So you want to design the most high performing rocket that you can. Great, but is it stable? Dynamic stability is tricky, as no hobbyist level programs have a very accurate Cp calculation system for dynamic stability (see “Rasero v. OpenRocket“) .
However, xCp isn’t the only thing that garners dynamic stability. A very important aspect of dynamic stability is the amplitude of how much your rocket can correct it’s path from a disturbance, known as the Corrective Moment Coefficient. I recommend reading the Apogee Rockets Newsletter on the topic, Tim has a very good explanation of the concept.
I have firsthand experience with a low corrective moment. My 54mm Guardian went unstable due to a very low correctional moment, had my fins been larger, they would have been able to force the rocket back onto a straight path much more effectively.
Another important note is that stability “calibers” is basically a “fudge factor” in the first place. Designing for efficiency at 1.00 calibers is missing the point of stability calibers in the first place. Theoretically, if the Cp is aft of the CG relative to the nose, the rocket is stable. This is why trying to maximize your performance based on stability margin optimization is going in circles.
Instead, find a fin shape that fits your flight profile. Change the dimensions, making the fin bigger and bigger until the apogee altitude starts going down – you’ve reached the theoretical limit for optimization. Then, make the fin bigger again. At some point in this region is the sweet spot for higher corrective moment without trading too much altitude.
Use this handy chart to visualize the effects of different fin sizes.
-Fins are too small. There isn’t enough force of lift or corrective force for the rocket to be stable.
-Slightly small fins. If the fins are large enough for the rocket to be stable, but not quite, your apogee altitude will be reduced due to coning or other dynamic instabilities that cannot be cancelled by the small corrective moment.
-The theoretical maximum altitude. If the fins were any bigger, apogee altitude goes down. Any smaller, the rocket isn’t stable enough. However, due to many unknown circumstances such as wind shear, the corrective moment can prove to not be large enough, causing the rocket to be unstable. Success chances are low. (Guardian fits here).
-Larger corrective moment. The tradeoff in possible success is worth the reduced potential altitude. Success chances are high. (Colossus fits here).
-Fins start to get too big, increasing drag force and reducing altitude far too much. (Most rockets fit into this category due to lack of optimization)
-Fins are too large! The material fails due to large aerodynamic loads on the surface area.
In summary, make your fins bigger than you think they should be. You’ll be happy if you do.