Abstract:
A firearm cartridge has a case configured with a relatively straight-walled portion and a shoulder portion for housing a quantity of propellant. The case further includes a neck for retaining a bullet. The straight-walled portion defines a base cavity having an interior base diameter. The interior base diameter is approximately twice or more the neck diameter. The diameter ratios of the base and neck optimize combustion efficiency to reduce heat and acceleration losses. The cartridge body cavity is sized and configured to contain a sufficient quantity of propellant such that igniting the propellant causes formation of a propellant plug having a diameter that is approximately the diameter of the bullet, and wherein the propellant plug shears free from unburned propellant that is disposed adjacent the relatively straight-walled body portion

Description:
RELATED APPLICATIONS  
       [0001]    This is a continuation of application Ser. No. 09/946,127, filed Sep. 4, 2001, which claims the benefit of U.S. Provisional Application No. 60/236,233, filed Sep. 28, 2000, which are hereby incorporated by reference. 
     
    
     
       BACKGROUND  
         [0002]    1. The Field of the Invention  
           [0003]    The invention is directed to cartridges and corresponding chambers for use with firearms of various sizes.  
           [0004]    2. The Background Art  
           [0005]    Firearm technology has advanced from the early muzzleloader wherein blackpowder and projectiles where separately loaded into the muzzle of a firearm barrel. Modern firearms use a cartridge which includes a case, housing a propellant, a primer, and a projectile. Cartridges have greatly reduced the frequency of misfires that were commonly experienced with case-less ammunition. For rifle and handgun ammunition the case is typically metallic, such as brass. A case may or may not utilize a shoulder disposed below a case neck. The case neck retains a projectile. Configured with a shoulder, the case body may have a larger interior diameter than the projectile. For shotgun ammunition, the case is typically paper or plastic with a metal head and is called a shell. The primer is the ignition component which is affixed to the case in a manner to be in communication with the propellant through a flash hole. The primer includes pyrotechnic material such as metallic fulminate or lead styphnate and may be located within the center base of the case or on a rim.  
           [0006]    The rear portion of a firearm barrel includes a chamber which is designed to receive the cartridge. The firearm includes a firing mechanism that drives a firing pin or an electrical charge to ignite the pyrotechnic material in the primer. A combustion process is initiated within the cartridge when the primer ignites. Hot high-pressure gases and particulates are produced by ignition of the primer pyrotechnic. The gases exit through a flash hole or holes into the case, which contains the propellant and trapped air. The propellant is typically a combustible powder having various configurations of granules or grains. The propellant and entrained air not ignited by the primer-blast is compressed into a solid mass having the characteristics of a very viscous fluid.  
           [0007]    Firearm cartridges are divided into two basic types, straight-walled and bottlenecked, which are distinct in shape and function. Straight-walled cases are so named because they have a cylindrical or slightly tapered shape with an inside diameter equal to or slightly greater than the projectile diameter. Bottlenecked or shouldered cases are so named because they taper from a base to a conical shoulder and neck which holds the projectile.  
           [0008]    The straight-walled and bottlenecked two cartridge shapes have distinctly different combustion characteristics and efficiencies. In the straight-walled case, propellant that was not initially ignited by the primer, burns from the aft, or flash hole, end forward with most of the propellant following the projectile into the barrel bore. The propellant along the case wall, although sheared away from the case wall by projectile movement, may not ignite because the case wall has 20 to 40 times the thermal conductivity of the propellant and significantly greater specific heat. This has the effect of cooling and quenching ignition at the case wall in addition to causing significant heat loss to the gun chamber.  
           [0009]    Acceleration losses are high and powder burn rates must be very fast to minimize such losses. Any propellant not consumed before the projectile leaves the muzzle will be expelled and cannot contribute to projectile acceleration. Heat loss caused by burning propellant in the barrel are very high.  
           [0010]    The bottlenecked or shouldered case is somewhat more efficient. As propellant is ignited at the primer flash hole or holes, a shock wave moves through the propellant that compresses and heats the propellant. The shock wave is partially reflected off the case shoulder toward a central interior portion of the case. As pressure behind the shock wave begins to move the projectile, the propellant plug approximately the diameter of the projectile is sheared away from the body of the charge. Ignition along the resulting shear surface is rapid because only an infinitesimal gas path out of the shear layer exists causing a rapid pressure and temperature buildup. The portion of the propellant plug which is exposed to the case neck can only burn from the aft end forward due to the quenching effect of the case neck and later the barrel bore.  
