Appendix B 



Derivation of Maximum Load-Loss Rate 



Beginning with w = w^T, the net load is expressed as 



w = PnB6 

 n F 



where 



Pp = ovendry particle density 



6 = depth of the fuel basket or fuel slice 



6 = packing ratio, the fraction of the bulk volume occupied by fuel. 



The other term in the expression for w is the reaction velocity, r. Rothermel (1972) 

 provides a set of parametric equations for obtaining r from initial fuel parameters. 



r = n n r- 



s m 



where 



and 



= mineral damping coefficient = f (silica free ash content) 

 = moisture damping coefficient = f (fuel moisture content) 

 r" - optimum reaction velocity 



r' = r' (6/e )^exp[A(l-6/6 )] 

 max^ op op 



= 3.348 o" 



max 



0. 8189 



op 



A = 1/(4.774 a 1 - 7.27) 



a - particle surface area-to-volume ratio 



Substituting w and r into w gives 



From Rothermel 's (1972) original data 



Pp = 26.12 lbs/ft^ 



6 = 0.375 ft 



n = 0.694 @ M- = 0.05 

 m r 



n = 0.507 (a S = 0.0036 



s e 



Substituting into w we have 



w = 0.0280 3 r' 

 with a = 1,848 ft~^ for excelsior 



r' = 15.237 eO-3498 e"^']0-3^98 



where 



6' = 6/0.00707 



11 



