Aerodynamic Effects of Fin Length-to-Diameter Ratio on Spherical Projectile Range and Velocity Decay

This report presents an experimental–theoretical investigation of how fin geometry influences aerodynamic drag, deceleration, and range in the atmospheric flight of a spherical projectile treated as a simplified re-entry capsule analogue. The analysis builds from the quadratic drag model and discusses how fin length-to-diameter ratio can modify the effective drag through changes in reference area and an effective drag coefficient, while also affecting stability and wake development. A hollow steel sphere fitted with two symmetric triangular fins was tested across multiple fin length-to-diameter (L/D) configurations, with repeated launch trials used to estimate variability and uncertainty. Horizontal range was measured experimentally, and time-resolved kinematics were extracted from high-speed (240 fps) video using Tracker, producing velocity–time profiles and velocity decay estimates that allow direct comparison with drag-dominated expectations. The discussion interprets trends and anomalies using fluid-dynamics concepts beyond standard school projectile motion—wake dynamics, vortex formation/vortex shedding, boundary-layer behaviour and separation, and the limitations of assuming a constant across changing flow regimes. A Spearman rank correlation analysis is included to quantify the monotonic relationship between fin ratio and velocity decay. The report concludes with a structured evaluation of uncertainty and limitations, and proposes extensions for higher-fidelity testing (e.g., improved launch control, controlled-flow comparison, or computational modelling).