           [0011]    Burning rates for propellants used in the bottleneck case must be slower because of the additional burning surface of the propellant plug and exposed propellant sheer surface. In the region where unignited powder exists, exposure of the case wall to combustion gas occurs when the propellant is consumed. As this material burns forward from the base and through from the interior surface, more of the case is exposed to direct heating, therefore, heat loss increases. Thus, heat and acceleration losses are lower with the bottleneck case but are still excessive. Ballistic calculations utilize empirically derived coefficients known as progressivity, regressivity, and vivasity to define the pressure in a cartridge as a function of time or bullet movement. However, the burning surfaces of the propellant are not quantitatively defined.  
           [0012]    In firearm manufacturing, it is desirable to increase the propulsion of the projectile for improved range and accuracy. Projectile velocity and propulsive efficiency have been increased through the use of high energy smokeless powders. Other improvements have resulted from increased case capacity, improved primer design, and better metallurgy for cases and firearms with higher operating pressures. The shape of the case has also been altered, as discussed above, to create the bottlenecked case that increases case capacity to reduce heat and acceleration losses. Improvements thus far have relied upon empirically derived coefficients that do not accurately model pressure over time. Thus, such improvements fail to provide an optimal configuration.  
           [0013]    In improving a cartridge several design parameters must be considered within the framework of the combustion process described above. One parameter is to minimize heat losses to the cartridge case, projectile base, and gun barrel. This may be done by protecting cartridge surfaces from combustion heat where possible. Heat losses may also be minimized by reducing the interior surface area of the case as much as possible for the required propellant volume. Another parameter is to maximize the pressure-time integral of propellant combustion within pressure limitations of the firearm design. A further parameter is to complete as much combustion as possible within the cartridge case to minimize heat loss and damage to the firearm barrel. Yet another parameter is to minimize acceleration of uncombusted propellant to conserve combustion energy.  
           [0014]    Thus, it would be an advancement in the art to improve the propulsive efficiency of a cartridge. It would be an advancement in the art to increase bullet velocity for a given amount of propulsive medium, such as gun powder. It would be a further advancement in the art to minimize heat and acceleration losses within the pressure limits of the firearm and minimize damage to the bore of the firearm barrel. It would also be an advancement in the art to be able to calculate pressure as a function of time directly from propellant burn rates and surface areas without resorting to empirically derived coefficients. Such a cartridge and case-less gun chamber design is disclosed herein.  
         BRIEF SUMMARY  
         [0015]    This disclosure describes the mode of propellant combustion and a design process for the design of metal cased cartridges and for case-less gun chambers for all gun sizes. In one embodiment the firearm cartridge has a case configured with a straight-walled portion that is connected to a base. The straight-walled portion defines a base cavity having an interior base diameter and containing a propellant. The case further includes a radial shoulder connected to the straight-walled portion. The radial shoulder transitions into a non-radial neck/shoulder junction that connects the shoulder to a neck. The interior base diameter is at least twice the neck diameter. A bullet is partially nested within the neck.  
           [0016]    A case-less gun chamber may be configured similarly to the cartridge. As such, the chamber would have a base diameter that would be approximately two or more times the size of a neck chamber. The chamber would include a radial shoulder that would be connected to the neck through a non-radial neck shoulder junction.  
           [0017]    The two to one or greater ratio of the base diameter to neck diameter optimizes combustion efficiency. The increased diameter creates a greater primary ignition zone and reduces heat loss by having a thicker layer of propellant on the interior case surface until burnout. Acceleration losses are reduced as the length of the propellant plug is reduced. The case dimensions further provide for simultaneous burn in the propellant plug and propellant wall to reduce inefficiency and waste. This results in more burning in the neck and case interior rather than within the barrel. The radial shoulder focuses a shockwave just far enough from the bullet base to reduce heat loss to the bullet and support bullet retention in the neck for a longer period of time.  
           [0018]    The neck, case wall, and the bullet base may further be coated with a reflective, insulation coating to reduce quenching of the propellant adjacent the neck and bullet base. The coating accelerates burning fronts, reduces heating and acceleration losses, and further adds to the propulsive forces behind the bullet base.  
