US2002128090A1PendingUtilityA1

Golf putter with improved curved striking face, putter system, and method of making same

Assignee: TEARDROP GOLF COMPANYPriority: Nov 7, 1997Filed: Feb 1, 2001Published: Sep 12, 2002
Est. expiryNov 7, 2017(expired)· nominal 20-yr term from priority
A63B 53/0433A63B 53/005A63B 53/0408A63B 53/0487
38
PatentIndex Score
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Cited by
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0
Claims

Abstract

An improved vertically-curved strike face for a golf putter, the roll radius for which is determined based on the given strike face height and loft selected, wherein, regardless of a given golfer's putting stroke style, and of variations within that stroke style, the improved curved strike face as determined permits consistently impacting the golf ball in a critical true roll zone just slightly below the equator. Custom-fitting, to accommodate a given golfer's extreme putting style, or a given course's daily Stimpmeter (trademark) reading, or green speed or mowed putting green conditions, can be achieved by selecting a given curved strike face loft and the resultant strike face roll radius. A basic form of the invention comprises a series of putters with different roll radii, for a given loft and strike face height.

Claims

exact text as granted — not AI-modified
We claim:  
     
         1 . The method of forming an optimal vertically curved strike face for a golf putter, for allowing the curved strike face to consistently impact the golf ball at a point within the ball's true roll impact zone in a range from approximately 0.015 inch to 0.073 inch below the ball's equator, and regardless of the putting stroke style used by a given golfer, comprising the steps of: 
 a) selecting a putter design having a given strike face height;    b) selecting a static loft for the curved strike face based on the putting green speed condition; and    c) calculating the required roll radius for the curved strike face, as based on the selected face height and static loft, to allow impacting the ball within the true roll impact zone, using the equations of: 
 (1) “A”=sin (static loft) (0.5) (face height)  
 (2) “C”=tan (static loft) (A)  
 (3) h={square root}{square root over (A 2 +C 2 )} 
               Diameter   =       (       h   2     +       (     0.5                 face                 height     )     2       )     h             (   4   )                 Curved                 Radius     =     Diameter   2             (   5   )                         
 wherein A, C, and h are as set forth in FIG. 18 of the DRAWINGS.  
   
     
     
         2 . The method of  claim 1 , and wherein the selected static loft falls within the range of from approximately 1° to 5° positive.  
     
     
         3 . The method of  claim 1 , and wherein the resulting dynamic loft delivered to the golf ball at impact falls within the range of from approximately 2°to 4° positive.  
     
     
         4 . The method of  claim 1 , and wherein the selected static loft is so custom selected that, for use with relatively fast greens having a mowed grass height of from approximately 0.125 inch to 0.156 inch, the resultant putter's curved strike face static loft is from approximately 1° to 3° positive.  
     
     
         5 . The method of  claim 1 , and wherein the selected static loft is so custom selected that, for use with relatively moderate speed greens having a mowed grass height of from approximately 0.156 inch to 0.281 inch, the resultant putter's curved strike face static loft is from approximately 2° to 4° positive.  
     
     
         6 . The method of  claim 1 , and wherein the selected static loft is so custom selected that, for use with relatively slow speed greens having a mowed grass height of from approximately 0.172 inch to 0.281 inch, the resultant putter's curved strike face static loft is from 3° to 5° positive.  
     
     
         7 . The method of  claim 1 , and, so as to accommodate the dynamic shaft angle delivered by a golfer having an extreme forward press putting stroke style, of increasing said static loft in the range of from approximately 3° to 5° positive loft for said static loft selected in step (b) above.  
     
     
         8 . The method of  claim 1 , and, so as to accommodate the dynamic short angle delivered by a golfer having an extreme broken wrist putting stroke style, of reducing said static loft in the range of from approximately 1° to 3° positive loft from said static loft selected in step (b) above.  
     
     
         9 . The method of  claim 1 , and determining the required X and Y displacements to find the center of curvature of the optimal roll radius calculated by step (c) above, wherein X and Y are determined using the equations of: 
 (1) “A”=sin (static loft) (0.5) (face height)                  (   2   )                     “   D   ”       =     A     tan                   (     static                 loft     )                                        (3) “C”=tan (static loft) (A)    (4) “B”=D+C    (5) “E”=sin (static loft) (face radius)    (6) “Y” dimension=B−E    (7) “X” dimension=cos (static loft) (face radius)    wherein A, B, C, D, and E are as set forth in FIG. 18 of the DRAWINGS.    
     
     
         10 . A plurality of vertically curved strike face putters, each said putter of the plurality, while having substantially the same face height and static loft, having a different roll radius for that given said putter's curved strike face, whereby a golfer on a given day can select which respective putter within the plurality best accommodates that golfer's putting stroke style and that given day's putting green conditions.  
     
     
         11 . An improved vertically curved strike face putter having an optimal roll radius to permit impacting the golf ball within a true roll impact zone falling within the range from approximately 0.018 inch to 0.073 inch below the ball's equator, the improvement comprising in combination: 
 a) a known face height (FH) for said curved strike face,    b) a known static loft selected for said curved strike face, and    c) said optimal roll radius formed on said curved strike face, based on said known face height (FH) and said known static loft, determined through the equations of: 
 (1) “A”=sin (static loft) (0.5) (face height)  
 (2) “C”=tan (static loft) (A)  
               (   3   )                   h     =           A   2     +     C   2                                                            (   4   )                   Diameter     =       (       h   2     +       (     0.5                 face                 height     )     2       )     h                                  
                 Curved                 Radius     =     Diameter   2             (   5   )                         
   
     
     
         12 . The invention of  claim 11 , and wherein said known static loft falls within the range from approximately 1° to 5° positive loft.  
     
     
         13 . The method of determining an optimal roll radius for a vertically curved strike face putter, comprising the steps of: 
 a) determining the face height of the selected design of curved strike face putter;    b) selecting the static loft of the curved strike face; and    c) determining the required optimal roll radius, as a function of said determined face height and said selected static loft, whereby said optimal roll radius permits said curved strike face putter, regardless of a given golfer's putting stroke style and the golfer's own tolerance variations within that style, to consistently impact the golf ball within a true roll impact zone below the ball's equator so that the ball will achieve the earliest true roll.    
     
     
         14 . The method of  claim 13 , and wherein said true roll impact zone is in the range from approximately 0.015 inch to 0.073 inch below the ball's equator.  
     
     
         15 . The method of  claim 13 , and wherein said true roll impact zone for use on relatively fast speed putting greens is in the range from approximately 0.015 inch to 0.044 inch below the ball's equator.  
     
     
         16 . The method of  claim 13 , and wherein said true roll impact zone for use on relatively average speed putting greens, is in the range from approximately 0.024 inch to 0.059 inch below the ball's equator.  
     
     
         17 . The method of  claim 13 , and wherein said two roll impact zone for use on relatively slow speed putting greens is in the range of from approximately 0.044 inch to 0.073 inch below the ball's equator.  
     
     
         18 . An improved vertically-curved strike face putter able to consistently impact a golf ball within the ball's true roll impact zone below the ball's equator, regardless of a given golfers putting stroke style, said putter's curved strike face formed of a selected face height and of a selected static loft, said curved strike face having an optimal roll radius resulting from said face height and static loft, said face height and said static loft selected from, and said resultant optimal roll radii, and the correlating X and Y displacement data for the center-of-curvature location for such resultant optimal roll radii, are established in, the following optimum roll radii charts:  
       
         
           
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                     
                 
                     
                 
                   Loft Angle 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                   0.5 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.002 
                   0.002 
                   0.003 
                   0.003 
                   0.003 
                   0.003 
                   0.003 
                   0.004 
                   0.004 
                   0.004 
                   0.004 
                   0.005 
                   0.005 
                   0.005 
                   0.005 
                   0.005 
                   0.006 
                   0.006 
                   0.006 
                   0.006 
                   0.007 
                 
                   C = 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                 
                   h = 
                   0.002 
                   0.002 
                   0.003 
                   0.003 
                   0.003 
                   0.003 
                   0.003 
                   0.004 
                   0.004 
                   0.004 
                   0.004 
                   0.005 
                   0.005 
                   0.005 
                   0.005 
                   0.005 
                   0.006 
                   0.006 
                   0.006 
                   0.006 
                   0.007 
                 
                   Diameter = 
                   28.649 
                   31.514 
                   34.379 
                   37.244 
                   40.109 
                   42.974 
                   45.839 
                   48.704 
                   51.569 
                   54.434 
                   57.299 
                   60.164 
                   63.029 
                   65.893 
                   68.758 
                   71.623 
                   74.488 
                   77.353 
                   80.218 
                   83.083 
                   85.948 
                 
                   D = 
                   0.250 
                   0.275 
                   0.300 
                   0.325 
                   0.350 
                   0.375 
                   0.400 
                   0.425 
                   0.450 
                   0.475 
                   0.500 
                   0.525 
                   0.550 
                   0.575 
                   0.600 
                   0.625 
                   0.650 
                   0.675 
                   0.700 
                   0.725 
                   0.750 
                 
