2. The summation of heat absorbed by each elemental area (A. or B. bounded by 



T . . and T . up to T . = T . ) . 

 3-1 3 3 ig 



For example, the heat of preignition for the transverse member is 



T < 100° C, 

 o — 



i J =m _ 



L = Qi + T 1 A. [fC + C n + C. (T. + T )/2] (T. - T ) 



<A x l A . _j j L w 1 j o J v 3 o 



1 j=n 



+ ± Z A. (fC (100 - T ) + f Q 



A . , 3 w o Hv 

 3=m+l J 



* [C Q + CjCT + T o )/2][T - T q ]), (6a) 



where : 



0. = [fC + C + C, (T + T )/2](T - T ) 

 x l L w 1 o a J o a 



T > 100° C. 

 o 



1 J=n 



Q A = ( W Z AEC^C (T + T o )/2](T -T o ), (6b) 

 j = 1 J J 



where : 



Q 2 - f[C w (100 - y + Qj + [C Q + C x (T Q + T a )/2](T o - T & ) 



and, 



f. = (T. , + TO/2 

 J 3-1 3 



T . < 100° C. for j < m 

 J 



f. = 100° C. for j = m 

 J 



f . > 100° C. for j > m 

 3 



T_. = maximum average temperature of A^ for j = n. 



The value for Qg is obtained by applying equations (6a) and (6b) to the longitu- 

 dinal member after replacing the summing area A with B. Both results are readily 

 evaluated by using a simple iterative computer program to sum the heat absorbed by 

 each elemental area. 



Finally, the effective heating number, e, is evaluated by comparing the ratio of 

 the total heat absorbed within the unit volume, p£t 2 (Q A + Qg) , to the total heat that 

 would have been absorbed had the unit volume been heated uniformly to ignition, 

 2pU 2 Q ig . Thus, 



e = (Q A + Q B )/2Qig- ^ 



7 