           [0019]    In another embodiment, the invention includes a straight walled cartridge with a reflective, insulation coating disposed on the case interior. The coating may further be disposed on the bullet base. The coating reduces quenching of the propellant adjacent the case and the bullet base. This increases propellant burn along the shear surface at the case wall and the bullet base as the bullet moves forward. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0020]    In order that the manner in which the above-recited and other advantages and features of the invention are obtained, a more particular description of the invention summarized above will be rendered by reference to the appended drawings. Understanding that these drawings only provide selected embodiments of the invention and are not therefore to be considered limiting of its scope, the invention will be described and explained with additional specificity and detail through the use of the accompanying drawings in which:  
         [0021]    [0021]FIGS. 1A, 1B, and  1 C are side views of firearm cartridges;  
         [0022]    [0022]FIGS. 2A, 2B, and  2 C are cross-sectional views of a straight-walled cartridge undergoing combustion;  
         [0023]    [0023]FIGS. 3A, 3B, and  3 C are cross-sectional views of a bottle-necked cartridge undergoing combustion;  
         [0024]    [0024]FIGS. 4A and 4B are cross-sectional views of cartridges experiencing shockwaves from primer ignition;  
         [0025]    [0025]FIGS. 5A, 5B, and  5 C are cross-sectional views of cartridges experiencing shockwaves from primer ignition;  
         [0026]    [0026]FIGS. 6A and 6B are cross-sectional views of cartridges experiencing shockwaves from primer ignition;  
         [0027]    [0027]FIGS. 7A and 7B are cross-sectional views of cases undergoing combustion;  
         [0028]    [0028]FIGS. 8A and 8B are cross-sectional views of cartridges undergoing primer ignition;  
         [0029]    [0029]FIG. 9 is a cross-sectional view of one embodiment of a cartridge of the present invention during primer ignition;  
         [0030]    [0030]FIG. 10 is a cross-sectional view of one embodiment of a cartridge of the present invention;  
         [0031]    [0031]FIG. 11 is a cross-sectional view of an alternative embodiment of a cartridge of the present invention;  
         [0032]    [0032]FIG. 12 is a cross-sectional view of an alternative embodiment of a cartridge of the present invention;  
         [0033]    [0033]FIG. 13 is a cross-sectional view of a cartridge of the present invention disposed within a gun chamber;  
         [0034]    [0034]FIG. 14 is a cross-sectional view of one embodiment of a case-less gun chamber of the present invention;  
         [0035]    [0035]FIG. 15 is a graphical representation of pressure experienced by a projectile over time during the combustion process; and  
         [0036]    [0036]FIGS. 16A and 16B are cross-sectional views of straight-walled cartridges undergoing the combustion process. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0037]    The presently preferred embodiments of the present invention will be best understood by reference to the drawings, wherein like parts are designated by like numerals throughout. It will be readily understood that the components of the present invention, as generally described and illustrated in the figures herein, could be arranged and designed in a wide variety of different configurations. Thus, the following more detailed description of the embodiments of the apparatus, system, and method of the present invention, as represented in FIGS. 1 through 10, is not intended to limit the scope of the invention, as claimed, but is merely representative of presently preferred embodiments of the invention.  
         [0038]    The present invention is directed to improved cartridges and case-less gun chambers with reduced heat and acceleration losses. With all cartridges experiencing combustion, that portion of a propellant not initially ignited is quickly compressed into a heterogeneous mass with properties similar to a very high viscosity fluid. The trapped air contained in the propellant has more compressibility than the propellant granules. The trapped air heats the powder it is in contact with by adiabatic compression, thereby increasing the subsequent combustion rate. As the ignited propellant granules begin to burn, the pressure rises further. The increased pressure compresses the unignited propellant until the projectile begins to move from a cartridge case into the barrel. A shock wave caused by the ignition of the primer is transmitted through the propellant and trapped air to the case wall. A part of the shock wave is then reflected back into the compressed propellant and throughout the cartridge and chamber.  
         [0039]    As the projectile begins to move, a plug of propellant of approximately the same diameter as the projectile is sheared away from the compressed mass of the powder or the case wall. The plug may be subsequently ignited along the sheared interface depending on whether the sheared surface is in the propellant or along the case wall. The plug follows the projectile until it is either consumed by the combustion process or combustion slows or ceases due to the pressure drop caused by projectile acceleration or by the projectile exiting the muzzle. Combustion of the remainder of the propellant begins within the cartridge case or as the granules become entrained into flowing combustion gases as the gases flow into the case neck and barrel bore. By better understanding the combustion process, improvements may be made to conventional cartridges and case-less gun chambers. These improvements are disclosed herein.  
         [0040]    Referring to FIGS. 1A, 1B, and  1 C, side views of conventional firearm cartridges are shown. FIG. 1A illustrates a straight-walled cartridge  10  that has a cylindrical case  12  with little or no taper. FIG. 1B illustrates a bottlenecked cartridge  14  having a case  16  configured with a conical shoulder  18  that tapers to a neck  20 . FIG. 1C illustrates an alternative bottleneck cartridge  22  having a case  24  configured with a radius shoulder  26  that tapers with a reverse radius to a neck  28 . The design differences between the straight-walled cartridge  10  and the bottleneck cartridge  14 ,  22  result in different performances and functions.  
