RIFLE BARREL GEOMETRY

Abstract

A firearm barrel comprising of an elongated barrel body defining a bore and having a breech end and a muzzle end. The bore includes a rifled surface with rifling having a gain twist with a twist rate of a first amount proximate the breech end and a greater second amount proximate the muzzle end. The rifling having an eased rifling profile along the length of the rifling. The eased rifling includes a radiused transition from lands to grooves and is continuous and smoothly transitioned from the groove articulated at a vertex from the land. The eased rifling includes angled surfaces transitioning between lands and grooves with angled surfaces angularly offset from radial to the bore or are offset from adjacent grooves by an obtuse angle or are offset from adjacent lands by an obtuse angle.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This claims priority to U.S. Provisional Patent Application No. 63/754,816 filed on Feb. 6, 2025 entitled “RIFLE BARREL GEOMETRY” hereby incorporated by reference in its entirety for all that is taught and disclosed therein.

FIELD OF THE TECHNOLOGY

The present disclosure relates to firearms and firearm barrels.

BACKGROUND AND SUMMARY

Firearms operate by sending a bullet projectile through a barrel. The barrel has an interior called a bore through which the bullet passes. The bullet is traditionally partially protruding from a metallic casing placed within the chamber of the barrel at the breech end of the barrel, and exits through the opposing end called the muzzle. The bullet is set within a part of the barrel called the throat, a tapered portion of the bore in front of the chamber where the barrel diameter diminishes to meet the rifling. The throat, also sometimes referred to as the leade, is the first area through which the bullet first moves as it leaves the case before engaging the rifling. The rifling of the surface of the bore that imparts a spinning motion on the bullet as the bullet passes through the barrel bore. Conventionally, this surface consists of lands and grooves. The lands are elevated portions that engage the surface of the projectile. The grooves are lower portions relative to the lands. The rifling has a predominantly helical form along the length of the barrel, though some sections may be relatively straight. The number of helical turns of the lands and grooves define a barrel twist rate, or simply twist. Part of this measure is called the degrees per inch, which is the degree of projectile rotation per length of barrel. For example, one complete 360 degree turn of the helically twisting land and groove per ten inches of barrel length at a constant helical angle is referred to as a 1:10 (one-in-ten) twist rate. For a given projectile velocity, the lower the ratio, the “faster” the twist rate, and the faster the bullet is expected to rotate as it travels through the barrel and upon exiting the barrel. One rotation being 360 degrees, there are 36 degrees of rotation per inch of bullet travel down the barrel.

The geometry of the rifling can vary. There is Schalk-Pope rifling, where the bullet diameter just touches and rides on top of the lands and center of the flat bottom grooves and was common in black-powder rifles where the bullet was pre-seated in the bore ahead of the case via muzzle-loading. Metford rifling created slightly shallow rounded grooves and lands used often in high-end black-powder English rifles. With the improvement of propellants from black powder to smokeless powder, different rifling was developed. Perhaps the most common type for small arms such as rifles is Enfield rifling, where square corner grooves and lands are created by a cutter or broach that cuts or engraves the required grooves in the inner surface of the barrel. Sometimes this is referred to as hook rifling. The sharp edges engrave, imprint, or cut into bearing surface of the bullet.

In contrast to the sharp edges of the lands and grooves used in Enfield or cut rifling, polygonal rifling has smooth rounded hills and valleys. This approach has been around since the 1800s and was first popularized in cannons. This rifling is generally considered to provide less accurate firing compared to Enfield rifling. Despite decreased accuracy, some rifles did implement polygonal rifling, such as the British Lee-Metford rifles, American M1895 Lee Navy rifles and the Japanese Arisaka rifles. It was also used in MG42 machinegun, the H&K G3A3 and the H&K SL7.

Similar to, but distinct from polygonal rifling, Multi-Radial Rifling (MRR) does not have sharp edges and instead has different alternating radiuses for the raised and lower portions of the rifled bore surface. As a result, the barrel does not impart a conventional rifling pattern onto the bearing surface of the bullet. Instead, the rifling compresses the bullet to fill the geometric bore. The benefits of this approach include a tighter seal between the bore and the bullet, better preventing gases behind fired bullet from escaping past the bullet, and thus yielding an increased muzzle velocity and less bore fouling. There is some overlap between polygonal rifling and multi-radial rifling and the terms here may be used equivocally unless specifically distinguished.

However, this approach to rifling is considered to result in decreased accuracy compared to other rifling types. MRR with a constant twist rate has a negative effect on accuracy. The initial acceleration of the bullet, the “spin up” time, is longer and the lack of aggressive driving surfaces compared to other rifling types affects bullet lock. Bullet lock is how long it takes the bullet to be fully driven by the rifling and twisting at the rifling twist rate. The spin up time/distance can vary somewhat but it is on the order of the first few millimeters of rifling. As the bullet accelerates and is twisted, the grooves are misshapen on the bearing surface and need to be re-grooved as the bullet travels down the barrel.

As the bullet travels linearly down the barrel, the rifling imparts torque on the bullet and causes the bullet to spin as it travels linearly down the barrel. The bullet's spin is the gyroscopic motion that results in bullet stability as it travels through the air upon leaving the barrel. It is created when a bullet's bearing surface, the predominantly lengthwise section of the bullet, contacts the lands of the barrel and is made to follow the spiral path of the rifling. The bullet itself travels linearly while the center has moment of inertia. Cut rifling and polygonal rifling imparts on the bearing surface the rifling pattern.

The magnitude of the spin is dependent on the rifling twist rate and projectile velocity. The twist rate is selected based on the geometry of the bullet, as certain factors like bullet length, specifically the bearing surface, necessitates specific twist rates for bullet trajectory and flight stability after it leaves the barrel.

A proper twist rate or range of twist rates is critical to a bullet's spin. Too little or too much spin can result in destabilization. Too much torque on the bullet from too high of a twist rate can damage the projectile. A bullet may benefit from different twist rates at different stages of its travel. The proper twist rate for a specific bullet caliber and length is the length of rifling in the barrel is critical to ensuring the twist rate can provide adequate spin on the bullet. A shorter barrel means there is less time that the bullet is traveling along the rifling, and thus having less time to accelerate to a proper spin. This requires a higher twist rate to compensate for the decrease acceleration time. The bullet will stabilize at a certain RPM which is a combination of the muzzle velocity upon barrel exit and the twist rate. Shorter barrels have a lower muzzle velocity thus necessitating a faster twist rate to achieve the same RPM However, a higher initial twist rate can cause too much torque upon the bullet and damage it.

