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Bullet Trajectory refers to the path traveled by a projectile (such as a bullet, shell, etc.) through the air, encompassing the entire process from the moment of firing, through its flight in the air, to the point where it impacts the target.

2. Calculation of Ballistic Coefficient

· Ballistic Coefficient (BC) is a parameter used to evaluate the air resistance a bullet encounters while flying through the air. A higher BC value indicates less air resistance, meaning the bullet is better at maintaining its speed and energy during flight. This results in a more stable trajectory and better performance, especially for long-range shooting. BC values are typically provided on the bullet packaging or listed on firearm websites.

When calculating the BC, the G1 model is commonly used, which is suitable for most non-streamlined projectiles (such as the majority of rifle bullets). The general formula for BC calculation is as follows:

Involved parameters:

· Mass(m)：The weight of the bullet, typically measured in grains (gr).

· Diameter(d)：The caliber of the bullet, measured in inches.

· Form Factor(i)：A coefficient related to the shape and aerodynamic characteristics of the projectile. In the G1 model, the bullet is typically designed with a flat or pointed tip, which is common for hunting ammunition.

Here are some common hunting bullets and their corresponding BC values:

Bullet Model	Common Bullet Weight(grains)	BC Value Range	Form Factor（i）
.223 Remington	55–77 gr	0.200–0.400	1.0–1.2
.243 Winchester	55–105 gr	0.300–0.500	0.95–1.1
.270 Winchester	130–150 gr	0.400–0.500	0.9–1.0
.30-06 Springfield	150–180 gr	0.400–0.615	0.9–1.05
6.5mm Creedmoor	120–147 gr	0.500–0.650	0.85–1.0
7mm Remington Magnum	140–175 gr	0.500–0.620	0.85–1.0
.338 Lapua Magnum	250–300 gr	0.600–0.800	0.85–0.95

3. Firearm Classification and Ballistic Characteristics

For ballistic calculation, the classification of firearms is crucial, as different types of firearms exhibit significant differences in their dynamic characteristics during firing. Firearms are primarily classified into two main categories:

1) Air Rifles

Air rifles use compressed air or carbon dioxide as a propellant. Compared to gunpowder gun, air rifles have lower power, produce less recoil, and have a more concentrated shot group, making them highly accurate at close range. Air rifles typically use two types of lead pellets, with weights ranging from 0.8 grams to 3.0 grams. Due to the light weight and simple shape of lead pellets, their ballistic coefficient (BC) is relatively low, usually below 0.1. Because of their limited power, air rifles are generally used for close-range target shooting.

Common types of hunting air rifles include:

① Spring Piston Air Rifles: Suitable for hunting small game at short distances. Examples include the Weihrauch HW97K, Diana 34 EMS, and Gamo Whisper Fusion Mach series.

② Pre-Charged Pneumatic (PCP) Air Rifles: Capable of multiple shots, suitable for precise hunting at medium to long distances. Examples include the Air Arms S510 series, FX Impact, and Benjamin Marauder.

③ CO2 Air Rifles: Typically suited for short-range hunting and stable temperature environments. An example is the Crosman 2240.

④ Multi-Pump Pneumatic Air Rifles: Suitable for hunting small game. An example is the Crosman 2100B.

2) Firearms

Firearms use the explosive force of gunpowder to propel the bullet, providing significant power and recoil. Firearms are suitable for long-range shooting and offer higher precision, but due to their greater power, they also generate more recoil. Firearms typically use bullets weighing over 10 grams, with ballistic coefficients (BC) ranging from 0.3 to 0.6. The ballistic calculation for firearms is more complex due to the numerous influencing factors, particularly in long-range shooting, where external conditions such as airflow and temperature significantly affect the trajectory.

Common types of hunting firearms include:

① Rifles: Includes bolt-action rifles, semi-automatic rifles, lever-action rifles, and pump-action rifles, suitable for long-range shooting of medium to large game, especially for precise hunting. Examples include the Remington 700, Winchester Model 70, and Savage Axis series.

② Shotguns: Suitable for hunting birds, rabbits, wild boar, and other close-range game, typically using shot pellets. Examples include the Benelli Super Black Eagle series, Mossberg 500 series, and Remington 870 series.

4. Zeroing Adjustment

Zeroing is a core step in ballistic calculator. It is generally recommended that users start by zeroing at a closer distance and then progressively adjust to longer distances. Typically, the zeroing process involves identifying three key points: close-range zero, long-range zero, and intermediate adjustment points. This ensures that the bullet aligns with the point of aim throughout its flight. After zeroing, users should make fine adjustments based on actual shooting conditions to achieve optimal shooting accuracy.

