Originally, I put three C.V. analysis diagrams in a thread by BigDaddy found here:
https://www.rocketryforum.com/showt...y-hope!/page5&highlight=gas+dynamic+induction
I found that several good GDS (Gas Dynamic Stabilization) threads on TRF can be found using "gas dynamic induction" as a filter.
Nyt, I would be interested in exchanging ideas here, but I have too many project going to devote too much time to this subject. Conceivably, this project on a theoretical basis can be as big as the report that was given on a different thread discussing equations for optimum piston launch volumes. (I was thinking of printing out that report and studying, but don't have the time now.)
It's a good way to start the problem, but it looks as if you're forces are dependent on the velocity of the rocket driving air entering the control volume while neglecting the exhaust's role in the dynamic stability.
You are correct that the simplified C.V. analysis on post #30 does not include the exhaust. As a minimum it looks like the restoring force (perpendicular force) should have something like the equation shown in post #30. Note that in this analysis we don't know exactly what the mass flowrate into the rocket model is. One could always use the external velocity multiplied by a typical flow area and use a fudge factor. Perhaps, the fudge factor could be determined by a CFD analysis, assuming that the fudge factor is constant and does not change much with angle of attack. Probably, after motor burn-out the restoring force will have this simple relationship. I tend to think that partial cut-out vents, which your designs seem to have, may offer offer more surface area for the development of side force than struts that have hardly any surface area at all.
While the motor is burning, one can bring up the issue of the exhaust. As I recall (I could be wrong) I think Dean had all the incoming flow acquiring the exhaust velocity. It this was so, it was extremely optimistic. If the incoming flow is accelerated to some fraction of the exhaust velocity, but ends up exerting a force exactly in line with the model axis and goes through the c.g., it will have no moment-arm and will not exert a restoring force at all.