Construction of a ballistic model of the motion of uncontrolled cargo during its autonomous high-precision drop from a fixed-wing unmanned aerial vehicle - Humennyi, Andrii; Oleynick, Sergey; Malashta, Pavlo; Pidlisnyi, Oleksandr; Aleinikov, Vitalii (Eastern-European Journal of Enterprise Technologies, 2024)
The object of this study is the process related to the fall of an uncontrolled cargo from a height of 400–600 meters relative to sea level in an air environment under the influence of gravity, air drag, and wind in the presence of an initial air speed of about 20 m/s. The study solves the task to build a ballistic model of the movement of an unguided cargo during autonomous high-precision dropping from an unmanned aerial vehicle of aircraft type. A system of equations was derived that explicitly describes the dependence of the cargo’s travel speed and coordinates on time and takes into account the effect of gravity, air drag, and the influence of wind. The scope of application of the equations corresponds to drop heights of up to 400 m relative to the surface of the earth and the initial horizontal speed of the cargo up to 20 m/s. The resulting equations were analyzed using an example of a spherical load weighing 10 kg and the largest cross-sectional area of 7.1·10-2 m2 when it falls from heights of 200, 300, and 400 m relative to the earth’s surface. In the absence of wind, the horizontal component of the load’s speed at the moment of falling is ≈(13–15) m/s, and the vertical component is ≈(50–60) m/s. At the same time, the horizontal displacement of the load under the conditions of a weak crosswind can reach ≈(150–220) m. With a vertical wind speed profile, the equivalent constant wind speed can be determined, resulting in the same effect on the load as a variable speed wind. An algorithm for determining the point of unloading the cargo has been proposed. The cargo delivery error has been evaluated. The most important parameters are the flight time of the cargo and the drop height. In order to achieve a hit accuracy of ±5 m, an error in determining the time of the fall of the load is not more than ≈0.16 s, and an error in determining the height of the drop is not more than ±8 m