                   B = 
                   0.250 
                   0.275 
                   0.300 
                   0.325 
                   0.350 
                   0.375 
                   0.400 
                   0.425 
                   0.450 
                   0.475 
                   0.500 
                   0.525 
                   0.550 
                   0.575 
                   0.600 
                   0.625 
                   0.650 
                   0.675 
                   0.700 
                   0.725 
                   0.750 
                 
                   E = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.225 
                   0.238 
                   0.250 
                   0.263 
                   0.275 
                   0.288 
                   0.300 
                   0.313 
                   0.325 
                   0.338 
                   0.350 
                   0.363 
                   0.375 
                 
                   “Y” = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.225 
                   0.238 
                   0.250 
                   0.263 
                   0.275 
                   0.288 
                   0.300 
                   0.313 
                   0.325 
                   0.338 
                   0.350 
                   0.363 
                   0.375 
                 
                   “X” = 
                   14.324 
                   15.757 
                   17.189 
                   18.621 
                   20.054 
                   21.486 
                   22.919 
                   24.351 
                   25.783 
                   27.216 
                   28.648 
                   30.081 
                   31.513 
                   32.945 
                   34.378 
                   35.810 
                   37.243 
                   38.675 
                   40.108 
                   41.540 
                   42.972 
                 
                   Roll Radius 
                   14.325 
                   15.757 
                   17.190 
                   18.622 
                   20.055 
                   21.487 
                   22.919 
                   24.352 
                   25.784 
                   27.217 
                   28.649 
                   30.082 
                   31.514 
                   32.947 
                   34.379 
                   35.812 
                   37.244 
                   38.677 
                   40.109 
                   41.542 
                   42.974 
                 
                   Loft Angle 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                   1 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.004 
                   0.005 
                   0.005 
                   0.006 
                   0.006 
                   0.007 
                   0.007 
                   0.007 
                   0.008 
                   0.008 
                   0.009 
                   0.009 
                   0.010 
                   0.010 
                   0.010 
                   0.011 
                   0.011 
                   0.012 
                   0.012 
                   0.013 
                   0.013 
                 
                   C = 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                 
                   h = 
                   0.004 
                   0.005 
                   0.005 
                   0.006 
                   0.006 
                   0.007 
                   0.007 
                   0.007 
                   0.008 
                   0.008 
                   0.009 
                   0.009 
                   0.010 
                   0.010 
                   0.010 
                   0.011 
                   0.011 
                   0.012 
                   0.012 
                   0.013 
                   0.013 
                 
                   Diameter = 
                   14.327 
                   15.760 
                   17.192 
                   18.625 
                   20.058 
                   21.490 
                   22.923 
                   24.356 
                   25.788 
                   27.221 
                   28.654 
                   30.086 
                   31.519 
                   32.952 
                   34.384 
                   35.817 
                   37.250 
                   38.683 
                   40.115 
                   41.548 
                   42.981 
                 
                   D = 
                   0.250 
                   0.275 
                   0.300 
                   0.325 
                   0.350 
                   0.375 
                   0.400 
                   0.425 
                   0.450 
                   0.475 
                   0.500 
                   0.525 
                   0.550 
                   0.575 
                   0.600 
                   0.625 
                   0.650 
                   0.675 
                   0.700 
                   0.725 
                   0.750 
                 
                   B = 
                   0.250 
                   0.275 
                   0.300 
                   0.325 
                   0.350 
                   0.375 
                   0.400 
                   0.425 
                   0.450 
                   0.475 
                   0.500 
                   0.525 
                   0.550 
                   0.575 
                   0.600 
                   0.625 
                   0.650 
                   0.675 
                   0.700 
                   0.725 
                   0.750 
                 
                   E = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.225 
                   0.238 
                   0.250 
                   0.263 
                   0.275 
                   0.288 
                   0.300 
                   0.313 
                   0.325 
                   0.338 
                   0.350 
                   0.363 
                   0.375 
                 
                   “Y” = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.225 
                   0238 
                   0.250 
                   0.263 
                   0.275 
                   0.288 
                   0.300 
                   0.313 
                   0.325 
                   0.338 
                   0.350 
                   0.363 
                   0.375 
                 
                   “X” = 
                   7.162 
                   7.879 
                   8.595 
                   9.311 
                   10.027 
                   10.744 
                   11.460 
                   12.176 
                   12.892 
                   13.608 
                   14.325 
                   15.041 
                   15.757 
                   16.473 
                   17.190 
                   17.906 
                   18.622 
                   19.338 
                   20.055 
                   20.771 
                   21.487 
                 
                   Roll Radius 
                   7.163 
                   7.880 
                   8.596 
                   9.312 
                   10.029 
                   10.745 
                   11.461 
                   12.178 
                   12.894 
                   13.611 
                   14.327 
                   15.043 
                   15.760 
                   16.476 
                   17.192 
                   17.909 
                   18.625 
                   19.341 
                   20.058 
                   20.774 
                   21.490 
                 
                   Loft Angle 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                   1.5 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.007 
                   0.007 
                   0.008 
                   0.009 
                   0.009 
                   0.010 
                   0.010 
                   0.011 
                   0.012 
                   0.012 
                   0.013 
                   0.014 
                   0.014 
                   0.015 
                   0.016 
                   0.016 
                   0.017 
                   0.018 
                   0.018 
                   0.019 
                   0.020 
                 
                   C = 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.001 
                 
                   h = 
                   0.007 
                   0.007 
                   0.008 
                   0.009 
                   0.009 
                   0.010 
                   0.010 
                   0.011 
                   0.012 
                   0.012 
                   0.013 
                   0.014 
                   0.014 
                   0.015 
                   0.016 
                   0.016 
                   0.017 
                   0.018 
                   0.018 
                   0.019 
                   0.020 
                 
                   Diameter = 
                   9.554 
                   10.509 
                   11.464 
                   12.420 
                   13.375 
                   14.330 
                   15.286 
                   16.241 
                   17.197 
                   18.152 
                   19.107 
                   20.063 
                   21.018 
                   21.973 
                   22.929 
                   23.884 
                   24.840 
                   25.795 
                   26.750 
                   27.706 
                   28.681 
                 
                   D = 
                   0.250 
                   0.275 
                   0.300 
                   0.325 
                   0.350 
                   0.375 
                   0.400 
                   0.425 
                   0.450 
                   0.475 
                   0.500 
                   0.525 
                   0.550 
                   0.575 
                   0.600 
                   0.625 
                   0.650 
                   0.675 
                   0.700 
                   0.725 
                   0.750 
                 
                   B = 
                   0.250 
                   0.275 
                   0.300 
                   0.325 
                   0.350 
                   0.375 
                   0.400 
                   0.425 
                   0.450 
                   0.475 
                   0.500 
                   0.525 
                   0.550 
                   0.575 
                   0.600 
                   0.625 
                   0.650 
                   0.675 
                   0.700 
                   0.725 
                   0.750 
                 
                   E = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.225 
                   0.238 
                   0.250 
                   0.263 
                   0.275 
                   0.288 
                   0.300 
                   0.313 
                   0.325 
                   0.338 
                   0.350 
                   0.363 
                   0.375 
                 
                   “Y” = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.225 
                   0.238 
                   0.250 
                   0.263 
                   0.275 
                   0.288 
                   0.300 
                   0.313 
                   0.325 
                   0.338 
                   0.350 
                   0.363 
                   0.375 
                 
                   “X” = 
                   4.775 
                   5.253 
                   5.730 
                   6.208 
                   6.685 
                   7.163 
                   7.640 
                   8.118 
                   8.695 
                   9.073 
                   9.550 
                   10.028 
                   10.505 
                   10.983 
                   11.460 
                   11.938 
                   12.416 
                   12.893 
                   13.371 
                   13.848 
                   14.326 
                 
                   Roll Radius 
                   4.777 
                   5.255 
                   5.732 
                   6.210 
                   6.688 
                   7.165 
                   7.643 
                   8.121 
                   8.598 
                   9.076 
                   9.554 
                   10.031 
                   10.509 
                   10.987 
                   11.464 
                   11.942 
                   12.420 
                   12.897 
                   13.375 
                   13.853 
                   14.330 
                 
                   Loft Angle 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                   2 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.009 
                   0.010 
                   0.010 
                   0.011 
                   0.012 
                   0.013 
                   0.014 
                   0.015 
                   0.016 
                   0.017 
                   0.017 
                   0.018 
                   0.019 
                   0.020 
                   0.021 
                   0.022 
                   0.023 
                   0.024 
                   0.024 
                   0.025 
                   0.026 
                 
