Rocket Stability

 

Every high power rocketeer, and especially those who build large and/or scratch built designs, knows that for a rocket to be stable in flight, the center of pressure (CP) needs to be at least one body diameter (or “one caliber”) behind the center of gravity (CG). this is known as the “static margin”.


Determining the CG is easy - load up the rocket with everything it will carry in flight, motor included (or a simulation thereof) and find its balance point. This point is the CG. Determining the CP is a different story. For those using computer programs like RocSim, this calculation is made relatively easy. When the data is put in to the program, the CP is automatically calculated.


For those interested, the background to these CP calculations is worth exploring. Much credit goes to Jim Barrowman, a NASA aerodynamicist and avid amateur rocket builder, who, in 1966, proposed a simplified way of calculating the CP for model rockets. It is important to know that, in order to simplify what is otherwise very complex math, Jim made some key assumptions. These are:


  1. 1.That the angle of attack will be close to zero.

  2. 2.That the rocket will be traveling subsonically (less than the speed of sound)

  3. 3.That the rocket is long relative to its body diameter

  4. 4.That the airflow over the rocket is smooth

  5. 5.That the nose of the rocket is a point

  6. 6.That the rocket has an axially symmetric rigid body

  7. 7.That the fins are thin flat plates


For 90+ % of model rockets, these assumptions are reasonable. Note, however, that for very long, skinny rockets, more than 10 calibers might be needed for stability and for short, fat rockets, less than half a caliber may be enough. Designs like the V2 are a challenge for Barrowman’s equations, which assume that the fins are attached to an airframe of uniform diameter but we know the V2 has a conical aft end.


In general, using the above assumptions, the static margin will depend only on the shape of the rocket.


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