The most common form of rifling involves a consistent or near consistent twist rate throughout the length of the barrel that is rifled. An alternative approach is called gain twist rifling, where the twist rate not constant, but rather, increases from the breech end towards the muzzle end according to a specified mathematical relationship. Gain twist rifling is also sometimes referred to as progressive twist rifling, incremental twist rifling, transitional twist, or polyrifling. The gain portion of gain-twist rifling is often a linear function of length down the barrel, with the gain twist portion being a constant increasing rate of rotations per length of barrel. This is also referred to as advancement per degree. For example, in a 22.5 inch barrel with linear gain twist rifling, if the initial twist rate is zero degrees per inch, and the twist rate at the muzzle end of the barrel is 1:8, or 45 degrees per inch, then the advancement or gain is 2 degrees per inch over the barrel length of 22.5 inches.

One type of gain-twist rifling is Exponential Gain Twist Rifling (EGTR). With EGTR, the position down the barrel is raised to an exponential power. For example, if X is the position down the barrel, the gain-twist rifling would be X² X³, etc. Other types of gain-twist rifling include linear (position down the barrel raised to a power of one), and sinusoidal.

Having gain-twist allows a lower initial torque on the bullet and a greater, necessary spin upon the bullet reaching the muzzle end. Conventional twist rifling has a spike in torque on the bullet near the breech, then drops off toward the muzzle. The exponential twist smoothly increases towards the muzzle with the highest torque at the muzzle being lower than the peak torque of a constant twist barrel.

There are downsides to gain-twist rifling, such as excessive fouling from having too quick of a gain in twist rate. The barrel also wears out more at the muzzle, harming accuracy.

Gain-twist rifling has been implemented in small caliber firearms but without aggressive gains. For example, a barrel may have an initial 1:10 to 1:8 twist, that is revolutions per inch, with a 1:9 twist mid-way through the barrel, then a linear gain in twist. Cannons have typically been exponential gain twist, but this approach has not been adopted to small arms. In the past, rifling machinery could not adequately implement the approach due to limitations such as the sine bar, the measuring tool used to determine unknown angles of metal workpieces, dictating the twist rate. Modern computer numerical control (CNC) machines with servomotor-controlled equipment and programing make the exponential gain-twist approach feasible for small arms.

Up to now, there has been no motivation for most small caliber applications. However, with the introduction of new high-pressure cartridges that exceed 75,000 psi, the approach has yielded unexpected results. Ammunition pressures for cartridges is regulated by the Sporting Arms & Ammunition Manufacturing Institute (SAAMI). Most rifle cartridges have a maximum chamber pressure of 60,000 to 65,000 pound per square inch (psi). New cartridges such as the 6.8×51 mm, also known as the 0.277 Fury, and 7 mm Backcountry, go to 80,000 psi. Other cartridges may have a typical pressure range of over 80,000 psi and up to 100,000 psi. Most cartridges do not reach the SAAMI maximum of 60,000 to 65,000 psi, with modern rifles starting at 38,000 psi and going up to 55,000 psi. Beyond this range there is excessive wear on the throat of the barrel, the rifling, and excessive torque on the bullet.

New high-pressure rounds result in excessive torque that shears the projectiles. They require specific barrel blank, with preference to using the full length of the barrel for gaining, which is not versatile for inventory considerations because different barrel lengths will have a different twist profile. But, all end up at the same exit twist to stabilize the bullet unless the barrel is short and would require a higher twist to compensate for a lower resulting velocity from a shorter barrel. The need for a shorter length gain at the muzzle with constant twist, like cannons, but applied to small arms, overcomes the above-mentioned disincentives of gain-twist to small arms barrels.

Combining MRR with EGTR resulted in an unexpected benefit for improving bullet lock due to the initial shallow twist angle and less damage to the bullet as the twist rate increases. There is also an unexpected benefit to using MRR with gain-twist that yields a greater improvement in accuracy than by just MRR or gain-twist barrel approaches. For example, an order of half of the shot group size, from 1 MOA to 0.5 MOA. By having an initial section of barrel extending from the rifling leade being a very low twist angle, if not zero, a center section of gain twist with an increasing twist rate to a terminal twist rate according to a specific exponential equation depending on the cartridge and bullet used, and a final, constant twist rate or slight deceleration in twist rate from the middle section at the muzzle end of the barrel for at least a length of one bullet bearing surface, the desired results are observed.

It is possible to have the exponential gain twist extend all the way to the muzzle. However, in some cases it may be better to have a constant twist at the muzzle end, for example equivalent to one length of the bearing surface of the bullet used, to avoid excessive torquing on the tail end of the bullet and causing disruption in stability during bullet flight upon leaving the barrel.

Accordingly, there is a need for an improved barrel incorporating two unique features of rifling geometry that result in substantial improvements in precision and accuracy for small caliber rifles: Exponential Gain Twist Rifling (EGTR); and 2) Multi-Radius Rifling (MRR). The firearm barrel comprising of an elongated barrel body defining a bore and having a breech end and a muzzle end. The bore includes a rifled surface with rifling having a gain twist with a twist rate of a first amount proximate the breech end and a greater second amount proximate the muzzle end. The rifling has an eased rifling profile along the length of the rifling. The eased rifling includes a radiused transition from lands to grooves and is continuous and smoothly transitioned from the groove articulated at a vertex from the land. The eased rifling includes radiused transitioning between lands and grooves with angled surfaces angularly offset from radial to the bore or are offset from adjacent grooves by an obtuse angle or are offset from adjacent lands by an obtuse angle.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a side view of a barrel with key features of the rifling corresponding to different sections of the barrel.

FIG. 2 shows a side section view of a barrel.

FIG. 3A shows a cross-section view of a barrel with conventional geometry rifling.

FIG. 3B shows a cross-section view of an embodiment of the barrel with the multi-radiused rifling.

FIG. 4 shows a cross-section view of a multi-radiused rifled barrel greatly exaggerated differences between land and groove to better visualize what is happening.

FIG. 5A shows a cross-section view of an embodiment of a barrel with multi-radiused rifling having one variation of land width.

FIG. 5B shows a cross-section view of an embodiment of a barrel with multi-radiused rifling having a second variation of land width.

FIG. 5C shows a cross-section view of an embodiment of a barrel with multi-radiused rifling having a third variation of land width.

