Geometric Navigation of the Meteorological Aircraft’s Flight in Hurricane and Routing the Safe Trajectories via Mathematical Simulation

The hurricane phenomenon can be regarded as a rapidly rotating storm system identified by strong winds, a low pressure center, and a spiral arrangement of thunderstorms. This natural disaster can be analyzed by a particular meteorological aircraft and a weather reconnaissance device called dropsonde. The dropsonde is released when the plane reaches the eye (center) of the hurricane, normally at around 10,000 feet. In order to reduce the rate of probable accidents, identifying the safe and optimal time trajectories for the airplane, in order to exit the hurricane region is indispensable. In this paper, a comprehensive analysis of the routing the airplane flight in hurricane is presented via geometric simulation and mathematical modeling. Furthermore, it is demonstrated that the structure of the airplane flight in hurricane is of Randers type. Therefore, the safe and time optimal trajectories of this problem will be the geodesics of this Randers metric. Finally, we simulate a plane entering in a hurricane region and determine the differential equations corresponding to the time optimal and safe trajectories.

Keywords:

Geometric Simulation , Meteorological Aircraft , Dropsonde , Hurrican Phenomenon , Randers Metric , Geodesic Equations