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Greenhill Formula for Rifling Twists

The Time-honored Greenhill formula was originally used for determining twist rates in the new rifled artillery in the 19th Century.. It is important to note that it is projectile *length*, not *weight* which is the determining factor when considering the best twist rate for your intended use. Weight can vary for a specific bullet length from use of different material and also is determined to some degree by projectile shape. Often long-range match shooters utilizing low drag or VLD projectiles will voice a preference for "lazy" twists; i.e. just enough to stabilize the bullet. The requirements of a Shooter who is utilizing both high velocity and Subsonic ammunition are quite different.

When utilizing subsonic ammunition there is another factor to take into consideration. The projectile not only has only (about) 1/3 of the forward velocity of standard ammunition in Rifle calibers, it also has 1/3 of the *rotational* velocity...think "RPM's". This makes for a less gyroscopically-stable projectile, so a faster rate of twist is indicated than by simply applying Greenhill alone. This wisdom was imparted to me in a conversation with the great barrel-maker Boots Obermeyer. It makes perfect sense, and doubly so coming from him, so we'll take it as Gospel.

Greenhill Formula For Rifling Twists

T*B=150*Sqrt (Density of Lead/Density of Bullet)

T=Twist

B= Bullet length

Both units have to be in 'Calibers', density portion is optional

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To determine the *approximate* twist rate for a given projectile (this varies a bit by shape):

Using the a 190 gr Sierra MatchKing bullet #2210M (.,30 cal) as an example. If we measure the bullet's length it is 1.375" long .

B=Bullet length in *Calibers* (Length/Diameter), hence 1.375/0.308= 4.46 *calibers* long

From formula we have T=150/4.46=33.6. This figure is now in *calibers*, so we convert the twist from calibers to inches. So T=33.6 x 0.308=10.34".

This is why most commercial rifles in .300 Win. Magnum come with a 1:10" twist barrel.

***********

One can go further and get involved in formulas for density, but for most conventional lead/gilding metal projectiles, the above will suffice. Note that this is for a normal High Velocity loading. Subsonics generally require a somewhat faster twist rate. If one plans to use both High Velocity and Subsonic loads in the same platform, a good compromise which works acceptably for both must be found. If the platform is a "dedicated" gun in which subsonic ammunition alone will be used, then a faster rate can be utilized in order to be able to accurately shoot longer (and thus heavier) projectiles subsonically and with good accuracy.

Example:

Twist rates for 7.62mm/.308:

High Velocity only: 1:11-1/8" to 1:12"
Both: 1:10"
Subsonic ONLY: 1:8"

Bear in mind that "dedicated" back at the shop might not be "dedicated" in the field. Most knowledgeable end users prefer to have the option of utilizing both loads so as to be able to address changing tactical requirements on the spot.

Engel Ballistic Research, Inc.
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