Rate of Spread

Rate of spread is the horizontal distance that the flame zone moves per unit of time (feet per minute) and usually refers to the head fire segment of the fire perimeter. However, rate of spread can be measured from any point on the fire perimeter in a direction that is perpendicular to the perimeter. Because rate of spread can vary significantly over the area of the fire, it is generally taken to be an average value over some given period of time. The fastest rate of spread is along the forward moving perimeter located at the head of the fire. The slowest rate of spread will be found on the windward (back) side of the perimeter. The rate of spread along the flanks will be intermediate between the head and backing rates of spread (see: Fire shape). Rates of spread can easily be estimated by timing the passage of the flaming front between two landmarks of known distance apart. To determine rate of spread within the interior of a fire, firecrackers placed at known intervals along a transect perpendicular to the flame front have also been used. More technical techniques of measuring rates of spread involve videography or the use of thermocouples to record the passage of the flaming front.

Rate of spread is directly related to the amount of heat received by the fuels ahead of the flaming zone, and the heat is a function of the energy release rate per unit area of fire front (I_R reaction intensity = Btu/ft²/minute, see Rothermels equation below). The rate of spread is a key component in planning and decisions for conducting prescribed fires and suppressing wildfires.

As Rothermel’s equation below demonstrates, rate of spread is strongly influenced by fuels, winds, and topography. Rates of spread generally increase with increasing wind speed, slope, and amount of fine fuels. More information is provided in the following pages:

• Effects of weather on fire intensity and rate of spread

• Effects of fuel on fire intensity and rate of spread

• Effects of topography on fire intensity and rate of spread

When fire growth leads to extreme fire behavior the fire itself becomes a fourth factor that influences rate of spread. Fire can produce enough heat to modify local winds, contribute to atmospheric instability, and cause cloud development (Pyne et al. 1996).

<equation> Rate of spread as a function of energy release was mathematically expressed by Rothermel’s equation which has been the basis for most computerized fire spread prediction models such as Behave Plus. The rate of spread equation is simply the heat received by fuels ahead of the fire (numerator) divided by the heat required to ignite the fuels (denominator):

R=I_R ξ(1+ Φ_W + Φ_S) / ρ_η ε Q_ig

where:

• R = rate of spread of the flaming front
• I_R = reaction intensity (defined in Fire Intensity)
• ξ = proportion of the reaction intensity that heats adjacent fuel particles to ignition
• Φ_W = dimensionless multiplier accounting for the effect of wind in increasing the proportion of heat that reaches adjacent fuels
• Φ_S = dimensionless multiplier accounting for the effect of slope in increasing the proportion of heat that reaches adjacent fuels
• ρ_η = ovendry fuel per cubic foot of fuel bed (lb/ft)
• ε = dimensionless number accounting for the proportion of a fuel particle that is heated to ignition temperature at the time flaming combustion starts (near unity for fine fuels and decreases toward zero as fuel size increases)
• Q_ig = heat of pre-ignition, or the amount of heat required to ignite one pound of fuel (Btu/lb) (Pyne et al. 1996).