Rifling

Twist rate

For best performance, the barrel should have a twist rate sufficient to spin-stabilize any bullet that it would reasonably be expected to fire, but not significantly more. Large-diameter bullets provide more stability, as the larger radius provides more gyroscopic inertia. In contrast, long bullets are harder to stabilize, as they tend to be very back-heavy and the aerodynamic pressures have a longer arm ("lever") to act on. The slowest twist rates are found in muzzle-loading firearms meant to fire a round ball; these will have twist rates as low as 1 in 72 inches (180 cm), or slightly longer, although for a typical multi-purpose muzzleloader rifle, a twist rate of 1 in 48 inches (120 cm) is very common. The M16A2 rifle, which is designed to fire the 5.56×45mm NATO SS109 ball and L110 tracer bullets, has a 1 in 7-inch (18 cm) or 32 calibers twist. Civilian AR-15 rifles are commonly found in 1 in 12 inches (30 cm) (54.8 cal) for older rifles and 1 in 9 inches (23 cm) (41.1 cal) for most newer rifles. However, some are made with 1 in 7 inches (18 cm) or 32-caliber twist rates, the same as those used for the M16 rifle. Rifles, which generally fire longer, smaller diameter bullets, will in general have higher twist rates than handguns, which fire shorter, larger diameter bullets.

There are three methods in use to describe the twist rate:

Traditionally, the most common method expresses the twist rate in terms of the 'travel' (length) required to complete one full revolution of the projectile in the rifled barrel. This method does not provide a straightforward understanding of whether a twist rate is relatively slow or fast when comparing bores of different diameters.

The second method describes the 'rifled travel' required to complete one full projectile revolution in calibers or bore diameters:

$${\displaystyle \text{twist}=\frac{L}{D_{\text{bore}}},}$$

where ${\displaystyle \text{twist}}$ is the twist rate expressed in bore diameters; ${\displaystyle L}$ is the twist length required to complete one full projectile revolution (in mm or in); and ${\displaystyle D_{\text{bore}}}$ is the bore diameter (diameter of the lands, in mm or in).

The twist travel ${\displaystyle L}$ and the bore diameter ${\displaystyle D_{\text{bore}}}$ must be expressed in a consistent unit of measure, i.e. metric (mm) or imperial (in).

The third method simply reports the angle of the grooves relative to the bore axis, measured in degrees.

The latter two methods have the inherent advantage of expressing twist rate as a ratio and provide an easy way to understand whether a twist rate is relatively slow or fast, even when comparing bores of differing diameters.

In 1879, George Greenhill, a professor of mathematics at the Royal Military Academy (RMA) at Woolwich, London, UK developed a rule of thumb for calculating the optimal twist rate for lead-core bullets. This shortcut uses the bullet's length and requires no allowances for weight or nose shape The eponymous Greenhill Formula, still used today, is:

$${\displaystyle \text{twist}=\frac{C{D}^2}{L}\times \sqrt{\frac{\mathrm{S}\mathrm{G}}{10.9}}}$$

where ${\displaystyle C}$ is 150 (use 180 for muzzle velocities higher than 2,800 f/s); ${\displaystyle D}$ is the bullet's diameter in inches; ${\displaystyle L}$ is the bullet's length in inches; and ${\displaystyle \mathrm{S}\mathrm{G}}$ is the bullet's specific gravity (10.9 for lead-core bullets, which cancels out the second half of the equation).

The original value of ${\displaystyle C}$ was 150, which yields a twist rate in inches per turn, when given the diameter ${\displaystyle D}$ and the length ${\displaystyle L}$ of the bullet in inches. This works up to velocities of about 840 m/s (2800 ft/s); above those velocities, a ${\displaystyle C}$ of 180 should be used. For instance, with a velocity of 600 m/s (2000 ft/s), a diameter of 0.5 inches (13 mm) and a length of 1.5 inches (38 mm), the Greenhill formula would give a value of 25, which means 1 turn in 25 inches (640 mm).