         [0041]    Referring to FIGS. 2A, 2B,  2 C there is shown side cross-sectional views of the straight-walled cartridge  10  undergoing the combustion process in a gun chamber  30 . In FIG. 2A, a representation of the straight-walled cartridge  10  is shown shortly after primer ignition. The ignition releases a nascent gas pocket  32  through a flash path  34  and into the propellant  36  to create a zone of primary ignition  38 . The propellant  36  may be normal, black, or smokeless powder with entrained air. The unignited granules of the propellant  36  are compressed into a heterogeneous mass which has the properties of a viscous fluid.  
         [0042]    In FIG. 2B, the straight-walled cartridge  10  is shown as the bullet  40  begins to move forward towards the muzzle of the barrel. A zone of nascent ignition  42  proceeds through the propellant  36  to heat the propellant but does not completely combust all of the propellant  36 . Ignition is complete, but the propellant  36  continues to burn. Adjacent the flash path  34 , near complete combustion  44  of the propellant  36  occurs. A shock wave from the primer compresses the propellant  36  and pushes against the bullet base  46  to dislodge the bullet  40 . The propellant  36  is further compressed into a heterogenous mass of granules and trapped gases. During combustion, the propellant  36  shears from the case wall  12 . However, because of the higher thermal conductivity of the case wall  12  there is heat loss and propellant along the case wall is quenched and does not ignite.  
         [0043]    In FIG. 2C, the straight-walled cartridge is shown as the bullet  40  proceeds further towards the muzzle. Pressure near the bullet  40  drops as the bullet  40  accelerates thereby reducing the propellant  36  burn rate. Propellant  36  that is not consumed before the bullet  40  leaves the muzzle is expelled and does not contributed to bullet acceleration.  
         [0044]    Referring to FIGS. 3A, 3B,  3 C there is shown side cross-sectional views of the bottlenecked cartridge  14  undergoing the combustion process in a gun chamber  50 . In FIG. 3A, the bottlenecked cartridge  10  is shown shortly after primer ignition. The ignition releases a nascent gas pocket  52  through a flash path  54  and into the propellant  56  to create a zone of primary ignition  58 . The unignited granules of the propellant  56  are compressed into a heterogeneous solid.  
         [0045]    In FIG. 3B, the bottlenecked cartridge  14  is shown as the bullet  60  begins to move forward towards the muzzle of the barrel. A zone of nascent ignition  62  proceeds through the propellant  56  but does not completely combust all of the propellant  56 . Adjacent the flash path  54 , near complete combustion  64  of the propellant  56  occurs. A shock wave from the primer compresses and heats the propellant  56  and pushes the bullet base  66 . The shockwave partially reflects off the case shoulder  18  toward an internal central portion of cartridge  14  to dislodge the bullet  60 .  
         [0046]    A propellant plug  70  that is the approximately the diameter of the bullet  60  shears away from the remaining propellant  56 . The portion of the propellant plug  70  that is exposed to the case neck  20  during bullet  60  movement only burns from an aft end forward due to the quenching effect of the case neck  20  and the barrel bore. A base zone  72  of the propellant plug  70  is compressed and volume reduced by the shockwave of the primer ignition and subsequent pressure rise from propellant combustion. Pressures experienced by the zone  72  can be 3000 psi or more which reduces propellant volume by 10 to 20 percent.  
         [0047]    A shear zone  74  exists where the propellant plug  70  breaks from the remaining propellant  56 . Ignition in the shear zone  74  is quenched by the adjacent cooler and conductive case wall  16 . In bottlenecked cartridges, nascent ignition along the shear zone  74  increases combustion of the surface area. A high heat loss zone  76  develops where completely combusted propellant  56  exposes the conductive case wall  16 . After combustion, a void zone  78  develops within the cartridge  14  as a result of compression and displacement of unignited powder.  
         [0048]    In FIG. 3C, the bottlenecked cartridge is shown as the bullet  60  proceeds further towards the muzzle. Granules  80  are stripped away from the case wall  16  by convection as trapped mass flows into the neck  20 .  
         [0049]    Referring to FIGS. 4A and 4B, cross-sectional views of a straight-walled cartridge  10  and a bottlenecked cartridge  14  are shown. Shockwaves  82  generated from the primer ignition transmit through the propellant  36 ,  56  and push on the bullet base  46 ,  66 . Most shockwaves  82  reflect off the case  12 ,  16  before impacting the bullet base  46 ,  66 . Almost all energy generated by the shockwaves  82  reflects or directly impacts the bullet base  46 ,  66 . This is detrimental as the bullet  40 ,  60  is heated and dislodged prematurely before ignition of the propellent  36 ,  56  is well underway.  
