Satiability is the ability of the rocket to return to the desired path
after a momentary force deflects it from this path.
If your motor was perfectly aligned with the CG of the rocket and there
was no wind etc., then a cylinder would fly straight. Unfortunately the
motor thrust will not be perfectly aligned, the air friction is a
chaotic system and there are numerous other forces that will disturb the
The CG is the mathematical abstraction which sums the net gravitational
forces. Happily, this is easy to figure. CP is the mathematical
abstraction which sums the net aerodynamic forces and is a SWAG
(Scientific Wild Ass Guess) at best.
Disturb the rocket in flight and it will try to rotate. For this
example lets say the disturbance will create a clockwise rotation.
CP in front of CG (nose of rocket is front). The rocket's aerodynamics
will try to make the rocket spin in the clockwise direction (magnifying
If CP is right on the CG. The rocket's aerodynamics will do nothing to
change the rotation.
CP is behind the CG. Aerodynamic forces will create a force that will
try to rotate the rocket in the counter-clockwise direction (correcting
In the latter case the size of the corrective force is proportional to
the distance between the CG and CP, so it would look like a large
difference is best. This is true up to a point.
The actual behavior is called dampened harmonic motion. If you sit on a
swing and let some one give you a push, you'll experience dampened
harmonic motion (if you just sit there). Gravity dampens the
oscillations until you are once more at rest. The nose of of your
rocket will oscillate the same way until it, too, is pointed upward.
The further apart the CG and CP are, the slower the oscillations of your
rocket. Even more to the point, if the CG and CP are far enough apart,
then the rocket won't even oscillate. It will just choose a new path,
more or less upward if the disturbance is small relative to the other
forces acting on the rocket. That's what you're trying to avoid. You
want the rocket to oscillate until it finds up again. If it's over
stable, then it will just choose a new path and fly that direction until
another force disturbs it. You have to get the CG/CP pretty far appart
to achieve over dampened behavior like this, but it's possible and you
don't want to do it. Staying between 1 body diameter and 2.5 body
diameters is a good rule of thumb, but it still won't assure stability.
"By the time we've made it, we've had it." -- Malcolm Forbes