#
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 s**_{g}
and derive a **static (or gyroscopic) stability
condition**,
which simply demands that this factor must exceed unity.

As an example, the 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 condition**
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 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
condition**
is fulfilled.