Originally posted by Micromister
Doug, the cardboard cutout method, when actually done on cardboard, gives a very good laterial center of pressure location. If anything it always errs on the WAY overstable side.
Micromister is correct in saying that the cutout method very often gives excessively conservative answers. When you stop and think about it, if your rocket is turned around and presenting its SIDE to the oncoming airflow, you have more problems than stability. A good bunker would be advisable.
Estimating or calculating actual stability characteristics is quite complex, as you can probably imagine. Think of a rocket traveling in an idealized attitude (straight into the airflow) and picture the head-on view of the rocket. You see the leading edge of the fins and the nose cone (simplifying assumption being that there are no body transitions to larger diameters). Yeah, if you look really close, there is maybe a launch lug or some buttons, but they are small and I'm ignoring them.
Now picture a similar view, only the rocket has a small perturbation from the flight path. Say, a small angle like 4 or 6 degrees. The fins now become wings, at an angle of attack to the relative airflow that equals that small angle (the 4 or 6 degrees). The fins generate a lifting force, perpendicular to the body axis, that tends to push the tail of the vehicle back in line with the flight path. The stability of the model is directly affected by the ability of the fins to efficiently generate aerodynamic lift. Like, did you sand the edges square, or round, or did you put some semblance of a real airfoil on your fins?
At the same time, the nose cone and the rocket fore-body are also at that same angle of attack. Unfortunately, the sides of these surfaces that are AWAY from the flight path are the place where airflow must accelerate to get around, causing reduced dynamic pressure and tending to pull the nose farther away from the flight path.
Who wins? The fins or the nose? This is where all the complicated aerodynamics comes in and makes everything messy. Also, vehicle weights and especially longitudinal mass distribution affect the dynamic motion response, and the energy expended (making the rocket wobble back and forth) makes the stability analysis worse. Now add in varying atmospheric conditions, barometric pressures, humidities, launch altitude, and air densities, and you begin to get the idea that you could spend the rest of your natural life trying to mathematically analyze this problem. (Oops, I left out thrust misalignments, launcher tip-off dynamics, misalignment of fins and nose cones, effects of off-center parachute packing, .....)
The practical engineering approach is to load a wad of weight in the nose. Yes, performance is a little worse. So make a few flights and then remove part of the nose ballast and test again. This is simple, and simple is good. Besides, it's an excuse to launch the rocket again (if you need one).
Your design looks really great! Take your time deciding on the paint job and choose something that really plays up your unique design. Maybe paint it to look like the lower portions of the fins are for a booster that just happens to be closely nested to the upper stage?