where : 



R = steady rate of spread, ft./hr. ■ 

 Substituting and integrating equation (2): 



The quantity, Q = B.t.u./£t.^, must be modified so Q. , B.t.u./lb. can be used. This 

 is accomplished by: 



a 



where: - . 



= fuel particle density, Ib./ft.^ (g./cm.^) 



- fuel particle projected surface area to volume ratio, ft.^/ft.^ (cm.^/cm.^). 



The attenua.tion factor "a" must be put into some measurable form. It is assumed to be 

 proportional to the total projected area of fuel in a unit volume of space (Committee 

 on Fire Research, 1961, p. 126). 



1_ 



4X 



(5) 



where : 



X = void volume per total surface area 

 1/4 = projected portion of surface area. 



Equations 4 and 5 are substituted in equation 3, which takes the form: 



o AE 



R . (6) 

 f ig 



This mathematical description states that the rate of spread is dependent on the 

 emissive power of the fire and will be modified by the size of the fuel particles, o 

 porosity of the fuel bed, A; density of the fuel particles, p^; and the amount of 

 energy required for ignition (primarily a function of the amount of moisture in the 

 fuel), Qig- The emissive power of the fire is made up of two components: (1) the 

 combustion zone within the fuel bed; (2) the flame plume above the fuel bed. Both 

 components contribute to radiant heating. However, convective heating takes place 

 only in the fuel bed and in the region of the fuel bed-fire plume interface. In the 

 study reported herein we are concerned with describing rate of spread in absence 

 of wind with the assumption that radiation was the primary source of heat. 



The fuel descriptors are independent of the two source components. However, 

 the contributions of heat to the fuel are dependent on the relative weight and influence 

 of each mode of heat transfer. The radiant heat from each component is defined thus: 



E^ = ae^T^^ (combustion zone emissive power) 

 ^f ~ ^^f'^f^ (flame emissive power) . 



The impact of the flame's emissive power on the fuel ahead of the fire is a function of 

 distance and shape of the flame; these must be taken into account. This modification 



3 



