Mathematical model of optimal logistics routes of fire tank trucks when extinguishing landscape fires

Almazov Kamran

Academy of the Ministry of Emergency Situations

https://orcid.org/0000-0001-6483-351X

Mykhailovska Yuliia

National University of Civil Protection of Ukraine

https://orcid.org/0000-0003-1090-5033

DOI: https://doi.org/10.52363/2524-0226-2025-42-12

Keywords: : logistical routes, firefighting vehicles, landscape fires, mathematical model, terrain parameters

Аnnotation

The paper builds a mathematical model of the optimal route based on the minimum time criterion, in off-road conditions depending on the tactical and technical characteristics of the vehicle and the parameters of the landscape, taking into account the stability of this vehicle to overturning. This model is based on the application of computer technologies of geographic information systems. In this case, geographic information analytical models and vector-functional models of the relief of rough terrain where the occurrence, development and spread of a landscape fire are possible were used. When creating the model, it was taken into account that in conditions of ascent and descent when overcoming uneven terrain, the speed of the fire vehicle decreases, and some directions of movement of this vehicle are prohibited, from the point of view of the maximum engine power that can be developed in these conditions. In addition, the possibility of overturning of vehicles transporting fire-extinguishing fluid in an appropriate capacity, such as fire tankers, must be taken into account. The risk of overturning can be increased by a sudden shift of the center of mass due to the movement of the liquid in the container with the formation of splashes, as well as the action of inertial forces. To build safe and optimal routes, taking into account such aspects, the features of the terrain should be analyzed using geographic information systems, permitted directions should be determined, and conditions for possible deceleration when overcoming irregularities should be taken into account. To solve the problem of obtaining optimal routes, a mathematical model was built that establishes the dependence of the azimuthal speed of the vehicle depending on their tactical and technical characteristics and local data on the relief of the rough terrain. The developed mathematical model can be used to predict relatively safe and convenient logistical routes of firefighting vehicles to the fire center in real-world conditions.

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