Analytical model to predict the self-induced acceleration and deceleration of a head fire

Domingos Xavier Viegas; Carlos Ribeiro; Luís M. Ribeiro; Miguel Almeida; Tiago Rodrigues; Thiago Fernandes Barbosa

doi:10.1071/WF24166

RESEARCH ARTICLE (Open Access)

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Analytical model to predict the self-induced acceleration and deceleration of a head fire

Domingos Xavier Viegas ^A ^* , Carlos Ribeiro

^A , Luís M. Ribeiro

^A , Miguel Almeida ^A , Tiago Rodrigues ^A and Thiago Fernandes Barbosa ^A

+ Author Affiliations

- Author Affiliations

^A Department of Mechanical Engineering, ADAI, University of Coimbra, Rua Luís Reis Santos, Pólo II, 3030‐788 Coimbra, Portugal.

^* Correspondence to: xavier.viegas@dem.uc.pt

International Journal of Wildland Fire 34, WF24166 https://doi.org/10.1071/WF24166

Submitted: 14 October 2024 Accepted: 22 May 2025 Published: 8 July 2025

© 2025 The Author(s) (or their employer(s)). Published by CSIRO Publishing on behalf of IAWF. This is an open access article distributed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND)

Abstract

Background

Current fire behaviour modelling assumes that the head fire rate of spread (ROS) depends on the three factors of the classical fire environment triangle (fuel, meteorology and topography) without considering the convective processes resulting from the interaction between fire and the environment.

Aims

An analytical model is proposed to predict the large-amplitude oscillations of the head fire ROS caused by this interaction, which often lead to rapid acceleration and deceleration of the fire.

Methods

A mathematical model proposed earlier is applied to the head fire’s acceleration and deceleration phases, using results from laboratory, field-scale and wildfires, to develop the parameters.

Key results

Two sets of model parameters were proposed to predict the temporal variation of the ROS in the laboratory and field-scale fires. Using data from wildfires, the present model predicts the time lapses of given periods of acceleration or deceleration with sufficient accuracy.

Conclusions

An analytical model is proposed to predict the large amplitude temporal variation of the head fire ROS during large fires. This model will go beyond current fire behaviour models that do not explain and predict these acceleration and deceleration processes.

Implications

The present analytical model to predict the acceleration and deceleration of the head fire proposes a novel interpretation of the fire behaviour, considering its dynamic effects and their inclusion in fire spread modelling.

Keywords: acceleration fires, canonical cases, deceleration fires, dynamic fire behaviour, eruptive fires, extreme fire behaviour, fire dynamics, fire modelling, fire spread.

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