where r (D) is distance from the point of ignition to the front edge of the fire 

 at the ?ime the suppression work begins. If, however, the work begins at the back 

 edge of the fire, then 



\ = R(e^) = (Vg/Vp) rJO) (14) 



Figure 3 shows examples of final fire shapes computed according to equation 10. Both 

 tactics are illustrated in each sketch of figure 3; the upper half of each diagram 

 shows the result of attacking the head fire first and the lower half shows the 

 result of attacking the backing fire first. 



The time required to complete the work (At) is obtained from equations 4, 6, 

 and 10: 



At = (R(0 )/A) / {exp(/ f (0')d0')/sin a}d0 (15) 



° 







where sin a is given by equation 4. 



The total burned area (S) is given simply by 



TT +TT 



S = / R2(9)de = r2(0 ) r" exp(2/ f(0')d0')d0 



° 0^ ^0 







+TT 







Figure 3. — Shape of burned area for suacessfulhj contained fires according to equation 

 10. In each sketchy, the upper half corresponds to attacking the head fire first and 

 the lower half corresponds to attacking the same fire from the hack. The fire shape 

 parameters are given in each sketch (see equation 9). Ratio ^/^^^ is the rate of 

 line construction divided by the forward rate of spread. 



7 



