Aerodynamic sectional modeling with the use of extended vectors

This paper presents the dynamic model of an Unmanned Aerial Vehicle (UAV), specifically, a fixed-wing aircraft PT-40, using extended vectors in ℝ⁶. This representation of cartesian coordinates in the Euclidian space simplifies the representation of the model to express each term in a single six dimensional vectorial equation, instead of the three dimensional, conventional linear and angular movement equations. The algebra to manipulate these elements reduces the number of operations and defines the basic transformations between the reference frames. The UAV is a free rigid body in ℝ³ subject to aerodynamic forces, which are included in the model as exogenous forces. Typically these forces are calculated using dimensionless coefficients that capture the geometric complexity of the aircraft in the Aerodynamic Center of Pressure, resulting in a model with lumped aerodynamic parameters. Due to the advantages of the extended vectors, the aerodynamic forces acting on each component of the aircraft can be included in the mathematical model as independent effects.