Geometric modeling of airship device for extension of large forest fires

Kutsenko Leonid

National University of Civil Protection of Ukraine

https://orcid.org/0000-0003-1554-8848

Ishchuk Maksim

National University of Civil Protection of Ukraine

http://orcid.org/0009-0004-0170-1201

Kalynovskyi Andrii

State Emergency Service of Ukraine

http://orcid.org/0000-0002-1021-5799

Kovalenko Roman

National University of Civil Protection of Ukraine

https://orcid.org/0000-0003-2083-7601

DOI: https://doi.org/10.52363/2524-0226-2025-42-4

Keywords: airship model, container with fire extinguishing agent, differential equation, fire, trajectory

Аnnotation

A mathematical model of the airship's motion has been developed by constructing a system of differential equations, as well as a method for estimating the time during which a container released from a cannon will fly horizontally a certain distance before falling to the ground in the zone of a probable fire and the height of its fall based on a geometric approach. Extinguishing and monitoring large-scale forest fires is conveniently carried out using an airship. In a trivial case, fire-extinguishing chemicals can simply be dropped from the airship directly onto the fire, protecting against the hot thermal gases of the fire. In practice, it is better to use a special container filled with chemicals to extinguish a fire. In this case, the container is moved to the fire center along a pre-calculated trajectory. Stabilized movement of the container is ensured by its rotation around its axis. The problem lies in the initial determination of the necessary parameter values, taking into account which, it is possible to accurately hit the container into the area where the fire center is located. The proposed mathematical model and method are quite simplified compared to more complex computer models, but at the same time they allow to more quickly establish the main characteristics of the airship's motion, as well as to predict the trajectories of a container released horizontally from the cannon of this airship. It has been established that the main dangers for airships are their dependence on weather conditions, low speed and maneuverability. The danger for the airship is represented by ascending flows of hot rarefied air with their inherent high turbulence in the zone of occurrence and spread of a forest fire. The results of the research can be used when designing airships with technical means installed on them for discrete supply of fire extinguishing agents.

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