                   C = 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.000 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                 
                   h = 
                   0.009 
                   0.010 
                   0.010 
                   0.011 
                   0.012 
                   0.013 
                   0.014 
                   0.015 
                   0.016 
                   0.017 
                   0.017 
                   0.018 
                   0.019 
                   0.020 
                   0.021 
                   0.022 
                   0.023 
                   0.024 
                   0.024 
                   0.025 
                   0.026 
                 
                   Diameter = 
                   7.168 
                   7.885 
                   8.601 
                   9.318 
                   10.035 
                   10.752 
                   11.468 
                   12.185 
                   12.902 
                   13.619 
                   14.336 
                   15.052 
                   15.769 
                   16.486 
                   17.203 
                   17.919 
                   18.636 
                   19.353 
                   20.070 
                   20.787 
                   21.503 
                 
                   D = 
                   0.250 
                   0.275 
                   0.300 
                   0.325 
                   0.350 
                   0.375 
                   0.400 
                   0.425 
                   0.450 
                   0.475 
                   0.500 
                   0.525 
                   0.550 
                   0.575 
                   0.600 
                   0.625 
                   0.650 
                   0.675 
                   0.700 
                   0.725 
                   0.750 
                 
                   B = 
                   0.250 
                   0.275 
                   0.300 
                   0.325 
                   0.350 
                   0.375 
                   0.400 
                   0.425 
                   0.450 
                   0.475 
                   0.500 
                   0.525 
                   0.550 
                   0.575 
                   0.600 
                   0.625 
                   0.650 
                   0.675 
                   0.700 
                   0.725 
                   0.750 
                 
                   E = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.225 
                   0.238 
                   0.250 
                   0.263 
                   0.275 
                   0.288 
                   0.300 
                   0.313 
                   0.325 
                   0.338 
                   0.350 
                   0.363 
                   0.375 
                 
                   “Y” = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.225 
                   0.238 
                   0.250 
                   0.263 
                   0.275 
                   0.288 
                   0.300 
                   0.313 
                   0.325 
                   0.338 
                   0.350 
                   0.363 
                   0.375 
                 
                   “X” = 
                   3.582 
                   3.940 
                   4.298 
                   4.656 
                   5.014 
                   5.373 
                   5.731 
                   6.089 
                   6.447 
                   6.085 
                   7.163 
                   7.522 
                   7.880 
                   8.238 
                   8.596 
                   8.954 
                   9.312 
                   9.671 
                   10.029 
                   10.387 
                   10.745 
                 
                   Roll Radius 
                   3.584 
                   3.942 
                   4.301 
                   4.659 
                   5.017 
                   5.376 
                   5.734 
                   6.093 
                   6.451 
                   6.809 
                   7.168 
                   7.526 
                   7.885 
                   8.243 
                   8.601 
                   8.960 
                   9.318 
                   9.677 
                   10.035 
                   10.393 
                   10.752 
                 
                   Loft Angle 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                   2.5 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.011 
                   0.012 
                   0.013 
                   0.014 
                   0.015 
                   0.016 
                   0.017 
                   0.019 
                   0.020 
                   0.021 
                   0.022 
                   0.023 
                   0.024 
                   0.0225 
                   0.026 
                   0.027 
                   0.028 
                   0.0.029 
                   0.031 
                   0.032 
                   0.033 
                 
                   C = 
                   0.000 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                 
                   h = 
                   0.011 
                   0.012 
                   0.013 
                   0.014 
                   0.015 
                   0.016 
                   0.017 
                   0.019 
                   0.020 
                   0.021 
                   0.022 
                   0.023 
                   0.024 
                   0.025 
                   0.026 
                   0.027 
                   0.028 
                   0.029 
                   0.031 
                   0.032 
                   0.033 
                 
                   Diameter = 
                   5.737 
                   6.311 
                   6.884 
                   7.458 
                   8.032 
                   8.605 
                   9.179 
                   9.753 
                   10.326 
                   10.900 
                   11.474 
                   12.047 
                   12.621 
                   13.195 
                   13.768 
                   14.342 
                   14.916 
                   15.490 
                   16.063 
                   16.637 
                   17.211 
                 
                   D = 
                   0.250 
                   0.275 
                   0.300 
                   0.325 
                   0.350 
                   0.375 
                   0.400 
                   0.425 
                   0.450 
                   0.475 
                   0.500 
                   0.525 
                   0.550 
                   0.575 
                   0.600 
                   0.625 
                   0.650 
                   0.675 
                   0.700 
                   0.725 
                   0.750 
                 
                   B = 
                   0.250 
                   0.275 
                   0.300 
                   0.325 
                   0.350 
                   0.375 
                   0.400 
                   0.425 
                   0.450 
                   0.475 
                   0.500 
                   0.525 
                   0.550 
                   0.575 
                   0.600 
                   0.625 
                   0.650 
                   0.675 
                   0.700 
                   0.725 
                   0.750 
                 
                   E = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.225 
                   0.238 
                   0.250 
                   0.263 
                   0.275 
                   0.288 
                   0.300 
                   0.313 
                   0.325 
                   0.338 
                   0.350 
                   0.363 
                   0.375 
                 
                   “Y” = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.225 
                   0.238 
                   0.250 
                   0.263 
                   0.275 
                   0.288 
                   0.300 
                   0.313 
                   0.325 
                   0.338 
                   0.350 
                   0.363 
                   0.375 
                 
                   “X” = 
                   2.866 
                   3.152 
                   3.439 
                   3.725 
                   4.012 
                   4.299 
                   4.585 
                   4.872 
                   5.158 
                   5.445 
                   5.731 
                   6.018 
                   6.305 
                   6.591 
                   6.878 
                   7.164 
                   7.451 
                   7.737 
                   8.024 
                   8.311 
                   8.597 
                 
                   Roll Radius 
                   2.868 
                   3.155 
                   3.442 
                   3.729 
                   4.016 
                   4.303 
                   4.589 
                   4.876 
                   5.163 
                   5.450 
                   5.737 
                   6.024 
                   6.311 
                   6.597 
                   6.884 
                   7.171 
                   7.458 
                   7.745 
                   8.032 
                   8.318 
                   8.605 
                 
                   Loft Angle 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                   3 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.013 
                   0.014 
                   0.016 
                   0.017 
                   0.018 
                   0.020 
                   0.021 
                   0.022 
                   0.024 
                   0.025 
                   0.026 
                   0.027 
                   0.029 
                   0.030 
                   0.031 
                   0.033 
                   0.034 
                   0.035 
                   0.037 
                   0.038 
                   0.039 
                 
                   C = 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                 
                   h = 
                   0.013 
                   0.014 
                   0.016 
                   0.017 
                   0.018 
                   0.020 
                   0.021 
                   0.022 
                   0.024 
                   0.025 
                   0.026 
                   0.028 
                   0.029 
                   0.030 
                   0.031 
                   0.033 
                   0.034 
                   0.035 
                   0.037 
                   0.038 
                   0.039 
                 
                   Diameter = 
                   4.783 
                   5.262 
                   5.740 
                   6.218 
                   6.697 
                   7.175 
                   7.653 
                   8.132 
                   8.610 
                   9.088 
                   9.567 
                   10.045 
                   10.523 
                   11.002 
                   11.480 
                   11.958 
                   12.437 
                   12.915 
                   13.393 
                   13.872 
                   14.350 
                 
                   D = 
                   0.250 
                   0.275 
                   0.300 
                   0.325 
                   0.350 
                   0.375 
                   0.400 
                   0.425 
                   0.450 
                   0.475 
                   0.500 
                   0.525 
                   0.550 
                   0.575 
                   0.600 
                   0.625 
                   0.650 
                   0.675 
                   0.700 
                   0.725 
                   0.750 
                 
                   B = 
                   0.250 
                   0.275 
                   0.300 
                   0.325 
                   0.350 
                   0.375 
                   0.400 
                   0.425 
                   0.450 
                   0.475 
                   0.500 
                   0.525 
                   0.550 
                   0.575 
                   0.600 
                   0.625 
                   0.650 
                   0.675 
                   0.700 
                   0.725 
                   0.750 
                 
                   E = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.225 
                   0.238 
                   0.250 
                   0.263 
                   0.275 
                   0.288 
                   0.300 
                   0.313 
                   0.325 
                   0.338 
                   0.350 
                   0.363 
                   0.375 
                 
                   “Y” = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.225 
                   0.238 
                   0.250 
                   0.263 
                   0.275 
                   0.288 
                   0.300 
                   0.313 
                   0.325 
                   0.338 
                   0.350 
                   0.363 
                   0.375 
                 
                   “X” = 
                   2.388 
                   2.627 
                   2.866 
                   3.105 
                   3.344 
                   3.583 
                   3.821 
                   4.060 
                   4.299 
                   4.538 
                   4.777 
                   5.016 
                   5.255 
                   5.493 
                   5.732 
                   5.971 
                   6.210 
                   6.449 
                   6.688 
                   6.926 
                   7.165 
                 
