Safe distance determining algorithm in terms of the thrust force dependence on the aircraft speed during takeoff-run

The importance of air communication between various points of the globe in the modern world is difficult to overestimate. Yet the employment of this means of transport is associated with high risks for passengers, crew, cargo and the aircraft itself due to the possibility of serious accidents at all phases of the flight, but especially during takeoff and landing. This article presents a physical and mathematical model of an aircraft takeoff-run. Its analysis helps to avoid accidents in the event of emergency situations. This model enables the creation of an electronic device for monitoring takeoff dynamic characteristics and warning the aircraft crew about arising inconsistencies. The article presents differential equations describing the dynamic characteristics of the aircraft during takeoff-run. Additionally, solutions of these equations are obtained, which explicitly determine the functional dependencies of the distance necessary for a safe takeoff on the time elapsed since the start of the takeoff-run. The influence of external factors, such as ambient air temperature, wind speed during takeoff and runway slope on the calculated characteristics is considered. As an example, the article also offers the results of an emergency takeoff modeling with the aid of modern software (flight simulator flightgear 2020.3, GeoGebra mathematical program). From the authors’ point of view, the materials of the article may be of practical value for developers of non-embedded on-board control devices, as well as for users of these devices.

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