Since the initial fire area is equal to the square of r (0) multiplied by a shape 

 factor (table 1) which decreases as the fire becomes more elongated in shape (V^/\'^, 



Vg/V^ decreasing, n increasing) , one can assert that the initial fire area is of 

 extreme importance in determining final burned area. 



The time required for containment can be found in ratio to the idealized time 

 elapsed from ignition to the beginning of suppression through the following relation- 

 ships : 



At = r Co)/V (17) 

 so r 



At = (Pq/^) (AAt/P^), (IS) 



where 



At^ = idealized time between ignition and start of suppression 

 At = time required for containment 



= fire perimeter length at tlie start of suppression 

 (AAt/P^) = values given in table 3. 

 Dividing equation 17 by equation 18, we find 



At/At, = (P /r (0)) (AAt/P )/(A/V„) (19) 



b )■ 



where values of (P^/r^(o)) are tabulated in table 1. 



Note, however, that while the values given in table 1 are limited to the range 



2 < P /r (0) < 2n, the ratio (AAt/P )/(A/V^) can take on a very wide range of values. 



— 00— oF 



To find the value of this highly variable quantity, one merely divides the entries in 

 table 3 by the values of (A/V^) given in the left most column. When this is done one 

 obtains, approximately, the ratio of the time recjuired for containment to tlie idealized 

 time since ignition, because the value of P /r (Q) is of the order of unit}'. In this 

 way one readily sees tliat one of the most important factors in determining the time 

 required for containment is the rate of suppression in ratio to the forward rate of 

 spread (A/V ) . This parameter is far more influential than fire slia])e or choice of 

 tactics. Tlie idealized time since ignition (At J is the normalizing value for At in 

 equation 19, and is very important when A/V^, is' less tlian about three. IVlien A/V^ falls 

 below three, the ratio At/At (according to equation 19 and table 3) becomes greater 

 tlian one under tactic 1. IJiiier tactic 2 the ratio is generally greater tlian one 

 when A/Vj, is less than 2.5. 



From this sensitivity analysis we can reinforce conventional wisdom with regard to 



tlie two most important factors in determining the burned area and time required for 



containment: (1) minimize the time between ignition and start of suppression (At , and 



indirectly, r (0)); and (2) use tiie maximum available suppression force (A). In addition 



we have estalolished a means of cjuantifying the influence of these factors for tlie 

 purpose of assessing overall effectiveness of fire supjircssi on forces. 



11 



