FORMULA FOR CALCULATING TWIST RATE IN GIVEN PROJECTILE

 

FORMULA FOR CALCULATING TWIST RATE IN GIVEN PROJECTILE

The Greenhill formula is a simpler equation used to estimate the rifling twist rate required to stabilize a projectile. It was developed by Sir Alfred George Greenhill in the 19th century and remains widely used, particularly for small arms ballistics.



How much Twist?

Of course, the more turns the rifling makes in the bore – the twist rate – the faster the projectile will spin. What remained to be discovered is just how fast a round ball needed to spin to be stabilized for greater accuracy. That is, what twist rate for rifling.

Twist rate is expressed as a ratio of how many complete 360 degree turns the rifling makes per inch barrel, such as 1:10 inch meaning one complete twist per 10 inches. Note the barrel length has no bearing in the twist rate; a rate of 1:10 remains 1:10 whether a barrel is three inches or three feet long.

The twist rate of a rifle barrel is crucial in determining how well it stabilizes a projectile in flight. It refers to the rate at which the rifling inside the barrel spins the projectile, usually expressed as the distance in inches it takes for the rifling to complete one full rotation also the twist rate affects how well a projectile is stabilized, which directly influences accuracy and consistency. Here’s a detailed breakdown of how twist rates interact with heaver and lighter projectiles.

Stability is primarily influenced by the Length of the Projectile, which correlates closely with its weight (heavier projectiles are often longer). The gyroscopic effect produced by spin stabilizes the projectile in flight, preventing it from tumbling. And the required twist rate for stabilization is determined using the Greenhill formula or the more precise Miller Stability formula.

Heavier Projectiles are typically longer and require a faster twist rate that is a lower numerical value for example 1:7. A faster twist rate generates more spin, ensuring that the projectile is gyroscopically stable in flight.

Lighter projectiles are shorter and require a slower twist rate that is higher numerical value for example 1:14 twist rate. If these projectile spins too fast, lighter projectile may destabilize due to over-stabilization, which can increase drag and disrupt the flight path.

GREENHILL FORMULA:

 

Where:

T = Twist rate in inches per turn (distance the bullet travels to make one full rotation).

C = Constant, typically 150 for lead core (or 180 for supersonic speeds).

D = Bullet diameter in inches.

L = Bullet length in inches.

SG = Specific gravity of the bullet material (usually around 10.9 for lead-core bullets).

Using a Nosler spitzer bullet in a 30.06 Springfield, which is similar to the one pictured above, and substituting values for the variables, we determine the estimated optimum twist rate by using the above green hill formula



 where

m = 180 grains

s = 2.0 (the safe value noted above)

d = .308 inches

l = 1.180" /.308" = 3.83 calibers

Solution:

D2 = (0.308)2 = 0.094864

Now calculate the twist rate

T = 150 x 0.094864 / 1.180

T = 14.2296 / 1.180

T = 12.06 inches per turn.

MILLERS FORMULA:


m = bullet mass in grains (defined as 64.79891 milligrams)

s = gyroscopic stability factor (dimensionless)

d = bullet diameter in inches

l = bullet length in calibers (that is, length in relation to the diameter)

t = twist rate in calibers per turn


T= Ttwist rate in inches per turn



L = Lbullet length in inches.



 Using a Nosler spitzer bullet in a 30.06 Springfield, which is similar to the one pictured above, and substituting values for the variables, we determine the estimated optimum twist rate by using the above green hill formula



where

m = 180 grains

s = 2.0 (the safe value noted above)

d = .308 inches

l = 1.180" /.308" = 3.83 calibers

When computing using this formula, Miller suggests several safe values that can be used for some of the more difficult to determine variables.

 For example, he states that a Mach number of M= 2.5 (roughly 2800 ft/sec, assuming standard conditions at sea level where 1 Mach is roughly 1116 ft/sec) is a safe value to use for velocity. He also states that rough estimates involving temperature should be use 2.0.



 Substituting the t value in T



39.2511937 / .308 = 12.0893677

Thus, the optimum rate of twist for this bullet should be approximately 12 inches per turn. The typical twist of .30-06 caliber rifle barrels is 10 inches per turn, accommodating heavier bullets than in this example. A different twist rate often helps explain why some bullets work better in certain rifles when fired under similar conditions.

 

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