Calculation of Critical Water Flow Rates for Wildfire Suppression
2. Materials and Methods
- Water is applied to fuel surfaces not yet involved in fire, preventing pyrolysis and the production of combustion gases;
- Water is applied directly into the flames, cooling the flame below the critical temperature; or
- Water is applied directly to the burning fuel surface, cooling the fuel and resulting in a reduced pyrolysis rate and quenching of the flames.
- is the critical water application rate assuming no external heat flux, identified as ≈0.0129 Lm−2s−1 ,
- is the efficiency of water application, representing the portion of water leaving the firefighting branch which actually contributes to fire extinguishment, conservatively assumed to be 0.7 ,
- is the enthalpy change of water, identified as 2640 kJkg−1,
- is external heat flux, calculated using Equation (2),
- I is fire line intensity in kWm−1 calculated using Byram’s fire line intensity equation , calculated using Equation (3),
- is flame length in m, calculated using Equation (4),
- is depth of the active flame in m,
- is atmospheric transmissivity, assumed to be 1 due to the proximity of the unburned fuel in respect to the flames,
- is view factor, assumed to be 1 due to the proximity of the unburned fuel in respect to the flames,
- h is the convective heat transfer coefficient set at 0.077 kW/m2K assuming a forced convection and air velocity at 10 ms−1 ,
- Tfuel is the fuel temperature of the fuel, assumed to be 588 K, being the ignition surface temperature for pine-needle fuel beds .
- W is total fuel load in tha−1, considering fine fuels typically less than 6 mm in diameter 
- RoS is the forward Rate of Spread corrected for slope in kmh−1, calculated using Equation (5). Noting that terrain influences RoS, slope is assumed to be flat for the purposes of the study.
- FDI is Forest Fire Danger Index, a dimensionless factor incorporating the chance of a fire starting, its Rate of Spread, its intensity and the difficulty of its suppression, according to various combinations of air temperature, relative humidity, wind speed and both the long- and short-term drought effects ,
- w is understorey fuel load in tha−1, considering fine fuels typically less than 6 mm in diameter .
- The analysis incorporates the full spectrum of fire weather conditions and understorey fuel loads. Therefore the CF can be rapidly estimated by Incident Controllers without requiring current or predicted fire weather conditions (an essential component for calculating FDI) or understorey fuel loads (w) which may vary across the landscape. Both these inputs are required for calculating CF refer to Equations (1)–(5); and
- It provides Incident Controllers both visual and mathematical tools to assess the potential suitability of suppression strategies.
- real time fire appliance and aircraft telemetry that records active fire suppression time, water application rates and location;
- enhanced quantitative measurement of wildfire behaviour such as that available through aerial intelligence and analysis ;
- further experimental study in scaled controlled wildfires through natural vegetation structures with a specific focus on CF requirements.
Conflicts of Interest
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|Type||Name||Water Capacity (L)||Flow Rate (Ls−1)|
|Aircraft-Rotary 1 ||Dauphin Type 2||1000–1200||~333–400|
|Aircraft-Rotary 2 ||Erikson S64E Aircrane||7560||~1512|
|Aircraft-Fixed wing 3 ||AirTractor AT802F||3150||~1050|
|Appliance 4WD 4 [32,33,34]||Light Tanker||~500||2.5|
|Appliance 4WD 4,5 [31,33,34,35]||Heavy Tanker||~3000||3.8–7.9|
|Rate of Spread, RoS (kmh−1)|
|Active Flame Depth (m)||Function|
|2||CF2 = 2.72 RoS0.42|
|3||CF3 = 3.97 RoS0.43|
|4||CF4 = 5.12 RoS0.44|
|5||CF5 = 6.24 RoS0.44|
|6||CF6 = 7.23 RoS0.45|
|7||CF7 = 8.30 RoS0.45|
|8||CF8 = 9.23 RoS0.45|
|9||CF9 = 10.20 RoS0.45|
|10||CF10 = 11.11 RoS0.46|
|Intensity, I (kWm−1)|
|Active Flame Depth (m)||Function|
|2||CF2 = 0.11(I)0.33|
|3||CF3 = 0.15(I)0.34|
|4||CF4 = 0.12(I)0.35|
|5||CF5 = 0.22(I)0.35|
|6||CF6 = 0.24(I)0.36|
|7||CF7 = 0.27(I)0.36|
|8||CF8 = 0.30(I)0.36|
|9||CF9 = 0.32(I)0.36|
|10||CF10 = 0.35(I)0.36|
|Flame Length, Lf (m)|
|Active Flame Depth (m)||Function|
|2||CF2 = 0.64 Lf0.62|
|3||CF3 = 0.90 Lf0.63|
|4||CF4 = 1.14 Lf0.65|
|5||CF5 = 1.35 Lf0.65|
|6||CF6 = 1.56 Lf0.66|
|7||CF7 = 1.74 Lf0.67|
|8||CF8 = 1.93 Lf0.67|
|9||CF9 = 2.11 Lf0.68|
|10||CF10 = 2.28 Lf0.68|
|Input||% Change to Base Input||% Change to Critical Flow (CF)|
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Penney, G.; Habibi, D.; Cattani, M.; Carter, M. Calculation of Critical Water Flow Rates for Wildfire Suppression. Fire 2019, 2, 3. https://doi.org/10.3390/fire2010003
Penney G, Habibi D, Cattani M, Carter M. Calculation of Critical Water Flow Rates for Wildfire Suppression. Fire. 2019; 2(1):3. https://doi.org/10.3390/fire2010003Chicago/Turabian Style
Penney, Greg, Daryoush Habibi, Marcus Cattani, and Murray Carter. 2019. "Calculation of Critical Water Flow Rates for Wildfire Suppression" Fire 2, no. 1: 3. https://doi.org/10.3390/fire2010003