Editing Rifling (section)

== Twist rate ==
[[Image:Rus122shrapnel.JPG|thumb|Russian 122 mm shrapnel shell (which has been fired) showing rifling marks on the [[copper]] alloy [[driving band]] around its base, indicating clockwise spin]]
[[File:Cannonball equiped with winglets for rifled cannons circa 1860.jpg|thumb|[[Round shot|Cannonball]] equipped with winglets inside the bore of a  rifled cannon c. 1860]]
[[File:Shell La Hitte.jpg|thumb|upright|Ogival shell of the [[La Hitte system]], 1858, designed to engage with clockwise rifling]]

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 [[angular momentum|gyroscopic inertia]], while long bullets are harder to stabilize, as they tend to be very backheavy 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 {{convert|72|in|cm}}, or slightly longer, although for a typical multi-purpose muzzleloader rifle, a twist rate of 1 in {{convert|48|in|cm}} is very common. The [[M16 rifle|M16A2]] rifle, which is designed to fire the [[5.56×45mm NATO|5.56×45mm NATO SS109 ball and L110 tracer]] bullets, has a 1 in {{convert|7|in|cm|adj=on}} or 32 calibers twist. Civilian [[AR-15]] rifles are commonly found with 1 in {{convert|12|in|cm}} or 54.8 calibers for older rifles and 1 in {{convert|9|in|cm}} or 41.1 calibers for most newer rifles, although some are made with 1 in {{convert|7|in|cm}} or 32 calibers twist rates, the same as 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:

The, traditionally speaking, most common method expresses the twist rate in terms of the 'travel' (length) required to complete one full projectile revolution in the rifled barrel. This method does not give an easy or straightforward understanding of whether a twist rate is ''relatively'' slow or fast when bores of different diameters are compared.

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

<math display=block>\text{twist} = \frac{L}{D_\text{bore}},</math>

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

The twist travel <math>L</math> and the bore diameter <math>D_\text{bore}</math> 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 give an easy understanding if 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, Woolwich|Royal Military Academy (RMA) at Woolwich]], London, UK<ref>[http://www-history.mcs.st-andrews.ac.uk/~history/Biographies/Greenhill.html "Alfred George Greenhill." (October 2003).] School of Mathematics and Statistics, University of St Andrews, Scotland.</ref> developed a [[rule of thumb]] for calculating the optimal twist rate for lead-core bullets. This shortcut uses the bullet's length, needing no allowances for weight or nose shape.<ref>Mosdell, Matthew. ''The Greenhill Formula''.http://www.mamut.net/MarkBrooks/newsdet35.htm (Accessed 2009 AUG 19)</ref> The eponymous ''Greenhill Formula'', still used today, is:

<math display=block>\text{twist} = \frac{C D^2}{L} \times \sqrt{\frac{\mathrm{SG}}{10.9}}</math>

where <math>C</math> is 150 (use 180 for muzzle velocities higher than 2,800 f/s); <math>D</math> is the bullet's diameter in inches; <math>L</math> is the bullet's length in inches; and <math>\mathrm{SG}</math> 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 <math>C</math> was 150, which yields a twist rate in inches per turn, when given the diameter <math>D</math> and the length <math>L</math> of the bullet in inches. This works to velocities of about 840&nbsp;m/s (2800&nbsp;ft/s); above those velocities, a <math>C</math> of 180 should be used. For instance, with a velocity of 600&nbsp;m/s (2000&nbsp;ft/s), a diameter of {{convert|0.5|in|mm}} and a length of {{convert|1.5|in|mm}}, the Greenhill formula would give a value of 25, which means 1 turn in {{convert|25|in|mm}}.

