APPENDIX I: DELAY TIME 



The delay time of a cell is the time that must elapse from the time that the 

 cell is ignited until it is able to ignite adjacent cells. In the simulation, we 

 are concerned with fire behavior only at the resolution of the cell size. The 

 fire is viewed as jumping into a cell at ignition and then waiting out the delay 

 time before jumping into unignited adjacent cells. However, to develop a method 

 of calculating delay time, the behavior of the fire within a cell must be considered. 



After cell (i+1) is ignited by cell i, the fire spreads a transition distance, 

 D' , before it reaches a quasi-steady state. During the time that it takes the fire 

 to spread this distance, the influence of cell i is decreasing and the influence of 

 cell (i+1) is increasing. The fire spreads the remainder of the distance through 

 (i+1) at a rate which is calculated according to the uniform fire spread model 

 CRothermel 19 72) . 



The delay time is expressed as the sum of the residence time and the time 

 that it takes the fire to spread the remaining distance (D-D') at a uniform rate: 



t , = (t ) . -, + (D - D')/R. , 

 d ^ r-^i+1 ^ ^ 1 + 1 



where 



Ct ) . 1 = residence of cell (i+1) 

 D = cell width 



D' = transition distance 



Rj^^^ = quasi-steady state rate of spread in cell (i + 1). 



The residence time, (t ) . , , is the amount of time that fire exists at a given 



r 1 + 1 



point as it spreads through a fuel array. Residence time is assumed to be a mea- 

 sure of the time that it takes a fire in cell (i+1) to achieve the quasi-steady 

 state where it is no longer influenced by cell i and spreads at a rate dependent 

 only on the fuel parameters of cell (i+1) . Our goal in constructing the hexagonal 

 fuel array is to choose the cell size such that the time for the fire to spread 

 through the cell is greater than the characteristic residence time of the fuel 

 particles in cell (i+1) . 



The residence time is expressed as the ratio of the combustion zone depth (ap- 

 proximately the horizontal region of active flaming) to the rate of spread. Ander- 

 son (1969) found the following approximation for the residence time in terms of 

 the particle diameter d: 



T = 3.15d 

 r 



where is in minutes and d is in cm. The diameter, d, can be expressed in terms 

 of the surface area-to-volume ratio: 



d = 4/a. 



23 



