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
m = 180 grains
s = 2.0 (the safe value
noted above)
d = .308 inches
l = 1.180"
/.308" = 3.83 calibers
Solution:
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= twist rate in inches per turn
L
=
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
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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