                   Roll Radius 
                   2.392 
                   2.631 
                   2.870 
                   3.109 
                   3.348 
                   3.588 
                   3.827 
                   4.066 
                   4.305 
                   4.544 
                   4.783 
                   5.023 
                   5.262 
                   5.501 
                   5.740 
                   5.979 
                   6.218 
                   6.458 
                   6.697 
                   6.936 
                   7.175 
                 
                   Loft Angle 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                   3.5 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.015 
                   0.017 
                   0.018 
                   0.020 
                   0.021 
                   0.023 
                   0.024 
                   0.026 
                   0.027 
                   0.029 
                   0.031 
                   0.032 
                   0.034 
                   0.035 
                   0.037 
                   0.038 
                   0.040 
                   0.041 
                   0.043 
                   0.044 
                   0.046 
                 
                   C = 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.001 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.003 
                   0.003 
                   0.003 
                   0.003 
                 
                   h = 
                   0.015 
                   0.017 
                   0.018 
                   0.020 
                   0.021 
                   0.023 
                   0.024 
                   0.026 
                   0.028 
                   0.029 
                   0.031 
                   0.032 
                   0.034 
                   0.035 
                   0.037 
                   0.038 
                   0.040 
                   0.041 
                   0.043 
                   0.044 
                   0.046 
                 
                   Diameter = 
                   4.103 
                   4.513 
                   4.923 
                   5.334 
                   5.744 
                   6.154 
                   6.564 
                   6.975 
                   7.385 
                   7.795 
                   8.206 
                   8.616 
                   9.026 
                   9.436 
                   9.847 
                   10.257 
                   10.667 
                   1.077 
                   11.488 
                   11.898 
                   12.308 
                 
                   D = 
                   0.250 
                   0.275 
                   0.300 
                   0.325 
                   0.350 
                   0.375 
                   0.400 
                   0.425 
                   0.450 
                   0.475 
                   0.500 
                   0.525 
                   0.550 
                   0.575 
                   0.600 
                   0.625 
                   0.650 
                   0.675 
                   0.700 
                   0.725 
                   0.750 
                 
                   B = 
                   0.250 
                   0.275 
                   0.300 
                   0.325 
                   0.350 
                   0.375 
                   0.400 
                   0.425 
                   0.450 
                   0.475 
                   0.500 
                   0.525 
                   0.550 
                   0.575 
                   0.600 
                   0.625 
                   0.650 
                   0.675 
                   0.700 
                   0.725 
                   0.750 
                 
                   E = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.225 
                   0.238 
                   0.250 
                   0.263 
                   0.275 
                   0.288 
                   0.300 
                   0.313 
                   0.325 
                   0.338 
                   0.350 
                   0.363 
                   0.375 
                 
                   “Y” = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.225 
                   0.238 
                   0.250 
                   0.263 
                   0.275 
                   0.288 
                   0.300 
                   0.313 
                   0.325 
                   0.338 
                   0.350 
                   0.363 
                   0.375 
                 
                   “X” = 
                   2.048 
                   2.252 
                   2.457 
                   2.662 
                   2.867 
                   3.071 
                   3.276 
                   3.481 
                   3.686 
                   3.890 
                   4.095 
                   4.300 
                   4.505 
                   4.709 
                   4.914 
                   5.119 
                   5.324 
                   5.528 
                   5.733 
                   5.938 
                   6.143 
                 
                   Roll Radius 
                   2.051 
                   2.257 
                   2.462 
                   2.667 
                   2.872 
                   3.077 
                   3.282 
                   3.487 
                   3.692 
                   3.898 
                   4.103 
                   4.308 
                   4.513 
                   4.718 
                   4.923 
                   5.128 
                   5.334 
                   5.539 
                   5.744 
                   5.949 
                   6.154 
                 
                   Loft Angle 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                   4 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.017 
                   0.019 
                   0.021 
                   0.023 
                   0.024 
                   0.026 
                   0.028 
                   0.030 
                   0.031 
                   0.033 
                   0.035 
                   0.037 
                   0.038 
                   0.040 
                   0.042 
                   0.044 
                   0.045 
                   0.047 
                   0.049 
                   0.051 
                   0.052 
                 
                   C = 
                   0,001 
                   0.001 
                   0.001 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.003 
                   0/003 
                   0/003 
                   0.003 
                   0.003 
                   0.003 
                   0.003 
                   0.003 
                   0.004 
                   0.004 
                 
                   h = 
                   0.017 
                   0.019 
                   0.021 
                   0.023 
                   0.024 
                   0.026 
                   0.028 
                   0.030 
                   0.031 
                   0.033 
                   0.035 
                   0.037 
                   0.038 
                   0.040 
                   0.042 
                   0.044 
                   0.045 
                   0.047 
                   0.049 
                   0.051 
                   0.052 
                 
                   Diameter = 
                   3.593 
                   3.952 
                   4.311 
                   4.670 
                   5.030 
                   5.389 
                   5.748 
                   6.108 
                   6.467 
                   6.826 
                   7.185 
                   7.545 
                   7.904 
                   8.263 
                   8.622 
                   8.982 
                   9.341 
                   9.700 
                   10.059 
                   10.419 
                   10.778 
                 
                   D = 
                   0.249 
                   0.274 
                   0.299 
                   0.324 
                   0.349 
                   0.374 
                   0.399 
                   0.424 
                   0.449 
                   0.474 
                   0.499 
                   0.524 
                   0.549 
                   0.574 
                   0.599 
                   0.623 
                   0.648 
                   0.673 
                   0.698 
                   0.723 
                   0.748 
                 
                   B = 
                   0.251 
                   0.276 
                   0.301 
                   0.326 
                   0.351 
                   0.376 
                   0.401 
                   0.426 
                   0.451 
                   0.476 
                   0.501 
                   0.526 
                   0.551 
                   0.576 
                   0.601 
                   0.627 
                   0.652 
                   0.677 
                   0.702 
                   0.727 
                   0.752 
                 
                   E = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.226 
                   0.238 
                   0.251 
                   0.263 
                   0.276 
                   0.288 
                   0.301 
                   0.313 
                   0.326 
                   0.338 
                   0.351 
                   0.363 
                   0.376 
                 
                   “Y” = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.226 
                   0.238 
                   0.251 
                   0.263 
                   0.276 
                   0.288 
                   0.301 
                   0.313 
                   0.326 
                   0.338 
                   0.351 
                   0.363 
                   0.376 
                 
                   “X” = 
                   1.792 
                   1.971 
                   2.150 
                   2.330 
                   2.509 
                   2.688 
                   2.867 
                   3.046 
                   3.226 
                   3.405 
                   3.584 
                   3.763 
                   3.942 
                   4.121 
                   4.301 
                   4.480 
                   4.659 
                   4.838 
                   5.017 
                   5.197 
                   5.376 
                 
                   Roll Radius 
                   1.796 
                   1.976 
                   2.156 
                   2.335 
                   2.515 
                   2.694 
                   2.874 
                   3.054 
                   3.233 
                   3.413 
                   3.593 
                   3.772 
                   3.952 
                   4.132 
                   4.311 
                   4.491 
                   4.670 
                   4.850 
                   5.030 
                   5.209 
                   5.389 
                 
                   Loft Angle 
                   4.5 
                   4.5 
                   4.5 
                   4.5 
                   4.5 
                   4.5 
                   4.5 
                   4.5 
                   4.5 
                   4.5 
                   4.5 
                   4.5 
                   4.5 
                   4.5 
                   4.5 
                   4.5 
                   4.5  
                   4.5 
                   4.5 
                   4.5 
                   4.5 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.020 
                   0.022 
                   0.024 
                   0.025 
                   0.027 
                   0.029 
                   0.031 
                   0.033 
                   0.035 
                   0.037 
                   0.039 
                   0.041 
                   0.043 
                   0.045 
                   0.047 
                   0.049 
                   0.051 
                   0.053 
                   0.055 
                   0.057 
                   0.059 
                 
                   C = 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.003 
                   0.003 
                   0.003 
                   0.003 
                   0.003 
                   0.003 
                   0.004 
                   0.004 
                   0.004 
                   0.004 
                   0.004 
                   0.004 
                   0.004 
                   0.005 
                 
                   h = 
                   0.020 
                   0.022 
                   0.024 
                   0.025 
                   0.027 
                   0.029 
                   0.031 
                   0.033 
                   0.035 
                   0.037 
                   0.039 
                   0.041 
                   0.043 
                   0.045 
                   0.047 
                   0.049 
                   0.051 
                   0.053 
                   0.055 
                   0.057 
                   0.059 
                 
                   Diameter = 
                   3.196 
                   3.516 
                   3.835 
                   4.155 
                   4.475 
                   4.794 
                   5.114 
                   5.434 
                   5.753 
                   6.073 
                   6.392 
                   6.712 
                   7.032 
                   7.351 
                   7.671 
                   7.991 
                   8.310 
                   8.630 
                   8.949 
                   9.269 
                   9.589 
                 
