CHANGING TACTICS: 

 INDIRECT ATTACK ON RAPID HEAD FIRE 



In the mathematical formulations above, a necessary condition for successful 

 containment of a fire is that A>Vp, or that the rate of suppression must exceed the 

 forward rate of spread of the fire. But as every firefighter knows, this condition can 

 be violated and yet the fire can be contained. If the head fire is advancing too 

 rapidly to be contained by suppression action at the edge of the fire, in many cases 

 the firefighting team will construct a "fire break" or barrier ahead of the advancing 

 fire to stop its forward progress. Then working against the flanking fire either 

 from the forward or the rear direction, the encirclement can be completed by work at the 

 edge of the fire. 



In figure 4 we sketch such an attack against a rapidly advancing head fire. The 

 first step, shown in figure 4a, is to establish a barrier ahead of the fire, perpen- 

 dicular to the direction of maximum rate of spread. When the fire reaches this barrier, 

 as shown in figure 4b, work proceeds back toward the flanks of the fire. When the crew 

 meets the advancing edge of the fire, as shown in figure 4c, work can proceed at the 

 edge of the fire from that point on around to the rear, since the perpendicular rate of 

 fire spread at the point of meeting is less than the rate of suppression. 



For the purpose of carrying out a mathematical analysis of this tactic, we idealize 

 the situation as follows: 



(1) Work proceeds symmetrically, by two crews, and the rate of line construction 

 is everywhere the same (=A, as before). 



(2) At the instant the forward edge of the fire reaches the perpendicular barrier, 

 the crews change direction of work and proceed in straight lines back toward the fire 

 flanks . 



(5) The direction chosen for the second straight segment of barrier line is such 

 as to bring the crew into contact with the edge of the fire in a direction tangent to 

 the instantaneous fire boundary. 



Clearly there is a mathematical solution to the problem of choosing the best 

 distance (a) ahead of the fire front, and likewise a best (probably curved) path to 

 follow to bring the crews into contact with the edge of the fire. Such a solution 

 would be interesting as a mathematical problem, but of little practical significance. 

 The idealization chosen is, hopefully, a compromise between mathematical perfection and 

 realizable practice. It should be noted that this idealization is not tied to any 

 particular method of line construction (machine-aided hand line, hand line with back 

 firing, machine construction, explosive construction, etc.) 



The use of the tactic as described would be rare in the United States and is 

 infrequent in the Soviet Union. But, when conditions permit its use with due regard for 

 crew safety, the reward in terms of burned area and time of control can be substantial 

 in some cases. 



As the procedure is outlined above, for any given set of fire shape parameters 

 ■(V^/Vp, Vg/V^, and n) and given value of A/Vp, the final area and perimeter are 

 completely determined by the choice of a value for the distance (a) ahead of the fire 

 at which the initial barrier is constructed. We normalize this distance by the initial 

 distance from the point of ignition to the front of the fire, r (O) • 



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