claviger
2018-06-16 21:04:00 UTC
Bullet Trajectory: Fact and Myth
By Mike Nelson
https://www.chuckhawks.com/bullet_trajectory.htm
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.
Thought Question. When sighted in for a typical hunting or target
situation, what is the path of the bullet in relation to the sight picture
if the rifle is aimed directly up or down?
By Mike Nelson
https://www.chuckhawks.com/bullet_trajectory.htm
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.
Thought Question. When sighted in for a typical hunting or target
situation, what is the path of the bullet in relation to the sight picture
if the rifle is aimed directly up or down?
