Aerobatic Aircraft Modeling Based on Aerodynamic Quaternions

Abstract

A simulation model for aerobatic aircraft is derived that accounts for a proper inclusion of static, convective and time-dependent wind fields. Two different depths of modeling are regarded, namely a point-mass simulation model and a full, nonlinear 6-DoF simulation model. Both simulation models make use of the aerodynamic flight path angles as translational states to describe the respective aircraft trajectories since the aerodynamic quantities physically determine the motion of the aircraft. The kinematic quantities are then a function of the aerodynamic quantities and the wind influence. The 6-DoF simulation model is based on a sequential structure, where the aircraft’s attitude and rotational dynamics are given with respect to its aerodynamic trajectory. Thus, the aerodynamic angle of attack and the aerodynamic sideslip angle are used to describe the attitude of the aircraft with respect to the Aerodynamic Frame instead of Euler Angles that would describe the aircraft’s attitude with respect to the North-East-Down Frame. In order to avoid the singularity that occurs for aerodynamic flight-path inclination angles of , quaternions are utilized to replace the aerodynamic flight-path course angle, the aerodynamic flight-path inclination angle and the aerodynamic bank angle instead of replacing the Euler Angles or the kinematic flight-path angles as it is commonly the case.