Fighting with wildfire: unsteady discharge flow dynamics and drop pattern prediction for air tankers

• Based on the non-constant Bernoulli equation and the law of rigid body rotation, a analytical model for the non-constant flow of tank discharge is proposed. • A drop pattern model for variable flow conditions is presented. • The performance of the model in simulating tank discharge processes as well as ground contour distribution characteristics is verified. • The induced effects of tank geometry configuration, discharge system type, liquid viscosity, and others on the tank discharge flow and drop pattern are revealed. • Providing substantial steps towards the design of a firefighting aircraft firefighting mission system and a coordinated firefighting mission program for multiple firefighting aircraft, which would help societies respond to future fire events. The global increase in the frequency, intensity as well as adverse social and economic impacts of wildfires highlights the ongoing need for fire containment and suppression equipment. Aerial firefighting has become an indispensable method for combating wildfires due to its high mobility and reduced terrain limitations. Although considerable research has been conducted on modeling discharge flow and drop patterns, existing models are abstractions that do not find a direct mapping relationship between the key parameters of delivery systems (e.g., tank geometry configuration, tank door layout, discharge system type, and others) and the discharge flow as well as drop pattern. This study develops an analytical model for unsteady discharge flow dynamics and drop pattern prediction in air tankers. This model establishes a direct mapping between the influencing factors and the discharge flow as well as drop pattern, thereby helping to provide viable proposals for firefighting aircraft performance improvement and fire suppression mission planning. Leveraging data from full-scale discharge experiments and previously published drop tests by the authors, the performance of the model in simulating tank discharge processes as well as ground contour distribution characteristics have been verified. The results indicate that the average relative error in the line lengths for the coverage level between the extended model predictions and the experimental data is 8.17%, and the maximum relative error is ±16.06%. The volume changes calculated by the extended model and the cumulative amount of deposited material along the x-axis agree well with the experimental data. The relative error between the cumulative deposition predicted by the extended model and the experimental data is -6.51%, which is significantly smaller than the 23.55% error of the original model. As shown theoretically and verified experimentally, various factors, such as tank geometry configuration, tank door layout, discharge system type, and others, have induced effects on the tank discharge flow and drop pattern. These findings provide substantial steps towards the design of a firefighting aircraft firefighting mission system and a coordinated firefighting mission program for multiple firefighting aircraft, which would help societies respond to future fire events.