EXTERNAL BALLISTICS IN SMALL ARMS

 

External Ballistics in Small arms

External ballistics is the branch of ballistics that deals with the behavior of a projectile in flight after it leaves the muzzle of a fire arm or launching device until it hits the target. It primarily focuses on the force acting on the projectile, such as gravity, air resistance (drag), wind, and other environmental factors, which influence the projectiles trajectory and accuracy.

       i.          Projectile and Projectile Motion:

A projectile is any object thrown, launched, or otherwise projected into the air that is only acted upon by gravity and air resistance.

Projectile motion refers to the motion of an object projected into the air, subject to the force of gravity and air resistance. And the motion is broken in two independent components: Horizontal and Vertical component.

 

     ii.          Horizontal and Vertical Component:

In the absence of air resistance, a projectile moves horizontally with constant velocity and the projectile experiences a constant acceleration due to gravity in vertically is known as vertical component.

 

    iii.          Trajectory:  

The path followed by a projectile under the influence of gravity is a parabola. The shape is determined by the initial velocity and angle of projection. This is due to the constant horizontal velocity and the uniformly accelerated motion in the vertical direction.

 

    iv.          Range of Projectile:

The range is the horizontal distance travelled by the projectile before it returns to the same vertical level from which it was projected. And the range is maximized when the angle of projection is 45^o

And the maximum range is the furthest distance a projectile can travel when fired at an optimal angle of elevation usually around 45 degrees in a vacuum. Extreme range refers to the furthest distance a projectile can travel under real world conditions, taking into account air resistance and other factors.

 

      v.          Maximum Height:

The maximum height is the highest vertical position reached by the projectile. At this point the vertical component of the velocity becomes zero.

 

    vi.          Time of Flight:

The time of flight is the total time the projectile is in the air. It depends on the initial vertical velocity and the height from which the projectile is launched.

 

  vii.          Acceleration Due to Gravity:

The acceleration that pulls the projectile downward. Near the Earth surface, this acceleration is approximately 9.8-meter second squad. Gravity is the only force acting on the projectile once it is in motion.

 

 viii.          Air Resistance:

A force that opposes the projectiles motion, typically ignored in basic physics but crucial in real world scenarios. Or Air resistance is the drag force exerted by the atmosphere against the forward motion of the projectile. It depends on factors like the projectiles speed, shape, and the density of the air. Higher speeds and less aerodynamic shapes result in greater air resistance.

 

    ix.          Symmetry of Flight:

For projectile launched and landing at the same height, the ascent and descent are symmetric in time and velocity magnitude.

 

      x.          Initial Velocity:

The speed at which a projectile is launched. It has two components horizontal and vertical.

 

    xi.          Launch Angle:

The angle at which a projectile is launched relative to the horizontal axis. It influences both the range and height of the projectile.

 

  xii.          Impact Velocity:

The speed and direction at which a projectile hits its target or the ground, taking into account both horizontal and vertical components.

 

 xiii.          Energy Considerations:

Kinetic energy: Varies during flight due to changes in speed.

Potential energy: varies with height.

 

 xiv.          Striking Angle:

The striking angle or angle of impact in projectile motion refers to the angle at which projectile, such as a bullet or artillery shell, strikes its target or the ground relative to a flat, horizontal surface.

Or

It is the angle between the path of the projectile and the surface it hits when it makes contact. This angle can vary depending on factors like the projectile trajectory, speed, and distance travelled.

 

   xv.          Angle of Fire:

The angle of fire refers to the angle at which a projectile is launched of fired relative to the horizontal plane. In simple terms it is the angle between the direction of the gun barrel and the ground when the projectile is fired. This angle is crucial in determining the projectiles trajectory, range, and point of impact.

The mentioned above is the basic physics in External Ballistics and projectiles and their flights. Let us see one by one in detail

       i.          Gradations Effect:

The term gradations effect generally refers to how changes in various factors such as environmental conditions or projectiles characteristics can influence the performance and trajectory of a projectile. It is an overarching term that covers how minor various can impart the projectiles behavior.

 

     ii.          Muzzle Velocity:

Muzzle velocity is the speed of a projectile as it exits the barrel of a firearm. It is crucial because it determines the initial kinetic energy and affects the trajectory, range, and accuracy of the projectile. Higher muzzle velocity usually results in a flatter trajectory and longer range.

