# Short ranges

In the preceding chapter, the physics of bullet motion under the influence of 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.