This may not really be an answer to the question you are asking. It is more a post on approach.
There are likely lots of ways to approach designing a rocket. The approach you choose should support whatever your goals might be. And the design process is generally iterative - one of successive refinements until one is satisfied, or says it is good enough, or gives up!
So what is your goal?
If it is for instance related to performance in some capacity, then the place to start is to suppose a flight profile that supports meeting the performance goal. Then work backwards from the flight profile to a hypothetical rocket that could meet that profile.
Perhaps the goal is to put on a good show. Here, a rocket that is too light or too heavy for its size and draggy for its size could allow everything to happen lower down where it is more visible.
Perhaps your goal is to make the cheapest rocket you can make that can fly reliably and repeatedly on a J.
So start with the goal. Then identify characteristics of the rocket which could meet your goals, and then refine that rocket. Part of that refinement is defining the fins.
Fins do have a lot of impact on appearance. They have a lot of impact on stability. But they have less of an impact on performance.
I'll give you a rather lengthy thought experiment on designing a rocket, since it is one that I'm considering. But, due to circumstances outside my control, one I probably won't get to do, or at least not in the near future.
My goal was a modest sized rocket to be able to punch well beyond 100Kft. Say, total impulse not beyond the O range. However I wanted high survivability. By that I mean the intent is to avoid excessive velocity, particularly lower down. That reduces or eliminates aeroheating and flutter concerns, and generally reduces structural issues. I was willing to take on other issues in exchange. Nothing is for free!
Ah, never mind. It probably has nothing to do with whatever your goal(s) might be.
Just start by stating your goals, perhaps just a simple paragraph like what I just did. It gives you a place to start, and tends to reduce the time spent getting spun up in different directions that are interesting but otherwise do not contribute towards achieving your goals.
Then start sketching out the rocket that might meet your goals. There might be several such. How big is it? Or how big of a motor, or how small of a motor, does it use? What sort of recovery? What sort of electronics is required to make that recovery work? Any other air events than recovery related ones (staging, for instance)?
Refine the airframe and contents, then worry about the fins. Even for a high performance rocket, you can sim it with sketched in fins. That will tell you what the fins have to survive. Then you can start designing the fins.
For a partial answer to your original question:
It is best for each fin to stick out farther than the greatest diameter of the airframe.
Four fins are more resistant to coning than three.
For near optimal stiffness distribution for the available mass, the tips of the fins should be roughly a third the thickness of the root of the fin. That helps keep your flutter speed high. Flutter is BAD. But for a BDR going subsonic it might not be a concern. And kits of course don't do it because it is more work. Easier to cut out a slab fin and bevel it. And quite often that is fully sufficient, and cheaper, which can make it the best choice.
Oh, FWIW, the 1 to 2 calibers thing is incorrect. It is an oversimplification; just a rule of thumb. It's often good, but not always. A long skinny rocket you might want more like 10%. And if high supersonic, say around M3 or so, you need to pay attention to the speed-dependent movement of the CP. And of course the CG probably moves as the propellant is burned. Heck, even the CP depends on whether the motor is burning, or not, since it alters the drag distribution by altering the base drag, affecting stability.
But for a generic rocket design flying in an average sort of way, 1 to 2 calibers is probably fine.
The thing about rocket science is there is almost always a deeper level. The more you learn, the more you realize there is left to learn.
Gerald
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