Bullet path, from 0 to 1000yds, of a 175gr HPBT Sierra Mach King bullet, fired at 2700fps of muzzle velocity

From the moment it leaves the muzzle, a bullet starts to follow a parabolic trajectory. Which means that, as the bullet travels further, the rate at which it approaches the ground increases. This parabolic trajectory is caused by gravity and drag.

The trajectory will have an ascending and a descending part because to compensate for the drop we usually incline the barrel axis upward. If you shot with the barrel parallel to the ground, you’d have only a descending trajectory. Relative to the barrel axis, the bullet always descends toward the ground. Drop is always negative.

In fact, as soon as the bullet exits the barrel, it begins to fall toward the ground, attracted by gravity. The amount of drop caused by gravity is a function of the time of flight. Given a distance, the higher the bullet speed, the less is the time it is subjected to the effect of gravity and the less is its drop.

This graph depicts the speed drop of the same 175gr HPBT SMK shown in the previous graph. You can observe how the speed drops while the bullet travels downrange.

However, bullet speed is not constant; it starts to decrease as soon as the bullet exits the muzzle due to drag, the resistance that air offers to the bullet travel. As the speed decreases, the time the bullet is subjected to gravity increases, which, in turn, increases the amount of drop. This what gives the bullet its parabolic trajectory.

The amount of drag is determined by:

Bullet speed: Drag increases when the bullet speed, relative to the air, increases.

Ballistic coefficient: Bullets with higher BC are more efficient against drag.

Air density: The higher the air density, the higher is the drag. Density of the air depends essentially on:

  1. Altitude/Atmospheric pressure: the higher the atmospheric pressure, the higher the air density.
  2. Temperature: The lower the air temperature, the higher the air density.
  3. Relative humidity: The lower the humidity, the higher the air density. Anyway, humidity has negligible effects on bullet drop, at least under 1000yds.

         Wind: If wind has a tail or head component, that is, if it does not blow perpendicular to the trajectory, it changes the speed of the air through which the bullet is flying. Therefore, the bullet speed relative to the air can change because of the wind changing the amount of drag on the bullet.

Wind can also affect the vertical component of the trajectory in a non-drag related manner. In fact, when a wind blows against a mountainside, a hillside, or a tall building, it generates a vertical component. A vertical wind can blow upward or downward, and the trajectory of a bullet that flies through it is deflected in that direction.

The Coriolis Effect is the effect of Coriolis force, that is, the force of the Earth’s rotation, on the bullet trajectory. Its effect is negligible, at least under about 1000yds, but we will examine this phenomenon in greater detail in the future.

Other factors must also be taken into account when dealing with the vertical component of the trajectory. These factors do not actually affect the trajectory, but are aiming or prospective related errors. They are:

Firing elevation/depression angle: When shooting at an angle, in other words, shooting uphill or downhill, with a certain amount of line of sight angle relative to the horizon, the bullet always hits higher than the aimed point. This happens whether you are shooting uphill or downhill. The wider the firing angle, the higher the point of impact. It has a considerable effect on bullet impact, so it must be taken into account, even at short ranges, if the angle is more than 30°.

Light: The amount of light, and the direction from which it came, changes the way we see the target through a telescopic sight because of optical effects and distortions. This leads to point of aim and, consequently, point of impact changes.

I will talk about uphill/downhill shooting and light’s effect more thoroughly in the future. But, in the next article, we’ll focus on what determines the horizontal component of the bullet trajectory.