Overview

Stability is the tendency for a rocket to return to a nominal attitude (that is, it's previous heading) after having it's flight perturbed. The stability of a rocket in flight is determined by the positions of its center of gravity (CG) and center of pressure (CP). The center of gravity can be easily understood as the balancing point along the length of an axially symmetric rocket. The center of pressure of a rocket is the location where the sum of aerodynamic forces on the vehicle yield and equivalent torque equivalent to integrating the aerodynamic forces on the wetted (area in contact with air) surface of the rocket.

Here we see a simple diagram. The sum of aerodynamic forces on the rocket yields a force vector, applied at the center of pressure. The body will rotate around its center of mass, so the aerodynamic force creates a torque around the CG in a rocket body centered frame.

A rocket is stable as long as the rocket has a stable equilibrium point at 0° angle of attack. Practically this means the vehicle must experience an increasing restoring aerodynamic force as the angle of attack increases. If the position of the CP rises above that of the CG, the direction of the torque is reversed and the vehicle becomes unstable.

Calibers of Stability

The moment arm of the aerodynamic forces has a significant effect on their ability to stabilize the rocket. Since more massive rockets require larger torques to control them, it is valuable to consider a dimensionless way to compare the stability of several rockets, rocket designs, or to scale the stability of a model to a full scale design. This quantity is calibers of stability. The calibers of stability can be computed by dividing the distance between the CP and CG of the rocket by the average diameter of the vehicle. This values should be greater than 1 for subsonic flights and greater than 2 during trans-sonic and supersonic flight. This is a design suggestion and may be waived by analytic heroics or other mitigating factors. Shorter and lighter rockets can get away with less stability than a fast, long, or heavy rocket.