From the story. One of the boys' rockets, Hickam recalls, bounced off a tree and chased them through the woods. A rocket that doesn't fly straight goes wherever the air pushes it. (More in October Sky.)
Two points decide whether a rocket flies straight. The center of mass (CM) is its balance point. The center of pressure (CP) is where the air's sideways push effectively acts; fins move it toward the tail.
Key idea
Stable when the CM is ahead of (closer to the nose than) the CP. Then a gust that tips the rocket makes the air push the tail back, turning the nose into the wind like a weather vane. CM position: $x = \dfrac{\sum m_i x_i}{\sum m_i}$. Weight in the nose moves the CM forward; bigger fins move the CP back.
Worked example: Balance point
Nose cone $20\ \text{g}$ at $5\ \text{cm}$, body $30\ \text{g}$ at $25\ \text{cm}$, motor and fins $40\ \text{g}$ at $45\ \text{cm}$ from the tip. The CP is at $38\ \text{cm}$. Stable?
- $x = \dfrac{20(5) + 30(25) + 40(45)}{90} = \dfrac{2{,}650}{90} \approx 29.4\ \text{cm}$.
- CM at $29.4$ is ahead of CP at $38$: stable.
Answer: Yes: CM at $\approx 29.4\ \text{cm}$ is ahead of the CP
Common mistake
Thinking a heavier tail steadies a rocket. Weight at the back moves the CM toward the CP and makes it less stable.
NASA's guide describes a simple check used with model rockets: tie a string at the center of mass and swing the rocket in a circle. A stable rocket points its nose the way it is moving.