## The Stability a Model Rocket

The Stability of a model rocket is dependent on how all the forces act on a model rocket. There are several categories of stability. The first is positively stable, or just stable. The second is neutrally stable, and the third is negatively stable, or unstable. The fourth type is dynamic instability, which is a little different from being stable in that it's almost impossible to find out whether a rocket is dynamically unstable, even with calculus, but it's where a simulation excels.

Neutral and Disturbed Positions  Neutral, and disturbed locations, and the shift between them are what stability concerns. A neutral position is the a place where an object can rest at, without any additional force. Imagine you have a bowl, and a small rubber ball. The neutral location would be in the center of the bowl. If you moved it to a location along the side of the bowl, it would roll down, and oscillate between the sides of the bowl until it settled in the neutral location -- the center again. When the ball was along the side of the bowl, it was in a disturbed location. In a disturbed location, the object wants to move towards a more stable position.

Positive Stability  Positive stability is when an object oscillates towards the neutral location. It may overshoot the neutral location, but with each oscillation getting smaller until it reaches a neutral location. If you were to put a ball along the inside of a bowl, and it moved towards the neutral location at the bottom of the bowl, and oscillated back and forth up and down the sides of of the bowl, with the apogees getting closer to the neutral location, it would be called positively stable.
A rocket should be positively stable, in order to reach the maximum altitude it can, and be safe to fly. The rocket will oscillate back and forth slightly if disturbed by the wind, or other force, and eventually regain it's neutral orientation, if it has enough time before it begins to fall. A good rule of thumb to insure positive stability, is to keep the center of pressure about one static margin behind the center of gravity.

Neutral Stability  Neutral stability is when an object is at a neutral location anywhere it moves. It won't have any oscillation to return to it's neutral location, because it's always there. Breaking from the bowl example, because the ball won't exhibit neutral stability when it's in a bowl, instead use a flat, level plank. The ball is at a neutral location anywhere along the plank, so it doesn't move at all on it's own. If something did cause it to move, it still be neutrally stable, because it's at a neutral location at any point during it's movement.
Neutral stability is probably the least important of the four types of stability, because a rocket rarely exhibits neutral stability while flying. It would exhibit neutral stability only if the center of pressure and center of gravity coincide.

Negative Stability  Negative stability is when an object moves in the wrong direction to return to a neutral location. This is different from the below mentioned dynamic instability, because in dynamic instability, the object is moving in the correct direction. Negative stability can be illustrated by flipping the bowl upside down. The neutral location for the ball would be balanced on the top in the center. If it's moved to a disturbed location along the side of the bowl, it will move away from the neutral location, and never make it back.
In a rocket, negative stability occurs when the center of pressure is ahead of the center of gravity, causing the rocket to spin erratically. A rule of thumb to prevent negative stability is to make sure the center of pressure is about one static margin behind the center of gravity.

Dynamic Instability  Dynamic Instability is when an object oscillates to return to a neutral location, but inertia causes it to overshoot the neutral location, and the oscillations continue to increase. It's similar to positive stability, except that the oscillations increase, which in the case of a rocket will cause it to flip eventually. Following along with the bowl example, in dynamic instability, the ball would start to oscillate, move in the correct direction, but overshoot the neutral location, and continue in larger and larger oscillations until it flew out of the bowl. This requires the object to have an internal power source, which while most balls lack, a rocket does have. If this were a rocket, the rocket would have moved from the disturbed orientation, towards the neutral orientation, but had so much energy, that inertia carried it even further from the neutral than it had started. Eventually the rocket would have flipped completely over. While unlikely, it is possible for the rocket to return to an upright position, due again to the inertia which started the whole mess, and continue going up, until it flips again. However, it is more likely that it might hit you, someone standing nearby, or the ground.
Dynamic instability is more prevalent with a larger engine, because the forces involved are so much greater. This is another reason for testing a rocket the first time with a small engine, and then moving up to larger ones, because if it shows a little dynamic instability with the smaller engine, then it will definitely show much more with the larger engine.
It's dynamic instability predictions that a simulator really shines at. Using The Rocket Simulator, you can see dynamic instability if you take a rocket which weighs about 0.03 KG, and use a "D" type engine. Adding sufficient nose ballast will make the rocket stable.

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Nicholas Burlett, Nathaniel Grady and William