Abstract:
A piston/cylinder type engine having increased horsepower and torque wherein the basic components of the engine are constructed and arranged as a standard production single cylinder, “in-line” or “V” engine, but wherein one or more cylinders are bored at an angle of from about 0.025° up to about 15° around the axis of the wrist pin affixing the piston to a connecting rod at TDC, to thereby rotate the bore axis laterally of the crankshaft axis while retaining conventional intersection of the crankshaft axis with the wrist pin axis.

Description:
This application claims priority under 35 U.S.C. 119(e)(1) based on Applicants Provisional U.S. Patent Application Ser. No. 60/276,165 filed Mar. 15, 2001 and titled “Angle Bored Cylinder Engine”. 
    
    
     BACKGROUND OF INVENTION 
     1. Field 
     The present invention concerns piston/cylinder type engines, particularly internal combustion engines and gas compressors, wherein in accordance with the present invention the cylinders are angle bored, e.g., up to about 15 degrees or more with respect to the bore of conventional engines wherein each cylinder bore is aligned with both of its associated crankpin axis and crankshaft axis at top dead center and bottom dead center of the piston. The present angle bore gives enhanced operation to the engine such as increased horsepower and/or efficiency. 
     2. Prior Art 
     The concept of parallel offsetting of the cylinder bore axis to one side of the crankshaft axis in order to enhance the operations of internal combustion engines and compressors is well documented in the literature as evidenced by U.S. Pat. Nos. 3,985,475; 5,186,127; 5,394,839; and 5,076,220, the disclosures of which are hereby incorporated herein in their entireties. 
     It is apparent from these disclosures that at least most of the major structural components of these engines such as cylinder block, crankshaft, crankpin, connecting rod, camshaft, head, intake and exhaust systems and the like must be specifically designed to accommodate the offset, as well as altering operative elements of combustion such as ignition timing. In other words such offset engines are, for the most part, manufactured from the ground up rather than by a simple modification of existing conventional engines or of their manufacturing processes. 
     The present invention makes it a relatively simple matter however, to modify an actual existing conventional single cylinder, “in-line” or “V” engine, or to modify its manufacturing process to produce the present angle bored cylinder engine whereby giving the cylinder bore an angled axis is the only significant structural alteration required. 
     SUMMARY OF THE INVENTION 
     The present invention is summarized as a piston/cylinder type engine wherein the basic components of the engine are constructed and arranged as a standard production single cylinder, “in-line”, “opposed cylinder”, or “V” engine, but wherein one or more cylinders are bored at an angle “α” of from about 0.025° up to about 15° around the axis or very near, e.g., a few thousandths of an inch, the axis of the wrist pin affixing the piston to a connecting rod at TDC, to thereby rotate the bore axis generally laterally of the crankshaft axis while retaining intersection of the crankshaft axis with the wrist pin axis as in conventional engines. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention will be further understood from the drawings herein wherein the structures shown are not drawn to scale or proportion, and wherein: 
     FIG. 1 is a schematic of pertinent structures an internal combustion engine showing exaggerated piston/cylinder clearance for clarity; and 
     FIGS. 2-6 shows a basic conventional small-block V8 engine cylinder case with nominal dimensions, to which the present invention is applicable; and 
     FIG. 7 shows a comparison of side forces generated by the present ABC engine and a traditional engine. 
    