FIG. 5D shows a cross-section view of an embodiment of a barrel with multi-radiused rifling having a fourth variation of land width.

FIG. 6A show a cross-section view of an embodiment of a barrel with an exaggerated scale of a bore maintaining the bore area by varying the land width and large radius tangent to the groove diameter.

FIG. 6B show a cross-section view of an embodiment of a barrel with an exaggerated scale of a bore maintaining the bore area by varying the land width and large radius tangent to the groove diameter.

FIG. 6C show a cross-section view of an embodiment of a barrel with an exaggerated scale of a bore maintaining the bore area by varying the land width and large radius tangent to the groove diameter.

FIG. 6C show a cross-section view of an embodiment of a barrel with an exaggerated scale of a bore maintaining the bore area by varying the land width and large radius tangent to the groove diameter.

FIG. 7 shows a graph of the relationship of degrees a bullet is rotated versus the position along the length of a barrel and instantaneous twist.

FIG. 8 shows a graph of the relationship of the degrees a bullet is rotated versus the position and instantaneous twist, with a discontinuity that occurs if factors are not set properly.

FIG. 9 shows a graph of the experimental data on the torque on a bullet through a conventional twist barrel.

FIG. 10 shows a graph of the experimental data on the torque on a bullet through a gain-twist barrel.

FIG. 11A shows a graph of the Degrees Rotated versus the Position and Instantaneous Twist in Degrees per Inch when certain variables are changed.

FIG. 11B shows a graph of the Degrees Rotated versus the Position and Instantaneous Twist in Degrees per Inch when certain variables are changed.

FIG. 11C shows a graph of the Degrees Rotated versus the Position and Instantaneous Twist in Degrees per Inch when certain variables are changed.

FIG. 11D shows a graph of the Degrees Rotated versus the Position and Instantaneous Twist in Degrees per Inch when certain variables are changed.

FIG. 11E shows a graph of the Degrees Rotated versus the Position and Instantaneous Twist in Degrees per Inch when certain variables are changed.

FIG. 11F shows a graph of the Degrees Rotated versus the Position and Instantaneous Twist in Degrees per Inch when certain variables are changed.

FIG. 11G shows a graph of the Degrees Rotated versus the Position and Instantaneous Twist in Degrees per Inch when certain variables are changed.

FIG. 11H shows a graph of the Degrees Rotated versus the Position and Instantaneous Twist in Degrees per Inch when certain variables are changed.

FIG. 11I shows a graph of the Degrees Rotated versus the Position and Instantaneous Twist in Degrees per Inch when certain variables are changed.

FIG. 11J shows a graph of the Degrees Rotated versus the Position and Instantaneous Twist in Degrees per Inch when certain variables are changed.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

FIG. 1 shows a side view of an embodiment of the barrel 10 having a breech end 12 and muzzle end 14 and middle section 16 therebetween. The breech end has a breech face 20, chamber 22, and a first non-exponential twist section 24 having a start twist start rate or angle 26. The middle section begins at a gain start distance (GSD) 30 from the breech face and has an exponential gain twist 32 until a gain finish distance (GFD) 34. The muzzle end has a second non-exponential twist section 40 with an end twist rate or angle 42 that begins at the gain finish distance and ends at the muzzle face 44. In the current embodiment the first non-exponential section has a constant twist rate and the second non-exponential twist section can have a constant or mild deceleration twist rate.

FIG. 2 shows a side section view of a portion of an embodiment of the barrel 10. The barrel extends from the breech face 20 at the breech end 12 to the muzzle face 44 at the muzzle end 14. There is a chamber 22 at the muzzle end with a free bore section 52 that lacks any rifling, and a leade 46, also referred to as a forcing cone. The leade is the beginning of the rifling where the chamber terminates at the freebore, a section with no rifling, and the rifling angle ramps up in height from the freebore diameter (approximately 0.0005 inches over bullet diameter) to meet the bore diameter approximately 0.004 to 0.008 inches under bullet diameter on small caliber rifling. The chamber and free bore have no rifling, the leade may have 0 or only a shallow rifling start angle 50. Forward of the leade is first non-exponential twist section 24 having constant rifling 26, leading to the exponential gain twist section 32 with an increasing rate of twist. The twist rate in the first section forward of the leade is dependent on where the GSD 30 is located. If the GSD is forward of the leade then there will be constant twist or no twist for some portion in front of the leade. If the gain twist stars at the breech then the leade will be in the exponential gain twist portion of the rifling. It all depends on where the GSD is relative to the chamber leade. The exponential gain section transitions from a first exponential twist rate 54 at the Gain Start Distance (GSD) 30, to a second exponential twist rate 56 before transitioning to a constant or mild deceleration twist rate 40 at the Gain Finish Distance (GFD) 34. In other embodiments the gain twist can start at the breech face in some embodiments. In other embodiments the exponential gain twist goes all the way to the muzzle face, but accuracy may suffer.

The barrel is initially created by rifling the full length of the barrel with either the gain twist starting at the breech face or a constant twist section up to the gain start distance. The chamber then cuts out everything from the beech face to the forcing cone. The forcing cone will be the twist rate that existed there before the chamber was cut into the barrel. For example, if there is a constant section of 2.5 inches from the breech face at 500 twist and the leade starts at 2.4 inches, the barrel will have a 500 twist at the leade/forcing cone.

FIGS. 3A through 6D show cross sections of barrel bores. Only FIG. 3A shows a non-MRR rifled bore. While MRR results in raised and lowered radius portions, sometimes referred to as hills and valleys, that lack the sharp transitions and corners as discussed above, for the purposes of this disclosure the raised radius or hill portions are referred to with the more conventional “lands” designation and the lower radius or valleys are referred to with the more conventional “grooves” designation. Further, because of the nature of barrel rifling, a cross section will not result in lands and grooves being exactly opposite to one another, so a figure may show a groove being directly opposite to a land. This is just a function of even or odd numbers of lands and grooves. Even number will have a land directly opposing a land, while odd will have a land opposing a groove. Similarly, when a diameter is designated, it may extend from what appears to be a land to a groove, but in fact may be the diameter between two opposing lands or between two opposing grooves.

The MRR in embodiments is an eased rifling profile, including non-perpendicular, not right angle transitions from lands and grooves. The rifling may be radiused, polygonal, slanted transition surfaces between land and groove surfaces centered on the bore axis. Multiple radiuses that are all tangent (or close to tangent) to each other to create the hills and valleys, otherwise referred to as lands and grooves. In one embodiment the radiuses could be approximated by multiple line segments that could produce a nearly equivalent profile not sure if this is in the patent further down.