Night Stalker 4K is DAY & NIGHT VISION RIFLE SCOPE launched by PARD in 2024, featuring a 4K CMOS sensor and round display with a full-screen centered reticle. The round display and 100mm eye relief design closely mimics the traditional hunting habits, offering the same look and feel as a daytime scope. The following are the complete zeroing steps using the PARD Night Stalker 4K as an example:

① Set the target at the zeroing distance so that the device can obtain a good image.

② Select the zero setting sub-menu: please refer to the reticle adjustment option in the menu operation mode for specific steps.

③ Fire a 1st shot after focusing on the image, ensuring that you can see a clear point of impact on the screen after the shot has been taken.

④ Keep the scope in a stable position after shooting, and then press the knob to move the cursor to the "X" and "Y" items. Rotate the knob to freeze the screen and adjust the values of "X" and "Y" until the point of impact on the display screen is moved to the center point of the reticle.

⑤ To save and exit - set the "Save" item to "Y", after the setting is completed, press and hold the knob to save and exit. The actual point of impact is moved to the center point of the reticle (the reticle is always at the center of the screen, which can maximize the use of the whole observation field).

Note: The first item in the sub-menu represents the saved “zero” setting, there are five profiles A-E. The "X" and "Y" values represent the corresponding display positions of the reticle. "Style" represents the corresponding reticle type. "Color" represents the corresponding color of the reticle.

5. Key Parameter of Ballistic Calculator

Intelligent ballistic calculator uses high-precision ballistic algorithms to calculate the trajectory of the projectile. After inputting relevant parameters that affect the trajectory, the system provides accurate reference markings based on the calculations, allowing even beginners to easily get started and quickly hit their targets.

Below is an explanation of each parameter and recommendations for how to set them:

1) Velocity

·  Definition: The instantaneous velocity of the bullet as it exits the muzzle. The higher the muzzle velocity, the farther the bullet will travel, and the less it will be affected by gravity and air resistance. Therefore, in ballistic calculator, muzzle velocity is one of the core variables affecting the trajectory, typically measured in meters per second (m/s) or feet per second (ft/s).

·  Setting: This value is usually provided by the ammunition manufacturer or can be measured using tools such as a chronograph.

2) Bullet Wt

·  Definition: Bullets of different weights experience different gravitational forces after leaving the barrel, which affects the trajectory. This is typically measured in grams (g) or grains (gr).

·  Setting: This value can be derived from the bullet specifications provided by the manufacturer or measured by yourself.

3) Bullet BC

·  Definition: As mentioned earlier, the BC value reflects the bullet's ability to overcome air resistance, which is an important indicator of the projectile’s flight performance. Bullets with higher BC values experience less resistance during flight, maintain speed more effectively, travel longer distances, and have more stable trajectories.

·  Setting: Use the ballistic coefficient provided by the manufacturer or calculate it using ballistic calculators available on websites or apps.

4) Altitude

·  Definition: The elevation of the shooting location, measured in meters (m) or feet (ft). Elevation affects air density, which in turn impacts the bullet’s trajectory. As altitude increases, the air becomes thinner, reducing the bullet's flight resistance and increasing its range.

·  Setting: Use GPS or geographic tools to determine the altitude. In civilian applications, the effect of temperature and altitude on the trajectory is often negligible, so approximate values can be used.

5) Temperature

·  Definition: The ambient air temperature, measured in Celsius (°C) or Fahrenheit (°F). Temperature affects air density, which in turn influences the bullet’s flight resistance. In hotter conditions, air density decreases, reducing the flight resistance.

·  Setting: Enter the current or expected temperature of the shooting environment. This can be obtained from weather station data or weather apps.

6) Baseline Height

·  Definition: Baseline height refers to the vertical distance between the optical axis of the scope and the barrel axis, measured in millimeters (mm) or inches (in). This height affects the bullet’s trajectory. A larger baseline height will result in greater bullet drop at longer distances, so it must be considered in ballistic calculator.

·  Setting: Accurately measure the distance between the center of the scope and the center of the barrel using measuring tools.

7) Zeroing Distance

·  Definition: Zeroing refers to adjusting the scope at a specific distance so that the center of the reticle aligns with the point of impact, and this distance is referred to as the zeroing distance, measured in meters (m) or yards (yds).

·  Setting: Set the value according to the actual zeroing distance.

Among these, the bullet's velocity and BC value are important variables, while zeroing distance and baseline height are key factors that affect the trajectory. These parameters need to be accurately entered into devices with ballistic calculator systems, which will then provide the correct reference markings through intelligent calculation.

 

Summary:

In conclusion, ballistic calculator involve multiple complex variables. By accurately setting parameters like bullet velocity, BC value, and zeroing distance, and considering environmental factors such as temperature and altitude, one can more effectively predict the bullet's flight path. Mastering the basic principles and methods of ballistic calculation can significantly improve shooting success rates and efficiency. This technical document aims to provide valuable guidance for users, helping achieve higher shooting precision and performance in practical applications.