         [0050]    Referring to FIGS. 5A, 5B, and  5 C different embodiments of bottleneck cartridges  14  are shown. The shoulder  18  may be configured to focus shockwaves  82  at different points. In FIGS. 5A and 5B, the bottleneck cartridges  84 ,  86  are configured with 15 and 30 degree conical shoulders  18  respectively. The bottleneck cartridges  84 ,  86  are termed in the art as a “long case” due to a common predesignated case length. Most of the shockwave  82  energy reflects onto the bullet base  66  and prematurely dislodge the bullet  60 .  
         [0051]    In FIG. 5C, the bottleneck cartridge  88  is configured with a 30 degree conical shoulder  18  and is termed in the art as a “short case.” A short case may have a case  16  that is 30 to 50 percent shorter than a long case. With the bottleneck cartridge  88 , more shockwave  82  energy reflects into the propellant  56  adjacent the bullet base  66 . This region is referred to herein as the focus zone  89 , as this is where shockwaves  82  should be focused for improved performance. This is advantageous as heating in this zone  89  of the propellant  56  accelerates subsequent granule ignition and burning in this zone  89 . As this region later becomes the propellant plug  70 , burning and ignition in this zone  89  is greatly increased. Furthermore, premature dislodging of the bullet  60  is reduced.  
         [0052]    Referring to FIGS. 6A and 6B alternative embodiments of bottleneck cartridges  14  are shown. In FIG. 6A, the bottleneck cartridge  90  is configured with a 45 degree conical shoulder  18  and is a long case. A conical shoulder  18  with an angle greater than 40 degrees may dissipate the shockwaves  82  rather than direct the shockwaves  82  to the focus zone  89 . Dissipation is also dependent on the case length. Thus, the bottleneck cartridge  90  focuses some of the shockwaves  89  into the focus zone  89  and dissipates other shockwaves  82 .  
         [0053]    In FIG. 6B, the bottleneck cartridge  92  is configured with a 60 degree shoulder  18  and is a long case. With this shoulder angle, little shockwave  82  energy reflects into the focus zone  89 . Instead, the shockwaves  82  are largely dissipated throughout the propellant  56 . Resultant granule heating is of little benefit as heating occurs in granules that do not require additional heating. These granules are almost entirely consumed during initial combustion and through burn.  
         [0054]    Referring to FIGS. 7A and 7B, cross-sectional side views of different embodiments of cases  16  for bottleneck cartridges  14  are shown. In FIG. 7A, a conventional long case  96  is shown which has a relatively small diameter compared to the case length. In FIG. 7B, one embodiment of a case  98  of the present invention is shown. The case  98  has an internal base diameter  100  that is approximately two or more times the bullet diameter or the internal neck diameter  102 . The case  98  is also configured to be a short case in that the length of a straight walled portion  104  of the case  98  is substantially shorter than a conventional long case. Configured as such, the case  98  may have approximately the same internal volume as the long case shown  96 .  
         [0055]    For purposes of reference, a case  98  having an internal base diameter  100  of two or more times greater than the internal neck diameter  102  is referred to herein as a “fat” case. A cartridge having a fat case is referred to herein as a “fat” cartridge. The surface area-to-volume ratio of the fat cartridge is less than a bottleneck cartridge. The unique ratio of the fat cartridge reduces the area heated by combustion and reduces subsequent heat loss.  
         [0056]    Both cases  96 ,  98  are shown in a state of combustion. The fat case  98  has less propellant  56  in its propellant plug  70  than the case  96  has in its propellant plug  70 . The plug  70  of the fat case  98  is shorter which reduces the mass of the plug  70  that is accelerated with the bullet  60 . This reduces acceleration and heat loss that occurs with a plug  70  of greater mass.  
         [0057]    A further advantage of the fat case  98  is that the case  98  maximizes the amount of pressure time. The pressure tends to rise to a peak more rapidly due to the larger surface area at an aft end  103 of the case  98 . The pressure remains high until almost all the propellant  56  is consumed. A sharp drop off in pressure then occurs.  
         [0058]    Another advantage of the fat case  98  is that as combustion proceeds, the total area of the interior fat case  98  insulated by unburned powder is substantially greater. Thus, much of the internal case surface is covered with unburned propellant until it is consumed by burning. During subsequent burning that occurs after ignition, there is a thicker wall  106  of propellant  56  adjacent the case wall. It requires more time to burn through the propellant wall  106  of the fat case  98  than it does to burn through the propellant wall  106  of the case  96 . Total exposure of the case wall to heat is a function of exposed area multiplied by time. Because more time is required to burn through the propellant wall  106 , exposure of the interior case wall to heat and propellant gases is reduced. Heat losses to the interior case wall are reduced in the case  98 .  
