#
Stability

We are now in a position to discuss the conditions a bullet has to fulfill
to fly **stable**. By saying that a bullet flies stable 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, saying 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-done" 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°. 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 with 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. Even in some recent publications, the
findings "bullet is unstable" and "bullet shows a (big) yaw angle" are
synonymously used which is **not** legitimate. 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, while 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 to follow 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.