 

    iii.          Flatter Trajectory:

A flatter trajectory in the context of projectiles or ballistic paths refers to a path where the projectile travels with less vertical displacement relative to its horizontal distance. In simpler terms, it means that the projectile moves in a straighter line rather than a steep arc.

The main advantages of a flagger trajectory are,

·        Improved Accuracy: A flatter trajectory reduces the effect of gravity over the distance travelled, which can make it easier to hit a target accurately, especially at longer ranges.

·        Reduced Wind Drift: The shorter time the projectile spends in the air, the less it is affected by crosswinds, which helps in maintaining accuracy.

·        Simple Targeting: With less drop over distance, shooters or gunners can use simpler aiming techniques and less adjustment for distance, which can be beneficial in fast paced or dynamic situations.

·        Higher Impact Energy: A flatter trajectory can result in a higher impact velocity at the target, which may translate into more kinetic energy and grater effectiveness.

 

    iv.          Angle and Elevation of the Barrel:

The angle of elevation is the angle at which the firearms barrel is tilted upwards relative to the horizontal plane. This angle influences the trajectory of the projectile range but also increases the time of flight and the maximum height it will reach.

 

      v.          Sectional Density of the Bullet:

Sectional density is the ratio of a bullets mass to its cross-sectional area. It is calculated as

Sectional density = Mass / Diameter²

 

    vi.          Bullet Shape:

The shape of a bullet affects its aerodynamic properties. Common shapes include;

·        Spitzer or Pointed: Reduces air resistance and improves long range accuracy.

·        Round-nosed: More drag, suitable for shorter ranges.

·        Boat tail: Reduces drag and improves long range stability.

  vii.          Drop of Fall:

Drop of fall refers to the vertical distance a projectile fall from its original line of sight due to gravity. As a projectile travels, it will drop progressively more, following a parabolic path.

 

 viii.          Angle of Fall:

The angle of fall is the angle at which the projectile impacts the target relative to the ground. It is influenced by the trajectory and the range of the projectile.

Or

It is the angle at which a projectile drops down to the surface before reaching the target or after being hit to the target.

 

    ix.          Remaining velocity:

Remaining velocity is the speed of the projectile at any point during its flight after accounting for losses due to air resistance and gravitational effects. It decreases from the initial muzzle velocity.

 

      x.          Spin and drift:

·        Spin: This is the rotational motion imparted to a projectile, usually by the rifling inside the barrel of a firearm. The spin stabilizes the projectile, helping to maintain a straighter path through the air. It counteracts destabilizing forces and contributes to the accuracy and consistency of the projectiles flight.

·        Drift: This term typically refers to the lateral movement of the projectile due to external forces, primarily the Coriolis effect, which is caused by the rotation of the Earth. Drift can also be influenced by other factors such as wind or the projectiles design. In practical terms, drift means that a projectile may not hit exactly where aimed, and adjustments need to be made to compensate for this lateral deviation.

 

Coriolis Effect: Due to earths rotation, a projectile travelling over long distances will experience a slight deviation in its trajectory. In the Northern hemisphere, this causes a projectile to drift to the right, while in the southern Hemisphere, it drifts to the left.

 

Wind: Cross winds can push a projectile off course laterally, causing it to drift form the intended path.

 

Projectile Spin: The spin induced by the rifling in a firearm can also create a phenomenon known as gyroscopic drift where the projectile may drift due to its rotational motion interacting with aerodynamic forces.

 

 xvi.          Gyroscope Effect:

The gyroscope effect, or gyroscopic stability, refers to the tendency of a spinning object to maintain its orientation due to its angular momentum. When an object spins, it resists changes to its axis of rotation because of this angular momentum. This resistance is what stabilizes the object and helps it maintain its orientation, making it less likely to wobble or change direction.

 

xvii.          Structure of Projectiles:

The structure of projectiles involves their design and construction, which includes materials used such as lead, copper, or steel, shape and internal mechanisms like hollow points or fragmentation. This structure imparts the projectile performance, penetration, and terminal effects.

 

xviii.          Gravitational Pull:

Gravitational pull is the force exerted by the earth that attracts the projectile downward. It causes the projectile to follow a curved path, resulting in the drop of fall over distance.

 

 xix.          Weather Conditions:

Weather conditions, such as wind speed, temperature, and humidity, affect the projectiles flight. Wind can cause drift, temperature and humidity can influence air density, and all these factors can alter the trajectory and accuracy of the projectile.