         [0059]    It is further advantageous to have the plug  70  and the propellant wall  106  burn and expire simultaneously so that both contribute to the propulsion. The dimensions of the fat case  98  provide this by having the propellant wall  106  being approximately half as thick as the plug  70 .  
         [0060]    Referring to FIGS. 8A and 8B, cross-sectional side views of a conventional cartridge  108  and a fat cartridge  110  of the present invention is shown. The cartridges  108 ,  110  are shown in a state of primary ignition. As shown, the fat case  110  has dimensions that create a greater primary ignition zone  58  than the case  108 . Thus, there is a greater initial combustion with greater heat and pressure with the fat case  110 . Less propellant remains unignited which results in less burn time and less time for heat loss. Furthermore the length  112  of the column of unignited propellant  56  to be accelerated is less with the fat case  110 . This results in reduced acceleration losses.  
         [0061]    Referring to FIG. 9 a cross-sectional view of one embodiment of a fat cartridge  110  of the present invention is shown. In the embodiment shown, the fat cartridge  110  is configured as a bottleneck cartridge having a shoulder  114 . Although the shoulder  114  is advantageous, the fat cartridge  110  may be configured as a straight-walled cartridge. Alternatively, the fat cartridge  110  may be configured without a straight-walled portion. However, the straight-walled portion provides additional powder capacity.  
         [0062]    In the embodiment of FIG. 9, the shoulder  114  is radial and centers a longitudinal axis (not shown) of the cartridge  110 . The radial shape of the shoulder  114  may be defined by an ellipsoid, sphere, or paraboloid configuration. As such, a phantom ellipsoid, sphere, or paraboloid may be overlaid the shoulder  114  and centered around the longitudinal axis. This differs from conventional radial shoulders which are configured independent of the longitudinal axis.  
         [0063]    The radial shoulder  114  focuses the reflected shockwaves  82  into the focus zone  89  which is adjacent the bullet base  66 . The optimal configuration for a shoulder  114  is a factor of focus points of an ellipse between the flash hole  54  and near but not at the bullet base  66 . When the focus points converge, the shoulder configuration becomes spherical. When the fat case  98  is elongated, a single focus point is located near the bullet base  66  and the shoulder configuration becomes parabolic. Further discussion on the defining shoulder configuration follows below.  
         [0064]    Focusing of the shockwaves  82  to the focus zone  89  results in an increase in the ignition rate and burn of the propellant  56  in the zone  89  by adiabatic heating of trapped air and reduces losses associated with acceleration of unignited propellant  56 . Focus of the shockwaves  82  away from the bullet base  66  further reduces the tendency to dislodge the bullet  60  from the neck  20  until ignition of the propellent is further advanced. This further reduces heat loss to the bullet base  66  and neck  20  due to compression of air trapped within the propellant  56 . Furthermore, the amount of unburned propellant in the plug  70  is reduced and less propellant  56  accelerates down the bore with the bullet. Focus of the shockwaves  82  further results in less shock energy being transmitted axially to the gun barrel which results in less barrel vibration and greater intrinsic accuracy of the gun.  
         [0065]    The base portion  112  of the cartridge  110  is defined as the straight-walled portion of the fat case  98  that extends from the aft end  103  to the junction  116  where the shoulder  114  begins. The length of the base portion  112  may vary based on required propellant capacity. In one embodiment, the base portion  112  has a length that approximates a short case. The bullet  60  is preferably seated such that the bullet base  66  is at a neck/shoulder junction  118 .  
         [0066]    Although the shoulder  114  may be configured as being radial, in that it is elliptical, spherical, or parabolic, the neck/shoulder junction  118  is non-radial. This differs from the cartridge  22  of FIG. 1C. A radial neck/shoulder junction  118  is detrimental because it facilitates movement of the unignited propellant  56  into the barrel. This movement increases case interior exposure to the flame front and acceleration losses due to excessive propellant  56  movement. This causes destructive heating due to combustion in the barrel. Thus, the present invention does not provide a reverse radial of the shoulder curvature.  
         [0067]    During combustion, the primer ignition creates a developing nascent gas pocket  52  within the propellant  56  that pulverizes and compresses the granules. The primary ignition zone  58  results in direct granule ignition. In between the focus zone  89  and the primary ignition zone  58  is a zone referred to herein as a compression zone  120 . The compression zone  120  experiences substantial granule compression from the primer ignition and the nascent combustion.  