                   D = 
                   0.249 
                   0.274 
                   0.299 
                   0.324 
                   0.349 
                   0.374 
                   0.399 
                   0.424 
                   0.449 
                   0.474 
                   0.499 
                   0.524 
                   0.549 
                   0.574 
                   0.599 
                   0.623 
                   0.648 
                   0.673 
                   0.698 
                   0.723 
                   0.748 
                 
                   B = 
                   0.251 
                   0.276 
                   0.301 
                   0.326 
                   0.351 
                   0.376 
                   0.401 
                   0.426 
                   0.451 
                   0.476 
                   0.501 
                   0.526 
                   0.551 
                   0.576 
                   0.601 
                   0.627 
                   0.652 
                   0.677 
                   0.702 
                   0.727 
                   0.752 
                 
                   E = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.226 
                   0.238 
                   0.251 
                   0.263 
                   0.276 
                   0.288 
                   0.301 
                   0.313 
                   0.326 
                   0.339 
                   0.351 
                   0.363 
                   0.376 
                 
                   “Y” = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.226 
                   0.238 
                   0.251 
                   0.263 
                   0.276 
                   0.288 
                   0.301 
                   0.313 
                   0.326 
                   0.339 
                   0.351 
                   0.363 
                   0.376 
                 
                   “X” = 
                   1.593 
                   1.753 
                   1.912 
                   2.071 
                   2.230 
                   2.390 
                   2.549 
                   2.708 
                   2.868 
                   3.027 
                   3.186 
                   3.346 
                   3.505 
                   3.664 
                   3.824 
                   3.983 
                   4.142 
                   4.302 
                   4.461 
                   4.620 
                   4.780 
                 
                   Roll Radius 
                   1.598 
                   1.758 
                   1.918 
                   2.078 
                   2.237 
                   2.397 
                   2.557 
                   2.717 
                   2.887 
                   3.036 
                   3.196 
                   3.356 
                   3.516 
                   3.676 
                   3.835 
                   3.995 
                   4.155 
                   4.315 
                   4.475 
                   4.635 
                   4.794 
                 
                   Loft Angle 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                   5 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.022 
                   0.024 
                   0.026 
                   0.028 
                   0.031 
                   0.033 
                   0.035 
                   0.037 
                   0.039 
                   0.041 
                   0.044 
                   0.046 
                   0.048 
                   0.050 
                   0.052 
                   0.054 
                   0.057 
                   0.059 
                   0.061 
                   0.063 
                   0.065 
                 
                   C = 
                   0.002 
                   0.002 
                   0.002 
                   0.002 
                   0.003 
                   0.003 
                   0.003 
                   0.003 
                   0.003 
                   0.004 
                   0.004 
                   0.004 
                   0.004 
                   0.004 
                   0.005 
                   0.005 
                   0.005 
                   0.005 
                   0.005 
                   0.006 
                   0.006 
                 
                   h = 
                   0.022 
                   0.024 
                   0.026 
                   0.028 
                   0.031 
                   0.033 
                   0.035 
                   0.037 
                   0.039 
                   0.041 
                   0.044 
                   0.046 
                   0.048 
                   0.050 
                   0.052 
                   0.054 
                   0.057 
                   0.059 
                   0.061 
                   0.063 
                   0.065 
                 
                   Diameter = 
                   2.879 
                   3.167 
                   3.455 
                   3.743 
                   4.031 
                   4.319 
                   4.607 
                   4.895 
                   5.183 
                   5.471 
                   5.759 
                   6.047 
                   6.335 
                   6.623 
                   6.911 
                   7.198 
                   7.486 
                   7.774 
                   8.062 
                   8.350 
                   8.638 
                 
                   D = 
                   0.249 
                   0.274 
                   0.299 
                   0.324 
                   0.349 
                   0.374 
                   0.399 
                   0.424 
                   0.449 
                   0.474 
                   0.499 
                   0.524 
                   0.549 
                   0.574 
                   0.599 
                   0.623 
                   0.648 
                   0.673 
                   0.698 
                   0.723 
                   0.748 
                 
                   B = 
                   0.251 
                   0.276 
                   0.301 
                   0.326 
                   0.351 
                   0.376 
                   0.401 
                   0.426 
                   0.451 
                   0.476 
                   0.501 
                   0.526 
                   0.551 
                   0.576 
                   0.601 
                   0.627 
                   0.652 
                   0.677 
                   0.702 
                   0.727 
                   0.752 
                 
                   E = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.226 
                   0.238 
                   0.251 
                   0.263 
                   0.276 
                   0.288 
                   0.301 
                   0.313 
                   0.326 
                   0.339 
                   0.351 
                   0.363 
                   0.376 
                 
                   “Y” = 
                   0.125 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.226 
                   0.238 
                   0.251 
                   0.263 
                   0.276 
                   0.288 
                   0.301 
                   0.313 
                   0.326 
                   0.339 
                   0.351 
                   0.363 
                   0.376 
                 
                   “X” = 
                   1.434 
                   1.578 
                   1.721 
                   1.864 
                   2.008 
                   2.151 
                   2.295 
                   2.438 
                   2.582 
                   2.725 
                   2.868 
                   3.012 
                   3.155 
                   3.299 
                   3.442 
                   3.586 
                   3.729 
                   3.872 
                   4.016 
                   4.159 
                   4.303 
                 
                   Roll Radius 
                   1.440 
                   1.584 
                   1.728 
                   1.872 
                   2.016 
                   2.160 
                   2.304 
                   2.447 
                   2.591 
                   2.735 
                   2.879 
                   3.023 
                   3.167 
                   3.311 
                   3.455 
                   3.599 
                   3.743 
                   3.887 
                   4.031 
                   4.175 
                   4.319 
                 
                   Loft Angle 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                   5.5 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.024 
                   0.026 
                   0.029 
                   0.031 
                   0.034 
                   0.036 
                   0.038 
                   0.041 
                   0.043 
                   0.046 
                   0.048 
                   0.050 
                   0.053 
                   0.055 
                   0.058 
                   0.060 
                   0.062 
                   0.065 
                   0.067 
                   0.069 
                   0.072 
                 
                   C = 
                   0.002 
                   0.003 
                   0.003 
                   0.003 
                   0.003 
                   0.003 
                   0.004 
                   0.004 
                   0.004 
                   0.004 
                   0.005 
                   0.005 
                   0.005 
                   0.005 
                   0.006 
                   0.006 
                   0.006 
                   0.006 
                   0.006 
                   0.007 
                   0.007 
                 
                   h = 
                   0.024 
                   0.026 
                   0.029 
                   0.031 
                   0.034 
                   0.036 
                   0.038 
                   0.041 
                   0.043 
                   0.046 
                   0.048 
                   0.050 
                   0.053 
                   0.055 
                   0.058 
                   0.060 
                   0.062 
                   0.065 
                   0.067 
                   0.069 
                   0.072 
                 
                   Diameter = 
                   2.620 
                   2.882 
                   3.145 
                   3.407 
                   3.669 
                   3.931 
                   4.193 
                   4.455 
                   4.717 
                   4,979 
                   5.241 
                   5.503 
                   5.765 
                   6.027 
                   6.289 
                   6.551 
                   6.813 
                   7.075 
                   7.337 
                   7.599 
                   7.861 
                 
                   D = 
                   0.249 
                   0.274 
                   0.299 
                   0.324 
                   0.349 
                   0.374 
                   0.399 
                   0.424 
                   0.449 
                   0.474 
                   0.499 
                   0.524 
                   0.549 
                   0.574 
                   0.599 
                   0.623 
                   0.648 
                   0.673 
                   0.698 
                   0.723 
                   0.748 
                 
                   B = 
                   0.251 
                   0.276 
                   0.301 
                   0.326 
                   0.351 
                   0.376 
                   0.401 
                   0.426 
                   0.451 
                   0.476 
                   0.501 
                   0.526 
                   0.551 
                   0.576 
                   0.601 
                   0.627 
                   0.652 
                   0.677 
                   0.702 
                   0.727 
                   0.752 
                 
                   E = 
                   0.126 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.226 
                   0.238 
                   0.251 
                   0.263 
                   0.276 
                   0.288 
                   0.301 
                   0.313 
                   0.327 
                   0.339 
                   0.352 
                   0.363 
                   0.377 
                 
                   “Y” = 
                   0.126 
                   0.138 
                   0.150 
                   0.163 
                   0.175 
                   0.188 
                   0.200 
                   0.213 
                   0.226 
                   0.238 
                   0.251 
                   0.263 
                   0.276 
                   0.288 
                   0.301 
                   0.313 
                   0.327 
                   0.339 
                   0.352 
                   0.363 
                   0.377 
                 