    
     DETAILED DESCRIPTION 
     Shown in FIG. 1 are basic components, not in proportion or to scale, of a conventional internal combustion engine comprising crankshaft  10  having a center or axis  11 , crankpin  12  having a center or axis  13 , piston  14  shown at TDC (top dead center), piston rings  15 , wrist pin  16  having a center or axis  25 , connecting rod  17 , block  18  having a planar cylinder bank face means  19 , cylinder bore  20  having a bore axis  21  at right angle to face means  19 , head  22  and compression chamber  24  in the head. A typical engine size would be a 350 cu. in., that is, the piston is 4 in., in diameter with 1½″ extending above the center  25  (axis) of the wrist pin, wherein the connecting rod is  6 ″ center (axis  25 ) to center (axis  13 ), and the crankpin generates a 3½″ piston stroke. The center (axis  11 ) of the mains to the top  19  of the block is 9.025 in. 
     In FIG. 1, the dotted bore lines  26  represent the diameter of bore  23  angled as “α” in accordance with the present invention wherein the axis  28  of the angled bore passes through the center (axis)  25  of the wrist pin. It is noted that where the angled bore  23  represents a reboring of a conventional cylinder bore such as  20 , it may be desirable to employ an oversized piston in known manner, particularly where the bore angle α is in the higher portion of the range. 
     With reference to FIG.  1  and the claims hereof the present invention comprises a gas compression and/or expansion engine having cylinder block means  18  formed with a planar cylinder bank face means  19 , a cylinder bore  23  formed in said block means on a bore axis  28  and opening thru said face means  19 , a crankshaft  10  mounted in said block means and having an axis  11  lying parallel to said face means  19 , a piston  14  reciprocably positioned in said cylinder, a wrist pin  16  having an axis  25  and mounted thru one end of a connecting rod  17 , the other end of said rod being rotatably mounted on a crankpin  12  of said crankshaft, said crankpin having an axis  13  parallel to said crankshaft axis, wherein said wrist pin axis and crankshaft axis lie in a common plane  30  which intersects said planar face means  19  at a right angle, wherein said cylinder bore axis  28  is angled around said wrist pin axis  25  from 0.025 to 15 degrees with respect to said common plane  30  whereby said common plane and bore axis intersect at said wrist pin axis. It is noted that with reference to FIG. 1, for an internal combustion engine said the crankshaft rotation is clockwise, while in a gas compressor the rotation is counterclockwise. 
     For engines having the present angled bore, the intake and exhaust valves can, without adjustment, open and close also at the theoretical TDC and BDC of the conventional engine. It is noted however that since the piston in the present angle bored cylinder is further down in the cylinder at BDC the intake valving can be adjusted to stay open longer and thus enhance the engine efficiency by increasing the total intake of gases, e.g., fuel air mixture on the suction stroke. Also, the exhaust valving can be adjusted to stay open longer because of the longer power stroke. 
     A hemihead is shown for clarity in the drawing and the invention involves a simple modification to the block that will result in about a 10% increase in power output. The idea is simply to angle bore the cylinder at an angle “α” of a desired value such as a preferred 3° to about 6°, in the direction of crankshaft rotation. The center of rotation of the piston for the angled bore is preferably exactly the location of the center (axis) of the wrist pin at TDC in the conventional engine, and consequently, and very importantly, the connecting rod length, ignition and piston cam timing and TDC remain the same. The angled bore causes the centerline (bore axis) of the cylinder not to intersect with the centerline (axis) of the crankshaft mains. 
     The increase in horsepower in accordance with the present invention results, in a major way, from reducing piston friction through a reduction in the side forces on the piston, which friction is normally generated in conventional engines through contact of the piston and/or rings with the cylinder wall. In this regard, the combustion pressure pushes the piston axially down thru the cylinder, however, the piston pushes the rod and consequently thru opposite forces, the piston itself at a given angle toward the cylinder wall as the crankshaft turns. The equation to determine piston side force directed perpendicular to the cylinder wall is SIN φ Rod Force acting on the crankpin, wherein φ is the angle which the rod axis makes with the cylinder bore axis. 
     A computer generated comparison of the piston side force between a conventional and angle bored cylinder is presented in TABLE I. The average piston side force reduction is 59.9% less with the angle bored (α=4°) cylinder referred to herein as ABC. Computer generated FIG. 7 shows how the force is distributed on the cylinder wall as the crankshaft turns through the power stroke. At 14 degrees there is zero side force with the ABC while the conventional engine has 682 lbs., of side forces. 
     Another factor in increasing horsepower is that the ABC engine keeps the piston higher in the cylinder longer than the conventional engine. When the piston in the ABC engine is at BDC, the conventional engine has passed BDC by, e.g., 3 degrees. This means that for the ABC engine the power stroke is longer, and more importantly, the intake stroke is longer. It is noted that the fuel combustion pressure drops very fast just after TDC, and since gas pressure on the piston is the main factor in producing HP, the longer the piston remains in the higher pressure area the more HP will be attained. 
     Another aspect of increasing horsepower is that the torque produced at any moment is a function of the rod force on the crankpin and the moment arm. The rod force is calculated from the piston force through the rod angle. The moment arm is the distance 90 degrees from the rod force to the axis of the crank (crankshaft). The torque is the rod force multiplied by the moment arm. Shown in computer generated TABLE II is the torque produced every 5 degrees during the power stroke for one cylinder of a conventional engine. The average torque is given in inch-pounds. Computer generated TABLE III shows the increase of 2.37% in torque produced by one (ABC) cylinder. 
     The HP gain from an angle bored cylinder is the result of several factors such as: 
     1. the side load on the piston is significantly less which results in less frictional drag on the piston as well as longer piston and cylinder life; 
     2. the piston stays higher in the cylinder under higher pressure longer than a standard engine giving more time for completing combustion; 
     3. the moment arm becomes longer giving more torque toward the end of the power cycle; and 
     4. the stroke of the engine is longer which allows for a longer intake stroke sucking more fuel in the cylinder for the compression stroke. 
     The engine cylinder being angle bored with its axis crossing the axis of the standard cylinder at the wrist pin center has several advantages over parallel offset cylinders or rods or the like including that: 
     a. the connecting rod is the same length: 
     b. the camshaft timing is the same; 
     c. the ignition timing is the same; and 
     d. the average piston deck height is the same. 
     Using the present invention, many engines now in production can be angle bored and use all of the current production parts. The production cost over current manufactured engines should be nominal with the only significant anticipated production changes being adjustment of the boring and casting machines at start-up. 
     In an actual test, the test engine was an 800 cu. in., engine that was used in a drag race car. The conventional engine had a peak HP of 1598. A second engine block had the cylinders bored at 1.5° from the crankshaft centerline in accordance with the present invention. The parts from the conventional engine were installed in the angle bored block and the peak HP thereof was 1666. 
     The specification for the test engine in its conventional condition are as follows: 
     