Improved formulas for determining stability and twist rates include the Miller Twist Rule and the McGyro program developed by Bill Davis and Robert McCoy.

If an insufficient twist rate is used, the bullet will begin to yaw and then tumble; this is usually seen as "keyholing", where bullets leave elongated holes in the target as they strike at an angle. Once the bullet starts to yaw, any hope of accuracy is lost, as the bullet will begin to veer off in random directions as it precesses.

Conversely, a rate of twist that is too high can also cause problems. The excessive twist can cause accelerated barrel wear and, coupled with high velocities, induce a very high spin rate, which can lead to projectile jacket ruptures, causing high-velocity spin-stabilized projectiles to disintegrate in flight. Projectiles made of a single metal cannot practically achieve flight and spin velocities high enough to cause disintegration in flight. Smokeless powder can produce muzzle velocities of approximately 1,600 m/s (5,200 ft/s) for spin stabilized projectiles and more advanced propellants used in smoothbore tank guns can produce muzzle velocities of approximately 1,800 m/s (5,900 ft/s). A higher twist than needed can also cause more subtle problems with accuracy; any inconsistency within the bullet, such as a void that causes an unequal distribution of mass, may be magnified by the spin. Undersized bullets also have problems, as they may not enter the rifling exactly concentric and coaxial to the bore, and excess twist will exacerbate the accuracy problems this causes.

A bullet fired from a rifled barrel can spin at over 300,000 rpm (5 kHz), depending on the bullet's muzzle velocity and the barrel's twist rate.

The general definition of the spin ${\displaystyle S}$ of an object rotating around a single axis can be written as:

$${\displaystyle S=\frac{\upsilon }{C}}$$

where ${\displaystyle \upsilon }$ is the linear velocity of a point in the rotating object (in units of distance/time) and ${\displaystyle C}$ refers to the circumference of the circle that this measuring point performs around the axis of rotation.

A bullet that matches the rifling of the firing barrel will exit that barrel with a spin:

$${\displaystyle S=\frac{{\upsilon }_0}{L}}$$ where ${\displaystyle {\upsilon }_0}$ is the muzzle velocity and ${\displaystyle L}$ is the twist rate.

For example, an M4 Carbine with a twist rate of 1 in 7 inches (177.8 mm) and a muzzle velocity of 3,050 feet per second (930 m/s) will give the bullet a spin of 930 m/s / 0.1778 m ≈ 5.230 kHz (313,835 rpm).

Excessive rotational speed can exceed the bullet's designed limits, and the resulting centrifugal force can cause the bullet to disintegrate radially during flight.

Design

A barrel of circular bore cross-section is not capable of imparting a spin to a projectile, so a rifled barrel has a non-circular cross-section. Typically, the rifled barrel contains one or more grooves that run down its length, giving it a cross-section resembling an internal gear. However, it can also take the shape of a polygon, usually with rounded corners. Since the barrel is not circular in cross-section, it cannot be accurately described with a single diameter. Rifled bores may be described by the bore diameter or land diameter (the diameter between lands or high points in the rifling), or by groove diameter (the diameter between grooves or low points in the rifling). Differences in naming conventions for cartridges can confuse; for example, the projectiles of the .303 British are actually slightly larger in diameter than the projectiles of the .308 Winchester, because the ".303" refers to the bore diameter in inches (bullet is .312), while the ".308" refers to the bullet diameter in inches (7.92 mm and 7.82 mm, respectively).

Despite differences in form, the common goal of rifling is to deliver the projectile accurately to the target. In addition to imparting spin to the bullet, the barrel must hold the projectile securely and concentrically as it travels down the barrel. This requires that the rifling meet several tasks:

• It must be sized so that the projectile will swage or obturate upon firing to fill the bore.
• The diameter should be consistent, and must not increase towards the muzzle.
• The rifling should be consistent down the length of the bore, without changes in cross-section, such as variations in groove width or spacing.
• It should be smooth, with no scratches lying perpendicular to the bore, so it does not abrade material from the projectile.
• The chamber and crown must smoothly transition the projectile into and out of the rifling.