                   “X” = 
                   1.304 
                   1.435 
                   1.565 
                   1.695 
                   1.826 
                   1.956 
                   2.087 
                   2.217 
                   2.348 
                   2.478 
                   2.608 
                   2.739 
                   2.869 
                   3.000 
                   3.130 
                   3.260 
                   3.391 
                   3.521 
                   3.652 
                   3.782 
                   3.913 
                 
                   Roll Radius 
                   1.310 
                   1,441 
                   1.572 
                   1.703 
                   1.834 
                   1.965 
                   2.096 
                   2.227 
                   2.358 
                   2.489 
                   2.620 
                   2.751 
                   2.882 
                   3.013 
                   3.145 
                   3.276 
                   3.407 
                   3.538 
                   3.669 
                   3.800 
                   3.931 
                 
                   Loft Angle 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                   6 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.026 
                   0.029 
                   0.031 
                   0.034 
                   0.037 
                   0.039 
                   0.042 
                   0.044 
                   0.047 
                   0.050 
                   0.052 
                   0.055 
                   0.057 
                   0.060 
                   0.063 
                   0.065 
                   0.068 
                   0.071 
                   0.073 
                   0.076 
                   0.078 
                 
                   C = 
                   0.003 
                   0.003 
                   0.003 
                   0.004 
                   0.004 
                   0.004 
                   0.004 
                   0.005 
                   0.005 
                   0.005 
                   0.005 
                   0.006 
                   0.006 
                   0.006 
                   0.007 
                   0.007 
                   0.007 
                   0.007 
                   0.008 
                   0.008 
                   0.008 
                 
                   h = 
                   0.026 
                   0.029 
                   0.032 
                   0.034 
                   0.037 
                   0.039 
                   0.042 
                   0.045 
                   0.047 
                   0.050 
                   0.053 
                   0.055 
                   0.058 
                   0.060 
                   0.063 
                   0.066 
                   0.068 
                   0.071 
                   0.074 
                   0.076 
                   0.079 
                 
                   Diameter = 
                   2.405 
                   2.645 
                   2.886 
                   3.126 
                   3.367 
                   3.607 
                   3.848 
                   4.088 
                   4.329 
                   4.569 
                   4.810 
                   5.050 
                   5.291 
                   5.531 
                   5.772 
                   6.012 
                   6.253 
                   6.493 
                   6.734 
                   6.974 
                   7.215 
                 
                   D = 
                   0.249 
                   0.273 
                   0.298 
                   0.323 
                   0.348 
                   0.373 
                   0.398 
                   0.423 
                   0.448 
                   0.472 
                   0.497 
                   0.522 
                   0.547 
                   0.572 
                   0.597 
                   0.622 
                   0.646 
                   0.671 
                   0.696 
                   0.721 
                   0.746 
                 
                   B = 
                   0.251 
                   0.277 
                   0.302 
                   0.327 
                   0.352 
                   0.377 
                   0.402 
                   0.427 
                   0.452 
                   0.478 
                   0.503 
                   0.528 
                   0.553 
                   0.578 
                   0.603 
                   0.628 
                   0.654 
                   0.679 
                   0.704 
                   0.729 
                   0.754 
                 
                   E = 
                   0.126 
                   0.138 
                   0.151 
                   0.163 
                   0.176 
                   0.189 
                   0.201 
                   0.214 
                   0.226 
                   0.239 
                   0.251 
                   0.264 
                   0.277 
                   0.289 
                   0.302 
                   0.314 
                   0.327 
                   0.339 
                   0.352 
                   0.364 
                   0.377 
                 
                   “Y” = 
                   0.126 
                   0.138 
                   0.151 
                   0.163 
                   0.176 
                   0.189 
                   0.201 
                   0.214 
                   0.226 
                   0.239 
                   0.251 
                   0.264 
                   0.277 
                   0.289 
                   0.302 
                   0.314 
                   0.327 
                   0.339 
                   0.352 
                   0.364 
                   0.377 
                 
                   “X” = 
                   1.196 
                   1.315 
                   1.435 
                   1.555 
                   1.674 
                   1.794 
                   1.913 
                   2.033 
                   2.153 
                   2.272 
                   2.392 
                   2.511 
                   2.631 
                   2.750 
                   2.870 
                   2.990 
                   3.109 
                   3.229 
                   3.348 
                   3.468 
                   3.588 
                 
                   Roll Radius 
                   1.202 
                   1.323 
                   1.443 
                   1.563 
                   1.683 
                   1.804 
                   1.924 
                   2.044 
                   2.164 
                   2.285 
                   2.405 
                   2.525 
                   2.645 
                   2.766 
                   2.886 
                   3.006 
                   3.126 
                   3.247 
                   3.367 
                   3.487 
                   3.607 
                 
                   Loft Angle 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                   6.5 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.028 
                   0.031 
                   0.034 
                   0.037 
                   0.040 
                   0.042 
                   0.045 
                   0.048 
                   0.051 
                   0.054 
                   0.057 
                   0.059 
                   0.062 
                   0.065 
                   0.068 
                   0.071 
                   0.074 
                   0.076 
                   0.079 
                   0.082 
                   0.085 
                 
                   C = 
                   0.003 
                   0.004 
                   0.004 
                   0.004 
                   0.005 
                   0.005 
                   0.005 
                   0.005 
                   0.006 
                   0.006 
                   0.006 
                   0.007 
                   0.007 
                   0.007 
                   0.008 
                   0.008 
                   0.008 
                   0.009 
                   0.009 
                   0.009 
                   0.010 
                 
                   h = 
                   0.028 
                   0.031 
                   0.034 
                   0.037 
                   0.040 
                   0.043 
                   0.046 
                   0.048 
                   0.051 
                   0.054 
                   0.057 
                   0.060 
                   0.063 
                   0.066 
                   0.068 
                   0.071 
                   0.074 
                   0.077 
                   0.080 
                   0.083 
                   0.085 
                 
                   Diameter = 
                   2.223 
                   2.445 
                   2.667 
                   2.890 
                   3.112 
                   3.334 
                   3.556 
                   3.779 
                   4.001 
                   4.223 
                   4.445 
                   4.668 
                   4.890 
                   5.112 
                   5.334 
                   5.557 
                   5.779 
                   6.001 
                   6.224 
                   6.446 
                   6.668 
                 
                   D = 
                   0.248 
                   0.273 
                   0.298 
                   0.323 
                   0.348 
                   0.373 
                   0.397 
                   0.422 
                   0.447 
                   0.472 
                   0.497 
                   0.522 
                   0.546 
                   0.571 
                   0.596 
                   0.621 
                   0.646 
                   0.671 
                   0.696 
                   0.720 
                   0.745 
                 
                   B = 
                   0.252 
                   0.277 
                   0.302 
                   0.327 
                   0.352 
                   0.377 
                   0.403 
                   0.428 
                   0.453 
                   0.478 
                   0.503 
                   0.528 
                   0.554 
                   0.579 
                   0.604 
                   0.629 
                   0.654 
                   0.679 
                   0.705 
                   0.730 
                   0.755 
                 
                   E = 
                   0.126 
                   0.138 
                   0.151 
                   0.164 
                   0.176 
                   0.189 
                   0.201 
                   0.214 
                   0.226 
                   0.239 
                   0.252 
                   0.264 
                   0.277 
                   0.289 
                   0.302 
                   0.315 
                   0.327 
                   0.340 
                   0.352 
                   0.365 
                   0.377 
                 
                   “Y” = 
                   0.126 
                   0.138 
                   0.151 
                   0.164 
                   0.176 
                   0.189 
                   0.201 
                   0.214 
                   0.226 
                   0.239 
                   0.252 
                   0.264 
                   0.277 
                   0.289 
                   0.302 
                   0.315 
                   0.327 
                   0.340 
                   0.352 
                   0.365 
                   0.377 
                 
                   “X” = 
                   1.104 
                   1.215 
                   1.325 
                   1.435 
                   1.546 
                   1.656 
                   1.767 
                   1.877 
                   1.988 
                   2.098 
                   2.208 
                   2.319 
                   2.249 
                   2.540 
                   2.650 
                   2.761 
                   2.871 
                   2.981 
                   3.092 
                   3.202 
                   3.313 
                 
                   Roll Radius 
                   1.111 
                   1.222 
                   1.334 
                   1.445 
                   1.556 
                   1.667 
                   1.778 
                   1.889 
                   2.000 
                   2.112 
                   2.223 
                   2.334 
                   2.445 
                   2.556 
                   2.667 
                   2.778 
                   2.890 
                   3.001 
                   3.112 
                   3.223 
                   3.334 
                 
                   Loft Angle 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                   7 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.07 
                   0.75 
                   0.08 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.030 
                   0.034 
                   0.037 
                   0.040 
                   0.043 
                   0.046 
                   0.049 
                   0.052 
                   0.055 
                   0.058 
                   0.061 
                   0.064 
                   0.067 
                   0.070 
                   0.073 
                   0.076 
                   0.079 
                   0.082 
                   0.085 
                   0.088 
                   0.091 
                 
