What to Remember When Calculating Bullet Trajectory
Bullet trajectory is one of the most important aspects of accurate long-range shooting. Unfortunately, it is also one of the most misunderstood. Let us help you understand bullet trajectory and how it is corrected or compensated for so you can be a better shooter.
What is bullet trajectory?
The simplest definition of bullet trajectory is “a bullet’s line of travel as it flies from a gun and hits an object/the ground.”
We have all seen movies or television shows in which the crime technician places a dowel in a bullet hole, runs a string from it, and announces, “The shooter was there,” while pointing to a distant rooftop. If only it were that easy. While this method may get you close to the shooter’s position, it will be a ballpark at best. Why? Because it does not take into account any of the factors that influence the bullet’s flight path or trajectory.
Factors That Influence Bullet Trajectory
The first thing to remember is that a bullet’s trajectory is rarely flat at long distances. Instead, it is arced, like when an outfielder throws a baseball toward home plate.
Second, each bullet will have a different degree of arc and, thus, a different trajectory.
Bullet Characteristics, weight, muzzle velocity, powder load, and even composition will impact how the bullet flies through the air and its exact trajectory. Although identical bullets from the same manufacturer will have very similar characteristics, similar bullets by different manufacturers can vary greatly. This is why experienced shooters have specific loads that they feel “perform best” in each firearm.
Bullet Coefficient – also known as BC, bullet coefficient represents how easily the projectile overcomes air resistance or how much a projectile will slow over time. BC is expressed as a number between 0-1, with higher BCs associated with more aerodynamic rounds, such as a .223, while lower numbers are associated with fatter, bulkier rounds, such as a .45.
Weather- humidity, wind speed, wind direction, and temperature are all common considerations when determining bullet trajectory. Wind speed and directions are obvious influences, but the new shooter often overlooks humidity and temperature. Both change air density, which in turn changes the resistance of the bullet.
Distance to Target – because a bullet’s flight path follows an arc rather than a flat line, the distance to the target is essential to determining bullet trajectory. Although the degree of arc and its impact can vary significantly between different calibers and loads, all will have some degree of arc and eventually hit the ground. To calculate trajectory, you must know the distance to the target. The more accurate this distance is, the more precise the calculation will be.
Coriolis Effect- this is the most fascinating aspect of calculating bullet trajectory because it considers the Earth’s rotation and curve. For most shooters, this is of little consequence. However, the long-range shooter knows that the Coriolis Effect is not only real but a serious consideration.
Calculating Bullet Trajectory
Formulas – If you have the time and mathematical ability, it is possible to calculate a bullet’s trajectory using a mathematical formula. The basic formula is the parametric equation: (x(t)=v₀cos(θ)t, y(t)=v₀sin(θ)t−(1/2)gt²), where v₀ is the initial velocity, θ is the launch angle, t is time, g is the acceleration due to gravity, and x(t) and y(t) represent horizontal and vertical positions, respectively. It’s not the easiest method of calculating bullet trajectory on the go.
Trajectory charts—Many ammunition manufacturers have trajectory charts available for their various calibers. The chart will show the bullet path (in inches or MOA) with predetermined wind drift, energy, and velocity at various ranges within the specific ammunition’s standard range. Of course, some math will still be necessary to calculate differences associated with variations in wind drift, temperature, elevation of shot, and altitude.
Ballistic Calculators – ballistic calculators were once a luxury most shooters did not have access to or could not afford. However, technological advances allow a simple-to-use ballistic calculator to be downloaded to a smartphone, tablet, or even your watch. Regardless of the type of calculator utilized, the shooter will still need to input necessary information such as ammunition specifics, firearm zeroing information, and environmental factors. The first is available from the ammunition manufacturer; the second should be known to the shooter, but the third must be determined on-site. For this, you will need some specialized equipment.
Tools & Equipment for Calculating Bullet Trajectory
Rangefinders: These small handheld devices will provide both the distance to the target and, if shooting uphill or downhill, the appropriate angle.
Weather meter- there are a variety of weather meters for the long-range shooter. The simplest will provide wind speed, temperature, humidity, and altitude. This information can then be entered into a ballistics calculator to determine trajectory and associated corrections.
More advanced models will not only determine the weather-related factors but, in conjunction with an onboard calculator, provide the trajectory and necessary corrections.
Conclusion
Although only some shooters can fully understand the complexities of calculating bullet trajectory, each must realize its importance and the available options for determining a specific bullet’s trajectory. This information will mean the difference between a bull’s eye or a downed trophy and a flyer you have no control over.