Improved formulas for determining stability and twist rates include the [[Miller Twist Rule]]<ref>Miller, Don. ''[http://www.jbmballistics.com/bibliography/articles/miller_stability_2.pdf How Good Are Simple Rules For Estimating Rifling Twist]{{dead link|date=April 2018 |bot=InternetArchiveBot |fix-attempted=yes }}'', Precision Shooting, June 2009</ref> and the McGyro program<ref>{{cite web |url=http://www.jbmballistics.com/ballistics/downloads/text/mcgyro.txt |type=BASIC |format=TXT |title=McGyro |author=R. L. McCoy<!--Not stated--> |date=April 1986 |website=JBM Ballistics |access-date=November 18, 2017 |archive-date=October 12, 2017 |archive-url=https://web.archive.org/web/20171012150803/http://www.jbmballistics.com/ballistics/downloads/text/mcgyro.txt |url-status=live }}</ref> developed by Bill Davis and Robert McCoy.

[[Image:parrottgun.jpg|right|thumbnail|A [[Parrott rifle]], used by both [[Confederate States Army|Confederate]] and [[Union Army|Union]] forces in the [[American Civil War]].]]

If an insufficient twist rate is used, the bullet will begin to [[Yaw angle|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 [[Precession|precesses]].

Conversely, too high a rate of twist can also cause problems. The excessive twist can cause accelerated barrel wear, and coupled with high velocities also induce a very high spin rate which can cause projectile [[Bullet#Materials|jacket]] ruptures causing high velocity spin stabilized projectiles to disintegrate in flight. Projectiles made out of mono metals cannot practically achieve flight and spin velocities such that they disintegrate in flight due to their spin rate.<ref>{{cite web|url=http://www.gsgroup.co.za/22x64.html|title=GS CUSTOM BULLETS&nbsp;— The 22x64 Experiment|access-date=2011-12-09|archive-date=2012-03-20|archive-url=https://web.archive.org/web/20120320024136/http://gsgroup.co.za/22x64.html|url-status=live}}</ref> [[Smokeless powder]] can produce muzzle velocities of approximately {{convert|1600|m/s|ft/s|abbr=on}} for spin stabilized projectiles and more advanced propellants used in [[smoothbore]] tank guns can produce muzzle velocities of approximately {{convert|1800|m/s|ft/s|abbr=on}}.<ref>{{cite web | url=http://www.defense-update.com/products/digits/120ke.htm | title=120mm Tank Gun KE Ammunition | publisher=Defense Update | access-date=2007-09-03 | date=2006-11-22 | archive-url=https://web.archive.org/web/20070805005735/http://www.defense-update.com/products/digits/120ke.htm | archive-date=2007-08-05 | url-status=dead }}</ref> 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 [[Revolutions per minute|rpm]] (5 [[kHz]]), depending on the bullet's [[muzzle velocity]] and the barrel's [[twist rate]].

The general definition of the spin <math>S</math> of an object rotating around a single axis can be written as:

<math display=block>S = \frac{\upsilon}{C}</math>

where <math>\upsilon</math> is the linear [[velocity]] of a point in the rotating object (in units of distance/time) and <math>C</math> 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:

<math display=block>S = \frac{\upsilon_0}{L}</math>
where <math>\upsilon_0</math> is the muzzle velocity and <math>L</math> is the twist rate.<ref>{{cite web |url= http://accurateshooter.wordpress.com/2008/06/03/calculating-bullet-rpm-spin-rates-and-stability/ |title= Calculating Bullet RPM |date= 3 June 2008 |access-date= 4 February 2015 |archive-date= 8 August 2010 |archive-url= https://web.archive.org/web/20100808011856/http://accurateshooter.wordpress.com/2008/06/03/calculating-bullet-rpm-spin-rates-and-stability/ |url-status= live }}</ref>

For example, an M4 Carbine with a twist rate of 1 in {{convert|7|in|mm|1}} and a muzzle velocity of {{convert|3050|ft/s|m/s|0}} will give the bullet a spin of 930&nbsp;m/s / 0.1778 m = 5.2&nbsp;kHz (314,000 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.<ref>{{cite web|url=http://www.loadammo.com/Topics/July01.htm |title=Twist Rate |date=18 August 2012 |access-date=4 February 2015 |url-status=dead |archive-url=https://web.archive.org/web/20130512015023/http://www.loadammo.com/Topics/July01.htm |archive-date=May 12, 2013 }}</ref>