The first fully-assembled rocket on a launcher with all components. Paper nosecone, plastic bag parachute, foamcore fins attached with hot glue and "reinforced" with orange brackets; Alpha prototype launcher.

The launcher jammed a little; the bottle launched; the nosecone fell off, the parachute tore off, and the fins broke on takeoff and further on landing. An first excellent high-yield test in all respects because it pointed to next design steps.

Fins designed by a 3-year-old helper mainly for their aesthetics, though the grown-up would not have been able to do an aerodynamic critique yet. Early fins were simply "try it and see" while focusing on the launcher mechanics. Mounted on a Beta prototype launcher (60º leg angles, inseparable Core, new socket crossbars).

You can see the multiple hot-glue repairs already performed. Fins tore off again on launch and on landing, just like they did the first time they were tested. Consistency!

The first Clamp-compatible flange mount (gold) used a ring with six internal radial brackets that clicked onto the flange. These brackets allowed space for the six Clamps (blue) to hold onto the bottle's flange. A thin ring (red) clicked onto these brackets, ostensibly to hold them in place. Mounted on a Version 1.0 launcher (45º Legs; thickened Launch Pin; not yet thickened around Leg sockets)

Fins were thick and printed with 2 walls so they wouldn't break on landing, since I did not yet have parachutes. They were flat bottomed to 3D-print on the flat bed.  This made them back-heavy, though I didn't understand the aerodynamic implications yet.

Large fins were even heavier and rockets didn't go as high. They didn't enhance stability, either. They also were aesthetically odd because they were upward curved sweeps of a flat profile instead of circular sweeps of a radial profile.

Addition of fins caused the mount to pop off as the lever action on the bracket disengaged it from the flange.

The initial solution was a cut bottle cap to hold the mount in place. 

@DaveTheYellowDart on Printables designed a 3D-printed threaded retainer for the fins. It worked well and was much safer than cutting a cap with a knife. 

The large fin also concentrated stress in the center and fractured the inner-most ring (hidden by gray Clamps). I tried one-wall prints and added reinforcement in the weaker inner fin areas where I had layer separation. This didn't help.

Fins extend from conformal rotary extrusions, which were stabilized at the top by a pop-on ring.

Another version expanded fin size, but it became clear that this design was too heavy. The fin alone was 43g. The 1L PET bottle was 34g. This design pulled the center of mass rearward more than it did the center of pressure.

The ring helped, but hard landings still fractured the fragile flange mount.

Alignment of the fin with the bracket further concentrated the forces on weak junctions.

Meanwhile, @DaveTheYellowDart on Printables built on the flange mount and made a classic ring fin design. This was the first remix of any aspect of the design and a great encouragement that there was interest in the project. I was so happy.

Design and picture by @DaveTheYellowDart on Printables.com

Image license: CC BY-SA 4.0

Meanwhile, in my own development, I broke my Prusa Mini+ through a heat-creep front-end clog. It failed during a print of a fin-less flange mount. The image is from OctoPrint's GCode Viewer Plugin from around the time of failure; red/blue triangles are retraction/de-retraction events; green lines are travels. Grid scale is 1cm. I realized that my design file is a setup for heat-creep failures: many small print segments in a string of retractions. The Mini+ is notably vulnerable to this and my printer repair involved installing the Bondtech extruder and heatbreak replacements.

I revised the flange mount design to reduce short extrusion runs in the center, though it likely wouldn't make a practical difference on fin prints since the long print segments of the fins counteracted heat-creep issues.

I made a couple test ring fin designs with the new flange mounts. They printed fine but still suffered from the fundamental strength issue at the flange mount. I also noticed how ring fins had higher drag than thin fins.

As I was looking for new ways of attaching fins without adhesives, I found @HowToHomemade's unaffiliated fin design on Printables. It has several brilliant design features:

• Fins are joined together in a wide ring, which removes concentrated strain

• It snaps into place under the flange and is held in compression and needs no glue

• Fins extend rearward past the flange, pushing back the center of pressure

Design and picture from @HowToHomemade on Printables.

Image license: CC BY-NC 4.0

I designed a remix from scratch to include:

• Geometry to fit my 1L Polar Seltzer bottles

• Space for Clamps

• Groove to further secure with zip-tie

• Thinner fins and size options

• Clip-away bridges on large fins to stabilize for printing (air resistance forces on my bed-slinger 3D printer moved the fin enough to collide with the nozzle)

The fin's "fingers" fit between the Clamps to push against the flange. Since they are under a compressive force, the small cross-section of the finger is plenty strong. A zip-tie provides extra security though isn't strictly necessary. Fins extend rearward past the Collar pushing back the center of pressure further.

Three fin sizes provide options for tuning rocket aerodynamics in conjunction with payload development. The small fin has 130 square centimeters of surface per fin (one side).

Parachute deployment was improving, allowing for thinner fins printed with 1 wall and 3D honeycomb infill.

With thin fins, infill pattern choice matters. 3D honeycomb (top) is the best, providing a consistent supporting pattern for every fin. Gyroid (middle), my usual favorite, is inconsistent. Some options like cubic (bottom) are worse with some layers with almost no infill. 

The large fins with zip tie weigh only 33g and have a large area rear of the flange. The 3D infill's even pattern shows through the single wall of translucent PETG.

One more attempt at universal fins. Having learned to model threads, and to design the flat side of the mount to be facing forward, it was possible to develop a threaded fin that fit between the Clamps. 

The fins connect to the ring between the ribs of the mount for added flexibility. Fins work in testing but are in early stages of being made robust enough to survive falls. They are compatible with PCO-1881 bottles commonly found in North America. Other bottles use slightly different threads.