 

   xx.          Muzzle Energy:

Muzzle energy is the kinetic energy of the projectile as it exits the barrel. It is calculated using

 

Muzzle Energy = ½ x Mass x Muzzle Velocity²

 

 xxi.          Momentum:

Momentum is the quantity of motion of the projectile, given by

 

Momentum = Mass x Muzzle Velocity

 

xxii.          Trajectory formation:

Trajectory formation refers to the path that the projectile follows through the air. It is influenced by the initial velocity, angel of elevation, gravity, air resistance, and other factors. The trajectory typically follows a parabolic path under ideal conditions.

 

xxiii.          Escape Velocity:

Escape velocity is the minimum speed needed for a projectile to break free from the Earth’s gravitational influence without further propulsion. It is around 11.2 km/s about 25,000 mph at the Earth’s surface.

 

xxiv.          Wind of Deflection:

If the wind is against the projectile, then the velocity is decreased. If the wind is along the direction of the projectile, then the velocity is increased.

·        So far, the velocity of the wind is concerned it will make drift to the left when blowing from the right of the bullet to its left.

·        If the wind direction is from the left of the bullet to its right, the bullet will get a drift to its right.

·        If the motion of the wind is in the same direction as the at of the bullet, it adds to the velocity of the projectile.

·        Similarly, the wind blowing against the direction of the bullet will decrease the velocity of the bullet.

 

 

xxv.          Zero Range:

It is the range where a projectile intersects the line of sight. It occurs twice, once the way up and the other on the way down.

 

xxvi.          Temperature:

In cold temperature, more density causes decreases in velocity, and in cold temperature low chamber pressure develops which also reduces the initial velocity because the many propellants are temperature sensitive. In colder temperatures, the burn rate of the propellent may slow down, leading to reduced pressure within the chamber. This can result in lower muzzle velocity and potential performance issues.

And in hot temperatures, less density causes less air resistance that is very less reduction in velocity. And many propellent are more volatile in higher temperatures. The increased heat can cause the propellent to burn faster, leading to higher chamber pressure. This can result in higher muzzle velocities but also increases the risk of overpressure situations, which can be dangerous.

 

xxvii.          Ricochet of Bullet:

It is a phenomenon that refers to the deflection of the projectile from its trajectory on the line of motion after hitting hard objects even from bones. A ricocheted bullet is deviated from its trajectory by striking an intermediary object.

·        Critical Angle: It is the minimum angle at which the bullet may produce a ricochet phenomenon is known as the critical angle. Ricochet angle is the actual degree to which a bullet producing ricochet from the surface is know as a ricochet angle.

Ricochet of a bullet may vary with:

·        Bullet shape

·        Bullet material

·        Bullet spin

·        Velocity of bullet

·        Intermediary surface

·        Angle of incidence

·        Nose of bullet

 

xxviii.          Different Behaviors of Bullet:

Some times when a bullet leaves the barrel, the bullet is in the slightly unstable condition which is due to three main factors:

 

·        Yaw: The yaw in external ballistics refers to the wobbling or tilting of a bullet left or right as it flies through the air. Instead of flying perfectly straight with its nose pointed directly along its path, the bullet might wobble slightly form side to side or up and down. This wobble can happen right after the bullet leaves the barrel or continue as it flies. Too much yaw can make the bullet less accurate and slow it down due to increased air resistance.

 

Or

In the context of the external ballistics, yaw refers to the angular deviation of a projectile nose from its line of flight. Essentially, it is the side to side or up and down wobbling motion of the projectiles travels through the air.

 

When the bullet is fired, ideally, it should travel with its nose perfectly aligned with its trajectory, minimizing air resistance and maximizing stability. However, due various factors such as imperfections in the barrel, spin rate or atmospheric conditions), the bullet may not follow this ideal path, causing it to yaw.

 

·        Precession: Precession refers to the circular or spiral motion of a spinning bullets nose as it tries to align with its flight path. When a bullet spins due to the rifling in the barrel, the forces acting on it such as gravity and air resistance can cause the bullets nose to move in a circular pattern around its Centre of mass. This motion is called precession.

 

·        Nutation: After a bullet is fired, as it spins through the air, its nose might not just follow a smooth circular path (precession), but it also can wiggle or oscillate around that path. This wobbling or oscillation is called nutation.