Basic Computational Algorithms for Representing an Aircraft Flight (Calculation of 3D Displacement and Displaying)

Abstract

This manuscript describes the computational process to calculate an airplane path and display it in a 2D and 3D coordinate system on a computer screen. The airplane movement is calculated as a function of its dynamic’s conditions according to physical and logical theory. Here, the flight is divided into maneuvers and the aircraft conditions are defined as boundary conditions. Then the aircraft position is calculated using nested loops, which execute the calculation procedure at every step time (Δt). The calculation of the aircraft displacement is obtained as a function of the aircraft speed and heading angles. The simulator was created using the C++ programming language, and each part of the algorithm was compiled independently to reduce the source code, allow easy modification, and improve the programming efficiency. Aerial navigation involves very complex phenomena to be considered for an appropriate representation; moreover, in this manuscript, the influence of the mathematical approach to properly represent the aircraft flight is described in detail. The flight simulator was successfully tested by simulating some basic theoretical flights with different maneuvers, which include stationary position, running along the way, take off, and some movements in the airspace. The maximum aircraft speed tested was 120 km/h, the maximum maneuver time was 12 min, and the space for simulation was assumed to be without obstacles. Here, the geometrical description of path and speed is analyzed according to the symmetric and asymmetric results. Finally, an analysis was conducted to evaluate the approach of the numerical methods used; after that, it was possible to confirm that precision increased as the step time was reduced. According to this analysis, no more than 500 steps are required for a good approach in the calculation of the aircraft displacement.