Determining Sphere Arc Length for 4D Routing Problem

Abstract

The concept of dimension is prominent in the researches of physics and mathematics and is also a subject of research in many sciences. While it is mentioned in many theories that the universe is multidimensional or even infinite, in this thesis study, the concept of dimension is addressed up to the fourth dimension. While the fourth dimension is examined in particular, the concepts of latitude, longitude, altitude and time are mentioned, and the concept of 4D navigation with the fourth dimension allows for the accurate prediction of the orbits defined in both time and space, and since it comes to the forefront more in the aviation field, its developments in this sector are mentioned. In the thesis study, it is aimed to determine the most suitable and closest flight path by performing route analysis with geodetic methods in 4-dimensional orbit determination. Thus, the application of the 4D orbit determination method will be investigated by SESAR and NextGen and will allow air traffic controllers to accurately predict the effect of a disturbance in air traffic flow in the near future. In addition, the closest distance calculated with different approaches of flight routes was compared on the sphere and ellipsoid, and 7 flight routes were examined by taking Samsun as the center. In addition, the route length was calculated from the sum of the distances between the intermediate points forming the flight route.