Multi-objective optimization of a fin shape for a passive supersonic rocket stage

Stability is one of the crucial aspects of any rocket's design. It can be achieved in multiple ways, both passively and actively. Smaller rockets tend to rely on passive stability provided by aerodynamic fins. The stability that a particular fin can offer depends on its size, shape and mounting location. Although it is obvious that a larger fin located further down towards the base of the rocket will provide greater stability, it is difficult to intuitively determine the best shape of the fin. Furthermore, stability is not the only factor taken into account during the design. As the rockets are usually designed to fly as fast or as high/far as possible it is common to minimize their aerodynamic drag. This makes the optimization of fins a multi-objective problem. This paper presents an optimization of a fin shape for a passively stabilized supersonic rocket during passive (non-propelled) flight. This study references to the Grot rocket – a supersonic, high-altitude, multi-stage sounding rocket being developed by the Rocketry Division of the Students' Space Association at the Warsaw University of Technology since 2018. As future iterations of the Grot rocket are to fly higher and faster, a new fin design is developed. The fin shapes utilized in the study are defined by bounded values of aspect ratio, taper ratio and leading-edge sweep angle. Fins' drag, static margin and/or pitching moment are estimated based on CFD simulations for various Mach numbers. A set of Pareto optimal designs is determined for each Mach number. Then the final design is chosen based on the time the rocket spends in each flight regime. Finally, a comparison between old and new designs is presented based on a simulation in an in-house-developed flight simulation software.