Topic of the Month: October
2001
Bullet Trajectory
Simply stated, the trajectory of a bullet
is the path the bullet takes from the muzzle of the gun to the target. It is not a
straight linear line. The bullet begins to drop the second it emerges from the barrel
because of the force of gravity and air resistance. If the gun is fired horizontally to
the ground the trajectory is illustrated in Fig. 1.
Fig 1
If the barrel is tipped up slightly the
trajectory will look similar to Fig. 2.
Fig. 2
Note that the bullet crosses the sight line
near the muzzle and again at the zero or sighting-in point. A common misconception is that
the bullet rises when it leaves the barrel and then falls back into the target. The bullet
only rises because the barrel is tipped up. Actually the bullet never rises above the bore
line, but continually drops until it impacts the target.
We sometimes get questions on the angle of
departure or how much the barrel is tilted up to get the desired trajectory. Generally,
this angle is very small unless you are zeroing you rifle for a very long range. As an
example, I zeroed a scoped Remington 788 rifle in .44 Magnum caliber for 100 yards. The
bolt was removed and the rifle was placed on sandbags and moved until the scope cross
hairs intersected the target bullseye. Without moving the rifle I looked through the
barrel and the bore line intersected the target at about 12 inches above the bullseye. The
bullet drop and the range formed two sides of a right triangle while the bore line
completed the hypotenuse. The tangent of the angle of departure is equal to:
Tan q = drop/range
Tan q = 12/ (100 X 36) = .00333
q = 0.191 degrees or 11.5 minutes
You can see this is a relative small angle
even for the slow moving .44 Magnum. The angle would be even less for a high velocity
rifle shooting bullets having a high BC.
The firearm is considered to be sighted-in
when the bullet impacts the same spot that the sight line passes through. For example when
the intersection of scope cross hairs are aligned on the target’s bullseye and the
fired bullets also strikes at this same spot the rifle is said to be sighted-in. In other
words the bullets are striking at your aiming point.
The important factors in developing a
trajectory curve are the bullet ballistic coefficient and the muzzle velocity. Once this
information is known the remaining velocity and time of flight for a given range are
calculated (using data from Ingalls or similar tables together with test firings) and
finally the drop is calculated. Today most external ballistic software programs calculate
these properties quickly and accurately and generate trajectory curves and tables for
whatever shooting conditions you may want.
Let’s look at a real trajectory for
the .223 Remington. For this example the 55 gr. bullet, we are shooting, has a muzzle
velocity of 3,600 f.p.s. and a bullet coefficient of 0.237 (see last month’s
"Topic of the Month" to learn about ballistic coefficient). The scope-mounted
rifle is zeroed for 200 yds. The end range is set at 400 yd. and the trajectory range
increment is 25 yds. The trajectory is shown in Fig. 3 below.
Fig. 3
In Fig. 3 the zero height line is the line
of sight. Note that the bullet exits the gun barrel muzzle at a height of –1.5
inches. This is the typical distance between the centerline of the scope and the
centerline of the bore. The bullet crosses the line of sight about 50 yds. down range and
again at the designated zero point for the rifle, which is 200 yd. These are the only two
points that the rifle is considered "dead-on." The bullet’s flight will be
higher than the line of sight between 50 - 200 yds. and the bullet’s flight will be
lower than the line of sight at any distance greater than 200 yds. The bullet drops 18
inches below the line of sight at 400 yds. The midrange trajectory height is the highest
point the bullet will get above the line of sight and usually occurs at about 55% of the
downrange distance to the target.
A trajectory concept that is important to
hunters is the "Point Blank Range." The point blank range of any gun is the
distance out to which the hunter can hold right on a game animal and be assured of a hit
within a vital zone of the animal. It is a measure of how flat a gun will shoot. For
example, if we were trying to dispatch a varmint that had a kill zone of 4 inches and we
were using the .223 Remington as sighted in Fig. 3, the bullet would be within the 4 inch
span (+/- 2 inches) from the muzzle to about 250 yds. We will discuss this further in
another "Topic of the Month."
Watch our web site for the next topic of
interest "How does wind affect the bullet’s flight." Until then, shoot
safely and know where your bullets are going.
Sincerely,
The Ballistician
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