Therefore, residence time can be calculated from the characteristic surface area- 

 to- volume ratio: 



T = 12.6/5 

 r 



where a has the units of cm 



Each hexagonal cell has a characteristic surface area-to-volume ratio obtained 

 from the average particle diameter weighted by the total exposed surface area of 

 each size class of fuels within the cell (Rothermel 1972). Thus, the residence 

 time is an average property of the cell. 



The values required for each cell for the delay time calculation are 1^^, , 

 5, 4)^, ())^, and T^. These values are calculated in turn from measurable fuel proper- 

 ties. The reaction intensity, I , may be thought of as the "heat source" affecting 

 adjacent cells. The second term, , is the product of the effective heating 



number, e, and the volumetric heat of preignition, ofj^g- This term may be thought 



of as the "heat sink," the absorption of heat required for the fire to advance into 

 the cell. The propagating flux ratio, g, is the heat coupling coefficient operating 

 on the reaction intensity to obtain the propagating flux. The wind and slope fac- 

 tors, (p^ and (j)^ , are used along with the direction of spread in relation to the 



directions of the wind and slope to calculate a wind-slope factor, gi.'i'^A^) Cal- 

 culation of I„, eoi. , E,, ii , and <i is described in Rothermel [1972). 

 R ig w s 



The rate of spread in cell (i+1) is initially influenced by the cell i. The 



fire is assumed to have achieved a quasi-steady state when the residence time of 



cell (i+l) has elapsed. To smooth the change in rate of spread within cell (i+1), 



a gradual change is assumed. Two possible cases must be considered: 



I- (t ) • < Ct ) • , , and II. fx ) . > fx ). For case 1 the influence of cell i 



^ r'^i — ^ ^ r^i ^ r'^i+l 



terminates at time C^^)^- The influence of cell (i+1) continues increasing until 



time fx ) ■ 1 when the fire reaches its quasi-steady state. For case II the influ- 

 ^ r'^i + 1 ^ 



ence of cell i is terminated at time (x ) . ^ rather than (x ).. At (x ) . , the 



^ r 1+1 r 1 r 1+1 



rear of the combustion zone leaves the boundary between the cells producing a 

 burned out area between the cells whereupon cell i is assumed to no longer influ- 

 ence cell (i+1) . Frank Albini of the Northern Forest Fire Laboratory suggested 

 the following mathematical model for expressing these influences. 



The distance, s, that the fire has traveled in cell (i+1) by time t is: 



Case I : (x ) . < (x ) . , 

 r 1 — r 1+1 



= r f (t)dt + R r h(t)dt 



^Albini, see footnote 1 



24 