       
         
               
               
               
               
             
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 Stroke: 
                 5.750 
                 in. 
               
               
                   
                 Bore: 
                 4,750 
                 in. 
               
               
                   
                 Rod Length: 
                 7.750 
                 in. 
               
               
                   
                 Center of Crankshaft 
                 12.00 
                 in 
               
               
                   
                 To top of block: 
               
             
          
           
               
                   
                 Timing of approximately 25° BTDC. 
               
               
                   
                   
               
             
          
         
       
     
     The invention has been described in detail with particular reference to preferred embodiments thereof, but it will be understood that variations and modifications will be effected with the spirit and scope of the invention. 
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
             
           
               
                 TABLE I 
               
             
             
               
                   
               
               
                 Side Forces* 
               
             
          
           
               
                   
                 ABC 
                 ABC 
                 ABC 
                 Traditional 
                 Traditional 
                 Traditional 
                 Percent 
               
               
                 Crank 
                 Rod 
                 Rod 
                 Side 
                 Rod 
                 Rod 
                 Side 
                 Difference In 
               
               
                 Angle 
                 Force 
                 Angle 
                 Force** 
                 Force 
                 Angle 
                 Force 
                 Side Force 
               
               
                 (degrees) 
                 (lbf) 
                 (degrees) 
                 (lbf) 
                 (lbf) 
                 (degrees) 
                 (lbf) 
                 (%) 
               
               
                   
               
             
          
           
               
                 0 
                 10053.1 
                 0.0 
                 0.0 
                 10053.1 
                 0.0 
                 0.0 
                 0.0 
               
               
                 5 
                 9837.4 
                 −2.5 
                 −437.5 
                 9827.8 
                 1.5 
                 255.6 
                 −271.2 
               
               
                 10 
                 9207.0 
                 −1.1 
                 −179.9 
                 9204.4 
                 2.9 
                 497.8 
                 −136.1 
               
               
                 15 
                 8318.4 
                 0.3 
                 40.4 
                 8314.2 
                 4.3 
                 694.8 
                 −94.2 
               
               
                 20 
                 7320.7 
                 1.6 
                 208.9 
                 7308.4 
                 5.7 
                 829.4 
                 −74.8 
               
               
                 25 
                 6333.0 
                 2.9 
                 324.9 
                 6309.5 
                 7.1 
                 900.9 
                 −63.9 
               
               
                 30 
                 5428.3 
                 4.2 
                 396.2 
                 5393.2 
                 8.4 
                 920.1 
                 −56.9 
               
               
                 35 
                 4638.0 
                 5.4 
                 433.4 
                 4592.8 
                 9.6 
                 902.2 
                 −52.0 
               
               
                 40 
                 3969.4 
                 6.5 
                 446.6 
                 3916.1 
                 10.8 
                 861.1 
                 −48.1 
               
