A 4" diameter rocket has its CG four inches behind the CP. Is this rocket likely to be stable?

A rocket's stability can be analyzed by examining the relationship between its center of gravity (CG) and its center of pressure (CP). For a rocket to maintain stable flight, its center of gravity must be ahead of its center of pressure when in flight.

In this situation, the CG is positioned four inches behind the CP. This configuration is inherently unstable because it implies that the aerodynamic forces acting on the rocket will create a tendency for the rocket to pitch over or rotate uncontrollably. Stability relies on the CG being forward of the CP, allowing the aerodynamic forces to create a restoring moment that aligns the rocket back into the oncoming airflow. When the CG is behind the CP, any disturbance, such as a wind gust or slight angle of attack, can worsen the instability rather than correcting it.

The fact that the rocket has a 4-inch diameter does not significantly influence its stability based solely on the positions of the CG and CP. Stability is determined primarily by their relative locations, so the rocket's diameter is not a critical factor in this case.

Thus, the identification of the rocket as not stable stems from the fundamental principles of stability in rocketry, which dictates that for stable flight, the CG must always be ahead of the CP.