Procedure for constructing a mathematical model to determine the time of the initial stage of fire evolution




fireproof wood, fire retardant, impregnating substance, ignition temperature, fire impact


To develop appropriate measures and means of fire protection at facilities, it is relevant to form an idea of the phenomenology of the processes of the occurrence, evolution, and termination of combustion. This paper proposes procedures for building mathematical models of the energy component of those physicochemical processes that occur in wood under the influence of fire, which make it possible to determine the time from the beginning of such an impact to the onset of the phase of flame combustion. The adequacy of mathematical modeling was tested experimentally at a standardized installation for studying flame propagation over the surface of wood. The samples used for the reported theoretical and experimental studies were the specimens of unprotected wood made from 20-mm-thick pine sapwood with a density of 400‒550 kg/m3. The samples of fireproof wood (of the same variety, thickness, and density) were impregnated with a fire retardant based on diammonium phosphate and ammonium sulfate (at consumption of 168.2 g/m2 of dry fire-retardant components). The modeling employed the results from the experimental determining of the ignition temperature of unprotected and fire-proof wood, specifically: 235 °C – for unprotected wood, 410 °C – for fire-proof wood, respectively.

The results of mathematical modeling and experimental studies confirm the possibility of significant lengthening of time from the onset of fire exposure to the ignition of fire load from wood when nitrogen-phosphorus impregnating agents are used for fire protection.

Procedures of mathematical modeling have been proposed to build models for determining the cooling effect from the use of impregnating fire retardants to protect the wood on the prolongation of the stage of a fire start.

Mathematical modeling data could be applied when making impregnating fire retardants

Author Biographies

Sergii Zhartovskyi, Institute of Public Administration and Research in Civil Protection

Doctor of Technical Sciences

Scientific Testing Center

Olexander Titenko, Institute of Public Administration and Research in Civil Protection


Scientific Testing Center

Oksana Kyrychenko , Cherkasy Institute of Fire Safety named after Chornobyl Heroes of National University of Civil Protection of Ukraine

Doctor of Technical Sciences, Professor

Department of Fire Prevention Work

Ievgen Tyshchenko, Educational and Methodological Centre of Civil Protection and Life Safety of Cherkasy Region

Doctor of Technical Sciences, Associate Professor, Deputy Head of Educational and Methodological Center

Roman Motrichuk, Department of the Ukrainian SSNU in Cherkassy Region


Valentyn Melnyk, Cherkasy Institute of Fire Safety named after Chornobyl Heroes of National University of Civil Protection of Ukraine