Rifling may not begin immediately forward of the chamber. There may be an unrifled throat ahead of the chamber, so a cartridge may be chambered without pushing the bullet into the rifling. This reduces the force required to load a cartridge into the chamber and prevents a bullet from being left stuck in the rifling when an unfired cartridge is removed from the chamber. The specified diameter of the throat may be somewhat greater than the groove diameter, and may be enlarged by use if hot powder gas melts the interior barrel surface when the rifle is fired. Freebore is a groove-diameter length of smoothbore barrel without lands forward of the throat. Freebore allows the bullet to transition from static friction to sliding friction and gain linear momentum before encountering the resistance of increasing rotational momentum. Freebore may allow more effective use of propellants by reducing the initial pressure peak during the minimum volume phase of internal ballistics before the bullet starts moving down the barrel. Barrels with freebore length exceeding the rifled length have been known by a variety of trade names, including paradox.

Manufacture

An early method of introducing rifling to a pre-drilled barrel was to use a cutter mounted on a square-section rod, accurately twisted into a spiral of the desired pitch, mounted in two fixed square-section holes. As the cutter was advanced through the barrel, it twisted at a uniform rate governed by the pitch. The first cut was shallow. The cutter points were gradually expanded with repeated cuts. The blades were in slots in a wooden dowel, and the slots were gradually packed with slips of paper until the required depth was obtained. The process was finished off by casting a slug of molten lead inside the barrel, withdrawing it, and using it with a paste of emery and oil to smooth the bore.

Most rifling is created by either:

• Cutting one groove at a time with a tool (cut rifling or single point cut rifling);
• Cutting all grooves in one pass with a special progressive broaching bit (broached rifling);
• Pressing all grooves at once with a tool called a "button" that is pushed or pulled down the barrel (button rifling);
• Forging the barrel over a mandrel containing a reverse image of the rifling, and often the chamber as well (hammer forging);
• Flow forming the barrel preform over a mandrel containing a reverse image of the rifling (rifling by flow forming)
• Using non-contact forces such as chemical reaction or heat from laser source to etch the rifling pattern (etched rifling)
• Machining the rifling grooves texture on a thin metal plate, then folding the plate into the inner bore of the barrel (liner rifling)

The grooves are the spaces that are cut out, and the resulting ridges are called lands. These lands and grooves can vary in number, depth, shape, direction of twist (right or left), and twist rate. The spin imparted by rifling significantly improves the stability of the projectile, improving both range and accuracy. Typically, rifling is a constant rate down the barrel, usually measured by the length of travel required to produce a single turn. Occasionally, firearms are encountered with a gain twist, where the rate of spin increases from chamber to muzzle. While intentional gain twists are rare, slight gain twists due to manufacturing variance are, in fact, fairly common. Since a reduction in twist rate is very detrimental to accuracy, gunsmiths who are machining a new barrel from a rifled blank will often measure the twist carefully so they may put the faster rate, no matter how minute the difference is, at the muzzle end.

Projectiles

The original firearms were loaded from the muzzle by forcing a ball from the muzzle to the chamber. Whether using a rifled or smooth bore, a good fit was needed to seal the bore and provide the best possible accuracy from the gun. To ease the force required to load the projectile, these early guns used an undersized ball, and a patch made of cloth, paper, or leather to fill the windage (the gap between the ball and the walls of the bore). The patch acted as a wadding, provided some degree of pressure sealing, kept the ball seated on the charge of black powder, and kept the ball concentric with the bore. In rifled barrels, the patch also provided a means to transfer the spin from the rifling to the bullet, as the patch is engaged rather than the ball. Until the advent of the hollow-based Minié ball, which expands and obturates upon firing to seal the bore and engage the rifling, the patch provided the best means of getting the projectile to engage the rifling.