               
                 45 
                 3411.8 
                 7.5 
                 443.6 
                 3352.9 
                 11.9 
                 807.7 
                 −45.1 
               
               
                 50 
                 2951.5 
                 8.4 
                 430.5 
                 2889.1 
                 12.9 
                 749.1 
                 −42.5 
               
               
                 55 
                 2572.1 
                 9.2 
                 411.3 
                 2508.1 
                 13.8 
                 690.3 
                 −40.4 
               
               
                 60 
                 2259.2 
                 9.9 
                 388.7 
                 2195.1 
                 14.6 
                 633.5 
                 −38.6 
               
               
                 65 
                 2000.7 
                 10.5 
                 364.5 
                 1937.7 
                 15.3 
                 580.3 
                 −37.2 
               
               
                 70 
                 1785.7 
                 11.0 
                 339.8 
                 1724.8 
                 15.9 
                 531.1 
                 −36.0 
               
               
                 75 
                 1607.3 
                 11.3 
                 315.4 
                 1549.2 
                 16.4 
                 485.9 
                 −35.1 
               
               
                 80 
                 1457.1 
                 11.5 
                 291.4 
                 1402.2 
                 16.7 
                 445.0 
                 −34.5 
               
               
                 85 
                 1330.3 
                 11.6 
                 268.1 
                 1279.1 
                 16.9 
                 407.4 
                 −34.2 
               
               
                 90 
                 1222.8 
                 11.6 
                 245.6 
                 1175.5 
                 17.0 
                 373.1 
                 −34.2 
               
               
                 95 
                 1131.2 
                 11.4 
                 224.0 
                 1088.0 
                 16.9 
                 341.5 
                 −34.4 
               
               
                 100 
                 1052.9 
                 11.1 
                 203.1 
                 1013.8 
                 16.7 
                 312.5 
                 −35.0 
               
               
                 105 
                 985.6 
                 10.7 
                 183.0 
                 950.7 
                 16.4 
                 285.6 
                 −35.9 
               
               
                 110 
                 927.6 
                 10.2 
                 163.6 
                 896.8 
                 15.9 
                 260.6 
                 −37.2 
               
               
                 115 
                 877.6 
                 9.5 
                 144.8 
                 850.8 
                 15.3 
                 237.1 
                 −38.9 
               
               
                 120 
                 834.4 
                 8.7 
                 126.6 
                 811.4 
                 14.6 
                 214.9 
                 −41.1 
               
               
                 125 
                 797.1 
                 7.8 
                 108.9 
                 777.8 
                 13.8 
                 193.9 
                 −43.9 
               
               
                 130 
                 765.0 
                 6.9 
                 91.6 
                 749.1 
                 12.9 
                 173.8 
                 −47.3 
               
               
                 135 
                 737.4 
                 5.8 
                 74.7 
                 724.6 
                 11.9 
                 154.5 
                 −51.7 
               
               
                 140 
                 713.8 
                 4.7 
                 58.1 
                 703.8 
                 10.8 
                 135.8 
                 −57.3 
               
               
                 145 
                 693.9 
                 3.4 
                 41.7 
                 686.3 
                 9.6 
                 117.7 
                 −64.6 
               
               
                 150 
                 677.3 
                 2.2 
                 25.6 
                 671.8 
                 8.4 
                 100.1 
                 −74.5 
               
               
                 155 
                 663.7 
                 0.8 
                 9.6 
                 660.0 
                 7.1 
                 82.8 
                 −88.4 
               
               
                 160 
                 653.0 
                 −0.6 
                 −6.3 
                 650.6 
                 5.7 
                 65.8 
                 −109.6 
               
               
                 165 
                 645.0 
                 −2.0 
                 −22.2 
                 643.5 
                 4.3 
                 49.1 
                 −145.2 
               
               
                 170 
                 639.4 
                 −3.4 
                 −38.1 
                 638.5 
                 2.9 
                 32.6 
                 −217.0 
               
               
                 175 
                 636.4 
                 −4.9 
                 −54.1 
                 635.6 
                 1.5 
                 16.2 
                 −433.3 
               
               
                 180 
                 635.7 
                 −6.3 
                 −70.2 
                 634.6 
                 0.0 
                 0.0 
                 — 
               
               
                 183.3 
                 636.5 
                 −7.3 
                 −80.9 
                 — 
                 — 
                 — 
                 — 
               
             
          
           
               
                   
                 Average Side Force = 164.3 
                 Average Side Force = 409.7 
                   
               
             
          
           
               
                   
                 Percent Difference of Average Side Force = 59.9% 
               
               
                   
                   
               
               
                   
                 *Side force is perpendicular to cylinder wall.  
               