The barrel has a wall thickness 116 proportional to the diameter of chamber 22 as necessary to accommodate a desired chamber pressure.

FIG. 3A shows a cross-section view of a rifle bore 70 with conventional cut rifling showing lands 60 and grooves 62 having a certain width 64 separating adjacent lands. The bore is centered around bore axis 72 and the height of the lands 66, which corresponds to the depth 150 of the grooves, is measures relative to the distance 74 from the axis. The abrupt transitions 76a between the lands and grooves, and corners of the lands 76b, are distinguished as sharp edges.

FIG. 3B shows a bore 80 of an embodiment of the barrel with multi-radiused rifling (MRR). The alternating raised and lowered radiuses for the lands 84 and grooves 86 of the rifled bore surface are contrasted with the conventional cut rifling of FIG. 3A. The lands have a crest 110 measured as the radius distance 90 from the bore axis 82 to give a lands diameter 92, also referred to as the bore diameter. The grooves have a nadir 112 measured as the radius distance 94 from the bore axis to give a grooves diameter 96.

FIG. 4 shows a cross section of an embodiment of a barrel 10 with an external outer diameter 114 and an MRR bore 80 centered around a bore axis 82 and having alternating lands 84 and grooves 86. The lands have a width 100 between the grooves. The grooves have a width 102. There is a small radius 104 tangent to the bore diameter and a large radius 106 tangent to the grooves diameter. The large radius tangent to the groove diameter is radius for the segment 107 of the bore that transitions from groove to land and is also referred to as the transition radius. The small radius tangent to the bore diameter is not visible in the figure and arrow 104 is merely an indication of where it would be expected to be found. The small radius tangent to the bore diameter does not need to exist because the angle between the end of the small radius and the bore diameter is shallow, but may be beneficial to have. The radius transitions are ideally tangent or near tangent to each other. The radiuses used in transition areas are sized to ensure that a minimum bore area is maintained depending on land width. The large radius 106 that is tangent to the groove diameter and transitions to the land may be replaced by another shape such as an ellipsoid or several line segments that can perform equivocally to provide a smooth transition between the bore diameter and the groove diameter. The bore diameter 92 and grooves diameter 96 are shown, though the opposing end points for lands and grooves do not appear to be touching two lands or two grooves due to the nature of a rifled barrel cross section. For example, the line designated as the bore diameter does not reach the all the way to where a groove is shown.

The top of the lands 84 may have a width 100 of approximately 0.003 inches up to approximately 0.03 inches with a maximum width of approximately 0.050 inches for calibers from 0.177 up to 0.308 inches. For calibers above 0.308 inches up to 0.510 inches the lands may have a width of approximately 0.080 inches. Below a land width of 0.003 inches there may not be sufficient “crest” 110 of the lands to adequately secure the bullet. Above 0.03 inches for some calibers the width may begin to affect the radius of the large radius between the groove diameter 96 and the small radius that connects to the bore diameter 92. A minimum bore area must be maintained to stay within SAAMI minimum bore area parameters. Changing the width of the lands requires a smaller radius where the lands transition to grooves to maintain minimum bore area. For calibers between 0.177 and 0.308 inches, by the time the land width 100 is approximately 0.050 inches, it necessitates that the large radius 106 that is tangent to the groove diameter be very small and becomes essentially conventional land and groove rifling geometry. Above 0.308 inch caliber and up to 0.510 inch caliber, the raised radius portions are capable of being up to approximately 0.080 inches before the large groove radius tangent to the groove 106 becomes impractically small.

In the MMR embodiments discussed below through FIGS. 5A to 6D, the bore area remains the same for a given caliber, accomplished by establishing widths of lands and grooves. The transitions between lands and grooves may be arcuate with different radii shown. Each transition must be positioned or located to ensure the bore area has a proper groove and land balance. The radius of a transition between land and groove is not changed, the position of the radius is changed to maintain the bore area. The transition radius measurement does not affect any changes to the bore area. These figures are examples of land widths and associated large radii (also referred to as transition radii) that could maintain the appropriate bore area as specified by SAAMI.

As the land width is changed, the radius tangent to groove diameter, also referred to as the transition radius, changes to maintain a constant bore area.

FIGS. 5A through 5D show the geometric effects of changing the large groove radius 106 (see FIG. 4).

FIG. 5A shows an embodiment MRR bore 120a around a bore axis 122a with lands 124a having a width 130a of 0.0470 inches bore diameter 134a of 0.0300 inches, and grooves 126a having a grooves diameter 136a of 0.308 inches. A land 140a is illustrated below groove 142a. Land 140a is the same as land 124a and groove 142a is the same as grooves 126a, merely designated differently here for understanding and demonstration purposes for the bore diameter, which touches the land 140a but not the illustrated adjacent groove 142a. Similarly, groove 144a is shown as an arcuate line extending above the land demonstrating width 130a to illustrate how the nature of a rifle bore will have lands and grooves in front of or behind one another as an observer looks down a bore. Groove 144a is the same as other grooves 126a. The transition between lands and grove are shown between points 152a and 154a as transition segment 162a (not visible here) with a transition radius dimension (or simply transition radius) 150a measuring 0.004 inches. The transition radii are equal to one another and are also referred to as the large radius tangent to the groove diameter. Although the lands are said to crest, shown as 156a here, such as the term used for a hill, a term used for the elevated radius portions of an MRR bore, the lands here exaggerate the arcuate path away from the bore axis. The lands are the raised portions that engrave the bullet.

FIG. 5B shows an embodiment MRR bore 1120b around a bore axis 122b with lands 124b having a width 130b of 0.0300 inches and bore diameter 134b of 0.0300 inches, and grooves 126b having a grooves diameter 136b of 0.308 inches, the same diameters as in FIG. 5A. Only the land width 130b and transition radius dimension (or simply transition radius) 150b, with corresponding transition segment 162b, have changed. A land 140b is illustrated below groove 142b. Land 140b is the same as land 124b and groove 142b is the same as grooves 126b, merely designated differently here for understanding and demonstration purposes for the lands diameter, which touches the land 140b but not the illustrated adjacent groove 142b. Similarly, groove 144b is shown as an arcuate line extending above the land demonstrating width 130b to illustrate how the nature of a rifle bore will have lands and grooves in front of or behind one another as an observer looks down a bore. Groove 144b is the same as other grooves 126b. The transition radius 150b is between land points 154b and groove points 152b, which are shown spaced farther apart as compared to FIG. 5A. The change in land width to 0.0300 inches from the width of 0.0470 inches in FIG. 5A has the transition radius increasing from 0.004 in FIG. 5A to 0.062 in FIG. 5B. Two adjacent inner land points 154b are flanked by outer groove points 152b. The groove segments 160b on either side of each land, being the arcuate segments between groove points designated 152b and having no land points 154b therebetween, are equal to one another.