In breech-loading firearms, the task of seating the projectile into the rifling is handled by the throat of the chamber. Next is the freebore, which is the portion of the throat down which the projectile travels before the rifling starts. The last section of the throat is the throat angle, where the throat transitions into the rifled barrel.

The throat is usually sized slightly larger than the projectile, so that the loaded cartridge can be inserted and removed easily, but the throat should be as close as practical to the groove diameter of the barrel. Upon firing, the projectile expands under the pressure from the chamber and obturates to fit the throat. The bullet then travels down the throat and engages the rifling, where it is engraved, and begins to spin. Engraving the projectile requires significant force, and in some firearms, the substantial freebore helps keep chamber pressures low by allowing the propellant gases to expand before they are required to engrave the projectile. Minimizing freebore improves accuracy by reducing the likelihood that a projectile will deform before entering the rifling.

When the projectile is swaged into the rifling, it takes on a mirror image of the rifling as the lands push into the projectile in a process called engraving. Engraving captures not only the major features of the bore, such as the lands and grooves, but also minor features, such as scratches and tool marks. The relationship between the bore characteristics and the engraving on the projectile is often used in forensic ballistics.

Deep-cut groove rifling barrels can be found in automatic firearms to deliberately ease out the gas pressure (although it can affect their velocity), thereby surpassing the projectile. The Heckler & Koch VP70 is an example that uses this to ease pressure on the pistol slide.

Recent developments

The grooves most commonly used in modern rifling have fairly sharp edges. More recently, polygonal rifling, a throwback to the earliest types of rifling, has become popular, especially in handguns. Polygonal barrels tend to have longer service lives because the reduction of the sharp edges of the land (the grooves are the spaces that are cut out, and the resulting ridges are called lands) reduces erosion of the barrel. Supporters of polygonal rifling also claim higher velocities and greater accuracy. Polygonal rifling is currently seen on pistols from CZ, Heckler & Koch, Glock, Tanfoglio, and the Kahr Arms (P series only), as well as the Desert Eagle.

For field artillery pieces, the extended range, full bore (ERFB) concept developed in early 1970s by Dennis Hyatt Jenkins and Luis Palacio of Gerald Bull's Space Research Corporation for the GC-45 howitzer replaces the bourrelet with small nubs, which both tightly fit into lands of the barrel. Guns capable of firing these projectiles have achieved significant increases in range, but this is compensated with a significantly (3–4 times) decreased accuracy, due to which they were not adopted by NATO militaries. Unlike a shell narrower than the gun's bore with a sabot, ERFB shells use the full bore, permitting a larger payload. Examples include the South African G5 and the German PzH 2000. ERFB may be combined with base bleed.

Variable pitch rifling

A gain-twist or progressive rifling begins with a slow twist rate that gradually increases down the bore, resulting in very little initial change in the projectile's angular momentum during the first few inches of bullet travel after it enters the throat. This enables the bullet to remain essentially undisturbed and true to the case mouth. After engaging the rifling at the throat, the bullet is progressively subjected to accelerated angular momentum as it is propelled down the barrel. The theoretical advantage is that by gradually increasing the spin rate, torque is imparted along a much longer bore length, allowing thermomechanical stress to be spread over a larger area rather than being focused predominantly at the throat, which typically wears out much faster than other parts of the barrel. Gain-twist rifling was used before and during the American Civil War (1861–65). Colt Army and Navy revolvers both employed gain-twist rifling. Gain-twist rifling, however, is more difficult to produce than uniform rifling and, therefore, is more expensive. The military has used gain-twist rifling in a variety of weapons, such as the 20 mm M61 Vulcan Gatling gun used in some current fighter jets and the larger 30 mm GAU-8 Avenger Gatling gun used in the A10 Thunderbolt II close air support jet. In these applications, it enables lighter barrel construction by reducing chamber pressures through low initial twist rates while ensuring the projectiles have sufficient stability once they leave the barrel. It is seldom used in commercially available products, though notably on the Smith & Wesson Model 460 (X-treme Velocity Revolver).