               
                   
                 **Negative force acts in the opposite direction of positive force.  
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
             
           
               
                 TABLE II 
               
             
             
               
                   
               
               
                 Traditional Engine Parameters 
               
             
          
           
               
                 Crank 
                 Distance 
                 Moment 
                 Rod 
                   
                 Rod 
                 Piston 
                   
               
               
                 Angle 
                 From TDC 
                 Arm 
                 Angle 
                 Pressure 
                 Force 
                 Force 
                 Torque 
               
               
                 (degrees) 
                 (inches) 
                 (inches) 
                 (degrees) 
                 (psig) 
                 (lbf) 
                 (lbf) 
                 (in*lb) 
               
               
                   
               
             
          
           
               
                 0 
                 0.000 
                 0.000 
                 0.000 
                 800.0 
                 10053.1 
                 10053.1 
                 0.0 
               
               
                 5 
                 0.009 
                 0.197 
                 1.457 
                 782.1 
                 9827.8 
                 9824.6 
                 1934.0 
               
               
                 10 
                 0.034 
                 0.391 
                 2.903 
                 732.5 
                 9204.4 
                 9192.6 
                 3596.9 
               
               
                 15 
                 0.077 
                 0.579 
                 4.329 
                 661.6 
                 8314.2 
                 8290.5 
                 4815.9 
               
               
                 20 
                 0.135 
                 0.760 
                 5.725 
                 581.6 
                 7308.4 
                 7272.0 
                 5551.5 
               
               
                 25 
                 0.210 
                 0.929 
                 7.080 
                 502.1 
                 6309.5 
                 6261.4 
                 5864.3 
               
               
                 30 
                 0.299 
                 1.087 
                 8.386 
                 429.2 
                 5393.2 
                 5335.5 
                 5860.5 
               
               
                 35 
                 0.401 
                 1.229 
                 9.630 
                 365.5 
                 4592.8 
                 4528.1 
                 5646.5 
               
               
                 40 
                 0.516 
                 1.356 
                 10.806 
                 311.6 
                 3916.1 
                 3846.7 
                 5311.3 
               
               
                 45 
                 0.642 
                 1.466 
                 11.902 
                 266.8 
                 3352.9 
                 3280.8 
                 4915.5 
               
               
                 50 
                 0.777 
                 1.558 
                 12.911 
                 229.9 
                 2889.1 
                 2816.1 
                 4501.3 
               
               
                 55 
                 0.920 
                 1.632 
                 13.823 
                 199.6 
                 2508.1 
                 2435.4 
                 4092.7 
               
               
                 60 
                 1.070 
                 1.687 
                 14.631 
                 174.7 
                 2195.1 
                 2123.9 
                 3704.1 
               
               
                 65 
                 1.224 
                 1.725 
                 15.328 
                 154.2 
                 1937.7 
                 1868.8 
                 3342.8 
               
               
                 70 
                 1.381 
                 1.746 
                 15.907 
                 137.3 
                 1724.8 
                 1658.7 
                 3010.6 
               
               
                 75 
                 1.540 
                 1.750 
                 16.363 
                 123.3 
                 1549.2 
                 1486.4 
                 2710.3 
               
               
                 80 
                 1.699 
                 1.738 
                 16.693 
                 111.6 
                 1402.2 
                 1343.1 
                 2437.1 
               
               
                 85 
                 1.856 
                 1.712 
                 16.891 
                 101.8 
                 1279.1 
                 1223.9 
                 2190.3 
               
               
                 90 
                 2.011 
                 1.674 
                 16.958 
                 93.5 
                 1175.5 
                 1124.4 
                 1967.7 
               
               
                 95 
                 2.161 
                 1.624 
                 16.891 
                 86.6 
                 1088.0 
                 1041.1 
                 1766.7 
               
               
                 100 
                 2.307 
                 1.564 
                 16.693 
                 80.7 
                 1013.8 
                 971.1 
                 1585.1 
               
               
                 105 
                 2.446 
                 1.494 
                 16.363 
                 75.7 
                 950.7 
                 912.2 
                 1420.6 
               
