Theory behind the muzzle rise in AK 47

 

Theory behind the muzzle rise in AK 47

Hi guys!

Thanks for tuning into another blog, I hope all of you are fine, in this blog we saw about what factor behind the muzzle rise in AK 47

Let us see how the muzzle rise happens in sustained fire? The below image shows the center axis bore is misaligned with the buttstock also the buttstock is angled.




Before going into the topic, you must know the buttstock of the AK 47 is not in line with the axis of the bore

Recoil force transmission:

Recoil force in AK

Ø When a bullet is fired, the expanding gases generate a backward force on the rifle is known as recoil according to newtons third law of motion.

 

Ø Generally, the recoil force is generated along the bore axis (straight line along which the bullet travels).

 

Stock design:

Ø In AK 47 has a stock that is angled downward relative to the bore axis. This means the stock is not in line with the bore axis but slopes downward towards the shoulder.

Transmission of force and angled stock:

Force transmission:

Ø The recoil force travels along the path of least resistance, which in this case is the structure of the rifle, from the bore axis through the stock to the shooters shoulder.

 

Angled stock:

Ø Because the stock is angled downward relative to the bore axis, the direction in which the force is transmitted changes. The force is no longer purely horizontal but has to follow the angled path of the stock.

 

                                                     Or

Because the buttstock is angled, the recoil force (which acts along the bore axis) does not align perfectly with the direction in which the buttstock presses into the shoulder.

 

Decomposition of recoil force:

Force vector components:

Ø   The recoil force can be decomposed into two components: horizontal and vertical due to the miss alignment of stock.

 

Ø The angle of the stock means that the force vector (recoil) has a backward (horizontal) component and an upward (vertical) component due to the geometry of the angle.

 

Note:

An angle is a measure of the rotation or the amount of turn between two intersecting lines, rays or segments. It’s quantified in degrees, radians, or other units. An angle essentially tells you how wide or narrow the turn is at the point where the lines intersect.

 

Geometry of an angle refers to the study of the properties, relationships, and components of an angle, including its vertex, sides and how it interacts with other geometric figures.

 

 

Mathematical representation:

Ø If the stock were perfectly horizontal and in line with the bore axis, the recoil force would be directed straight back or purely horizontal.

 

Ø With the angled stock, the recoil force can be split into two vectors.

·       A horizontal vector that pushes the rifle backward.

·       A vertical vector that pushers the rifle upward.

 

Ø If the angle between the bore axis and the buttstock is (\ theta), the decomposition can be mathematically represented as:

 

·       (R- {\ parallel} = R\cos(\theta))

·       (R-{\Perpendicular} = R\ sin(\theta))

Where:

·            (R) is the magnitude of the total recoil force.

·    (R- {\ parallel} is the magnitude of the force component parallel to the buttstock.

·       (R-{\Perpendicular}is the magnitude of the force component perpendicular to the buttstock/

·           (\ theta) is the angle between the bore axis and the buttstock.

Torque and rotational effect:

Generation of torque:

·       The angled buttstock of the Ak 47 causes the recoil force to be misaligned with the direction of the buttstock. This misalignment means the recoil force is decomposed into two components.

 

·       One that pushes straight back (parallel to the buttstock) and one that pushes upward (perpendicular to the buttstock).

 

·       The upward component creates a torque around the center of mass of the fire arm, leading to muzzle rise.

 

Note: The process of decomposing a single force into two components based on an angle is a fundamental principle of vector decomposition in physics.

 

Center of mass:

·       The center of the mass of the AK 47 is typically below the bore axis. For example:

   In horizontal the area of the magazine well act as a center of mass.

  In vertical slightly above the trigger group but below the bore axis.

 

·       When the recoil force has a vertical component, it creates a rotational effect because the force is applied above the center of mass, causing the muzzle to lift.

Lever arm effect:

·       The distance between the bore axis (where the recoil force acts) and the point where the buttstock contacts the shoulder forms a lever arm. The angled buttstock increases this distance, magnifying the rotational effect and contributing to greater muzzle rise.

 

Visualization of forces:

Perfectly aligned stock:

·       If the stock were perfectly in line with the bore axis, the recoil force would push straight back into the shooters, shoulder with minimal rotational effect, resulting in less muzzle rise.

 

Angled stock:

·       With the angled stock, the recoil force follows the angled path of the stock, splitting into horizontal and vertical components.

 

·       Here the splitting of the force is due to the angle theta.

 

·       The vertical component lifts the muzzle, causing the rifle to pivot around its center of mass and resulting in muzzle rise.

 

 

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