Bullet Trajectory: Fact and Myth
By Mike Nelson
Myths and errors regarding the path of a bullet generally come from a lack of understanding of the forces acting on the bullet before, during, and after its path through the barrel. This article will deal with the primary forces on a bullet's trajectory, and it will mention a few of the secondary forces. The approach is directed toward the average reader. There is no attempt to address concerns of the mathematician or physicist, who should either know this material or should read a more technical and comprehensive treatise.
One of the more pervasive myths associated with bullet trajectory is that "bullets always rise right after they leave the barrel." In general, bullets do rise after leaving the barrel, and they immediately begin to drop. This is not a contradiction, and the explanation is not difficult to understand.
Bullets are affected by gravity whether in flight or not, and, when they leave the barrel, they no longer have any physical support, such as the brass, the box, your pocket, the magazine, the chamber, or the barrel, so they begin to fall. In addition, they are traveling through air, so air resistance progressively slows their flight. On most occasions the barrel is slanted upward slightly to compensate for this immediate drop; thus, for all but extreme shots, since the barrel is aimed slightly upward, the bullet does, indeed, rise slightly after it leaves the barrel, but it bullet never rises above the axis of the barrel. (Just like a football generally rises above the player when they throw a pass. The longer the pass, the greater the starting angle, and the higher the "rise" before the ball begins to fall.)
In scientific terms, "thrown" objects, whether by hand, explosion, springs, compressed air, or other forces, are called "projectiles," their path in space is called their "trajectory," and the study of their trajectories is called "ballistics." Those who fail to understand the elementary physics of ballistics often misinterpret the configuration of barrel and the line of sight and assume that something "special" happens to the bullet during its flight. Many things happen, but nothing "special;" bullets fly just like any other projectile and are subject to the same laws of physics.
The following drawings, though not to exact scale, show the typical paths of bullets and the relationship of these paths to the line of sight, whether determined by open sights or optical sights.
Horizontal Shot. If the barrel is horizontal to the surface of the earth when fired, the bullet never rises above the barrel, and gravity causes an immediate descent.
Typical Alignment. Generally, for what we consider a "horizontal" shot, the sight alignment places the barrel in a slightly upward tilt, and the bullet starts its arc, rises slightly above the level of the muzzle, but never above the axis of the barrel, reaches a peak, then descends. Figure 2 is the graph of a centerfire rifle cartridge that stays within a 6 inch circle for a distance of about 210 yards. Sighted in at approximately 170 yards, this round is approximately 3 inches high at 100 yards and three inches low at approximately 210 yards. You must, of course, always check trajectory data for your particular rifle and cartridge combination.
Velocity. The velocity is a factor in determining energy on impact and the horizontal velocity determines how far the bullet travels before it hits the ground. The above illustrations apply to all ballistic projectiles whether bullets, rocks, or ping pong balls.
Low Velocity Bullets. Bullets at nominally 800 fps to perhaps 1600 fps, such as 22 LR, most pistols, and older rifle cartridges, must follow a rather high arc in order to reach a target 100 yards away. In fact, most of these slower cartridges are only useful to about 50 yards, perhaps 75 yards for some in the upper end of this range.
High Velocity Bullets. Bullets at 2600 fps and up, such as the .223, 22-250, .243/6mm, .270, .308, 30-06, follow a much lower arc to reach a target, and their useful range can be upward of 200 yards. These are often referred to as "flatter" trajectories. With higher velocities, these bullets go much further before gravity and air resistance cause them to fall below the initial line of sight.
Since the barrel is generally directed at an angle to the line of sight, sighting directly upward or directly downward results in a trajectory that deviates even more from the line of sight than the typical, relatively level shot. Still, the effects of gravity and air resistance are the same as far as the bullet is concerned, it is just that the trajectory at such a steep angle is more divergent from the line of sight.
Secondary Ballistics Phenomena. In general, bullets follow a parabolic arc. In reality, that arc is modified significantly by air resistance, which slows the bullet during flight and effects a shortening of the arc down range. That is why the highest point of the usable portion of the trajectory is not the midpoint of that trajectory. Bullet shape and the spin from rifling also influence the trajectory slightly by reducing air resistance and stabilizing bullet orientation. That is why a 500 grain rifle bullet, for example, has a much better trajectory than a 500 grain ball from a smooth bore, all other things being equal.
Fact or Myth. So, does a bullet rise after it leaves the muzzle? One says, "yes." Another says, "no." Who is correct? Both could be correct because of different meanings associated with the word, "rise." They might argue incessantly, but their argument will not change the physical aspects of the path of the bullet. If they would concentrate on discussing the physical events, they would eventually conclude that they were each using the word, "rise," differently or that one of them did not understand elementary ballistics.
