Abstract
Forest fires cause great damage to the environment and are difficult to predict and eliminate. Mathematical models of temperature regimes of forest fires can create a scientific basis for improving the effectiveness of firefighting measures. The study of fire propagation processes and temperature regimes during a fire is an urgent task that many researchers are engaged in. The processes of heat exchange in the process of fire are very complex and include many factors. For this reason, they are difficult to model. The equations of heat transfer processes themselves are also difficult to solve and obtain analytical solutions.The aim of this work is to create a mathematical model of the ignition of a needle from the flame of a moving ground fire. The solution of the set tasks was carried out by the method of direct integration.The model of the process of heating the lower part of the tree crown due to the moving grass fire described in this paper has the advantage that it is based on mathematical calculations that can be easily performed using the mathematical software package Maple. The program in the Maple package is offered, which, depending on the input data: the size of the fire area, the speed of fire spread, the distance from the ground to the bottom of the crown, calculates the air temperature. These results can be used to calculate and assess the operational situation during forest fires.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Fires in Greece: the death toll rose to 74, more than 180 injured (2018). https://www.eurointegration.com.ua/news/2018/07/24/7084762/
The fires in California covered 809 thousand hectares (2020). https://lb.ua/world/2020/09/08/465498_pozhezhi_kalifornii_ohopili_809_tisyach.html
Fires in southern Europe: the situation is getting worse (2021). https://www.dw.com/uk/pozhezhi-na-pivdni-yevropy-sytuatsiia-zahostriuietsia/a-58775185
The average area of forest fires in Ukraine has increased 7 times (2022). https://lb.ua/society/2022/03/29/511485_cerednya_ploshcha_lisovoi_pozhezhi.html
In Colorado, fires destroyed hundreds of homes within hours (2022). https://lb.ua/world/2022/01/01/502250_kolorado_pozhezhi_zruynuvali_sotni.htmll
Dorrer, G.: Mathematical Models of Forest Fire Dynamics. Forest Industry, Moscow (1979)
Egorova, V.N., Trucchia, A., Pagnini, G.: Fire-spotting generated fires. part II: the role of flame geometry and slope. Appl. Math. Model. 104, 1–20 (2022). https://doi.org/10.1016/j.apm.2021.11.010
Ervilha, A., Pereira, J., Pereira, J.: On the parametric uncertainty quantification of the Rothermel’s rate of spread model. Appl. Math. Model. 41, 37–53 (2017). https://doi.org/10.1016/j.apm.2016.06.026
Gulida, E., Smotr, O.: Forest fire forecasting. Fire Saf. Issues 21, 73–80 (2007)
Hramov, V., et al.: Modeling of forest fires on Grid clusters. Comput. Tools Netw. Syst. 21, 47–57 (2012)
Kononov, M., Sudakov, O., Hramov, V.: Features of modeling of fires on clusters in Grid. Bull. Taras Shevchenko Natl. Univ. Kyiv. Phys. Math. Sci. Collect. Sci. works 2, 185 (2011)
Kuzyk, A., Tovaryansky, V.I.: Mathematical modeling of conductive and radiative heat transfer processes during a fire in pine forests (2017)
Li, X., et al.: Simulating forest fire spread with cellular automation driven by a LSTM based speed model. Fire 5(1), 13 (2022). https://doi.org/10.3390/fire5010013
Morvan, D.: Validation of wildfire spread models. In: Manzello, S., et al. (eds.) Encyclopedia of Wildfires and Wildland-Urban Interface (WUI) Fires, pp. 1031–1037. Springer, Cham (2020). https://doi.org/10.1007/978-3-319-52090-2_59
Nelson Jr., R.: Byram’s energy criterion for wildland fires: units and equations. Research Note INT-US Department of Agriculture (1993)
Smotr, O., Grytsyuk, Y.: Modeling of forest fire contours. Fire Secur. 20, 169–179 (2012)
Soznik, O., Kalinovsky, A.: Geometric model of the rate of spread of landscape fires and some of its consequences. In: Applied Geometry and Engineering Graphics. Proceedings - Tavriya State Agrotechnical Academy 4, 94–98 (2004)
Sullivan, A.: Convective Froude number and Byram’s energy criterion of Australian experimental grassland fires. Proc. Combust. Inst. 31(2), 2557–2564 (2007)
Sullivan, A.L.: Inside the inferno: fundamental processes of wildland fire behaviour. Curr. Forestry Rep. 3(2), 132–149 (2017). https://doi.org/10.1007/s40725-017-0057-0
Tatsiy, R.M., Pazen, O.Y., Vovk, S.Y., Ropyak, L.Y., Pryhorovska, T.O.: Numerical study on heat transfer in multilayered structures of main geometric forms made of different materials. J. Serb. Soc. Comput. Mech. 13(2), 36–55 (2019). https://doi.org/10.24874/jsscm.2019.13.02.04
Weise, D.R., Biging, G.S.: Effects of wind velocity and slope on flame properties. Can. J. For. Res. 26(10), 1849–1858 (1996)
Weise, D.R., et al.: Fire behavior in chaparral–evaluating flame models with laboratory data. Combust. Flame 191, 500–512 (2018). https://doi.org/10.1016/j.combustflame.2018.02.012
Weise, D., Zhou, X., Sun, L., Mahalingam, S.: Fire spread in chaparral (2005)
Zelensky, K., Hazel, V.: Mathematical modeling of aerodynamics of horse forest fires. Sci. Notes 27, 110–115 (2010)
Zhang, X., Liu, P.: Research on the improvement of Wang Zhengfei’s forest fire spreading model. Shandong Forest. Sci. Technol. 50(01), 1–6 (2020)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Karabyn, O., Smotr, O., Kuzyk, A., Malets, I., Karabyn, V. (2023). Mathematical and Computer Model of the Tree Crown Ignition Process from a Mobile Grassroots Fire. In: Babichev, S., Lytvynenko, V. (eds) Lecture Notes in Data Engineering, Computational Intelligence, and Decision Making. ISDMCI 2022. Lecture Notes on Data Engineering and Communications Technologies, vol 149. Springer, Cham. https://doi.org/10.1007/978-3-031-16203-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-031-16203-9_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-16202-2
Online ISBN: 978-3-031-16203-9
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)