Fins
The goal of fins on a rocket are to maintain stability, and a good fin design allows for this while maintaining a high apogee for the rocket. For Prometheus, we aimed for a stability always greater than 1.5 calibers (Spaceport requirement) but closer to 2 (team guideline) for the booster and a stability of 2 calibers for the sustainer. Although we decided to make our fins clipped-delta early on, we used simulation software (RASAero) to determine the size and dimensions of this trapezoidal shape. Since changes to parts in other subteams meant a different weight and CG for our rocket, we needed to re-run simulations whenever a change was made in another subteam and change the size and dimensions of our fins such that stability requirements were still met. For this reason, Prometheus' fins were one of the last parts to be manufactured. Lastly, we had four holes at the bottom of the fins that allowed the fins to be screwed together with the fillets. Below is a picture of a fin in Solidworks.
Fillets
The main function of Prometheus' fillets were to attach the fins to the fin can. Each fin had a fillet on each side, each with four holes that aligned with the holes on the fin. To secure the fillet to the fin, screws are simply screwed into these holes.
This is a fillet profile. The slightly curved bottom of the profile is what epoxys to the fin can. To ensure that this curvature matched that of the fin can, we created a circle sketch the size of the fin can, and used a small section of that circle to base our fillet off of. The straight edge on the left is what sits flush against the fin. The top left and bottom right edges were rounded to improve the aerodynamics of the rocket. The length of the fillets varied depending what stage they were on; booster fillets were 8.5 inches long, whereas sustainer fillets were 5 inches long.
Transitions
Now of course, we didn't want the entire top of our fillets to be exposed to the air during launch. To circumvent this, we added "transitions" to the top and bottom of the fillets, which essentially taper off the fillet's cross sectional area to a tip.
These are the forward transitions, which aerodynamically transition from the motor case to fillets.
These are the rear transitions, which aerodynamically transition from the fillets to the fin can.
To make the transitions, we used 3D-printed PETG.