         [0068]    In one embodiment, the inside surface of the neck  20  and the bullet base  66  are coated with a reflective, thermally insulating coating to reduce heat quenching. The coating has a thermal breakdown temperature higher than the ignition temperature of the propellant  56  to advance the flame front by reflecting heat and increase burning at the interior case wall. This allows more complete ignition of the propellant  56  in the adjacent areas by reducing heat loss and subsequent propellant ignition quenching at the interior surface of the neck  20  and the bullet base  66 . With the insulated coating, the burning front advances further up the neck  20  and along a shear zone  74 .  
         [0069]    An uninsulated interior case surface can quench combustion due to the high thermal conductivity and heat capacity of the case. The quenching may continue until the interior case surface is heated above the ignition temperature of the propellant. This results in significant heat loss and retards the movement of the burning front along the interior case wall and along the shear zone  74 .  
         [0070]    Referring to FIG. 10, a cross-sectional view of the case  98  of FIG. 9 is shown to illustrate geometrical dimensions. In the embodiment shown, the shoulder  114  of FIG. 10 is ellipsoidal in that is defined by an ellipsoid  122 . The ellipsoid  122  and the shoulder  114  are centered around the longitudinal axis  123 . A cross-section of the ellipsoid  122  (shown in phantom) is illustrated in FIG. 10. The defining ellipsoid  122  has a minor diameter  124  that approximates the internal case diameter  100  and is two or more times the bullet diameter or the internal neck diameter  102 . The ellipsoid  122  has a focus  126  adjacent the face of the flash hole  54 . The second focus  128  of the ellipsoid  124  is adjacent but not in contact with the bullet base  66 . The second focus  128  is approximately the location of the desired focus zone  89 . Shockwaves are directed to the second focus  128  and heat loss to the case  98  and to the bullet are reduced.  
         [0071]    As per the definition of an ellipse, the sum of the distances from the foci  126 ,  128  to a reference point  130  on the ellipse is a given constant. Thus, 1 1 +1 2 =constant (C). Properties for an ellipse further provide the following relationships for the illustrated angles: 
         γ−α=β+α; 
         γ−β=2α; and 
         α=(γ−β)/2. 
         [0072]    The radius, r 2 , of the minor axis is equal to twice the radius, r 1 , of the internal surface of the neck  20 . The variable S is defined as the distance from the major axis to the reference point  130 . The variable F is defined as the distance between the focus point  126  and the intersection of S with the major axis. The variable h is defined as the distance between the two foci  126 ,  128 .  
         [0073]    For these given relationships and variables the following equations are derived: 
           C= (( F ) 2 +( S ) 2 ) ½ +(( h−F ) 2 +( S ) 2 ) ½ ; 
         β=arcTan( S/F ); 
         γ=arcTan( S/ ( h−F )); and 
         α={fraction ( 1 / 2 )}[arcTan( S/F )−arcTan( S/ ( h−F ))]. 
         [0074]    Referring to FIG. 11, a cross-sectional view of an alternative embodiment of the case  98  is shown to illustrate geometrical dimensions. In the embodiment shown, the shoulder  114  is spherical in that is defined by a sphere  132  (shown in phantom) that is centered around the longitudinal axis  123 . If the difference between the major and minor axis of the ellipsoid  122  becomes zero or negative as a result of a small case capacity, the foci converge and the shoulder  114  may be spherical. A spherical shoulder  114  may also be desirable if is necessary to limit the degree of the focus zone  89  to prevent ignition from adiabatic heating of air from just below the bullet base  66 .  
         [0075]    As shown in FIG. 11, the sphere  132  has a center  134  and all points on the shoulder  114  are equidistant from the center  134 . The center  134  may be disposed at the face of the flash hole  54 . Shockwaves  82  are directed to the center  134  which serves as the approximate location of the focus zone  89 . In the embodiment of FIG. 11, the sphere  132  configures to the shoulder  114  and the touches the face of the flash hole  54  at its circumference. However, the sphere  132  may be configured in various ways to adjust the center  134 . Thus, the sphere  132  need not necessarily contact the flash hole  54  and the center  134  may be moved closer or further from the bullet base  66 .  
         [0076]    Referring to FIG. 12, a cross-sectional view of an alternative embodiment of the case  16  is shown. In the embodiment shown, the shoulder  114  is parabolic in that is defined by a paraboloid  136  (shown in phantom) that is centered around the longitudinal axis  123  and has a focus point  138 . A parabolic shoulder  114  may be used for relatively long cases  16  where the foci of an ellipse diverge. Alternatively, the parabolic shoulder  114  is applicable when the primer charge is not centrally located as in some rimfire and Berdan-primed cartridge designs. Configured as a rimfire cartridge, the flash path  54  is located along a lower peripheral edge. As in the embodiments of FIG. 10 and  11 , the parabolic shoulder  114  focuses a shockwave at a focus zone  89  just far enough from the bullet base  66  to prevent conductive heat loss into the bullet  60 . The focus point  138  may serve as the proximate location of the focus zone  89 . Thus, the paraboloid  136  may be adjusted to provide shoulders  114  that focus the shockwaves  82  into the desired focus zone  89  location.  