FIG. 5C shows an embodiment MRR bore 120c around a bore axis 122c with lands 124c having a width 130c of 0.0150 inches and bore diameter 134c of 0.0300 inches, and grooves 126c having a grooves diameter 136b of 0.308 inches, the same diameters as in FIGS. 5A and 5B. Only the land width 130c and transition radius 150c, with corresponding transition segment 162c, have changed. A land 140c is illustrated below groove 142c. Land 140c is the same as land 124c and groove 142c is the same as grooves 126c, merely designated differently here for understanding and demonstration purposes for the lands diameter, which touches the land 140c but not the illustrated adjacent groove 142c. Similarly, groove 144c is shown as an arcuate line extending above the land demonstrating width 130c to illustrate how the nature of a rifle bore will have lands and grooves in front of or behind one another as an observer looks down a bore. However, unlike in FIGS. 5A and 5B the groove 144c appears to be viewer to above almost the entire span of the land showing measurement 130c. Groove 144c is the same as other grooves 126c. The transition radius 150c is the between land points 154c and groove points 152c, which are shown spaced farther apart as compared to FIG. 5B. The change in land width to 0.0150 inches from the width of 0.0300 inches in FIG. 5B has the transition radius 150c increasing from 0.062 in FIG. 5B to 0.105 in FIG. 5C.

FIG. 5D shows an embodiment MRR bore 120d around a bore axis 122d with lands 124d having a width 130d of 0.0050 inches and bore diameter 134d of 0.0300 inches, and grooves 126d having a grooves diameter 136d of 0.308 inches, the same diameters as in FIGS. 5A-C. Only the land width 130c and transition radius 150d, with corresponding transition segment 162c, have changed. A land 140d is illustrated below groove 142d. Land 140d is the same as land 124d and groove 142d is the same as grooves 126d, merely designated differently here for understanding and demonstration purposes for the lands diameter, which touches the land 140d but not the illustrated adjacent groove 142d. Similarly, groove 144d is shown as an arcuate line extending above the land demonstrating width 130d to illustrate how the nature of a rifle bore will have lands and grooves in front of or behind one another as an observer looks down a bore. However, unlike in FIGS. 5A-C the groove 144d appears to be viewer to above the entire span of the land showing measurement 130d. Groove 144c is the same as other grooves 126d. The transition radius 150c is the between land points 154c and groove points 152c, which are shown spaced farther apart as compared to FIG. 5C. The change in land width to 0.0050 inches from the width of 0.0150 inches in FIG. 5B has the transition radius 150d increasing from 0.105 in FIG. 5C to 0.120 in FIG. 5D. Two adjacent inner land points 154d are flanked by outer groove points 152d. The groove segment 160d on either side of each land, being the arcuate segments between groove points designated 152d and having no land points 154d therebetween, are equal to one another.

FIGS. 6A through 6D show an exaggerated scale of embodiments for MMR bores that maintain the same bore area by varying the land width and transition radius. The land effective areas, that is the areas of the gaps between grooves designated with series number 210, the space above where the lands protrude into the bore, are the same across FIG. 6A-D. The illustrations differ for simplicity.

FIG. 6A shows an embodiment of an MMR bore 170a around a bore axis 172a and having lands 174a with a width 180a, here 0.120 inches, and a bore diameter 184a, here 0.300 inches, and grooves 176a with a groove diameter 186a, here 0.320 inches. A land 190a is illustrated below groove 192a. Land 190a is the same as land 184a and groove 192a is the same as grooves 196a, merely designated differently here for understanding and demonstration purposes for the bore diameter, which touches the land 190a but not the illustrated adjacent groove 192a. Similarly, groove 194a is shown as an arcuate line extending above the land demonstrating width 180a to illustrate how the nature of a rifle bore will have lands and grooves in front of or behind one another as an observer looks down a bore. Groove 194a is the same as other grooves 186a. The transition between lands and grove are shown between points 204a and 206a as transition segment 202a having a transition radius 200a measuring 0.0100 inches. The transition radii on either side of the land are equal to one another and is also referred to as the large radius tangent to the groove diameter.

FIG. 6B shows an embodiment MRR bore 170b around a bore axis 172b with lands 174b having a width 180b of 0.0350 inches and bore diameter 134b of 0.0300 inches, and grooves 176b having a grooves diameter 186b of 0.320 inches, the same diameters as in FIG. 6A. Only the land width 180b and transition radius 200b, with corresponding transition segment 202b, have changed. A land 190b is illustrated below groove 192b. Land 190b is the same as land 174b and groove 192b is the same as grooves 176b, merely designated differently here for understanding and demonstration purposes for the lands diameter, which touches the land 190b but not the illustrated adjacent groove 192b. Similarly, groove 194b is shown as an arcuate line extending above the land demonstrating width 180b to illustrate how the nature of a rifle bore will have lands and grooves in front of or behind one another as an observer looks down a bore. Groove 194b is the same as other grooves 176b. The transition radius 200b measuring 0.0810 is between land points 204a and groove points 206b, which are shown spaced farther apart as compared to FIG. 6A. The change in land width to 0.0350 inches from the width of 0.0300 inches in FIG. 6A has the transition radius increasing from 0.010 in FIG. 6A to 0.0810 in FIG. 6B.

FIG. 6C shows an embodiment MRR bore 170c around a bore axis 172c with lands 174c having a width 180c of 0.0200 inches and bore diameter 134c of 0.0300 inches, and grooves 176c having a grooves diameter 186c of 0.320 inches, the same diameters as in FIGS. 6A and 6B. Only the land width 180c and transition radius 200c, with corresponding transition segment 202c, have changed. A land 190c is illustrated below groove 192c. Land 190c is the same as land 174c and groove 192c is the same as grooves 176c, merely designated differently here for understanding and demonstration purposes for the lands diameter, which touches the land 190c but not the illustrated adjacent groove 192c. Similarly, groove 194c is shown as an arcuate line extending above the land demonstrating width 180c to illustrate how the nature of a rifle bore will have lands and grooves in front of or behind one another as an observer looks down a bore. Groove 194b is the same as other grooves 176c. The transition radius 200c measuring 0.0965 is between land points 204c and groove points 206c, which are shown spaced farther apart as compared to FIGS. 6A and 6B. The change in land width to 0.0.0200 inches from the width of 0.0350 inches in FIG. 6B has the transition radius increasing from 0.0810 in FIG. 6B to 0.0965 in FIG. 6C.

