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Short ranges
In the preceding chapter, the physics of bullet motion under the influence
of mass forces and aerodynamic forces has been studied. The remaining part
of this document will be dedicated to experimental observations for handgun
bullets which will generally confirm these findings.
Experimental set-up
The experimental set-up which is used by ballistic research institutes
to study the yawing motion of bullets, is shown in the figure .
The bullet coming into the field of view of a camera is illuminated by
a light flash of short duration which must be concentrated in a point.
By means of an optical system, consisting of two mirrors and two scotchlite
reflecting foils, two shadowgraphs are taken: first, a direct side view
picture from the standpoint of the camera, and second a picture taken from
above.
From the two bullet views which are available on a single photographic
plate, the spatial orientation of the bullet's longitudinal axis can be
evaluated, especially the spatial yaw angle can be determined.
Numerous photographic stations can be set up, one behind the other,
allowing to determine the yaw angle, the angle of precession, and the location
of the CG as a function of the traveling distance.
Yawing motion of handgun projectiles
Using this sophisticated and labor-intensive photographic technique, numerous
brands of handgun projectiles were investigated and the results for some
selected bullets are presented hereafter.
Stable bullets
The figure
shows the trace, the tip of a M193 bullet (caliber 5.56 x 45) would
leave in space from the moment it exits the muzzle, up to a distance of
8000 calibers, which corresponds to approximately 150 feet (45 m). If one
imagines that the bullet's CG moves on a straight line, which is located
in the center of the box, the curved path displays the location of the
bullet's tip in space as it travels through the air.
You may also read approximate values for the maximum yaw angle, which
does not exceed two degrees in this example. Although the drawing does
not display it very clearly, the yawing motion of this M193 bullet is undamped.
However, other experiments have shown that the M193 bullet may show small
damping as well.
The next example (see figure)
shows the yawing motion of a hard core, armor piercing bullet of
the same caliber (5.56 x 45). This time it is undoubted that the yawing
motion is damped, or with other words, the projectile is dynamically stable.
However, a maximum yaw angle of more than five degrees could be observed
close to the muzzle.
The distance between two successive extremes in yaw is about seven meters.
The next figure
displays the yawing motion of the Russian M74 bullet. One can observe
maximum yawing angles of up to three degrees close to the muzzle. Again
the yawing motion is damped, but has become more complicated. It requires
quite a bit of perseverance to follow the path of the bullet's tip.
The fast modal arm is damped to one half after a traveling distance
of 30 meters, whereas the slow modal arms requires twice as much to be
damped to one half.
Our consideration of military bullets will be finished by two investigations
on 7.62 x 51 Nato bullets.
The next figure
presents the behavior of a hard core armor piercing bullet, showing
a very symmetric and easy to follow path. However, yawing angles of more
than ten degrees have been observed in this example.
The yawing period, the spatial distance between two successive extremes
in yaw, is approximately eight meters.
The final example (see figure)
refers to the standard M80 bullet (7.62 x 51 Nato). Obviously, the
yawing motion has become very complicated and the path of the bullet's
tip is not easy to follow, yet still shows a symmetric and repetitive structure.
So far we have only met good-natured bullets. All of them had sufficient
static stability with a static stability factor at the muzzle ranging between
1.1 and 2. In almost all of the cases, the yawing motion was damped, saying
that the bullets were also dynamically stable.
This conclusion is not very surprising. All of these bullets were designed
for military use and warfare. Many engineers and scientists in ballistic
research institutes were occupied in optimizing this ammunition. Each of
those bullets probably has undergone multiple ballistic improvements and
refinements, based on shooting experiments and wind tunnel tests. Therefore,
it would be more than amazing, to find any bad exterior ballistic properties
with these bullets.
Over-stabilized bullets
It can be asked, whether bullets fired from pistols and revolvers show
the same behavior as those well-designed military projectiles.
The next figure
shows an investigation for the .357 magnum KTW bullet, fired from
a Colt revolver at a maximum shooting distance of approximately 240 feet
(70 m). The path of the bullet's nose shown in this drawing is characteristic
for an over-stabilized bullet. Too much spin is transferred to the bullet.
The frequency of the fast mode oscillation, also called nutational frequency,
is very high (more than 1000 revolutions per second) and the bullet responds
in a very nervous way. Obviously, the yawing motion is damped, as the maximum
yaw angle continuously decreases, with a half life for the fast mode oscillation
of 22 meters.
A second example is presented in another figure.
A 9 mm Luger FMJ RN bullet displays a similar behavior. An evaluation
shows that the bullet has a static stability factor at the muzzle of 22.5.
This is much too high as compared with the necessary value of one. The
bullet shows very good damping. After a traveling distance of approximately
6000 calibers (170 feet = 50 m) the maximum yaw has been damped to almost
nothing.
It has been a general observation that many bullets fired from pistols
and revolvers are over-stabilized. However, the question remains to
be answered, whether excessive spin, as demonstrated for the last two examples,
may express in any ballistic disadvantages.
If one considers only short ranges, let us say, up to a few thousand
calibers, which is generally the distance, within which pistols and revolvers
are used, excessive spin does not influence accuracy. However, if fired
at high angles of elevation, the bullet's longitudinal axis may not follow
the curved trajectory path, tends to keep its orientation in space and,
as a consequence, the bullet may impact base first.
 
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