BACKGROUND

The present disclosure relates generally to the field of avionics. More specifically, the present disclosure relates to systems and methods for determining flight paths to avoid weather vortices (e.g., wind vortices).

Wind vortices can be produced as a result of wind patterns, storms, hurricanes, tornadoes, etc. Typically, wind vortices can cause aircrafts to be blown off course since they present the pilot and the avionic systems of the aircraft with a complex problem. The flight path as determined by some flight management systems may simply avoid the storm cells altogether, thereby increasing travel time. Increasing travel time by avoiding storm cells can decrease flight efficiency and increase costs associated with flights. On some occasions, pilots may judgmentally determine a route to take to avoid storm cells and may attempt to use vortex currents to speed up the aircrafts. However, the judgment of the pilot is prone to error and this may result in the aircraft being blown significantly off course, thereby increasing flight time. Additionally, flying through headwinds can increase flight time. Some pilots may attempt to use tailwinds to help decrease flight time and fuel consumption, however, this is largely judgmental. Flying too close to an eye of a vortex or a storm cell causes strong side/cross winds that can cause the aircraft so spend extra time and consume more fuel to compensate for the cross winds. However, flying too far from the eye of the vortex or storm cell results in a large deviation from the original flight path and results in the aircraft catching weak tailwinds despite the opportunity for the aircraft to catch stronger tailwinds. There is a need for a system to determine a flight path which avoids storm cells yet uses vortex currents when possible to catch tailwinds such that flight time and fuel consumption of the aircraft are minimized.

SUMMARY

In one aspect, the inventive concepts disclosed herein are directed to a controller for an aircraft. In some embodiments, the controller is configured to receive a starting point, a desired ending point, an initial time, a current aircraft speed, a wind vortex strength, and a wind vortex position. In some embodiments, the controller is configured to determine components of wind speed of at least one of the wind vortex, a wind source, and a uni-directional wind. In some embodiments, the controller is configured to determine one or more boundary conditions for a boundary value optimization problem. In some embodiments, the controller is configured to determine an initial estimate for the boundary value optimization problem, define the boundary value optimization problem as one or more differential equations based on the starting point, the desired ending point, the initial time, the current aircraft speed, the components of the wind speed, and a control variable of the aircraft. In some embodiments, the controller is configured to determine a solution for the boundary value optimization problem based on the one or more boundary conditions, the one or more differential equations and the initial estimate. In some embodiments, the controller is configured to evaluate the solution to determine a flight path and control variable values for the flight path. In some embodiments, the controller is configured to at least one of provide a display representing the determined flight path and the control variable values to a user, and adjust an operation of the aircraft to use the control variable values to follow the determined flight path.

In a further aspect, embodiments of the inventive concepts disclosed herein are directed to a method for determining a flight path around a wind vortex and controlling an aircraft to follow the flight path. In some embodiments, the method includes receiving a starting point, a desired ending point, an initial time, and a current aircraft speed. In some embodiments, the method also includes determining components of wind speed of a wind vortex. In some embodiments, the method also includes determining one or more boundary conditions for an optimization problem. In some embodiments the method also includes determining an initial estimate for the optimization problem. In some embodiments, the method includes defining the optimization problem as one or more differential equations based on the starting point, the desired ending point, the initial time, the current aircraft speed, the components of the wind speed, and a control variable of the aircraft. In some embodiments, the method also includes determining a solution for the boundary value optimization problem based on the one or more boundary conditions, the one or more differential equations, and the initial estimate. In some embodiments, the method also includes evaluating the solution to determine a flight path and control variable values for the flight path. In some embodiments, the method also includes adjusting an operation of the control variable of the aircraft to cause the aircraft to follow the determined flight path.

In still further aspect, embodiments of the inventive concepts disclosed herein are directed to an avionic system for an aircraft. In some embodiments, the system includes a user interface device and a controller. In some embodiments, the controller is configured to receive a present location of the aircraft, a present location of one or more wind vortices, a strength of the one or more wind vortices, and a desired ending point of the aircraft. In some embodiments, the desired ending point of the aircraft is received from the user interface device. In some embodiments, the controller is configured to define an optimization problem, and determine a solution to the optimization problem. In some embodiments, the solution to the optimization problem includes a flight path and steering angle values to achieve the flight path. In some embodiments, the flight path results in a minimum time to reach the desired ending point. In some embodiments, the controller is configured to cause the user interface device to display a map including the flight path.