         [0077]    Referring to FIG. 13, a cross-sectional view of a fat cartridge  110  in a chamber  50  is shown after combustion. The case  98  has an interior base diameter  100  that is approximately twice or more the interior neck diameter  102 . The bullet  60  travels down the barrel  140  towards the muzzle. Propellant  56  in the plug  70  and in the propellant wall  104  adjacent the interior case surface  98  burn simultaneously and completely before the bullet  60  exits the muzzle. This is efficient as both the plug  70  and the propellant wall  104  contribute to the overall propulsion of the bullet  60 .  
         [0078]    Referring to FIG. 14, there is shown a case-less gun chamber  150  of the present invention. Although the discussion has been directed to cartridges, the present invention further includes case-less gun chambers. The chamber  150  may be configured with a base  152  and shoulder  153  for containing a propellant  56 , and a neck  154  for containing the bullet  60 . The bullet base  66  seats approximately at the juncture of the neck  154  and the shoulder  153 .  
         [0079]    The chamber  150  is similarly configured to the fat case  98  in that the base diameter  156  is approximately two or more times the size of the neck diameter  158 . The shoulder  153  may further be defined by a ellipsoid, sphere, or paraboloid similar to FIGS.  10  to  12 . Thus configured, the gun chamber  150  provides similar benefits in directing primer ignition shockwave, improving combustion efficiency, and reducing heat acceleration and losses.  
         [0080]    Referring to FIG. 15, a graphical representation of the total pressure increase experienced using fat cartridges  110  and case-less chambers  150  of the present invention. The projectile base pressure is shown on the y-axis and the projectile travel time is shown on the x-axis. The present invention experiences a loss  160  in maximum pressure. The graph charts the performance by a fat cartridge  110  of the present invention and a conventional cartridge having the same propellant capacity. However, the present invention provides gains  162  in pressure over conventional cartridges and does so over a longer period of time. Overall the present invention optimizes the pressure-time integral. The bullet  60  is able to achieve a given velocity sooner because pressure rises faster and remains close to peak for a longer time before dropping off.  
         [0081]    Referring to FIGS. 16A and 16B, cross sectional views of a conventional straight-walled cartridge  10  and an insulated straight-walled cartridge  170  are shown. Both cartridges  10 ,  170  are shown during the combustion process when the bullet  40  begins to move and the propellant  56  becomes a heterogeneous mass and reaches nearly full compression. The insulated straight-walled cartridge includes a reflective, thermally insulating coating that is applied on a substantial portion of the interior case wall  172  and bullet base  66 .  
         [0082]    The coating has a thermal breakdown temperature higher than the ignition temperature of the propellant. The coating advances the flame front by reflecting heat to aid ignition at the interior case wall  172  and accelerates the burning front along the case wall  172 . The burning acceleration decreases the amount of propellant  56  pushed into the barrel behind the bullet  40 . The burning acceleration increases chamber pressure and bullet velocity while reducing acceleration and heat losses in the barrel. The reflective insulation coating also reduces heat losses to the case. With the conventional case  10 , quenching along the interior case wall  172  is encouraged due to thermal conductivity of the case. With the insulated cartridge  170 , the total area of combusting surface is greater than with the conventional cartridge  10  which improves combustion efficiency.  
         [0083]    The present invention provides a two to one or greater ratio of base column to bullet diameter or bottlenecked cases to optimize combustion efficiency. The increased diameter creates a greater primary ignition zone and reduces heat loss by having a thicker layer of propellant on the interior case surface until burnout. The present invention further reduces acceleration loss by reducing the size of the propellant plug. The present invention further provides simultaneous burn in the propellant plug and propellant wall to reduce inefficiency and waste. The present invention provides more burning of the propellant in the neck and case interior rather than within the barrel. Reduced propellant burning in the barrel reduces erosive damage to the throat and leade areas. The cartridge is configured to focus a shockwave just far enough from the bullet base to reduce heat loss to the bullet and support bullet retention in the neck for a longer period of time.  
         [0084]    It should be appreciated that the apparatus and methods of the present invention are capable of being incorporated in the form of a variety of embodiments, only a few of which have been illustrated and described above. The invention may be embodied in other forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive and the scope of the invention.