FIG. 6D shows an embodiment MRR bore 170d around a bore axis 172d with lands 174d having a width 180d of 0.0050 inches and bore diameter 134d of 0.0300 inches, and grooves 176d having a grooves diameter 186c of 0.320 inches, the same diameters as in FIGS. 6A-C. Only the land width 180d and transition radius 200d, with corresponding transition segment 202d, have changed. A land 190d is illustrated below groove 192d. Land 190d is the same as land 174d and groove 192d is the same as grooves 176d, merely designated differently here for understanding and demonstration purposes for the lands diameter, which touches the land 190d but not the illustrated adjacent groove 192d. Similarly, groove 194d is shown as an arcuate line extending above the land demonstrating width 180d to illustrate how the nature of a rifle bore will have lands and grooves in front of or behind one another as an observer looks down a bore. Groove 194b is the same as other grooves 176d. The transition radius 200d measuring 0.0.110 is between land points 204a and groove points 206d, which are shown spaced farther apart as compared to FIG. 6C. The change in land width to 0.0050 inches from the width of 0.0200 inches in FIG. 6C has the transition radius increasing from 0.0965 in FIG. 6C to 0.110 in FIG. 6D.

The exponential gain twist section 32 should have a smooth and continuous rifling curve to prevent the projectile from experiencing abrupt twist rate changes at the transitions between constant twist rate and gain-twist rate regions. This is accomplished by using a multi-radial rifling, which lacking sharp edges. For example, if the initial twist rate is 500 inches per revolution for 3 inches from the breech face, then the exponential gain twist must start at 500 inches per revolution. Similarly, if there is a constant final twist rate of 8 inches per revolution for two inches from the muzzle the exponential gain twist must terminate at 8 inches per revolution. A gain start distance of zero would mean that the exponential gain twist starts at the breech face. And, if the gain finish distance is equivalent to the barrel length, then it would mean that the exponential equation persists until the muzzle and bullet exit.

The gain twist rifling 32 is determined by the following equation being a combination of an exponential and polynomial equation Math 1 below.

$\begin{array}{cc}y=\mathrm{Factor}1*\mathrm{SR}*\left(x-\mathrm{GSD}\right)+\mathrm{Factor}2*\frac{\mathrm{ER}-\mathrm{SR}}{\mathrm{GFD}-\mathrm{GSD}}*{\left(x-\mathrm{GSD}\right)}^{\mathrm{Exponent}}& \mathrm{Math}1\end{array}$

• • y is the number of degrees rotated around the bore
  • x is the position down the barrel from the breech face
  • Factor1 is a coefficient.
  • Factor2 is a coefficient.
  • SR is the start degrees per inch rate
  • ER is the End Degrees per inch rate
  • GSD is the Gain Start Distance from the breech face
  • GFD is the Gain Finish Distance from the breech face
  • Exponent is an exponential numerical value

Referencing to FIG. 1 and FIG. 2, SR is the start rate/angle 26, ER is the twist end rate/angle 40, GSD is the gain start distance 30, GFD is the gain finish distance 34 which is the distance along the barrel from the breech face that starts the constant or decelerating twist length at the muzzle end 14 of the barrel.

Factor1 and Factor2 can be adjusted to ensure that the curves are smooth and continuous and also influence the strength of the linear and exponential factors

The preferred range for the exponential rotational gain rate for the above equation in this embodiment is 1-2 degrees per inch per inch, but with an overall range of approximately 0.25-4 degrees per inch per inch. Below a gain rate of 0.25 the starting rate must be very close to the beginning twist rate so much so as to not lower the initial torque on the bullet with finish twist rates (the higher twist rates before transitioning to a constant or decelerating twist rate) appropriate for conventional small-caliber rifle bullets in the range of 0.177 inches to 0.510 inches. Above approximately 4 the muzzle end 14 of the barrel 10 may experience increased wear due to a very aggressive end gain where the rifling is smearing the bullet bearing surface severely towards the muzzle in order to achieve the desired twist rate upon exiting the barrel.

The preferred embodiment has an Exponent range between 1.5 and 2.5, but can be as low as 1.1 or as high as approximately 4. An Exponent of 1 would be linearly increasing rotation throughout the barrel, which results in a constant twist barrel.

Gain Start Distance (GSD) 30 can be tailored to accommodate different length cartridges. A typical range in this embodiment may be from approximately 1 inch to approximately 4.5 inches from the breech face 20. The GSD may start near the end of the chamber approximately from the free bore section of the cartridge to approximately 2 inches down the barrel from the free bore of the particular cartridge. A GSD of zero would result in the exponential gain twist starts at the breech face.

If the GFD is equivalent to the barrel length, it would mean the exponential equation persists until the muzzle face 44.

The initial rifling leade 46 twist rate is dependent on the finish twist rate 56, muzzle end constant twist rate length 40, and GSD 30. These parameters determine the maximum appropriate twist rate for the breech end section to keep the twist acceleration parameter in a preferred approximate range of 0.25 to 4 degrees per inch per inch.

Table 1 below shows parameters that drive the exponential gain twist equation.

TABLE 1
GSD (inches)                     0
GFD (inches)                     23
Initial Twist (inches/revolution) 500
Final Twist (inches/revolution)  8
SR (degrees/inch)                0.72
ER (degrees/inch)                45
Bore Diameter (inches)           0.300
Start Angle of Groove (degrees)  0.108
Finish Angle of Groove (degrees) 6.719

Table 1 above gives an initial twist rate of 500 in/revolution which is 0.72 degrees per inch and the angle of the rifling relative to the bore axis is 0.108°. If there was zero twist at the breech, that is the rifling grooves in the direction of the bore axis, the twist rate would be infinite, and the degrees rotated per inch would be zero and the angle of the rifling to the bore axis would also be zero.

The start angle of the groove and finish angle of the groove are results obtained from the equation.

Table 2 below includes an example of Factor1 and Factor2 and the Exponent that govern the behavior of the exponential gain twist region of the rifling.