Department of Fire Prevention Work


  1. Coen, J. L., Riggan, P. J. (2014). Simulation and thermal imaging of the 2006 Esperanza wildfire in southern California: application of a coupled weather-wildland fire model. International Journal of Wildland Fire, 23 (6), 755–770. doi:
  2. Uniting and strengthening America by providing appropriate tools required to intercept and obstruct terrorism (2001). Available at:
  3. Special underground facilities (UGF-s) serving for the critical infrastructure (2006). New challenges in the field of military science international scientific conference. Available at:
  4. Lowden, L. A., Hull, T. R. (2013). Flammability behaviour of wood and a review of the methods for its reduction. Fire Science Reviews, 2, 4. doi:
  5. Baratov, A. N., Andrianov, R. A., Korol'chenko, A. Ya. et. al. (1988). Pozharnaya opasnost' stroitel'nyh materialov. Moscow, 380.
  6. Zhartovskiy, S. V. (2013). A systematic approach to fire protection of objects using water fire retardant and fire extinguishing means. Pozharovzryvobezopasnost', 22 (9), 25–32. doi:
  7. Baratov, A. N., Molchadskiy, I. S. (2011). Gorenie na pozhare. Moscow, 503.
  8. Lopes, A. M. G., Ribeiro, L. M., Viegas, D. X., Raposo, J. R. (2017). Effect of two-way coupling on the calculation of forest fire spread: model development. International Journal of Wildland Fire, 26 (9), 829–843. doi:
  9. Kutateladze, S. S. (1979). Osnovy teorii teploobmena. Moscow, 416.
  10. Yeoh, G. H., Yuen, K. K. (Eds.) (2008). Computational fluid dynamics in fire engineering: theory, modelling and practice. Butterworth-Heinemann, 544. doi:
  11. Melihov, A. S. (2017). Issledovanie protsessa rasprostraneniya tleniya i usloviy ego prekrashcheniya vnutri massiva gazopronitsaemogo melkodispersnogo materiala. Pozharnaya bezopasnost', 4, 74–89.
  12. Markus, E., Snegirev, A., Kuznetsov, E., Tanklevskiy, L. (2018). Application of a simplified pyrolysis model to predict fire development in rack storage facilities. Journal of Physics: Conference Series, 1107, 042012. doi:
  13. Bartlett, A. I., Hadden, R. M., Bisby, L. A. (2018). A Review of Factors Affecting the Burning Behaviour of Wood for Application to Tall Timber Construction. Fire Technology, 55 (1), 1–49. doi:
  14. Liu, Q., Shen, D., Xiao, R., Zhang, H., Fang, M. (2013). A mathematical description of thermal decomposition and spontaneous ignition of wood slab under a truncated-cone heater. Korean Journal of Chemical Engineering, 30 (3), 613–619. doi:
  15. Grieco, E., Baldi, G. (2011). Analysis and modelling of wood pyrolysis. Chemical Engineering Science, 66 (4), 650–660. doi:
  16. Nizhnyk, V., Shchipets, S., Tarasenko, O., Kropyvnytskyi, V., Medvid, B. (2018). A Method of Experimental Studies of Heat Transfer Processes between Adjacent Facilities. International Journal of Engineering & Technology, 7 (4.3), 288. doi:
  17. Molchadskiy, I. S. (2005). Pozhar v pomeshchenii. Moscow, 456.
  18. Chumachenko, S. N., Zhartovskyi, S. V., Titenko, A. N. (2016). Methods of creating a mathematical model of an energy component of chemical and physical processes that occur in wood when it is heated prior to the flaming phase. BiTP, 44 (4), 131–137. doi:
  19. Chumachenko, S. M., Zhartovskyi, S. V., Titenko, O. M. (2016). The Methodology of Creating the Mathematical Model of Cooling Effect during Heating of Wood Sample Impregnated by Water Based Flameproofing Matter. Scientific Bulletin of UNFU, 26 (8), 337–347. doi:
  20. Baratov, A. N., Korol'chenko, A. Ya., Kravchuk, G. N. et. al. (1990). Pozharovzryvoopasnost' veshchestv i materialov i sredstva ih tusheniya. Moscow, 496.
  21. Zhartovskyi, V. M., Tsapko, Yu. V. (2006). Profilaktyka horinnia tseliulozovmisnykh materialiv. Teoriya ta praktyka. Kyiv, 248.
  22. Rodzhers, D., Adams, Dzh. (2001). Matematicheskie osnovy mashinnoy grafiki. Moscow, 604.
  23. Shreter, V., Lautenshleger, K., Bibrak, H. et. al. (1989). Himiya. Moscow, 648.
  24. Bolgarskiy, A. V., Muhachev, G. A., Shchukin, V. K. (1975). Termodinamika i teploperedacha. Moscow, 495.
  25. Solodov, A. P. (2015). Teplomassoobmen v energeticheskih ustanovkah. Inzhenernye metody rascheta. Moskva, 124.
  26. Chumachenko, S. M., Zhartovskyi, S. V., Titenko, O. M., Trotsko, V. V. (2016). Methodology of Mathematical Model Creation of Flame Retardants Distribution in Fire Protected Wood. Scientific Bulletin of UNFU, 26 (5), 378–385. doi:
  27. DSTU 8829:2019. Fire and explosion hazard of substances and materials. Nomenclature of indices and methods of their determination. Classification.




How to Cite

Zhartovskyi, S., Titenko, O., Kyrychenko , O., Tyshchenko, I., Motrichuk, R., & Melnyk, V. (2021). Procedure for constructing a mathematical model to determine the time of the initial stage of fire evolution . Eastern-European Journal of Enterprise Technologies, 1(10 (109), 45–52.