Pros And Cons Of Rifling

Why are gun barrels rifled?

Background to rifling

Rifling consists of lands and grooves in the inside of a barrel, the lands are the part of the barrel which is not cut away while the grooves are the part of the barrel which is cut away. Lancaster oval bore, eight groove rifling and polygonal rifling are only a few example of rifling forms. Lancaster oval bore rifles have a smooth barrel interior. Unlike Lancaster oval bore rifles, grooved rifles have grooves which are engraved into the interior of the barrel. The polygonal rifle involves replacing the rectangle grooves with hills. The barrel consists as a polygonal shape of either a hexagon or octagon. [1]

Why are gun barrels actually rifled? Bullets should travel in a parabolic path; however, there are a number of factors which affect the path of a bullet. These include the forces acting on the bullet, twist rate and gyroscopic rate.
Once the bullet is fired from the gun, the bullet is no longer constrained by the interior of the gun therefore making its’ motion of path unpredictable.
The main forces acting on the bullet are gravity, air resistance and wind. Wind causes the bullet to move away from its course of path. If there is wind blowing from the left side of the bullet then this will cause the bullet to move to the right and vice versa. Gravity will cause the bullet to accelerate downwards at a rate of 9.81 m/s, whilst air resistance will cause the bullet to decelerate downwards with a force proportional to the square of its velocity thus, decreasing the velocity and kinetic energy. Hence, these three forces need to be considered when predicting the path of the
bullet. In ballistics, a projectile rotating about an axis perpendicular to its longitudinal axis is said to be in yawing motion, whereas rotation about a longitudinal axis is called a spinning motion. [2] This yawing motion causes the nose of the bullet to be travelling in a slightly different direction to where the bullet should be travelling, which changes the bullet’s stability. A force known as the Magnus force needs to act on the bullet which is perpendicular to the direction the bullet is travelling in, this causes the bullet to have some lift. The Magnus effect acts on the centre of pressure which affects the bullet’s stability. [3] This in turn affects the yaw angle, causing the bullet to spin.

[4]
Figure 2. Illustration of the forces acting on a bullet( Taken from Firearms, the law and forensic ballistics, Tom A. Warlow, CRC Press, 2nd edition 2004)

Figure 2 illustrates the forces acting on a bullet once it leaves the muzzle. The centre of pressure is near the tip of the nose whilst the centre of gravity is further away from the tip causing bullet instability. It is impossible to have the centre of gravity near to the bullet; therefore a rotation spin needs to be applied to the bullet to make it become stable. [4] This spin is due to an overturning moment which goes through the centre of gravity and perpendicular to the plane of air resistance. If this spin did not occur then the yaw angle would increase.
“A bullet has a spin axis, which is initially is aligned with its velocity vector. As the trajectory progresses, gravity accelerates the bullet downwards, introducing a velocity component. [5]
If insufficient spin is produced on the bullet, this will cause an unstable flight. In this type of situation the aerodynamic forces overpower the spin and the projectile wobbles and rotates violently, just like a gyroscope. If there is too much spin then the yaw angle is too large for the projectile to turn at the top, and it will then fall base down. It also does not produce the gyroscopic effect. With sufficient spin the bullet´s longitudinal axis moves into the direction of the overturning moment. This axis shift however alters the plane of drag, which then rotates about the velocity vector. This movement is called precession. [6]
A bullet requires a twist rate which stabilises a bullet spin to ensure maximum performance, preventing the bullet from yawing. This twist rate is calculated using the Greenhill formula:

where
D = bullet diameter in inches and L = bullet length in inches. [1]

When a bullet is spinning, the bullet is rotating about an axis, assuming the bullet is spinning clockwise then at the top of the ball, its clockwise spin is moving in a direction opposite to the airflow. This produces drag, slowing the ball, increasing pressure, and thus forcing it downward. At the bottom end of the ball, the clockwise motion is flowing with the air, thus resulting in higher velocity and lower pressure. As per Bernoulli's principle, this tends to pull the ball downward.

Conclusion
The main reason as to why gun barrels are rifled is to make the path of the bullet more accurate by stabilising the bullet. When the gun is fired, the grooves cause the bullet to spin and will continue to spin once the bullet exits the barrel. “The nose of the bullet follows the velocity vector. Turning the axis of rotation results in the nose pointing slightly to the right this results in a sideways drift known as ‘gyroscopic drift’ which stabilises the bullet.” [5] When a smoothbore gun fired a tapered bullet, it tumbled through the air creating more air resistance causing the bullet to slow down and decrease the accuracy, hence why gun barrels were rifled. [7]

Reference:

[1]Handbook of Firearms and Ballistics: Examining and Interpreting Forensic
Brian J. Heard, John Wiley & Sons 2nd edition 2008

[2] Mathematical theory of rocket flight, John Barkley Rosser, Robert R. Newton, McGraw-Hill Book Co, 1947

[3] Fundamentals of Fluid Mechanics (SI Version), Bruce R Munson, Donald F Young, John Wiley & Sons 6th edition

[4] Firearms, the law and forensic ballistics, Tom A. Warlow, CRC Press, 2nd edition 2004

[5] Gyroscopic Drift and Coreolis Acceleration, Brian Litz http://bryanlitz.bravehost.com/GyroCor.html

[6] Gyroscopic effect, http://www.nennstiel-ruprecht.de/bullfly/fig8.html

[7] Force and Motion (Physics in Our World), Kyle Kirkland, 1st edition 2007