TABLE 2
Exponent 2.0
Factor1  1.0
Factor2  0.5

If the gain twist begins at the GSD may begin a set distance from the breech face so that the gain begins at the chamber leade, the gain twist equation will take the form of the multi part equation given below by Math 2.

• • If: position from breech≤GSD
  • Then: rifle at zero or initial twist rate until GSD is reached
  • Else if: position from breech>GSD and position from breech<GFD

$y=\mathrm{Factor}1*\mathrm{SR}*\left(x-\mathrm{GSD}\right)+\mathrm{Factor}2*\frac{\mathrm{ER}-\mathrm{SR}}{G\mathrm{FD}-\mathrm{GSD}}*{\left(x-\mathrm{GSD}\right)}^{\mathrm{Exponent}}$

• • Else if: position from breech>GFD
  • Then: Then rifle at specified ER until barrel length is reached, or decelerate mildly to minimize rotational acceleration

When the equation in Math 2 above is used, Factor1 and Factor 2 may need to be adjusted so that there is not a discontinuity in the rotation rate.

Because the GSD is a variable that is some distance from the breech face, it could be 0 (starting at the breech face) or a non-zero distance such as 2.5 inches from the breech face, that would place the gain start at approximately the end of the leade on some short action calibers.

FIG. 7 shows a graph of the Degrees Rotated versus the Position and Instantaneous Twist in Degrees per Inch, with the left vertical axis being the Twist Rate in inches per revolution and Rate in Degrees per inch, and the right vertical axis being the degrees rotated, with respect to changes in the barrel length. The graph illustrates a condition where the gain twist equation starts at the breech face and finishes at 15 inches. Curve 400 shows the degrees rotated in degrees. Curve 500 shows the instantaneous numerical rate in degrees per inch. Curve 600 is the twist rate in inches per revolution.

The initial portion of the barrel twist rate is determined by the final twist rate parameter, ER. FIG. 3 shows properly adjusted factors where the rotation is continuous.

FIG. 8 shows a discontinuity in rotation rate if the factors are not set properly. shows a graph of the Degrees Rotated versus the Position and Instantaneous Twist in Degrees per Inch, with the left vertical axis being the Twist Rate in inches per revolution and Rate in Degrees per inch, and the right vertical axis being the degrees rotated, with respect to changes in the barrel length. The graph illustrates a condition where the gain twist equation starts at the breech face and finishes at 15 inches. Curve 400a shows the degrees rotated in degrees. Curve 500a shows the instantaneous numerical rate in degrees per inch. Curve 600a is the twist rate in inches per revolution. The discontinuity in twist rate will cause stress on the projectile and accuracy issues will present because of the immediate twist rate change 502a. This presents as a “kink” in the rifling at the discontinuity.

With conventional bullets, the longer the engagement length of the rifling on the bearing surface of the bullet the greater the amount of transfer of the jacket as the rifling progresses from a shallow angle relative to the bore axis (i.e. a slower twist rate) near the breech end 12 of the barrel to a higher angle relative to the bore axis (i.e. a faster twist rate) near the breech end 14 of the barrel. Thus, the progressive twist spin up rate is important for conventional bullets.

Small caliber projectiles in the diameter range of 0.204 to 0.510 inches are constructed with the majority of the center length section of the projectile engraving the rifling. Such projectiles being spun up too quickly has deleterious effects on the bullet and thus ballistics. Accuracy is dramatically improved if the start twist rate SR 26 is a value such that the maximum twist per inch per inch is not more than approximately 2 degrees per inch per inch. The GFD 40, that is the constant twist length at the muzzle end 14 of the barrel, will reduce the length of the gain twist portion of the barrel so the constant twist length needs to be at least one bullet bearing surface long or slightly longer. However, if an excessively long section at the end of the barrel because that will decrease the initial twist rate. The decrease is necessary to maintain the desired acceleration of the rifling.

Because any amount of constant twist at the muzzle end limits the amount of initial barrel length that is usable for gain twist, there needs to be only a minimal length of constant twist to be beneficial. This is approximately one bullet bearing surface length, or potentially a small length longer. For example, if the gain finish distance on a 24 inch barrel is 1 inch then there remains 23 inches over which to implement the gain twist portion. If the GFD is 6 inches that only leaves you 18 inches over which to do the gain twist.

A preferred range for the twist acceleration is between approximately 0.5-4 degrees per inch per inch. In some cases such as short barrels and very fast twist rates such as one revolution in five inches or one revolution in 3 inches, where the spin up rate will be higher than 4 or can be as high as 12 degrees per inch per inch.

For barrels that shoot heavy for caliber bullets, such as 77 grain bullets in the .224 caliber, a long projectile length-to-bore diameter ratio tends to have a rifling finish or exit angle relative to the bore axis of approximately 5.5 to 6.5 degrees. This is shown by the equation in Math 3 below converts the twist rate to an angle using the rifling twist rate and bore diameter.

$Y={\tan }^{-1}\left(\frac{\pi *\mathrm{Bore}\mathrm{Diameter}}{\mathrm{Twist}\mathrm{Rate}}\right)*\left(\frac{180}{\pi }\right)$

The twist rate may vary by caliber, but if the twist rate is converted using the equation above, the angle is approximately constant for all barrels that shoot heavy for caliber projectiles. For example, a fast twist rate barrel for heavy .224 caliber projectiles is typically around a 1:7 twist rate (7 twist), which would calculate to an angle of 5.59 degrees. A fast twist barrel for heavy .308 caliber projectiles typically has a twist rate of approximately 8, which calculates to approximately 6.71 degrees. A fast twist rate barrel for a heavy .338 caliber projectile is typically a 9.4 twist which calculates to an angle of approximately 6.29 degrees.

For a given length of barrel using the exit angle, also referred to as the finish angle, required for proper bullet stabilization and a spin of approximately 2 degrees per inch per inch, it is relatively simple to determine the starting twist rate so the bullet is not spun up too quickly. For example, in the case of a 20-inch long barrel for a .308 caliber bullet with a finish twist rate of one revolution per 8 inches of barrel, assuming that the progressive twist starts at the breech face 20 and there is one inch of constant twist section 24 after which the multi-part gain twist equation Math 2 is implemented. Using an Exponent of 2, Factor1 of 1, and Factor2 of 0.5, the starting twist rate would be approximately 1 revolution per 52 inches at the breech face, which is approximately 7 degrees rotated per inch. Inputting the numbers into the rest of the equation: 7 degrees/inch+19 inches*2 degrees/in/in results in a 45 degrees/in finish angle.