               
                 110 
                 2.578 
                 1.417 
                 15.907 
                 71.4 
                 896.8 
                 862.5 
                 1271.2 
               
               
                 115 
                 2.703 
                 1.334 
                 15.328 
                 67.7 
                 850.8 
                 820.5 
                 1135.1 
               
               
                 120 
                 2.820 
                 1.245 
                 14.631 
                 64.6 
                 811.4 
                 785.1 
                 1010.6 
               
               
                 125 
                 2.928 
                 1.152 
                 13.823 
                 61.9 
                 777.8 
                 755.3 
                 896.2 
               
               
                 130 
                 3.027 
                 1.055 
                 12.911 
                 59.6 
                 749.1 
                 730.1 
                 790.5 
               
               
                 135 
                 3.116 
                 0.956 
                 11.902 
                 57.7 
                 724.6 
                 709.0 
                 692.4 
               
               
                 140 
                 3.197 
                 0.854 
                 10.806 
                 56.0 
                 703.8 
                 691.3 
                 600.8 
               
               
                 145 
                 3.268 
                 0.750 
                 9.630 
                 54.6 
                 686.3 
                 676.7 
                 514.6 
               
               
                 150 
                 3.330 
                 0.645 
                 8.386 
                 53.5 
                 671.8 
                 664.7 
                 433.1 
               
               
                 155 
                 3.382 
                 0.538 
                 7.080 
                 52.5 
                 660.0 
                 655.0 
                 355.4 
               
               
                 160 
                 3.424 
                 0.432 
                 5.725 
                 51.8 
                 650.6 
                 647.4 
                 280.8 
               
               
                 165 
                 3.457 
                 0.324 
                 4.329 
                 51.2 
                 643.5 
                 641.7 
                 208.5 
               
               
                 170 
                 3.481 
                 0.216 
                 2.903 
                 50.8 
                 638.5 
                 637.7 
                 138.1 
               
               
                 175 
                 3.495 
                 0.108 
                 1.457 
                 50.6 
                 635.6 
                 635.4 
                 68.7 
               
               
                 180 
                 3.500 
                 0.000 
                 0.000 
                 50.5 
                 634.6 
                 634.6 
                 0.0 
               
             
          
           
               
                 Average Torque = 
                 2350.6 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
               
             
           
               
                 TABLE III 
               
             
             
               
                   
               
               
                 ABC Engine Parameters 
               
             
          
           
               
                 Crank 
                 Distance 
                 Moment 
                 Rod 
                   
                 Rod 
                 Piston 
                   
               
               
                 Angle 
                 From TDC 
                 Arm 
                 Angle 
                 Pressure 
                 Force 
                 Force 
                 Torque 
               
               
                 (degrees) 
                 (inches) 
                 (inches) 
                 (degrees) 
                 (psig) 
                 (lbf) 
                 (lbf) 
                 (in*lb) 
               
               
                   
               
             
          
           
               
                 0 
                 0.000 
                 0.000 
                 0.0 
                 800.0 
                 10053.1 
                 10053.1 
                 0.0 
               
               
                 5 
                 0.009 
                 0.197 
                 −2.5 
                 782.1 
                 9837.4 
                 9827.6 
                 1934.2 
               
               
                 10 
                 0.034 
                 0.390 
                 −1.1 
                 732.5 
                 9207.0 
                 9205.2 
                 3591.7 
               
               
                 15 
                 0.077 
                 0.578 
                 0.3 
                 661.9 
                 8318.4 
                 8318.3 
                 4806.1 
               
               
                 20 
                 0.135 
                 0.757 
                 1.6 
                 582.3 
                 7320.7 
                 7317.7 
                 5542.6 
               
               
                 25 
                 0.208 
                 0.926 
                 2.9 
                 503.3 
                 6333.0 
                 6324.6 
                 5863.2 
               
               
                 30 
                 0.296 
                 1.082 
                 4.2 
                 430.8 
                 5428.3 
                 5413.8 
                 5872.7 
               
               
                 35 
                 0.397 
                 1.224 
                 5.4 
                 367.5 
                 4638.0 
                 4617.7 
                 5675.0 
               
               
                 40 
                 0.510 
                 1.350 
                 6.5 
                 313.9 
                 3969.4 
                 3944.2 
                 5357.0 
               
               
                 45 
                 0.634 
                 1.459 
                 7.5 
                 269.2 
                 3411.8 
                 3382.8 
                 4977.2 
               
