Design, Sizing, and Analytical Performance Modeling of a Small-Scale UAV

Performance modeling is a key aspect in the design of any vehicle that soars in the sky. From modest gliders to astounding hypersonic vehicles, the ability to predict the behaviour of such systems is of paramount importance for mission success. Engineers are tasked with the challenge of characterising systems that do not yet exist, bridging the gap between theoretical concepts and physical reality. This thesis proposes a hybrid framework that reconciles the elegance of an analytical core with the flexibility of numerical graftings whenever the algebraic manipulation alone is insufficient. This approach is applied to the derivation of takeoff performance for a small-scale Unmanned Aerial Vehicle (UAV). Starting from first principles, aerodynamic contributions are obtained and corrected for three-dimensional effects; tribological phenomena are modeled specifically for the small-scale UAV regime; and finally, the propeller thrust curve is constructed by fitting BEMT simulations to a polynomial function. Throughout the derivation, meticulous care is taken to preserve the natural structure of the Riccati differential equation of motion. This ensures a closed-form solution for the takeoff distance, velocity, and time, providing a computationally efficient yet physically rigorous tool for early-stage, iterative design and performance estimation