FIG. 9 shows a graph of the torque applied on bullets by conventional twist rifling. The vertical axis is the torque in foot-pounds and the horizontal axis if the projectiles position in the barrel. Specifically, the graph shows exponential twist having a smoothly increase in torque on the bullet towards the muzzle with the highest torque at the muzzle being lower than the peak torque of a constant twist barrel. Early in the barrel, there is a relatively low amount of torque, that drastically increases for the first few inches of barrel length, peaking at around 12 to 16 foot-pounds between approximately 4 and 5 inches of barrel, before drastically decreasing and then gradually decreasing at approximately 10 inches of barrel.

FIG. 10 shows a graph of the torque applied on bullets by exponential gain twist rifling (EGTR). The vertical axis is the torque in foot-pounds and the horizontal axis if the projectiles position in the barrel. Specifically, the graph shows exponential twist having a smoothly increase in torque on the bullet towards the muzzle with the highest torque at the muzzle being lower than the peak torque of a constant twist barrel Compared to a conventional twist rate barrel, the preferred embodiment barrel shows a gradual increase in torque with high, but still lower than the maximum torque value of the conventional twist rate barrel of FIG. 9, occurring at approximately 20-inches of barrel length.

The reduction in the peak torque on the projectile improves the shooting performance of the rifle, including the torque felt by the end user. A firearm twists in hand or shoulder as the bullet experiences torque in the barrel. With a low initial torque and gradual increase to an overall lower torque compared to conventional twist rate barrels, the user experiences less torque. Also, the maximum torque being delayed until the projectile is much closer to exiting the muzzle of the barrel improves the user's accuracy potential and overall experience. The ability to see through an optic mounted on the firearm is also improved because the recoil event is improved through the reduced torque that the shooter experiences.

Fouling of the barrel is also improved. Fouling is an important consideration when it comes to exponential twist rate determination. The fouling, leading to accuracy deterioration and premature barrel wear out, occurs at the muzzle end due to high frictional and shear forces if the twist acceleration is too great. For example, a 16-inch barrel with EGTR that gains from 500:1 to 8:1 will experience accuracy degradation due to fouling at the muzzle end. Cleaning will restore accuracy. However, this fouling is an early indication of barrel wear that will continue and lead to early barrel deterioration. A 22-24 inch barrel with EGTR that gains from 500:1 to 8:1 does not experience fouling (leading to accuracy deterioration), or accelerated barrel wear. It was discovered that one of the unanticipated benefits of a MRR:EGTR approach is reduced barrel wear and barrel life extension of greater than 25%. That number is anticipated to increase as compared to conventional constant twist rate barrels for a given high pressure cartridge (e.g. 6.8×51 mm).

FIGS. 11A through 11J show graphs of the Degrees Rotated versus the Position and Instantaneous Twist in Degrees per Inch, with the left vertical axis being the Twist Rate in inches per revolution and Rate in Degrees per inch, and the right vertical axis being the degrees rotated, with respect to changes in the barrel length. The graphs illustrate conditions where changes to the value of variable such as Factor1, Factor2, and Exponent can affect Twist Rate or Degrees Rotated, or the Start Twist and End Twist.

Claims

1. A firearm barrel comprising:

an elongated barrel body defining a bore and having a breech end and a muzzle end;

the bore including a rifled surface defining rifling;

the rifling having a gain twist with a twist rate of a first amount proximate the breech end and a greater second amount proximate the muzzle end; and

the rifling having an eased rifling profile along the length of the rifling.

2. The barrel of claim 1 wherein the barrel body defines a cartridge chamber proximate the breech end.

3. The barrel of claim 2 wherein the barrel has a diameter at the chamber configured to contain a rated chamber pressure of at least 70,000 PSI.

4. The barrel of claim 3 wherein the barrel has a diameter at the chamber configured to contain a rated chamber pressure of at least 80,000 PSI.

5. The barrel of claim 1 wherein the bore defines a caliber at least 0.17 inches.

6. The barrel of claim 1 wherein the bore defines a caliber at most 0.50 inches.

7. The barrel of claim 1 wherein the barrel has a length of at most 34 inches.

8. The barrel of claim 1 wherein the barrel body is a barrel blank having rifling extending the entire length.

9. The barrel of claim 1 wherein the eased rifling is polygonal.

10. The barrel of claim 1 wherein the eased rifling includes a radiused transition from lands to grooves.

11. The barrel of claim 10 wherein the radiused transition is continuous and smoothly transitioned from the groove.

12. The barrel of claim 11 wherein the radiused transition is articulated at a vertex from the land.

13. The barrel of claim 1 wherein the eased rifling includes angled surfaces transitioning between lands and grooves, and wherein the angled surfaces are angularly offset from radial to the bore.

14. The barrel of claim 13 wherein the angled surfaces are offset from adjacent grooves by an obtuse angle.

15. The barrel of claim 13 wherein the angled surfaces are offset from adjacent lands by an obtuse angle.

16. A firearm barrel comprising of a breech end with a breech face and an opposing muzzle end with a muzzle face defining a bore therebetween,

the breech end defining a chamber for accommodating a cartridge,

the bore having a helixed surface of alternating raised radiused portions and lowered radiused portions that transition from one to another along a radial length and result in a given number of degrees rotated around the bore,

the bore having a first region forward of the chamber with a constant number of degrees rotated around the bore for the raised and lowered radiused portions, a second region aft of the muzzle with a constant number of degrees rotated around the bore for the raised and lowered radiused portions,

and a third region therebetween with a non-constant number of degrees rotated around the bore for the raised and lowered radiused portions the bore where the number of degrees rotated gains in number as it progresses from a gain start distance from the first region to a gain finish distance towards the second region.

17. The barrel of claim 16 wherein the number of degrees rotated around the bore is determined by the following mathematical formula where Factor1 and Factor2 are coefficients, x is a position along the bore of the barrel measured from the breech face, SR is a first number of degrees per inch rate, ER is a second number of degrees per inch rate, GSD is a distance from the breech face where the non-constant number of degrees rotated around the bore begins, and GFD is a distance from the breech face where a constant number of degrees rotated around the bore transitions to a non-constant number of degrees rotated around the bore transitions to a constant number of degrees rotated around the bore, and Exponent is an exponential numerical value. Factor ⁢ 1 * SR * ( x - GSD ) + Factor ⁢ 2 * ER - SR GFD - GSD * ( x - GSD ) Exponent