               
                 50 
                 0.767 
                 1.551 
                 8.4 
                 232.4 
                 2951.5 
                 2919.9 
                 4576.8 
               
               
                 55 
                 0.907 
                 1.625 
                 9.2 
                 202.0 
                 2572.1 
                 2539.0 
                 4179.2 
               
               
                 60 
                 1.053 
                 1.681 
                 9.9 
                 177.1 
                 2259.2 
                 2225.5 
                 3798.6 
               
               
                 65 
                 1.204 
                 1.721 
                 10.5 
                 156.5 
                 2000.7 
                 1967.2 
                 3442.5 
               
               
                 70 
                 1.358 
                 1.743 
                 11.0 
                 139.5 
                 1785.7 
                 1753.1 
                 3113.0 
               
               
                 75 
                 1.514 
                 1.750 
                 11.3 
                 125.4 
                 1607.3 
                 1576.1 
                 2812.8 
               
               
                 80 
                 1.669 
                 1.742 
                 11.5 
                 113.6 
                 1457.1 
                 1427.7 
                 2538.1 
               
               
                 85 
                 1.824 
                 1.720 
                 11.6 
                 103.7 
                 1330.3 
                 1303.0 
                 2288.1 
               
               
                 90 
                 1.975 
                 1.686 
                 11.6 
                 95.3 
                 1222.8 
                 1197.9 
                 2061.2 
               
               
                 95 
                 2.124 
                 1.640 
                 11.4 
                 88.2 
                 1131.2 
                 1108.8 
                 1855.3 
               
               
                 100 
                 2.267 
                 1.584 
                 11.1 
                 82.2 
                 1052.9 
                 1033.1 
                 1668.2 
               
               
                 105 
                 2.405 
                 1.520 
                 10.7 
                 77.1 
                 985.6 
                 968.4 
                 1498.2 
               
               
                 110 
                 2.537 
                 1.448 
                 10.2 
                 72.7 
                 927.6 
                 913.0 
                 1343.3 
               
               
                 115 
                 2.662 
                 1.370 
                 9.5 
                 68.9 
                 877.6 
                 865.5 
                 1201.9 
               
               
                 120 
                 2.779 
                 1.286 
                 8.7 
                 65.6 
                 834.4 
                 824.7 
                 1072.6 
               
               
                 125 
                 2.889 
                 1.197 
                 7.8 
                 62.8 
                 797.1 
                 789.6 
                 954.0 
               
               
                 130 
                 2.990 
                 1.104 
                 6.9 
                 60.4 
                 765.0 
                 759.5 
                 844.7 
               
               
                 135 
                 3.083 
                 1.008 
                 5.8 
                 58.4 
                 737.4 
                 733.6 
                 743.6 
               
               
                 140 
                 3.167 
                 0.910 
                 4.7 
                 56.6 
                 713.8 
                 711.5 
                 649.6 
               
               
                 145 
                 3.242 
                 0.810 
                 3.4 
                 55.1 
                 693.9 
                 692.7 
                 561.7 
               
               
                 150 
                 3.308 
                 0.707 
                 2.2 
                 53.9 
                 677.3 
                 676.8 
                 479.0 
               
               
                 155 
                 3.366 
                 0.604 
                 0.8 
                 52.8 
                 663.7 
                 663.7 
                 400.6 
               
               
                 160 
                 3.414 
                 0.499 
                 −0.6 
                 52.0 
                 653.0 
                 653.0 
                 325.6 
               
               
                 165 
                 3.453 
                 0.393 
                 −2.0 
                 51.3 
                 645.0 
                 644.6 
                 253.4 
               
               
                 170 
                 3.482 
                 0.286 
                 −3.4 
                 50.8 
                 639.4 
                 638.3 
                 183.1 
               
               
                 175 
                 3.503 
                 0.179 
                 −4.9 
                 50.5 
                 636.4 
                 634.1 
                 114.0 
               
               
                 180 
                 3.514 
                 0.071 
                 −6.3 
                 50.3 
                 635.7 
                 631.8 
                 45.4 
               
               
                 183.3 
                 3.516 
                 0.000 
                 −7.3 
                 50.2 
                 636.5 
                 631.4 
                 0.1 
               
             
          
           
               
                   
                 Average Torque = 
                 2406.2 
               
               
                   
                 Traditional Torque = 
                 2350.6 
               
               
                   
                 Percent Increase = 
                 2.37