GENERAL PROBLEM 



Research in fire physics and fuel science at the Northern Forest Fire Laboratory 

 (Missoula, Montana) is directed toward understanding and describing fire propagation 

 through forest fuels and determining how the rate of fire spread is influenced by 

 atmospheric, topographic, and fuel variables. Considerable qualitative information 

 has been collected over the years; but quantitative data have become available only 

 recently. An increase in this information has raised new questions and posed new 

 problems. One fundamental question is: What are the relative roles of the several 

 mechanisms of heat transfer (radiation, convection, conduction, and mass transport) in 

 activating and sustaining the spread of fire? 



Test fires in mat-type fuel beds of pine needles burned in still air and with 

 controlled wind conditions demonstrated that radiation significantly influenced fire 

 spread in still air (Rothermel and Anderson 1966). Several mathematical models of fire 

 spread by the various heat transfer mechanisms have been developed and tested to some 

 degree (Pons 1946; Emmons 1963; Hottel et al . 1965; Thomas and Law 1965). From this 

 research and from results of our own experiments, we have developed and tested a 

 mathematical description of fire spread (under no-wind condition) based on -radiant 

 heat transfer. This paper presents the development of the mathematical description, 

 and the test procedures and results, and compares data from these tests with those 

 from other fire research. 



Fuel moisture content has long been recognized as a major influence on ignition 

 and fire spread (Gisborne 1928); therefore, any mathematical description of fire spread 

 must include the influence of moisture. My approach to this task is to estimate the 

 total heat required to remove the moisture and subsequently raise the fuel to ignition 

 temperature. Various earlier researchers (Pons 1950; Martin 1964; Simms 1960, 1961, 

 1963) indicate a temperature of 300° to 380°C. typifies the pilot ignition point. 

 Research at the Northern Forest Fire Laboratory (Mutch 1964) showed that a temperature 

 of 320°C. (608°F.) would produce pilot ignitions in ground forest fuels. This tempera- 

 ture agrees with results of other research and was selected to represent pilot ignition 

 temperature . 



The energy required to remove the water contained in a pound of wet fuel and then 

 to ignite it was determined from data published by Byram et al . (1952). These data 

 were developed into an equation that estimates the energy input per pound of fuel at 

 any moisture content up to 20 percent of ovendry weight. The equation takes into account 

 the heat required to raise the fuel to ignition, the heat required to raise the moisture 

 to boiling temperature, the heat of desorption, the latent heat of vaporization, and 

 the variation in boiling temperature with moisture content. Until now, no consideration 

 had been given to the endothermic heat of pyrolysis that leads to the ignition of fuel. 



DEVELOPMENT OF MATHEMATICAL DESCRIPTION 



MOISTURE CONTENT 



Q = Cp(T. - Ti) + C^[M(T2 - Ti) + [71 ( 



(1) 



0.83^^0 



_niR9 T -5.92 To 



- M(71M ^•'^^)] H- lAi~) ]^ 



+ H(M) 



Ti 



where : 



= B.t.u./lb. (cal./g.) 

 C = 0.327, specific heat of fuel 



r 



C^ = 1.0, specific heat of water 

 Tl - ambient temperature 



