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smith & wesson semi-auto

Stability

We are now in a position to discuss the conditions a bullet has to fulfill to fly in a stable condition. By saying that a bullet flies in a stable state, we generally mean that the bullet's longitudinal axis tends to point into the general direction of movement.

It can be shown that a stable bullet has to fulfil three different conditions:

Static stability

If the gyroscopic effect takes place, so that a bullet responds to the wind force by moving its nose into the direction of the overturning moment, one says that the bullet is statically (or equivalently: gyroscopically) stable. If a bullet is not statically stable, for example, if it is fired from a smooth bore barrel, the overturning moment will cause the bullet to tumble. A bullet can be made statically stable by sufficiently spinning it.

Statically unstable handgun bullets will hardly be met in "real life", because such a projectile would be useless. However, when fired with insufficient spin, "well-designed" bullets may be statically unstable.

It is possible to define a static stability factor sg and derive a static (or gyroscopic) stability conditionGo to formula, which simply demands that this factor must exceed unity.

As an example, the figureGo to figure displays the static stability factor for the 7.62 x 51 Nato M80 bullet, fired at 32° to the horizontal. The M80 bullet exits the muzzle with a static stability factor of 1.35. Obviously, the static stability factor continuously increases at least for the major part of the trajectory or more generally, always exceeds its value at the muzzle. Generally, it can be assumed that if a bullet is statically stable at the muzzle, it will be statically stable for the rest of its flight.

Dynamic stability

A bullet is said to be dynamically stable, if an angle of yaw, induced at the muzzle, is damped out with time, or in other words if the angle of yaw decreases as the bullet travels on. It can be shown that this is true, if the dynamic stability conditionGo to formula is fulfilled.

If, on the contrary, a bullet is dynamically unstable, the angle of yaw increases.

The occurrence of an initial yaw close to the muzzle is by no means an indicator of bullet instability. In some recent publications, the statements "bullet is unstable" and "bullet shows a (big) yaw angle" are used synonymously which is incorrect. On the contrary, an initial yaw angle at the muzzle is inevitable and results from various perturbations.

Bullets fired from handguns are not automatically dynamically stable. Bullets can be dynamically unstable at the moment they leave the barrel. Other bullets are dynamically stable close to the muzzle and loose dynamic stability as they continue to travel on, as the flowfield changes.

Tractability

According to our general definition of stability, a bullet may become unstable by being over-stabilized. Over-stabilization means that the bullet rotates too fast and becomes incapable of following the bending trajectory, as its longitudinal axis tends to keep its direction in space. This effect is often observed for high-angle shooting, but is of minor interest in normal shooting situations.

The figureGo to figure schematically shows an over-stabilized bullet fired at a high angle of elevation, which lands base first.

Mathematically, a bullet is said to be tractable, if the tractability conditionGo to formula is fulfilled.

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