                   C = 
                   0.004 
                   0.004 
                   0.004 
                   0.005 
                   0,005 
                   0.006 
                   0.006 
                   0.006 
                   0.007 
                   0.007 
                   0.007 
                   0.008 
                   0.008 
                   0.009 
                   0.009 
                   0.009 
                   0.010 
                   0.010 
                   0.010 
                   0.011 
                   0.011 
                 
                   h = 
                   0.031 
                   0.034 
                   0.037 
                   0.040 
                   0.043 
                   0.046 
                   0.049 
                   0.052 
                   0.055 
                   0.058 
                   0.061 
                   0.064 
                   0.068 
                   0.071 
                   0.074 
                   0.077 
                   0.080 
                   0.083 
                   0.086 
                   0.089 
                   0.092 
                 
                   Diameter = 
                   2.067 
                   2.273 
                   2.480 
                   2.687 
                   2.893 
                   3.100 
                   3.307 
                   3.514 
                   3.720 
                   3.927 
                   4.134 
                   4.340 
                   4.547 
                   4.754 
                   4.960 
                   5.167 
                   5.374 
                   5.580 
                   5.787 
                   5.994 
                   6.200 
                 
                   D = 
                   0.248 
                   0.273 
                   0.298 
                   0.323 
                   0.347 
                   0.372 
                   0.397 
                   0.422 
                   0.447 
                   0.471 
                   0.496 
                   0.521 
                   0.546 
                   0.571 
                   0.596 
                   0.620 
                   0.645 
                   0.670 
                   0.695 
                   0.720 
                   0.744 
                 
                   B = 
                   0.252 
                   0.277 
                   0.302 
                   0.327 
                   0.353 
                   0.378 
                   0.403 
                   0.428 
                   0.453 
                   0.479 
                   0.504 
                   0.529 
                   0.554 
                   0.579 
                   0.605 
                   0.630 
                   0.655 
                   0.680 
                   0.705 
                   0.730 
                   0.756 
                 
                   E = 
                   0.126 
                   0.139 
                   0.151 
                   0.164 
                   0.176 
                   0.189 
                   0.202 
                   0.214 
                   0.227 
                   0.239 
                   0.252 
                   0.264 
                   0.277 
                   0.290 
                   0.302 
                   0.315 
                   0.327 
                   0.340 
                   0.353 
                   0.365 
                   0.378 
                 
                   “Y” = 
                   0.126 
                   0.139 
                   0.151 
                   0.164 
                   0.176 
                   0.189 
                   0.202 
                   0.214 
                   0.227 
                   0.239 
                   0.252 
                   0.264 
                   0.277 
                   0.290 
                   0.302 
                   0.315 
                   0.327 
                   0.340 
                   0.353 
                   0.365 
                   0.378 
                 
                   “X” = 
                   1.026 
                   1.128 
                   1.231 
                   1.333 
                   1.436 
                   1.539 
                   1.641 
                   1.744 
                   1.846 
                   1.949 
                   2.051 
                   2.154 
                   2.257 
                   2.359 
                   2.462 
                   2.564 
                   2.667 
                   2.769 
                   2.872 
                   2.974 
                   3.077 
                 
                   Roll Radius 
                   1.033 
                   1.137 
                   1.240 
                   1.343 
                   1.447 
                   1.550 
                   1.653 
                   1.757 
                   1.860 
                   1.963 
                   2.067 
                   2.170 
                   2.273 
                   2.377 
                   2.480 
                   2.583 
                   2.867 
                   2.790 
                   2.893 
                   2.997 
                   3.100 
                 
                   Loft Angle 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                   7.5 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.033 
                   0.036 
                   0.039 
                   0.042 
                   0.046 
                   0.049 
                   0.052 
                   0.055 
                   0.059 
                   0.062 
                   0.065 
                   0.069 
                   0.072 
                   0.075 
                   0.078 
                   0.082 
                   0.085 
                   0.088 
                   0.091 
                   0.095 
                   0.098 
                 
                   C = 
                   0.004 
                   0.005 
                   0.005 
                   0.006 
                   0.006 
                   0.006 
                   0.007 
                   0.007 
                   0.008 
                   0.008 
                   0.009 
                   0.009 
                   0.009 
                   0.010 
                   0.010 
                   0.011 
                   0.011 
                   0.012 
                   0.012 
                   0.012 
                   0.013 
                 
                   h = 
                   0.033 
                   0.036 
                   0.039 
                   0.043 
                   0.046 
                   0.049 
                   0.053 
                   0.056 
                   0.059 
                   0.063 
                   0.066 
                   0.069 
                   0.072 
                   0.076 
                   0.079 
                   0.082 
                   0.086 
                   0.089 
                   0.092 
                   0.095 
                   0.099 
                 
                   Diameter = 
                   1.932 
                   2.125 
                   2.318 
                   2.511 
                   2.705 
                   2.898 
                   3.091 
                   3.284 
                   3.477 
                   3.671 
                   3.864 
                   4.057 
                   4.250 
                   4.443 
                   4.636 
                   4.830 
                   5.023 
                   5.216 
                   5.409 
                   5.602 
                   5.796 
                 
                   D = 
                   0.248 
                   0.273 
                   0.297 
                   0.322 
                   0.347 
                   0.372 
                   0.397 
                   0.421 
                   0.446 
                   0.471 
                   0.496 
                   0.521 
                   0.545 
                   0.570 
                   0.595 
                   0.620 
                   0.644 
                   0.669 
                   0.694 
                   0.719 
                   0.744 
                 
                   B = 
                   0.252 
                   0.277 
                   0.303 
                   0.328 
                   0.353 
                   0.378 
                   0.403 
                   0.429 
                   0.454 
                   0.479 
                   0.504 
                   0.530 
                   0.555 
                   0.580 
                   0.605 
                   0.630 
                   0.656 
                   0.681 
                   0.706 
                   0.731 
                   0.756 
                 
                   E = 
                   0.126 
                   0.139 
                   0.151 
                   0.164 
                   0.177 
                   0.189 
                   0.202 
                   0.214 
                   0.227 
                   0.240 
                   0.252 
                   0.265 
                   0.277 
                   0.290 
                   0.303 
                   0.315 
                   0.328 
                   0.340 
                   0.353 
                   0.366 
                   0.378 
                 
                   “Y” = 
                   0.126 
                   0.139 
                   0.151 
                   0.164 
                   0.177 
                   0.189 
                   0.202 
                   0.214 
                   0.227 
                   0.240 
                   0.252 
                   0.265 
                   0.277 
                   0.290 
                   0.303 
                   0.315 
                   0.328 
                   0.340 
                   0.353 
                   0.366 
                   0.378 
                 
                   “X” = 
                   0.958 
                   1.053 
                   1.149 
                   1.245 
                   1.341 
                   1.436 
                   1.632 
                   1.628 
                   1.724 
                   1.820 
                   1.915 
                   2.011 
                   2.107 
                   2.203 
                   2.298 
                   2.394 
                   2.490 
                   2.586 
                   2.681 
                   2.777 
                   2.873 
                 
                   Roll Radius 
                   0.966 
                   1.063 
                   1.159 
                   1.256 
                   1.352 
                   1.449 
                   1.545 
                   1.642 
                   1.739 
                   1.835 
                   1.932 
                   2.028 
                   2.125 
                   2.222 
                   2.318 
                   2.415 
                   2.511 
                   2.608 
                   2.705 
                   2.801 
                   2.898 
                 
                   Loft Angle 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                   8 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calculations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.035 
                   0.038 
                   0.042 
                   0.045 
                   0.049 
                   0.052 
                   0.056 
                   0.059 
                   0.063 
                   0.066 
                   0.070 
                   0.073 
                   0.077 
                   0.080 
                   0.084 
                   0.087 
                   0.090 
                   0.094 
                   0.097 
                   0.101 
                   0.104 
                 
                   C = 
                   0.005 
                   0.005 
                   0.006 
                   0.006 
                   0.007 
                   0.007 
                   0.008 
                   0.008 
                   0.009 
                   0.009 
                   0.010 
                   0.010 
                   0.011 
                   0.011 
                   0.012 
                   0.012 
                   0.013 
                   0.013 
                   0.014 
                   0.014 
                   0.015 
                 
                   h = 
                   0.035 
                   0.039 
                   0.042 
                   0.046 
                   0.049 
                   0.053 
                   0.056 
                   0.060 
                   0.063 
                   0.067 
                   0.070 
                   0.074 
                   0.077 
                   0.081 
                   0.084 
                   0.088 
                   0.091 
                   0.095 
                   0.098 
                   0.102 
                   0.105 
                 
