Adding Atmospheric Turbulence to a Mathematical Model of an Aircraft

Regardless of the design, all types of aircraft are affected by atmospheric turbulence and air currents. Depending on the size, type and altitude of the flight, atmospheric disturbances affect them differently. The same disturbance acting on an unmanned aerial vehicle flying at high altitude, for example, a Predator UAV, and on a quadcopter flying a few meters above the ground, will have in the first case minimal or no impact on the flight parameters, and hence on the correct performance of the task, while in the case of a quadcopter it can even lead to a collision with the ground or a nearby obstacle (building, tree, etc.).

The article examines the types of translational and turbulent atmospheric disturbances. The reasons for their occurrence are described. The article uses a mathematical model of an aircraft with six degrees of freedom. To create it, Euler’s standard differential equations for the change in the amount of momentum and the theorem for the change in angular momentum were used. It is examined in detail how atmospheric disturbances should be added to the differential equations describing the aircraft. It is studied how wind gusts are converted into forces that affect the flight parameters. Depending on the type and size of the aircraft, these forces are of different magnitude and have different effects on the behavior of the aircraft in flight.