Originally posted by Rick Dickinson at the above mentioned link
First, CP is not a fixed point, as we generally assume. It actually varies with angle of attack. Also, the Barrowman equations are based on some simplifying assumptions, which the FPoD violates.
Barrowman assumed that the rocket wuld be "conventionally" shaped -- a tube with a pointy bit at the front, and fins at the back, with somewhere in the neighborhood of a 10:1 length:diameter ratio. He also assumed that the only "significant" portions of the rocket would be the nose and fins, with the body contributing only marginally to the CP, since the angle of attck (AoA) would be assumed to be less than 10 degrees. Based on these assumptions, 1 to 2 calibers of margin between the calculated CP and the CG of the rocket would yield a stable design.
In reality, the "margin" is only there to ensure Dynamic stability. If the CG is in front of the CP *at all*, the rocket is statically stable. As the rocket hits larger AoAs, the CP moves forward due to larger contributions by the body tube. With 1-2 calibers of margin, there is enough "headroom" for the rocket to swing straight again before the CP moves too far forward.
Real long rockets (Mean Machine, etc.) need *larger* stability margins, since the body tube moves the CP farther forward for the same AoA. Conversely, shorter rockets need smaller margins. A stock "Fat Boy" has about 0.5 calibers of margin on a C6 engine, and flies fine.
The FPoD is a special case. Not only is it very short compared to the "diameter" (which diameter to use is an interesting question, since it obviously tapers), but it also reacts differently than a tube would to varying AoAs. A symmetrical cylinder would have it's CG and CP at the geometric center, regardless of AoA. But a Pyramid or Cone would have it's CP about 1/3 of the way from the rear at a 0 AoA, and, in my opinion, further back at slightly larger AoAs, up to the point where one side becomes "vertical" compared to the direction of travel.
