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). Please read the CP article before reading this one.

We will first consider the rocket flight straight through the air, then with a small angle of attack.

PICTURE OF BASIC ROCKET FBD W/ CG & CP

This represents a stable rocket well into its flight - the rocket is flying straight. If a gust hits the rocket, there is a small force applied to the entire rocket.  The net force F_aero is represented as a point force acting on the CP. (Since the center of pressure is the equivalent center of aerodynamic force, we can see this effect as a point force on the CP) we see that the rocket turns about the CG into the wind.

PICTURE OF BASIC ROCKET FBD W/ CG, CP AND GUST VECTOR

Let's consider the similar situation where the rocket is leaving the launch rail. It is guided vertically during the initial portion of its flight by the rail, and when the final rail button comes off of the rail, the rocket is free to move in 3 dimensions. If there is a relative wind, we end up with the following:

PICTURE OF BASIC ROCKET LEAVING THE RAIL W/ V_RAIL EXIT, AND V_WIND

This moment in the rocket flight is key. This is the moment when the rocket is moving the slowest, and the least stable point in the ascent. The angle of attack is almost always maximum at this point because the rocket is going relatively slow.

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.

Image Added

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.

 To be continued.......