of the present invention. For example, methods of design may be applied to methods of manufacture.