                   Diameter = 
                   1.814 
                   1.995 
                   2.177 
                   2.358 
                   2.540 
                   2.721 
                   2.902 
                   3.084 
                   3.265 
                   3.447 
                   3.628 
                   3.809 
                   3.991 
                   4.172 
                   4.354 
                   4.535 
                   4.716 
                   4.898 
                   5.079 
                   5.261 
                   5.442 
                 
                   D = 
                   0.248 
                   0.272 
                   0.297 
                   0.322 
                   0.347 
                   0.371 
                   0.396 
                   0.421 
                   0.446 
                   0.470 
                   0.495 
                   0.520 
                   0.545 
                   0.569 
                   0.594 
                   0.619 
                   0.644 
                   0.668 
                   0.693 
                   0.718 
                   0.743 
                 
                   B = 
                   0.252 
                   0.278 
                   0.303 
                   0.328 
                   0.353 
                   0.379 
                   0.404 
                   0.429 
                   0.454 
                   0.480 
                   0.505 
                   0.530 
                   0.555 
                   0.581 
                   0.606 
                   0.631 
                   0.656 
                   0.682 
                   0.707 
                   0.732 
                   0.757 
                 
                   E = 
                   0.126 
                   0.139 
                   0.151 
                   0.164 
                   0.177 
                   0.189 
                   0.202 
                   0.215 
                   0.227 
                   0.240 
                   0.252 
                   0.265 
                   0.278 
                   0.290 
                   0.303 
                   0.316 
                   0.328 
                   0.341 
                   0.353 
                   0.366 
                   0.379 
                 
                   “Y” = 
                   0.126 
                   0.139 
                   0.151 
                   0.164 
                   0.177 
                   0.189 
                   0.202 
                   0.215 
                   0.227 
                   0.240 
                   0.252 
                   0.265 
                   0.278 
                   0.290 
                   0.303 
                   0.316 
                   0.328 
                   0.341 
                   0.353 
                   0.366 
                   0.379 
                 
                   “X” = 
                   0.898 
                   0.988 
                   1.078 
                   1.168 
                   1.257 
                   1.347 
                   1.437 
                   1.527 
                   1.617 
                   1.707 
                   1.796 
                   1.886 
                   1.976 
                   2.066 
                   2.156 
                   2.245 
                   2.335 
                   2.425 
                   2.515 
                   2.605 
                   2.694 
                 
                   Roll Radius 
                   0.907 
                   0.998 
                   1.088 
                   1.179 
                   1.270 
                   1.360 
                   1.451 
                   1.542 
                   1.633 
                   1.723 
                   1.814 
                   1.905 
                   1.995 
                   2.086 
                   2.177 
                   2.267 
                   2.358 
                   2.449 
                   2.540 
                   2.630 
                   2.721 
                 
                   Loft Angle 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                   8.5 
                 
                   Face Height 
                   0.5 
                   0.55 
                   0.6 
                   0.65 
                   0.7 
                   0.75 
                   0.8 
                   0.85 
                   0.9 
                   0.95 
                   1 
                   1.05 
                   1.1 
                   1.15 
                   1.2 
                   1.25 
                   1.3 
                   1.35 
                   1.4 
                   1.45 
                   1.5 
                 
                 
               
                   Calcalations 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
                 
               
                   A = 
                   0.037 
                   0.041 
                   0.044 
                   0.048 
                   0.052 
                   0.055 
                   0.059 
                   0.063 
                   0.067 
                   0.070 
                   0.074 
                   0.078 
                   0.081 
                   0.085 
                   0.089 
                   0.092 
                   0.096 
                   0.100 
                   0.103 
                   0.107 
                   0.111 
                 
                   C = 
                   0.006 
                   0.006 
                   0.007 
                   0.007 
                   0.008 
                   0.008 
                   0.009 
                   0.009 
                   0.010 
                   0.010 
                   0.011 
                   0.012 
                   0.012 
                   0.013 
                   0.013 
                   0.014 
                   0.014 
                   0.015 
                   0.015 
                   0.016 
                   0.017 
                 
                   h = 
                   0.037 
                   0.041 
                   0.045 
                   0.049 
                   0.052 
                   0.056 
                   0.060 
                   0.064 
                   0.067 
                   0.071 
                   0.075 
                   0.078 
                   0.082 
                   0.086 
                   0.090 
                   0.093 
                   0.097 
                   0.101 
                   0.105 
                   0.108 
                   0.112 
                 
                   Diameter = 
                   1.710 
                   1.881 
                   2.052 
                   2.223 
                   2.394 
                   2.565 
                   2.736 
                   2.907 
                   3.078 
                   3.249 
                   3.420 
                   3.591 
                   3.762 
                   3.933 
                   4.104 
                   4.275 
                   4.446 
                   4.617 
                   4.788 
                   4.959 
                   5.130 
                 
                   D = 
                   0.247 
                   0.272 
                   0.297 
                   0.321 
                   0.346 
                   0.371 
                   0.396 
                   0.420 
                   0.445 
                   0.470 
                   0.495 
                   0.519 
                   0.544 
                   0.569 
                   0.593 
                   0.618 
                   0.643 
                   0.668 
                   0.692 
                   0.717 
                   0.742 
                 
                   B = 
                   0.253 
                   0.278 
                   0.303 
                   0.329 
                   0.354 
                   0.379 
                   0.404 
                   0.430 
                   0.455 
                   0.480 
                   0.506 
                   0.531 
                   0.556 
                   0.581 
                   0.607 
                   0.632 
                   0.657 
                   0.682 
                   0.708 
                   0.733 
                   0.758 
                 
                   E= 
                   0.126 
                   0.139 
                   0.152 
                   0.164 
                   0.177 
                   0.190 
                   0.202 
                   0.215 
                   0.227 
                   0.240 
                   0.253 
                   0.265 
                   0.278 
                   0.291 
                   0.303 
                   0.316 
                   0.329 
                   0.341 
                   0.354 
                   0.367 
                   0.379 
                 
                   “Y” = 
                   0.126 
                   0.139 
                   0.152 
                   0.164 
                   0.177 
                   0.190 
                   0.202 
                   0.215 
                   0.227 
                   0.240 
                   0.253 
                   0.265 
                   0.278 
                   0.291 
                   0.303 
                   0.316 
                   0.329 
                   0.341 
                   0.354 
                   0.367 
                   0.379 
                 
                   “X” = 
                   0.846 
                   0.930 
                   1.015 
                   1.099 
                   1.184 
                   1.269 
                   1.353 
                   1.438 
                   1.522 
                   1.607 
                   1.691 
                   1.776 
                   1.861 
                   1.945 
                   2.030 
                   2.114 
                   2.199 
                   2.283 
                   2.368 
                   2.452 
                   2.537 
                 
                   Roll Radius 
                   0.855 
                   0.941 
                   1.026 
                   1.112 
                   1.197 
                   1.283 
                   1.368 
                   1.454 
                   1.539 
                   1.625 
                   1.710 
                   1.796 
                   1.881 
                   1.967 
                   2.052 
                   2.138 
                   2.223 
                   2.309 
                   2.394 
                   2.480 
                   2.565 
                 
                     
                 
                     
                 
             
                
                
               
               
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
             
                
               
            
             
                
                
                
                
                
                
                
                
                
                
                
                
               
            
           
         
       
       as comprising FIGS. 20A through 20E, inclusive, of the Drawings.  
     
     
         19 . The improved curved strike face putter of  claim 18 , wherein said true roll impact zone falls within the range of approximately 0.015 inch to 0.073 inch below the ball's equator.  
     
     
         20 . An improved vertically-curved face golf putter formed with a curved strike for having an optimal roll radius so as to permit consistently impacting a golf ball, regardless of a specific golfers putting stroke style, within the true roll impact zone below the golf ball's equator, said curved strike face having a given face height and a selected static loft, said face height and static loft, and the resultant said optimal roll radius thereof, are as set forth in the charts comprising FIGS. 20A through 20E, inclusive, of the Drawings.  
     
     
         21 . The improved vertically-curved face golf putter of  claim 20 , and wherein the required X- and Y- displacements for locating the center of curvature for the resultant said optimal roll radius are as given in the charts comprising FIGS. 20A through 20E, inclusive, of the Drawings.  
     
     
         22 . The invention of  claim 20 , and wherein said putter includes two different roll radii, a first roll radius being the primary strike roll radius for impacting the golf ball in the true roll impact zone, said first roll radius vertically extending within the range of approximately 45% to 85% of the lower height of said curved strike face; a second roll radius being provided to create the visual appearance of a curved strike face, said second roll radius vertically extending within the range of approximately 15% to 40% of the upper height of said curved strike face; and the radius of said second roll radius is less than the radius of said first roll radius.  
     
     
         23 . The invention of  claim 22 , and a third roll radius for said curved strike face and formed at the lowermost edge portion of said curved strike face.  
     
     
         24 . The invention of  claim 22 , wherein the value for said first roll radius is selected from the charts of FIGS. 20A to  20 E, inclusive, of the Drawings.

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